%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW328+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 : n002.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 18:07:34 EDT 2024 % Result : Theorem 174.01s 173.88s % Output : CNFRefutation 174.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWW328+1 : TPTP v8.2.0. Released v5.2.0. % 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n002.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Jun 19 06:39:39 EDT 2024 % 0.12/0.33 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 173.50/173.72 %------------------------------------------- % 173.50/173.72 % File :CSE---1.7 % 173.50/173.72 % Problem :theBenchmark % 173.50/173.72 % Transform :cnf % 173.50/173.72 % Format :tptp:raw % 173.50/173.72 % Command :java -jar mcs_scs.jar %d %s % 173.50/173.72 % 173.50/173.72 % Result :Theorem 158.910000s % 173.50/173.72 % Output :CNFRefutation 158.910000s % 173.50/173.72 %------------------------------------------- % 173.59/173.73 %------------------------------------------------------------------------------ % 173.59/173.73 % File : SWW328+1 : TPTP v8.2.0. Released v5.2.0. % 173.59/173.73 % Domain : Software Verification % 173.59/173.73 % Problem : Hoare's Logic with Procedures 435107, 5000 axioms selected % 173.59/173.73 % Version : Especial. % 173.59/173.73 % English : % 173.59/173.73 % 173.59/173.73 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 173.59/173.73 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 173.59/173.73 % Source : [Bla11] % 173.59/173.73 % Names : hoare_435107.5000.p [Bla11] % 173.59/173.73 % 173.59/173.73 % Status : ContradictoryAxioms % 173.59/173.73 % Rating : 0.67 v8.2.0, 0.64 v8.1.0, 0.67 v7.5.0, 0.69 v7.4.0, 0.80 v7.3.0, 0.79 v7.2.0, 0.76 v7.1.0, 0.74 v7.0.0, 0.77 v6.4.0, 0.73 v6.3.0, 0.75 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.87 v5.5.0, 0.89 v5.2.0 % 173.59/173.73 % Syntax : Number of formulae : 5211 (1708 unt; 0 def) % 173.59/173.73 % Number of atoms : 12622 (4538 equ) % 173.59/173.73 % Maximal formula atoms : 13 ( 2 avg) % 173.59/173.73 % Number of connectives : 8504 (1093 ~; 158 |; 715 &) % 173.59/173.73 % ( 875 <=>;5663 =>; 0 <=; 0 <~>) % 173.59/173.73 % Maximal formula depth : 22 ( 6 avg) % 173.59/173.73 % Maximal term depth : 19 ( 2 avg) % 173.59/173.73 % Number of predicates : 141 ( 140 usr; 1 prp; 0-7 aty) % 173.59/173.73 % Number of functors : 394 ( 394 usr; 63 con; 0-10 aty) % 173.59/173.73 % Number of variables : 16775 (16646 !; 129 ?) % 173.59/173.73 % SPC : FOF_CAX_RFO_SEQ % 173.59/173.73 % 173.59/173.73 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 173.59/173.73 % 2011-03-01 11:58:08 % 173.59/173.73 %------------------------------------------------------------------------------ % 173.59/173.73 %----Relevant facts (4983) % 173.59/173.73 fof(fact_ext,axiom, % 173.59/173.73 ! [V_g_2,V_f_2] : % 173.59/173.73 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 173.59/173.73 => V_f_2 = V_g_2 ) ). % 173.59/173.73 % 173.59/173.73 fof(fact_hoare__valids__def,axiom, % 173.59/173.73 ! [V_ts_2,V_Ga_2,T_b] : % 173.59/173.73 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_ts_2) % 173.59/173.73 <=> ! [B_n] : % 173.59/173.73 ( ! [B_x] : % 173.59/173.73 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2)) % 173.59/173.73 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) % 173.59/173.73 => ! [B_x] : % 173.59/173.73 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2)) % 173.59/173.73 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ) ). % 173.59/173.73 % 173.59/173.73 fof(fact_evaln_OWhileFalse,axiom, % 173.59/173.73 ! [V_n_2,V_ca_2,V_s_2,V_ba_2] : % 173.59/173.73 ( ~ hBOOL(hAPP(V_ba_2,V_s_2)) % 173.59/173.73 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),V_s_2,V_n_2,V_s_2) ) ). % 173.59/173.73 % 173.59/173.73 fof(fact_evaln_OWhileTrue,axiom, % 173.59/173.73 ! [V_s2_2,V_s1_2,V_n_2,V_ca_2,V_s0_2,V_ba_2] : % 173.59/173.73 ( hBOOL(hAPP(V_ba_2,V_s0_2)) % 173.59/173.73 => ( c_Natural_Oevaln(V_ca_2,V_s0_2,V_n_2,V_s1_2) % 173.59/173.73 => ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),V_s1_2,V_n_2,V_s2_2) % 173.59/173.73 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),V_s0_2,V_n_2,V_s2_2) ) ) ) ). % 173.59/173.73 % 173.59/173.73 fof(fact_evaln_Oequations_I7_J,axiom, % 173.59/173.73 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 173.59/173.73 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a2_2) % 173.59/173.73 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.59/173.73 => ? [B_s1] : % 173.59/173.73 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1) % 173.59/173.73 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a2_2) ) ) ) ). % 173.59/173.73 % 173.59/173.73 fof(fact_evaln_Oequations_I8_J,axiom, % 173.59/173.73 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 173.59/173.73 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a6_2) % 173.59/173.73 <=> ( ( V_a6_2 = V_a2_2 % 173.59/173.73 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 173.59/173.73 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.59/173.73 & ? [B_s1] : % 173.59/173.74 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1) % 173.59/173.74 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a6_2) ) ) ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I5_J,axiom, % 173.59/173.74 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 173.59/173.74 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 173.59/173.74 <=> ( V_fun_2 = V_fun_H_2 % 173.59/173.74 & V_com_2 = V_com_H_2 ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_triples__valid__Suc,axiom, % 173.59/173.74 ! [V_n_2,V_ts_2,T_b] : % 173.59/173.74 ( ! [B_x] : % 173.59/173.74 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2)) % 173.59/173.74 => c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 173.59/173.74 => ! [B_x] : % 173.59/173.74 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2)) % 173.59/173.74 => c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x) ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_triple__valid__def2,axiom, % 173.59/173.74 ! [V_Q_2,V_ca_2,V_Pa_2,V_n_2,T_b] : % 173.59/173.74 ( 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)) % 173.59/173.74 <=> ! [B_Z,B_s] : % 173.59/173.74 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 173.59/173.74 => ! [B_s_H] : % 173.59/173.74 ( c_Natural_Oevaln(V_ca_2,B_s,V_n_2,B_s_H) % 173.59/173.74 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_evaln__WHILE__case,axiom, % 173.59/173.74 ! [V_t_2,V_n_2,V_s_2,V_ca_2,V_ba_2] : % 173.59/173.74 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),V_s_2,V_n_2,V_t_2) % 173.59/173.74 => ( ( V_t_2 = V_s_2 % 173.59/173.74 => hBOOL(hAPP(V_ba_2,V_s_2)) ) % 173.59/173.74 => ~ ( hBOOL(hAPP(V_ba_2,V_s_2)) % 173.59/173.74 => ! [B_s1] : % 173.59/173.74 ( c_Natural_Oevaln(V_ca_2,V_s_2,V_n_2,B_s1) % 173.59/173.74 => ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),B_s1,V_n_2,V_t_2) ) ) ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_triple__valid__Suc,axiom, % 173.59/173.74 ! [V_t,V_n,T_a] : % 173.59/173.74 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 173.59/173.74 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I69_J,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_evaln_OSkip,axiom, % 173.59/173.74 ! [V_n,V_s] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s) ). % 173.59/173.74 % 173.59/173.74 fof(fact_evaln__elim__cases_I1_J,axiom, % 173.59/173.74 ! [V_t,V_n,V_s] : % 173.59/173.74 ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) % 173.59/173.74 => V_t = V_s ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_triple_Oinject,axiom, % 173.59/173.74 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] : % 173.59/173.74 ( 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) % 173.59/173.74 <=> ( V_fun1_2 = V_fun1_H_2 % 173.59/173.74 & V_com_2 = V_com_H_2 % 173.59/173.74 & V_fun2_2 = V_fun2_H_2 ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I64_J,axiom, % 173.59/173.74 ! [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 ). % 173.59/173.74 % 173.59/173.74 fof(fact_evaln__Suc,axiom, % 173.59/173.74 ! [V_s_H,V_n,V_s,V_c] : % 173.59/173.74 ( c_Natural_Oevaln(V_c,V_s,V_n,V_s_H) % 173.59/173.74 => c_Natural_Oevaln(V_c,V_s,hAPP(c_Nat_OSuc,V_n),V_s_H) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_evaln_Oequations_I1_J,axiom, % 173.59/173.74 ! [V_a2,V_a1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_a1,V_a2,V_a1) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I17_J,axiom, % 173.59/173.74 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I16_J,axiom, % 173.59/173.74 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 173.59/173.74 % 173.59/173.74 fof(fact_triple_Orecs,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_triple_Osimps_I2_J,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_n__not__Suc__n,axiom, % 173.59/173.74 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 173.59/173.74 % 173.59/173.74 fof(fact_Suc__n__not__n,axiom, % 173.59/173.74 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 173.59/173.74 % 173.59/173.74 fof(fact_nat_Oinject,axiom, % 173.59/173.74 ! [V_nat_H_2,V_nat_2] : % 173.59/173.74 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 173.59/173.74 <=> V_nat_2 = V_nat_H_2 ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_Suc__inject,axiom, % 173.59/173.74 ! [V_y,V_x] : % 173.59/173.74 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 173.59/173.74 => V_x = V_y ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_evaln_OSemi,axiom, % 173.59/173.74 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] : % 173.59/173.74 ( c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1) % 173.59/173.74 => ( c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2) % 173.59/173.74 => c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2) ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Orecs_I1_J,axiom, % 173.59/173.74 ! [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 ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I67_J,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Orecs_I6_J,axiom, % 173.59/173.74 ! [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)) ). % 173.59/173.74 % 173.59/173.74 fof(fact_evaln__elim__cases_I5_J,axiom, % 173.59/173.74 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_ba_2] : % 173.59/173.74 ( 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) % 173.59/173.74 => ( ( hBOOL(hAPP(V_ba_2,V_s_2)) % 173.59/173.74 => ~ c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_t_2) ) % 173.59/173.74 => ~ ( ~ hBOOL(hAPP(V_ba_2,V_s_2)) % 173.59/173.74 => ~ c_Natural_Oevaln(V_c2_2,V_s_2,V_n_2,V_t_2) ) ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_evaln_OIfFalse,axiom, % 173.59/173.74 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_ba_2] : % 173.59/173.74 ( ~ hBOOL(hAPP(V_ba_2,V_s_2)) % 173.59/173.74 => ( c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_s1_2) % 173.59/173.74 => 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) ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_evaln_OIfTrue,axiom, % 173.59/173.74 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_ba_2] : % 173.59/173.74 ( hBOOL(hAPP(V_ba_2,V_s_2)) % 173.59/173.74 => ( c_Natural_Oevaln(V_c0_2,V_s_2,V_n_2,V_s1_2) % 173.59/173.74 => 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) ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I44_J,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I45_J,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I3_J,axiom, % 173.59/173.74 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 173.59/173.74 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 173.59/173.74 <=> ( V_com1_2 = V_com1_H_2 % 173.59/173.74 & V_com2_2 = V_com2_H_2 ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I4_J,axiom, % 173.59/173.74 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 173.59/173.74 ( 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) % 173.59/173.74 <=> ( V_fun_2 = V_fun_H_2 % 173.59/173.74 & V_com1_2 = V_com1_H_2 % 173.59/173.74 & V_com2_2 = V_com2_H_2 ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Orecs_I4_J,axiom, % 173.59/173.74 ! [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)) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Orecs_I5_J,axiom, % 173.59/173.74 ! [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)) ). % 173.59/173.74 % 173.59/173.74 fof(fact_evaln_Oequations_I5_J,axiom, % 173.59/173.74 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] : % 173.59/173.74 ( 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) % 173.59/173.74 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.59/173.74 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) ) % 173.59/173.74 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.59/173.74 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_evaln_Oequations_I6_J,axiom, % 173.59/173.74 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] : % 173.59/173.74 ( 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) % 173.59/173.74 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.59/173.74 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) ) % 173.59/173.74 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.59/173.74 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I53_J,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I52_J,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_evaln_Oequations_I4_J,axiom, % 173.59/173.74 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] : % 173.59/173.74 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_a1_2,V_a5_2),V_a2_2,V_a3_2,V_a6_2) % 173.59/173.74 <=> ? [B_s1] : % 173.59/173.74 ( c_Natural_Oevaln(V_a1_2,V_a2_2,V_a3_2,B_s1) % 173.59/173.74 & c_Natural_Oevaln(V_a5_2,B_s1,V_a3_2,V_a6_2) ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I15_J,axiom, % 173.59/173.74 ! [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 ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I14_J,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I46_J,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I47_J,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I13_J,axiom, % 173.59/173.74 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I12_J,axiom, % 173.59/173.74 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I68_J,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_evaln__elim__cases_I4_J,axiom, % 173.59/173.74 ! [V_t,V_n,V_s,V_c2,V_c1] : % 173.59/173.74 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c1,V_c2),V_s,V_n,V_t) % 173.59/173.74 => ~ ! [B_s1] : % 173.59/173.74 ( c_Natural_Oevaln(V_c1,V_s,V_n,B_s1) % 173.59/173.74 => ~ c_Natural_Oevaln(V_c2,B_s1,V_n,V_t) ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 173.59/173.74 ! [V_i_2,V_n_2,V_inc_2,T_b] : % 173.59/173.74 ( class_Rings_Osemiring__1(T_b) % 173.59/173.74 => 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)) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_nat__case__Suc,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_nat__rec__Suc,axiom, % 173.59/173.74 ! [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)) ). % 173.59/173.74 % 173.59/173.74 fof(fact_WTs__elim__cases_I4_J,axiom, % 173.59/173.74 ! [V_c2,V_c1] : % 173.59/173.74 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2))) % 173.59/173.74 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 173.59/173.74 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I66_J,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_com_Osimps_I71_J,axiom, % 173.59/173.74 ! [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) ). % 173.59/173.74 % 173.59/173.74 fof(fact_WTs__elim__cases_I5_J,axiom, % 173.59/173.74 ! [V_c2_2,V_c1_2,V_ba_2] : % 173.59/173.74 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_ba_2,V_c1_2,V_c2_2))) % 173.59/173.75 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 173.59/173.75 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I65_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WTs__elim__cases_I6_J,axiom, % 173.59/173.75 ! [V_ca_2,V_ba_2] : % 173.59/173.75 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_ba_2,V_ca_2))) % 173.59/173.75 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I70_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WTs__elim__cases_I3_J,axiom, % 173.59/173.75 ! [V_ca_2,V_a_2,V_Y_2] : % 173.59/173.75 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) % 173.59/173.75 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WTs__elim__cases_I8_J,axiom, % 173.59/173.75 ! [V_a_2,V_Pa_2,V_X_2] : % 173.59/173.75 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_Pa_2,V_a_2))) % 173.59/173.75 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_Pa_2))) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WT_OCall,axiom, % 173.59/173.75 ! [V_a_2,V_X_2,V_pn_2] : % 173.59/173.75 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2))) % 173.59/173.75 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WT_OLocal,axiom, % 173.59/173.75 ! [V_a_2,V_Y_2,V_ca_2] : % 173.59/173.75 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 173.59/173.75 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I2_J,axiom, % 173.59/173.75 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 173.59/173.75 ( 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) % 173.59/173.75 <=> ( V_loc_2 = V_loc_H_2 % 173.59/173.75 & V_fun_2 = V_fun_H_2 % 173.59/173.75 & V_com_2 = V_com_H_2 ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I7_J,axiom, % 173.59/173.75 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] : % 173.59/173.75 ( 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) % 173.59/173.75 <=> ( V_vname_2 = V_vname_H_2 % 173.59/173.75 & V_pname_2 = V_pname_H_2 % 173.59/173.75 & V_fun_2 = V_fun_H_2 ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I1_J,axiom, % 173.59/173.75 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] : % 173.59/173.75 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) % 173.59/173.75 <=> ( V_vname_2 = V_vname_H_2 % 173.59/173.75 & V_fun_2 = V_fun_H_2 ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I6_J,axiom, % 173.59/173.75 ! [V_pname_H_2,V_pname_2] : % 173.59/173.75 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 173.59/173.75 <=> V_pname_2 = V_pname_H_2 ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WT_Oequations_I8_J,axiom, % 173.59/173.75 ! [V_a3_2,V_a1_2,V_a2_2] : % 173.59/173.75 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2))) % 173.59/173.75 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WT_Oequations_I3_J,axiom, % 173.59/173.75 ! [V_a1_2,V_a3_2,V_a2_2] : % 173.59/173.75 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2))) % 173.59/173.75 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WT_Oequations_I2_J,axiom, % 173.59/173.75 ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I42_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I43_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I23_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I33_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I40_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I63_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I22_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I32_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I30_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I41_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I62_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I31_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WT_OAssign,axiom, % 173.59/173.75 ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I58_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I59_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I54_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I55_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I48_J,axiom, % 173.59/173.75 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I49_J,axiom, % 173.59/173.75 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I18_J,axiom, % 173.59/173.75 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I19_J,axiom, % 173.59/173.75 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 173.59/173.75 % 173.59/173.75 fof(fact_While,axiom, % 173.59/173.75 ! [V_ba_2,V_ca_2] : % 173.59/173.75 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 173.59/173.75 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_ba_2,V_ca_2))) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WT_Oequations_I6_J,axiom, % 173.59/173.75 ! [V_a1_2,V_a2_2] : % 173.59/173.75 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2))) % 173.59/173.75 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WT_OIf,axiom, % 173.59/173.75 ! [V_ba_2,V_c1_2,V_c0_2] : % 173.59/173.75 ( hBOOL(hAPP(c_Com_OWT,V_c0_2)) % 173.59/173.75 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 173.59/173.75 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_ba_2,V_c0_2,V_c1_2))) ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WT_Oequations_I5_J,axiom, % 173.59/173.75 ! [V_a2_2,V_a1_2,V_a3_2] : % 173.59/173.75 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2))) % 173.59/173.75 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 173.59/173.75 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WT_OSemi,axiom, % 173.59/173.75 ! [V_c1,V_c0] : % 173.59/173.75 ( hBOOL(hAPP(c_Com_OWT,V_c0)) % 173.59/173.75 => ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 173.59/173.75 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WT_Oequations_I4_J,axiom, % 173.59/173.75 ! [V_a2_2,V_a1_2] : % 173.59/173.75 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2))) % 173.59/173.75 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 173.59/173.75 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WT_OSkip,axiom, % 173.59/173.75 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 173.59/173.75 % 173.59/173.75 fof(fact_WT_Oequations_I1_J,axiom, % 173.59/173.75 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I29_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I28_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I38_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I61_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I39_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I60_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I27_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I26_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I36_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I37_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I56_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I57_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I25_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I24_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I8_J,axiom, % 173.59/173.75 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I9_J,axiom, % 173.59/173.75 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I34_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I51_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I35_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I50_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I20_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I10_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I21_J,axiom, % 173.59/173.75 ! [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 ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Osimps_I11_J,axiom, % 173.59/173.75 ! [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 ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Orecs_I7_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Orecs_I2_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Orecs_I3_J,axiom, % 173.59/173.75 ! [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)) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com_Orecs_I8_J,axiom, % 173.59/173.75 ! [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) ). % 173.59/173.75 % 173.59/173.75 fof(fact_Body__triple__valid__0,axiom, % 173.59/173.75 ! [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)) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evaln__elim__cases_I2_J,axiom, % 173.59/173.75 ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] : % 173.59/173.75 ( c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,V_t_2) % 173.59/173.75 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evaln_OAssign,axiom, % 173.59/173.75 ! [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))) ). % 173.59/173.75 % 173.59/173.75 fof(fact_Body__triple__valid__Suc,axiom, % 173.59/173.75 ! [V_Q_2,V_pn_2,V_Pa_2,V_n_2,T_b] : % 173.59/173.75 ( 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)) % 173.59/173.75 <=> 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)) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_def__nat__rec__Suc,axiom, % 173.59/173.75 ! [V_n_2,V_h_2,V_ca_2,T_b,V_f_2] : % 173.59/173.75 ( ! [B_n] : hAPP(V_f_2,B_n) = hAPP(c_Nat_Onat_Onat__rec(T_b,V_ca_2,V_h_2),B_n) % 173.59/173.75 => 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)) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evaln_Oequations_I2_J,axiom, % 173.59/173.75 ! [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))) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evaln_OBody,axiom, % 173.59/173.75 ! [V_s1,V_n,V_s0,V_pn] : % 173.59/173.75 ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1) % 173.59/173.75 => c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,hAPP(c_Nat_OSuc,V_n),V_s1) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evaln_Oequations_I9_J,axiom, % 173.59/173.75 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : % 173.59/173.75 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),V_a2_2,hAPP(c_Nat_OSuc,V_a3_2),V_a4_2) % 173.59/173.75 <=> 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) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 173.59/173.75 ! [V_i_2,V_inc_2,T_b] : % 173.59/173.75 ( class_Rings_Osemiring__1(T_b) % 173.59/173.75 => 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 ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_nat__rec__0,axiom, % 173.59/173.75 ! [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 ). % 173.59/173.75 % 173.59/173.75 fof(fact_evalc_OSkip,axiom, % 173.59/173.75 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evalc__elim__cases_I1_J,axiom, % 173.59/173.75 ! [V_t,V_s] : % 173.59/173.75 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t)) % 173.59/173.75 => V_t = V_s ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evalc_OWhileFalse,axiom, % 173.59/173.75 ! [V_ca_2,V_s_2,V_ba_2] : % 173.59/173.75 ( ~ hBOOL(hAPP(V_ba_2,V_s_2)) % 173.59/173.75 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_s_2),V_s_2)) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evalc_OWhileTrue,axiom, % 173.59/173.75 ! [V_s2_2,V_s1_2,V_ca_2,V_s0_2,V_ba_2] : % 173.59/173.75 ( hBOOL(hAPP(V_ba_2,V_s0_2)) % 173.59/173.75 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s0_2),V_s1_2)) % 173.59/173.75 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_s1_2),V_s2_2)) % 173.59/173.75 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_s0_2),V_s2_2)) ) ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evalc_OIfFalse,axiom, % 173.59/173.75 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_ba_2] : % 173.59/173.75 ( ~ hBOOL(hAPP(V_ba_2,V_s_2)) % 173.59/173.75 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2)) % 173.59/173.75 => 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)) ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evalc_OIfTrue,axiom, % 173.59/173.75 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_ba_2] : % 173.59/173.75 ( hBOOL(hAPP(V_ba_2,V_s_2)) % 173.59/173.75 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2)) % 173.59/173.75 => 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)) ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evalc__elim__cases_I5_J,axiom, % 173.59/173.75 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_ba_2] : % 173.59/173.75 ( 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)) % 173.59/173.75 => ( ( hBOOL(hAPP(V_ba_2,V_s_2)) % 173.59/173.75 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) ) % 173.59/173.75 => ~ ( ~ hBOOL(hAPP(V_ba_2,V_s_2)) % 173.59/173.75 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evalc_OSemi,axiom, % 173.59/173.75 ! [V_s2,V_c1,V_s1,V_s0,V_c0] : % 173.59/173.75 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1)) % 173.59/173.75 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2)) % 173.59/173.75 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evalc_OAssign,axiom, % 173.59/173.75 ! [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)))) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evalc__elim__cases_I2_J,axiom, % 173.59/173.75 ! [V_t_2,V_s_2,V_a_2,V_X_2] : % 173.59/173.75 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2)) % 173.59/173.75 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evalc__elim__cases_I6_J,axiom, % 173.59/173.75 ! [V_s1,V_s,V_P] : % 173.59/173.75 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1)) % 173.59/173.75 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evalc_OBody,axiom, % 173.59/173.75 ! [V_s1,V_s0,V_pn] : % 173.59/173.75 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1)) % 173.59/173.75 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_com__det,axiom, % 173.59/173.75 ! [V_u,V_t,V_s,V_c] : % 173.59/173.75 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 173.59/173.75 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u)) % 173.59/173.75 => V_u = V_t ) ) ). % 173.59/173.75 % 173.59/173.75 fof(fact_evalc_Oequations_I9_J,axiom, % 173.59/173.75 ! [V_a3_2,V_a2_2,V_a1_2] : % 173.59/173.75 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2)) % 173.59/173.76 <=> 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)) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_evalc_Oequations_I2_J,axiom, % 173.59/173.76 ! [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)))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_Suc__neq__Zero,axiom, % 173.59/173.76 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.59/173.76 % 173.59/173.76 fof(fact_Zero__neq__Suc,axiom, % 173.59/173.76 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat_Osimps_I3_J,axiom, % 173.59/173.76 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.59/173.76 % 173.59/173.76 fof(fact_Suc__not__Zero,axiom, % 173.59/173.76 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat_Osimps_I2_J,axiom, % 173.59/173.76 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 173.59/173.76 % 173.59/173.76 fof(fact_Zero__not__Suc,axiom, % 173.59/173.76 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 173.59/173.76 % 173.59/173.76 fof(fact_eval__eq,axiom, % 173.59/173.76 ! [V_t_2,V_s_2,V_ca_2] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),V_t_2)) % 173.59/173.76 <=> ? [B_n] : c_Natural_Oevaln(V_ca_2,V_s_2,B_n,V_t_2) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_evaln__evalc,axiom, % 173.59/173.76 ! [V_t,V_n,V_s,V_c] : % 173.59/173.76 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t) % 173.59/173.76 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_evalc_Oequations_I7_J,axiom, % 173.59/173.76 ! [V_a2_2,V_a3_2,V_a1_2] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2)) % 173.59/173.76 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.59/173.76 => ? [B_s1] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 173.59/173.76 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_evalc_Oequations_I8_J,axiom, % 173.59/173.76 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2)) % 173.59/173.76 <=> ( ( V_a5_2 = V_a2_2 % 173.59/173.76 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 173.59/173.76 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.59/173.76 & ? [B_s1] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 173.59/173.76 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_evalc_Oequations_I5_J,axiom, % 173.59/173.76 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] : % 173.59/173.76 ( 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)) % 173.59/173.76 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.59/173.76 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) % 173.59/173.76 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.59/173.76 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_evalc_Oequations_I6_J,axiom, % 173.59/173.76 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] : % 173.59/173.76 ( 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)) % 173.59/173.76 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.59/173.76 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) % 173.59/173.76 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 173.59/173.76 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_evalc_Oequations_I4_J,axiom, % 173.59/173.76 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2)) % 173.59/173.76 <=> ? [B_s1] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1)) % 173.59/173.76 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_evalc_Oequations_I1_J,axiom, % 173.59/173.76 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat__case__0,axiom, % 173.59/173.76 ! [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 ). % 173.59/173.76 % 173.59/173.76 fof(fact_triple_Osize_I1_J,axiom, % 173.59/173.76 ! [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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_triple_Osize_I2_J,axiom, % 173.59/173.76 ! [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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_evaln__elim__cases_I6_J,axiom, % 173.59/173.76 ! [V_s1,V_n,V_s,V_P] : % 173.59/173.76 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1) % 173.59/173.76 => ~ ! [B_n] : % 173.59/173.76 ( V_n = hAPP(c_Nat_OSuc,B_n) % 173.59/173.76 => ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_evalc__elim__cases_I4_J,axiom, % 173.59/173.76 ! [V_t,V_s,V_c2,V_c1] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t)) % 173.59/173.76 => ~ ! [B_s1] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1)) % 173.59/173.76 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I1_J,axiom, % 173.59/173.76 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I8_J,axiom, % 173.59/173.76 ! [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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I2_J,axiom, % 173.59/173.76 ! [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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I7_J,axiom, % 173.59/173.76 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I9_J,axiom, % 173.59/173.76 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I16_J,axiom, % 173.59/173.76 ! [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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I10_J,axiom, % 173.59/173.76 ! [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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I15_J,axiom, % 173.59/173.76 ! [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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I11_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I12_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I3_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I4_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I13_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I5_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I14_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_com_Osize_I6_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_WT_OBody,axiom, % 173.59/173.76 ! [V_pn] : % 173.59/173.76 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) % 173.59/173.76 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_WT_Oequations_I7_J,axiom, % 173.59/173.76 ! [V_a_2] : % 173.59/173.76 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) % 173.59/173.76 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__right__imp__eq,axiom, % 173.59/173.76 ! [V_c,V_a,V_b,T_a] : % 173.59/173.76 ( class_Groups_Ocancel__semigroup__add(T_a) % 173.59/173.76 => ( 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) % 173.59/173.76 => V_b = V_c ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__imp__eq,axiom, % 173.59/173.76 ! [V_c,V_b,V_a,T_a] : % 173.59/173.76 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 173.59/173.76 => ( 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) % 173.59/173.76 => V_b = V_c ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__left__imp__eq,axiom, % 173.59/173.76 ! [V_c,V_b,V_a,T_a] : % 173.59/173.76 ( class_Groups_Ocancel__semigroup__add(T_a) % 173.59/173.76 => ( 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) % 173.59/173.76 => V_b = V_c ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__right__cancel,axiom, % 173.59/173.76 ! [V_ca_2,V_a_2,V_ba_2,T_b] : % 173.59/173.76 ( class_Groups_Ocancel__semigroup__add(T_b) % 173.59/173.76 => ( 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) % 173.59/173.76 <=> V_ba_2 = V_ca_2 ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__left__cancel,axiom, % 173.59/173.76 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 173.59/173.76 ( class_Groups_Ocancel__semigroup__add(T_b) % 173.59/173.76 => ( 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) % 173.59/173.76 <=> V_ba_2 = V_ca_2 ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 173.59/173.76 ! [V_c,V_b,V_a,T_a] : % 173.59/173.76 ( class_Groups_Oab__semigroup__add(T_a) % 173.59/173.76 => 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)) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat__add__commute,axiom, % 173.59/173.76 ! [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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat__add__left__commute,axiom, % 173.59/173.76 ! [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)) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat__add__assoc,axiom, % 173.59/173.76 ! [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)) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat__add__left__cancel,axiom, % 173.59/173.76 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.76 ( 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) % 173.59/173.76 <=> V_m_2 = V_n_2 ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat__add__right__cancel,axiom, % 173.59/173.76 ! [V_n_2,V_k_2,V_m_2] : % 173.59/173.76 ( 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) % 173.59/173.76 <=> V_m_2 = V_n_2 ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add_Ocomm__neutral,axiom, % 173.59/173.76 ! [V_a,T_a] : % 173.59/173.76 ( class_Groups_Ocomm__monoid__add(T_a) % 173.59/173.76 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__0__right,axiom, % 173.59/173.76 ! [V_a,T_a] : % 173.59/173.76 ( class_Groups_Omonoid__add(T_a) % 173.59/173.76 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_double__zero__sym,axiom, % 173.59/173.76 ! [V_a_2,T_b] : % 173.59/173.76 ( class_Groups_Olinordered__ab__group__add(T_b) % 173.59/173.76 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) % 173.59/173.76 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__0,axiom, % 173.59/173.76 ! [V_a,T_a] : % 173.59/173.76 ( class_Groups_Ocomm__monoid__add(T_a) % 173.59/173.76 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__0__left,axiom, % 173.59/173.76 ! [V_a,T_a] : % 173.59/173.76 ( class_Groups_Omonoid__add(T_a) % 173.59/173.76 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_plus__nat_Oadd__0,axiom, % 173.59/173.76 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 173.59/173.76 % 173.59/173.76 fof(fact_Nat_Oadd__0__right,axiom, % 173.59/173.76 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__is__0,axiom, % 173.59/173.76 ! [V_n_2,V_m_2] : % 173.59/173.76 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.76 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.76 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__eq__self__zero,axiom, % 173.59/173.76 ! [V_n,V_m] : % 173.59/173.76 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 173.59/173.76 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__Suc__shift,axiom, % 173.59/173.76 ! [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)) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__Suc,axiom, % 173.59/173.76 ! [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)) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__Suc__right,axiom, % 173.59/173.76 ! [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)) ). % 173.59/173.76 % 173.59/173.76 fof(fact_one__is__add,axiom, % 173.59/173.76 ! [V_n_2,V_m_2] : % 173.59/173.76 ( 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) % 173.59/173.76 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 173.59/173.76 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.59/173.76 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.76 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__is__1,axiom, % 173.59/173.76 ! [V_n_2,V_m_2] : % 173.59/173.76 ( 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)) % 173.59/173.76 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 173.59/173.76 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.59/173.76 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.76 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_zero__reorient,axiom, % 173.59/173.76 ! [V_x_2,T_b] : % 173.59/173.76 ( class_Groups_Ozero(T_b) % 173.59/173.76 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2 % 173.59/173.76 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_WT__bodiesD,axiom, % 173.59/173.76 ! [V_b,V_pn] : % 173.59/173.76 ( c_Com_OWT__bodies % 173.59/173.76 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) % 173.59/173.76 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_WTs__elim__cases_I7_J,axiom, % 173.59/173.76 ! [V_P] : % 173.59/173.76 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P))) % 173.59/173.76 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_the_Osimps,axiom, % 173.59/173.76 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 173.59/173.76 % 173.59/173.76 fof(fact_not__None__eq,axiom, % 173.59/173.76 ! [T_b,V_x_2] : % 173.59/173.76 ( V_x_2 != c_Option_Ooption_ONone(T_b) % 173.59/173.76 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_not__Some__eq,axiom, % 173.59/173.76 ! [T_b,V_x_2] : % 173.59/173.76 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y) % 173.59/173.76 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_option_Osimps_I3_J,axiom, % 173.59/173.76 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 173.59/173.76 % 173.59/173.76 fof(fact_option_Osimps_I2_J,axiom, % 173.59/173.76 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 173.59/173.76 % 173.59/173.76 fof(fact_option_Osize_I2_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_double__eq__0__iff,axiom, % 173.59/173.76 ! [V_a_2,T_b] : % 173.59/173.76 ( class_Groups_Olinordered__ab__group__add(T_b) % 173.59/173.76 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 173.59/173.76 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__0__iff,axiom, % 173.59/173.76 ! [V_a_2,V_ba_2,T_b] : % 173.59/173.76 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 173.59/173.76 => ( V_ba_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_a_2) % 173.59/173.76 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 173.59/173.76 ! [V_a,T_a] : % 173.59/173.76 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.76 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 173.59/173.76 ! [V_c,V_a,T_a] : % 173.59/173.76 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.76 => 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) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 173.59/173.76 ! [V_d,V_c,V_a,T_a] : % 173.59/173.76 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.76 => 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)) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 173.59/173.76 ! [V_d,V_c,V_a,T_a] : % 173.59/173.76 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.76 => 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) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 173.59/173.76 ! [V_c,V_b,V_a,T_a] : % 173.59/173.76 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.76 => 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)) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 173.59/173.76 ! [V_c,V_b,V_a,T_a] : % 173.59/173.76 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.76 => 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) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 173.59/173.76 ! [V_d,V_c,V_b,V_a,T_a] : % 173.59/173.76 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.76 => 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)) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_option_Osize_I1_J,axiom, % 173.59/173.76 ! [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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_option_Oinject,axiom, % 173.59/173.76 ! [V_a_H_2,V_a_2,T_b] : % 173.59/173.76 ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2) % 173.59/173.76 <=> V_a_2 = V_a_H_2 ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 173.59/173.76 ! [V_a,T_a] : % 173.59/173.76 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.76 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat_Osize_I2_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat_Osize_I4_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_option_Osize_I4_J,axiom, % 173.59/173.76 ! [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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_option_Osize_I3_J,axiom, % 173.59/173.76 ! [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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_option_Orecs_I2_J,axiom, % 173.59/173.76 ! [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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_option_Osimps_I5_J,axiom, % 173.59/173.76 ! [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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_option_Orecs_I1_J,axiom, % 173.59/173.76 ! [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 ). % 173.59/173.76 % 173.59/173.76 fof(fact_option_Osimps_I4_J,axiom, % 173.59/173.76 ! [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 ). % 173.59/173.76 % 173.59/173.76 fof(fact_bool_Osize_I1_J,axiom, % 173.59/173.76 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.59/173.76 % 173.59/173.76 fof(fact_bool_Osize_I2_J,axiom, % 173.59/173.76 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.59/173.76 % 173.59/173.76 fof(fact_is__none__code_I2_J,axiom, % 173.59/173.76 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat__size,axiom, % 173.59/173.76 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat_Osize_I3_J,axiom, % 173.59/173.76 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) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat_Osize_I1_J,axiom, % 173.59/173.76 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.59/173.76 % 173.59/173.76 fof(fact_is__none__def,axiom, % 173.59/173.76 ! [V_x_2,T_b] : % 173.59/173.76 ( c_Option_Ois__none(T_b,V_x_2) % 173.59/173.76 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_is__none__code_I1_J,axiom, % 173.59/173.76 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ). % 173.59/173.76 % 173.59/173.76 fof(fact_bool_Osize_I4_J,axiom, % 173.59/173.76 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.59/173.76 % 173.59/173.76 fof(fact_bool_Osize_I3_J,axiom, % 173.59/173.76 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.59/173.76 % 173.59/173.76 fof(fact_def__nat__rec__0,axiom, % 173.59/173.76 ! [V_h_2,V_ca_2,T_b,V_f_2] : % 173.59/173.76 ( ! [B_n] : hAPP(V_f_2,B_n) = hAPP(c_Nat_Onat_Onat__rec(T_b,V_ca_2,V_h_2),B_n) % 173.59/173.76 => hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_ca_2 ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_evalc__WHILE__case,axiom, % 173.59/173.76 ! [V_t_2,V_s_2,V_ca_2,V_ba_2] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_s_2),V_t_2)) % 173.59/173.76 => ( ( V_t_2 = V_s_2 % 173.59/173.76 => hBOOL(hAPP(V_ba_2,V_s_2)) ) % 173.59/173.76 => ~ ( hBOOL(hAPP(V_ba_2,V_s_2)) % 173.59/173.76 => ! [B_s1] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),B_s1)) % 173.59/173.76 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),B_s1),V_t_2)) ) ) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_pair__box_Osize_I1_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_evalc__evaln,axiom, % 173.59/173.76 ! [V_t,V_s,V_c] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 173.59/173.76 => ? [B_n] : c_Natural_Oevaln(V_c,V_s,B_n,V_t) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_sum_Osize_I1_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_sum_Osize_I2_J,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_option_Oexhaust,axiom, % 173.59/173.76 ! [T_a,V_y] : % 173.59/173.76 ( V_y != c_Option_Ooption_ONone(T_a) % 173.59/173.76 => ~ ! [B_a] : V_y != hAPP(c_Option_Ooption_OSome(T_a),B_a) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_zero__less__Suc,axiom, % 173.59/173.76 ! [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))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_not0__implies__Suc,axiom, % 173.59/173.76 ! [V_n] : % 173.59/173.76 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.76 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_less__zeroE,axiom, % 173.59/173.76 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_lessI,axiom, % 173.59/173.76 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_Suc__mono,axiom, % 173.59/173.76 ! [V_n,V_m] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat__less__cases,axiom, % 173.59/173.76 ! [V_Pa_2,V_n_2,V_m_2] : % 173.59/173.76 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.59/173.76 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 173.59/173.76 => ( ( V_m_2 = V_n_2 % 173.59/173.76 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 173.59/173.76 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 173.59/173.76 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) % 173.59/173.76 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_less__not__refl3,axiom, % 173.59/173.76 ! [V_t,V_s] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 173.59/173.76 => V_s != V_t ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_less__not__refl2,axiom, % 173.59/173.76 ! [V_m,V_n] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 173.59/173.76 => V_m != V_n ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_less__irrefl__nat,axiom, % 173.59/173.76 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 173.59/173.76 % 173.59/173.76 fof(fact_linorder__neqE__nat,axiom, % 173.59/173.76 ! [V_y,V_x] : % 173.59/173.76 ( V_x != V_y % 173.59/173.76 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 173.59/173.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat__neq__iff,axiom, % 173.59/173.76 ! [V_n_2,V_m_2] : % 173.59/173.76 ( V_m_2 != V_n_2 % 173.59/173.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.59/173.76 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_less__not__refl,axiom, % 173.59/173.76 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 173.59/173.76 % 173.59/173.76 fof(fact_pair__box_Oinject,axiom, % 173.59/173.76 ! [V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] : % 173.59/173.76 ( 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) % 173.59/173.76 <=> ( V_a_2 = V_a_H_2 % 173.59/173.76 & V_ba_2 = V_b_H_2 ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__less__cancel__right,axiom, % 173.59/173.76 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 173.59/173.76 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 173.59/173.76 => ( 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))) % 173.59/173.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__less__cancel__left,axiom, % 173.59/173.76 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 173.59/173.76 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 173.59/173.76 => ( 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))) % 173.59/173.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__strict__right__mono,axiom, % 173.59/173.76 ! [V_c,V_b,V_a,T_a] : % 173.59/173.76 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 173.59/173.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.59/173.76 => 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))) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__strict__left__mono,axiom, % 173.59/173.76 ! [V_c,V_b,V_a,T_a] : % 173.59/173.76 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 173.59/173.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.59/173.76 => 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))) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__strict__mono,axiom, % 173.59/173.76 ! [V_d,V_c,V_b,V_a,T_a] : % 173.59/173.76 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 173.59/173.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.59/173.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 173.59/173.76 => 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))) ) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__less__imp__less__right,axiom, % 173.59/173.76 ! [V_b,V_c,V_a,T_a] : % 173.59/173.76 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.59/173.76 => ( 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))) % 173.59/173.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__less__imp__less__left,axiom, % 173.59/173.76 ! [V_b,V_a,V_c,T_a] : % 173.59/173.76 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.59/173.76 => ( 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))) % 173.59/173.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_gr0I,axiom, % 173.59/173.76 ! [V_n] : % 173.59/173.76 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_gr__implies__not0,axiom, % 173.59/173.76 ! [V_n,V_m] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.76 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_less__nat__zero__code,axiom, % 173.59/173.76 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_neq0__conv,axiom, % 173.59/173.76 ! [V_n_2] : % 173.59/173.76 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_not__less0,axiom, % 173.59/173.76 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 173.59/173.76 % 173.59/173.76 fof(fact_not__less__eq,axiom, % 173.59/173.76 ! [V_n_2,V_m_2] : % 173.59/173.76 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.59/173.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_less__Suc__eq,axiom, % 173.59/173.76 ! [V_n_2,V_m_2] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 173.59/173.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.59/173.76 | V_m_2 = V_n_2 ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_Suc__less__eq,axiom, % 173.59/173.76 ! [V_n_2,V_m_2] : % 173.59/173.76 ( 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))) % 173.59/173.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_not__less__less__Suc__eq,axiom, % 173.59/173.76 ! [V_m_2,V_n_2] : % 173.59/173.76 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 173.59/173.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 173.59/173.76 <=> V_n_2 = V_m_2 ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_less__antisym,axiom, % 173.59/173.76 ! [V_m,V_n] : % 173.59/173.76 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 173.59/173.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 173.59/173.76 => V_m = V_n ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_less__SucI,axiom, % 173.59/173.76 ! [V_n,V_m] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_Suc__lessI,axiom, % 173.59/173.76 ! [V_n,V_m] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.76 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 173.59/173.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_less__trans__Suc,axiom, % 173.59/173.76 ! [V_k,V_j,V_i] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.59/173.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 173.59/173.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_less__SucE,axiom, % 173.59/173.76 ! [V_n,V_m] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 173.59/173.76 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.76 => V_m = V_n ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_Suc__lessD,axiom, % 173.59/173.76 ! [V_n,V_m] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 173.59/173.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_Suc__less__SucD,axiom, % 173.59/173.76 ! [V_n,V_m] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 173.59/173.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__lessD1,axiom, % 173.59/173.76 ! [V_k,V_j,V_i] : % 173.59/173.76 ( 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)) % 173.59/173.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_less__add__eq__less,axiom, % 173.59/173.76 ! [V_n,V_m,V_l,V_k] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 173.59/173.76 => ( 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) % 173.59/173.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__less__mono,axiom, % 173.59/173.76 ! [V_l,V_k,V_j,V_i] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.59/173.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 173.59/173.76 => 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))) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__less__mono1,axiom, % 173.59/173.76 ! [V_k,V_j,V_i] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.59/173.76 => 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))) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_trans__less__add2,axiom, % 173.59/173.76 ! [V_m,V_j,V_i] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.59/173.76 => 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))) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_trans__less__add1,axiom, % 173.59/173.76 ! [V_m,V_j,V_i] : % 173.59/173.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.59/173.76 => 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))) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_nat__add__left__cancel__less,axiom, % 173.59/173.76 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.76 ( 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))) % 173.59/173.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_not__add__less2,axiom, % 173.59/173.76 ! [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)) ). % 173.59/173.76 % 173.59/173.76 fof(fact_not__add__less1,axiom, % 173.59/173.76 ! [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)) ). % 173.59/173.76 % 173.59/173.76 fof(fact_even__less__0__iff,axiom, % 173.59/173.76 ! [V_a_2,T_b] : % 173.59/173.76 ( class_Rings_Olinordered__idom(T_b) % 173.59/173.76 => ( 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))) % 173.59/173.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 173.59/173.76 % 173.59/173.76 fof(fact_add__neg__neg,axiom, % 173.59/173.76 ! [V_b,V_a,T_a] : % 173.59/173.76 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.59/173.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_add__pos__pos,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 173.59/173.77 ! [V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Olinordered__ab__group__add(T_b) % 173.59/173.77 => ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 173.59/173.77 ! [V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Olinordered__ab__group__add(T_b) % 173.59/173.77 => ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_less__Suc__eq__0__disj,axiom, % 173.59/173.77 ! [V_n_2,V_m_2] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 173.59/173.77 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.77 | ? [B_j] : % 173.59/173.77 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 173.59/173.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_less__Suc0,axiom, % 173.59/173.77 ! [V_n_2] : % 173.59/173.77 ( 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)))) % 173.59/173.77 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_gr0__conv__Suc,axiom, % 173.59/173.77 ! [V_n_2] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 173.59/173.77 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_add__gr__0,axiom, % 173.59/173.77 ! [V_n_2,V_m_2] : % 173.59/173.77 ( 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))) % 173.59/173.77 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 173.59/173.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_less__iff__Suc__add,axiom, % 173.59/173.77 ! [V_n_2,V_m_2] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.59/173.77 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_less__add__Suc2,axiom, % 173.59/173.77 ! [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)))) ). % 173.59/173.77 % 173.59/173.77 fof(fact_less__add__Suc1,axiom, % 173.59/173.77 ! [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)))) ). % 173.59/173.77 % 173.59/173.77 fof(fact_pair__box_Osize_I2_J,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_pair__box_Orecs,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_pair__box_Osimps_I2_J,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_pos__add__strict,axiom, % 173.59/173.77 ! [V_c,V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__semidom(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_Inl__not__Inr,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_sum_Osimps_I3_J,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_Inr__not__Inl,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_sum_Osimps_I4_J,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_sum_Osize_I3_J,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_sum_Osize_I4_J,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_termination__basic__simps_I1_J,axiom, % 173.59/173.77 ! [V_z,V_y,V_x] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 173.59/173.77 => 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))) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_linorder__neqE__linordered__idom,axiom, % 173.59/173.77 ! [V_y,V_x,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__idom(T_a) % 173.59/173.77 => ( V_x != V_y % 173.59/173.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_Inr__inject,axiom, % 173.59/173.77 ! [V_y,V_x,T_a,T_b] : % 173.59/173.77 ( hAPP(c_Sum__Type_OInr(T_b,T_a),V_x) = hAPP(c_Sum__Type_OInr(T_b,T_a),V_y) % 173.59/173.77 => V_x = V_y ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_sum_Osimps_I2_J,axiom, % 173.59/173.77 ! [V_b_H_2,V_ba_2,T_b,T_c] : % 173.59/173.77 ( 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) % 173.59/173.77 <=> V_ba_2 = V_b_H_2 ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_Inl__inject,axiom, % 173.59/173.77 ! [V_y,V_x,T_b,T_a] : % 173.59/173.77 ( hAPP(c_Sum__Type_OInl(T_a,T_b),V_x) = hAPP(c_Sum__Type_OInl(T_a,T_b),V_y) % 173.59/173.77 => V_x = V_y ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_sum_Osimps_I1_J,axiom, % 173.59/173.77 ! [V_a_H_2,V_a_2,T_c,T_b] : % 173.59/173.77 ( 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) % 173.59/173.77 <=> V_a_2 = V_a_H_2 ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_termination__basic__simps_I2_J,axiom, % 173.59/173.77 ! [V_y,V_z,V_x] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 173.59/173.77 => 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))) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_Projl_Osimps,axiom, % 173.59/173.77 ! [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 ). % 173.59/173.77 % 173.59/173.77 fof(fact_Projr_Osimps,axiom, % 173.59/173.77 ! [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 ). % 173.59/173.77 % 173.59/173.77 fof(fact_sum_Orecs_I1_J,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_sum_Orecs_I2_J,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_Suml_Osimps,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_Sumr_Osimps,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__nat__0__less__iff,axiom, % 173.59/173.77 ! [V_n_2,T_b] : % 173.59/173.77 ( class_Rings_Olinordered__semidom(T_b) % 173.59/173.77 => ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_less__imp__Suc__add,axiom, % 173.59/173.77 ! [V_n,V_m] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.77 => ? [B_k] : V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),B_k)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_less__imp__add__positive,axiom, % 173.59/173.77 ! [V_j,V_i] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.59/173.77 => ? [B_k] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_k)) % 173.59/173.77 & hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),B_k) = V_j ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_gr0__implies__Suc,axiom, % 173.59/173.77 ! [V_n] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.59/173.77 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__nat__eq__iff,axiom, % 173.59/173.77 ! [V_n_2,V_m_2,T_b] : % 173.59/173.77 ( class_Nat_Osemiring__char__0(T_b) % 173.59/173.77 => ( 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) % 173.59/173.77 <=> V_m_2 = V_n_2 ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_Suml__inject,axiom, % 173.59/173.77 ! [V_g_2,V_f_2,T_c,T_d,T_b] : % 173.59/173.77 ( 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) % 173.59/173.77 => V_f_2 = V_g_2 ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_Sumr__inject,axiom, % 173.59/173.77 ! [V_g_2,V_f_2,T_b,T_d,T_c] : % 173.59/173.77 ( 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) % 173.59/173.77 => V_f_2 = V_g_2 ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_int__eq__0__conv,axiom, % 173.59/173.77 ! [V_n_2] : % 173.59/173.77 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.77 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_int__0,axiom, % 173.59/173.77 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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zless__iff__Suc__zadd,axiom, % 173.59/173.77 ! [V_z_2,V_w_2] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 173.59/173.77 <=> ? [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))) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zless__int,axiom, % 173.59/173.77 ! [V_n_2,V_m_2] : % 173.59/173.77 ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zadd__int__left,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zadd__int,axiom, % 173.59/173.77 ! [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)) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zero__less__int__conv,axiom, % 173.59/173.77 ! [V_n_2] : % 173.59/173.77 ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__nat__less__0__iff,axiom, % 173.59/173.77 ! [V_m,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__semidom(T_a) % 173.59/173.77 => ~ 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))) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__nat__0,axiom, % 173.59/173.77 ! [T_a] : % 173.59/173.77 ( class_Rings_Osemiring__1(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__nat__less__imp__less,axiom, % 173.59/173.77 ! [V_n,V_m,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__semidom(T_a) % 173.59/173.77 => ( 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))) % 173.59/173.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_less__imp__of__nat__less,axiom, % 173.59/173.77 ! [V_n,V_m,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__semidom(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.77 => 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))) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__nat__less__iff,axiom, % 173.59/173.77 ! [V_n_2,V_m_2,T_b] : % 173.59/173.77 ( class_Rings_Olinordered__semidom(T_b) % 173.59/173.77 => ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__nat__add,axiom, % 173.59/173.77 ! [V_n,V_m,T_a] : % 173.59/173.77 ( class_Rings_Osemiring__1(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_lift__Suc__mono__less__iff,axiom, % 173.59/173.77 ! [V_m_2,V_n_2,V_f_2,T_b] : % 173.59/173.77 ( class_Orderings_Oorder(T_b) % 173.59/173.77 => ( ! [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)))) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_m_2))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_lift__Suc__mono__less,axiom, % 173.59/173.77 ! [V_n_H_2,V_n_2,V_f_2,T_b] : % 173.59/173.77 ( class_Orderings_Oorder(T_b) % 173.59/173.77 => ( ! [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)))) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_n_H_2)) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 173.59/173.77 ! [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)) ). % 173.59/173.77 % 173.59/173.77 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 173.59/173.77 ! [V_y_2,V_x_2] : % 173.59/173.77 ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 173.59/173.77 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)) ). % 173.59/173.77 % 173.59/173.77 fof(fact_order__less__irrefl,axiom, % 173.59/173.77 ! [V_x,T_a] : % 173.59/173.77 ( class_Orderings_Opreorder(T_a) % 173.59/173.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_linorder__neq__iff,axiom, % 173.59/173.77 ! [V_y_2,V_x_2,T_b] : % 173.59/173.77 ( class_Orderings_Olinorder(T_b) % 173.59/173.77 => ( V_x_2 != V_y_2 % 173.59/173.77 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 173.59/173.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_not__less__iff__gr__or__eq,axiom, % 173.59/173.77 ! [V_y_2,V_x_2,T_b] : % 173.59/173.77 ( class_Orderings_Olinorder(T_b) % 173.59/173.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 173.59/173.77 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 173.59/173.77 | V_x_2 = V_y_2 ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_linorder__less__linear,axiom, % 173.59/173.77 ! [V_y,V_x,T_a] : % 173.59/173.77 ( class_Orderings_Olinorder(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.77 | V_x = V_y % 173.59/173.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_linorder__antisym__conv3,axiom, % 173.59/173.77 ! [V_x_2,V_y_2,T_b] : % 173.59/173.77 ( class_Orderings_Olinorder(T_b) % 173.59/173.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 173.59/173.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 173.59/173.77 <=> V_x_2 = V_y_2 ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_int__less__0__conv,axiom, % 173.59/173.77 ! [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))) ). % 173.59/173.77 % 173.59/173.77 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 173.59/173.77 ! [V_y_2,V_x_2] : % 173.59/173.77 ( 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) % 173.59/173.77 <=> V_x_2 = V_y_2 ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_int__int__eq,axiom, % 173.59/173.77 ! [V_n_2,V_m_2] : % 173.59/173.77 ( 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) % 173.59/173.77 <=> V_m_2 = V_n_2 ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zadd__assoc,axiom, % 173.59/173.77 ! [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)) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zadd__left__commute,axiom, % 173.59/173.77 ! [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)) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zadd__commute,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zadd__0,axiom, % 173.59/173.77 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 173.59/173.77 % 173.59/173.77 fof(fact_zadd__0__right,axiom, % 173.59/173.77 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 173.59/173.77 % 173.59/173.77 fof(fact_zadd__strict__right__mono,axiom, % 173.59/173.77 ! [V_k,V_j,V_i] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 173.59/173.77 => 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))) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zless__linear,axiom, % 173.59/173.77 ! [V_y,V_x] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 173.59/173.77 | V_x = V_y % 173.59/173.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_linorder__cases,axiom, % 173.59/173.77 ! [V_y,V_x,T_a] : % 173.59/173.77 ( class_Orderings_Olinorder(T_a) % 173.59/173.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.77 => ( V_x != V_y % 173.59/173.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_order__less__asym,axiom, % 173.59/173.77 ! [V_y,V_x,T_a] : % 173.59/173.77 ( class_Orderings_Opreorder(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_xt1_I10_J,axiom, % 173.59/173.77 ! [V_z,V_x,V_y,T_a] : % 173.59/173.77 ( class_Orderings_Oorder(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 173.59/173.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_order__less__trans,axiom, % 173.59/173.77 ! [V_z,V_y,V_x,T_a] : % 173.59/173.77 ( class_Orderings_Opreorder(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 173.59/173.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_xt1_I2_J,axiom, % 173.59/173.77 ! [V_c,V_a,V_b,T_a] : % 173.59/173.77 ( class_Orderings_Oorder(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 173.59/173.77 => ( V_b = V_c % 173.59/173.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_ord__less__eq__trans,axiom, % 173.59/173.77 ! [V_c,V_b,V_a,T_a] : % 173.59/173.77 ( class_Orderings_Oord(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.59/173.77 => ( V_b = V_c % 173.59/173.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_xt1_I1_J,axiom, % 173.59/173.77 ! [V_c,V_b,V_a,T_a] : % 173.59/173.77 ( class_Orderings_Oorder(T_a) % 173.59/173.77 => ( V_a = V_b % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 173.59/173.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_ord__eq__less__trans,axiom, % 173.59/173.77 ! [V_c,V_b,V_a,T_a] : % 173.59/173.77 ( class_Orderings_Oord(T_a) % 173.59/173.77 => ( V_a = V_b % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 173.59/173.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_xt1_I9_J,axiom, % 173.59/173.77 ! [V_a,V_b,T_a] : % 173.59/173.77 ( class_Orderings_Oorder(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 173.59/173.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_order__less__asym_H,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Orderings_Opreorder(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.59/173.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_order__less__imp__not__eq2,axiom, % 173.59/173.77 ! [V_y,V_x,T_a] : % 173.59/173.77 ( class_Orderings_Oorder(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.77 => V_y != V_x ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_order__less__imp__not__eq,axiom, % 173.59/173.77 ! [V_y,V_x,T_a] : % 173.59/173.77 ( class_Orderings_Oorder(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.77 => V_x != V_y ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_order__less__imp__not__less,axiom, % 173.59/173.77 ! [V_y,V_x,T_a] : % 173.59/173.77 ( class_Orderings_Opreorder(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_order__less__not__sym,axiom, % 173.59/173.77 ! [V_y,V_x,T_a] : % 173.59/173.77 ( class_Orderings_Opreorder(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_less__imp__neq,axiom, % 173.59/173.77 ! [V_y,V_x,T_a] : % 173.59/173.77 ( class_Orderings_Oorder(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.77 => V_x != V_y ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_linorder__neqE,axiom, % 173.59/173.77 ! [V_y,V_x,T_a] : % 173.59/173.77 ( class_Orderings_Olinorder(T_a) % 173.59/173.77 => ( V_x != V_y % 173.59/173.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zero__less__imp__eq__int,axiom, % 173.59/173.77 ! [V_k] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 173.59/173.77 => ? [B_n] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 173.59/173.77 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__int__0__less__iff,axiom, % 173.59/173.77 ! [V_z_2,T_b] : % 173.59/173.77 ( class_Rings_Olinordered__idom(T_b) % 173.59/173.77 => ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__int__less__0__iff,axiom, % 173.59/173.77 ! [V_z_2,T_b] : % 173.59/173.77 ( class_Rings_Olinordered__idom(T_b) % 173.59/173.77 => ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zmult__zless__mono2__lemma,axiom, % 173.59/173.77 ! [V_k,V_j,V_i] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 173.59/173.77 => 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))) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_negative__zless__0,axiom, % 173.59/173.77 ! [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))) ). % 173.59/173.77 % 173.59/173.77 fof(fact_split__nat,axiom, % 173.59/173.77 ! [V_i_2,V_Pa_2] : % 173.59/173.77 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2))) % 173.59/173.77 <=> ( ! [B_n] : % 173.59/173.77 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 173.59/173.77 => hBOOL(hAPP(V_Pa_2,B_n)) ) % 173.59/173.77 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.77 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zero__less__nat__eq,axiom, % 173.59/173.77 ! [V_z_2] : % 173.59/173.77 ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_negative__zless,axiom, % 173.59/173.77 ! [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))) ). % 173.59/173.77 % 173.59/173.77 fof(fact_int__Suc,axiom, % 173.59/173.77 ! [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)) ). % 173.59/173.77 % 173.59/173.77 fof(fact_odd__less__0,axiom, % 173.59/173.77 ! [V_z_2] : % 173.59/173.77 ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 173.59/173.77 ! [V_m,V_a,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 173.59/173.77 ! [V_a,V_m,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 173.59/173.77 ! [V_m,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_less__1__mult,axiom, % 173.59/173.77 ! [V_n,V_m,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__semidom(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_square__eq__iff,axiom, % 173.59/173.77 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.77 ( class_Rings_Oidom(T_b) % 173.59/173.77 => ( 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) % 173.59/173.77 <=> ( V_a_2 = V_ba_2 % 173.59/173.77 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_square__eq__1__iff,axiom, % 173.59/173.77 ! [V_x_2,T_b] : % 173.59/173.77 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 173.59/173.77 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 173.59/173.77 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b) % 173.59/173.77 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_minus__mult__minus,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Oring(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_minus__mult__commute,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Oring(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_minus__mult__left,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Oring(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_minus__mult__right,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Oring(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 173.59/173.77 ! [V_c,V_b,V_a,T_a] : % 173.59/173.77 ( class_Groups_Oab__semigroup__mult(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_neg__equal__iff__equal,axiom, % 173.59/173.77 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_b) % 173.59/173.77 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) % 173.59/173.77 <=> V_a_2 = V_ba_2 ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_minus__equation__iff,axiom, % 173.59/173.77 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_b) % 173.59/173.77 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_ba_2 % 173.59/173.77 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) = V_a_2 ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_equation__minus__iff,axiom, % 173.59/173.77 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_b) % 173.59/173.77 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) % 173.59/173.77 <=> V_ba_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult_Ocomm__neutral,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Groups_Ocomm__monoid__mult(T_a) % 173.59/173.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__1__right,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Groups_Omonoid__mult(T_a) % 173.59/173.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_one__reorient,axiom, % 173.59/173.77 ! [V_x_2,T_b] : % 173.59/173.77 ( class_Groups_Oone(T_b) % 173.59/173.77 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2 % 173.59/173.77 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__1,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Groups_Ocomm__monoid__mult(T_a) % 173.59/173.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__1__left,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Groups_Omonoid__mult(T_a) % 173.59/173.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_minus__minus,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_a) % 173.59/173.77 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 173.59/173.77 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 173.59/173.77 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 173.59/173.77 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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))) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 173.59/173.77 ! [V_rx,V_ly,V_lx,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zmult__assoc,axiom, % 173.59/173.77 ! [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)) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 173.59/173.77 ! [V_rx,V_ly,V_lx,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__int__eq__iff,axiom, % 173.59/173.77 ! [V_z_2,V_w_2,T_b] : % 173.59/173.77 ( class_Int_Oring__char__0(T_b) % 173.59/173.77 => ( 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) % 173.59/173.77 <=> V_w_2 = V_z_2 ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zmult__zminus,axiom, % 173.59/173.77 ! [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)) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 173.59/173.77 ! [V_ry,V_rx,V_lx,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 173.59/173.77 ! [V_ry,V_rx,V_lx,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zmult__commute,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zmult__1__right,axiom, % 173.59/173.77 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zmult__1,axiom, % 173.59/173.77 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__int__mult,axiom, % 173.59/173.77 ! [V_z,V_w,T_a] : % 173.59/173.77 ( class_Rings_Oring__1(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__int__minus,axiom, % 173.59/173.77 ! [V_z,T_a] : % 173.59/173.77 ( class_Rings_Oring__1(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zminus__zminus,axiom, % 173.59/173.77 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 173.59/173.77 ! [V_x,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__ring__1(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__int__1,axiom, % 173.59/173.77 ! [T_a] : % 173.59/173.77 ( class_Rings_Oring__1(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__nat__mult,axiom, % 173.59/173.77 ! [V_n,V_m,T_a] : % 173.59/173.77 ( class_Rings_Osemiring__1(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__nat__1,axiom, % 173.59/173.77 ! [T_a] : % 173.59/173.77 ( class_Rings_Osemiring__1(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__int__of__nat,axiom, % 173.59/173.77 ! [V_k,T_a] : % 173.59/173.77 ( class_Rings_Oring__1(T_a) % 173.59/173.77 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.77 => 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)))) ) % 173.59/173.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.77 => 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)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_nat__zminus__int,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_nat__1,axiom, % 173.59/173.77 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 173.59/173.77 % 173.59/173.77 fof(fact_pos__zmult__eq__1__iff,axiom, % 173.59/173.77 ! [V_n_2,V_m_2] : % 173.59/173.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 173.59/173.77 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 173.59/173.77 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 173.59/173.77 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_minus__zero,axiom, % 173.59/173.77 ! [T_a] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_a) % 173.59/173.77 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_neg__0__equal__iff__equal,axiom, % 173.59/173.77 ! [V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_b) % 173.59/173.77 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 173.59/173.77 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_equal__neg__zero,axiom, % 173.59/173.77 ! [V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Olinordered__ab__group__add(T_b) % 173.59/173.77 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 173.59/173.77 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_neg__equal__0__iff__equal,axiom, % 173.59/173.77 ! [V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_b) % 173.59/173.77 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 173.59/173.77 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_neg__equal__zero,axiom, % 173.59/173.77 ! [V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Olinordered__ab__group__add(T_b) % 173.59/173.77 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2 % 173.59/173.77 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_neg__less__iff__less,axiom, % 173.59/173.77 ! [V_a_2,V_ba_2,T_b] : % 173.59/173.77 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.77 => ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_minus__less__iff,axiom, % 173.59/173.77 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),V_a_2)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_less__minus__iff,axiom, % 173.59/173.77 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_minus__add__distrib,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Groups_Oab__group__add(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_minus__add,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_add__minus__cancel,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_a) % 173.59/173.77 => 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 ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_minus__add__cancel,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_a) % 173.59/173.77 => 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 ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__zero__left,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Rings_Omult__zero(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__zero__right,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Rings_Omult__zero(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__eq__0__iff,axiom, % 173.59/173.77 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.77 ( class_Rings_Oring__no__zero__divisors(T_b) % 173.59/173.77 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) % 173.59/173.77 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 173.59/173.77 | V_ba_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_no__zero__divisors,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Ono__zero__divisors(T_a) % 173.59/173.77 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.77 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_divisors__zero,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Ono__zero__divisors(T_a) % 173.59/173.77 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.77 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.77 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_one__neq__zero,axiom, % 173.59/173.77 ! [T_a] : % 173.59/173.77 ( class_Rings_Ozero__neq__one(T_a) % 173.59/173.77 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zero__neq__one,axiom, % 173.59/173.77 ! [T_a] : % 173.59/173.77 ( class_Rings_Ozero__neq__one(T_a) % 173.59/173.77 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zminus__0,axiom, % 173.59/173.77 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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_nat__int,axiom, % 173.59/173.77 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 173.59/173.77 ! [V_z,V_y,V_x,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_crossproduct__noteq,axiom, % 173.59/173.77 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.59/173.77 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 173.59/173.77 => ( ( V_a_2 != V_ba_2 % 173.59/173.77 & V_ca_2 != V_d_2 ) % 173.59/173.77 <=> 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)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 173.59/173.77 ! [V_c,V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 173.59/173.77 ! [V_b,V_m,V_a,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_crossproduct__eq,axiom, % 173.59/173.77 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] : % 173.59/173.77 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 173.59/173.77 => ( 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)) % 173.59/173.77 <=> ( V_w_2 = V_x_2 % 173.59/173.77 | V_y_2 = V_z_2 ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__semiring__class_Odistrib,axiom, % 173.59/173.77 ! [V_c,V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Ocomm__semiring(T_a) % 173.59/173.77 => 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)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_combine__common__factor,axiom, % 173.59/173.77 ! [V_c,V_b,V_e,V_a,T_a] : % 173.59/173.77 ( class_Rings_Osemiring(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zminus__zadd__distrib,axiom, % 173.59/173.77 ! [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)) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zadd__zmult__distrib2,axiom, % 173.59/173.77 ! [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)) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zadd__zmult__distrib,axiom, % 173.59/173.77 ! [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)) ). % 173.59/173.77 % 173.59/173.77 fof(fact_int__0__neq__1,axiom, % 173.59/173.77 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 173.59/173.77 % 173.59/173.77 fof(fact_of__int__int__eq,axiom, % 173.59/173.77 ! [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) ). % 173.59/173.77 % 173.59/173.77 fof(fact_one__less__nat__eq,axiom, % 173.59/173.77 ! [V_z_2] : % 173.59/173.77 ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_neg__less__nonneg,axiom, % 173.59/173.77 ! [V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Olinordered__ab__group__add(T_b) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_neg__less__0__iff__less,axiom, % 173.59/173.77 ! [V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.77 => ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_neg__0__less__iff__less,axiom, % 173.59/173.77 ! [V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.77 => ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_less__minus__self__iff,axiom, % 173.59/173.77 ! [V_a_2,T_b] : % 173.59/173.77 ( class_Rings_Olinordered__idom(T_b) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_minus__unique,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_a) % 173.59/173.77 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.77 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_ab__left__minus,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Groups_Oab__group__add(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_left__minus,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_eq__neg__iff__add__eq__0,axiom, % 173.59/173.77 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_b) % 173.59/173.77 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) % 173.59/173.77 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_right__minus,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Groups_Ogroup__add(T_a) % 173.59/173.77 => 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) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_nat__0,axiom, % 173.59/173.77 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.59/173.77 % 173.59/173.77 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 173.59/173.77 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 173.59/173.77 % 173.59/173.77 fof(fact_not__square__less__zero,axiom, % 173.59/173.77 ! [V_a,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__ring(T_a) % 173.59/173.77 => ~ 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))) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__less__cancel__right__disj,axiom, % 173.59/173.77 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 173.59/173.77 ( class_Rings_Olinordered__ring__strict(T_b) % 173.59/173.77 => ( 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))) % 173.59/173.77 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.59/173.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) % 173.59/173.77 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.59/173.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__less__cancel__left__disj,axiom, % 173.59/173.77 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 173.59/173.77 ( class_Rings_Olinordered__ring__strict(T_b) % 173.59/173.77 => ( 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))) % 173.59/173.77 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.59/173.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) % 173.59/173.77 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.59/173.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__less__cancel__left__pos,axiom, % 173.59/173.77 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 173.59/173.77 ( class_Rings_Olinordered__ring__strict(T_b) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.59/173.77 => ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__pos__pos,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__pos__neg,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__pos__neg2,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zero__less__mult__pos,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.77 => ( 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))) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_zero__less__mult__pos2,axiom, % 173.59/173.77 ! [V_a,V_b,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.77 => ( 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))) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__less__cancel__left__neg,axiom, % 173.59/173.77 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 173.59/173.77 ( class_Rings_Olinordered__ring__strict(T_b) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.59/173.77 => ( 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))) % 173.59/173.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__neg__pos,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__neg__neg,axiom, % 173.59/173.77 ! [V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__ring__strict(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__strict__right__mono,axiom, % 173.59/173.77 ! [V_c,V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__strict__left__mono,axiom, % 173.59/173.77 ! [V_c,V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_comm__mult__strict__left__mono,axiom, % 173.59/173.77 ! [V_c,V_b,V_a,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__strict__right__mono__neg,axiom, % 173.59/173.77 ! [V_c,V_a,V_b,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__ring__strict(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.77 => 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))) ) ) ) ). % 173.59/173.77 % 173.59/173.77 fof(fact_mult__strict__left__mono__neg,axiom, % 173.59/173.77 ! [V_c,V_a,V_b,T_a] : % 173.59/173.77 ( class_Rings_Olinordered__ring__strict(T_a) % 173.59/173.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_not__one__less__zero,axiom, % 173.59/173.78 ! [T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semidom(T_a) % 173.59/173.78 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zero__less__one,axiom, % 173.59/173.78 ! [T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semidom(T_a) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__scale__eq__noteq,axiom, % 173.59/173.78 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 173.59/173.78 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 173.59/173.78 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.78 => ( ( V_a = V_b % 173.59/173.78 & V_c != V_d ) % 173.59/173.78 => 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)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_sum__squares__eq__zero__iff,axiom, % 173.59/173.78 ! [V_y_2,V_x_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__ring__strict(T_b) % 173.59/173.78 => ( 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) % 173.59/173.78 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 173.59/173.78 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_less__add__one,axiom, % 173.59/173.78 ! [V_a,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semidom(T_a) % 173.59/173.78 => 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)))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zadd__zminus__inverse2,axiom, % 173.59/173.78 ! [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) ). % 173.59/173.78 % 173.59/173.78 fof(fact_negative__eq__positive,axiom, % 173.59/173.78 ! [V_m_2,V_n_2] : % 173.59/173.78 ( 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) % 173.59/173.78 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.78 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_not__int__zless__negative,axiom, % 173.59/173.78 ! [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)))) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zmult__zless__mono2,axiom, % 173.59/173.78 ! [V_k,V_j,V_i] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_int__0__less__1,axiom, % 173.59/173.78 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))) ). % 173.59/173.78 % 173.59/173.78 fof(fact_odd__nonzero,axiom, % 173.59/173.78 ! [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) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zless__add1__eq,axiom, % 173.59/173.78 ! [V_z_2,V_w_2] : % 173.59/173.78 ( 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)))) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 173.59/173.78 | V_w_2 = V_z_2 ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_of__int__0,axiom, % 173.59/173.78 ! [T_a] : % 173.59/173.78 ( class_Rings_Oring__1(T_a) % 173.59/173.78 => 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) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_of__int__0__eq__iff,axiom, % 173.59/173.78 ! [V_z_2,T_b] : % 173.59/173.78 ( class_Int_Oring__char__0(T_b) % 173.59/173.78 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) % 173.59/173.78 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_of__int__eq__0__iff,axiom, % 173.59/173.78 ! [V_z_2,T_b] : % 173.59/173.78 ( class_Int_Oring__char__0(T_b) % 173.59/173.78 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b) % 173.59/173.78 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_of__int__less__iff,axiom, % 173.59/173.78 ! [V_z_2,V_w_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__idom(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_of__int__add,axiom, % 173.59/173.78 ! [V_z,V_w,T_a] : % 173.59/173.78 ( class_Rings_Oring__1(T_a) % 173.59/173.78 => 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)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_of__int__of__nat__eq,axiom, % 173.59/173.78 ! [V_n,T_a] : % 173.59/173.78 ( class_Rings_Oring__1(T_a) % 173.59/173.78 => 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) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__mono__iff,axiom, % 173.59/173.78 ! [V_w_2,V_z_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zless__nat__conj,axiom, % 173.59/173.78 ! [V_z_2,V_w_2] : % 173.59/173.78 ( 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))) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 173.59/173.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zless__nat__eq__int__zless,axiom, % 173.59/173.78 ! [V_z_2,V_m_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 173.59/173.78 <=> 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)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_not__sum__squares__lt__zero,axiom, % 173.59/173.78 ! [V_y,V_x,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__ring(T_a) % 173.59/173.78 => ~ 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_sum__squares__gt__zero__iff,axiom, % 173.59/173.78 ! [V_y_2,V_x_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__ring__strict(T_b) % 173.59/173.78 => ( 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)))) % 173.59/173.78 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.59/173.78 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zero__less__two,axiom, % 173.59/173.78 ! [T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semidom(T_a) % 173.59/173.78 => 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)))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_of__nat__Suc,axiom, % 173.59/173.78 ! [V_m,T_a] : % 173.59/173.78 ( class_Rings_Osemiring__1(T_a) % 173.59/173.78 => 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)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_int__Suc0__eq__1,axiom, % 173.59/173.78 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) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__aux__def,axiom, % 173.59/173.78 ! [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) ). % 173.59/173.78 % 173.59/173.78 fof(fact_negD,axiom, % 173.59/173.78 ! [V_x] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.78 => ? [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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_sgn__if,axiom, % 173.59/173.78 ! [V_x,T_a] : % 173.59/173.78 ( class_Groups_Osgn__if(T_a) % 173.59/173.78 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.78 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 173.59/173.78 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.78 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.59/173.78 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 173.59/173.78 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.59/173.78 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_sgn__neg,axiom, % 173.59/173.78 ! [V_a,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__idom(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_sgn__1__neg,axiom, % 173.59/173.78 ! [V_a_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__idom(T_b) % 173.59/173.78 => ( 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)) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zsgn__def,axiom, % 173.59/173.78 ! [V_i] : % 173.59/173.78 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.78 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.59/173.78 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.78 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 173.59/173.78 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 173.59/173.78 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 173.59/173.78 => 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)) ) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 173.59/173.78 ! [V_z] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.59/173.78 => 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)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__less__iff,axiom, % 173.59/173.78 ! [V_m_2,V_w_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 173.59/173.78 <=> 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_convex__bound__lt,axiom, % 173.59/173.78 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 173.59/173.78 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 173.59/173.78 => 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)) ) ) ) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_sgn__1__pos,axiom, % 173.59/173.78 ! [V_a_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__idom(T_b) % 173.59/173.78 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__refl,axiom, % 173.59/173.78 ! [V_x,T_a] : % 173.59/173.78 ( class_Orderings_Opreorder(T_a) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le0,axiom, % 173.59/173.78 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_negative__zle,axiom, % 173.59/173.78 ! [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))) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__le__mono,axiom, % 173.59/173.78 ! [V_l,V_k,V_j,V_i] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__le__mono2,axiom, % 173.59/173.78 ! [V_k,V_j,V_i] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.59/173.78 => 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__le__mono1,axiom, % 173.59/173.78 ! [V_k,V_j,V_i] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.59/173.78 => 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__mult__assoc,axiom, % 173.59/173.78 ! [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)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__mult__eq__1__iff,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 173.59/173.78 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 173.59/173.78 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__mult__commute,axiom, % 173.59/173.78 ! [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) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__mult__1__right,axiom, % 173.59/173.78 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__1__eq__mult__iff,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 173.59/173.78 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 173.59/173.78 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__mult__1,axiom, % 173.59/173.78 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__cube,axiom, % 173.59/173.78 ! [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)))) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__square,axiom, % 173.59/173.78 ! [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))) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__eq__self__implies__10,axiom, % 173.59/173.78 ! [V_n,V_m] : % 173.59/173.78 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 173.59/173.78 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 173.59/173.78 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Suc__mult__le__cancel1,axiom, % 173.59/173.78 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.78 ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zle__refl,axiom, % 173.59/173.78 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zle__linear,axiom, % 173.59/173.78 ! [V_w,V_z] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 173.59/173.78 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zle__trans,axiom, % 173.59/173.78 ! [V_k,V_j,V_i] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zle__antisym,axiom, % 173.59/173.78 ! [V_w,V_z] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 173.59/173.78 => V_z = V_w ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_sgn__sgn,axiom, % 173.59/173.78 ! [V_a,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__idom(T_a) % 173.59/173.78 => 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) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__fun__def,axiom, % 173.59/173.78 ! [V_g_2,V_f_2,T_b,T_c] : % 173.59/173.78 ( class_Orderings_Oord(T_c) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 173.59/173.78 <=> ! [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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_linorder__linear,axiom, % 173.59/173.78 ! [V_y,V_x,T_a] : % 173.59/173.78 ( class_Orderings_Olinorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.59/173.78 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__eq__iff,axiom, % 173.59/173.78 ! [V_y_2,V_x_2,T_b] : % 173.59/173.78 ( class_Orderings_Oorder(T_b) % 173.59/173.78 => ( V_x_2 = V_y_2 % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.59/173.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__eq__refl,axiom, % 173.59/173.78 ! [V_y,V_x,T_a] : % 173.59/173.78 ( class_Orderings_Opreorder(T_a) % 173.59/173.78 => ( V_x = V_y % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__funD,axiom, % 173.59/173.78 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 173.59/173.78 ( class_Orderings_Oord(T_c) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__antisym__conv,axiom, % 173.59/173.78 ! [V_x_2,V_y_2,T_b] : % 173.59/173.78 ( class_Orderings_Oorder(T_b) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.59/173.78 <=> V_x_2 = V_y_2 ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_ord__eq__le__trans,axiom, % 173.59/173.78 ! [V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Orderings_Oord(T_a) % 173.59/173.78 => ( V_a = V_b % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_xt1_I3_J,axiom, % 173.59/173.78 ! [V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Orderings_Oorder(T_a) % 173.59/173.78 => ( V_a = V_b % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_ord__le__eq__trans,axiom, % 173.59/173.78 ! [V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Orderings_Oord(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => ( V_b = V_c % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_xt1_I4_J,axiom, % 173.59/173.78 ! [V_c,V_a,V_b,T_a] : % 173.59/173.78 ( class_Orderings_Oorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.59/173.78 => ( V_b = V_c % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__antisym,axiom, % 173.59/173.78 ! [V_y,V_x,T_a] : % 173.59/173.78 ( class_Orderings_Oorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.59/173.78 => V_x = V_y ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__trans,axiom, % 173.59/173.78 ! [V_z,V_y,V_x,T_a] : % 173.59/173.78 ( class_Orderings_Opreorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_xt1_I5_J,axiom, % 173.59/173.78 ! [V_x,V_y,T_a] : % 173.59/173.78 ( class_Orderings_Oorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.59/173.78 => V_x = V_y ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_xt1_I6_J,axiom, % 173.59/173.78 ! [V_z,V_x,V_y,T_a] : % 173.59/173.78 ( class_Orderings_Oorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__funE,axiom, % 173.59/173.78 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 173.59/173.78 ( class_Orderings_Oord(T_c) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_linorder__le__cases,axiom, % 173.59/173.78 ! [V_y,V_x,T_a] : % 173.59/173.78 ( class_Orderings_Olinorder(T_a) % 173.59/173.78 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_of__nat__le__iff,axiom, % 173.59/173.78 ! [V_n_2,V_m_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__semidom(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 173.59/173.78 ! [V_y_2,V_x_2] : % 173.59/173.78 ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zle__int,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_of__int__le__iff,axiom, % 173.59/173.78 ! [V_z_2,V_w_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__idom(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_one__le__mult__iff,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( 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))) % 173.59/173.78 <=> ( 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)) % 173.59/173.78 & 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)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__le__cancel1,axiom, % 173.59/173.78 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.78 ( 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))) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__le__cancel2,axiom, % 173.59/173.78 ! [V_n_2,V_k_2,V_m_2] : % 173.59/173.78 ( 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))) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 173.59/173.78 ! [V_y_2,V_x_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_xt1_I8_J,axiom, % 173.59/173.78 ! [V_z,V_x,V_y,T_a] : % 173.59/173.78 ( class_Orderings_Oorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__le__less__trans,axiom, % 173.59/173.78 ! [V_z,V_y,V_x,T_a] : % 173.59/173.78 ( class_Orderings_Opreorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_xt1_I7_J,axiom, % 173.59/173.78 ! [V_z,V_x,V_y,T_a] : % 173.59/173.78 ( class_Orderings_Oorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__less__le__trans,axiom, % 173.59/173.78 ! [V_z,V_y,V_x,T_a] : % 173.59/173.78 ( class_Orderings_Opreorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_xt1_I11_J,axiom, % 173.59/173.78 ! [V_a,V_b,T_a] : % 173.59/173.78 ( class_Orderings_Oorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.59/173.78 => ( V_a != V_b % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__le__neq__trans,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Orderings_Oorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => ( V_a != V_b % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__le__imp__less__or__eq,axiom, % 173.59/173.78 ! [V_y,V_x,T_a] : % 173.59/173.78 ( class_Orderings_Oorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.78 | V_x = V_y ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_linorder__antisym__conv2,axiom, % 173.59/173.78 ! [V_y_2,V_x_2,T_b] : % 173.59/173.78 ( class_Orderings_Olinorder(T_b) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.59/173.78 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 173.59/173.78 <=> V_x_2 = V_y_2 ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__less__imp__le,axiom, % 173.59/173.78 ! [V_y,V_x,T_a] : % 173.59/173.78 ( class_Orderings_Opreorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_leD,axiom, % 173.59/173.78 ! [V_x,V_y,T_a] : % 173.59/173.78 ( class_Orderings_Olinorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.59/173.78 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_xt1_I12_J,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Orderings_Oorder(T_a) % 173.59/173.78 => ( V_a != V_b % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__neq__le__trans,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Orderings_Oorder(T_a) % 173.59/173.78 => ( V_a != V_b % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_linorder__antisym__conv1,axiom, % 173.59/173.78 ! [V_y_2,V_x_2,T_b] : % 173.59/173.78 ( class_Orderings_Olinorder(T_b) % 173.59/173.78 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.59/173.78 <=> V_x_2 = V_y_2 ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_not__leE,axiom, % 173.59/173.78 ! [V_x,V_y,T_a] : % 173.59/173.78 ( class_Orderings_Olinorder(T_a) % 173.59/173.78 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_leI,axiom, % 173.59/173.78 ! [V_y,V_x,T_a] : % 173.59/173.78 ( class_Orderings_Olinorder(T_a) % 173.59/173.78 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__le__less,axiom, % 173.59/173.78 ! [V_y_2,V_x_2,T_b] : % 173.59/173.78 ( class_Orderings_Oorder(T_b) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 173.59/173.78 | V_x_2 = V_y_2 ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_less__le__not__le,axiom, % 173.59/173.78 ! [V_y_2,V_x_2,T_b] : % 173.59/173.78 ( class_Orderings_Opreorder(T_b) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.59/173.78 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_order__less__le,axiom, % 173.59/173.78 ! [V_y_2,V_x_2,T_b] : % 173.59/173.78 ( class_Orderings_Oorder(T_b) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.59/173.78 & V_x_2 != V_y_2 ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_linorder__le__less__linear,axiom, % 173.59/173.78 ! [V_y,V_x,T_a] : % 173.59/173.78 ( class_Orderings_Olinorder(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.59/173.78 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_linorder__not__le,axiom, % 173.59/173.78 ! [V_y_2,V_x_2,T_b] : % 173.59/173.78 ( class_Orderings_Olinorder(T_b) % 173.59/173.78 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_linorder__not__less,axiom, % 173.59/173.78 ! [V_y_2,V_x_2,T_b] : % 173.59/173.78 ( class_Orderings_Olinorder(T_b) % 173.59/173.78 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__le__imp__le__left,axiom, % 173.59/173.78 ! [V_b,V_a,V_c,T_a] : % 173.59/173.78 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.59/173.78 => ( 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))) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__le__imp__le__right,axiom, % 173.59/173.78 ! [V_b,V_c,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.59/173.78 => ( 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))) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__mono,axiom, % 173.59/173.78 ! [V_d,V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__left__mono,axiom, % 173.59/173.78 ! [V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__right__mono,axiom, % 173.59/173.78 ! [V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__le__cancel__left,axiom, % 173.59/173.78 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 173.59/173.78 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__le__cancel__right,axiom, % 173.59/173.78 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 173.59/173.78 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__0,axiom, % 173.59/173.78 ! [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) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__0__right,axiom, % 173.59/173.78 ! [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) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__is__0,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.78 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.78 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__cancel1,axiom, % 173.59/173.78 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.78 ( 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) % 173.59/173.78 <=> ( V_m_2 = V_n_2 % 173.59/173.78 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__cancel2,axiom, % 173.59/173.78 ! [V_n_2,V_k_2,V_m_2] : % 173.59/173.78 ( 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) % 173.59/173.78 <=> ( V_m_2 = V_n_2 % 173.59/173.78 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Suc__mult__cancel1,axiom, % 173.59/173.78 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.78 ( 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) % 173.59/173.78 <=> V_m_2 = V_n_2 ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 173.59/173.78 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__0__eq,axiom, % 173.59/173.78 ! [V_n_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 173.59/173.78 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__minus__iff,axiom, % 173.59/173.78 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.78 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_minus__le__iff,axiom, % 173.59/173.78 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.78 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.78 => ( 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)) % 173.59/173.78 <=> 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)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_neg__le__iff__le,axiom, % 173.59/173.78 ! [V_a_2,V_ba_2,T_b] : % 173.59/173.78 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__imp__neg__le,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__ab__group__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__mult__distrib2,axiom, % 173.59/173.78 ! [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)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__mult__distrib,axiom, % 173.59/173.78 ! [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)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Suc__leD,axiom, % 173.59/173.78 ! [V_n,V_m] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__SucE,axiom, % 173.59/173.78 ! [V_n,V_m] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 173.59/173.78 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.59/173.78 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__SucI,axiom, % 173.59/173.78 ! [V_n,V_m] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Suc__le__mono,axiom, % 173.59/173.78 ! [V_m_2,V_n_2] : % 173.59/173.78 ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__Suc__eq,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.59/173.78 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_not__less__eq__eq,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Suc__n__not__le__n,axiom, % 173.59/173.78 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 173.59/173.78 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))) ). % 173.59/173.78 % 173.59/173.78 fof(fact_termination__basic__simps_I5_J,axiom, % 173.59/173.78 ! [V_y,V_x] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__less__le,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.59/173.78 & V_m_2 != V_n_2 ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__eq__less__or__eq,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.59/173.78 | V_m_2 = V_n_2 ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_less__imp__le__nat,axiom, % 173.59/173.78 ! [V_n,V_m] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__neq__implies__less,axiom, % 173.59/173.78 ! [V_n,V_m] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.59/173.78 => ( V_m != V_n % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_less__or__eq__imp__le,axiom, % 173.59/173.78 ! [V_n,V_m] : % 173.59/173.78 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.78 | V_m = V_n ) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_termination__basic__simps_I4_J,axiom, % 173.59/173.78 ! [V_y,V_z,V_x] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 173.59/173.78 => 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_termination__basic__simps_I3_J,axiom, % 173.59/173.78 ! [V_z,V_y,V_x] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 173.59/173.78 => 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__add2,axiom, % 173.59/173.78 ! [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))) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__add1,axiom, % 173.59/173.78 ! [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))) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__iff__add,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.59/173.78 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__add__left__cancel__le,axiom, % 173.59/173.78 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.78 ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_trans__le__add1,axiom, % 173.59/173.78 ! [V_m,V_j,V_i] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.59/173.78 => 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_trans__le__add2,axiom, % 173.59/173.78 ! [V_m,V_j,V_i] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.59/173.78 => 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__le__mono1,axiom, % 173.59/173.78 ! [V_k,V_j,V_i] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.59/173.78 => 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__le__mono,axiom, % 173.59/173.78 ! [V_l,V_k,V_j,V_i] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__leD2,axiom, % 173.59/173.78 ! [V_n,V_k,V_m] : % 173.59/173.78 ( 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)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__leD1,axiom, % 173.59/173.78 ! [V_n,V_k,V_m] : % 173.59/173.78 ( 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)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__leE,axiom, % 173.59/173.78 ! [V_n,V_k,V_m] : % 173.59/173.78 ( 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)) % 173.59/173.78 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.59/173.78 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zless__le,axiom, % 173.59/173.78 ! [V_w_2,V_z_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 173.59/173.78 & V_z_2 != V_w_2 ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zadd__left__mono,axiom, % 173.59/173.78 ! [V_k,V_j,V_i] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 173.59/173.78 => 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_evaln__nonstrict,axiom, % 173.59/173.78 ! [V_m,V_t,V_n,V_s,V_c] : % 173.59/173.78 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.59/173.78 => c_Natural_Oevaln(V_c,V_s,V_m,V_t) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__le__eq__zle,axiom, % 173.59/173.78 ! [V_z_2,V_w_2] : % 173.59/173.78 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.59/173.78 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 173.59/173.78 ! [V_y,V_x] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.59/173.78 => 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)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__mult__distrib,axiom, % 173.59/173.78 ! [V_z_H,V_z] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.59/173.78 => 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)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_of__int__0__le__iff,axiom, % 173.59/173.78 ! [V_z_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__idom(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_of__int__le__0__iff,axiom, % 173.59/173.78 ! [V_z_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__idom(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_sgn__0__0,axiom, % 173.59/173.78 ! [V_a_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__idom(T_b) % 173.59/173.78 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 173.59/173.78 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_sgn0,axiom, % 173.59/173.78 ! [T_a] : % 173.59/173.78 ( class_Groups_Osgn__if(T_a) % 173.59/173.78 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_sgn__times,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__idom(T_a) % 173.59/173.78 => 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)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__mult__distrib__neg,axiom, % 173.59/173.78 ! [V_z_H,V_z] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.78 => 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 173.59/173.78 ! [V_a_2,T_b] : % 173.59/173.78 ( class_Groups_Olinordered__ab__group__add(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 173.59/173.78 ! [V_a_2,T_b] : % 173.59/173.78 ( class_Groups_Olinordered__ab__group__add(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__nonneg__nonneg,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__nonneg__eq__0__iff,axiom, % 173.59/173.78 ! [V_y_2,V_x_2,T_b] : % 173.59/173.78 ( class_Groups_Oordered__comm__monoid__add(T_b) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2)) % 173.59/173.78 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b) % 173.59/173.78 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 173.59/173.78 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__increasing,axiom, % 173.59/173.78 ! [V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__increasing2,axiom, % 173.59/173.78 ! [V_a,V_b,V_c,T_a] : % 173.59/173.78 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__nonpos__nonpos,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_split__mult__neg__le,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Oordered__cancel__semiring(T_a) % 173.59/173.78 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 173.59/173.78 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_split__mult__pos__le,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Oordered__ring(T_a) % 173.59/173.78 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 173.59/173.78 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__mono,axiom, % 173.59/173.78 ! [V_d,V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Oordered__semiring(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => 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))) ) ) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__mono_H,axiom, % 173.59/173.78 ! [V_d,V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Oordered__semiring(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => 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))) ) ) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__left__mono__neg,axiom, % 173.59/173.78 ! [V_c,V_a,V_b,T_a] : % 173.59/173.78 ( class_Rings_Oordered__ring(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__right__mono__neg,axiom, % 173.59/173.78 ! [V_c,V_a,V_b,T_a] : % 173.59/173.78 ( class_Rings_Oordered__ring(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_comm__mult__left__mono,axiom, % 173.59/173.78 ! [V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Oordered__comm__semiring(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__left__mono,axiom, % 173.59/173.78 ! [V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Oordered__semiring(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__right__mono,axiom, % 173.59/173.78 ! [V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Oordered__semiring(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__nonpos__nonpos,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Oordered__ring(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__nonpos__nonneg,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Oordered__cancel__semiring(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__nonneg__nonpos2,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Oordered__cancel__semiring(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__nonneg__nonpos,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Oordered__cancel__semiring(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__nonneg__nonneg,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Oordered__cancel__semiring(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__le__0__iff,axiom, % 173.59/173.78 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__ring__strict(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 173.59/173.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 173.59/173.78 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.59/173.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zero__le__mult__iff,axiom, % 173.59/173.78 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__ring__strict(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 173.59/173.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) % 173.59/173.78 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.59/173.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zero__le__square,axiom, % 173.59/173.78 ! [V_a,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__ring(T_a) % 173.59/173.78 => 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__le__less__mono,axiom, % 173.59/173.78 ! [V_d,V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__less__le__mono,axiom, % 173.59/173.78 ! [V_d,V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zero__le__one,axiom, % 173.59/173.78 ! [T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semidom(T_a) % 173.59/173.78 => 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_not__one__le__zero,axiom, % 173.59/173.78 ! [T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semidom(T_a) % 173.59/173.78 => ~ 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_neg__0__le__iff__le,axiom, % 173.59/173.78 ! [V_a_2,T_b] : % 173.59/173.78 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__minus__self__iff,axiom, % 173.59/173.78 ! [V_a_2,T_b] : % 173.59/173.78 ( class_Groups_Olinordered__ab__group__add(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_neg__le__0__iff__le,axiom, % 173.59/173.78 ! [V_a_2,T_b] : % 173.59/173.78 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_minus__le__self__iff,axiom, % 173.59/173.78 ! [V_a_2,T_b] : % 173.59/173.78 ( class_Groups_Olinordered__ab__group__add(T_b) % 173.59/173.78 => ( 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)) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__eq__1__iff,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( 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)) % 173.59/173.78 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 173.59/173.78 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_of__nat__0__le__iff,axiom, % 173.59/173.78 ! [V_n,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semidom(T_a) % 173.59/173.78 => 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zero__le__imp__of__nat,axiom, % 173.59/173.78 ! [V_m,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semidom(T_a) % 173.59/173.78 => 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))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_nat__0__less__mult__iff,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( 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))) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 173.59/173.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__less__cancel1,axiom, % 173.59/173.78 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.78 ( 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))) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.59/173.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__less__cancel2,axiom, % 173.59/173.78 ! [V_n_2,V_k_2,V_m_2] : % 173.59/173.78 ( 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))) % 173.59/173.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.59/173.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__less__mono1,axiom, % 173.59/173.78 ! [V_k,V_j,V_i] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__less__mono2,axiom, % 173.59/173.78 ! [V_k,V_j,V_i] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Suc__mult__less__cancel1,axiom, % 173.59/173.78 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.78 ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__Suc__right,axiom, % 173.59/173.78 ! [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)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__Suc,axiom, % 173.59/173.78 ! [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)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_One__nat__def,axiom, % 173.59/173.78 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_less__eq__Suc__le,axiom, % 173.59/173.78 ! [V_m_2,V_n_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_less__Suc__eq__le,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Suc__le__eq,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__imp__less__Suc,axiom, % 173.59/173.78 ! [V_n,V_m] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Suc__leI,axiom, % 173.59/173.78 ! [V_n,V_m] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_le__less__Suc__eq,axiom, % 173.59/173.78 ! [V_n_2,V_m_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 173.59/173.78 <=> V_n_2 = V_m_2 ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Suc__le__lessD,axiom, % 173.59/173.78 ! [V_n,V_m] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Suc__eq__plus1__left,axiom, % 173.59/173.78 ! [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) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Suc__eq__plus1,axiom, % 173.59/173.78 ! [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)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 173.59/173.78 ! [V_y,V_x] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 173.59/173.78 ! [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))) ). % 173.59/173.78 % 173.59/173.78 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 173.59/173.78 ! [V_Pa_2] : % 173.59/173.78 ( ? [B_x] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 173.59/173.78 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 173.59/173.78 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 173.59/173.78 ! [V_Pa_2] : % 173.59/173.78 ( ! [B_x] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 173.59/173.78 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 173.59/173.78 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zero__zle__int,axiom, % 173.59/173.78 ! [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))) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 173.59/173.78 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))) ). % 173.59/173.78 % 173.59/173.78 fof(fact_ex__nat,axiom, % 173.59/173.78 ! [V_Pa_2] : % 173.59/173.78 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 173.59/173.78 <=> ? [B_x] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 173.59/173.78 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_all__nat,axiom, % 173.59/173.78 ! [V_Pa_2] : % 173.59/173.78 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 173.59/173.78 <=> ! [B_x] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 173.59/173.78 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 173.59/173.78 ! [V_y_2,V_x_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 173.59/173.78 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 173.59/173.78 <=> V_x_2 = V_y_2 ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_eq__nat__nat__iff,axiom, % 173.59/173.78 ! [V_z_H_2,V_z_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 173.59/173.78 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 173.59/173.78 <=> V_z_2 = V_z_H_2 ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zadd__zless__mono,axiom, % 173.59/173.78 ! [V_z,V_z_H,V_w,V_w_H] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 173.59/173.78 ! [V_y,V_x] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.59/173.78 => 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))) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 173.59/173.78 ! [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)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zmult__int,axiom, % 173.59/173.78 ! [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)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_int__mult,axiom, % 173.59/173.78 ! [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)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_zle__iff__zadd,axiom, % 173.59/173.78 ! [V_z_2,V_w_2] : % 173.59/173.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 173.59/173.78 <=> ? [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)) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 173.59/173.78 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)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_int__1,axiom, % 173.59/173.78 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) ). % 173.59/173.78 % 173.59/173.78 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 173.59/173.78 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__pos__nonneg,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__nonneg__pos,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__strict__increasing,axiom, % 173.59/173.78 ! [V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__strict__increasing2,axiom, % 173.59/173.78 ! [V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__neg__nonpos,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_add__nonpos__neg,axiom, % 173.59/173.78 ! [V_b,V_a,T_a] : % 173.59/173.78 ( class_Groups_Oordered__comm__monoid__add(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 173.59/173.78 => 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))) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__left__le__imp__le,axiom, % 173.59/173.78 ! [V_b,V_a,V_c,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.78 => ( 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))) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__right__le__imp__le,axiom, % 173.59/173.78 ! [V_b,V_c,V_a,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.78 => ( 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))) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__less__imp__less__left,axiom, % 173.59/173.78 ! [V_b,V_a,V_c,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.78 => ( 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))) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__left__less__imp__less,axiom, % 173.59/173.78 ! [V_b,V_a,V_c,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semiring(T_a) % 173.59/173.78 => ( 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))) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__less__imp__less__right,axiom, % 173.59/173.78 ! [V_b,V_c,V_a,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.78 => ( 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))) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__right__less__imp__less,axiom, % 173.59/173.78 ! [V_b,V_c,V_a,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semiring(T_a) % 173.59/173.78 => ( 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))) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__le__less__imp__less,axiom, % 173.59/173.78 ! [V_d,V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => 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))) ) ) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__less__le__imp__less,axiom, % 173.59/173.78 ! [V_d,V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => 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))) ) ) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__strict__mono_H,axiom, % 173.59/173.78 ! [V_d,V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => 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))) ) ) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__strict__mono,axiom, % 173.59/173.78 ! [V_d,V_c,V_b,V_a,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__semiring__strict(T_a) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.59/173.78 => 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))) ) ) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__le__cancel__left__neg,axiom, % 173.59/173.78 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__ring__strict(T_b) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__le__cancel__left__pos,axiom, % 173.59/173.78 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__ring__strict(T_b) % 173.59/173.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_sum__squares__le__zero__iff,axiom, % 173.59/173.78 ! [V_y_2,V_x_2,T_b] : % 173.59/173.78 ( class_Rings_Olinordered__ring__strict(T_b) % 173.59/173.78 => ( 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))) % 173.59/173.78 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 173.59/173.78 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_sum__squares__ge__zero,axiom, % 173.59/173.78 ! [V_y,V_x,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__ring(T_a) % 173.59/173.78 => 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)))) ) ). % 173.59/173.78 % 173.59/173.78 fof(fact_mult__left__le__one__le,axiom, % 173.59/173.78 ! [V_y,V_x,T_a] : % 173.59/173.78 ( class_Rings_Olinordered__idom(T_a) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 173.59/173.79 => 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)) ) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mult__right__le__one__le,axiom, % 173.59/173.79 ! [V_y,V_x,T_a] : % 173.59/173.79 ( class_Rings_Olinordered__idom(T_a) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 173.59/173.79 => 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)) ) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_sgn__less,axiom, % 173.59/173.79 ! [V_a_2,T_b] : % 173.59/173.79 ( class_Rings_Olinordered__idom(T_b) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_sgn__greater,axiom, % 173.59/173.79 ! [V_a_2,T_b] : % 173.59/173.79 ( class_Rings_Olinordered__idom(T_b) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_one__less__mult,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( 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)) % 173.59/173.79 => ( 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)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_n__less__n__mult__m,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( 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)) % 173.59/173.79 => ( 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)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_n__less__m__mult__n,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( 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)) % 173.59/173.79 => ( 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)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_int__le__0__conv,axiom, % 173.59/173.79 ! [V_n_2] : % 173.59/173.79 ( 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))) % 173.59/173.79 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__0__iff,axiom, % 173.59/173.79 ! [V_i_2] : % 173.59/173.79 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__le__0,axiom, % 173.59/173.79 ! [V_z] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_int__one__le__iff__zero__less,axiom, % 173.59/173.79 ! [V_z_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__0__le,axiom, % 173.59/173.79 ! [V_z] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.59/173.79 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_int__eq__iff,axiom, % 173.59/173.79 ! [V_z_2,V_m_2] : % 173.59/173.79 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 173.59/173.79 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_int__nat__eq,axiom, % 173.59/173.79 ! [V_z] : % 173.59/173.79 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.59/173.79 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 173.59/173.79 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.59/173.79 => 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) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zless__imp__add1__zle,axiom, % 173.59/173.79 ! [V_z,V_w] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_add1__zle__eq,axiom, % 173.59/173.79 ! [V_z_2,V_w_2] : % 173.59/173.79 ( 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)) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zle__add1__eq__le,axiom, % 173.59/173.79 ! [V_z_2,V_w_2] : % 173.59/173.79 ( 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)))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_int__zle__neg,axiom, % 173.59/173.79 ! [V_m_2,V_n_2] : % 173.59/173.79 ( 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)))) % 173.59/173.79 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_negative__zle__0,axiom, % 173.59/173.79 ! [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))) ). % 173.59/173.79 % 173.59/173.79 fof(fact_convex__bound__le,axiom, % 173.59/173.79 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 173.59/173.79 ( class_Rings_Olinordered__semiring__1(T_a) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 173.59/173.79 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 173.59/173.79 => 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)) ) ) ) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__less__eq__zless,axiom, % 173.59/173.79 ! [V_z_2,V_w_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 173.59/173.79 ! [V_y_2,V_x_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__eq__iff,axiom, % 173.59/173.79 ! [V_m_2,V_w_2] : % 173.59/173.79 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 173.59/173.79 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.59/173.79 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 173.59/173.79 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.59/173.79 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__eq__iff2,axiom, % 173.59/173.79 ! [V_w_2,V_m_2] : % 173.59/173.79 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 173.59/173.79 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.59/173.79 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 173.59/173.79 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 173.59/173.79 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__add__distrib,axiom, % 173.59/173.79 ! [V_z_H,V_z] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 173.59/173.79 ! [V_y,V_x] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__imp__0__less,axiom, % 173.59/173.79 ! [V_z] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.59/173.79 => 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))) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_not__zle__0__negative,axiom, % 173.59/173.79 ! [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))))) ). % 173.59/173.79 % 173.59/173.79 fof(fact_of__nat__nat,axiom, % 173.59/173.79 ! [V_z,T_a] : % 173.59/173.79 ( class_Rings_Oring__1(T_a) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.59/173.79 => 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) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_sgn__pos,axiom, % 173.59/173.79 ! [V_a,T_a] : % 173.59/173.79 ( class_Rings_Olinordered__idom(T_a) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.59/173.79 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_self__quotient__aux2,axiom, % 173.59/173.79 ! [V_q,V_r,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.59/173.79 => ( 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)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 173.59/173.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_self__quotient__aux1,axiom, % 173.59/173.79 ! [V_q,V_r,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.59/173.79 => ( 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)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 173.59/173.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_q__pos__lemma,axiom, % 173.59/173.79 ! [V_r_H,V_q_H,V_b_H] : % 173.59/173.79 ( 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))) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 173.59/173.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_q__neg__lemma,axiom, % 173.59/173.79 ! [V_r_H,V_q_H,V_b_H] : % 173.59/173.79 ( 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))) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 173.59/173.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_unique__quotient__lemma,axiom, % 173.59/173.79 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 173.59/173.79 ( 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))) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 173.59/173.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__mono2__lemma,axiom, % 173.59/173.79 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 173.59/173.79 ( 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) % 173.59/173.79 => ( 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))) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 173.59/173.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_unique__quotient__lemma__neg,axiom, % 173.59/173.79 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 173.59/173.79 ( 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))) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 173.59/173.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__mono2__neg__lemma,axiom, % 173.59/173.79 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 173.59/173.79 ( 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) % 173.59/173.79 => ( 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))) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 173.59/173.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__mult__le__cancel1,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__refl,axiom, % 173.59/173.79 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__le__linear,axiom, % 173.59/173.79 ! [V_n,V_m] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_eq__imp__le,axiom, % 173.59/173.79 ! [V_n,V_m] : % 173.59/173.79 ( V_m = V_n % 173.59/173.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__trans,axiom, % 173.59/173.79 ! [V_k,V_j,V_i] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 173.59/173.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__antisym,axiom, % 173.59/173.79 ! [V_n,V_m] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.59/173.79 => V_m = V_n ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_less__fun__def,axiom, % 173.59/173.79 ! [V_g_2,V_f_2,T_b,T_c] : % 173.59/173.79 ( class_Orderings_Oord(T_c) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 173.59/173.79 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 173.59/173.79 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__mult__eq__cancel__disj,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.79 ( 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) % 173.59/173.79 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 | V_m_2 = V_n_2 ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_left__add__mult__distrib,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__mult__eq__cancel1,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.59/173.79 => ( 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) % 173.59/173.79 <=> V_m_2 = V_n_2 ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__mult__less__cancel1,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_transfer__morphism__nat__int,axiom, % 173.59/173.79 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))) ). % 173.59/173.79 % 173.59/173.79 fof(fact_compl__le__compl__iff,axiom, % 173.59/173.79 ! [V_y_2,V_x_2,T_b] : % 173.59/173.79 ( class_Lattices_Oboolean__algebra(T_b) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_compl__mono,axiom, % 173.59/173.79 ! [V_y,V_x,T_a] : % 173.59/173.79 ( class_Lattices_Oboolean__algebra(T_a) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_ex__least__nat__less,axiom, % 173.59/173.79 ! [V_n_2,V_Pa_2] : % 173.59/173.79 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 173.59/173.79 => ( hBOOL(hAPP(V_Pa_2,V_n_2)) % 173.59/173.79 => ? [B_k] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 173.59/173.79 & ! [B_i] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 173.59/173.79 => ~ hBOOL(hAPP(V_Pa_2,B_i)) ) % 173.59/173.79 & 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)))) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_divmod__int__rel__mod__eq,axiom, % 173.59/173.79 ! [V_y,V_q_1,V_b_1,V_a_1] : % 173.59/173.79 ( 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) % 173.59/173.79 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 173.59/173.79 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 173.59/173.79 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmult2__lemma__aux2,axiom, % 173.59/173.79 ! [V_q,V_r,V_b,V_c] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => 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))) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmult2__lemma__aux1,axiom, % 173.59/173.79 ! [V_q,V_r,V_b,V_c] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => 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))) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmult2__lemma__aux4,axiom, % 173.59/173.79 ! [V_q,V_b,V_r,V_c] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 173.59/173.79 => 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))) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mod__trivial,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__0,axiom, % 173.59/173.79 ! [V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__by__0,axiom, % 173.59/173.79 ! [V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__self,axiom, % 173.59/173.79 ! [V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__add__self2,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__add__self1,axiom, % 173.59/173.79 ! [V_a,V_b,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__add__right__eq,axiom, % 173.59/173.79 ! [V_c,V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__add__left__eq,axiom, % 173.59/173.79 ! [V_c,V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__add__eq,axiom, % 173.59/173.79 ! [V_c,V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__simps_I2_J,axiom, % 173.59/173.79 ! [V_c,V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__simps_I1_J,axiom, % 173.59/173.79 ! [V_b,V_c,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__add__cong,axiom, % 173.59/173.79 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 173.59/173.79 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 173.59/173.79 => 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) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__right__eq,axiom, % 173.59/173.79 ! [V_c,V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__left__eq,axiom, % 173.59/173.79 ! [V_c,V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__eq,axiom, % 173.59/173.79 ! [V_c,V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__mult1,axiom, % 173.59/173.79 ! [V_b,V_a,V_c,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__mult2,axiom, % 173.59/173.79 ! [V_b,V_c,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__simps_I4_J,axiom, % 173.59/173.79 ! [V_b,V_c,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__cong,axiom, % 173.59/173.79 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 173.59/173.79 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 173.59/173.79 => 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) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__minus__eq,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Oring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__minus__cong,axiom, % 173.59/173.79 ! [V_a_H,V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Oring__div(T_a) % 173.59/173.79 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 173.59/173.79 => 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) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__zero,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__self,axiom, % 173.59/173.79 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__simps_I3_J,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__zmult1__eq,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zminus__zmod,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__zminus__zminus,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__zminus2,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__self2__is__0,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__self1__is__0,axiom, % 173.59/173.79 ! [V_a,V_b,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__self2,axiom, % 173.59/173.79 ! [V_c,V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__self1,axiom, % 173.59/173.79 ! [V_b,V_c,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__by__1,axiom, % 173.59/173.79 ! [V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__le__nonneg__dividend,axiom, % 173.59/173.79 ! [V_k,V_m] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 173.59/173.79 ! [V_y,V_x] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_neg__mod__bound,axiom, % 173.59/173.79 ! [V_a,V_b] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => 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))) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_pos__mod__bound,axiom, % 173.59/173.79 ! [V_a,V_b] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__eq__0__iff,axiom, % 173.59/173.79 ! [V_d_2,V_m_2] : % 173.59/173.79 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__zminus2__not__zero,axiom, % 173.59/173.79 ! [V_l,V_k] : % 173.59/173.79 ( 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) % 173.59/173.79 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__zminus1__not__zero,axiom, % 173.59/173.79 ! [V_l,V_k] : % 173.59/173.79 ( 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) % 173.59/173.79 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__neg__neg__trivial,axiom, % 173.59/173.79 ! [V_b,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 173.59/173.79 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_neg__mod__conj,axiom, % 173.59/173.79 ! [V_a,V_b] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => ( 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))) % 173.59/173.79 & 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_neg__mod__sign,axiom, % 173.59/173.79 ! [V_a,V_b] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => 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))) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__pos__pos__trivial,axiom, % 173.59/173.79 ! [V_b,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 173.59/173.79 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_pos__mod__conj,axiom, % 173.59/173.79 ! [V_a,V_b] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.59/173.79 => ( 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))) % 173.59/173.79 & 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_pos__mod__sign,axiom, % 173.59/173.79 ! [V_a,V_b] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.59/173.79 => 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))) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mult__left__idem,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mult__idem,axiom, % 173.59/173.79 ! [V_x,T_a] : % 173.59/173.79 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 173.59/173.79 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_times_Oidem,axiom, % 173.59/173.79 ! [V_a,T_a] : % 173.59/173.79 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 173.59/173.79 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_compl__eq__compl__iff,axiom, % 173.59/173.79 ! [V_y_2,V_x_2,T_b] : % 173.59/173.79 ( class_Lattices_Oboolean__algebra(T_b) % 173.59/173.79 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2) % 173.59/173.79 <=> V_x_2 = V_y_2 ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_uminus__apply,axiom, % 173.59/173.79 ! [V_x_2,V_A_2,T_c,T_b] : % 173.59/173.79 ( class_Groups_Ouminus(T_b) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_double__compl,axiom, % 173.59/173.79 ! [V_x,T_a] : % 173.59/173.79 ( class_Lattices_Oboolean__algebra(T_a) % 173.59/173.79 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__pos__neg__trivial,axiom, % 173.59/173.79 ! [V_b,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.59/173.79 => ( 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))) % 173.59/173.79 => 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) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_split__zmod,axiom, % 173.59/173.79 ! [V_k_2,V_n_2,V_Pa_2] : % 173.59/173.79 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 173.59/173.79 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 173.59/173.79 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 173.59/173.79 => ! [B_i,B_j] : % 173.59/173.79 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 173.59/173.79 & 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) ) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) % 173.59/173.79 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => ! [B_i,B_j] : % 173.59/173.79 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 & 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) ) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmult2__lemma__aux3,axiom, % 173.59/173.79 ! [V_q,V_b,V_r,V_c] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 173.59/173.79 => 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))) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_z3mod__def,axiom, % 173.59/173.79 ! [V_k,V_l] : % 173.59/173.79 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 173.59/173.79 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 173.59/173.79 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_split__pos__lemma,axiom, % 173.59/173.79 ! [V_n_2,V_Pa_2,V_k_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> ! [B_i,B_j] : % 173.59/173.79 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 173.59/173.79 & 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) ) % 173.59/173.79 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_split__neg__lemma,axiom, % 173.59/173.79 ! [V_n_2,V_Pa_2,V_k_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> ! [B_i,B_j] : % 173.59/173.79 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 & 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) ) % 173.59/173.79 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__zmult2__eq,axiom, % 173.59/173.79 ! [V_b,V_a,V_c] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 173.59/173.79 ! [V_y,V_x] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_split__zdiv,axiom, % 173.59/173.79 ! [V_k_2,V_n_2,V_Pa_2] : % 173.59/173.79 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 173.59/173.79 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.59/173.79 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 173.59/173.79 => ! [B_i] : % 173.59/173.79 ( ? [B_j] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 173.59/173.79 & 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) ) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) % 173.59/173.79 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => ! [B_i] : % 173.59/173.79 ( ? [B_j] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 & 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) ) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_divmod__int__rel__div__eq,axiom, % 173.59/173.79 ! [V_r_1,V_y,V_b_1,V_a_1] : % 173.59/173.79 ( 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) % 173.59/173.79 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 173.59/173.79 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 173.59/173.79 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_split__div_H,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_Pa_2] : % 173.59/173.79 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 173.59/173.79 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 173.59/173.79 | ? [B_q] : % 173.59/173.79 ( 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)) % 173.59/173.79 & 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)))) % 173.59/173.79 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__add1__eq,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__int,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult2__eq,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mult1__eq,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__le__mono,axiom, % 173.59/173.79 ! [V_k,V_n,V_m] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 => 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))) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__le__dividend,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__zero,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mult2__eq,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__less,axiom, % 173.59/173.79 ! [V_n,V_m] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__less__eq__dividend,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__distrib,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__distrib2,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__zminus2,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__zminus__zminus,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__0,axiom, % 173.59/173.79 ! [V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__by__0,axiom, % 173.59/173.79 ! [V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__by__1,axiom, % 173.59/173.79 ! [V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__div__distrib,axiom, % 173.59/173.79 ! [V_y,V_x] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 173.59/173.79 ! [V_y,V_x] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__1,axiom, % 173.59/173.79 ! [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 ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__less,axiom, % 173.59/173.79 ! [V_n,V_m] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__mult__div__cancel__disj,axiom, % 173.59/173.79 ! [V_n,V_m,V_k] : % 173.59/173.79 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 => 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) ) % 173.59/173.79 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 => 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) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__Suc,axiom, % 173.59/173.79 ! [V_n,V_m] : % 173.59/173.79 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 173.59/173.79 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.59/173.79 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__1,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 173.59/173.79 ! [V_y,V_x] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__less__divisor,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 173.59/173.79 ! [V_a_2,V_ba_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 173.59/173.79 ! [V_a_2,V_ba_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__neg__pos__less0,axiom, % 173.59/173.79 ! [V_b,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__self,axiom, % 173.59/173.79 ! [V_a] : % 173.59/173.79 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__eq__0__iff,axiom, % 173.59/173.79 ! [V_d_2,V_m_2] : % 173.59/173.79 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_DIVISION__BY__ZERO,axiom, % 173.59/173.79 ! [V_a] : % 173.59/173.79 ( 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) % 173.59/173.79 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__zdiv__trivial,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__self3,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__zadd1__eq,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__int,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mult__mult1,axiom, % 173.59/173.79 ! [V_b,V_a,V_c,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.79 => 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) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mult__mult2,axiom, % 173.59/173.79 ! [V_b,V_a,V_c,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.79 => 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) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mult__self1__is__id,axiom, % 173.59/173.79 ! [V_a,V_b,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.79 => 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 ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mult__self2__is__id,axiom, % 173.59/173.79 ! [V_a,V_b,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.79 => 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 ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mult__mult1__if,axiom, % 173.59/173.79 ! [V_b,V_a,V_c,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.79 => 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) ) % 173.59/173.79 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.79 => 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) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__self,axiom, % 173.59/173.79 ! [V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.79 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__div__trivial,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__le__mono2,axiom, % 173.59/173.79 ! [V_k,V_n,V_m] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mult__self__is__m,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.59/173.79 => 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 ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mult__self1__is__m,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.59/173.79 => 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 ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__mult__div__cancel1,axiom, % 173.59/173.79 ! [V_n,V_m,V_k] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__less__dividend,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__eq__0__iff,axiom, % 173.59/173.79 ! [V_k_2,V_i_2] : % 173.59/173.79 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 173.59/173.79 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 173.59/173.79 ! [V_a_2,V_ba_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 173.59/173.79 ! [V_i_2,V_k_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 173.59/173.79 ! [V_ba_2,V_a_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),V_a_2)) % 173.59/173.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__mono2,axiom, % 173.59/173.79 ! [V_b,V_b_H,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 173.59/173.79 => 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))) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__nonneg__neg__le0,axiom, % 173.59/173.79 ! [V_b,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__pos__pos__trivial,axiom, % 173.59/173.79 ! [V_b,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 173.59/173.79 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 173.59/173.79 ! [V_a_2,V_ba_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__nonpos__pos__le0,axiom, % 173.59/173.79 ! [V_b,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__mono2__neg,axiom, % 173.59/173.79 ! [V_b,V_b_H,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 173.59/173.79 => 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))) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__neg__neg__trivial,axiom, % 173.59/173.79 ! [V_b,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 173.59/173.79 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__mono1,axiom, % 173.59/173.79 ! [V_b,V_a_H,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__mono1__neg,axiom, % 173.59/173.79 ! [V_b,V_a_H,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__le__divisor,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_int__div__less__self,axiom, % 173.59/173.79 ! [V_k,V_x] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__zmult2__eq,axiom, % 173.59/173.79 ! [V_b,V_a,V_c] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__mult__self4,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__zmod__equality2,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__zmod__equality,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__zmult1__eq,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__zdiv__equality,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mult__self1,axiom, % 173.59/173.79 ! [V_c,V_a,V_b,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mult__self2,axiom, % 173.59/173.79 ! [V_c,V_a,V_b,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__add__self1,axiom, % 173.59/173.79 ! [V_a,V_b,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__add__self2,axiom, % 173.59/173.79 ! [V_a,V_b,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mod__equality,axiom, % 173.59/173.79 ! [V_c,V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mod__equality2,axiom, % 173.59/173.79 ! [V_c,V_a,V_b,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__div__equality,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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 ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__div__equality2,axiom, % 173.59/173.79 ! [V_a,V_b,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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 ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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 ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_split__div,axiom, % 173.59/173.79 ! [V_k_2,V_n_2,V_Pa_2] : % 173.59/173.79 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 173.59/173.79 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 173.59/173.79 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 => ! [B_i,B_j] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 173.59/173.79 => ( 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) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__lemma,axiom, % 173.59/173.79 ! [V_q,V_b,V_r,V_c] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_split__mod,axiom, % 173.59/173.79 ! [V_k_2,V_n_2,V_Pa_2] : % 173.59/173.79 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 173.59/173.79 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,V_n_2)) ) % 173.59/173.79 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 => ! [B_i,B_j] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 173.59/173.79 => ( 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) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Suc__times__mod__eq,axiom, % 173.59/173.79 ! [V_m,V_k] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__mod__distrib,axiom, % 173.59/173.79 ! [V_y,V_x] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 173.59/173.79 ! [V_y,V_x] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_split__div__lemma,axiom, % 173.59/173.79 ! [V_m_2,V_q_2,V_n_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 173.59/173.79 => ( ( 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)) % 173.59/173.79 & 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)))) ) % 173.59/173.79 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_z3div__def,axiom, % 173.59/173.79 ! [V_k,V_l] : % 173.59/173.79 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 173.59/173.79 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 173.59/173.79 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__zminus1__eq__if,axiom, % 173.59/173.79 ! [V_a,V_b] : % 173.59/173.79 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => 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)) ) % 173.59/173.79 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => 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)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiv__zminus2__eq__if,axiom, % 173.59/173.79 ! [V_a,V_b] : % 173.59/173.79 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => 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)) ) % 173.59/173.79 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => 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)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__div__geq,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__div__decomp,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Osemiring__div(T_a) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 173.59/173.79 ! [V_y,V_x] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_incr__mult__lemma,axiom, % 173.59/173.79 ! [V_k_2,V_Pa_2,V_d_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 173.59/173.79 => ( ! [B_x] : % 173.59/173.79 ( hBOOL(hAPP(V_Pa_2,B_x)) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 173.59/173.79 => ! [B_x] : % 173.59/173.79 ( hBOOL(hAPP(V_Pa_2,B_x)) % 173.59/173.79 => 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)))) ) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_field__le__mult__one__interval,axiom, % 173.59/173.79 ! [V_y,V_x,T_a] : % 173.59/173.79 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.59/173.79 => ( ! [B_z] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 173.59/173.79 => 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)) ) ) % 173.59/173.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__commute,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__eq__diff__eq,axiom, % 173.59/173.79 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.59/173.79 ( class_Groups_Oab__group__add(T_b) % 173.59/173.79 => ( 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) % 173.59/173.79 => ( V_a_2 = V_ba_2 % 173.59/173.79 <=> V_ca_2 = V_d_2 ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_of__int__diff,axiom, % 173.59/173.79 ! [V_z,V_w,T_a] : % 173.59/173.79 ( class_Rings_Oring__1(T_a) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_minus__apply,axiom, % 173.59/173.79 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 173.59/173.79 ( class_Groups_Ominus(T_b) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_of__nat__diff,axiom, % 173.59/173.79 ! [V_m,V_n,T_a] : % 173.59/173.79 ( class_Rings_Oring__1(T_a) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiff__int,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__eq__diff__less__eq,axiom, % 173.59/173.79 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.59/173.79 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.79 => ( 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) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_right__minus__eq,axiom, % 173.59/173.79 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.79 ( class_Groups_Ogroup__add(T_b) % 173.59/173.79 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) % 173.59/173.79 <=> V_a_2 = V_ba_2 ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_eq__iff__diff__eq__0,axiom, % 173.59/173.79 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.79 ( class_Groups_Oab__group__add(T_b) % 173.59/173.79 => ( V_a_2 = V_ba_2 % 173.59/173.79 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__self,axiom, % 173.59/173.79 ! [V_a,T_a] : % 173.59/173.79 ( class_Groups_Ogroup__add(T_a) % 173.59/173.79 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__0__right,axiom, % 173.59/173.79 ! [V_a,T_a] : % 173.59/173.79 ( class_Groups_Ogroup__add(T_a) % 173.59/173.79 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__eq__diff__less,axiom, % 173.59/173.79 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.59/173.79 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.79 => ( 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) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_add__diff__cancel,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Groups_Ogroup__add(T_a) % 173.59/173.79 => 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 ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__add__cancel,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Groups_Ogroup__add(T_a) % 173.59/173.79 => 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 ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_minus__diff__eq,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Groups_Oab__group__add(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__diff__right__eq,axiom, % 173.59/173.79 ! [V_c,V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Oring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__diff__left__eq,axiom, % 173.59/173.79 ! [V_c,V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Oring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__diff__eq,axiom, % 173.59/173.79 ! [V_c,V_b,V_a,T_a] : % 173.59/173.79 ( class_Divides_Oring__div(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__diff__cong,axiom, % 173.59/173.79 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 173.59/173.79 ( class_Divides_Oring__div(T_a) % 173.59/173.79 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 173.59/173.79 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 173.59/173.79 => 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) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__0__eq__0,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_minus__nat_Odiff__0,axiom, % 173.59/173.79 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__self__eq__0,axiom, % 173.59/173.79 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diffs0__imp__equal,axiom, % 173.59/173.79 ! [V_n,V_m] : % 173.59/173.79 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 => V_m = V_n ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Suc__diff__diff,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__Suc__Suc,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_less__imp__diff__less,axiom, % 173.59/173.79 ! [V_n,V_k,V_j] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__less__mono2,axiom, % 173.59/173.79 ! [V_l,V_n,V_m] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__if,axiom, % 173.59/173.79 ! [V_n,V_m] : % 173.59/173.79 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 173.59/173.79 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 => 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) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mod__geq,axiom, % 173.59/173.79 ! [V_n,V_m] : % 173.59/173.79 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__add__inverse2,axiom, % 173.59/173.79 ! [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 ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__add__inverse,axiom, % 173.59/173.79 ! [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 ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__diff__left,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__cancel,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__cancel2,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__diff__iff,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Nat_Odiff__diff__eq,axiom, % 173.59/173.79 ! [V_n,V_m,V_k] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 173.59/173.79 => 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) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_eq__diff__iff,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 173.59/173.79 => ( 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) % 173.59/173.79 <=> V_m_2 = V_n_2 ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__diff__cancel,axiom, % 173.59/173.79 ! [V_n,V_i] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 173.59/173.79 => 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 ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__le__mono,axiom, % 173.59/173.79 ! [V_l,V_n,V_m] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 => 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))) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__le__mono2,axiom, % 173.59/173.79 ! [V_l,V_n,V_m] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 => 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))) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__le__self,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__mod__geq,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiff__zmult__distrib2,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiff__zmult__distrib,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__mult__distrib,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__mult__distrib2,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiff__zmod__right,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiff__zmod__left,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__diff__distrib,axiom, % 173.59/173.79 ! [V_z,V_z_H] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zdiff__int__split,axiom, % 173.59/173.79 ! [V_y_2,V_x_2,V_Pa_2] : % 173.59/173.79 ( 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)))) % 173.59/173.79 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 173.59/173.79 => 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)))) ) % 173.59/173.79 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__iff__diff__le__0,axiom, % 173.59/173.79 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.79 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 173.59/173.79 <=> 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_less__iff__diff__less__0,axiom, % 173.59/173.79 ! [V_ba_2,V_a_2,T_b] : % 173.59/173.79 ( class_Groups_Oordered__ab__group__add(T_b) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 173.59/173.79 <=> 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_eq__add__iff1,axiom, % 173.59/173.79 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 173.59/173.79 ( class_Rings_Oring(T_b) % 173.59/173.79 => ( 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) % 173.59/173.79 <=> 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 ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_eq__add__iff2,axiom, % 173.59/173.79 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 173.59/173.79 ( class_Rings_Oring(T_b) % 173.59/173.79 => ( 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) % 173.59/173.79 <=> 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) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__0,axiom, % 173.59/173.79 ! [V_a,T_a] : % 173.59/173.79 ( class_Groups_Ogroup__add(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__minus__eq__add,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Groups_Ogroup__add(T_a) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_ab__diff__minus,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Groups_Oab__group__add(T_a) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__def,axiom, % 173.59/173.79 ! [V_b,V_a,T_a] : % 173.59/173.79 ( class_Groups_Ogroup__add(T_a) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 173.59/173.79 ! [V_y,V_x,T_a] : % 173.59/173.79 ( class_Rings_Ocomm__ring__1(T_a) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_less__bin__lemma,axiom, % 173.59/173.79 ! [V_l_2,V_k_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 173.59/173.79 <=> 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))) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zero__less__diff,axiom, % 173.59/173.79 ! [V_m_2,V_n_2] : % 173.59/173.79 ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__less,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__less__Suc,axiom, % 173.59/173.79 ! [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))) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__add__0,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__is__0__eq,axiom, % 173.59/173.79 ! [V_n_2,V_m_2] : % 173.59/173.79 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__is__0__eq_H,axiom, % 173.59/173.79 ! [V_n,V_m] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_less__diff__conv,axiom, % 173.59/173.79 ! [V_k_2,V_j_2,V_i_2] : % 173.59/173.79 ( 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))) % 173.59/173.79 <=> 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_add__diff__inverse,axiom, % 173.59/173.79 ! [V_n,V_m] : % 173.59/173.79 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.79 => 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 ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Suc__diff__le,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_less__diff__iff,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_k_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__less__mono,axiom, % 173.59/173.79 ! [V_c,V_b,V_a] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 173.59/173.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 173.59/173.79 => 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__add__assoc2,axiom, % 173.59/173.79 ! [V_i,V_j,V_k] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_add__diff__assoc2,axiom, % 173.59/173.79 ! [V_i,V_j,V_k] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__add__assoc,axiom, % 173.59/173.79 ! [V_i,V_j,V_k] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__imp__diff__is__add,axiom, % 173.59/173.79 ! [V_k_2,V_j_2,V_i_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 173.59/173.79 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 173.59/173.79 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__add__diff__inverse2,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.59/173.79 => 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 ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__diff__conv2,axiom, % 173.59/173.79 ! [V_i_2,V_j_2,V_k_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_add__diff__assoc,axiom, % 173.59/173.79 ! [V_i,V_j,V_k] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__add__diff__inverse,axiom, % 173.59/173.79 ! [V_m,V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.59/173.79 => 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 ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__add__diff,axiom, % 173.59/173.79 ! [V_m,V_n,V_k] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 173.59/173.79 => 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))) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__diff__conv,axiom, % 173.59/173.79 ! [V_i_2,V_k_2,V_j_2] : % 173.59/173.79 ( 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)) % 173.59/173.79 <=> 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))) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__diff__right,axiom, % 173.59/173.79 ! [V_i,V_j,V_k] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__int__def,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__int__def__symmetric,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__Suc__eq__diff__pred,axiom, % 173.59/173.79 ! [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) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__Suc__1,axiom, % 173.59/173.79 ! [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 ). % 173.59/173.79 % 173.59/173.79 fof(fact_div__mod__equality_H,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_mult__div__cancel,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Divides_Omod__div__equality_H,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_tsub__eq,axiom, % 173.59/173.79 ! [V_x,V_y] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 173.59/173.79 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__add__iff1,axiom, % 173.59/173.79 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 173.59/173.79 ( class_Rings_Oordered__ring(T_b) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_le__add__iff2,axiom, % 173.59/173.79 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 173.59/173.79 ( class_Rings_Oordered__ring(T_b) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_less__add__iff1,axiom, % 173.59/173.79 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 173.59/173.79 ( class_Rings_Oordered__ring(T_b) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_less__add__iff2,axiom, % 173.59/173.79 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] : % 173.59/173.79 ( class_Rings_Oordered__ring(T_b) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__Suc__less,axiom, % 173.59/173.79 ! [V_i,V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Suc__pred,axiom, % 173.59/173.79 ! [V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.59/173.79 => 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 ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__diff__split,axiom, % 173.59/173.79 ! [V_ba_2,V_a_2,V_Pa_2] : % 173.59/173.79 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_ba_2))) % 173.59/173.79 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 173.59/173.79 & ! [B_d] : % 173.59/173.79 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d) % 173.59/173.79 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__diff__split__asm,axiom, % 173.59/173.79 ! [V_ba_2,V_a_2,V_Pa_2] : % 173.59/173.79 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_ba_2))) % 173.59/173.79 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 173.59/173.79 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 173.59/173.79 | ? [B_d] : % 173.59/173.79 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d) % 173.59/173.79 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zle__diff1__eq,axiom, % 173.59/173.79 ! [V_z_2,V_w_2] : % 173.59/173.79 ( 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)))) % 173.59/173.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__Suc__diff__eq2,axiom, % 173.59/173.79 ! [V_m,V_j,V_k] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_diff__Suc__diff__eq1,axiom, % 173.59/173.79 ! [V_m,V_j,V_k] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__le__add__iff1,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__diff__add__eq1,axiom, % 173.59/173.79 ! [V_n,V_m,V_u,V_i,V_j] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 173.59/173.79 => 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) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__eq__add__iff1,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 173.59/173.79 => ( 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) % 173.59/173.79 <=> 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 ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__le__add__iff2,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> 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))) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__diff__add__eq2,axiom, % 173.59/173.79 ! [V_n,V_m,V_u,V_j,V_i] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 173.59/173.79 => 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)) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__eq__add__iff2,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 173.59/173.79 => ( 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) % 173.59/173.79 <=> 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) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__zminus2__eq__if,axiom, % 173.59/173.79 ! [V_b,V_a] : % 173.59/173.79 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => 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) ) % 173.59/173.79 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => 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) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__zminus1__eq__if,axiom, % 173.59/173.79 ! [V_b,V_a] : % 173.59/173.79 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => 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) ) % 173.59/173.79 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.59/173.79 => 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmod__zdiv__equality_H,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_zmult__div__cancel,axiom, % 173.59/173.79 ! [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)) ). % 173.59/173.79 % 173.59/173.79 fof(fact_tsub__def,axiom, % 173.59/173.79 ! [V_x,V_y] : % 173.59/173.79 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 173.59/173.79 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 173.59/173.79 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 173.59/173.79 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Suc__diff__1,axiom, % 173.59/173.79 ! [V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.59/173.79 => 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 ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_Suc__pred_H,axiom, % 173.59/173.79 ! [V_n] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.59/173.79 => 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))) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__less__add__iff1,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> 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)) ) ) ). % 173.59/173.79 % 173.59/173.79 fof(fact_nat__less__add__iff2,axiom, % 173.59/173.79 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 173.59/173.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 173.59/173.79 => ( 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))) % 173.59/173.79 <=> 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))) ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_add__eq__if,axiom, % 173.59/173.80 ! [V_n,V_m] : % 173.59/173.80 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.80 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 173.59/173.80 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.80 => 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)) ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_div__if,axiom, % 173.59/173.80 ! [V_m,V_n] : % 173.59/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.59/173.80 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.80 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.59/173.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.80 => 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)) ) ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_div__geq,axiom, % 173.59/173.80 ! [V_m,V_n] : % 173.59/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.59/173.80 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.59/173.80 => 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)) ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_mult__eq__if,axiom, % 173.59/173.80 ! [V_n,V_m] : % 173.59/173.80 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.80 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.59/173.80 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.80 => 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)) ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_int__power__div__base,axiom, % 173.59/173.80 ! [V_k,V_m] : % 173.59/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 173.59/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 173.59/173.80 => 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)))) ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_decr__mult__lemma,axiom, % 173.59/173.80 ! [V_k_2,V_Pa_2,V_d_2] : % 173.59/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 173.59/173.80 => ( ! [B_x] : % 173.59/173.80 ( hBOOL(hAPP(V_Pa_2,B_x)) % 173.59/173.80 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 173.59/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 173.59/173.80 => ! [B_x] : % 173.59/173.80 ( hBOOL(hAPP(V_Pa_2,B_x)) % 173.59/173.80 => 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)))) ) ) ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_incr__lemma,axiom, % 173.59/173.80 ! [V_x,V_z,V_d] : % 173.59/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 173.59/173.80 => 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)))) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_decr__lemma,axiom, % 173.59/173.80 ! [V_z,V_x,V_d] : % 173.59/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 173.59/173.80 => 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)) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_nat__mod__eq__lemma,axiom, % 173.59/173.80 ! [V_y,V_n,V_x] : % 173.59/173.80 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 173.59/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 173.59/173.80 => ? [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)) ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_mod__induct__0,axiom, % 173.59/173.80 ! [V_i_2,V_Pa_2,V_p_2] : % 173.59/173.80 ( ! [B_i] : % 173.59/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 173.59/173.80 => ( hBOOL(hAPP(V_Pa_2,B_i)) % 173.59/173.80 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 173.59/173.80 => ( hBOOL(hAPP(V_Pa_2,V_i_2)) % 173.59/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 173.59/173.80 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_expand__Suc,axiom, % 173.59/173.80 ! [V_v] : % 173.59/173.80 ( 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))) % 173.59/173.80 => 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))) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_nat__gcd_Osimps,axiom, % 173.59/173.80 ! [V_x,V_y] : % 173.59/173.80 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.80 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 173.59/173.80 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.59/173.80 => 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)) ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_of__int__power,axiom, % 173.59/173.80 ! [V_n,V_z,T_a] : % 173.59/173.80 ( class_Rings_Oring__1(T_a) % 173.59/173.80 => 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) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_of__int__number__of__eq,axiom, % 173.59/173.80 ! [V_v,T_a] : % 173.59/173.80 ( class_Int_Onumber__ring(T_a) % 173.59/173.80 => 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) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_abs__idempotent,axiom, % 173.59/173.80 ! [V_a,T_a] : % 173.59/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.59/173.80 => 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) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_eq__number__of,axiom, % 173.59/173.80 ! [V_y_2,V_x_2,T_b] : % 173.59/173.80 ( ( class_Int_Onumber__ring(T_b) % 173.59/173.80 & class_Int_Oring__char__0(T_b) ) % 173.59/173.80 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 173.59/173.80 <=> V_x_2 = V_y_2 ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_number__of__reorient,axiom, % 173.59/173.80 ! [V_x_2,V_w_2,T_b] : % 173.59/173.80 ( class_Int_Onumber(T_b) % 173.59/173.80 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2 % 173.59/173.80 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_zero__le__zpower__abs,axiom, % 173.59/173.80 ! [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))) ). % 173.59/173.80 % 173.59/173.80 fof(fact_abs__le__D1,axiom, % 173.59/173.80 ! [V_b,V_a,T_a] : % 173.59/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.59/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 173.59/173.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_abs__ge__self,axiom, % 173.59/173.80 ! [V_a,T_a] : % 173.59/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.59/173.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_abs__zero,axiom, % 173.59/173.80 ! [T_a] : % 173.59/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.59/173.80 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_abs__eq__0,axiom, % 173.59/173.80 ! [V_a_2,T_b] : % 173.59/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 173.59/173.80 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 173.59/173.80 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_abs__add__abs,axiom, % 173.59/173.80 ! [V_b,V_a,T_a] : % 173.59/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.59/173.80 => 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)) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_abs__mult__self,axiom, % 173.59/173.80 ! [V_a,T_a] : % 173.59/173.80 ( class_Rings_Olinordered__idom(T_a) % 173.59/173.80 => 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) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_abs__mult,axiom, % 173.59/173.80 ! [V_b,V_a,T_a] : % 173.59/173.80 ( class_Rings_Olinordered__idom(T_a) % 173.59/173.80 => 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)) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_abs__minus__commute,axiom, % 173.59/173.80 ! [V_b,V_a,T_a] : % 173.59/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.59/173.80 => 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)) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_abs__one,axiom, % 173.59/173.80 ! [T_a] : % 173.59/173.80 ( class_Rings_Olinordered__idom(T_a) % 173.59/173.80 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_abs__minus__cancel,axiom, % 173.59/173.80 ! [V_a,T_a] : % 173.59/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.59/173.80 => 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) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 173.59/173.80 ! [V_q,V_y,V_x,T_a] : % 173.59/173.80 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.80 => 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)) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_abs__of__nat,axiom, % 173.59/173.80 ! [V_n,T_a] : % 173.59/173.80 ( class_Rings_Olinordered__idom(T_a) % 173.59/173.80 => 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) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_abs__int__eq,axiom, % 173.59/173.80 ! [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) ). % 173.59/173.80 % 173.59/173.80 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 173.59/173.80 ! [V_q,V_p,V_x,T_a] : % 173.59/173.80 ( class_Rings_Ocomm__semiring__1(T_a) % 173.59/173.80 => 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)) ) ). % 173.59/173.80 % 173.59/173.80 fof(fact_zpower__zpower,axiom, % 173.59/173.80 ! [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)) ). % 173.59/173.80 % 173.59/173.80 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 173.82/173.80 ! [V_x,T_a] : % 173.82/173.80 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.80 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zpower__zmod,axiom, % 173.82/173.80 ! [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) ). % 173.82/173.80 % 173.82/173.80 fof(fact_of__nat__number__of__lemma,axiom, % 173.82/173.80 ! [V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => ( ( 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))) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ 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))) % 173.82/173.80 => 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) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of__eq,axiom, % 173.82/173.80 ! [V_k,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__number__of,axiom, % 173.82/173.80 ! [V_x,T_a] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_a) % 173.82/173.80 & class_Rings_Olinordered__idom(T_a) ) % 173.82/173.80 => ( ( 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))) % 173.82/173.80 => 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)) ) % 173.82/173.80 & ( ~ 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))) % 173.82/173.80 => 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) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zero__less__zpower__abs__iff,axiom, % 173.82/173.80 ! [V_n_2,V_x_2] : % 173.82/173.80 ( 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))) % 173.82/173.80 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.80 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__of__nonneg,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.80 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__le__zero__iff,axiom, % 173.82/173.80 ! [V_a_2,T_b] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__ge__zero,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__not__less__zero,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => ~ 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zero__less__abs__iff,axiom, % 173.82/173.80 ! [V_a_2,T_b] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__of__pos,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.80 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__triangle__ineq,axiom, % 173.82/173.80 ! [V_b,V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => 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)))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__mult__less,axiom, % 173.82/173.80 ! [V_d,V_b,V_c,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 173.82/173.80 => 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))) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__triangle__ineq2__sym,axiom, % 173.82/173.80 ! [V_b,V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => 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)))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__triangle__ineq2,axiom, % 173.82/173.80 ! [V_b,V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => 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)))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__triangle__ineq3,axiom, % 173.82/173.80 ! [V_b,V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => 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)))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__ge__minus__self,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__le__iff,axiom, % 173.82/173.80 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 173.82/173.80 => ( 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)) % 173.82/173.80 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 173.82/173.80 & 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)) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__leI,axiom, % 173.82/173.80 ! [V_b,V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 173.82/173.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__le__D2,axiom, % 173.82/173.80 ! [V_b,V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 173.82/173.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__less__iff,axiom, % 173.82/173.80 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.80 ( class_Rings_Olinordered__idom(T_b) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_ba_2)) % 173.82/173.80 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 173.82/173.80 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_le__number__of__eq__not__less,axiom, % 173.82/173.80 ! [V_w_2,V_v_2,T_b] : % 173.82/173.80 ( ( class_Int_Onumber(T_b) % 173.82/173.80 & class_Orderings_Olinorder(T_b) ) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> ~ 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))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_left__distrib__number__of,axiom, % 173.82/173.80 ! [V_v,V_b,V_a,T_b] : % 173.82/173.80 ( ( class_Int_Onumber(T_b) % 173.82/173.80 & class_Rings_Osemiring(T_b) ) % 173.82/173.80 => 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_right__distrib__number__of,axiom, % 173.82/173.80 ! [V_c,V_b,V_v,T_b] : % 173.82/173.80 ( ( class_Int_Onumber(T_b) % 173.82/173.80 & class_Rings_Osemiring(T_b) ) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 173.82/173.80 ! [V_q,V_x,T_a] : % 173.82/173.80 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 173.82/173.80 ! [V_q,V_x,T_a] : % 173.82/173.80 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 173.82/173.80 ! [V_q,V_x,T_a] : % 173.82/173.80 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_left__diff__distrib__number__of,axiom, % 173.82/173.80 ! [V_v,V_b,V_a,T_b] : % 173.82/173.80 ( ( class_Int_Onumber(T_b) % 173.82/173.80 & class_Rings_Oring(T_b) ) % 173.82/173.80 => 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_right__diff__distrib__number__of,axiom, % 173.82/173.80 ! [V_c,V_b,V_v,T_b] : % 173.82/173.80 ( ( class_Int_Onumber(T_b) % 173.82/173.80 & class_Rings_Oring(T_b) ) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_le__number__of,axiom, % 173.82/173.80 ! [V_y_2,V_x_2,T_b] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_b) % 173.82/173.80 & class_Rings_Olinordered__idom(T_b) ) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 173.82/173.80 ! [V_x,T_a] : % 173.82/173.80 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 173.82/173.80 ! [V_q,V_p,V_x,T_a] : % 173.82/173.80 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__number__of,axiom, % 173.82/173.80 ! [V_y_2,V_x_2,T_b] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_b) % 173.82/173.80 & class_Rings_Olinordered__idom(T_b) ) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of__add,axiom, % 173.82/173.80 ! [V_w,V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__number__of__eq,axiom, % 173.82/173.80 ! [V_w,V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__number__of__left,axiom, % 173.82/173.80 ! [V_z,V_w,V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 173.82/173.80 ! [V_n,V_x] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.82/173.80 => 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_mult__number__of__left,axiom, % 173.82/173.80 ! [V_z,V_w,V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_arith__simps_I32_J,axiom, % 173.82/173.80 ! [V_w,V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of__mult,axiom, % 173.82/173.80 ! [V_w,V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__zmult__eq__1,axiom, % 173.82/173.80 ! [V_n,V_m] : % 173.82/173.80 ( 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) % 173.82/173.80 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of__diff,axiom, % 173.82/173.80 ! [V_w,V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zpower__zadd__distrib,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of__minus,axiom, % 173.82/173.80 ! [V_w,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_arith__simps_I30_J,axiom, % 173.82/173.80 ! [V_w,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_mult__sgn__abs,axiom, % 173.82/173.80 ! [V_x,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.80 => 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 ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__sgn,axiom, % 173.82/173.80 ! [V_k,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__mult__pos,axiom, % 173.82/173.80 ! [V_y,V_x,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.82/173.80 => 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)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__eq__mult,axiom, % 173.82/173.80 ! [V_b,V_a,T_a] : % 173.82/173.80 ( class_Rings_Oordered__ring__abs(T_a) % 173.82/173.80 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.80 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 173.82/173.80 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.82/173.80 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 173.82/173.80 => 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)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__diff__triangle__ineq,axiom, % 173.82/173.80 ! [V_d,V_c,V_b,V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => 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))))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__triangle__ineq4,axiom, % 173.82/173.80 ! [V_b,V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => 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)))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__of__nonpos,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.80 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__minus__le__zero,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__if,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Groups_Oabs__if(T_a) % 173.82/173.80 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.80 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.80 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__of__neg,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.80 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zabs__less__one__iff,axiom, % 173.82/173.80 ! [V_z_2] : % 173.82/173.80 ( 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))) % 173.82/173.80 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__number__of__diff1,axiom, % 173.82/173.80 ! [V_c,V_w,V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zabs__def,axiom, % 173.82/173.80 ! [V_i] : % 173.82/173.80 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.80 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.80 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_minus__number__of__mult,axiom, % 173.82/173.80 ! [V_z,V_w,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__abs__mult__distrib,axiom, % 173.82/173.80 ! [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))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_diff__number__of__eq,axiom, % 173.82/173.80 ! [V_w,V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__number__of__diff2,axiom, % 173.82/173.80 ! [V_w,V_c,V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__strict__mono,axiom, % 173.82/173.80 ! [V_n,V_b,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.82/173.80 => 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))) ) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_one__less__power,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.82/173.80 => 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))) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__increasing__iff,axiom, % 173.82/173.80 ! [V_y_2,V_x_2,V_ba_2,T_b] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_b) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_ba_2)) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__le__imp__le__exp,axiom, % 173.82/173.80 ! [V_n,V_m,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.82/173.80 => ( 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))) % 173.82/173.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__decreasing,axiom, % 173.82/173.80 ! [V_a,V_N,V_n,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 173.82/173.80 => 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))) ) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__strict__decreasing,axiom, % 173.82/173.80 ! [V_a,V_N,V_n,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 173.82/173.80 => 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))) ) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__Suc__less__one,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 173.82/173.80 => 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))) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of__is__id,axiom, % 173.82/173.80 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__eq__number__of__int__code,axiom, % 173.82/173.80 ! [V_l_2,V_k_2] : % 173.82/173.80 ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__number__of__int__code,axiom, % 173.82/173.80 ! [V_l_2,V_k_2] : % 173.82/173.80 ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_plus__numeral__code_I9_J,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_times__numeral__code_I5_J,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_minus__numeral__code_I5_J,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__Suc__0,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 173.82/173.80 ! [V_m_2,V_x_2] : % 173.82/173.80 ( 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)) % 173.82/173.80 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.80 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__power__less__imp__less,axiom, % 173.82/173.80 ! [V_n,V_m,V_i] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 173.82/173.80 => ( 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))) % 173.82/173.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__zero__less__power__iff,axiom, % 173.82/173.80 ! [V_n_2,V_x_2] : % 173.82/173.80 ( 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))) % 173.82/173.80 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 173.82/173.80 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_int__number__of__def,axiom, % 173.82/173.80 ! [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) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__one__le__power,axiom, % 173.82/173.80 ! [V_n,V_i] : % 173.82/173.80 ( 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)) % 173.82/173.80 => 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__number__of,axiom, % 173.82/173.80 ! [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) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__number__of__def,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_int__power,axiom, % 173.82/173.80 ! [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) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zpower__int,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_minus__numeral__code_I6_J,axiom, % 173.82/173.80 ! [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))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__eq__if,axiom, % 173.82/173.80 ! [V_p,V_m] : % 173.82/173.80 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.80 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 173.82/173.80 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.80 => 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)))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_int__eq__iff__number__of,axiom, % 173.82/173.80 ! [V_v_2,V_m_2] : % 173.82/173.80 ( 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) % 173.82/173.80 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 173.82/173.80 & 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))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 173.82/173.80 ! [V_n,V_x] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__power__eq,axiom, % 173.82/173.80 ! [V_n,V_z] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_field__power__not__zero,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 173.82/173.80 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.80 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__commutes,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Groups_Omonoid__mult(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__mult__distrib,axiom, % 173.82/173.80 ! [V_n,V_b,V_a,T_a] : % 173.82/173.80 ( class_Groups_Ocomm__monoid__mult(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__one,axiom, % 173.82/173.80 ! [V_n,T_a] : % 173.82/173.80 ( class_Groups_Omonoid__mult(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_of__nat__power,axiom, % 173.82/173.80 ! [V_n,V_m,T_a] : % 173.82/173.80 ( class_Rings_Osemiring__1(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__mult,axiom, % 173.82/173.80 ! [V_n,V_m,V_a,T_a] : % 173.82/173.80 ( class_Groups_Omonoid__mult(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_one__div__nat__number__of,axiom, % 173.82/173.80 ! [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))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__abs,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__one__right,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Groups_Omonoid__mult(T_a) % 173.82/173.80 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zero__le__power,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.80 => 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))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__mono,axiom, % 173.82/173.80 ! [V_n,V_b,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.80 => 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))) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zero__less__power,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.80 => 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))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__eq__0__iff,axiom, % 173.82/173.80 ! [V_n_2,V_a_2,T_b] : % 173.82/173.80 ( ( class_Power_Opower(T_b) % 173.82/173.80 & class_Rings_Omult__zero(T_b) % 173.82/173.80 & class_Rings_Ono__zero__divisors(T_b) % 173.82/173.80 & class_Rings_Ozero__neq__one(T_b) ) % 173.82/173.80 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.80 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.80 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_one__le__power,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.82/173.80 => 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))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__0__Suc,axiom, % 173.82/173.80 ! [V_n,T_a] : % 173.82/173.80 ( ( class_Power_Opower(T_a) % 173.82/173.80 & class_Rings_Osemiring__0(T_a) ) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__inject__exp,axiom, % 173.82/173.80 ! [V_n_2,V_m_2,V_a_2,T_b] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_b) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)) % 173.82/173.80 => ( 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) % 173.82/173.80 <=> V_m_2 = V_n_2 ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__Suc,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Power_Opower(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__Suc2,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Groups_Omonoid__mult(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__0,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Power_Opower(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__add,axiom, % 173.82/173.80 ! [V_n,V_m,V_a,T_a] : % 173.82/173.80 ( class_Groups_Omonoid__mult(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__power__minus,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__less__imp__less__base,axiom, % 173.82/173.80 ! [V_b,V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( 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))) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.82/173.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__le__imp__le__base,axiom, % 173.82/173.80 ! [V_b,V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( 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)))) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.82/173.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__inject__base,axiom, % 173.82/173.80 ! [V_b,V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( 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)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.82/173.80 => V_a = V_b ) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__gt1__lemma,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.82/173.80 => 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)))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__less__power__Suc,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.82/173.80 => 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)))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__0__left,axiom, % 173.82/173.80 ! [V_n,T_a] : % 173.82/173.80 ( ( class_Power_Opower(T_a) % 173.82/173.80 & class_Rings_Osemiring__0(T_a) ) % 173.82/173.80 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.80 => 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) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__gt1,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.82/173.80 => 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)))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__strict__increasing,axiom, % 173.82/173.80 ! [V_a,V_N,V_n,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.82/173.80 => 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))) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__less__imp__less__exp,axiom, % 173.82/173.80 ! [V_n,V_m,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.82/173.80 => ( 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))) % 173.82/173.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__strict__increasing__iff,axiom, % 173.82/173.80 ! [V_y_2,V_x_2,V_ba_2,T_b] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_b) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_ba_2)) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zero__le__power__abs,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.80 => 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__increasing,axiom, % 173.82/173.80 ! [V_a,V_N,V_n,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 173.82/173.80 => 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))) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__minus,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Oring__1(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__Suc__less,axiom, % 173.82/173.80 ! [V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 173.82/173.80 => 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))) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__eq__imp__eq__base,axiom, % 173.82/173.80 ! [V_b,V_n,V_a,T_a] : % 173.82/173.80 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.80 => ( 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) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.82/173.80 => V_a = V_b ) ) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Nitpick_Onat__lcm__def,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Nitpick_Oint__gcd__def,axiom, % 173.82/173.80 ! [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)))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_one__mod__nat__number__of,axiom, % 173.82/173.80 ! [V_v_H] : % 173.82/173.80 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 173.82/173.80 => 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)) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 173.82/173.80 => 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))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__power__power,axiom, % 173.82/173.80 ! [T_b] : % 173.82/173.80 ( class_Power_Opower(T_b) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_div__nat__number__of,axiom, % 173.82/173.80 ! [V_v_H,V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_mod__nat__number__of,axiom, % 173.82/173.80 ! [V_v_H,V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 173.82/173.80 => 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))) ) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Nitpick_Oint__lcm__def,axiom, % 173.82/173.80 ! [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)))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_not__neg__0,axiom, % 173.82/173.80 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_not__neg__int,axiom, % 173.82/173.80 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_not__neg__1,axiom, % 173.82/173.80 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_not__neg__eq__ge__0,axiom, % 173.82/173.80 ! [V_x_2] : % 173.82/173.80 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_neg__def,axiom, % 173.82/173.80 ! [V_Z_2] : % 173.82/173.80 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_neg__nat,axiom, % 173.82/173.80 ! [V_z] : % 173.82/173.80 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 173.82/173.80 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_not__neg__nat,axiom, % 173.82/173.80 ! [V_z] : % 173.82/173.80 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 173.82/173.80 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power_Opower_Opower__0,axiom, % 173.82/173.80 ! [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 ). % 173.82/173.80 % 173.82/173.80 fof(fact_power_Opower_Opower__Suc,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_neg__imp__number__of__eq__0,axiom, % 173.82/173.80 ! [V_v] : % 173.82/173.80 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_neg__zminus__int,axiom, % 173.82/173.80 ! [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))))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_eq__nat__number__of,axiom, % 173.82/173.80 ! [V_v_H_2,V_v_2] : % 173.82/173.80 ( 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) % 173.82/173.80 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 173.82/173.80 => 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))) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 173.82/173.80 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 173.82/173.80 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 173.82/173.80 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__number__of__add__left,axiom, % 173.82/173.80 ! [V_k,V_v_H,V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 173.82/173.80 => 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) ) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_int__nat__number__of,axiom, % 173.82/173.80 ! [V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_of__nat__number__of__eq,axiom, % 173.82/173.80 ! [V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__nat__number__of__number__of,axiom, % 173.82/173.80 ! [V_w,V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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)) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power__nat__number__of,axiom, % 173.82/173.80 ! [V_n,V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Suc__nat__number__of__add,axiom, % 173.82/173.80 ! [V_n,V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Suc__nat__number__of,axiom, % 173.82/173.80 ! [V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 173.82/173.80 => 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)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zmod__minus1,axiom, % 173.82/173.80 ! [V_b] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_div__pos__neg__trivial,axiom, % 173.82/173.80 ! [V_b,V_a] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.82/173.80 => ( 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))) % 173.82/173.80 => 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) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat0__intermed__int__val,axiom, % 173.82/173.80 ! [V_k_2,V_f_2,V_n_2] : % 173.82/173.80 ( ! [B_i] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 173.82/173.80 => 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))) ) % 173.82/173.80 => ( 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)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 173.82/173.80 => ? [B_i] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 173.82/173.80 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_int__val__lemma,axiom, % 173.82/173.80 ! [V_k_2,V_f_2,V_n_2] : % 173.82/173.80 ( ! [B_i] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 173.82/173.80 => 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))) ) % 173.82/173.80 => ( 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)) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 173.82/173.80 => ? [B_i] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 173.82/173.80 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_eq__number__of__eq,axiom, % 173.82/173.80 ! [V_y_2,V_x_2,T_b] : % 173.82/173.80 ( class_Int_Onumber__ring(T_b) % 173.82/173.80 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 173.82/173.80 <=> 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)))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_diff__bin__simps_I2_J,axiom, % 173.82/173.80 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nonzero__number__of__Min,axiom, % 173.82/173.80 ! [T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I24_J,axiom, % 173.82/173.80 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I7_J,axiom, % 173.82/173.80 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_iszero__def,axiom, % 173.82/173.80 ! [V_z_2,T_b] : % 173.82/173.80 ( class_Rings_Osemiring__1(T_b) % 173.82/173.80 => ( c_Int_Oiszero(T_b,V_z_2) % 173.82/173.80 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_iszero__0,axiom, % 173.82/173.80 ! [T_a] : % 173.82/173.80 ( class_Rings_Osemiring__1(T_a) % 173.82/173.80 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_not__iszero__1,axiom, % 173.82/173.80 ! [T_a] : % 173.82/173.80 ( class_Rings_Osemiring__1(T_a) % 173.82/173.80 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_bin__less__0__simps_I2_J,axiom, % 173.82/173.80 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Int_OMin__def,axiom, % 173.82/173.80 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_mult__Min,axiom, % 173.82/173.80 ! [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) ). % 173.82/173.80 % 173.82/173.80 fof(fact_neg__number__of__Min,axiom, % 173.82/173.80 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_mult__minus1__right,axiom, % 173.82/173.80 ! [V_z,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_mult__minus1,axiom, % 173.82/173.80 ! [V_z,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_arith__simps_I31_J,axiom, % 173.82/173.80 ! [T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of__Min,axiom, % 173.82/173.80 ! [T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__minus__one,axiom, % 173.82/173.80 ! [T_a] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_a) % 173.82/173.80 & class_Rings_Olinordered__idom(T_a) ) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zmod__minus1__right,axiom, % 173.82/173.80 ! [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) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zmult__eq__1__iff,axiom, % 173.82/173.80 ! [V_n_2,V_m_2] : % 173.82/173.80 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 173.82/173.80 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 173.82/173.80 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 173.82/173.80 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 173.82/173.80 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 173.82/173.80 ! [V_n,V_m] : % 173.82/173.80 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 173.82/173.80 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 173.82/173.80 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_of__int__m1,axiom, % 173.82/173.80 ! [T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zdiv__minus1__right,axiom, % 173.82/173.80 ! [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) ). % 173.82/173.80 % 173.82/173.80 fof(fact_succ__def,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_abs__power__minus__one,axiom, % 173.82/173.80 ! [V_n,T_a] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_a) % 173.82/173.80 & class_Rings_Olinordered__idom(T_a) ) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_div__eq__minus1,axiom, % 173.82/173.80 ! [V_b] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of__succ,axiom, % 173.82/173.80 ! [V_k,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__1__add__number__of,axiom, % 173.82/173.80 ! [V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.82/173.80 => 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)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__number__of__add__1,axiom, % 173.82/173.80 ! [V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.82/173.80 => 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)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_eq__special_I3_J,axiom, % 173.82/173.80 ! [V_x_2,T_b] : % 173.82/173.80 ( class_Int_Onumber__ring(T_b) % 173.82/173.80 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.80 <=> 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)))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_eq__special_I1_J,axiom, % 173.82/173.80 ! [V_y_2,T_b] : % 173.82/173.80 ( class_Int_Onumber__ring(T_b) % 173.82/173.80 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 173.82/173.80 <=> 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)))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_neg__number__of__pred__iff__0,axiom, % 173.82/173.80 ! [V_v_2] : % 173.82/173.80 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 173.82/173.80 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__number__of__mult__left,axiom, % 173.82/173.80 ! [V_k,V_v_H,V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.82/173.80 => 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) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_mult__nat__number__of,axiom, % 173.82/173.80 ! [V_v_H,V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.82/173.80 => 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)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_pred__Pls,axiom, % 173.82/173.80 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 173.82/173.80 % 173.82/173.80 fof(fact_Pls__def,axiom, % 173.82/173.80 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I19_J,axiom, % 173.82/173.80 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I2_J,axiom, % 173.82/173.80 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__Pls,axiom, % 173.82/173.80 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__Pls__right,axiom, % 173.82/173.80 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 173.82/173.80 % 173.82/173.80 fof(fact_mult__Pls,axiom, % 173.82/173.80 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 173.82/173.80 % 173.82/173.80 fof(fact_diff__bin__simps_I1_J,axiom, % 173.82/173.80 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 173.82/173.80 % 173.82/173.80 fof(fact_minus__Pls,axiom, % 173.82/173.80 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I37_J,axiom, % 173.82/173.80 c_Int_OPls != c_Int_OMin ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I40_J,axiom, % 173.82/173.80 c_Int_OMin != c_Int_OPls ). % 173.82/173.80 % 173.82/173.80 fof(fact_succ__pred,axiom, % 173.82/173.80 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of__Pls,axiom, % 173.82/173.80 ! [T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_semiring__norm_I112_J,axiom, % 173.82/173.80 ! [T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__numeral__0,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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 ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__numeral__0__right,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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 ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_bin__less__0__simps_I1_J,axiom, % 173.82/173.80 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__number__of__Pls,axiom, % 173.82/173.80 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.82/173.80 % 173.82/173.80 fof(fact_semiring__norm_I113_J,axiom, % 173.82/173.80 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zero__is__num__zero,axiom, % 173.82/173.80 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Suc__diff__number__of,axiom, % 173.82/173.80 ! [V_m,V_v] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 173.82/173.80 => 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I20_J,axiom, % 173.82/173.80 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I23_J,axiom, % 173.82/173.80 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I3_J,axiom, % 173.82/173.80 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I6_J,axiom, % 173.82/173.80 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_eq__number__of__Pls__Min,axiom, % 173.82/173.80 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) ). % 173.82/173.80 % 173.82/173.80 fof(fact_not__neg__number__of__Pls,axiom, % 173.82/173.80 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_iszero__Numeral0,axiom, % 173.82/173.80 ! [T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_succ__Min,axiom, % 173.82/173.80 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 173.82/173.80 % 173.82/173.80 fof(fact_le__iff__pred__less,axiom, % 173.82/173.80 ! [V_l_2,V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_pred__def,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__Min__right,axiom, % 173.82/173.80 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__Min,axiom, % 173.82/173.80 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__number__of__diff__1,axiom, % 173.82/173.80 ! [V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 173.82/173.80 => 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)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_eq__0__number__of,axiom, % 173.82/173.80 ! [V_v_2] : % 173.82/173.80 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_eq__number__of__0,axiom, % 173.82/173.80 ! [V_v_2] : % 173.82/173.80 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of2,axiom, % 173.82/173.80 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))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__nat__number__of,axiom, % 173.82/173.80 ! [V_v_H_2,V_v_2] : % 173.82/173.80 ( 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))) % 173.82/173.80 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 173.82/173.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 173.82/173.80 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_le__nat__number__of,axiom, % 173.82/173.80 ! [V_v_H_2,V_v_2] : % 173.82/173.80 ( 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))) % 173.82/173.80 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 173.82/173.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_le__special_I1_J,axiom, % 173.82/173.80 ! [V_y_2,T_b] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_b) % 173.82/173.80 & class_Rings_Olinordered__idom(T_b) ) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_le__special_I3_J,axiom, % 173.82/173.80 ! [V_x_2,T_b] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_b) % 173.82/173.80 & class_Rings_Olinordered__idom(T_b) ) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__special_I3_J,axiom, % 173.82/173.80 ! [V_x_2,T_b] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_b) % 173.82/173.80 & class_Rings_Olinordered__idom(T_b) ) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__special_I1_J,axiom, % 173.82/173.80 ! [V_y_2,T_b] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_b) % 173.82/173.80 & class_Rings_Olinordered__idom(T_b) ) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__0__number__of,axiom, % 173.82/173.80 ! [V_v_2] : % 173.82/173.80 ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__nat__number__of,axiom, % 173.82/173.80 ! [V_v_H,V_v] : % 173.82/173.80 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 173.82/173.80 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 173.82/173.80 => 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) ) % 173.82/173.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 173.82/173.80 => 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)) ) ) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of__pred,axiom, % 173.82/173.80 ! [V_w,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_eq__special_I4_J,axiom, % 173.82/173.80 ! [V_x_2,T_b] : % 173.82/173.80 ( class_Int_Onumber__ring(T_b) % 173.82/173.80 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 173.82/173.80 <=> 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))))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_eq__special_I2_J,axiom, % 173.82/173.80 ! [V_y_2,T_b] : % 173.82/173.80 ( class_Int_Onumber__ring(T_b) % 173.82/173.80 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 173.82/173.80 <=> 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)))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_diff__special_I2_J,axiom, % 173.82/173.80 ! [V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_diff__special_I1_J,axiom, % 173.82/173.80 ! [V_w,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Suc__div__eq__add3__div,axiom, % 173.82/173.80 ! [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) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I51_J,axiom, % 173.82/173.80 ! [V_l_2,V_k_2] : % 173.82/173.80 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 173.82/173.80 <=> V_k_2 = V_l_2 ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I34_J,axiom, % 173.82/173.80 ! [V_l_2,V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__eq__int__code_I16_J,axiom, % 173.82/173.80 ! [V_k2_2,V_k1_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I17_J,axiom, % 173.82/173.80 ! [V_l_2,V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__int__code_I16_J,axiom, % 173.82/173.80 ! [V_k2_2,V_k1_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I39_J,axiom, % 173.82/173.80 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I46_J,axiom, % 173.82/173.80 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 173.82/173.80 % 173.82/173.80 fof(fact_Bit1__Min,axiom, % 173.82/173.80 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I43_J,axiom, % 173.82/173.80 ! [V_l_2] : % 173.82/173.80 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 173.82/173.80 <=> c_Int_OMin = V_l_2 ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I47_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 173.82/173.80 <=> V_k_2 = c_Int_OMin ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_bin__less__0__simps_I4_J,axiom, % 173.82/173.80 ! [V_w_2] : % 173.82/173.80 ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I22_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I12_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Bit1__def,axiom, % 173.82/173.80 ! [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) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I26_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I30_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I9_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I13_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_neg__number__of__Bit1,axiom, % 173.82/173.80 ! [V_w_2] : % 173.82/173.80 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 173.82/173.80 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_minus__Bit1,axiom, % 173.82/173.80 ! [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))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_iszero__number__of__Bit1,axiom, % 173.82/173.80 ! [V_w,T_a] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_a) % 173.82/173.80 & class_Int_Oring__char__0(T_a) ) % 173.82/173.80 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_succ__Pls,axiom, % 173.82/173.80 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of__Bit1,axiom, % 173.82/173.80 ! [V_w,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_mult__numeral__1__right,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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 ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_mult__numeral__1,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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 ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_numeral__1__eq__1,axiom, % 173.82/173.80 ! [T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_semiring__norm_I110_J,axiom, % 173.82/173.80 ! [T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I29_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I5_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_one__is__num__one,axiom, % 173.82/173.80 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Numeral1__eq1__nat,axiom, % 173.82/173.80 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_nat__numeral__1__eq__1,axiom, % 173.82/173.80 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 173.82/173.80 % 173.82/173.80 fof(fact_diff__bin__simps_I4_J,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_minus__Min,axiom, % 173.82/173.80 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 173.82/173.80 % 173.82/173.80 fof(fact_not__iszero__Numeral1,axiom, % 173.82/173.80 ! [T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_numeral__1__eq__Suc__0,axiom, % 173.82/173.80 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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_numeral__3__eq__3,axiom, % 173.82/173.80 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)))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_power3__eq__cube,axiom, % 173.82/173.80 ! [V_a,T_a] : % 173.82/173.80 ( class_Groups_Omonoid__mult(T_a) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 173.82/173.80 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))))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Suc3__eq__add__3,axiom, % 173.82/173.80 ! [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) ). % 173.82/173.80 % 173.82/173.80 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 173.82/173.80 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)))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 173.82/173.80 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)))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_le__special_I4_J,axiom, % 173.82/173.80 ! [V_x_2,T_b] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_b) % 173.82/173.80 & class_Rings_Olinordered__idom(T_b) ) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_le__special_I2_J,axiom, % 173.82/173.80 ! [V_y_2,T_b] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_b) % 173.82/173.80 & class_Rings_Olinordered__idom(T_b) ) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__special_I4_J,axiom, % 173.82/173.80 ! [V_x_2,T_b] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_b) % 173.82/173.80 & class_Rings_Olinordered__idom(T_b) ) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__special_I2_J,axiom, % 173.82/173.80 ! [V_y_2,T_b] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_b) % 173.82/173.80 & class_Rings_Olinordered__idom(T_b) ) % 173.82/173.80 => ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__special_I2_J,axiom, % 173.82/173.80 ! [V_w,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__special_I3_J,axiom, % 173.82/173.80 ! [V_v,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Suc__diff__eq__diff__pred,axiom, % 173.82/173.80 ! [V_m,V_n] : % 173.82/173.80 ( 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)) % 173.82/173.80 => 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)))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_mod__Suc__eq__mod__add3,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Suc__mod__eq__add3__mod,axiom, % 173.82/173.80 ! [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) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_div__Suc__eq__div__add3,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zmod__number__of__Bit1,axiom, % 173.82/173.80 ! [V_v,V_w] : % 173.82/173.80 ( ( 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))) % 173.82/173.80 => 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)) ) % 173.82/173.80 & ( ~ 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))) % 173.82/173.80 => 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)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_neg__zmod__mult__2,axiom, % 173.82/173.80 ! [V_b,V_a] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_pos__zdiv__mult__2,axiom, % 173.82/173.80 ! [V_b,V_a] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_neg__zdiv__mult__2,axiom, % 173.82/173.80 ! [V_b,V_a] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.80 => 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) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_pos__zmod__mult__2,axiom, % 173.82/173.80 ! [V_b,V_a] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.82/173.80 => 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))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_of__nat__double,axiom, % 173.82/173.80 ! [V_x,T_a] : % 173.82/173.80 ( class_Rings_Osemiring__1(T_a) % 173.82/173.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 173.82/173.80 => 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))) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I48_J,axiom, % 173.82/173.80 ! [V_l_2,V_k_2] : % 173.82/173.80 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 173.82/173.80 <=> V_k_2 = V_l_2 ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__eq__int__code_I13_J,axiom, % 173.82/173.80 ! [V_k2_2,V_k1_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I31_J,axiom, % 173.82/173.80 ! [V_l_2,V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__int__code_I13_J,axiom, % 173.82/173.80 ! [V_k2_2,V_k1_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I14_J,axiom, % 173.82/173.80 ! [V_l_2,V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I44_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 173.82/173.80 <=> V_k_2 = c_Int_OPls ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I38_J,axiom, % 173.82/173.80 ! [V_l_2] : % 173.82/173.80 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 173.82/173.80 <=> c_Int_OPls = V_l_2 ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Bit0__Pls,axiom, % 173.82/173.80 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I50_J,axiom, % 173.82/173.80 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I49_J,axiom, % 173.82/173.80 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 173.82/173.80 % 173.82/173.80 fof(fact_Bit0__def,axiom, % 173.82/173.80 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__Bit0__Bit0,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_mult__Bit0,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_diff__bin__simps_I7_J,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_minus__Bit0,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I45_J,axiom, % 173.82/173.80 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I42_J,axiom, % 173.82/173.80 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 173.82/173.80 % 173.82/173.80 fof(fact_bin__less__0__simps_I3_J,axiom, % 173.82/173.80 ! [V_w_2] : % 173.82/173.80 ( 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))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I27_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I21_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__eq__int__code_I14_J,axiom, % 173.82/173.80 ! [V_k2_2,V_k1_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I32_J,axiom, % 173.82/173.80 ! [V_l_2,V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I10_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I4_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__int__code_I15_J,axiom, % 173.82/173.80 ! [V_k2_2,V_k1_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I16_J,axiom, % 173.82/173.80 ! [V_l_2,V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__Bit1__Bit0,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__Bit0__Bit1,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_diff__bin__simps_I3_J,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_diff__bin__simps_I10_J,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_diff__bin__simps_I9_J,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I28_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I8_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_zdiv__number__of__Bit0,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_neg__number__of__Bit0,axiom, % 173.82/173.80 ! [V_w_2] : % 173.82/173.80 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 173.82/173.80 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_pred__Bit1,axiom, % 173.82/173.80 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 173.82/173.80 % 173.82/173.80 fof(fact_pred__Bit0,axiom, % 173.82/173.80 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_pred__Min,axiom, % 173.82/173.80 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 173.82/173.80 % 173.82/173.80 fof(fact_iszero__number__of__Bit0,axiom, % 173.82/173.80 ! [V_w_2,T_b] : % 173.82/173.80 ( ( class_Int_Onumber__ring(T_b) % 173.82/173.80 & class_Int_Oring__char__0(T_b) ) % 173.82/173.80 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2))) % 173.82/173.80 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_succ__Bit0,axiom, % 173.82/173.80 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 173.82/173.80 % 173.82/173.80 fof(fact_succ__Bit1,axiom, % 173.82/173.80 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of__Bit0,axiom, % 173.82/173.80 ! [V_w,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I15_J,axiom, % 173.82/173.80 ! [V_l_2,V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__int__code_I14_J,axiom, % 173.82/173.80 ! [V_k2_2,V_k1_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I33_J,axiom, % 173.82/173.80 ! [V_l_2,V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_less__eq__int__code_I15_J,axiom, % 173.82/173.80 ! [V_k2_2,V_k1_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_mult__Bit1,axiom, % 173.82/173.80 ! [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) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I25_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_rel__simps_I11_J,axiom, % 173.82/173.80 ! [V_k_2] : % 173.82/173.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 173.82/173.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_diff__bin__simps_I6_J,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_diff__bin__simps_I5_J,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_diff__bin__simps_I8_J,axiom, % 173.82/173.80 ! [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)) ). % 173.82/173.80 % 173.82/173.80 fof(fact_add__Bit1__Bit1,axiom, % 173.82/173.80 ! [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))) ). % 173.82/173.80 % 173.82/173.80 fof(fact_double__number__of__Bit0,axiom, % 173.82/173.80 ! [V_w,T_a] : % 173.82/173.80 ( class_Int_Onumber__ring(T_a) % 173.82/173.80 => 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)) ) ). % 173.82/173.80 % 173.82/173.80 fof(fact_number__of1,axiom, % 173.82/173.80 ! [V_n] : % 173.82/173.80 ( 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))) % 173.82/173.80 => ( 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)))) % 173.82/173.81 & 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)))) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_mult__2,axiom, % 173.82/173.81 ! [V_z,T_a] : % 173.82/173.81 ( class_Int_Onumber__ring(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_mult__2__right,axiom, % 173.82/173.81 ! [V_z,T_a] : % 173.82/173.81 ( class_Int_Onumber__ring(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_one__add__one__is__two,axiom, % 173.82/173.81 ! [T_a] : % 173.82/173.81 ( class_Int_Onumber__ring(T_a) % 173.82/173.81 => 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))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_zero__power2,axiom, % 173.82/173.81 ! [T_a] : % 173.82/173.81 ( class_Rings_Osemiring__1(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_zero__eq__power2,axiom, % 173.82/173.81 ! [V_a_2,T_b] : % 173.82/173.81 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 173.82/173.81 => ( 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) % 173.82/173.81 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_numeral__2__eq__2,axiom, % 173.82/173.81 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))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_semiring__norm_I115_J,axiom, % 173.82/173.81 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))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power2__eq__square,axiom, % 173.82/173.81 ! [V_a,T_a] : % 173.82/173.81 ( class_Groups_Omonoid__mult(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 173.82/173.81 ! [V_x,T_a] : % 173.82/173.81 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.81 => 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)))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 173.82/173.81 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))))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_add__2__eq__Suc,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_add__2__eq__Suc_H,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_one__power2,axiom, % 173.82/173.81 ! [T_a] : % 173.82/173.81 ( class_Rings_Osemiring__1(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power2__minus,axiom, % 173.82/173.81 ! [V_a,T_a] : % 173.82/173.81 ( class_Rings_Oring__1(T_a) % 173.82/173.81 => 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)))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nat__mult__2__right,axiom, % 173.82/173.81 ! [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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nat__mult__2,axiom, % 173.82/173.81 ! [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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__even__eq,axiom, % 173.82/173.81 ! [V_n,V_a,T_a] : % 173.82/173.81 ( class_Groups_Omonoid__mult(T_a) % 173.82/173.81 => 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)))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 173.82/173.81 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)))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 173.82/173.81 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)))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power2__abs,axiom, % 173.82/173.81 ! [V_a,T_a] : % 173.82/173.81 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.81 => 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)))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_abs__power2,axiom, % 173.82/173.81 ! [V_a,T_a] : % 173.82/173.81 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.81 => 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)))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nat__1__add__1,axiom, % 173.82/173.81 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))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_mod2__Suc__Suc,axiom, % 173.82/173.81 ! [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)))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_div2__Suc__Suc,axiom, % 173.82/173.81 ! [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))))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_zmod__number__of__Bit0,axiom, % 173.82/173.81 ! [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))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_add__self__div__2,axiom, % 173.82/173.81 ! [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 ). % 173.82/173.81 % 173.82/173.81 fof(fact_zero__le__power2,axiom, % 173.82/173.81 ! [V_a,T_a] : % 173.82/173.81 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.81 => 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)))))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power2__le__imp__le,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.81 => ( 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)))))) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.82/173.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power2__eq__imp__eq,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.81 => ( 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)))) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.82/173.81 => V_x = V_y ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_zero__less__power2,axiom, % 173.82/173.81 ! [V_a_2,T_b] : % 173.82/173.81 ( class_Rings_Olinordered__idom(T_b) % 173.82/173.81 => ( 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)))))) % 173.82/173.81 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power2__less__0,axiom, % 173.82/173.81 ! [V_a,T_a] : % 173.82/173.81 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.81 => ~ 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))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_sum__power2__eq__zero__iff,axiom, % 173.82/173.81 ! [V_y_2,V_x_2,T_b] : % 173.82/173.81 ( class_Rings_Olinordered__idom(T_b) % 173.82/173.81 => ( 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) % 173.82/173.81 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power2__eq__square__number__of,axiom, % 173.82/173.81 ! [V_w,T_b] : % 173.82/173.81 ( ( class_Groups_Omonoid__mult(T_b) % 173.82/173.81 & class_Int_Onumber(T_b) ) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_less__2__cases,axiom, % 173.82/173.81 ! [V_n] : % 173.82/173.81 ( 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))))) % 173.82/173.81 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.81 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nat__2,axiom, % 173.82/173.81 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))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power2__eq__1__iff,axiom, % 173.82/173.81 ! [V_a_2,T_b] : % 173.82/173.81 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 173.82/173.81 => ( 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) % 173.82/173.81 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b) % 173.82/173.81 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 173.82/173.81 ! [V_n,V_x,T_a] : % 173.82/173.81 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__minus__even,axiom, % 173.82/173.81 ! [V_n,V_a,T_a] : % 173.82/173.81 ( class_Rings_Oring__1(T_a) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power2__less__imp__less,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Rings_Olinordered__semidom(T_a) % 173.82/173.81 => ( 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)))))) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.82/173.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_sum__power2__le__zero__iff,axiom, % 173.82/173.81 ! [V_y_2,V_x_2,T_b] : % 173.82/173.81 ( class_Rings_Olinordered__idom(T_b) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_sum__power2__ge__zero,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.81 => 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))))))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_not__sum__power2__lt__zero,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.81 => ~ 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))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_sum__power2__gt__zero__iff,axiom, % 173.82/173.81 ! [V_y_2,V_x_2,T_b] : % 173.82/173.81 ( class_Rings_Olinordered__idom(T_b) % 173.82/173.81 => ( 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))))))) % 173.82/173.81 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power2__sum,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Int_Onumber__ring(T_a) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_zero__le__even__power_H,axiom, % 173.82/173.81 ! [V_n,V_a,T_a] : % 173.82/173.81 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.81 => 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)))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__odd__eq,axiom, % 173.82/173.81 ! [V_n,V_a,T_a] : % 173.82/173.81 ( class_Groups_Omonoid__mult(T_a) % 173.82/173.81 => 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))))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 173.82/173.81 ! [V_n,V_x,T_a] : % 173.82/173.81 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.81 => 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))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__minus1__even,axiom, % 173.82/173.81 ! [V_n,T_a] : % 173.82/173.81 ( class_Rings_Oring__1(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_zdiv__number__of__Bit1,axiom, % 173.82/173.81 ! [V_v,V_w] : % 173.82/173.81 ( ( 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))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_mod2__gr__0,axiom, % 173.82/173.81 ! [V_m_2] : % 173.82/173.81 ( 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)))))) % 173.82/173.81 <=> 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_div__2__gt__zero,axiom, % 173.82/173.81 ! [V_n] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 173.82/173.81 => 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)))))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power2__diff,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Int_Onumber__ring(T_a) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_odd__0__le__power__imp__0__le,axiom, % 173.82/173.81 ! [V_n,V_a,T_a] : % 173.82/173.81 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.81 => ( 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))))) % 173.82/173.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_odd__power__less__zero,axiom, % 173.82/173.81 ! [V_n,V_a,T_a] : % 173.82/173.81 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.81 => 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))) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__minus1__odd,axiom, % 173.82/173.81 ! [V_n,T_a] : % 173.82/173.81 ( class_Rings_Oring__1(T_a) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__m1__even,axiom, % 173.82/173.81 ! [V_n,T_a] : % 173.82/173.81 ( class_Int_Onumber__ring(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__m1__odd,axiom, % 173.82/173.81 ! [V_n,T_a] : % 173.82/173.81 ( class_Int_Onumber__ring(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Suc__n__div__2__gt__zero,axiom, % 173.82/173.81 ! [V_n] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.82/173.81 => 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)))))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_int__of__code,axiom, % 173.82/173.81 ! [V_k] : % 173.82/173.81 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.82/173.81 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.82/173.81 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.82/173.81 => ( ( 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) % 173.82/173.81 => 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)))))) ) % 173.82/173.81 & ( 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) % 173.82/173.81 => 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)) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_one__code__numeral__code,axiom, % 173.82/173.81 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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_half__gt__zero,axiom, % 173.82/173.81 ! [V_r,T_a] : % 173.82/173.81 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.82/173.81 & class_Int_Onumber__ring(T_a) ) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 173.82/173.81 => 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)))))) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_half__gt__zero__iff,axiom, % 173.82/173.81 ! [V_r_2,T_b] : % 173.82/173.81 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 & class_Int_Onumber__ring(T_b) ) % 173.82/173.81 => ( 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)))))) % 173.82/173.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 173.82/173.81 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nat__intermed__int__val,axiom, % 173.82/173.81 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 173.82/173.81 ( ! [B_i] : % 173.82/173.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 173.82/173.81 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 173.82/173.81 => 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))) ) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 173.82/173.81 => ? [B_i] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 173.82/173.81 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 173.82/173.81 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_code__numeral__zero__minus__one,axiom, % 173.82/173.81 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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__zero,axiom, % 173.82/173.81 ! [V_a,T_a] : % 173.82/173.81 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__zero__left,axiom, % 173.82/173.81 ! [V_a,T_a] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_add__divide__distrib,axiom, % 173.82/173.81 ! [V_c,V_b,V_a,T_a] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_a) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_times__divide__times__eq,axiom, % 173.82/173.81 ! [V_w,V_z,V_y,V_x,T_a] : % 173.82/173.81 ( class_Fields_Ofield__inverse__zero(T_a) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_times__divide__eq__right,axiom, % 173.82/173.81 ! [V_c,V_b,V_a,T_a] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_diff__divide__distrib,axiom, % 173.82/173.81 ! [V_c,V_b,V_a,T_a] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_a) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__1,axiom, % 173.82/173.81 ! [V_a,T_a] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_a) % 173.82/173.81 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_minus__divide__divide,axiom, % 173.82/173.81 ! [V_b,V_a,T_a] : % 173.82/173.81 ( class_Fields_Ofield__inverse__zero(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_minus__divide__right,axiom, % 173.82/173.81 ! [V_b,V_a,T_a] : % 173.82/173.81 ( class_Fields_Ofield__inverse__zero(T_a) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_minus__divide__left,axiom, % 173.82/173.81 ! [V_b,V_a,T_a] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__divide,axiom, % 173.82/173.81 ! [V_n,V_b,V_a,T_a] : % 173.82/173.81 ( class_Fields_Ofield__inverse__zero(T_a) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_abs__divide,axiom, % 173.82/173.81 ! [V_b,V_a,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 173.82/173.81 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 173.82/173.81 ! [V_y,V_x] : % 173.82/173.81 ( c_Nat__Transfer_Ois__nat(V_x) % 173.82/173.81 => ( c_Nat__Transfer_Ois__nat(V_y) % 173.82/173.81 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 173.82/173.81 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 173.82/173.81 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 173.82/173.81 ! [V_y,V_x] : % 173.82/173.81 ( c_Nat__Transfer_Ois__nat(V_x) % 173.82/173.81 => ( c_Nat__Transfer_Ois__nat(V_y) % 173.82/173.81 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 173.82/173.81 ! [V_y,V_x] : % 173.82/173.81 ( c_Nat__Transfer_Ois__nat(V_x) % 173.82/173.81 => ( c_Nat__Transfer_Ois__nat(V_y) % 173.82/173.81 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 173.82/173.81 ! [V_y,V_x] : % 173.82/173.81 ( c_Nat__Transfer_Ois__nat(V_x) % 173.82/173.81 => ( c_Nat__Transfer_Ois__nat(V_y) % 173.82/173.81 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 173.82/173.81 ! [V_n,V_x] : % 173.82/173.81 ( c_Nat__Transfer_Ois__nat(V_x) % 173.82/173.81 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_zero__le__divide__iff,axiom, % 173.82/173.81 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 173.82/173.81 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) % 173.82/173.81 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__le__0__iff,axiom, % 173.82/173.81 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 173.82/173.81 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 173.82/173.81 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__right__mono,axiom, % 173.82/173.81 ! [V_c,V_b,V_a,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__right__mono__neg,axiom, % 173.82/173.81 ! [V_c,V_b,V_a,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__strict__right__mono__neg,axiom, % 173.82/173.81 ! [V_c,V_a,V_b,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__strict__right__mono,axiom, % 173.82/173.81 ! [V_c,V_b,V_a,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__neg__neg,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__neg__pos,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__pos__neg,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__pos__pos,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__less__0__iff,axiom, % 173.82/173.81 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 173.82/173.81 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 173.82/173.81 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_zero__less__divide__iff,axiom, % 173.82/173.81 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 173.82/173.81 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) % 173.82/173.81 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_eq__divide__eq,axiom, % 173.82/173.81 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.81 ( class_Fields_Ofield__inverse__zero(T_b) % 173.82/173.81 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) % 173.82/173.81 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_ba_2 ) % 173.82/173.81 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__eq__eq,axiom, % 173.82/173.81 ! [V_a_2,V_ca_2,V_ba_2,T_b] : % 173.82/173.81 ( class_Fields_Ofield__inverse__zero(T_b) % 173.82/173.81 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) = V_a_2 % 173.82/173.81 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) % 173.82/173.81 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_mult__divide__mult__cancel__right,axiom, % 173.82/173.81 ! [V_b,V_a,V_c,T_a] : % 173.82/173.81 ( class_Fields_Ofield__inverse__zero(T_a) % 173.82/173.81 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_mult__divide__mult__cancel__left,axiom, % 173.82/173.81 ! [V_b,V_a,V_c,T_a] : % 173.82/173.81 ( class_Fields_Ofield__inverse__zero(T_a) % 173.82/173.81 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_frac__eq__eq,axiom, % 173.82/173.81 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] : % 173.82/173.81 ( class_Fields_Ofield(T_b) % 173.82/173.81 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => ( 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) % 173.82/173.81 <=> 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) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_eq__divide__imp,axiom, % 173.82/173.81 ! [V_b,V_a,V_c,T_a] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_a) % 173.82/173.81 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 173.82/173.81 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__eq__imp,axiom, % 173.82/173.81 ! [V_a,V_b,V_c,T_a] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_a) % 173.82/173.81 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 173.82/173.81 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nonzero__divide__eq__eq,axiom, % 173.82/173.81 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_b) % 173.82/173.81 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) = V_a_2 % 173.82/173.81 <=> V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nonzero__eq__divide__eq,axiom, % 173.82/173.81 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_b) % 173.82/173.81 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) % 173.82/173.81 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_ba_2 ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_right__inverse__eq,axiom, % 173.82/173.81 ! [V_a_2,V_ba_2,T_b] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_b) % 173.82/173.81 => ( V_ba_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ba_2) = c_Groups_Oone__class_Oone(T_b) % 173.82/173.81 <=> V_a_2 = V_ba_2 ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__self,axiom, % 173.82/173.81 ! [V_a,T_a] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_a) % 173.82/173.81 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__self__if,axiom, % 173.82/173.81 ! [V_a,T_a] : % 173.82/173.81 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 173.82/173.81 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 173.82/173.81 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nonzero__minus__divide__divide,axiom, % 173.82/173.81 ! [V_a,V_b,T_a] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_a) % 173.82/173.81 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nonzero__minus__divide__right,axiom, % 173.82/173.81 ! [V_a,V_b,T_a] : % 173.82/173.81 ( class_Rings_Odivision__ring(T_a) % 173.82/173.81 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nonzero__power__divide,axiom, % 173.82/173.81 ! [V_n,V_a,V_b,T_a] : % 173.82/173.81 ( class_Fields_Ofield(T_a) % 173.82/173.81 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nonzero__abs__divide,axiom, % 173.82/173.81 ! [V_a,V_b,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__one__over,axiom, % 173.82/173.81 ! [V_n,V_a,T_a] : % 173.82/173.81 ( class_Fields_Ofield__inverse__zero(T_a) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 173.82/173.81 ! [V_y,V_x] : % 173.82/173.81 ( c_Nat__Transfer_Ois__nat(V_x) % 173.82/173.81 => ( c_Nat__Transfer_Ois__nat(V_y) % 173.82/173.81 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__nonpos__neg,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__nonpos__pos,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_frac__le,axiom, % 173.82/173.81 ! [V_z,V_w,V_y,V_x,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 173.82/173.81 => 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))) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_frac__less,axiom, % 173.82/173.81 ! [V_z,V_w,V_y,V_x,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 173.82/173.81 => 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))) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_frac__less2,axiom, % 173.82/173.81 ! [V_z,V_w,V_y,V_x,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 173.82/173.81 => 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))) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__nonneg__neg,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__nonneg__pos,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__strict__left__mono__neg,axiom, % 173.82/173.81 ! [V_c,V_b,V_a,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.81 => ( 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))) % 173.82/173.81 => 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))) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__strict__left__mono,axiom, % 173.82/173.81 ! [V_c,V_a,V_b,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.82/173.81 => ( 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))) % 173.82/173.81 => 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))) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_neg__divide__less__eq,axiom, % 173.82/173.81 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_b) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => ( 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)) % 173.82/173.81 <=> 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)) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_neg__less__divide__eq,axiom, % 173.82/173.81 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_b) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_mult__imp__less__div__pos,axiom, % 173.82/173.81 ! [V_x,V_z,V_y,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.82/173.81 => ( 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)) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_mult__imp__div__pos__less,axiom, % 173.82/173.81 ! [V_z,V_x,V_y,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.82/173.81 => ( 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))) % 173.82/173.81 => 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)) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_pos__divide__less__eq,axiom, % 173.82/173.81 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_b) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => ( 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)) % 173.82/173.81 <=> 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_pos__less__divide__eq,axiom, % 173.82/173.81 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_b) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> 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)) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__less__eq,axiom, % 173.82/173.81 ! [V_a_2,V_ca_2,V_ba_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 => ( 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)) % 173.82/173.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_less__divide__eq,axiom, % 173.82/173.81 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_is__nat__def,axiom, % 173.82/173.81 ! [V_x_2] : % 173.82/173.81 ( c_Nat__Transfer_Ois__nat(V_x_2) % 173.82/173.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_add__num__frac,axiom, % 173.82/173.81 ! [V_x,V_z,V_y,T_a] : % 173.82/173.81 ( class_Fields_Ofield__inverse__zero(T_a) % 173.82/173.81 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_add__divide__eq__iff,axiom, % 173.82/173.81 ! [V_y,V_x,V_z,T_a] : % 173.82/173.81 ( class_Fields_Ofield(T_a) % 173.82/173.81 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_add__frac__num,axiom, % 173.82/173.81 ! [V_z,V_x,V_y,T_a] : % 173.82/173.81 ( class_Fields_Ofield__inverse__zero(T_a) % 173.82/173.81 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__add__eq__iff,axiom, % 173.82/173.81 ! [V_y,V_x,V_z,T_a] : % 173.82/173.81 ( class_Fields_Ofield(T_a) % 173.82/173.81 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_add__frac__eq,axiom, % 173.82/173.81 ! [V_w,V_x,V_z,V_y,T_a] : % 173.82/173.81 ( class_Fields_Ofield(T_a) % 173.82/173.81 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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)) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_diff__frac__eq,axiom, % 173.82/173.81 ! [V_w,V_x,V_z,V_y,T_a] : % 173.82/173.81 ( class_Fields_Ofield(T_a) % 173.82/173.81 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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)) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__diff__eq__iff,axiom, % 173.82/173.81 ! [V_y,V_x,V_z,T_a] : % 173.82/173.81 ( class_Fields_Ofield(T_a) % 173.82/173.81 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_diff__divide__eq__iff,axiom, % 173.82/173.81 ! [V_y,V_x,V_z,T_a] : % 173.82/173.81 ( class_Fields_Ofield(T_a) % 173.82/173.81 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => 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) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__eq__eq__number__of1,axiom, % 173.82/173.81 ! [V_a_2,V_w_2,V_ba_2,T_b] : % 173.82/173.81 ( ( class_Fields_Ofield__inverse__zero(T_b) % 173.82/173.81 & class_Int_Onumber(T_b) ) % 173.82/173.81 => ( 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 % 173.82/173.81 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__eq__eq__number__of,axiom, % 173.82/173.81 ! [V_w_2,V_ca_2,V_ba_2,T_b] : % 173.82/173.81 ( ( class_Fields_Ofield__inverse__zero(T_b) % 173.82/173.81 & class_Int_Onumber(T_b) ) % 173.82/173.81 => ( 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) % 173.82/173.81 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => 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) ) % 173.82/173.81 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_eq__divide__eq__number__of,axiom, % 173.82/173.81 ! [V_ca_2,V_ba_2,V_w_2,T_b] : % 173.82/173.81 ( ( class_Fields_Ofield__inverse__zero(T_b) % 173.82/173.81 & class_Int_Onumber(T_b) ) % 173.82/173.81 => ( 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) % 173.82/173.81 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => 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 ) % 173.82/173.81 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_eq__divide__eq__number__of1,axiom, % 173.82/173.81 ! [V_w_2,V_ba_2,V_a_2,T_b] : % 173.82/173.81 ( ( class_Fields_Ofield__inverse__zero(T_b) % 173.82/173.81 & class_Int_Onumber(T_b) ) % 173.82/173.81 => ( 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)) % 173.82/173.81 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => 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 ) % 173.82/173.81 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.81 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_gt__half__sum,axiom, % 173.82/173.81 ! [V_b,V_a,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_less__half__sum,axiom, % 173.82/173.81 ! [V_b,V_a,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 173.82/173.81 => 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))))) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__Numeral0,axiom, % 173.82/173.81 ! [V_x,T_a] : % 173.82/173.81 ( ( class_Fields_Ofield__inverse__zero(T_a) % 173.82/173.81 & class_Int_Onumber__ring(T_a) ) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_abs__div__pos,axiom, % 173.82/173.81 ! [V_x,V_y,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__numeral__1,axiom, % 173.82/173.81 ! [V_a,T_a] : % 173.82/173.81 ( ( class_Fields_Ofield(T_a) % 173.82/173.81 & class_Int_Onumber__ring(T_a) ) % 173.82/173.81 => 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 ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__Numeral1,axiom, % 173.82/173.81 ! [V_x,T_a] : % 173.82/173.81 ( ( class_Fields_Ofield(T_a) % 173.82/173.81 & class_Int_Onumber__ring(T_a) ) % 173.82/173.81 => 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 ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__minus1,axiom, % 173.82/173.81 ! [V_x,T_a] : % 173.82/173.81 ( ( class_Fields_Ofield__inverse__zero(T_a) % 173.82/173.81 & class_Int_Onumber__ring(T_a) ) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_zero__code__numeral__code,axiom, % 173.82/173.81 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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_le__divide__eq,axiom, % 173.82/173.81 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__le__eq,axiom, % 173.82/173.81 ! [V_a_2,V_ca_2,V_ba_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 => ( 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)) % 173.82/173.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_pos__le__divide__eq,axiom, % 173.82/173.81 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_b) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> 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)) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_pos__divide__le__eq,axiom, % 173.82/173.81 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_b) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => ( 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)) % 173.82/173.81 <=> 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_mult__imp__div__pos__le,axiom, % 173.82/173.81 ! [V_z,V_x,V_y,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.82/173.81 => ( 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))) % 173.82/173.81 => 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)) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_mult__imp__le__div__pos,axiom, % 173.82/173.81 ! [V_x,V_z,V_y,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 173.82/173.81 => ( 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)) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_neg__le__divide__eq,axiom, % 173.82/173.81 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_b) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_neg__divide__le__eq,axiom, % 173.82/173.81 ! [V_a_2,V_ba_2,V_ca_2,T_b] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_b) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => ( 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)) % 173.82/173.81 <=> 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)) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__left__mono,axiom, % 173.82/173.81 ! [V_c,V_a,V_b,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 173.82/173.81 => ( 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))) % 173.82/173.81 => 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))) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__left__mono__neg,axiom, % 173.82/173.81 ! [V_c,V_b,V_a,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 173.82/173.81 => ( 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))) % 173.82/173.81 => 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))) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_less__divide__eq__number__of1,axiom, % 173.82/173.81 ! [V_w_2,V_ba_2,V_a_2,T_b] : % 173.82/173.81 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 & class_Int_Onumber(T_b) ) % 173.82/173.81 => ( 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)))) % 173.82/173.81 <=> ( ( 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))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => ( ( 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))) % 173.82/173.81 => 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)))) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_less__divide__eq__number__of,axiom, % 173.82/173.81 ! [V_ca_2,V_ba_2,V_w_2,T_b] : % 173.82/173.81 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 & class_Int_Onumber(T_b) ) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => 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))) ) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__less__eq__number__of,axiom, % 173.82/173.81 ! [V_w_2,V_ca_2,V_ba_2,T_b] : % 173.82/173.81 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 & class_Int_Onumber(T_b) ) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => 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))) ) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__less__eq__number__of1,axiom, % 173.82/173.81 ! [V_a_2,V_w_2,V_ba_2,T_b] : % 173.82/173.81 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 & class_Int_Onumber(T_b) ) % 173.82/173.81 => ( 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)) % 173.82/173.81 <=> ( ( 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))) % 173.82/173.81 => 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)))) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => ( ( 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))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__diff,axiom, % 173.82/173.81 ! [V_m,V_n,V_a,T_a] : % 173.82/173.81 ( class_Fields_Ofield(T_a) % 173.82/173.81 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.82/173.81 => 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)) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_minus1__divide,axiom, % 173.82/173.81 ! [V_x,T_a] : % 173.82/173.81 ( ( class_Fields_Ofield__inverse__zero(T_a) % 173.82/173.81 & class_Int_Onumber__ring(T_a) ) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 173.82/173.81 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__le__eq__number__of1,axiom, % 173.82/173.81 ! [V_a_2,V_w_2,V_ba_2,T_b] : % 173.82/173.81 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 & class_Int_Onumber(T_b) ) % 173.82/173.81 => ( 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)) % 173.82/173.81 <=> ( ( 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))) % 173.82/173.81 => 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)))) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => ( ( 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))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divide__le__eq__number__of,axiom, % 173.82/173.81 ! [V_w_2,V_ca_2,V_ba_2,T_b] : % 173.82/173.81 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 & class_Int_Onumber(T_b) ) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => 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))) ) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_le__divide__eq__number__of,axiom, % 173.82/173.81 ! [V_ca_2,V_ba_2,V_w_2,T_b] : % 173.82/173.81 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 & class_Int_Onumber(T_b) ) % 173.82/173.81 => ( 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))) % 173.82/173.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) % 173.82/173.81 => 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))) ) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_le__divide__eq__number__of1,axiom, % 173.82/173.81 ! [V_w_2,V_ba_2,V_a_2,T_b] : % 173.82/173.81 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 173.82/173.81 & class_Int_Onumber(T_b) ) % 173.82/173.81 => ( 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)))) % 173.82/173.81 <=> ( ( 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))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => ( ( 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))) % 173.82/173.81 => 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)))) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nat__of__aux__code,axiom, % 173.82/173.81 ! [V_n,V_i] : % 173.82/173.81 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.82/173.81 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 173.82/173.81 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_code__numeral_Osize_I1_J,axiom, % 173.82/173.81 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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_code__numeral_Osize_I3_J,axiom, % 173.82/173.81 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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_code__numeral_Osimps_I4_J,axiom, % 173.82/173.81 ! [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 ). % 173.82/173.81 % 173.82/173.81 fof(fact_log_Osimps,axiom, % 173.82/173.81 ! [V_i,V_b] : % 173.82/173.81 ( ( ( 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))) % 173.82/173.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 173.82/173.81 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 173.82/173.81 & ( ~ ( 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))) % 173.82/173.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 173.82/173.81 => 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))) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_field__le__epsilon,axiom, % 173.82/173.81 ! [V_y,V_x,T_a] : % 173.82/173.81 ( class_Fields_Olinordered__field(T_a) % 173.82/173.81 => ( ! [B_e] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 173.82/173.81 => 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))) ) % 173.82/173.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_minus__shift__def,axiom, % 173.82/173.81 ! [V_r,V_l,V_k] : % 173.82/173.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 173.82/173.81 => 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) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 173.82/173.81 => 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) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_inc__shift__def,axiom, % 173.82/173.81 ! [V_k,V_v] : % 173.82/173.81 ( ( V_v = V_k % 173.82/173.81 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 173.82/173.81 & ( V_v != V_k % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_code__numeral_Osize_I4_J,axiom, % 173.82/173.81 ! [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))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_code__numeral_Osize_I2_J,axiom, % 173.82/173.81 ! [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))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_minus__code__numeral__code,axiom, % 173.82/173.81 ! [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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_subtract__code__numeral__def,axiom, % 173.82/173.81 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 173.82/173.81 % 173.82/173.81 fof(fact_code__numeral_Oinject,axiom, % 173.82/173.81 ! [V_code__numeral_H_2,V_code__numeral_2] : % 173.82/173.81 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 173.82/173.81 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_code__numeral_Osimps_I2_J,axiom, % 173.82/173.81 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 173.82/173.81 % 173.82/173.81 fof(fact_code__numeral_Osimps_I3_J,axiom, % 173.82/173.81 ! [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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_code__numeral_Osimps_I5_J,axiom, % 173.82/173.81 ! [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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Suc__code__numeral__minus__one,axiom, % 173.82/173.81 ! [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 ). % 173.82/173.81 % 173.82/173.81 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 173.82/173.81 ! [V_w] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ( 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)))) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ 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)))) % 173.82/173.81 => 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)))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_diff__nat__number__of,axiom, % 173.82/173.81 ! [V_v_2,V_v_H_2] : % 173.82/173.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 173.82/173.81 => 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) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_code__numeral_Orecs_I2_J,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__nat__step,axiom, % 173.82/173.81 ! [V_m,V_n] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_code__numeral__not__eq__zero,axiom, % 173.82/173.81 ! [V_i_2] : % 173.82/173.81 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 173.82/173.81 <=> 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_beyond__def,axiom, % 173.82/173.81 ! [V_l,V_k] : % 173.82/173.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 173.82/173.81 => c_Quickcheck_Obeyond(V_k,V_l) = V_l ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 173.82/173.81 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__nat__zero,axiom, % 173.82/173.81 ! [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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 173.82/173.81 ! [V_m_2,V_n_2] : % 173.82/173.81 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 173.82/173.81 <=> V_n_2 = V_m_2 ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 173.82/173.81 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 173.82/173.81 % 173.82/173.81 fof(fact_fun__Compl__def,axiom, % 173.82/173.81 ! [V_x_2,V_A_2,T_c,T_b] : % 173.82/173.81 ( class_Groups_Ouminus(T_b) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_fun__diff__def,axiom, % 173.82/173.81 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 173.82/173.81 ( class_Groups_Ominus(T_b) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 173.82/173.81 ! [V_n_2,V_m_2] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 173.82/173.81 <=> 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__nat__base,axiom, % 173.82/173.81 ! [V_n,V_m] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_less__eq__Suc__le__raw,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_diff__Suc,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nat__number__of__Bit0,axiom, % 173.82/173.81 ! [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))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_times__code__numeral__code,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__nat__div__mod,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__number__of__even,axiom, % 173.82/173.81 ! [V_w_2,V_z_2,T_b] : % 173.82/173.81 ( class_Int_Onumber__ring(T_b) % 173.82/173.81 => 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))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_zpower__number__of__even,axiom, % 173.82/173.81 ! [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))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_beyond__zero,axiom, % 173.82/173.81 ! [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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__number__of__even__number__of,axiom, % 173.82/173.81 ! [V_w_2,V_v_2,T_b] : % 173.82/173.81 ( class_Int_Onumber__ring(T_b) % 173.82/173.81 => 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))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_diff__nat__eq__if,axiom, % 173.82/173.81 ! [V_z_2,V_z_H_2] : % 173.82/173.81 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 173.82/173.81 => 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) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_negDivAlg__div__mod,axiom, % 173.82/173.81 ! [V_l,V_k] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_negDivAlg__minus1,axiom, % 173.82/173.81 ! [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))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 173.82/173.81 ! [V_n_2,T_b] : % 173.82/173.81 ( class_Rings_Osemiring__1(T_b) % 173.82/173.81 => 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_adjust__eq,axiom, % 173.82/173.81 ! [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))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_zero__code__numeral__def,axiom, % 173.82/173.81 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_one__code__numeral__def,axiom, % 173.82/173.81 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_less__code__numeral__code,axiom, % 173.82/173.81 ! [V_m_2,V_n_2] : % 173.82/173.81 ( 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))) % 173.82/173.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Suc__eq__number__of,axiom, % 173.82/173.81 ! [V_v_2,V_n_2] : % 173.82/173.81 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 173.82/173.81 <=> 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))))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_eq__number__of__Suc,axiom, % 173.82/173.81 ! [V_n_2,V_v_2] : % 173.82/173.81 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 173.82/173.81 <=> 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))))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nat__case__number__of,axiom, % 173.82/173.81 ! [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))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nat__rec__number__of,axiom, % 173.82/173.81 ! [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)))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_plus__code__numeral__code,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_less__eq__code__numeral__code,axiom, % 173.82/173.81 ! [V_m_2,V_n_2] : % 173.82/173.81 ( 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))) % 173.82/173.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nat__number__of__Bit1,axiom, % 173.82/173.81 ! [V_w_2] : % 173.82/173.81 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 173.82/173.81 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 173.82/173.81 => 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)))) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_less__Suc__number__of,axiom, % 173.82/173.81 ! [V_v_2,V_n_2] : % 173.82/173.81 ( 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))) % 173.82/173.81 <=> 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))))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_less__number__of__Suc,axiom, % 173.82/173.81 ! [V_n_2,V_v_2] : % 173.82/173.81 ( 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))) % 173.82/173.81 <=> 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)))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_le__Suc__number__of,axiom, % 173.82/173.81 ! [V_v_2,V_n_2] : % 173.82/173.81 ( 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))) % 173.82/173.81 <=> 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))))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_le__number__of__Suc,axiom, % 173.82/173.81 ! [V_n_2,V_v_2] : % 173.82/173.81 ( 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))) % 173.82/173.81 <=> 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)))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_subtract__code__numeral__code,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nat__case__add__eq__if,axiom, % 173.82/173.81 ! [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)))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nat__rec__add__eq__if,axiom, % 173.82/173.81 ! [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))))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__number__of__odd,axiom, % 173.82/173.81 ! [V_z_2,V_w_2,T_b] : % 173.82/173.81 ( class_Int_Onumber__ring(T_b) % 173.82/173.81 => ( ( 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))) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => 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) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_zpower__number__of__odd,axiom, % 173.82/173.81 ! [V_z_2,V_w_2] : % 173.82/173.81 ( ( 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))) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => 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) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_negDivAlg_Osimps,axiom, % 173.82/173.81 ! [V_b,V_a] : % 173.82/173.81 ( ( ( 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))) % 173.82/173.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ ( 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))) % 173.82/173.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.82/173.81 => 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))) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_power__number__of__odd__number__of,axiom, % 173.82/173.81 ! [V_v_2,V_w_2,T_b] : % 173.82/173.81 ( class_Int_Onumber__ring(T_b) % 173.82/173.81 => ( ( 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))) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => 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) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_code__numeral_Orecs_I1_J,axiom, % 173.82/173.81 ! [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 ). % 173.82/173.81 % 173.82/173.81 fof(fact_negDivAlg__eqn,axiom, % 173.82/173.81 ! [V_a,V_b] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.81 => ( ( 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))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_negDivAlg__eqn__number__of,axiom, % 173.82/173.81 ! [V_w,V_v] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ( 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)))) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ 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)))) % 173.82/173.81 => 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)))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_norm__frac_Osimps,axiom, % 173.82/173.81 ! [V_a_2,V_ba_2] : % 173.82/173.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.81 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.82/173.81 => 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))) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 173.82/173.81 ! [V_w] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ( 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))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => 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)))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_posDivAlg_Osimps,axiom, % 173.82/173.81 ! [V_b,V_a] : % 173.82/173.81 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 173.82/173.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.82/173.81 => 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) ) % 173.82/173.81 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 173.82/173.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.82/173.81 => 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))) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_adjust__def,axiom, % 173.82/173.81 ! [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))))))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_posDivAlg__eqn__number__of,axiom, % 173.82/173.81 ! [V_w,V_v] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ( 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))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ 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))) % 173.82/173.81 => 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)))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_posDivAlg__eqn,axiom, % 173.82/173.81 ! [V_a,V_b] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 173.82/173.81 => 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) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_posDivAlg__0,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_posDivAlg__div__mod,axiom, % 173.82/173.81 ! [V_l,V_k] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_of__int__num,axiom, % 173.82/173.81 ! [V_k_2,T_b] : % 173.82/173.81 ( class_Rings_Oring__1(T_b) % 173.82/173.81 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) ) % 173.82/173.81 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.81 => 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))) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.81 => 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))))) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_MGT__def,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 173.82/173.81 ! [V_a,V_r,V_q,V_c,V_b] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 173.82/173.81 => 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)))) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 173.82/173.81 ! [V_c,V_r,V_q,V_b,V_a] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 173.82/173.81 => 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)))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_negDivAlg_Opsimps,axiom, % 173.82/173.81 ! [V_ba_2,V_a_2] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ( ( 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))) % 173.82/173.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ ( 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))) % 173.82/173.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_accp__downward,axiom, % 173.82/173.81 ! [V_a_2,V_ba_2,V_r_2,T_b] : % 173.82/173.81 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_ba_2)) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 173.82/173.81 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_accp_Oequations,axiom, % 173.82/173.81 ! [V_a_2,V_r_2,T_b] : % 173.82/173.81 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 173.82/173.81 <=> ! [B_x] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 173.82/173.81 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_accp_Osimps,axiom, % 173.82/173.81 ! [V_a_2,V_r_2,T_b] : % 173.82/173.81 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 173.82/173.81 <=> ! [B_x] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 173.82/173.81 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__nat__rel__unique,axiom, % 173.82/173.81 ! [V_qr_H,V_qr,V_n,V_m] : % 173.82/173.81 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 173.82/173.81 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 173.82/173.81 => V_qr = V_qr_H ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_accp__subset,axiom, % 173.82/173.81 ! [V_R2_2,V_R1_2,T_b] : % 173.82/173.81 ( 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)) % 173.82/173.81 => 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))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__nat__eq,axiom, % 173.82/173.81 ! [V_qr,V_n,V_m] : % 173.82/173.81 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 173.82/173.81 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 173.82/173.81 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_mod__eq,axiom, % 173.82/173.81 ! [V_r,V_q,V_n,V_m] : % 173.82/173.81 ( 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))) % 173.82/173.81 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_div__eq,axiom, % 173.82/173.81 ! [V_r,V_q,V_n,V_m] : % 173.82/173.81 ( 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))) % 173.82/173.81 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__nat__rel,axiom, % 173.82/173.81 ! [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)))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__int__mod__div,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__nat__rel__add1__eq,axiom, % 173.82/173.81 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( 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))) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 173.82/173.81 => 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)))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_posDivAlg_Opsimps,axiom, % 173.82/173.81 ! [V_ba_2,V_a_2] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_ba_2)) % 173.82/173.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.82/173.81 => 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) ) % 173.82/173.81 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_ba_2)) % 173.82/173.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.82/173.81 => 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))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_norm__frac_Opsimps,axiom, % 173.82/173.81 ! [V_ba_2,V_a_2] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.81 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 173.82/173.81 => 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))) ) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Nitpick_OFrac__def,axiom, % 173.82/173.81 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)))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__int__def,axiom, % 173.82/173.81 ! [V_b,V_a] : % 173.82/173.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.81 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.81 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => 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))) ) ) ) ) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.81 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 173.82/173.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.81 => 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))) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_negDivAlg_Opinduct,axiom, % 173.82/173.81 ! [V_Pa_2,V_a1_2,V_a0_2] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ! [B_a,B_b] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ( ~ ( 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))) % 173.82/173.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.82/173.81 => 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))) ) % 173.82/173.81 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 173.82/173.81 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_negateSnd__eq,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_splitI,axiom, % 173.82/173.81 ! [T_c,T_b,V_ba_2,V_a_2,V_f_2] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_ba_2)) % 173.82/173.81 => 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))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_prod__caseI,axiom, % 173.82/173.81 ! [T_c,T_b,V_ba_2,V_a_2,V_f1_2] : % 173.82/173.81 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_ba_2)) % 173.82/173.81 => 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))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_posDivAlg_Opinduct,axiom, % 173.82/173.81 ! [V_Pa_2,V_a1_2,V_a0_2] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ! [B_a,B_b] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 173.82/173.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 173.82/173.81 => 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))) ) % 173.82/173.81 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 173.82/173.81 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_nat__gcd_Opsimps,axiom, % 173.82/173.81 ! [V_y_2,V_x_2] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.81 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 173.82/173.81 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.81 => 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)) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__int__pdivmod,axiom, % 173.82/173.81 ! [V_l_2,V_k_2] : % 173.82/173.81 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => 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) ) % 173.82/173.81 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => 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)))) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_apsnd__conv,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_split__paired__All,axiom, % 173.82/173.81 ! [T_c,T_b,V_Pa_2] : % 173.82/173.81 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 173.82/173.81 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Pair__eq,axiom, % 173.82/173.81 ! [V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.81 ( 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) % 173.82/173.81 <=> ( V_a_2 = V_a_H_2 % 173.82/173.81 & V_ba_2 = V_b_H_2 ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_Pair__inject,axiom, % 173.82/173.81 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 173.82/173.81 ( 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) % 173.82/173.81 => ~ ( V_a = V_a_H % 173.82/173.81 => V_b != V_b_H ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_negateSnd__def,axiom, % 173.82/173.81 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_split__weak__cong,axiom, % 173.82/173.81 ! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] : % 173.82/173.81 ( V_p_2 = V_q_2 % 173.82/173.81 => 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) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_prod_Osimps_I2_J,axiom, % 173.82/173.81 ! [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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_split__conv,axiom, % 173.82/173.81 ! [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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_splitD,axiom, % 173.82/173.81 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 173.82/173.81 ( 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))) % 173.82/173.81 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_ba_2)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_split__eta,axiom, % 173.82/173.81 ! [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 ). % 173.82/173.81 % 173.82/173.81 fof(fact_split__twice,axiom, % 173.82/173.81 ! [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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_pdivmod__def,axiom, % 173.82/173.81 ! [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))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_pdivmod__posDivAlg,axiom, % 173.82/173.81 ! [V_k,V_l] : % 173.82/173.81 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => 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)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__int__code,axiom, % 173.82/173.81 ! [V_l_2,V_k_2] : % 173.82/173.81 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => 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)) ) % 173.82/173.81 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => 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) ) % 173.82/173.81 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => 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)))) ) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_div__mod__code__numeral__def,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_zmult2__lemma,axiom, % 173.82/173.81 ! [V_c,V_r,V_q,V_b,V_a] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 173.82/173.81 => 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)))) ) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_mod__pos__neg__1__number__of,axiom, % 173.82/173.81 ! [V_w] : % 173.82/173.81 ( 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))) % 173.82/173.81 => 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))))) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_divmod__int__rel__def,axiom, % 173.82/173.81 ! [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))))))) ). % 173.82/173.81 % 173.82/173.81 fof(fact_norm__frac_Opinduct,axiom, % 173.82/173.81 ! [V_Pa_2,V_a1_2,V_a0_2] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ! [B_a,B_b] : % 173.82/173.81 ( 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))) % 173.82/173.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.81 => 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))) ) % 173.82/173.81 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 173.82/173.81 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_splitD_H,axiom, % 173.82/173.81 ! [V_ca_2,V_ba_2,V_a_2,V_R_2,T_d,T_c,T_b] : % 173.82/173.81 ( 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)) % 173.82/173.81 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_ba_2),V_ca_2)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_snd__conv,axiom, % 173.82/173.81 ! [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 ). % 173.82/173.81 % 173.82/173.81 fof(fact_snd__eqD,axiom, % 173.82/173.81 ! [V_a,V_y,V_x,T_a,T_b] : % 173.82/173.81 ( 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 % 173.82/173.81 => V_y = V_a ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_apsnd__eq__conv,axiom, % 173.82/173.81 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] : % 173.82/173.81 ( 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) % 173.82/173.81 <=> 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)) ) ). % 173.82/173.81 % 173.82/173.81 fof(fact_snd__apsnd,axiom, % 173.82/173.81 ! [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)) ). % 173.82/173.81 % 173.82/173.81 fof(fact_snd__def,axiom, % 173.82/173.81 ! [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) ). % 173.82/173.81 % 173.82/173.81 fof(fact_mod__int__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_divmod__int__rel__0,axiom, % 173.82/173.82 ! [V_b] : % 173.82/173.82 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.82 => 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)))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_self__remainder,axiom, % 173.82/173.82 ! [V_r,V_q,V_a] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.82 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_unique__quotient,axiom, % 173.82/173.82 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( 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))) % 173.82/173.82 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.82 => V_q = V_q_H ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_unique__remainder,axiom, % 173.82/173.82 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( 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))) % 173.82/173.82 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.82 => V_r = V_r_H ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_divmod__int__rel__neg,axiom, % 173.82/173.82 ! [V_qr,V_b,V_a] : % 173.82/173.82 ( 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)) % 173.82/173.82 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_divmod__int__correct,axiom, % 173.82/173.82 ! [V_a,V_b] : % 173.82/173.82 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.82 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_self__quotient,axiom, % 173.82/173.82 ! [V_r,V_q,V_a] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.82 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_divmod__int__rel__mod,axiom, % 173.82/173.82 ! [V_r,V_q,V_b,V_a] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.82 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_divmod__int__rel__div,axiom, % 173.82/173.82 ! [V_r,V_q,V_b,V_a] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.82 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_negDivAlg__correct,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.82 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_mod__neg__pos,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_divmod__int__rel__div__mod,axiom, % 173.82/173.82 ! [V_a,V_b] : % 173.82/173.82 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.82 => 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)))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_posDivAlg__correct,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.82 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_mod__pos__pos,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_mod__pos__pos__1__number__of,axiom, % 173.82/173.82 ! [V_w] : % 173.82/173.82 ( 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))) % 173.82/173.82 => 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_zadd1__lemma,axiom, % 173.82/173.82 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( 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))) % 173.82/173.82 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.82 => 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)))) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_zminus1__lemma,axiom, % 173.82/173.82 ! [V_r_2,V_q_2,V_ba_2,V_a_2] : % 173.82/173.82 ( 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))) % 173.82/173.82 => 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))))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_mod__pos__neg,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.82 => 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)))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_divmod__nat__if,axiom, % 173.82/173.82 ! [V_m_2,V_n_2] : % 173.82/173.82 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.82 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 173.82/173.82 => 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) ) % 173.82/173.82 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.82 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_divmod__int__relI,axiom, % 173.82/173.82 ! [V_r,V_q,V_b,V_a] : % 173.82/173.82 ( 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) % 173.82/173.82 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 173.82/173.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 173.82/173.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 173.82/173.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 173.82/173.82 => 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))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_mod__neg__neg,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.82 => 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)))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_zmult1__lemma,axiom, % 173.82/173.82 ! [V_a,V_r,V_q,V_c,V_b] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.82 => 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)))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_equalityI,axiom, % 173.82/173.82 ! [V_B_2,V_A_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.82 => V_A_2 = V_B_2 ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__pos__neg__1__number__of,axiom, % 173.82/173.82 ! [V_w] : % 173.82/173.82 ( 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))) % 173.82/173.82 => 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))))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_nat__gcd_Opinduct,axiom, % 173.82/173.82 ! [V_Pa_2,V_a1_2,V_a0_2] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( ! [B_x,B_y] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.82 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 173.82/173.82 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) ) % 173.82/173.82 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__neg__neg,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.82 => 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)))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__number__of__Suc,axiom, % 173.82/173.82 ! [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)))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__0L,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__0R,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__Suc__Suc,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__le__iff__disj,axiom, % 173.82/173.82 ! [V_z_2,V_y_2,V_x_2,T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => ( 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)) % 173.82/173.82 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 173.82/173.82 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf__le1,axiom, % 173.82/173.82 ! [V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf__le2,axiom, % 173.82/173.82 ! [V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Ole__iff__inf,axiom, % 173.82/173.82 ! [V_y_2,V_x_2,T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.82/173.82 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Ole__inf__iff,axiom, % 173.82/173.82 ! [V_z_2,V_y_2,V_x_2,T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => ( 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))) % 173.82/173.82 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.82/173.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Ole__infI1,axiom, % 173.82/173.82 ! [V_b,V_x,V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Ole__infI2,axiom, % 173.82/173.82 ! [V_a,V_x,V_b,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf__absorb1,axiom, % 173.82/173.82 ! [V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.82/173.82 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf__absorb2,axiom, % 173.82/173.82 ! [V_x,V_y,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.82/173.82 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Ole__infI,axiom, % 173.82/173.82 ! [V_b,V_a,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 173.82/173.82 => 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))) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf__greatest,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 173.82/173.82 => 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))) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf__mono,axiom, % 173.82/173.82 ! [V_d,V_b,V_c,V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 173.82/173.82 => 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))) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Ole__infE,axiom, % 173.82/173.82 ! [V_b,V_a,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( 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))) % 173.82/173.82 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.82/173.82 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__diff__distrib__left,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Groups_Oordered__ab__group__add(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oless__infI1,axiom, % 173.82/173.82 ! [V_b,V_x,V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oless__infI2,axiom, % 173.82/173.82 ! [V_a,V_x,V_b,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__less__iff__disj,axiom, % 173.82/173.82 ! [V_z_2,V_y_2,V_x_2,T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => ( 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)) % 173.82/173.82 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 173.82/173.82 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__less__iff__conj,axiom, % 173.82/173.82 ! [V_y_2,V_x_2,V_z_2,T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => ( 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))) % 173.82/173.82 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 173.82/173.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__add__distrib__left,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf__assoc,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf_Oassoc,axiom, % 173.82/173.82 ! [V_c,V_b,V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf__left__commute,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 173.82/173.82 ! [V_c,V_a,V_b,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf__left__idem,axiom, % 173.82/173.82 ! [V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 173.82/173.82 ! [V_b,V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf__commute,axiom, % 173.82/173.82 ! [V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf_Ocommute,axiom, % 173.82/173.82 ! [V_b,V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf_Oidem,axiom, % 173.82/173.82 ! [V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__diff,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_fst__eqD,axiom, % 173.82/173.82 ! [V_a,V_y,V_x,T_b,T_a] : % 173.82/173.82 ( 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 % 173.82/173.82 => V_x = V_a ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_fst__conv,axiom, % 173.82/173.82 ! [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 ). % 173.82/173.82 % 173.82/173.82 fof(fact_prod__eqI,axiom, % 173.82/173.82 ! [V_q,V_p,T_b,T_a] : % 173.82/173.82 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 173.82/173.82 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 173.82/173.82 => V_p = V_q ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Pair__fst__snd__eq,axiom, % 173.82/173.82 ! [T_c,T_b,V_t_2,V_s_2] : % 173.82/173.82 ( V_s_2 = V_t_2 % 173.82/173.82 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) % 173.82/173.82 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_fst__apsnd,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_fst__def,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__number__of,axiom, % 173.82/173.82 ! [V_v,V_u,T_b] : % 173.82/173.82 ( ( class_Int_Onumber(T_b) % 173.82/173.82 & class_Orderings_Oord(T_b) ) % 173.82/173.82 => ( ( 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))) % 173.82/173.82 => 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) ) % 173.82/173.82 & ( ~ 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))) % 173.82/173.82 => 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) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_surjective__pairing,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_pair__collapse,axiom, % 173.82/173.82 ! [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 ). % 173.82/173.82 % 173.82/173.82 fof(fact_prod__case__beta,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__int__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_mod__nat__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_split__beta,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_split__comp__eq,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_split__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_double__diff,axiom, % 173.82/173.82 ! [V_C_2,V_B_2,V_A_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.82/173.82 => 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 ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Diff__mono,axiom, % 173.82/173.82 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2)) % 173.82/173.82 => 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))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Diff__subset,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Compl__anti__mono,axiom, % 173.82/173.82 ! [V_B_2,V_A_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 => 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Compl__subset__Compl__iff,axiom, % 173.82/173.82 ! [V_B_2,V_A_2,T_b] : % 173.82/173.82 ( 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))) % 173.82/173.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_equalityE,axiom, % 173.82/173.82 ! [T_b,V_B_2,V_A_2] : % 173.82/173.82 ( V_A_2 = V_B_2 % 173.82/173.82 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_subset__trans,axiom, % 173.82/173.82 ! [V_C_2,V_B_2,V_A_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_equalityD2,axiom, % 173.82/173.82 ! [T_b,V_B_2,V_A_2] : % 173.82/173.82 ( V_A_2 = V_B_2 % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_equalityD1,axiom, % 173.82/173.82 ! [T_b,V_B_2,V_A_2] : % 173.82/173.82 ( V_A_2 = V_B_2 % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_set__eq__subset,axiom, % 173.82/173.82 ! [T_b,V_B_2,V_A_2] : % 173.82/173.82 ( V_A_2 = V_B_2 % 173.82/173.82 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_subset__refl,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_subset__psubset__trans,axiom, % 173.82/173.82 ! [V_C_2,V_B_2,V_A_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_psubset__subset__trans,axiom, % 173.82/173.82 ! [V_C_2,V_B_2,V_A_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_psubset__imp__subset,axiom, % 173.82/173.82 ! [V_B_2,V_A_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_subset__iff__psubset__eq,axiom, % 173.82/173.82 ! [V_B_2,V_A_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 | V_A_2 = V_B_2 ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_psubset__eq,axiom, % 173.82/173.82 ! [V_B_2,V_A_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 & V_A_2 != V_B_2 ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__Suc1,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__Suc2,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__neg__pos,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__pos__pos,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__pos__pos__1__number__of,axiom, % 173.82/173.82 ! [V_w] : % 173.82/173.82 ( 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))) % 173.82/173.82 => 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__pos__neg,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 173.82/173.82 => 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)))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__Suc__number__of,axiom, % 173.82/173.82 ! [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)))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_prod__size__simp,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_conjI__realizer,axiom, % 173.82/173.82 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_Pa_2] : % 173.82/173.82 ( hBOOL(hAPP(V_Pa_2,V_p_2)) % 173.82/173.82 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 173.82/173.82 => ( 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)))) % 173.82/173.82 & 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)))) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_exI__realizer,axiom, % 173.82/173.82 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2)) % 173.82/173.82 => 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)))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__ord__min,axiom, % 173.82/173.82 ! [T_b] : % 173.82/173.82 ( class_Orderings_Oord(T_b) % 173.82/173.82 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_prod_Orecs,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Compl__eq__Compl__iff,axiom, % 173.82/173.82 ! [V_B_2,V_A_2,T_b] : % 173.82/173.82 ( 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) % 173.82/173.82 <=> V_A_2 = V_B_2 ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_double__complement,axiom, % 173.82/173.82 ! [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 ). % 173.82/173.82 % 173.82/173.82 fof(fact_Diff__idemp,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_psubset__trans,axiom, % 173.82/173.82 ! [V_C_2,V_B_2,V_A_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__nat__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_divmod__nat__rel__def,axiom, % 173.82/173.82 ! [V_qr_2,V_n_2,V_m_2] : % 173.82/173.82 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 173.82/173.82 <=> ( 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)) % 173.82/173.82 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.82 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.82/173.82 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.82 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 173.82/173.82 => ( 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))) % 173.82/173.82 & 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)) ) ) % 173.82/173.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 173.82/173.82 => ( 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))) % 173.82/173.82 & 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))) ) ) ) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_range,axiom, % 173.82/173.82 ! [V_s,V_k] : % 173.82/173.82 ( 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)) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_max__number__of__Suc,axiom, % 173.82/173.82 ! [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)))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_max__Suc__number__of,axiom, % 173.82/173.82 ! [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)))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_apsnd__apfst,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_max__diff__distrib__left,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Groups_Oordered__ab__group__add(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_less__max__iff__disj,axiom, % 173.82/173.82 ! [V_y_2,V_x_2,V_z_2,T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => ( 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))) % 173.82/173.82 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 173.82/173.82 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_max__less__iff__conj,axiom, % 173.82/173.82 ! [V_z_2,V_y_2,V_x_2,T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => ( 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)) % 173.82/173.82 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 173.82/173.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oless__supI2,axiom, % 173.82/173.82 ! [V_a,V_b,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 173.82/173.82 => 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))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oless__supI1,axiom, % 173.82/173.82 ! [V_b,V_a,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 173.82/173.82 => 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))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup__inf__absorb,axiom, % 173.82/173.82 ! [V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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 ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf__sup__absorb,axiom, % 173.82/173.82 ! [V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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 ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup__inf__distrib1,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup__inf__distrib2,axiom, % 173.82/173.82 ! [V_x,V_z,V_y,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 173.82/173.82 ! [V_x,V_z,V_y,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_max__0L,axiom, % 173.82/173.82 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 173.82/173.82 % 173.82/173.82 fof(fact_max__0R,axiom, % 173.82/173.82 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 173.82/173.82 % 173.82/173.82 fof(fact_max__Suc__Suc,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_le__max__iff__disj,axiom, % 173.82/173.82 ! [V_y_2,V_x_2,V_z_2,T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => ( 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))) % 173.82/173.82 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) % 173.82/173.82 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_le__maxI1,axiom, % 173.82/173.82 ! [V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_le__maxI2,axiom, % 173.82/173.82 ! [V_x,V_y,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Ole__iff__sup,axiom, % 173.82/173.82 ! [V_y_2,V_x_2,T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.82/173.82 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Ole__sup__iff,axiom, % 173.82/173.82 ! [V_z_2,V_y_2,V_x_2,T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => ( 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)) % 173.82/173.82 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 173.82/173.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Ole__supI1,axiom, % 173.82/173.82 ! [V_b,V_a,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.82/173.82 => 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))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Ole__supI2,axiom, % 173.82/173.82 ! [V_a,V_b,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 173.82/173.82 => 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))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup__absorb2,axiom, % 173.82/173.82 ! [V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.82/173.82 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup__absorb1,axiom, % 173.82/173.82 ! [V_x,V_y,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.82/173.82 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Ole__supI,axiom, % 173.82/173.82 ! [V_b,V_x,V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 173.82/173.82 => 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)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup__least,axiom, % 173.82/173.82 ! [V_z,V_x,V_y,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 173.82/173.82 => 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)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup__mono,axiom, % 173.82/173.82 ! [V_d,V_b,V_c,V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 173.82/173.82 => 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))) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Ole__supE,axiom, % 173.82/173.82 ! [V_x,V_b,V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => ( 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)) % 173.82/173.82 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 173.82/173.82 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_max__add__distrib__left,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup__assoc,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup_Oassoc,axiom, % 173.82/173.82 ! [V_c,V_b,V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup__left__commute,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup_Oleft__commute,axiom, % 173.82/173.82 ! [V_c,V_a,V_b,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup__left__idem,axiom, % 173.82/173.82 ! [V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup_Oleft__idem,axiom, % 173.82/173.82 ! [V_b,V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup__commute,axiom, % 173.82/173.82 ! [V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup_Ocommute,axiom, % 173.82/173.82 ! [V_b,V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Osup_Oidem,axiom, % 173.82/173.82 ! [V_a,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_apfst__conv,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_apfst__eq__conv,axiom, % 173.82/173.82 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] : % 173.82/173.82 ( 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) % 173.82/173.82 <=> 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_fst__apfst,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_snd__apfst,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_max__number__of,axiom, % 173.82/173.82 ! [V_v,V_u,T_b] : % 173.82/173.82 ( ( class_Int_Onumber(T_b) % 173.82/173.82 & class_Orderings_Oord(T_b) ) % 173.82/173.82 => ( ( 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))) % 173.82/173.82 => 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) ) % 173.82/173.82 & ( ~ 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))) % 173.82/173.82 => 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) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Odistrib__inf__le,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_min__max_Odistrib__sup__le,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => 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)))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_minus__max__eq__min,axiom, % 173.82/173.82 ! [V_y,V_x,T_a] : % 173.82/173.82 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_minus__min__eq__max,axiom, % 173.82/173.82 ! [V_y,V_x,T_a] : % 173.82/173.82 ( class_Groups_Olinordered__ab__group__add(T_a) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_nat__minus__add__max,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_apsnd__apfst__commute,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_max__Suc1,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_max__Suc2,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_apfst__apsnd,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dual__min,axiom, % 173.82/173.82 ! [T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_max__ord__max,axiom, % 173.82/173.82 ! [T_b] : % 173.82/173.82 ( class_Orderings_Oord(T_b) % 173.82/173.82 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_code__numeral__decr,axiom, % 173.82/173.82 ! [V_k] : % 173.82/173.82 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 173.82/173.82 => 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Nitpick_Ozero__frac__def,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_pos__not__random__dseq__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 173.82/173.82 ! [V_l_2,V_k_2] : % 173.82/173.82 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 173.82/173.82 <=> V_k_2 = V_l_2 ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_code__numeral_Onat__of__inject,axiom, % 173.82/173.82 ! [V_y_2,V_x_2] : % 173.82/173.82 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 173.82/173.82 <=> V_x_2 = V_y_2 ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_nat__of__of__nat,axiom, % 173.82/173.82 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 173.82/173.82 % 173.82/173.82 fof(fact_of__nat__nat__of,axiom, % 173.82/173.82 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 173.82/173.82 % 173.82/173.82 fof(fact_nat__of__inverse,axiom, % 173.82/173.82 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 173.82/173.82 % 173.82/173.82 fof(fact_less__code__numeral__def,axiom, % 173.82/173.82 ! [V_m_2,V_n_2] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 173.82/173.82 <=> 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_nat__of__number,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_less__eq__code__numeral__def,axiom, % 173.82/173.82 ! [V_m_2,V_n_2] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 173.82/173.82 <=> 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_nat__of__code,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_nat__of__aux__def,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Min_Oidem,axiom, % 173.82/173.82 ! [V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Max_Oidem,axiom, % 173.82/173.82 ! [V_x,T_a] : % 173.82/173.82 ( class_Orderings_Olinorder(T_a) % 173.82/173.82 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dual__max,axiom, % 173.82/173.82 ! [T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Suc__code__numeral__def,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_minus__code__numeral__def,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_plus__code__numeral__def,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__code__numeral__def,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_times__code__numeral__def,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_mod__code__numeral__def,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Nitpick_Oone__frac__def,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Nitpick_Ofrac__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_surjective__sum,axiom, % 173.82/173.82 ! [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 ). % 173.82/173.82 % 173.82/173.82 fof(fact_iterate_Osimps,axiom, % 173.82/173.82 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 173.82/173.82 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.82/173.82 => 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) ) % 173.82/173.82 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_sum__case__KK,axiom, % 173.82/173.82 ! [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 ). % 173.82/173.82 % 173.82/173.82 fof(fact_scomp__scomp,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_sum__case__inject,axiom, % 173.82/173.82 ! [V_g2_2,V_g1_2,V_f2_2,V_f1_2,T_c,T_d,T_b] : % 173.82/173.82 ( 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) % 173.82/173.82 => ~ ( V_f1_2 = V_g1_2 % 173.82/173.82 => V_f2_2 != V_g2_2 ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_sum__case__weak__cong,axiom, % 173.82/173.82 ! [V_g_2,V_f_2,T_c,T_d,T_b,V_t_2,V_s_2] : % 173.82/173.82 ( V_s_2 = V_t_2 % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_scomp__Pair,axiom, % 173.82/173.82 ! [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 ). % 173.82/173.82 % 173.82/173.82 fof(fact_Pair__scomp,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_scomp__apply,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_sum_Osimps_I6_J,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_sum_Osimps_I5_J,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_scomp__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_scomp__unfold,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Nitpick_Oplus__frac__def,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_internal__split__def,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_transfer__morphism__int__nat,axiom, % 173.82/173.82 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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 173.82/173.82 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 173.82/173.82 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.82/173.82 => 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) ) % 173.82/173.82 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 173.82/173.82 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 173.82/173.82 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.82/173.82 => 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) ) % 173.82/173.82 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_internal__split__conv,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Nitpick_Otimes__frac__def,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Nitpick_Oof__frac__def,axiom, % 173.82/173.82 ! [V_q,T_a,T_b] : % 173.82/173.82 ( ( class_Rings_Oinverse(T_b) % 173.82/173.82 & class_Rings_Oring__1(T_b) ) % 173.82/173.82 => 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Nitpick_Oless__frac__def,axiom, % 173.82/173.82 ! [V_r_2,V_q_2,T_b] : % 173.82/173.82 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2) % 173.82/173.82 <=> 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 173.82/173.82 ! [V_r_2,V_q_2,T_b] : % 173.82/173.82 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2) % 173.82/173.82 <=> 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_New__DSequence_Opos__empty__def,axiom, % 173.82/173.82 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 173.82/173.82 % 173.82/173.82 fof(fact_pos__empty__def,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_neg__bind__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_New__DSequence_Opos__bind__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_predicate2D,axiom, % 173.82/173.82 ! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_c,T_b] : % 173.82/173.82 ( 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)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 173.82/173.82 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_rev__predicate2D,axiom, % 173.82/173.82 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 173.82/173.82 => ( 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)) % 173.82/173.82 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_predicate1D,axiom, % 173.82/173.82 ! [V_x_2,V_Q_2,V_Pa_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) % 173.82/173.82 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 173.82/173.82 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_rev__predicate1D,axiom, % 173.82/173.82 ! [V_Q_2,T_b,V_x_2,V_Pa_2] : % 173.82/173.82 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) % 173.82/173.82 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_pos__bind__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_The__split,axiom, % 173.82/173.82 ! [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))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Random_Osimps,axiom, % 173.82/173.82 ! [V_size_2,V_g_2,T_b,V_nrandom_2] : % 173.82/173.82 ( ( 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))) % 173.82/173.82 => 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)) ) % 173.82/173.82 & ( ~ 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))) % 173.82/173.82 => 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))))))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_exE__realizer,axiom, % 173.82/173.82 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_Pa_2] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( ! [B_x,B_y] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x)) % 173.82/173.82 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) ) % 173.82/173.82 => 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))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_curry__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_curryI,axiom, % 173.82/173.82 ! [V_ba_2,V_a_2,T_c,T_b,V_f_2] : % 173.82/173.82 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_curryD,axiom, % 173.82/173.82 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2)) % 173.82/173.82 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_curryE,axiom, % 173.82/173.82 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2)) % 173.82/173.82 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_curry__conv,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_split__curry,axiom, % 173.82/173.82 ! [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 ). % 173.82/173.82 % 173.82/173.82 fof(fact_curry__split,axiom, % 173.82/173.82 ! [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 ). % 173.82/173.82 % 173.82/173.82 fof(fact_split__paired__The,axiom, % 173.82/173.82 ! [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)))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_The__split__eq,axiom, % 173.82/173.82 ! [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) ). % 173.82/173.82 % 173.82/173.82 fof(fact_divmod__nat__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Random__Sequence_Oempty__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Random__Sequence_Osingle__def,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_the__eq__trivial,axiom, % 173.82/173.82 ! [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 ). % 173.82/173.82 % 173.82/173.82 fof(fact_the__sym__eq__trivial,axiom, % 173.82/173.82 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 173.82/173.82 % 173.82/173.82 fof(fact_Powp__def,axiom, % 173.82/173.82 ! [V_B_2,V_A_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2)) % 173.82/173.82 <=> ! [B_x] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 173.82/173.82 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_Powp__mono,axiom, % 173.82/173.82 ! [V_B_2,V_A_2,T_b] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.82 => 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_power__dvd__imp__le,axiom, % 173.82/173.82 ! [V_n,V_m,V_i] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__mult__cancel2,axiom, % 173.82/173.82 ! [V_n_2,V_m_2] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 173.82/173.82 => ( 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)) % 173.82/173.82 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__mult__cancel1,axiom, % 173.82/173.82 ! [V_n_2,V_m_2] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 173.82/173.82 => ( 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)) % 173.82/173.82 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_zdvd__mult__cancel1,axiom, % 173.82/173.82 ! [V_n_2,V_m_2] : % 173.82/173.82 ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.82 => ( 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)) % 173.82/173.82 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_arith__series__int,axiom, % 173.82/173.82 ! [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)))) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oorder__refl,axiom, % 173.82/173.82 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__0__right,axiom, % 173.82/173.82 ! [V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__1__left,axiom, % 173.82/173.82 ! [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)) ). % 173.82/173.82 % 173.82/173.82 fof(fact_setsum__abs,axiom, % 173.82/173.82 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.82 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 173.82/173.82 => 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_setsum__abs__ge__zero,axiom, % 173.82/173.82 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.82 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 173.82/173.82 => 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_zdvd__antisym__abs,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_b),V_a)) % 173.82/173.82 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_a) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_b) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_nat__dvd__1__iff__1,axiom, % 173.82/173.82 ! [V_m_2] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 173.82/173.82 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__if__abs__eq,axiom, % 173.82/173.82 ! [V_k,V_l,T_a] : % 173.82/173.82 ( class_Rings_Olinordered__idom(T_a) % 173.82/173.82 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_abs__dvd__iff,axiom, % 173.82/173.82 ! [V_k_2,V_m_2,T_b] : % 173.82/173.82 ( class_Rings_Olinordered__idom(T_b) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2)) % 173.82/173.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__abs__iff,axiom, % 173.82/173.82 ! [V_k_2,V_m_2,T_b] : % 173.82/173.82 ( class_Rings_Olinordered__idom(T_b) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2))) % 173.82/173.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__power__same,axiom, % 173.82/173.82 ! [V_n,V_y,V_x,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 173.82/173.82 => 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))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_one__dvd,axiom, % 173.82/173.82 ! [V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__0__left,axiom, % 173.82/173.82 ! [V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 173.82/173.82 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__add,axiom, % 173.82/173.82 ! [V_c,V_b,V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) % 173.82/173.82 => 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))) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_lessThan__eq__iff,axiom, % 173.82/173.82 ! [V_y_2,V_x_2,T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2) % 173.82/173.82 <=> V_x_2 = V_y_2 ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oeq__iff,axiom, % 173.82/173.82 ! [V_y_2,V_x_2] : % 173.82/173.82 ( V_x_2 = V_y_2 % 173.82/173.82 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 173.82/173.82 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Ole__less,axiom, % 173.82/173.82 ! [V_y_2,V_x_2] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 173.82/173.82 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 173.82/173.82 | V_x_2 = V_y_2 ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oless__le,axiom, % 173.82/173.82 ! [V_y_2,V_x_2] : % 173.82/173.82 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 173.82/173.82 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 173.82/173.82 & V_x_2 != V_y_2 ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oneq__le__trans,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( V_a != V_b % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oeq__refl,axiom, % 173.82/173.82 ! [V_y,V_x] : % 173.82/173.82 ( V_x = V_y % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oantisym__conv,axiom, % 173.82/173.82 ! [V_x_2,V_y_2] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 173.82/173.82 <=> V_x_2 = V_y_2 ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Ole__imp__less__or__eq,axiom, % 173.82/173.82 ! [V_y,V_x] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 173.82/173.82 | V_x = V_y ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Ole__neq__trans,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 173.82/173.82 => ( V_a != V_b % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oord__eq__le__trans,axiom, % 173.82/173.82 ! [V_c,V_b,V_a] : % 173.82/173.82 ( V_a = V_b % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oord__le__eq__trans,axiom, % 173.82/173.82 ! [V_c,V_b,V_a] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 173.82/173.82 => ( V_b = V_c % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__antisym,axiom, % 173.82/173.82 ! [V_n,V_m] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) % 173.82/173.82 => V_m = V_n ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oantisym,axiom, % 173.82/173.82 ! [V_y,V_x] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 173.82/173.82 => V_x = V_y ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oorder__trans,axiom, % 173.82/173.82 ! [V_z,V_y,V_x] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oord__eq__less__trans,axiom, % 173.82/173.82 ! [V_c,V_b,V_a] : % 173.82/173.82 ( V_a = V_b % 173.82/173.82 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) ) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Ole__less__trans,axiom, % 173.82/173.82 ! [V_z,V_y,V_x] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) ) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oless__imp__neq,axiom, % 173.82/173.82 ! [V_y,V_x] : % 173.82/173.82 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 173.82/173.82 => V_x != V_y ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oless__not__sym,axiom, % 173.82/173.82 ! [V_y,V_x] : % 173.82/173.82 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 173.82/173.82 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oless__imp__le,axiom, % 173.82/173.82 ! [V_y,V_x] : % 173.82/173.82 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oless__imp__not__less,axiom, % 173.82/173.82 ! [V_y,V_x] : % 173.82/173.82 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 173.82/173.82 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oless__imp__not__eq,axiom, % 173.82/173.82 ! [V_y,V_x] : % 173.82/173.82 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 173.82/173.82 => V_x != V_y ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oless__imp__not__eq2,axiom, % 173.82/173.82 ! [V_y,V_x] : % 173.82/173.82 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 173.82/173.82 => V_y != V_x ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oord__less__eq__trans,axiom, % 173.82/173.82 ! [V_c,V_b,V_a] : % 173.82/173.82 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) % 173.82/173.82 => ( V_b = V_c % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oless__le__trans,axiom, % 173.82/173.82 ! [V_z,V_y,V_x] : % 173.82/173.82 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oless__asym_H,axiom, % 173.82/173.82 ! [V_b,V_a] : % 173.82/173.82 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) % 173.82/173.82 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oless__trans,axiom, % 173.82/173.82 ! [V_z,V_y,V_x] : % 173.82/173.82 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 173.82/173.82 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) ) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd_Oless__asym,axiom, % 173.82/173.82 ! [V_y,V_x] : % 173.82/173.82 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 173.82/173.82 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 173.82/173.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__refl,axiom, % 173.82/173.82 ! [V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__trans,axiom, % 173.82/173.82 ! [V_c,V_b,V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__mod__imp__dvd,axiom, % 173.82/173.82 ! [V_n,V_m,V_k,T_a] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__mod,axiom, % 173.82/173.82 ! [V_n,V_m,V_k,T_a] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_mod__mod__cancel,axiom, % 173.82/173.82 ! [V_a,V_b,V_c,T_a] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) % 173.82/173.82 => 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) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__mod__iff,axiom, % 173.82/173.82 ! [V_m_2,V_n_2,V_k_2,T_b] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_b) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2)) % 173.82/173.82 => ( 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))) % 173.82/173.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_transfer__int__nat__relations_I4_J,axiom, % 173.82/173.82 ! [V_y_2,V_x_2] : % 173.82/173.82 ( 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))) % 173.82/173.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_zdvd__int,axiom, % 173.82/173.82 ! [V_y_2,V_x_2] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 173.82/173.82 <=> 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__triv__left,axiom, % 173.82/173.82 ! [V_b,V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__triv__right,axiom, % 173.82/173.82 ! [V_b,V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__mult2,axiom, % 173.82/173.82 ! [V_c,V_b,V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 173.82/173.82 => 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))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__mult,axiom, % 173.82/173.82 ! [V_b,V_c,V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) % 173.82/173.82 => 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))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_mult__dvd__mono,axiom, % 173.82/173.82 ! [V_d,V_c,V_b,V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d)) % 173.82/173.82 => 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))) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvdI,axiom, % 173.82/173.82 ! [V_k,V_b,V_a,T_a] : % 173.82/173.82 ( class_Rings_Odvd(T_a) % 173.82/173.82 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__mult__left,axiom, % 173.82/173.82 ! [V_c,V_b,V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => ( 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)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__mult__right,axiom, % 173.82/173.82 ! [V_c,V_b,V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => ( 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)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__dvd__div,axiom, % 173.82/173.82 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_b) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2)) % 173.82/173.82 => ( 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))) % 173.82/173.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ba_2),V_ca_2)) ) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_zdvd__zmod__imp__zdvd,axiom, % 173.82/173.82 ! [V_n,V_m,V_k] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_zdvd__zmod,axiom, % 173.82/173.82 ! [V_n,V_m,V_f] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n)) % 173.82/173.82 => 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))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_uminus__dvd__conv_I2_J,axiom, % 173.82/173.82 ! [V_t_2,V_d_2] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) % 173.82/173.82 <=> 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))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_uminus__dvd__conv_I1_J,axiom, % 173.82/173.82 ! [V_t_2,V_d_2] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) % 173.82/173.82 <=> 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_zdvd__zdiffD,axiom, % 173.82/173.82 ! [V_n,V_m,V_k] : % 173.82/173.82 ( 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))) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n)) % 173.82/173.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__reduce,axiom, % 173.82/173.82 ! [V_n_2,V_k_2] : % 173.82/173.82 ( 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))) % 173.82/173.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_of__nat__setsum,axiom, % 173.82/173.82 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.82 ( class_Rings_Osemiring__1(T_b) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__minus__iff,axiom, % 173.82/173.82 ! [V_y_2,V_x_2,T_b] : % 173.82/173.82 ( class_Rings_Ocomm__ring__1(T_b) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) % 173.82/173.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_minus__dvd__iff,axiom, % 173.82/173.82 ! [V_y_2,V_x_2,T_b] : % 173.82/173.82 ( class_Rings_Ocomm__ring__1(T_b) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2)) % 173.82/173.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__diff,axiom, % 173.82/173.82 ! [V_z,V_y,V_x,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__ring__1(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z)) % 173.82/173.82 => 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))) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_setsum__lessThan__Suc,axiom, % 173.82/173.82 ! [V_n_2,V_f_2,T_b] : % 173.82/173.82 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_of__int__setsum,axiom, % 173.82/173.82 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.82 ( class_Rings_Oring__1(T_b) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__diff__nat,axiom, % 173.82/173.82 ! [V_n,V_m,V_k] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 173.82/173.82 => 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))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_setsum__commute,axiom, % 173.82/173.82 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 173.82/173.82 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_setsum__0,axiom, % 173.82/173.82 ! [V_A_2,T_c,T_b] : % 173.82/173.82 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_setsum__addf,axiom, % 173.82/173.82 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 173.82/173.82 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_setsum__right__distrib,axiom, % 173.82/173.82 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] : % 173.82/173.82 ( class_Rings_Osemiring__0(T_b) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_setsum__left__distrib,axiom, % 173.82/173.82 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.82 ( class_Rings_Osemiring__0(T_b) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_setsum__product,axiom, % 173.82/173.82 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.82 ( class_Rings_Osemiring__0(T_b) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_setsum__subtractf,axiom, % 173.82/173.82 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 173.82/173.82 ( class_Groups_Oab__group__add(T_b) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_setsum__negf,axiom, % 173.82/173.82 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.82 ( class_Groups_Oab__group__add(T_b) % 173.82/173.82 => 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_setsum__divide__distrib,axiom, % 173.82/173.82 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.82 ( class_Fields_Ofield(T_b) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_abs__setsum__abs,axiom, % 173.82/173.82 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.82 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 173.82/173.82 => 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) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_transfer__nat__int__relations_I4_J,axiom, % 173.82/173.82 ! [V_y_2,V_x_2] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 173.82/173.82 => ( 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))) % 173.82/173.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_int__dvd__iff,axiom, % 173.82/173.82 ! [V_z_2,V_m_2] : % 173.82/173.82 ( 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)) % 173.82/173.82 <=> 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)))) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__int__iff,axiom, % 173.82/173.82 ! [V_m_2,V_z_2] : % 173.82/173.82 ( 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))) % 173.82/173.82 <=> 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)) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_lessThan__subset__iff,axiom, % 173.82/173.82 ! [V_y_2,V_x_2,T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => ( 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))) % 173.82/173.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__mult__cancel__left,axiom, % 173.82/173.82 ! [V_ba_2,V_a_2,V_ca_2,T_b] : % 173.82/173.82 ( class_Rings_Oidom(T_b) % 173.82/173.82 => ( 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))) % 173.82/173.82 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.82 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__mult__cancel__right,axiom, % 173.82/173.82 ! [V_ba_2,V_ca_2,V_a_2,T_b] : % 173.82/173.82 ( class_Rings_Oidom(T_b) % 173.82/173.82 => ( 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))) % 173.82/173.82 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.82 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__imp__mod__0,axiom, % 173.82/173.82 ! [V_b,V_a,T_a] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 173.82/173.82 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__eq__mod__eq__0,axiom, % 173.82/173.82 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_b) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) % 173.82/173.82 <=> c_Divides_Odiv__class_Omod(T_b,V_ba_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_lessThan__strict__subset__iff,axiom, % 173.82/173.82 ! [V_n_2,V_m_2,T_b] : % 173.82/173.82 ( class_Orderings_Olinorder(T_b) % 173.82/173.82 => ( 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))) % 173.82/173.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__add,axiom, % 173.82/173.82 ! [V_y,V_x,V_z,T_a] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y)) % 173.82/173.82 => 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)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__mult__div__cancel,axiom, % 173.82/173.82 ! [V_b,V_a,T_a] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 173.82/173.82 => 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 ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__mult__swap,axiom, % 173.82/173.82 ! [V_a,V_b,V_c,T_a] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) % 173.82/173.82 => 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) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__div__mult__self,axiom, % 173.82/173.82 ! [V_b,V_a,T_a] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 173.82/173.82 => 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 ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__div__mult,axiom, % 173.82/173.82 ! [V_c,V_b,V_a,T_a] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 173.82/173.82 => 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) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__mult__div__if__dvd,axiom, % 173.82/173.82 ! [V_w,V_z,V_x,V_y,T_a] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w)) % 173.82/173.82 => 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)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__div__neg,axiom, % 173.82/173.82 ! [V_x,V_y,T_a] : % 173.82/173.82 ( class_Divides_Oring__div(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__neg__div,axiom, % 173.82/173.82 ! [V_x,V_y,T_a] : % 173.82/173.82 ( class_Divides_Oring__div(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_power__le__dvd,axiom, % 173.82/173.82 ! [V_m,V_b,V_n,V_a,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => ( 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)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.82/173.82 => 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)) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_dvd__power__le,axiom, % 173.82/173.82 ! [V_m,V_n,V_y,V_x,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.82/173.82 => 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))) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_le__imp__power__dvd,axiom, % 173.82/173.82 ! [V_a,V_n,V_m,T_a] : % 173.82/173.82 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 173.82/173.82 => 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))) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_div__power,axiom, % 173.82/173.82 ! [V_n,V_x,V_y,T_a] : % 173.82/173.82 ( class_Divides_Osemiring__div(T_a) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 173.82/173.82 => 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)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_zdvd__antisym__nonneg,axiom, % 173.82/173.82 ! [V_n,V_m] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) % 173.82/173.82 => V_m = V_n ) ) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_zdvd__not__zless,axiom, % 173.82/173.82 ! [V_n,V_m] : % 173.82/173.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_m),V_n)) % 173.82/173.82 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ) ) ). % 173.82/173.82 % 173.82/173.82 fof(fact_zdvd__mono,axiom, % 173.82/173.82 ! [V_t_2,V_m_2,V_k_2] : % 173.82/173.82 ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2)) % 173.82/173.82 <=> 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))) ) ) ). % 173.82/173.82 % 173.82/173.83 fof(fact_zdvd__mult__cancel,axiom, % 173.82/173.83 ! [V_n,V_m,V_k] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_zdvd__reduce,axiom, % 173.82/173.83 ! [V_m_2,V_n_2,V_k_2] : % 173.82/173.83 ( 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)))) % 173.82/173.83 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_zdvd__period,axiom, % 173.82/173.83 ! [V_ca_2,V_t_2,V_x_2,V_d_2,V_a_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2)) % 173.82/173.83 => ( 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))) % 173.82/173.83 <=> 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd__1__iff__1,axiom, % 173.82/173.83 ! [V_m_2] : % 173.82/173.83 ( 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)))) % 173.82/173.83 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_nat__dvd__not__less,axiom, % 173.82/173.83 ! [V_n,V_m] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 173.82/173.83 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_nat__mult__dvd__cancel__disj,axiom, % 173.82/173.83 ! [V_n_2,V_m_2,V_k_2] : % 173.82/173.83 ( 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))) % 173.82/173.83 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.83 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_zdvd__mult__div__cancel,axiom, % 173.82/173.83 ! [V_m,V_n] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) % 173.82/173.83 => 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 ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_zmod__eq__dvd__iff,axiom, % 173.82/173.83 ! [V_y_2,V_n_2,V_x_2] : % 173.82/173.83 ( 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) % 173.82/173.83 <=> 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd__diffD1,axiom, % 173.82/173.83 ! [V_n,V_m,V_k] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd__diffD,axiom, % 173.82/173.83 ! [V_n,V_m,V_k] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_zdvd1__eq,axiom, % 173.82/173.83 ! [V_x_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) % 173.82/173.83 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_abs__div,axiom, % 173.82/173.83 ! [V_x,V_y] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_y),V_x)) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_nat__dvd__iff,axiom, % 173.82/173.83 ! [V_m_2,V_z_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2)) % 173.82/173.83 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 173.82/173.83 => 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))) ) % 173.82/173.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 173.82/173.83 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_arith__series__general,axiom, % 173.82/173.83 ! [V_n_2,V_d_2,V_a_2,T_b] : % 173.82/173.83 ( class_Rings_Ocomm__semiring__1(T_b) % 173.82/173.83 => 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)))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_unity__coeff__ex,axiom, % 173.82/173.83 ! [V_l_2,V_Pa_2,T_b] : % 173.82/173.83 ( ( class_Rings_Odvd(T_b) % 173.82/173.83 & class_Rings_Osemiring__0(T_b) ) % 173.82/173.83 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x))) % 173.82/173.83 <=> ? [B_x] : % 173.82/173.83 ( 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)))) % 173.82/173.83 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_inf__period_I3_J,axiom, % 173.82/173.83 ! [V_t_2,V_D_2,V_d_2,T_b] : % 173.82/173.83 ( ( class_Rings_Ocomm__ring(T_b) % 173.82/173.83 & class_Rings_Odvd(T_b) ) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) % 173.82/173.83 => ! [B_x,B_k] : % 173.82/173.83 ( 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))) % 173.82/173.83 <=> 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))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_inf__period_I4_J,axiom, % 173.82/173.83 ! [V_t_2,V_D_2,V_d_2,T_b] : % 173.82/173.83 ( ( class_Rings_Ocomm__ring(T_b) % 173.82/173.83 & class_Rings_Odvd(T_b) ) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) % 173.82/173.83 => ! [B_x,B_k] : % 173.82/173.83 ( 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))) % 173.82/173.83 <=> 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))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd__eq__mod__eq__0__number__of,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,T_b] : % 173.82/173.83 ( ( class_Divides_Osemiring__div(T_b) % 173.82/173.83 & class_Int_Onumber(T_b) ) % 173.82/173.83 => ( 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))) % 173.82/173.83 <=> 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd__div__div__eq__mult,axiom, % 173.82/173.83 ! [V_d_2,V_ba_2,V_ca_2,V_a_2,T_b] : % 173.82/173.83 ( class_Divides_Osemiring__div(T_b) % 173.82/173.83 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.83 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ca_2),V_d_2)) % 173.82/173.83 => ( 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) % 173.82/173.83 <=> 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) ) ) ) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd__div__eq__mult,axiom, % 173.82/173.83 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( class_Divides_Osemiring__div(T_b) % 173.82/173.83 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) % 173.82/173.83 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ba_2),V_a_2) = V_ca_2 % 173.82/173.83 <=> V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2) ) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_zdvd__imp__le,axiom, % 173.82/173.83 ! [V_n,V_z] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n)) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom, % 173.82/173.83 ! [V_y_2,V_x_2] : % 173.82/173.83 ( 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))) % 173.82/173.83 <=> 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd__imp__le,axiom, % 173.82/173.83 ! [V_n,V_k] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd__mult__cancel,axiom, % 173.82/173.83 ! [V_n,V_m,V_k] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_nat__mult__dvd__cancel1,axiom, % 173.82/173.83 ! [V_n_2,V_m_2,V_k_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 173.82/173.83 => ( 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))) % 173.82/173.83 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd__imp__le__int,axiom, % 173.82/173.83 ! [V_d,V_i] : % 173.82/173.83 ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d),V_i)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd__power,axiom, % 173.82/173.83 ! [V_x,V_n,T_a] : % 173.82/173.83 ( class_Rings_Ocomm__semiring__1(T_a) % 173.82/173.83 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 173.82/173.83 | V_x = c_Groups_Oone__class_Oone(T_a) ) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd_Ostrict__monoD,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,V_f_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( 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) % 173.82/173.83 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 173.82/173.83 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_arith__series__nat,axiom, % 173.82/173.83 ! [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)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd_OmonoD,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,V_f_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 173.82/173.83 => 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))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__natinterval__difff,axiom, % 173.82/173.83 ! [V_f_2,V_n_2,V_m_2,T_b] : % 173.82/173.83 ( class_Groups_Oab__group__add(T_b) % 173.82/173.83 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.82/173.83 => 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)))) ) % 173.82/173.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.82/173.83 => 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) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_gauss__sum,axiom, % 173.82/173.83 ! [V_n_2,T_b] : % 173.82/173.83 ( class_Rings_Ocomm__semiring__1(T_b) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 173.82/173.83 ! [V_k_2,V_f_2] : % 173.82/173.83 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd_Ostrict__mono__mono,axiom, % 173.82/173.83 ! [V_f_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( 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) % 173.82/173.83 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastatMost__subset__iff,axiom, % 173.82/173.83 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( 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))) % 173.82/173.83 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 173.82/173.83 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 173.82/173.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) ) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 173.82/173.83 ! [V_n_2,V_m_2,V_f_2,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 173.82/173.83 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_int__setsum,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastatMost__psubset__iff,axiom, % 173.82/173.83 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( 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))) % 173.82/173.83 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) % 173.82/173.83 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 173.82/173.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) % 173.82/173.83 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2)) % 173.82/173.83 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_d_2)) ) ) ) % 173.82/173.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__head__Suc,axiom, % 173.82/173.83 ! [V_f_2,V_n_2,V_m_2,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__cl__ivl__Suc,axiom, % 173.82/173.83 ! [V_f_2,V_m_2,V_n_2,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 173.82/173.83 => 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) ) % 173.82/173.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 173.82/173.83 => 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))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__ub__add__nat,axiom, % 173.82/173.83 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => ( 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)))) % 173.82/173.83 => 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)))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_all__nat__less,axiom, % 173.82/173.83 ! [V_Pa_2,V_n_2] : % 173.82/173.83 ( ! [B_m] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 173.82/173.83 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 173.82/173.83 <=> ! [B_x] : % 173.82/173.83 ( 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))) % 173.82/173.83 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ex__nat__less,axiom, % 173.82/173.83 ! [V_Pa_2,V_n_2] : % 173.82/173.83 ( ? [B_m] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 173.82/173.83 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 173.82/173.83 <=> ? [B_x] : % 173.82/173.83 ( 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))) % 173.82/173.83 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sum__diff__distrib,axiom, % 173.82/173.83 ! [V_n_2,V_Pa_2,V_Q_2] : % 173.82/173.83 ( ! [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))) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_geometric__sum,axiom, % 173.82/173.83 ! [V_n_2,V_x_2,T_b] : % 173.82/173.83 ( class_Fields_Ofield(T_b) % 173.82/173.83 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ex__nat__less__eq,axiom, % 173.82/173.83 ! [V_Pa_2,V_n_2] : % 173.82/173.83 ( ? [B_m] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 173.82/173.83 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 173.82/173.83 <=> ? [B_x] : % 173.82/173.83 ( 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))) % 173.82/173.83 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_all__nat__less__eq,axiom, % 173.82/173.83 ! [V_Pa_2,V_n_2] : % 173.82/173.83 ( ! [B_m] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 173.82/173.83 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 173.82/173.83 <=> ! [B_x] : % 173.82/173.83 ( 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))) % 173.82/173.83 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 173.82/173.83 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( 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) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 173.82/173.83 => V_ba_2 = V_d_2 ) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 173.82/173.83 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( 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) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 173.82/173.83 => V_a_2 = V_ca_2 ) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastLessThan__eq__iff,axiom, % 173.82/173.83 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) % 173.82/173.83 => ( 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) % 173.82/173.83 <=> ( V_a_2 = V_ca_2 % 173.82/173.83 & V_ba_2 = V_d_2 ) ) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeast0LessThan,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastLessThan__subset__iff,axiom, % 173.82/173.83 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( 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))) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2)) % 173.82/173.83 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) % 173.82/173.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) ) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 173.82/173.83 ! [V_n_2,V_m_2,V_f_2,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 173.82/173.83 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__diff,axiom, % 173.82/173.83 ! [V_m_2,V_n_2,V_i_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__add__nat__ivl,axiom, % 173.82/173.83 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 173.82/173.83 => 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)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__diff__nat__ivl,axiom, % 173.82/173.83 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] : % 173.82/173.83 ( class_Groups_Oab__group__add(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 173.82/173.83 => 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)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 173.82/173.83 ! [V_k_2,V_f_2,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__head__upt__Suc,axiom, % 173.82/173.83 ! [V_f_2,V_n_2,V_m_2,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__op__ivl__Suc,axiom, % 173.82/173.83 ! [V_f_2,V_m_2,V_n_2,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 173.82/173.83 => 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) ) % 173.82/173.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 173.82/173.83 => 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)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_bset_I6_J,axiom, % 173.82/173.83 ! [V_t_2,V_B_2,V_D_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.82/173.83 => ! [B_x] : % 173.82/173.83 ( ! [B_xa] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ! [B_xb] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 173.82/173.83 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 173.82/173.83 => 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)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_aset_I8_J,axiom, % 173.82/173.83 ! [V_t_2,V_A_2,V_D_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.82/173.83 => ! [B_x] : % 173.82/173.83 ( ! [B_xa] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ! [B_xb] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 173.82/173.83 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 173.82/173.83 => 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))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_periodic__finite__ex,axiom, % 173.82/173.83 ! [V_Pa_2,V_d_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 173.82/173.83 => ( ! [B_x,B_k] : % 173.82/173.83 ( hBOOL(hAPP(V_Pa_2,B_x)) % 173.82/173.83 <=> 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)))) ) % 173.82/173.83 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 173.82/173.83 <=> ? [B_x] : % 173.82/173.83 ( 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))) % 173.82/173.83 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_aset_I7_J,axiom, % 173.82/173.83 ! [V_t_2,V_A_2,V_D_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.82/173.83 => ! [B_x] : % 173.82/173.83 ( ! [B_xa] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ! [B_xb] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 173.82/173.83 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 173.82/173.83 => 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))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_bset_I5_J,axiom, % 173.82/173.83 ! [V_t_2,V_B_2,V_D_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.82/173.83 => ! [B_x] : % 173.82/173.83 ( ! [B_xa] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ! [B_xb] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 173.82/173.83 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 173.82/173.83 => 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)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_aset_I10_J,axiom, % 173.82/173.83 ! [V_t_2,V_A_2,V_D_2,V_d_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) % 173.82/173.83 => ! [B_x] : % 173.82/173.83 ( ! [B_xa] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ! [B_xb] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 173.82/173.83 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.83 => ( ~ 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))) % 173.82/173.83 => ~ 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))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_bset_I10_J,axiom, % 173.82/173.83 ! [V_t_2,V_B_2,V_D_2,V_d_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) % 173.82/173.83 => ! [B_x] : % 173.82/173.83 ( ! [B_xa] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ! [B_xb] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 173.82/173.83 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.83 => ( ~ 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))) % 173.82/173.83 => ~ 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))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_aset_I9_J,axiom, % 173.82/173.83 ! [V_t_2,V_A_2,V_D_2,V_d_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) % 173.82/173.83 => ! [B_x] : % 173.82/173.83 ( ! [B_xa] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ! [B_xb] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 173.82/173.83 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.83 => ( 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))) % 173.82/173.83 => 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))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_bset_I9_J,axiom, % 173.82/173.83 ! [V_t_2,V_B_2,V_D_2,V_d_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) % 173.82/173.83 => ! [B_x] : % 173.82/173.83 ( ! [B_xa] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ! [B_xb] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 173.82/173.83 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.83 => ( 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))) % 173.82/173.83 => 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))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__atLeastZeroLessThan__int,axiom, % 173.82/173.83 ! [V_u_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__head,axiom, % 173.82/173.83 ! [V_Pa_2,V_n_2,V_m_2,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd_Ostrict__monoI,axiom, % 173.82/173.83 ! [V_f_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( ! [B_x,B_y] : % 173.82/173.83 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) % 173.82/173.83 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x)) ) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) ) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__uminus__atLeastLessThan,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,T_b] : % 173.82/173.83 ( class_Groups_Oordered__ab__group__add(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__uminus__greaterThanAtMost,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,T_b] : % 173.82/173.83 ( class_Groups_Oordered__ab__group__add(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_subset__image__iff,axiom, % 173.82/173.83 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 173.82/173.83 ( 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))) % 173.82/173.83 <=> ? [B_AA] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) % 173.82/173.83 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__mono,axiom, % 173.82/173.83 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 <=> 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__image,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 <=> 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2] : % 173.82/173.83 ( V_A_2 = V_B_2 % 173.82/173.83 <=> 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__diff__subset,axiom, % 173.82/173.83 ! [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)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__uminus__atLeastAtMost,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,T_b] : % 173.82/173.83 ( class_Groups_Oordered__ab__group__add(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 173.82/173.83 ! [V_A_2,V_f_2,T_b] : % 173.82/173.83 ( ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 & class_Groups_Ocomm__monoid__mult(T_b) ) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 173.82/173.83 ! [V_n_2,V_m_2] : % 173.82/173.83 ( c_Nat__Transfer_Ois__nat(V_m_2) % 173.82/173.83 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__SucD,axiom, % 173.82/173.83 ! [V_n_2,V_A_2,V_f_2,T_b] : % 173.82/173.83 ( 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) % 173.82/173.83 => ? [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.83 & 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__ivl__cong,axiom, % 173.82/173.83 ! [V_g_2,V_f_2,V_d_2,V_ba_2,V_ca_2,V_a_2,T_b,T_c] : % 173.82/173.83 ( ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.83 & class_Orderings_Oord(T_b) ) % 173.82/173.83 => ( V_a_2 = V_ca_2 % 173.82/173.83 => ( V_ba_2 = V_d_2 % 173.82/173.83 => ( ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2)) % 173.82/173.83 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 173.82/173.83 => 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)) ) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__atLeastAtMost__int,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__uminus__lessThan,axiom, % 173.82/173.83 ! [V_x_2,T_b] : % 173.82/173.83 ( class_Groups_Oordered__ab__group__add(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__greaterThanAtMost__int,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_greaterThan__eq__iff,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2) % 173.82/173.83 <=> V_x_2 = V_y_2 ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__Suc__atLeastLessThan,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__Suc__atLeastAtMost,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__add__atLeastLessThan,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__add__atLeastAtMost,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__eq__setsum,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__int__nat__set__return__embed,axiom, % 173.82/173.83 ! [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 ). % 173.82/173.83 % 173.82/173.83 fof(fact_greaterThan__subset__iff,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( 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))) % 173.82/173.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__constant,axiom, % 173.82/173.83 ! [V_A_2,V_y_2,T_c,T_b] : % 173.82/173.83 ( class_Rings_Osemiring__1(T_b) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__atLeastZeroLessThan__int,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__atLeastLessThan__int,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__add__int__atLeastLessThan,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__uminus__greaterThan,axiom, % 173.82/173.83 ! [V_x_2,T_b] : % 173.82/173.83 ( class_Groups_Oordered__ab__group__add(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__greaterThanLessThan__int,axiom, % 173.82/173.83 ! [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)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 173.82/173.83 ! [V_f_2,V_A_2,T_b] : % 173.82/173.83 ( ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 & class_Groups_Ocomm__monoid__mult(T_b) ) % 173.82/173.83 => ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2] : % 173.82/173.83 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.83 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 <=> 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))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2] : % 173.82/173.83 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.83 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 <=> 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))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 173.82/173.83 ! [V_A_2] : % 173.82/173.83 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__lessThan,axiom, % 173.82/173.83 ! [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 ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2] : % 173.82/173.83 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.83 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.82/173.83 => ( V_A_2 = V_B_2 % 173.82/173.83 <=> 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) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__atLeastLessThan,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__greaterThanAtMost,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_nat__set__def,axiom, % 173.82/173.83 ! [V_S_2] : % 173.82/173.83 ( c_Nat__Transfer_Onat__set(V_S_2) % 173.82/173.83 <=> ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__uminus__greaterThanLessThan,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,T_b] : % 173.82/173.83 ( class_Groups_Oordered__ab__group__add(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 173.82/173.83 ! [V_y_2,V_x_2] : % 173.82/173.83 ( c_Nat__Transfer_Ois__nat(V_x_2) % 173.82/173.83 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__atLeastAtMost,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_subset__card__intvl__is__intvl,axiom, % 173.82/173.83 ! [V_k_2,V_A_2] : % 173.82/173.83 ( 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))))) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 173.82/173.83 ! [V_y_2,V_x_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 173.82/173.83 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__nat__int__set__return__embed,axiom, % 173.82/173.83 ! [V_A_2] : % 173.82/173.83 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.83 => 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 ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 173.82/173.83 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 173.82/173.83 ( ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 & class_Groups_Ocomm__monoid__mult(T_b) ) % 173.82/173.83 => ( V_A_2 = V_B_2 % 173.82/173.83 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.82/173.83 => ( ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 173.82/173.83 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 173.82/173.83 => 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) ) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I19_J,axiom, % 173.82/173.83 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 173.82/173.83 => 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) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I18_J,axiom, % 173.82/173.83 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 173.82/173.83 => 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) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup1E,axiom, % 173.82/173.83 ! [V_x_2,V_B_2,V_A_2,T_b] : % 173.82/173.83 ( 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)) % 173.82/173.83 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 173.82/173.83 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup1CI,axiom, % 173.82/173.83 ! [T_b,V_A_2,V_x_2,V_B_2] : % 173.82/173.83 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 173.82/173.83 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I9_J,axiom, % 173.82/173.83 ! [V_u_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__Un,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2] : % 173.82/173.83 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.83 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup1I1,axiom, % 173.82/173.83 ! [V_B_2,T_b,V_x_2,V_A_2] : % 173.82/173.83 ( hBOOL(hAPP(V_A_2,V_x_2)) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup1I2,axiom, % 173.82/173.83 ! [V_A_2,T_b,V_x_2,V_B_2] : % 173.82/173.83 ( hBOOL(hAPP(V_B_2,V_x_2)) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__absorb,axiom, % 173.82/173.83 ! [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 ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__commute,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__left__absorb,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__left__commute,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__assoc,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_bex__Un,axiom, % 173.82/173.83 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 173.82/173.83 ( ? [B_x] : % 173.82/173.83 ( 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))) % 173.82/173.83 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 173.82/173.83 <=> ( ? [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.83 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 173.82/173.83 | ? [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 173.82/173.83 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ball__Un,axiom, % 173.82/173.83 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 173.82/173.83 ( ! [B_x] : % 173.82/173.83 ( 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))) % 173.82/173.83 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 173.82/173.83 <=> ( ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.83 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 173.82/173.83 & ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 173.82/173.83 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup_Oidem,axiom, % 173.82/173.83 ! [V_a,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__idem,axiom, % 173.82/173.83 ! [V_x,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup_Ocommute,axiom, % 173.82/173.83 ! [V_b,V_a,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_inf__sup__aci_I5_J,axiom, % 173.82/173.83 ! [V_y,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Olattice(T_a) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__commute,axiom, % 173.82/173.83 ! [V_y,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup_Oleft__idem,axiom, % 173.82/173.83 ! [V_b,V_a,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_inf__sup__aci_I8_J,axiom, % 173.82/173.83 ! [V_y,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Olattice(T_a) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__left__idem,axiom, % 173.82/173.83 ! [V_y,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup_Oleft__commute,axiom, % 173.82/173.83 ! [V_c,V_a,V_b,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_inf__sup__aci_I7_J,axiom, % 173.82/173.83 ! [V_z,V_y,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Olattice(T_a) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__left__commute,axiom, % 173.82/173.83 ! [V_z,V_y,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup_Oassoc,axiom, % 173.82/173.83 ! [V_c,V_b,V_a,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_inf__sup__aci_I6_J,axiom, % 173.82/173.83 ! [V_z,V_y,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Olattice(T_a) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__assoc,axiom, % 173.82/173.83 ! [V_z,V_y,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__apply,axiom, % 173.82/173.83 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 173.82/173.83 ( class_Lattices_Olattice(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__fun__def,axiom, % 173.82/173.83 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 173.82/173.83 ( class_Lattices_Olattice(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__Diff__cancel,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__Diff__cancel2,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__Diff,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Sup__fin_Oidem,axiom, % 173.82/173.83 ! [V_x,T_a] : % 173.82/173.83 ( class_Lattices_Olattice(T_a) % 173.82/173.83 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__max,axiom, % 173.82/173.83 ! [T_b] : % 173.82/173.83 ( ( class_Lattices_Osemilattice__sup(T_b) % 173.82/173.83 & class_Orderings_Olinorder(T_b) ) % 173.82/173.83 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atMost__eq__iff,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2) % 173.82/173.83 <=> V_x_2 = V_y_2 ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_le__supE,axiom, % 173.82/173.83 ! [V_x,V_b,V_a,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => ( 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)) % 173.82/173.83 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 173.82/173.83 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__mono,axiom, % 173.82/173.83 ! [V_d,V_b,V_c,V_a,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 173.82/173.83 => 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))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__least,axiom, % 173.82/173.83 ! [V_z,V_x,V_y,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 173.82/173.83 => 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)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_le__supI,axiom, % 173.82/173.83 ! [V_b,V_x,V_a,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 173.82/173.83 => 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)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__absorb1,axiom, % 173.82/173.83 ! [V_x,V_y,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.82/173.83 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__absorb2,axiom, % 173.82/173.83 ! [V_y,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.82/173.83 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_le__supI2,axiom, % 173.82/173.83 ! [V_a,V_b,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_le__supI1,axiom, % 173.82/173.83 ! [V_b,V_a,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_le__sup__iff,axiom, % 173.82/173.83 ! [V_z_2,V_y_2,V_x_2,T_b] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_b) % 173.82/173.83 => ( 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)) % 173.82/173.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 173.82/173.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_le__iff__sup,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,T_b] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.82/173.83 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__ge2,axiom, % 173.82/173.83 ! [V_x,V_y,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_inf__sup__ord_I4_J,axiom, % 173.82/173.83 ! [V_x,V_y,T_a] : % 173.82/173.83 ( class_Lattices_Olattice(T_a) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__ge1,axiom, % 173.82/173.83 ! [V_y,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_inf__sup__ord_I3_J,axiom, % 173.82/173.83 ! [V_y,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Olattice(T_a) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__upper1,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__upper2,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_subset__Un__eq,axiom, % 173.82/173.83 ! [V_B_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__absorb1,axiom, % 173.82/173.83 ! [V_B_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__absorb2,axiom, % 173.82/173.83 ! [V_A_2,V_B_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.83 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__least,axiom, % 173.82/173.83 ! [V_B_2,V_C_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__mono,axiom, % 173.82/173.83 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_less__supI2,axiom, % 173.82/173.83 ! [V_a,V_b,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_less__supI1,axiom, % 173.82/173.83 ! [V_b,V_a,V_x,T_a] : % 173.82/173.83 ( class_Lattices_Osemilattice__sup(T_a) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__atMost,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I10_J,axiom, % 173.82/173.83 ! [V_u_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I7_J,axiom, % 173.82/173.83 ! [V_u_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I17_J,axiom, % 173.82/173.83 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 173.82/173.83 => 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) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Diff__partition,axiom, % 173.82/173.83 ! [V_B_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 => 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 ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Diff__subset__conv,axiom, % 173.82/173.83 ! [V_C_2,V_B_2,V_A_2,T_b] : % 173.82/173.83 ( 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)) % 173.82/173.83 <=> 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I20_J,axiom, % 173.82/173.83 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 173.82/173.83 => 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) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Compl__Diff__eq,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2] : % 173.82/173.83 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.83 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeast0AtMost,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__greaterThanLessThan,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_lessThan__Suc__atMost,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atMost__subset__iff,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( 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))) % 173.82/173.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I21_J,axiom, % 173.82/173.83 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 173.82/173.83 => 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) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastLessThan__add__Un,axiom, % 173.82/173.83 ! [V_k_2,V_j_2,V_i_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I8_J,axiom, % 173.82/173.83 ! [V_u_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I22_J,axiom, % 173.82/173.83 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 173.82/173.83 => 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) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I11_J,axiom, % 173.82/173.83 ! [V_u_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Compl__atMost,axiom, % 173.82/173.83 ! [V_k_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Compl__greaterThan,axiom, % 173.82/173.83 ! [V_k_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I15_J,axiom, % 173.82/173.83 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 173.82/173.83 => 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) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I16_J,axiom, % 173.82/173.83 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 173.82/173.83 => 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) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__atMost__Suc,axiom, % 173.82/173.83 ! [V_n_2,V_f_2,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I12_J,axiom, % 173.82/173.83 ! [V_u_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I13_J,axiom, % 173.82/173.83 ! [V_u_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_hoare__derivs_OBody,axiom, % 173.82/173.83 ! [V_Procs_2,V_Q_2,V_Pa_2,V_Ga_2,T_b] : % 173.82/173.83 ( 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)) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__le__eq__Un0,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__nat__def,axiom, % 173.82/173.83 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 173.82/173.83 % 173.82/173.83 fof(fact_asm,axiom, % 173.82/173.83 ! [V_Ga_2,V_ts_2,T_b] : % 173.82/173.83 ( 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)) % 173.82/173.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_weaken,axiom, % 173.82/173.83 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] : % 173.82/173.83 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2) % 173.82/173.83 => ( 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)) % 173.82/173.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_thin,axiom, % 173.82/173.83 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] : % 173.82/173.83 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) % 173.82/173.83 => ( 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)) % 173.82/173.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeast__eq__iff,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2) % 173.82/173.83 <=> V_x_2 = V_y_2 ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_cut,axiom, % 173.82/173.83 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] : % 173.82/173.83 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) % 173.82/173.83 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2) % 173.82/173.83 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_SUP1__iff,axiom, % 173.82/173.83 ! [V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 173.82/173.83 ( 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)) % 173.82/173.83 <=> ? [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.83 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_ba_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeast__Suc__greaterThan,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeast__subset__iff,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( 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))) % 173.82/173.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Compl__atLeast,axiom, % 173.82/173.83 ! [V_k_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Compl__lessThan,axiom, % 173.82/173.83 ! [V_k_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__le__add__shift,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I14_J,axiom, % 173.82/173.83 ! [V_u_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__uminus__atLeast,axiom, % 173.82/173.83 ! [V_x_2,T_b] : % 173.82/173.83 ( class_Groups_Oordered__ab__group__add(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__uminus__atMost,axiom, % 173.82/173.83 ! [V_x_2,T_b] : % 173.82/173.83 ( class_Groups_Oordered__ab__group__add(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_SUP__subset,axiom, % 173.82/173.83 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.83 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__extend__simps_I6_J,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__simps_I6_J,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_SUPR__apply,axiom, % 173.82/173.83 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 173.82/173.83 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ball__UN,axiom, % 173.82/173.83 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] : % 173.82/173.83 ( ! [B_x] : % 173.82/173.83 ( 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))) % 173.82/173.83 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 173.82/173.83 <=> ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 173.82/173.83 => ! [B_xa] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) % 173.82/173.83 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_SUP__commute,axiom, % 173.82/173.83 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 173.82/173.83 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__UN__flatten,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__simps_I9_J,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__extend__simps_I9_J,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_SUP__le__iff,axiom, % 173.82/173.83 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] : % 173.82/173.83 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.82/173.83 => ( 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)) % 173.82/173.83 <=> ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_less__SUP__iff,axiom, % 173.82/173.83 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] : % 173.82/173.83 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 173.82/173.83 & class_Orderings_Olinorder(T_b) ) % 173.82/173.83 => ( 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))) % 173.82/173.83 <=> ? [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 173.82/173.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__subset__iff,axiom, % 173.82/173.83 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : % 173.82/173.83 ( 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)) % 173.82/173.83 <=> ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__extend__simps_I10_J,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__UN,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__simps_I10_J,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__Un__distrib,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__Un,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_greaterThan__0,axiom, % 173.82/173.83 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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd_OatLeastatMost__psubset__iff,axiom, % 173.82/173.83 ! [V_d_2,V_ca_2,V_ba_2,V_a_2] : % 173.82/173.83 ( 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))) % 173.82/173.83 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) % 173.82/173.83 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2)) % 173.82/173.83 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_d_2)) % 173.82/173.83 & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2)) % 173.82/173.83 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ca_2)) ) % 173.82/173.83 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_d_2)) % 173.82/173.83 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_ba_2)) ) ) ) ) % 173.82/173.83 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_d_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd_OmonoI,axiom, % 173.82/173.83 ! [V_f_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( ! [B_x,B_y] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) ) % 173.82/173.83 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_upto_Opinduct,axiom, % 173.82/173.83 ! [V_Pa_2,V_a1_2,V_a0_2] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ( ! [B_i,B_j] : % 173.82/173.83 ( 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))) % 173.82/173.83 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 173.82/173.83 => 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)) ) % 173.82/173.83 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) % 173.82/173.83 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_top1I,axiom, % 173.82/173.83 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__UNIV__left,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__UNIV__right,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_subset__UNIV,axiom, % 173.82/173.83 ! [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)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_top__apply,axiom, % 173.82/173.83 ! [V_x_2,T_c,T_b] : % 173.82/173.83 ( class_Orderings_Otop(T_b) % 173.82/173.83 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_range__composition,axiom, % 173.82/173.83 ! [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)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_top__greatest,axiom, % 173.82/173.83 ! [V_x,T_a] : % 173.82/173.83 ( class_Orderings_Otop(T_a) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__top__right,axiom, % 173.82/173.83 ! [V_x,T_a] : % 173.82/173.83 ( class_Lattices_Obounded__lattice__top(T_a) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__top__left,axiom, % 173.82/173.83 ! [V_x,T_a] : % 173.82/173.83 ( class_Lattices_Obounded__lattice__top(T_a) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__lessThan__UNIV,axiom, % 173.82/173.83 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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__atMost__UNIV,axiom, % 173.82/173.83 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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__atLeast__UNIV,axiom, % 173.82/173.83 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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Compl__partition2,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Compl__partition,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Compl__eq__Diff__UNIV,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeast__0,axiom, % 173.82/173.83 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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_compl__sup__top,axiom, % 173.82/173.83 ! [V_x,T_a] : % 173.82/173.83 ( class_Lattices_Oboolean__algebra(T_a) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__compl__top,axiom, % 173.82/173.83 ! [V_x,T_a] : % 173.82/173.83 ( class_Lattices_Oboolean__algebra(T_a) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__UN__finite__eq,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd_OatLeastatMost__subset__iff,axiom, % 173.82/173.83 ! [V_d_2,V_ca_2,V_ba_2,V_a_2] : % 173.82/173.83 ( 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))) % 173.82/173.83 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) % 173.82/173.83 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2)) % 173.82/173.83 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_d_2)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_surj__Compl__image__subset,axiom, % 173.82/173.83 ! [V_A_2,V_f_2,T_b,T_c] : % 173.82/173.83 ( 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)) % 173.82/173.83 => 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)))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__finite2__subset,axiom, % 173.82/173.83 ! [V_B_2,V_k_2,V_A_2,T_b] : % 173.82/173.83 ( ! [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))) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__finite2__eq,axiom, % 173.82/173.83 ! [V_B_2,V_k_2,V_A_2,T_b] : % 173.82/173.83 ( ! [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) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__finite__subset,axiom, % 173.82/173.83 ! [V_C_2,V_A_2,T_b] : % 173.82/173.83 ( ! [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)) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__UNIV__bool,axiom, % 173.82/173.83 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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__ident,axiom, % 173.82/173.83 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 173.82/173.83 % 173.82/173.83 fof(fact_type__definition__code__numeral,axiom, % 173.82/173.83 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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__diff__nat,axiom, % 173.82/173.83 ! [V_f_2,V_A_2,V_B_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__diff,axiom, % 173.82/173.83 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.83 ( class_Groups_Oab__group__add(T_c) % 173.82/173.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.83 => 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)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__atLeastLessThan,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__atLeastAtMost__int,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__atLeastAtMost,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__lessThan,axiom, % 173.82/173.83 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__atMost,axiom, % 173.82/173.83 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__atLeastLessThan__int,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__greaterThanAtMost,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__greaterThanAtMost__int,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__greaterThanLessThan__int,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__greaterThanLessThan,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__insert__right,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__insert__left,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_subset__insertI,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_subset__insertI2,axiom, % 173.82/173.83 ! [V_ba_2,V_B_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_insert__mono,axiom, % 173.82/173.83 ! [V_a_2,V_D_2,V_C_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 173.82/173.83 ! [V_N_2] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 173.82/173.83 <=> ? [B_m] : % 173.82/173.83 ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__nat__set__iff__bounded,axiom, % 173.82/173.83 ! [V_N_2] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 173.82/173.83 <=> ? [B_m] : % 173.82/173.83 ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_insert__code,axiom, % 173.82/173.83 ! [V_x_2,V_A_2,V_y_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) % 173.82/173.83 <=> ( V_y_2 = V_x_2 % 173.82/173.83 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_insert__commute,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_insert__absorb2,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 173.82/173.83 ! [V_A_2] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 173.82/173.83 <=> 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__insert,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 173.82/173.83 ! [V_A_2] : % 173.82/173.83 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 173.82/173.83 <=> 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum_Oinfinite,axiom, % 173.82/173.83 ! [V_g_2,V_A_2,T_b,T_c] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.83 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__infinite,axiom, % 173.82/173.83 ! [V_f_2,V_A_2,T_b,T_c] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.83 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_lessThan__Suc,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atMost__Suc,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__eq__0__iff,axiom, % 173.82/173.83 ! [V_f_2,V_F_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 173.82/173.83 => ( 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) % 173.82/173.83 <=> ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 173.82/173.83 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__insert,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum_Odistrib,axiom, % 173.82/173.83 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastAtMostSuc__conv,axiom, % 173.82/173.83 ! [V_n_2,V_m_2] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__eq__Suc0__iff,axiom, % 173.82/173.83 ! [V_f_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => ( 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)) % 173.82/173.83 <=> ? [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.83 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 173.82/173.83 & ! [B_xa] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 173.82/173.83 => ( B_x != B_xa % 173.82/173.83 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__eq__1__iff,axiom, % 173.82/173.83 ! [V_f_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => ( 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) % 173.82/173.83 <=> ? [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.83 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 173.82/173.83 & ! [B_xa] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 173.82/173.83 => ( B_x != B_xa % 173.82/173.83 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__psubset,axiom, % 173.82/173.83 ! [V_A_2,V_B_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 => ( 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))) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_diff__card__le__card__Diff,axiom, % 173.82/173.83 ! [V_A_2,V_B_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.83 => 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)))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__Diff__subset,axiom, % 173.82/173.83 ! [V_A_2,V_B_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__Diff,axiom, % 173.82/173.83 ! [V_B_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite_OinsertI,axiom, % 173.82/173.83 ! [V_a_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__imageI,axiom, % 173.82/173.83 ! [V_h_2,T_c,V_F_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 173.82/173.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_infinite__UNIV__int,axiom, % 173.82/173.83 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UNIV__option__conv,axiom, % 173.82/173.83 ! [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)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__code,axiom, % 173.82/173.83 ! [V_A_2,T_b] : % 173.82/173.83 ( class_Finite__Set_Ofinite(T_b) % 173.82/173.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite,axiom, % 173.82/173.83 ! [V_A_2,T_b] : % 173.82/173.83 ( class_Finite__Set_Ofinite(T_b) % 173.82/173.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__UNIV__unit,axiom, % 173.82/173.83 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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_infinite__UNIV__nat,axiom, % 173.82/173.83 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__insert,axiom, % 173.82/173.83 ! [V_A_2,V_a_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) % 173.82/173.83 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_rev__finite__subset,axiom, % 173.82/173.83 ! [V_A_2,V_B_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__subset,axiom, % 173.82/173.83 ! [V_B_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__Prod__UNIV,axiom, % 173.82/173.83 ! [T_c,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 173.82/173.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 173.82/173.83 => 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)))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__fun__UNIVD2,axiom, % 173.82/173.83 ! [T_c,T_b] : % 173.82/173.83 ( 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)))) % 173.82/173.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__Plus__UNIV__iff,axiom, % 173.82/173.83 ! [T_c,T_b] : % 173.82/173.83 ( 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)))) % 173.82/173.83 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 173.82/173.83 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__option__UNIV,axiom, % 173.82/173.83 ! [T_b] : % 173.82/173.83 ( 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)))) % 173.82/173.83 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__UNIV,axiom, % 173.82/173.83 ! [T_b] : % 173.82/173.83 ( class_Finite__Set_Ofinite(T_b) % 173.82/173.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__Un,axiom, % 173.82/173.83 ! [V_Ga_2,V_F_2,T_b] : % 173.82/173.83 ( 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))) % 173.82/173.83 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 173.82/173.83 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__UnI,axiom, % 173.82/173.83 ! [V_Ga_2,V_F_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 173.82/173.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__Diff2,axiom, % 173.82/173.83 ! [V_A_2,V_B_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.83 => ( 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))) % 173.82/173.83 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__UN,axiom, % 173.82/173.83 ! [V_B_2,T_c,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => ( 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))) % 173.82/173.83 <=> ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__surj,axiom, % 173.82/173.83 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => ( 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))) % 173.82/173.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__Diff__insert,axiom, % 173.82/173.83 ! [V_B_2,V_a_2,V_A_2,T_b] : % 173.82/173.83 ( 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)))) % 173.82/173.83 <=> 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__infinite,axiom, % 173.82/173.83 ! [V_A_2,T_b] : % 173.82/173.83 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 173.82/173.83 ! [V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 173.82/173.83 => ( 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))) % 173.82/173.83 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__compl,axiom, % 173.82/173.83 ! [V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 173.82/173.83 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__range__imageI,axiom, % 173.82/173.83 ! [V_f_2,T_d,V_g_2,T_c,T_b] : % 173.82/173.83 ( 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))))) % 173.82/173.83 => 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))))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__ge__0__finite,axiom, % 173.82/173.83 ! [V_A_2,T_b] : % 173.82/173.83 ( 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))) % 173.82/173.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__insert__le,axiom, % 173.82/173.83 ! [V_x_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => 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)))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__mono,axiom, % 173.82/173.83 ! [V_A_2,V_B_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__seteq,axiom, % 173.82/173.83 ! [V_A_2,V_B_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 => ( 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))) % 173.82/173.83 => V_A_2 = V_B_2 ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__image__le,axiom, % 173.82/173.83 ! [V_f_2,T_c,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_psubset__card__mono,axiom, % 173.82/173.83 ! [V_A_2,V_B_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__UNIV__card__ge__0,axiom, % 173.82/173.83 ! [T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 173.82/173.83 => 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))))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite__fun__UNIVD1,axiom, % 173.82/173.83 ! [T_c,T_b] : % 173.82/173.83 ( 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)))) % 173.82/173.83 => ( 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)) % 173.82/173.83 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_type__definition_OAbs__image,axiom, % 173.82/173.83 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 173.82/173.83 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_type__definition_ORep__range,axiom, % 173.82/173.83 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 173.82/173.83 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 173.82/173.83 => 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 ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 173.82/173.83 ! [V_x_2,V_y_2,V_ca_2] : % 173.82/173.83 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 173.82/173.83 => 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)) ) % 173.82/173.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 173.82/173.83 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 173.82/173.83 => 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))) ) % 173.82/173.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 173.82/173.83 => 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)) ) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite_OemptyI,axiom, % 173.82/173.83 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_empty__subsetI,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_finite_Oequations_I1_J,axiom, % 173.82/173.83 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_singleton__inject,axiom, % 173.82/173.83 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( 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))) % 173.82/173.83 => V_a_2 = V_ba_2 ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_doubleton__eq__iff,axiom, % 173.82/173.83 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( 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)))) % 173.82/173.83 <=> ( ( V_a_2 = V_ca_2 % 173.82/173.83 & V_ba_2 = V_d_2 ) % 173.82/173.83 | ( V_a_2 = V_d_2 % 173.82/173.83 & V_ba_2 = V_ca_2 ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_insert__not__empty,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_empty__not__insert,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__empty__left,axiom, % 173.82/173.83 ! [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 ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__empty__right,axiom, % 173.82/173.83 ! [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 ). % 173.82/173.83 % 173.82/173.83 fof(fact_Un__empty,axiom, % 173.82/173.83 ! [V_B_2,V_A_2,T_b] : % 173.82/173.83 ( 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)) % 173.82/173.83 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_subset__empty,axiom, % 173.82/173.83 ! [V_A_2,T_b] : % 173.82/173.83 ( 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)))) % 173.82/173.83 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_not__psubset__empty,axiom, % 173.82/173.83 ! [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)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_bot__fun__def,axiom, % 173.82/173.83 ! [V_x_2,T_c,T_b] : % 173.82/173.83 ( class_Orderings_Obot(T_b) % 173.82/173.83 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_bot__apply,axiom, % 173.82/173.83 ! [V_x_2,T_c,T_b] : % 173.82/173.83 ( class_Orderings_Obot(T_b) % 173.82/173.83 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Diff__cancel,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Diff__empty,axiom, % 173.82/173.83 ! [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 ). % 173.82/173.83 % 173.82/173.83 fof(fact_empty__Diff,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ball__empty,axiom, % 173.82/173.83 ! [V_Pa_2,T_b,B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 173.82/173.83 => hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__is__empty,axiom, % 173.82/173.83 ! [V_A_2,V_f_2,T_b,T_c] : % 173.82/173.83 ( 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)) % 173.82/173.83 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__empty,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_empty__is__image,axiom, % 173.82/173.83 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.83 ( 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) % 173.82/173.83 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UNIV__not__empty,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_bot__least,axiom, % 173.82/173.83 ! [V_x,T_a] : % 173.82/173.83 ( class_Orderings_Obot(T_a) % 173.82/173.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_SUP__const,axiom, % 173.82/173.83 ! [V_M_2,T_b,V_A_2,T_c] : % 173.82/173.83 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 173.82/173.83 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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 ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UNION__empty__conv_I2_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2,T_b,T_c] : % 173.82/173.83 ( 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)) % 173.82/173.83 <=> ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 173.82/173.83 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__constant,axiom, % 173.82/173.83 ! [V_ca_2,T_c,T_b,V_A_2] : % 173.82/173.83 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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)) ) % 173.82/173.83 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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 ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__empty2,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UNION__empty__conv_I1_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2,T_c,T_b] : % 173.82/173.83 ( 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) % 173.82/173.83 <=> ! [B_x] : % 173.82/173.83 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 173.82/173.83 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__eq__bot__iff,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,T_b] : % 173.82/173.83 ( class_Lattices_Obounded__lattice__bot(T_b) % 173.82/173.83 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b) % 173.82/173.83 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b) % 173.82/173.83 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__bot__right,axiom, % 173.82/173.83 ! [V_x,T_a] : % 173.82/173.83 ( class_Lattices_Obounded__lattice__bot(T_a) % 173.82/173.83 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_sup__bot__left,axiom, % 173.82/173.83 ! [V_x,T_a] : % 173.82/173.83 ( class_Lattices_Obounded__lattice__bot(T_a) % 173.82/173.83 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum_Oempty,axiom, % 173.82/173.83 ! [V_g_2,T_c,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum__empty,axiom, % 173.82/173.83 ! [V_f_2,T_c,T_b] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_subset__singletonD,axiom, % 173.82/173.83 ! [V_x_2,V_A_2,T_b] : % 173.82/173.83 ( 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))))) % 173.82/173.83 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 | 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_insert__is__Un,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastatMost__empty__iff,axiom, % 173.82/173.83 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( 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)) % 173.82/173.83 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastatMost__empty__iff2,axiom, % 173.82/173.83 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( 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) % 173.82/173.83 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastatMost__empty,axiom, % 173.82/173.83 ! [V_a_2,V_ba_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_insert__Diff__single,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Diff__insert2,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Diff__insert,axiom, % 173.82/173.83 ! [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)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastLessThan__empty,axiom, % 173.82/173.83 ! [V_a_2,V_ba_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card_Oempty,axiom, % 173.82/173.83 ! [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) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastLessThan__empty__iff,axiom, % 173.82/173.83 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( 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)) % 173.82/173.83 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastLessThan__empty__iff2,axiom, % 173.82/173.83 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( 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) % 173.82/173.83 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Diff__UNIV,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastAtMost__singleton,axiom, % 173.82/173.83 ! [V_a_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastAtMost__singleton__iff,axiom, % 173.82/173.83 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( 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))) % 173.82/173.83 <=> ( V_a_2 = V_ba_2 % 173.82/173.83 & V_ba_2 = V_ca_2 ) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastAtMost__singleton_H,axiom, % 173.82/173.83 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( V_a_2 = V_ba_2 % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_subset__Compl__self__eq,axiom, % 173.82/173.83 ! [V_A_2,T_b] : % 173.82/173.83 ( 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))) % 173.82/173.83 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Compl__UNIV__eq,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_Compl__empty__eq,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastLessThan0,axiom, % 173.82/173.83 ! [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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_greaterThanAtMost__empty,axiom, % 173.82/173.83 ! [V_k_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_greaterThanAtMost__empty__iff,axiom, % 173.82/173.83 ! [V_l_2,V_k_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( 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)) % 173.82/173.83 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 173.82/173.83 ! [V_l_2,V_k_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( 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) % 173.82/173.83 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_greaterThanLessThan__empty,axiom, % 173.82/173.83 ! [V_k_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_lessThan__0,axiom, % 173.82/173.83 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)) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__constant__conv,axiom, % 173.82/173.83 ! [V_ca_2,T_c,T_b,V_A_2] : % 173.82/173.83 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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)) ) % 173.82/173.83 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__extend__simps_I1_J,axiom, % 173.82/173.83 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 173.82/173.83 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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))) ) % 173.82/173.83 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__singleton,axiom, % 173.82/173.83 ! [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 ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__simps_I1_J,axiom, % 173.82/173.83 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 173.82/173.83 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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)) ) % 173.82/173.83 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom, % 173.82/173.83 ! [V_ba_2,V_a_2] : % 173.82/173.83 ( 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) % 173.82/173.83 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd_OatLeastatMost__empty__iff,axiom, % 173.82/173.83 ! [V_ba_2,V_a_2] : % 173.82/173.83 ( 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)) % 173.82/173.83 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd_OatLeastatMost__empty,axiom, % 173.82/173.83 ! [V_a_2,V_ba_2] : % 173.82/173.83 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) % 173.82/173.83 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) ) % 173.82/173.83 => 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)) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__extend__simps_I2_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 173.82/173.83 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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 ) % 173.82/173.83 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__extend__simps_I3_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 173.82/173.83 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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 ) % 173.82/173.83 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__simps_I2_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 173.82/173.83 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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)) ) % 173.82/173.83 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_UN__simps_I3_J,axiom, % 173.82/173.83 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 173.82/173.83 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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)) ) % 173.82/173.83 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_compl__bot__eq,axiom, % 173.82/173.83 ! [T_a] : % 173.82/173.83 ( class_Lattices_Oboolean__algebra(T_a) % 173.82/173.83 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_compl__top__eq,axiom, % 173.82/173.83 ! [T_a] : % 173.82/173.83 ( class_Lattices_Oboolean__algebra(T_a) % 173.82/173.83 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__eq__0__iff,axiom, % 173.82/173.83 ! [V_A_2,T_b] : % 173.82/173.83 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.83 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_single__Diff__lessThan,axiom, % 173.82/173.83 ! [V_k_2,T_b] : % 173.82/173.83 ( class_Orderings_Oorder(T_b) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_image__eq__UN,axiom, % 173.82/173.83 ! [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)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastLessThan__singleton,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atMost__0,axiom, % 173.82/173.83 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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_type__definition_ORep__inverse,axiom, % 173.82/173.83 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 173.82/173.83 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 173.82/173.83 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_type__definition_ORep__inject,axiom, % 173.82/173.83 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 173.82/173.83 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 173.82/173.83 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 173.82/173.83 <=> V_x_2 = V_y_2 ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom, % 173.82/173.83 ! [V_ba_2,V_a_2] : % 173.82/173.83 ( V_a_2 = V_ba_2 % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd_OatLeastAtMost__singleton,axiom, % 173.82/173.83 ! [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))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom, % 173.82/173.83 ! [V_ca_2,V_ba_2,V_a_2] : % 173.82/173.83 ( 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))) % 173.82/173.83 <=> ( V_a_2 = V_ba_2 % 173.82/173.83 & V_ba_2 = V_ca_2 ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeast__Suc,axiom, % 173.82/173.83 ! [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)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_greaterThan__Suc,axiom, % 173.82/173.83 ! [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)))) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__gt__0__iff,axiom, % 173.82/173.83 ! [V_A_2,T_b] : % 173.82/173.83 ( 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))) % 173.82/173.83 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.83 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I2_J,axiom, % 173.82/173.83 ! [V_u_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_atLeastLessThanSuc,axiom, % 173.82/173.83 ! [V_n_2,V_m_2] : % 173.82/173.83 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.82/173.83 => 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)) ) % 173.82/173.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 173.82/173.83 => 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)) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I1_J,axiom, % 173.82/173.83 ! [V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => 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) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_setsum_Oinsert__remove,axiom, % 173.82/173.83 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 173.82/173.83 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.83 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => 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)))))) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__insert,axiom, % 173.82/173.83 ! [V_x_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => 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)))))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_card__Diff1__le,axiom, % 173.82/173.83 ! [V_x_2,V_A_2,T_b] : % 173.82/173.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.83 => 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))) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I6_J,axiom, % 173.82/173.83 ! [V_u_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I5_J,axiom, % 173.82/173.83 ! [V_u_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I3_J,axiom, % 173.82/173.83 ! [V_u_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.83 % 173.82/173.83 fof(fact_ivl__disj__un_I4_J,axiom, % 173.82/173.83 ! [V_u_2,V_l_2,T_b] : % 173.82/173.83 ( class_Orderings_Olinorder(T_b) % 173.82/173.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 173.82/173.83 => 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) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card_Oinsert__remove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => 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)))))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_the__elem__def,axiom, % 173.82/173.84 ! [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))))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_dvd_OgreaterThanLessThan__empty,axiom, % 173.82/173.84 ! [V_k_2,V_l_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_the__elem__eq,axiom, % 173.82/173.84 ! [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 ). % 173.82/173.84 % 173.82/173.84 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 173.82/173.84 ! [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))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_derivs__insertD,axiom, % 173.82/173.84 ! [V_ts_2,V_t_2,V_Ga_2,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 => ( 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)))) % 173.82/173.84 & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_hoare__derivs_Oinsert,axiom, % 173.82/173.84 ! [V_ts_2,V_t_2,V_Ga_2,T_b] : % 173.82/173.84 ( 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)))) % 173.82/173.84 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 173.82/173.84 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 173.82/173.84 ! [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))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_empty,axiom, % 173.82/173.84 ! [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))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_bot__nat__def,axiom, % 173.82/173.84 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Comp,axiom, % 173.82/173.84 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] : % 173.82/173.84 ( 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)))) % 173.82/173.84 => ( 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)))) % 173.82/173.84 => 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)))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 173.82/173.84 ! [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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_hoare__derivs_OSkip,axiom, % 173.82/173.84 ! [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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 173.82/173.84 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))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 173.82/173.84 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))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_LoopF,axiom, % 173.82/173.84 ! [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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_simp__from__to,axiom, % 173.82/173.84 ! [V_i_2,V_j_2] : % 173.82/173.84 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 173.82/173.84 => 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)) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_hoare__derivs_Oequations_I8_J,axiom, % 173.82/173.84 ! [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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ass,axiom, % 173.82/173.84 ! [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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_set__empty__eq,axiom, % 173.82/173.84 ! [V_xo_2,T_b] : % 173.82/173.84 ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_weak__Body,axiom, % 173.82/173.84 ! [V_Q_2,V_pn_2,V_Pa_2,V_Ga_2,T_b] : % 173.82/173.84 ( 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)))) % 173.82/173.84 => 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)))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_BodyN,axiom, % 173.82/173.84 ! [V_Ga_2,V_Q_2,V_pn_2,V_Pa_2,T_b] : % 173.82/173.84 ( 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)))) % 173.82/173.84 => 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)))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Body1,axiom, % 173.82/173.84 ! [V_pn_2,V_Procs_2,V_Q_2,V_Pa_2,V_Ga_2,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2)) % 173.82/173.84 => 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)))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_nat__def,axiom, % 173.82/173.84 ! [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)))))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__mono3,axiom, % 173.82/173.84 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 173.82/173.84 ( ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.84 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.84 => ( ! [B_x] : % 173.82/173.84 ( 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))) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 173.82/173.84 => 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))) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card__Diff__singleton,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_equalityCE,axiom, % 173.82/173.84 ! [V_ca_2,T_b,V_B_2,V_A_2] : % 173.82/173.84 ( V_A_2 = V_B_2 % 173.82/173.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.84 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) % 173.82/173.84 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_SUP2__I,axiom, % 173.82/173.84 ! [T_d,T_c,V_ca_2,V_ba_2,V_B_2,V_A_2,V_a_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_emptyE,axiom, % 173.82/173.84 ! [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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_insertE,axiom, % 173.82/173.84 ! [V_A_2,V_ba_2,V_a_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_A_2))) % 173.82/173.84 => ( V_a_2 != V_ba_2 % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_insertCI,axiom, % 173.82/173.84 ! [V_ba_2,V_B_2,V_a_2,T_b] : % 173.82/173.84 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 173.82/173.84 => V_a_2 = V_ba_2 ) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_B_2))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_subsetD,axiom, % 173.82/173.84 ! [V_ca_2,V_B_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_UNIV__I,axiom, % 173.82/173.84 ! [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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_image__eqI,axiom, % 173.82/173.84 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_ba_2] : % 173.82/173.84 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_UnE,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_UnCI,axiom, % 173.82/173.84 ! [V_A_2,V_B_2,V_ca_2,T_b] : % 173.82/173.84 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_DiffI,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_DiffE,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ComplI,axiom, % 173.82/173.84 ! [V_A_2,V_ca_2,T_b] : % 173.82/173.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_SUP1__I,axiom, % 173.82/173.84 ! [T_c,V_ba_2,V_B_2,V_A_2,V_a_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_UN__I,axiom, % 173.82/173.84 ! [V_B_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_mem__splitI,axiom, % 173.82/173.84 ! [T_d,T_c,V_ba_2,V_a_2,V_ca_2,V_z_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_ba_2))) % 173.82/173.84 => 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)))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_pair__imageI,axiom, % 173.82/173.84 ! [V_f_2,T_d,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_bot__empty__eq2,axiom, % 173.82/173.84 ! [V_y_2,V_x_2,T_c,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> 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)))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_equals0D,axiom, % 173.82/173.84 ! [V_a_2,T_b,V_A_2] : % 173.82/173.84 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_empty__iff,axiom, % 173.82/173.84 ! [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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ex__in__conv,axiom, % 173.82/173.84 ! [V_A_2,T_b] : % 173.82/173.84 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.84 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_all__not__in__conv,axiom, % 173.82/173.84 ! [V_A_2,T_b] : % 173.82/173.84 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.84 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Diff__iff,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.84 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_DiffD1,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_DiffD2,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_bot__empty__eq,axiom, % 173.82/173.84 ! [V_x_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ord_OatLeastAtMost__iff,axiom, % 173.82/173.84 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 173.82/173.84 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_pred__equals__eq2,axiom, % 173.82/173.84 ! [V_S_2,V_R_2,T_c,T_b] : % 173.82/173.84 ( 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) % 173.82/173.84 <=> V_R_2 = V_S_2 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_sup__Un__eq2,axiom, % 173.82/173.84 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_pred__subset__eq,axiom, % 173.82/173.84 ! [V_S_2,V_R_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Un__iff,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.84 | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_UnI1,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_UnI2,axiom, % 173.82/173.84 ! [V_A_2,V_B_2,V_ca_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_in__mono,axiom, % 173.82/173.84 ! [V_x_2,V_B_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_set__rev__mp,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_set__mp,axiom, % 173.82/173.84 ! [V_x_2,V_B_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_psubsetD,axiom, % 173.82/173.84 ! [V_ca_2,V_B_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Rep__Integ__inject,axiom, % 173.82/173.84 ! [V_y_2,V_x_2] : % 173.82/173.84 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 173.82/173.84 <=> V_x_2 = V_y_2 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_eq__mem__trans,axiom, % 173.82/173.84 ! [V_A_2,T_b,V_ba_2,V_a_2] : % 173.82/173.84 ( V_a_2 = V_ba_2 % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_eqelem__imp__iff,axiom, % 173.82/173.84 ! [V_A_2,T_b,V_y_2,V_x_2] : % 173.82/173.84 ( V_x_2 = V_y_2 % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_eqset__imp__iff,axiom, % 173.82/173.84 ! [V_x_2,T_b,V_B_2,V_A_2] : % 173.82/173.84 ( V_A_2 = V_B_2 % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_mem__def,axiom, % 173.82/173.84 ! [V_A_2,V_x_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_eq__mem,axiom, % 173.82/173.84 ! [V_y_2,V_x_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2))) % 173.82/173.84 <=> V_x_2 = V_y_2 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_pred__equals__eq,axiom, % 173.82/173.84 ! [V_S_2,V_R_2,T_b] : % 173.82/173.84 ( 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) % 173.82/173.84 <=> V_R_2 = V_S_2 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ComplE,axiom, % 173.82/173.84 ! [V_A_2,V_ca_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ComplD,axiom, % 173.82/173.84 ! [V_A_2,V_ca_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Compl__iff,axiom, % 173.82/173.84 ! [V_A_2,V_ca_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_type__definition_ORep,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 173.82/173.84 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_type__definition_OAbs__inverse,axiom, % 173.82/173.84 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 173.82/173.84 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 173.82/173.84 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_type__definition_OAbs__inject,axiom, % 173.82/173.84 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 173.82/173.84 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 173.82/173.84 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 173.82/173.84 <=> V_x_2 = V_y_2 ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_image__iff,axiom, % 173.82/173.84 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 173.82/173.84 <=> ? [B_x] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 173.82/173.84 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_imageI,axiom, % 173.82/173.84 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_rev__image__eqI,axiom, % 173.82/173.84 ! [T_c,V_f_2,V_ba_2,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( V_ba_2 = hAPP(V_f_2,V_x_2) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 173.82/173.84 ! [V_A_2,V_x_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 173.82/173.84 <=> 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_insertI1,axiom, % 173.82/173.84 ! [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))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_insert__iff,axiom, % 173.82/173.84 ! [V_A_2,V_ba_2,V_a_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_A_2))) % 173.82/173.84 <=> ( V_a_2 = V_ba_2 % 173.82/173.84 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_insert__ident,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 173.82/173.84 => ( 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) % 173.82/173.84 <=> V_A_2 = V_B_2 ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_insertI2,axiom, % 173.82/173.84 ! [V_ba_2,V_B_2,V_a_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_B_2))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_insert__absorb,axiom, % 173.82/173.84 ! [V_A_2,V_a_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_sup__Un__eq,axiom, % 173.82/173.84 ! [V_x_2,V_S_2,V_R_2,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_UN__iff,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ? [B_x] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 173.82/173.84 & hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,B_x))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_singletonE,axiom, % 173.82/173.84 ! [V_a_2,V_ba_2,T_b] : % 173.82/173.84 ( 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))))) % 173.82/173.84 => V_ba_2 = V_a_2 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_singleton__iff,axiom, % 173.82/173.84 ! [V_a_2,V_ba_2,T_b] : % 173.82/173.84 ( 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))))) % 173.82/173.84 <=> V_ba_2 = V_a_2 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_insert__subset,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 173.82/173.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_subset__insert,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( 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))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_insert__image,axiom, % 173.82/173.84 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_range__eqI,axiom, % 173.82/173.84 ! [T_c,T_b,V_x_2,V_f_2,V_ba_2] : % 173.82/173.84 ( V_ba_2 = hAPP(V_f_2,V_x_2) % 173.82/173.84 => 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))))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_rangeI,axiom, % 173.82/173.84 ! [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))))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_insert__Diff1,axiom, % 173.82/173.84 ! [V_A_2,V_B_2,V_x_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_insert__Diff__if,axiom, % 173.82/173.84 ! [V_A_2,V_B_2,V_x_2,T_b] : % 173.82/173.84 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 173.82/173.84 => 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) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_lessThan__iff,axiom, % 173.82/173.84 ! [V_k_2,V_i_2,T_b] : % 173.82/173.84 ( class_Orderings_Oord(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 173.82/173.84 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 173.82/173.84 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 173.82/173.84 ! [V_A_2,V_x_2] : % 173.82/173.84 ( c_Nat__Transfer_Ois__nat(V_x_2) % 173.82/173.84 => ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 173.82/173.84 <=> 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))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_atMost__iff,axiom, % 173.82/173.84 ! [V_k_2,V_i_2,T_b] : % 173.82/173.84 ( class_Orderings_Oord(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_atLeast__iff,axiom, % 173.82/173.84 ! [V_k_2,V_i_2,T_b] : % 173.82/173.84 ( class_Orderings_Oord(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_greaterThan__iff,axiom, % 173.82/173.84 ! [V_k_2,V_i_2,T_b] : % 173.82/173.84 ( class_Orderings_Oord(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_code__numeral_Oof__nat__inject,axiom, % 173.82/173.84 ! [V_y_2,V_x_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 173.82/173.84 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 173.82/173.84 <=> V_x_2 = V_y_2 ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_le__SUPI,axiom, % 173.82/173.84 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 173.82/173.84 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_nat__of,axiom, % 173.82/173.84 ! [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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 173.82/173.84 ! [V_x_2,V_A_2] : % 173.82/173.84 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 173.82/173.84 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_SUP__UN__eq2,axiom, % 173.82/173.84 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_UN__insert__distrib,axiom, % 173.82/173.84 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_UN__upper,axiom, % 173.82/173.84 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_SUP__UN__eq,axiom, % 173.82/173.84 ! [V_x_2,V_r_2,T_c,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_UN__absorb,axiom, % 173.82/173.84 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_elem__set,axiom, % 173.82/173.84 ! [V_xo_2,V_x_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2))) % 173.82/173.84 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_pred__subset__eq2,axiom, % 173.82/173.84 ! [V_S_2,V_R_2,T_c,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_insert__Diff,axiom, % 173.82/173.84 ! [V_A_2,V_a_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Diff__insert__absorb,axiom, % 173.82/173.84 ! [V_A_2,V_x_2,T_b] : % 173.82/173.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 173.82/173.84 ! [V_x_2,V_A_2] : % 173.82/173.84 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__delta_H,axiom, % 173.82/173.84 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 173.82/173.84 => 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) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__delta,axiom, % 173.82/173.84 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 173.82/173.84 => 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) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_image__constant,axiom, % 173.82/173.84 ! [V_ca_2,T_c,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_of__nat__inverse,axiom, % 173.82/173.84 ! [V_y_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 173.82/173.84 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum_Oinsert,axiom, % 173.82/173.84 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__insert,axiom, % 173.82/173.84 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_diff__single__insert,axiom, % 173.82/173.84 ! [V_B_2,V_x_2,V_A_2,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_subset__insert__iff,axiom, % 173.82/173.84 ! [V_B_2,V_x_2,V_A_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card__insert__if,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card__insert__disjoint,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card_Oinsert,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_psubset__insert__iff,axiom, % 173.82/173.84 ! [V_B_2,V_x_2,V_A_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 173.82/173.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__diff1__nat,axiom, % 173.82/173.84 ! [V_f_2,V_A_2,V_a_2,T_b] : % 173.82/173.84 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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)) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum_Oremove,axiom, % 173.82/173.84 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)))))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__diff1_H,axiom, % 173.82/173.84 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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)))))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__diff1,axiom, % 173.82/173.84 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Oab__group__add(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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)) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__diff1__ring,axiom, % 173.82/173.84 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Rings_Oring(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card__Suc__Diff1,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card__Diff2__less,axiom, % 173.82/173.84 ! [V_y_2,V_x_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 173.82/173.84 => 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))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card__Diff1__less,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card__Diff__insert,axiom, % 173.82/173.84 ! [V_B_2,V_a_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card_Oremove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)))))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card__Diff__singleton__if,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_in__rel__def,axiom, % 173.82/173.84 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2)) % 173.82/173.84 <=> 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_finite__pointwise,axiom, % 173.82/173.84 ! [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] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_U_2)) % 173.82/173.84 => ( ! [B_p] : % 173.82/173.84 ( 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)))) % 173.82/173.84 => 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)))) ) % 173.82/173.84 => ( 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)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 173.82/173.84 ! [V_f_2,V_A_2,T_b] : % 173.82/173.84 ( ! [B_x] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.84 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_bset_I8_J,axiom, % 173.82/173.84 ! [V_B_2,V_t_2,V_D_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.82/173.84 => ( 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)) % 173.82/173.84 => ! [B_x] : % 173.82/173.84 ( ! [B_xa] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ! [B_xb] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 173.82/173.84 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 173.82/173.84 => 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))) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_sup2CI,axiom, % 173.82/173.84 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] : % 173.82/173.84 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_sup2E,axiom, % 173.82/173.84 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_bot2E,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_less__by__empty,axiom, % 173.82/173.84 ! [V_B_2,T_b,V_A_2] : % 173.82/173.84 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_SUP2__iff,axiom, % 173.82/173.84 ! [V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> ? [B_x] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.84 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_sup2I2,axiom, % 173.82/173.84 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_sup2I1,axiom, % 173.82/173.84 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Nitpick_Orefl_H__def,axiom, % 173.82/173.84 ! [V_r_2,T_b] : % 173.82/173.84 ( c_Nitpick_Orefl_H(T_b,V_r_2) % 173.82/173.84 <=> ! [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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_aset_I6_J,axiom, % 173.82/173.84 ! [V_A_2,V_t_2,V_D_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.82/173.84 => ( 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)) % 173.82/173.84 => ! [B_x] : % 173.82/173.84 ( ! [B_xa] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ! [B_xb] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 173.82/173.84 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_dvd_OgreaterThan__iff,axiom, % 173.82/173.84 ! [V_k_2,V_i_2] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) % 173.82/173.84 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ord_OgreaterThan__iff,axiom, % 173.82/173.84 ! [V_k_2,V_less_2,V_i_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_dvd_OlessThan__iff,axiom, % 173.82/173.84 ! [V_k_2,V_i_2] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) % 173.82/173.84 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_aset_I4_J,axiom, % 173.82/173.84 ! [V_A_2,V_t_2,V_D_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 173.82/173.84 => ! [B_x] : % 173.82/173.84 ( ! [B_xa] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ! [B_xb] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 173.82/173.84 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.84 => ( B_x != V_t_2 % 173.82/173.84 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_bset_I4_J,axiom, % 173.82/173.84 ! [V_B_2,V_t_2,V_D_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 173.82/173.84 => ! [B_x] : % 173.82/173.84 ( ! [B_xa] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ! [B_xb] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 173.82/173.84 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.84 => ( B_x != V_t_2 % 173.82/173.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ord_OlessThan__iff,axiom, % 173.82/173.84 ! [V_k_2,V_less_2,V_i_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_bset_I3_J,axiom, % 173.82/173.84 ! [V_B_2,V_t_2,V_D_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.82/173.84 => ( 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)) % 173.82/173.84 => ( ! [B_x] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ! [B_xa] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 173.82/173.84 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 173.82/173.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_aset_I3_J,axiom, % 173.82/173.84 ! [V_A_2,V_t_2,V_D_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.82/173.84 => ( 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)) % 173.82/173.84 => ( ! [B_x] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ! [B_xa] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 173.82/173.84 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 173.82/173.84 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_aset_I5_J,axiom, % 173.82/173.84 ! [V_A_2,V_t_2,V_D_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 173.82/173.84 => ! [B_x] : % 173.82/173.84 ( ! [B_xa] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ! [B_xb] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 173.82/173.84 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_bset_I7_J,axiom, % 173.82/173.84 ! [V_B_2,V_t_2,V_D_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 173.82/173.84 => ! [B_x] : % 173.82/173.84 ( ! [B_xa] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ! [B_xb] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 173.82/173.84 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 173.82/173.84 => 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))) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_in__measure,axiom, % 173.82/173.84 ! [V_f_2,V_y_2,V_x_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_dvd_OatMost__iff,axiom, % 173.82/173.84 ! [V_k_2,V_i_2] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ord_OatMost__iff,axiom, % 173.82/173.84 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_dvd_OatLeast__iff,axiom, % 173.82/173.84 ! [V_k_2,V_i_2] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__image__simple_Oremove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 173.82/173.84 => 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)))))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__one_Oremove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( ( hAPP(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)) % 173.82/173.84 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 173.82/173.84 & ( hAPP(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)) % 173.82/173.84 => 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)))))) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__image__simple_Oempty,axiom, % 173.82/173.84 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 173.82/173.84 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__one_Osingleton,axiom, % 173.82/173.84 ! [V_x_2,V_F_2,V_f_2,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 173.82/173.84 => 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 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__image__simple_Oinsert,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__one_Oinsert,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 173.82/173.84 => 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)))))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__one_Oinsert__remove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ( hAPP(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)) % 173.82/173.84 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 173.82/173.84 & ( hAPP(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)) % 173.82/173.84 => 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)))))) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ord_OatLeast__iff,axiom, % 173.82/173.84 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 173.82/173.84 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( 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) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__mono2,axiom, % 173.82/173.84 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Oordered__comm__monoid__add(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.84 => ( ! [B_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) ) % 173.82/173.84 => 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))) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_flat__lub__def,axiom, % 173.82/173.84 ! [V_ba_2,V_A_2,T_b] : % 173.82/173.84 ( ( 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))))) % 173.82/173.84 => c_Partial__Function_Oflat__lub(T_b,V_ba_2,V_A_2) = V_ba_2 ) % 173.82/173.84 & ( ~ 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))))) % 173.82/173.84 => 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)))))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 173.82/173.84 ! [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) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 173.82/173.84 ! [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) ). % 173.82/173.84 % 173.82/173.84 fof(fact_mlex__leq,axiom, % 173.82/173.84 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ( 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)) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_mlex__less,axiom, % 173.82/173.84 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 173.82/173.84 ( 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))) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__bounded,axiom, % 173.82/173.84 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( ( class_Groups_Oordered__ab__semigroup__add(T_c) % 173.82/173.84 & class_Rings_Osemiring__1(T_c) ) % 173.82/173.84 => ( ! [B_i] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) ) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card__Suc__eq,axiom, % 173.82/173.84 ! [V_k_2,V_A_2,T_b] : % 173.82/173.84 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 173.82/173.84 <=> ? [B_b,B_B] : % 173.82/173.84 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) % 173.82/173.84 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B)) % 173.82/173.84 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2 % 173.82/173.84 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.84 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 173.82/173.84 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 173.82/173.84 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ord_OatLeastLessThan__iff,axiom, % 173.82/173.84 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 173.82/173.84 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_dvd_OgreaterThanAtMost__empty,axiom, % 173.82/173.84 ! [V_k_2,V_l_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_dvd_OatLeastLessThan__empty,axiom, % 173.82/173.84 ! [V_a_2,V_ba_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom, % 173.82/173.84 ! [V_l_2,V_k_2] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) % 173.82/173.84 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom, % 173.82/173.84 ! [V_ba_2,V_a_2] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) % 173.82/173.84 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom, % 173.82/173.84 ! [V_l_2,V_k_2] : % 173.82/173.84 ( 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) % 173.82/173.84 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) % 173.82/173.84 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom, % 173.82/173.84 ! [V_ba_2,V_a_2] : % 173.82/173.84 ( 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) % 173.82/173.84 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) % 173.82/173.84 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Nats__number__of,axiom, % 173.82/173.84 ! [V_w_2,T_b] : % 173.82/173.84 ( class_Int_Onumber__ring(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ints__odd__less__0,axiom, % 173.82/173.84 ! [V_a_2,T_b] : % 173.82/173.84 ( class_Rings_Olinordered__idom(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 173.82/173.84 => ( 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))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Sup__fin_Oremove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Lattices_Olattice(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( ( hAPP(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)) % 173.82/173.84 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 ) % 173.82/173.84 & ( hAPP(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)) % 173.82/173.84 => 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)))))) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Sup__fin_Osingleton,axiom, % 173.82/173.84 ! [V_x_2,T_b] : % 173.82/173.84 ( class_Lattices_Olattice(T_b) % 173.82/173.84 => 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 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ints__0,axiom, % 173.82/173.84 ! [T_b] : % 173.82/173.84 ( class_Rings_Oring__1(T_b) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ints__add,axiom, % 173.82/173.84 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.84 ( class_Rings_Oring__1(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b))) % 173.82/173.84 => 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))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ints__mult,axiom, % 173.82/173.84 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.84 ( class_Rings_Oring__1(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b))) % 173.82/173.84 => 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))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ints__diff,axiom, % 173.82/173.84 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.84 ( class_Rings_Oring__1(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b))) % 173.82/173.84 => 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))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ints__number__of,axiom, % 173.82/173.84 ! [V_w_2,T_b] : % 173.82/173.84 ( class_Int_Onumber__ring(T_b) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ints__1,axiom, % 173.82/173.84 ! [T_b] : % 173.82/173.84 ( class_Rings_Oring__1(T_b) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ints__minus,axiom, % 173.82/173.84 ! [V_a_2,T_b] : % 173.82/173.84 ( class_Rings_Oring__1(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ints__of__nat,axiom, % 173.82/173.84 ! [V_n_2,T_b] : % 173.82/173.84 ( class_Rings_Oring__1(T_b) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ints__power,axiom, % 173.82/173.84 ! [V_n_2,V_a_2,T_b] : % 173.82/173.84 ( class_Rings_Oring__1(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ints__of__int,axiom, % 173.82/173.84 ! [V_z_2,T_b] : % 173.82/173.84 ( class_Rings_Oring__1(T_b) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Sup__fin_Oin__idem,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Lattices_Olattice(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Nats__0,axiom, % 173.82/173.84 ! [T_b] : % 173.82/173.84 ( class_Rings_Osemiring__1(T_b) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Nats__add,axiom, % 173.82/173.84 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.84 ( class_Rings_Osemiring__1(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 173.82/173.84 => 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))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Nats__mult,axiom, % 173.82/173.84 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.84 ( class_Rings_Osemiring__1(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 173.82/173.84 => 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))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Nats__1,axiom, % 173.82/173.84 ! [T_b] : % 173.82/173.84 ( class_Rings_Osemiring__1(T_b) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_of__nat__in__Nats,axiom, % 173.82/173.84 ! [V_n_2,T_b] : % 173.82/173.84 ( class_Rings_Osemiring__1(T_b) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ints__double__eq__0__iff,axiom, % 173.82/173.84 ! [V_a_2,T_b] : % 173.82/173.84 ( class_Int_Oring__char__0(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 173.82/173.84 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 173.82/173.84 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Sup__fin_Oinsert__idem,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Lattices_Olattice(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Sup__fin_Osubset__idem,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( class_Lattices_Olattice(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Sup__fin_Ounion__idem,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( class_Lattices_Olattice(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Ints__odd__nonzero,axiom, % 173.82/173.84 ! [V_a_2,T_b] : % 173.82/173.84 ( class_Int_Oring__char__0(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 173.82/173.84 => 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) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Sup__fin_Oinsert,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Lattices_Olattice(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Sup__fin_Oinsert__remove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Lattices_Olattice(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ( hAPP(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)) % 173.82/173.84 => 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 ) % 173.82/173.84 & ( hAPP(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)) % 173.82/173.84 => 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)))))) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Sup__fin_Oclosed,axiom, % 173.82/173.84 ! [V_A_2,T_b] : % 173.82/173.84 ( class_Lattices_Olattice(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( ! [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)))))) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Max_Oremove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( ( hAPP(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)) % 173.82/173.84 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) % 173.82/173.84 & ( hAPP(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)) % 173.82/173.84 => 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)))))) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Min_Oremove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( ( hAPP(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)) % 173.82/173.84 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) % 173.82/173.84 & ( hAPP(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)) % 173.82/173.84 => 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)))))) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_minus__Max__eq__Min,axiom, % 173.82/173.84 ! [V_S_2,T_b] : % 173.82/173.84 ( class_Groups_Olinordered__ab__group__add(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.84 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_minus__Min__eq__Max,axiom, % 173.82/173.84 ! [V_S_2,T_b] : % 173.82/173.84 ( class_Groups_Olinordered__ab__group__add(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.84 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Max_Osingleton,axiom, % 173.82/173.84 ! [V_x_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => 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 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Min_Osingleton,axiom, % 173.82/173.84 ! [V_x_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => 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 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Max__ge,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Min__le,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Max__in,axiom, % 173.82/173.84 ! [V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Min__in,axiom, % 173.82/173.84 ! [V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Min_Oin__idem,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Max_Oin__idem,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Min__antimono,axiom, % 173.82/173.84 ! [V_N_2,V_M_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 173.82/173.84 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 173.82/173.84 => 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))) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Max__mono,axiom, % 173.82/173.84 ! [V_N_2,V_M_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 173.82/173.84 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 173.82/173.84 => 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))) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Min__insert,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Max__insert,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Min_Osubset__idem,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Max_Osubset__idem,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Min__Un,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Max__Un,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Min_Oinsert,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Max_Oinsert,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Min_Oinsert__remove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ( hAPP(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)) % 173.82/173.84 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 173.82/173.84 & ( hAPP(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)) % 173.82/173.84 => 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)))))) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Max_Oinsert__remove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ( hAPP(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)) % 173.82/173.84 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 173.82/173.84 & ( hAPP(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)) % 173.82/173.84 => 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)))))) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Max_Oclosed,axiom, % 173.82/173.84 ! [V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( ! [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)))))) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Min_Oclosed,axiom, % 173.82/173.84 ! [V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( ! [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)))))) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_iso__tuple__UNIV__I,axiom, % 173.82/173.84 ! [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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 173.82/173.84 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 173.82/173.84 | ? [B_x,B_y] : % 173.82/173.84 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 173.82/173.84 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2)) % 173.82/173.84 & 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) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_in__lex__prod,axiom, % 173.82/173.84 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( 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)) % 173.82/173.84 | ( V_a_2 = V_a_H_2 % 173.82/173.84 & 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card__Plus__conv__if,axiom, % 173.82/173.84 ! [V_B_2,T_c,V_A_2,T_b] : % 173.82/173.84 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 173.82/173.84 => 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)) ) % 173.82/173.84 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 173.82/173.84 => 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) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_InrI,axiom, % 173.82/173.84 ! [V_A_2,T_c,V_B_2,V_ba_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_B_2)) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_InlI,axiom, % 173.82/173.84 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Plus__eq__empty__conv,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_c,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Plus__def,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_finite__Plus__iff,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_c,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_finite__Plus,axiom, % 173.82/173.84 ! [V_B_2,T_c,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_finite__PlusD_I1_J,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_c,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_finite__PlusD_I2_J,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_c,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_UNIV__Plus__UNIV,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card__Plus,axiom, % 173.82/173.84 ! [V_B_2,T_c,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_same__fstI,axiom, % 173.82/173.84 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] : % 173.82/173.84 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 173.82/173.84 => ( 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))) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_in__finite__psubset,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.84 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OSup__fin_Oremove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( ( hAPP(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)) % 173.82/173.84 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 ) % 173.82/173.84 & ( hAPP(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)) % 173.82/173.84 => 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)))))) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 173.82/173.84 ! [V_x_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => 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 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 173.82/173.84 ! [V_a_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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 ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ( hAPP(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)) % 173.82/173.84 => 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 ) % 173.82/173.84 & ( hAPP(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)) % 173.82/173.84 => 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)))))) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 173.82/173.84 ! [V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( ! [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)))))) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OInf__le__Sup,axiom, % 173.82/173.84 ! [V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OInf__fin_Oremove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( ( hAPP(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)) % 173.82/173.84 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 ) % 173.82/173.84 & ( hAPP(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)) % 173.82/173.84 => 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)))))) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 173.82/173.84 ! [V_x_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => 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 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_Osup__Inf__absorb,axiom, % 173.82/173.84 ! [V_a_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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 ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ( hAPP(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)) % 173.82/173.84 => 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 ) % 173.82/173.84 & ( hAPP(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)) % 173.82/173.84 => 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)))))) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 173.82/173.84 ! [V_A_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( ! [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)))))) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__one_Oclosed,axiom, % 173.82/173.84 ! [V_A_2,V_F_2,V_f_2,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( ! [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)))))) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fun__upd__image,axiom, % 173.82/173.84 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)))))) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fun__upd__triv,axiom, % 173.82/173.84 ! [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 ). % 173.82/173.84 % 173.82/173.84 fof(fact_fun__upd__idem,axiom, % 173.82/173.84 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] : % 173.82/173.84 ( hAPP(V_f_2,V_x_2) = V_y_2 % 173.82/173.84 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fun__upd__other,axiom, % 173.82/173.84 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 173.82/173.84 ( V_z_2 != V_x_2 % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fun__upd__twist,axiom, % 173.82/173.84 ! [V_d_2,V_ba_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] : % 173.82/173.84 ( V_a_2 != V_ca_2 % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fun__upd__apply,axiom, % 173.82/173.84 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 173.82/173.84 ( ( V_z_2 = V_x_2 % 173.82/173.84 => 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 ) % 173.82/173.84 & ( V_z_2 != V_x_2 % 173.82/173.84 => 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) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fun__upd__same,axiom, % 173.82/173.84 ! [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 ). % 173.82/173.84 % 173.82/173.84 fof(fact_fun__upd__upd,axiom, % 173.82/173.84 ! [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) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fun__upd__idem__iff,axiom, % 173.82/173.84 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 173.82/173.84 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2 % 173.82/173.84 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fun__upd__def,axiom, % 173.82/173.84 ! [V_ba_2,V_f_2,T_c,T_b,V_a_2,V_x_2] : % 173.82/173.84 ( ( V_x_2 = V_a_2 % 173.82/173.84 => 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 ) % 173.82/173.84 & ( V_x_2 != V_a_2 % 173.82/173.84 => 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) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_finite__range__updI,axiom, % 173.82/173.84 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] : % 173.82/173.84 ( 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))))) % 173.82/173.84 => 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))))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_image__map__upd,axiom, % 173.82/173.84 ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_map__upd__nonempty,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_map__upd__Some__unfold,axiom, % 173.82/173.84 ! [V_y_2,V_x_2,V_ba_2,V_a_2,V_m_2,T_b,T_c] : % 173.82/173.84 ( 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) % 173.82/173.84 <=> ( ( V_x_2 = V_a_2 % 173.82/173.84 & V_ba_2 = V_y_2 ) % 173.82/173.84 | ( V_x_2 != V_a_2 % 173.82/173.84 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_map__upd__triv,axiom, % 173.82/173.84 ! [T_c,V_x_2,T_b,V_k_2,V_t_2] : % 173.82/173.84 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 173.82/173.84 => 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 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_map__upd__eqD1,axiom, % 173.82/173.84 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 => V_x_2 = V_y_2 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_empty__upd__none,axiom, % 173.82/173.84 ! [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) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ran__map__upd,axiom, % 173.82/173.84 ! [V_ba_2,T_c,T_b,V_a_2,V_m_2] : % 173.82/173.84 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fun__upd__None__restrict,axiom, % 173.82/173.84 ! [V_m_2,T_c,V_D_2,V_x_2,T_b] : % 173.82/173.84 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 173.82/173.84 => 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))))) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 173.82/173.84 => 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) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__gen__delta,axiom, % 173.82/173.84 ! [V_ca_2,V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 173.82/173.84 => 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)))) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_restrict__in,axiom, % 173.82/173.84 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__1,axiom, % 173.82/173.84 ! [V_A_2,T_c,T_b] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_of__int__setprod,axiom, % 173.82/173.84 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.84 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 173.82/173.84 & class_Rings_Oring__1(T_b) ) % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_of__nat__setprod,axiom, % 173.82/173.84 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.84 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 173.82/173.84 & class_Rings_Osemiring__1(T_b) ) % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_int__setprod,axiom, % 173.82/173.84 ! [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) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__timesf,axiom, % 173.82/173.84 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_abs__setprod,axiom, % 173.82/173.84 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.84 ( class_Fields_Olinordered__field(T_b) % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 173.82/173.84 ! [V_A_2,V_f_2,T_b] : % 173.82/173.84 ( ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.84 & class_Groups_Ocomm__monoid__mult(T_b) ) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__zero,axiom, % 173.82/173.84 ! [V_f_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Rings_Ocomm__semiring__1(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ? [B_x] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.84 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 173.82/173.84 => 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) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__zero__iff,axiom, % 173.82/173.84 ! [V_f_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( ( class_Rings_Ocomm__semiring__1(T_c) % 173.82/173.84 & class_Rings_Ono__zero__divisors(T_c) ) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( 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) % 173.82/173.84 <=> ? [B_x] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.84 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__empty,axiom, % 173.82/173.84 ! [V_f_2,T_c,T_b] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod_Oempty,axiom, % 173.82/173.84 ! [V_g_2,T_c,T_b] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__infinite,axiom, % 173.82/173.84 ! [V_f_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => 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) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod_Oinfinite,axiom, % 173.82/173.84 ! [V_g_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => 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) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__eq__1__iff,axiom, % 173.82/173.84 ! [V_f_2,V_F_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 173.82/173.84 => ( 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) % 173.82/173.84 <=> ! [B_x] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 173.82/173.84 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_restrict__map__empty,axiom, % 173.82/173.84 ! [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) ). % 173.82/173.84 % 173.82/173.84 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 173.82/173.84 ! [V_f_2,V_A_2,T_b] : % 173.82/173.84 ( ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.84 & class_Groups_Ocomm__monoid__mult(T_b) ) % 173.82/173.84 => ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod_Odistrib,axiom, % 173.82/173.84 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__dividef,axiom, % 173.82/173.84 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Fields_Ofield__inverse__zero(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_restrict__out,axiom, % 173.82/173.84 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_dvd__setprod,axiom, % 173.82/173.84 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Rings_Ocomm__semiring__1(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 173.82/173.84 => 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))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__pos__nat__iff,axiom, % 173.82/173.84 ! [V_f_2,V_S_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.84 => ( 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))) % 173.82/173.84 <=> ! [B_x] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 173.82/173.84 => 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))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__dvd__setprod__subset,axiom, % 173.82/173.84 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 173.82/173.84 ( ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 & class_Rings_Odvd(T_c) ) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.84 => 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))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_restrict__map__insert,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__delta,axiom, % 173.82/173.84 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 173.82/173.84 => 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) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__delta_H,axiom, % 173.82/173.84 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 173.82/173.84 => 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) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_restrict__map__def,axiom, % 173.82/173.84 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] : % 173.82/173.84 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_restrict__map__to__empty,axiom, % 173.82/173.84 ! [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) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__constant,axiom, % 173.82/173.84 ! [V_y_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod_Oinsert,axiom, % 173.82/173.84 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__insert,axiom, % 173.82/173.84 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ranI,axiom, % 173.82/173.84 ! [T_c,V_ba_2,T_b,V_a_2,V_m_2] : % 173.82/173.84 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_ba_2) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Map_Oran(T_c,T_b,V_m_2))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod_Oinsert__remove,axiom, % 173.82/173.84 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => 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)))))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fun__upd__restrict,axiom, % 173.82/173.84 ! [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) ). % 173.82/173.84 % 173.82/173.84 fof(fact_ran__empty,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod_Oremove,axiom, % 173.82/173.84 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => 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)))))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__diff1,axiom, % 173.82/173.84 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( class_Fields_Ofield(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c) % 173.82/173.84 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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)) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_fun__upd__restrict__conv,axiom, % 173.82/173.84 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_restrict__fun__upd,axiom, % 173.82/173.84 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] : % 173.82/173.84 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 173.82/173.84 => 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) ) % 173.82/173.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2)) % 173.82/173.84 => 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) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_restrict__complement__singleton__eq,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_restrict__upd__same,axiom, % 173.82/173.84 ! [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))))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__nonneg__leq__bound,axiom, % 173.82/173.84 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Oordered__ab__group__add(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 173.82/173.84 => ( ! [B_i] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 173.82/173.84 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2 % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__nonneg__0,axiom, % 173.82/173.84 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Oordered__ab__group__add(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 173.82/173.84 => ( ! [B_i] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 173.82/173.84 => ( 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) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 173.82/173.84 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_pair__lessI2,axiom, % 173.82/173.84 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_ba_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_pair__lessI1,axiom, % 173.82/173.84 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_pair__leqI2,axiom, % 173.82/173.84 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_ba_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_smax__insertI,axiom, % 173.82/173.84 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 173.82/173.84 => ( 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)) % 173.82/173.84 => ( 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)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_smin__insertI,axiom, % 173.82/173.84 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 173.82/173.84 => ( 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)) % 173.82/173.84 => ( 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)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_smin__emptyI,axiom, % 173.82/173.84 ! [V_X_2] : % 173.82/173.84 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_smax__emptyI,axiom, % 173.82/173.84 ! [V_Y_2] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 173.82/173.84 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_pair__leqI1,axiom, % 173.82/173.84 ! [V_t_2,V_s_2,V_ba_2,V_a_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2)) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_wmin__insertI,axiom, % 173.82/173.84 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 173.82/173.84 => ( 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)) % 173.82/173.84 => ( 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)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_wmax__insertI,axiom, % 173.82/173.84 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 173.82/173.84 => ( 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)) % 173.82/173.84 => ( 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)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 173.82/173.84 ! [V_f_2,V_A_2,T_b] : % 173.82/173.84 ( ! [B_x] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.84 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_wmax__emptyI,axiom, % 173.82/173.84 ! [V_X_2] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_wmin__emptyI,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__weak__def,axiom, % 173.82/173.84 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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_max__weak__def,axiom, % 173.82/173.84 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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__rpair__set,axiom, % 173.82/173.84 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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_max__strict__def,axiom, % 173.82/173.84 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 173.82/173.84 % 173.82/173.84 fof(fact_max__ext__additive,axiom, % 173.82/173.84 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 => ( 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))) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__strict__def,axiom, % 173.82/173.84 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 173.82/173.84 % 173.82/173.84 fof(fact_max__rpair__set,axiom, % 173.82/173.84 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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_max__extp__max__ext__eq,axiom, % 173.82/173.84 ! [V_xa_2,V_x_2,V_R_2,T_b] : % 173.82/173.84 ( 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) % 173.82/173.84 <=> 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_less__than__iff,axiom, % 173.82/173.84 ! [V_y_2,V_x_2] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_intrel__iff,axiom, % 173.82/173.84 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_pair__less__def,axiom, % 173.82/173.84 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 173.82/173.84 % 173.82/173.84 fof(fact_mlex__prod__def,axiom, % 173.82/173.84 ! [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))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_rp__inv__image__rp,axiom, % 173.82/173.84 ! [V_f_2,T_c,V_Pa_2,T_b] : % 173.82/173.84 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 173.82/173.84 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 173.82/173.84 ! [V_N_2,V_h_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( ! [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)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 173.82/173.84 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_rp__inv__image__def,axiom, % 173.82/173.84 ! [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))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_in__inv__image,axiom, % 173.82/173.84 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 173.82/173.84 ! [V_N_2,V_h_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( ! [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)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 173.82/173.84 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Max_Ohom__commute,axiom, % 173.82/173.84 ! [V_N_2,V_h_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( ! [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)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 173.82/173.84 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_measure__def,axiom, % 173.82/173.84 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ). % 173.82/173.84 % 173.82/173.84 fof(fact_irrefl__def,axiom, % 173.82/173.84 ! [V_r_2,T_b] : % 173.82/173.84 ( c_Relation_Oirrefl(T_b,V_r_2) % 173.82/173.84 <=> ! [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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Field__insert,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Id__on__def,axiom, % 173.82/173.84 ! [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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Id__on__def_H,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Id__on__empty,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Field__empty,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_mono__Field,axiom, % 173.82/173.84 ! [V_s_2,V_r_2,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Field__Un,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_finite__Field,axiom, % 173.82/173.84 ! [V_r_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 173.82/173.84 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Id__on__eqI,axiom, % 173.82/173.84 ! [V_A_2,T_b,V_ba_2,V_a_2] : % 173.82/173.84 ( V_a_2 = V_ba_2 % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.84 => 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))) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Id__on__iff,axiom, % 173.82/173.84 ! [V_A_2,V_y_2,V_x_2,T_b] : % 173.82/173.84 ( 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))) % 173.82/173.84 <=> ( V_x_2 = V_y_2 % 173.82/173.84 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Id__onE,axiom, % 173.82/173.84 ! [V_A_2,V_ca_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2))) % 173.82/173.84 => ~ ! [B_x] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.84 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Min_Ohom__commute,axiom, % 173.82/173.84 ! [V_N_2,V_h_2,T_b] : % 173.82/173.84 ( class_Orderings_Olinorder(T_b) % 173.82/173.84 => ( ! [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)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 173.82/173.84 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Sup__fin_Ohom__commute,axiom, % 173.82/173.84 ! [V_N_2,V_h_2,T_b] : % 173.82/173.84 ( class_Lattices_Olattice(T_b) % 173.82/173.84 => ( ! [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)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 173.82/173.84 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__mono__one__left,axiom, % 173.82/173.84 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 173.82/173.84 => ( ! [B_x] : % 173.82/173.84 ( 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))) % 173.82/173.84 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setprod__mono__one__right,axiom, % 173.82/173.84 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 173.82/173.84 => ( ! [B_x] : % 173.82/173.84 ( 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))) % 173.82/173.84 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__mono__zero__right,axiom, % 173.82/173.84 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 173.82/173.84 => ( ! [B_x] : % 173.82/173.84 ( 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))) % 173.82/173.84 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__mono__zero__left,axiom, % 173.82/173.84 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 173.82/173.84 => ( ! [B_x] : % 173.82/173.84 ( 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))) % 173.82/173.84 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_escape,axiom, % 173.82/173.84 ! [V_Q_2,V_ca_2,V_Ga_2,T_b,V_Pa_2] : % 173.82/173.84 ( ! [B_Z,B_s] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 173.82/173.84 => 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)))) ) % 173.82/173.84 => 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)))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_card__Pow,axiom, % 173.82/173.84 ! [V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_PowI,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Pow__insert,axiom, % 173.82/173.84 ! [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))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Pow__empty,axiom, % 173.82/173.84 ! [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))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Pow__bottom,axiom, % 173.82/173.84 ! [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))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Pow__not__empty,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Pow__top,axiom, % 173.82/173.84 ! [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))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_PowD,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Pow__iff,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Cantors__paradox,axiom, % 173.82/173.84 ! [V_A_2,T_b] : % 173.82/173.84 ~ ? [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) ). % 173.82/173.84 % 173.82/173.84 fof(fact_image__Pow__surj,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : % 173.82/173.84 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2 % 173.82/173.84 => 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) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Pow__UNIV,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_finite__Pow__iff,axiom, % 173.82/173.84 ! [V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2))) % 173.82/173.84 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Pow__mono,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Un__Pow__subset,axiom, % 173.82/173.84 ! [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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_UN__Pow__subset,axiom, % 173.82/173.84 ! [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)))) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Powp__Pow__eq,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_image__Pow__mono,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.84 ( 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)) % 173.82/173.84 => 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))) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_finite__empty__induct,axiom, % 173.82/173.84 ! [V_Pa_2,V_A_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(V_Pa_2,V_A_2)) % 173.82/173.84 => ( ! [B_a,B_A] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) % 173.82/173.84 => ( hBOOL(hAPP(V_Pa_2,B_A)) % 173.82/173.84 => 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)))))) ) ) ) % 173.82/173.84 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__one__idem_Ounion__idem,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_finite__subset__induct,axiom, % 173.82/173.84 ! [V_Pa_2,V_A_2,V_F_2,T_b] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 173.82/173.84 => ( ! [B_a,B_F] : % 173.82/173.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 173.82/173.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F)) % 173.82/173.84 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 173.82/173.84 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) ) % 173.82/173.84 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__one__idem_Oidem,axiom, % 173.82/173.84 ! [V_x_2,V_F_2,V_f_2,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 173.82/173.84 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__one__idem_Oin__idem,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.84 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 173.82/173.84 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_folding__one__idem_Osubset__idem,axiom, % 173.82/173.84 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 173.82/173.84 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.84 => 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) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__strict__mono,axiom, % 173.82/173.84 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 173.82/173.84 ( ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.84 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) ) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.84 => ( ! [B_x] : % 173.82/173.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 173.82/173.84 => 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))) ) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_equiv__intrel__iff,axiom, % 173.82/173.84 ! [V_y_2,V_x_2] : % 173.82/173.84 ( 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)))) % 173.82/173.84 <=> 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)) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_setsum__Plus,axiom, % 173.82/173.84 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 173.82/173.84 ( class_Groups_Ocomm__monoid__add(T_d) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 173.82/173.84 => 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)) ) ) ) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Image__empty,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Image__Un,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_Image__UN,axiom, % 173.82/173.84 ! [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)) ). % 173.82/173.84 % 173.82/173.84 fof(fact_image__compose,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_K__record__comp,axiom, % 173.82/173.85 ! [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 ). % 173.82/173.85 % 173.82/173.85 fof(fact_o__eq__dest__lhs,axiom, % 173.82/173.85 ! [V_v_2,V_ca_2,V_ba_2,V_a_2,T_b,T_c,T_d] : % 173.82/173.85 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = V_ca_2 % 173.82/173.85 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_apfst__compose,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_apsnd__compose,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_comp__cong,axiom, % 173.82/173.85 ! [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] : % 173.82/173.85 ( 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)) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_o__def,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_o__assoc,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_o__apply,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_o__eq__dest,axiom, % 173.82/173.85 ! [V_v_2,V_d_2,V_ca_2,T_e,V_ba_2,V_a_2,T_b,T_c,T_d] : % 173.82/173.85 ( 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) % 173.82/173.85 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_o__eq__elim,axiom, % 173.82/173.85 ! [V_d_2,V_ca_2,T_e,V_ba_2,V_a_2,T_b,T_c,T_d] : % 173.82/173.85 ( 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) % 173.82/173.85 => ! [B_v] : hAPP(V_a_2,hAPP(V_ba_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fun__upd__comp,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_comp__surj,axiom, % 173.82/173.85 ! [V_g_2,T_d,V_f_2,T_b,T_c] : % 173.82/173.85 ( 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)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Image__mono,axiom, % 173.82/173.85 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 173.82/173.85 => 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))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Un__Image,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Image__iff,axiom, % 173.82/173.85 ! [V_A_2,V_r_2,T_c,V_ba_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 173.82/173.85 <=> ? [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 173.82/173.85 & 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_rev__ImageI,axiom, % 173.82/173.85 ! [V_r_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Image__eq__UN,axiom, % 173.82/173.85 ! [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))))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Image__singleton__iff,axiom, % 173.82/173.85 ! [V_a_2,V_r_2,T_c,V_ba_2,T_b] : % 173.82/173.85 ( 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)))))) % 173.82/173.85 <=> 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_of__int,axiom, % 173.82/173.85 ! [V_j_2,V_i_2,T_b] : % 173.82/173.85 ( class_Rings_Oring__1(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_One__int__def,axiom, % 173.82/173.85 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))))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_mult,axiom, % 173.82/173.85 ! [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))))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_UN__o,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Rep__Integ__inverse,axiom, % 173.82/173.85 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 173.82/173.85 % 173.82/173.85 fof(fact_split__comp,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_number__of__code__numeral__def,axiom, % 173.82/173.85 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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_int__of__def,axiom, % 173.82/173.85 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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_minus,axiom, % 173.82/173.85 ! [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))))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Zero__int__def,axiom, % 173.82/173.85 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))))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_int__def,axiom, % 173.82/173.85 ! [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))))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_add,axiom, % 173.82/173.85 ! [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))))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_nat,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_minus__int__def,axiom, % 173.82/173.85 ! [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))))))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_less,axiom, % 173.82/173.85 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 173.82/173.85 ( 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))))))) % 173.82/173.85 <=> 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_le,axiom, % 173.82/173.85 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 173.82/173.85 ( 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))))))) % 173.82/173.85 <=> 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_hoare__derivs_OIf,axiom, % 173.82/173.85 ! [V_d_2,V_Q_2,V_ca_2,V_ba_2,V_Pa_2,V_Ga_2,T_b] : % 173.82/173.85 ( 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)))) % 173.82/173.85 => ( 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)))) % 173.82/173.85 => 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)))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Loop,axiom, % 173.82/173.85 ! [V_ca_2,V_ba_2,V_Pa_2,V_Ga_2,T_b] : % 173.82/173.85 ( 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)))) % 173.82/173.85 => 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)))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Nitpick_Odenom__def,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_peek__and__def,axiom, % 173.82/173.85 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2)) % 173.82/173.85 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) % 173.82/173.85 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Nitpick_Onum__def,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding_Oremove,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_eq__Abs__Integ,axiom, % 173.82/173.85 ! [V_z_2] : % 173.82/173.85 ~ ! [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))))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding_Oinsert__remove,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 173.82/173.85 ! [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] : % 173.82/173.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding_Ocommute__comp,axiom, % 173.82/173.85 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding_Ocommute__left__comp,axiom, % 173.82/173.85 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 173.82/173.85 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding_Ocommute__comp_H_H,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding_Ocommute__left__comp_H,axiom, % 173.82/173.85 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding_Ocommute__comp_H,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding_Oinsert,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setsum__reindex__nonzero,axiom, % 173.82/173.85 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__add(T_d) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.85 => ( ! [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 173.82/173.85 => ! [B_y] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2)) % 173.82/173.85 => ( B_x != B_y % 173.82/173.85 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 173.82/173.85 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) % 173.82/173.85 => 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) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Random__Sequence_Omap__def,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_quotient__def,axiom, % 173.82/173.85 ! [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)))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_quotient__is__empty,axiom, % 173.82/173.85 ! [V_r_2,V_A_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_quotient__is__empty2,axiom, % 173.82/173.85 ! [V_r_2,V_A_2,T_b] : % 173.82/173.85 ( 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) % 173.82/173.85 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_quotient__empty,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_quotientI,axiom, % 173.82/173.85 ! [V_r_2,V_A_2,V_x_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_singleton__quotient,axiom, % 173.82/173.85 ! [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))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_subset__equiv__class,axiom, % 173.82/173.85 ! [V_a_2,V_ba_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( 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)))))) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_quotientE,axiom, % 173.82/173.85 ! [V_r_2,V_A_2,V_X_2,T_b] : % 173.82/173.85 ( 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))) % 173.82/173.85 => ~ ! [B_x] : % 173.82/173.85 ( 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)))) % 173.82/173.85 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_eq__equiv__class__iff2,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 173.82/173.85 => ( 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) % 173.82/173.85 <=> 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_equiv__intrel,axiom, % 173.82/173.85 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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_equiv__class__self,axiom, % 173.82/173.85 ! [V_a_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => 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)))))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_equiv__class__eq,axiom, % 173.82/173.85 ! [V_ba_2,V_a_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_quotient__eq__iff,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( 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))) % 173.82/173.85 => ( 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))) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 173.82/173.85 => ( V_X_2 = V_Y_2 % 173.82/173.85 <=> 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)) ) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_quotient__eqI,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( 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))) % 173.82/173.85 => ( 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))) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_eq__equiv__class__iff,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 173.82/173.85 => ( 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)))) % 173.82/173.85 <=> 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_eq__equiv__class,axiom, % 173.82/173.85 ! [V_A_2,V_ba_2,V_a_2,V_r_2,T_b] : % 173.82/173.85 ( 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)))) % 173.82/173.85 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_equiv__class__eq__iff,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( 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)) % 173.82/173.85 <=> ( 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)))) % 173.82/173.85 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_equiv__class__subset,axiom, % 173.82/173.85 ! [V_ba_2,V_a_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)))))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_UN__equiv__class2,axiom, % 173.82/173.85 ! [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] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 173.82/173.85 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 173.82/173.85 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2)) % 173.82/173.85 => 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) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_UN__equiv__class,axiom, % 173.82/173.85 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => 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) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_equiv__class__nondisjoint,axiom, % 173.82/173.85 ! [V_ba_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( 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))))))) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf1I,axiom, % 173.82/173.85 ! [T_b,V_B_2,V_x_2,V_A_2] : % 173.82/173.85 ( hBOOL(hAPP(V_A_2,V_x_2)) % 173.82/173.85 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf1E,axiom, % 173.82/173.85 ! [V_x_2,V_B_2,V_A_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 173.82/173.85 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_IntE,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 173.82/173.85 ( 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))) % 173.82/173.85 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.85 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_IntI,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) % 173.82/173.85 => 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))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_finite__Int,axiom, % 173.82/173.85 ! [V_Ga_2,V_F_2,T_b] : % 173.82/173.85 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 173.82/173.85 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) % 173.82/173.85 => 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__eq__top__iff,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,T_b] : % 173.82/173.85 ( class_Lattices_Obounded__lattice__top(T_b) % 173.82/173.85 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b) % 173.82/173.85 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b) % 173.82/173.85 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__top__right,axiom, % 173.82/173.85 ! [V_x,T_a] : % 173.82/173.85 ( class_Lattices_Obounded__lattice__top(T_a) % 173.82/173.85 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__top__left,axiom, % 173.82/173.85 ! [V_x,T_a] : % 173.82/173.85 ( class_Lattices_Obounded__lattice__top(T_a) % 173.82/173.85 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__UNIV__right,axiom, % 173.82/173.85 ! [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 ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__UNIV__left,axiom, % 173.82/173.85 ! [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 ). % 173.82/173.85 % 173.82/173.85 fof(fact_IntD2,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 173.82/173.85 ( 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))) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_IntD1,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 173.82/173.85 ( 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))) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__iff,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_ca_2,T_b] : % 173.82/173.85 ( 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))) % 173.82/173.85 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.85 & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__Int__eq,axiom, % 173.82/173.85 ! [V_x_2,V_S_2,V_R_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 <=> 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_sup__inf__distrib2,axiom, % 173.82/173.85 ! [V_x,V_z,V_y,T_a] : % 173.82/173.85 ( class_Lattices_Odistrib__lattice(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__sup__distrib2,axiom, % 173.82/173.85 ! [V_x,V_z,V_y,T_a] : % 173.82/173.85 ( class_Lattices_Odistrib__lattice(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_sup__inf__distrib1,axiom, % 173.82/173.85 ! [V_z,V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Odistrib__lattice(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__sup__distrib1,axiom, % 173.82/173.85 ! [V_z,V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Odistrib__lattice(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_sup__inf__absorb,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Olattice(T_a) % 173.82/173.85 => 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 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__sup__absorb,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Olattice(T_a) % 173.82/173.85 => 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 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Un__Int__crazy,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Un__Int__distrib2,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__Un__distrib2,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Un__Int__distrib,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__Un__distrib,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__empty__left,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__empty__right,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_disjoint__iff__not__equal,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 <=> ! [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.85 => ! [B_xa] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) % 173.82/173.85 => B_x != B_xa ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__bot__left,axiom, % 173.82/173.85 ! [V_x,T_a] : % 173.82/173.85 ( class_Lattices_Obounded__lattice__bot(T_a) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__bot__right,axiom, % 173.82/173.85 ! [V_x,T_a] : % 173.82/173.85 ( class_Lattices_Obounded__lattice__bot(T_a) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_insert__inter__insert,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_restrict__restrict,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 173.82/173.85 ! [V_B_2,V_A_2] : % 173.82/173.85 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.85 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf1D1,axiom, % 173.82/173.85 ! [V_x_2,V_B_2,V_A_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf1D2,axiom, % 173.82/173.85 ! [V_x_2,V_B_2,V_A_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__absorb,axiom, % 173.82/173.85 ! [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 ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__commute,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__left__absorb,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__left__commute,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__assoc,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf_Oidem,axiom, % 173.82/173.85 ! [V_a,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__idem,axiom, % 173.82/173.85 ! [V_x,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf_Ocommute,axiom, % 173.82/173.85 ! [V_b,V_a,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__sup__aci_I1_J,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Olattice(T_a) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__commute,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf_Oleft__idem,axiom, % 173.82/173.85 ! [V_b,V_a,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__sup__aci_I4_J,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Olattice(T_a) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__left__idem,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf_Oleft__commute,axiom, % 173.82/173.85 ! [V_c,V_a,V_b,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__sup__aci_I3_J,axiom, % 173.82/173.85 ! [V_z,V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Olattice(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__left__commute,axiom, % 173.82/173.85 ! [V_z,V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf_Oassoc,axiom, % 173.82/173.85 ! [V_c,V_b,V_a,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__sup__aci_I2_J,axiom, % 173.82/173.85 ! [V_z,V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Olattice(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__assoc,axiom, % 173.82/173.85 ! [V_z,V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__apply,axiom, % 173.82/173.85 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__fun__def,axiom, % 173.82/173.85 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__min,axiom, % 173.82/173.85 ! [T_b] : % 173.82/173.85 ( ( class_Lattices_Osemilattice__inf(T_b) % 173.82/173.85 & class_Orderings_Olinorder(T_b) ) % 173.82/173.85 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__fin_Oidem,axiom, % 173.82/173.85 ! [V_x,T_a] : % 173.82/173.85 ( class_Lattices_Olattice(T_a) % 173.82/173.85 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_less__infI2,axiom, % 173.82/173.85 ! [V_a,V_x,V_b,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_less__infI1,axiom, % 173.82/173.85 ! [V_b,V_x,V_a,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Diff__Int2,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Diff__Int__distrib2,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__Diff,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Diff__Int__distrib,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_le__infE,axiom, % 173.82/173.85 ! [V_b,V_a,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => ( 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))) % 173.82/173.85 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.82/173.85 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__mono,axiom, % 173.82/173.85 ! [V_d,V_b,V_c,V_a,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 173.82/173.85 => 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))) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__greatest,axiom, % 173.82/173.85 ! [V_z,V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 173.82/173.85 => 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))) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_le__infI,axiom, % 173.82/173.85 ! [V_b,V_a,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 173.82/173.85 => 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))) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__absorb2,axiom, % 173.82/173.85 ! [V_x,V_y,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 173.82/173.85 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__absorb1,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 173.82/173.85 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_le__infI2,axiom, % 173.82/173.85 ! [V_a,V_x,V_b,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_le__infI1,axiom, % 173.82/173.85 ! [V_b,V_x,V_a,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_le__inf__iff,axiom, % 173.82/173.85 ! [V_z_2,V_y_2,V_x_2,T_b] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_b) % 173.82/173.85 => ( 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))) % 173.82/173.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.82/173.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_le__iff__inf,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,T_b] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_b) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 173.82/173.85 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__le2,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__sup__ord_I2_J,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Olattice(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__le1,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Osemilattice__inf(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__sup__ord_I1_J,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Olattice(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__lower1,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__lower2,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__absorb2,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.85 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__absorb1,axiom, % 173.82/173.85 ! [V_A_2,V_B_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.85 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__greatest,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_C_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) % 173.82/173.85 => 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))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__mono,axiom, % 173.82/173.85 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 173.82/173.85 => 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))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Pow__Int__eq,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__UN__distrib2,axiom, % 173.82/173.85 ! [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))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_UN__extend__simps_I4_J,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__UN__distrib,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_UN__extend__simps_I5_J,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_UN__simps_I4_J,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_UN__simps_I5_J,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_distrib__sup__le,axiom, % 173.82/173.85 ! [V_z,V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Olattice(T_a) % 173.82/173.85 => 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)))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_distrib__inf__le,axiom, % 173.82/173.85 ! [V_z,V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Olattice(T_a) % 173.82/173.85 => 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)))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__compl__bot,axiom, % 173.82/173.85 ! [V_x,T_a] : % 173.82/173.85 ( class_Lattices_Oboolean__algebra(T_a) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_compl__inf__bot,axiom, % 173.82/173.85 ! [V_x,T_a] : % 173.82/173.85 ( class_Lattices_Oboolean__algebra(T_a) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_diff__eq,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Oboolean__algebra(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_compl__inf,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Oboolean__algebra(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_compl__sup,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Oboolean__algebra(T_a) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__insert__left__if1,axiom, % 173.82/173.85 ! [V_B_2,V_C_2,V_a_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__insert__right__if1,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_a_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__insert__left__if0,axiom, % 173.82/173.85 ! [V_B_2,V_C_2,V_a_2,T_b] : % 173.82/173.85 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__insert__right__if0,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_a_2,T_b] : % 173.82/173.85 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__insert__left,axiom, % 173.82/173.85 ! [V_B_2,V_C_2,V_a_2,T_b] : % 173.82/173.85 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 173.82/173.85 => 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)) ) % 173.82/173.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 173.82/173.85 => 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__insert__right,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_a_2,T_b] : % 173.82/173.85 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => 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)) ) % 173.82/173.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_image__Int__subset,axiom, % 173.82/173.85 ! [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)))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Diff__disjoint,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Diff__triv,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Un__Int__assoc__eq,axiom, % 173.82/173.85 ! [V_C_2,V_B_2,V_A_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Diff__Int,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Diff__Un,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Un__Diff__Int,axiom, % 173.82/173.85 ! [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 ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I11_J,axiom, % 173.82/173.85 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 173.82/173.85 ! [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))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Compl__disjoint,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Compl__disjoint2,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Image__Int__subset,axiom, % 173.82/173.85 ! [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)))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Compl__Int,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Compl__Un,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Diff__eq,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Diff__Compl,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I14_J,axiom, % 173.82/173.85 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Image__Id__on,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 173.82/173.85 ! [V_B_2,V_A_2] : % 173.82/173.85 ( c_Nat__Transfer_Onat__set(V_A_2) % 173.82/173.85 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.82/173.85 => 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))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_congruent2__implies__congruent,axiom, % 173.82/173.85 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2) % 173.82/173.85 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__Sup__absorb,axiom, % 173.82/173.85 ! [V_a_2,V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => 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 ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_disjoint__eq__subset__Compl,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 <=> 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I15_J,axiom, % 173.82/173.85 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__atLeastAtMost,axiom, % 173.82/173.85 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__atLeastLessThan,axiom, % 173.82/173.85 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I4_J,axiom, % 173.82/173.85 ! [V_u_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I2_J,axiom, % 173.82/173.85 ! [V_u_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I16_J,axiom, % 173.82/173.85 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I12_J,axiom, % 173.82/173.85 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I13_J,axiom, % 173.82/173.85 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__greaterThanAtMost,axiom, % 173.82/173.85 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I9_J,axiom, % 173.82/173.85 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__greaterThanLessThan,axiom, % 173.82/173.85 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__atLeastAtMostL1,axiom, % 173.82/173.85 ! [V_d_2,V_ba_2,V_a_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__atLeastAtMostR1,axiom, % 173.82/173.85 ! [V_d_2,V_ca_2,V_ba_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I8_J,axiom, % 173.82/173.85 ! [V_u_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I7_J,axiom, % 173.82/173.85 ! [V_u_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__atLeastAtMostL2,axiom, % 173.82/173.85 ! [V_ca_2,V_ba_2,V_a_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Int__atLeastAtMostR2,axiom, % 173.82/173.85 ! [V_d_2,V_ca_2,V_a_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I3_J,axiom, % 173.82/173.85 ! [V_u_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I10_J,axiom, % 173.82/173.85 ! [V_u_2,V_m_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I1_J,axiom, % 173.82/173.85 ! [V_u_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I6_J,axiom, % 173.82/173.85 ! [V_u_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ivl__disj__int_I5_J,axiom, % 173.82/173.85 ! [V_u_2,V_l_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__image__simple_Ounion__inter,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_compl__unique,axiom, % 173.82/173.85 ! [V_y,V_x,T_a] : % 173.82/173.85 ( class_Lattices_Oboolean__algebra(T_a) % 173.82/173.85 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 173.82/173.85 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 173.82/173.85 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setsum__Un__Int,axiom, % 173.82/173.85 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setprod_Ounion__inter,axiom, % 173.82/173.85 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setprod__Un__Int,axiom, % 173.82/173.85 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_card__Un__Int,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => 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))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_card_Ounion__inter,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_card__Diff__subset__Int,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( 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))) % 173.82/173.85 => 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setsum__restrict__set,axiom, % 173.82/173.85 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding_Ounion__inter,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_quotient__disj,axiom, % 173.82/173.85 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( 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))) % 173.82/173.85 => ( 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))) % 173.82/173.85 => ( V_X_2 = V_Y_2 % 173.82/173.85 | 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_atMost__Int__atLeast,axiom, % 173.82/173.85 ! [V_n_2,T_b] : % 173.82/173.85 ( class_Orderings_Oorder(T_b) % 173.82/173.85 => 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__one_Ounion__inter,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__one_Ounion__disjoint,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_congruent__def,axiom, % 173.82/173.85 ! [V_f_2,V_r_2,T_c,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 173.82/173.85 <=> ! [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setsum__Un__disjoint,axiom, % 173.82/173.85 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setsum__Un,axiom, % 173.82/173.85 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Oab__group__add(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => 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))) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setprod__Un__disjoint,axiom, % 173.82/173.85 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setprod_Ounion__disjoint,axiom, % 173.82/173.85 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_card__Un__disjoint,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Sup__fin_Ounion__inter,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Min_Ounion__disjoint,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Min_Ounion__inter,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Max_Ounion__inter,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Max_Ounion__disjoint,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_congruent2D,axiom, % 173.82/173.85 ! [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] : % 173.82/173.85 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 173.82/173.85 => ( 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)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setsum__Un__nat,axiom, % 173.82/173.85 ! [V_f_2,V_B_2,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => 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))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding_Ounion,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_congruentD,axiom, % 173.82/173.85 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 173.82/173.85 => ( 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)) % 173.82/173.85 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_congruent2__implies__congruent__UN,axiom, % 173.82/173.85 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 173.82/173.85 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 173.82/173.85 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_UN__equiv__class__inject,axiom, % 173.82/173.85 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 173.82/173.85 => ( 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) % 173.82/173.85 => ( 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))) % 173.82/173.85 => ( 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))) % 173.82/173.85 => ( ! [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.85 => ! [B_y] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 173.82/173.85 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 173.82/173.85 => 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)) ) ) ) % 173.82/173.85 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_UN__equiv__class__type2,axiom, % 173.82/173.85 ! [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] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 173.82/173.85 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 173.82/173.85 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 173.82/173.85 => ( 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))) % 173.82/173.85 => ( 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))) % 173.82/173.85 => ( ! [B_x1] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2)) % 173.82/173.85 => ! [B_x2] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2)) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 173.82/173.85 => 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)) ) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_UN__equiv__class__type,axiom, % 173.82/173.85 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 173.82/173.85 => ( 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))) % 173.82/173.85 => ( ! [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__nat__def,axiom, % 173.82/173.85 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf__Int__eq2,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 <=> 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_card_Ounion__inter__neutral,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( ( ? [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))) % 173.82/173.85 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setprod__Un,axiom, % 173.82/173.85 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Fields_Ofield(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( ! [B_x] : % 173.82/173.85 ( 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))) % 173.82/173.85 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) ) % 173.82/173.85 => 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))) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Integ__def,axiom, % 173.82/173.85 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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf2I,axiom, % 173.82/173.85 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf2E,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 173.82/173.85 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf2D1,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inf2D2,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Rep__Integ,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_type__definition__Integ,axiom, % 173.82/173.85 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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setprod_Ounion__inter__neutral,axiom, % 173.82/173.85 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( ! [B_x] : % 173.82/173.85 ( 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))) % 173.82/173.85 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setprod__Un__one,axiom, % 173.82/173.85 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 173.82/173.85 => ( ! [B_x] : % 173.82/173.85 ( 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))) % 173.82/173.85 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setsum_Ounion__inter__neutral,axiom, % 173.82/173.85 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( ! [B_x] : % 173.82/173.85 ( 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))) % 173.82/173.85 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setsum__Un__zero,axiom, % 173.82/173.85 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 173.82/173.85 => ( ! [B_x] : % 173.82/173.85 ( 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))) % 173.82/173.85 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_refl__on__def_H,axiom, % 173.82/173.85 ! [V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 173.82/173.85 <=> ( ! [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 173.82/173.85 => 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)) ) % 173.82/173.85 & ! [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__fin_Oremove,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => ( ( hAPP(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)) % 173.82/173.85 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 ) % 173.82/173.85 & ( hAPP(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)) % 173.82/173.85 => 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)))))) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_refl__on__Id__on,axiom, % 173.82/173.85 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__fin_Osingleton,axiom, % 173.82/173.85 ! [V_x_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => 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 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_refl__on__empty,axiom, % 173.82/173.85 ! [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))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_refl__on__Un,axiom, % 173.82/173.85 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_refl__on__Int,axiom, % 173.82/173.85 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_sup__Inf__absorb,axiom, % 173.82/173.85 ! [V_a_2,V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => 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 ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__fin_Oin__idem,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => 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) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_refl__onD,axiom, % 173.82/173.85 ! [V_a_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_refl__onD1,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( 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)) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_refl__onD2,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( 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)) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__fin_Oinsert__idem,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__fin_Osubset__idem,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.85 => 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) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__fin_Ounion__idem,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => 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)) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__le__Sup,axiom, % 173.82/173.85 ! [V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => 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))) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__fin_Oinsert,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__fin_Oinsert__remove,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( ( hAPP(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)) % 173.82/173.85 => 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 ) % 173.82/173.85 & ( hAPP(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)) % 173.82/173.85 => 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)))))) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__fin_Ounion__inter,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__fin_Oclosed,axiom, % 173.82/173.85 ! [V_A_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( ! [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)))))) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_equiv__imp__dvd__card,axiom, % 173.82/173.85 ! [V_k_2,V_r_2,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => ( ! [B_x] : % 173.82/173.85 ( 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))) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x))) ) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__idem_Ounion__idem,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__idem_Oidem__left__comp,axiom, % 173.82/173.85 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__idem_Oidem__comp,axiom, % 173.82/173.85 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__idem_Oin__comp__idem,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => 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) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__idem_Oinsert__idem,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 173.82/173.85 => 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) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_equivp__equiv,axiom, % 173.82/173.85 ! [V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2) % 173.82/173.85 <=> 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_card__quotient__disjoint,axiom, % 173.82/173.85 ! [V_r_2,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( 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) % 173.82/173.85 => 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold__Un__disjoint,axiom, % 173.82/173.85 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__empty,axiom, % 173.82/173.85 ! [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))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__uminus,axiom, % 173.82/173.85 ! [V_A_2,T_b] : % 173.82/173.85 ( class_Groups_Oordered__ab__group__add(T_b) % 173.82/173.85 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__strict__subset,axiom, % 173.82/173.85 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.85 => 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))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__contraD,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( V_x_2 != V_y_2 % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 173.82/173.85 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__iff,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 173.82/173.85 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 173.82/173.85 <=> V_x_2 = V_y_2 ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__onD,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 173.82/173.85 => V_x_2 = V_y_2 ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__Un__image__eq__iff,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => ( 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) % 173.82/173.85 <=> V_A_2 = V_B_2 ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__comp,axiom, % 173.82/173.85 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) % 173.82/173.85 => 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))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__imageI,axiom, % 173.82/173.85 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] : % 173.82/173.85 ( 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) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_comp__inj__on,axiom, % 173.82/173.85 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_comp__inj__on__iff,axiom, % 173.82/173.85 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( 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)) % 173.82/173.85 <=> 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_card__image,axiom, % 173.82/173.85 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold__image__reindex,axiom, % 173.82/173.85 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] : % 173.82/173.85 ( class_Groups_Oab__semigroup__mult(T_d) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2) % 173.82/173.85 => 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) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold__image__empty,axiom, % 173.82/173.85 ! [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 ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__id2,axiom, % 173.82/173.85 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__def,axiom, % 173.82/173.85 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 <=> ! [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.85 => ! [B_xa] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 173.82/173.85 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 173.82/173.85 => B_x = B_xa ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__diff,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_subset__inj__on,axiom, % 173.82/173.85 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.85 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_finite__imageD,axiom, % 173.82/173.85 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 173.82/173.85 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) % 173.82/173.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__imageI2,axiom, % 173.82/173.85 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] : % 173.82/173.85 ( 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) % 173.82/173.85 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_identity__equivp,axiom, % 173.82/173.85 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ). % 173.82/173.85 % 173.82/173.85 fof(fact_equivp__def,axiom, % 173.82/173.85 ! [V_R_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 173.82/173.85 <=> ! [B_x,B_y] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 173.82/173.85 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_equivp__reflp,axiom, % 173.82/173.85 ! [V_x_2,V_R_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 173.82/173.85 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_equivp__symp,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_R_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 173.82/173.85 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_equivp__transp,axiom, % 173.82/173.85 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 173.82/173.85 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__image__eq__iff,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => ( 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) % 173.82/173.85 <=> V_A_2 = V_B_2 ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_injD,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 173.82/173.85 => V_x_2 = V_y_2 ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__eq,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 173.82/173.85 <=> V_x_2 = V_y_2 ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__fun,axiom, % 173.82/173.85 ! [T_d,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__Int,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__image__mem__iff,axiom, % 173.82/173.85 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => ( 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))) % 173.82/173.85 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_range__ex1__eq,axiom, % 173.82/173.85 ! [V_ba_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => ( 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))))) % 173.82/173.85 <=> ? [B_x] : % 173.82/173.85 ( V_ba_2 = hAPP(V_f_2,B_x) % 173.82/173.85 & ! [B_y] : % 173.82/173.85 ( V_ba_2 = hAPP(V_f_2,B_y) % 173.82/173.85 => B_y = B_x ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 173.82/173.85 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 173.82/173.85 => 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__iff__surj,axiom, % 173.82/173.85 ! [V_A_H_2,T_c,T_b,V_A_2] : % 173.82/173.85 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( ? [B_f] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 173.82/173.85 & 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)) ) % 173.82/173.85 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_endo__inj__surj,axiom, % 173.82/173.85 ! [V_f_2,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) % 173.82/173.85 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_finite__surj__inj,axiom, % 173.82/173.85 ! [V_f_2,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( 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))) % 173.82/173.85 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_finite__UNIV__surj__inj,axiom, % 173.82/173.85 ! [V_f_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 173.82/173.85 => ( 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)) % 173.82/173.85 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_finite__UNIV__inj__surj,axiom, % 173.82/173.85 ! [V_f_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 173.82/173.85 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__image__subset__iff,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => ( 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))) % 173.82/173.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__image__Int,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_image__Int,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__iff__eq__card,axiom, % 173.82/173.85 ! [V_f_2,T_c,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 <=> 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_eq__card__imp__inj__on,axiom, % 173.82/173.85 ! [V_f_2,T_c,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( 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) % 173.82/173.85 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__image__set__diff,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_image__set__diff,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setsum__reindex,axiom, % 173.82/173.85 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__add(T_d) % 173.82/173.85 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 173.82/173.85 => 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_pigeonhole,axiom, % 173.82/173.85 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( 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))) % 173.82/173.85 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__fun__updI,axiom, % 173.82/173.85 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 173.82/173.85 => 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setprod__reindex,axiom, % 173.82/173.85 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_d) % 173.82/173.85 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 173.82/173.85 => 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setprod__reindex__cong,axiom, % 173.82/173.85 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_d) % 173.82/173.85 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 173.82/173.85 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2) % 173.82/173.85 => 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) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__singleton,axiom, % 173.82/173.85 ! [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))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setsum_Oreindex,axiom, % 173.82/173.85 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 173.82/173.85 => 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) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_card__bij__eq,axiom, % 173.82/173.85 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( 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)) % 173.82/173.85 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) % 173.82/173.85 => ( 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)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 173.82/173.85 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setprod_Oreindex,axiom, % 173.82/173.85 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 173.82/173.85 => 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) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold__image__distrib,axiom, % 173.82/173.85 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__image__Compl__subset,axiom, % 173.82/173.85 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => 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)))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold__image__insert,axiom, % 173.82/173.85 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Oab__semigroup__mult(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setsum_OF__eq,axiom, % 173.82/173.85 ! [V_g_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.85 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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) ) % 173.82/173.85 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setsum_Oeq__fold,axiom, % 173.82/173.85 ! [V_g_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setprod_Oeq__fold,axiom, % 173.82/173.85 ! [V_g_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setprod_OF__eq,axiom, % 173.82/173.85 ! [V_g_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.85 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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) ) % 173.82/173.85 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__insert,axiom, % 173.82/173.85 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) % 173.82/173.85 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 & ~ 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))))))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__Un,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 173.82/173.85 & 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_card__inj__on__le,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( 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)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 173.82/173.85 => 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))) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__iff__card__le,axiom, % 173.82/173.85 ! [V_B_2,T_c,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 173.82/173.85 => ( ? [B_f] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 173.82/173.85 & 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)) ) % 173.82/173.85 <=> 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))) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_quotient__diff1,axiom, % 173.82/173.85 ! [V_a_2,V_A_2,V_r_2,T_b] : % 173.82/173.85 ( 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) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold__image__Un__Int,axiom, % 173.82/173.85 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => 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))) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_image__eq__fold__image,axiom, % 173.82/173.85 ! [V_f_2,T_c,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_card_Oeq__fold__g,axiom, % 173.82/173.85 ! [V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_card__def,axiom, % 173.82/173.85 ! [V_A_2,T_b] : % 173.82/173.85 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => 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) ) % 173.82/173.85 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_comm__monoid__big_OF__eq,axiom, % 173.82/173.85 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 173.82/173.85 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 173.82/173.85 => 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) ) % 173.82/173.85 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 173.82/173.85 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__image_Oreindex,axiom, % 173.82/173.85 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 173.82/173.85 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2) % 173.82/173.85 => 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) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold__image__Un__one,axiom, % 173.82/173.85 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 173.82/173.85 => ( ! [B_x] : % 173.82/173.85 ( 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))) % 173.82/173.85 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__Inr,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__Suc,axiom, % 173.82/173.85 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__Some,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__Inl,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__add__nat,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__of__nat,axiom, % 173.82/173.85 ! [T_b] : % 173.82/173.85 ( class_Nat_Osemiring__char__0(T_b) % 173.82/173.85 => 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__int,axiom, % 173.82/173.85 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))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_swap__inj__on,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__image_Odistrib,axiom, % 173.82/173.85 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__image_Oeq__fold,axiom, % 173.82/173.85 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 173.82/173.85 => 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) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_comm__monoid__big_Oinfinite,axiom, % 173.82/173.85 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 173.82/173.85 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 173.82/173.85 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_the__inv__into__comp,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) % 173.82/173.85 => ( 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)))) % 173.82/173.85 => 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) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_the__inv__into__into,axiom, % 173.82/173.85 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.85 => 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)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__vimage__singleton,axiom, % 173.82/173.85 ! [V_a_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => 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))))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimageI,axiom, % 173.82/173.85 ! [T_c,V_B_2,T_b,V_ba_2,V_a_2,V_f_2] : % 173.82/173.85 ( hAPP(V_f_2,V_a_2) = V_ba_2 % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_B_2)) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__Diff,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_image__vimage__subset,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_surj__image__vimage__eq,axiom, % 173.82/173.85 ! [V_A_2,V_f_2,T_b,T_c] : % 173.82/173.85 ( 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)) % 173.82/173.85 => 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 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__eq,axiom, % 173.82/173.85 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) % 173.82/173.85 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimageD,axiom, % 173.82/173.85 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2))) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimageI2,axiom, % 173.82/173.85 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__Un,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__empty,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__Compl,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__code,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2)) % 173.82/173.85 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__ident,axiom, % 173.82/173.85 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__mono,axiom, % 173.82/173.85 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.85 => 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__UN,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__compose,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__UNIV,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__Int,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__singleton__eq,axiom, % 173.82/173.85 ! [V_ba_2,V_f_2,T_c,V_a_2,T_b] : % 173.82/173.85 ( 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)))))) % 173.82/173.85 <=> hAPP(V_f_2,V_a_2) = V_ba_2 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__insert,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_finite__vimageD,axiom, % 173.82/173.85 ! [V_F_2,V_h_2,T_c,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) % 173.82/173.85 => ( 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)) % 173.82/173.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__subsetD,axiom, % 173.82/173.85 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] : % 173.82/173.85 ( 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)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_image__vimage__eq,axiom, % 173.82/173.85 ! [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)))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_finite__vimageI,axiom, % 173.82/173.85 ! [V_h_2,T_c,V_F_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 173.82/173.85 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 173.82/173.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__vimage__image__eq,axiom, % 173.82/173.85 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => 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 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__const,axiom, % 173.82/173.85 ! [T_c,V_A_2,V_ca_2,T_b] : % 173.82/173.85 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.85 => 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)) ) % 173.82/173.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__eq__UN,axiom, % 173.82/173.85 ! [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))))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_the__inv__into__f__f,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => 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 ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_the__inv__into__f__eq,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_the__inv__f__f,axiom, % 173.82/173.85 ! [V_x_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => 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 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_inj__on__the__inv__into,axiom, % 173.82/173.85 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_the__inv__into__onto,axiom, % 173.82/173.85 ! [V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => 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 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__subsetI,axiom, % 173.82/173.85 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.85 => ( 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))) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_the__inv__into__def,axiom, % 173.82/173.85 ! [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))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_vimage__if,axiom, % 173.82/173.85 ! [V_B_2,T_c,V_d_2,V_A_2,V_ca_2,T_b] : % 173.82/173.85 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.85 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 173.82/173.85 => 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)) ) % 173.82/173.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 173.82/173.85 => 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 ) ) ) % 173.82/173.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) % 173.82/173.85 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 173.82/173.85 => 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) ) % 173.82/173.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_f__the__inv__into__f,axiom, % 173.82/173.85 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 173.82/173.85 => 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 ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Inf__fin_Ohom__commute,axiom, % 173.82/173.85 ! [V_N_2,V_h_2,T_b] : % 173.82/173.85 ( class_Lattices_Olattice(T_b) % 173.82/173.85 => ( ! [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)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 173.82/173.85 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ImageE,axiom, % 173.82/173.85 ! [V_A_2,V_r_2,T_c,V_ba_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 173.82/173.85 => ~ ! [B_x] : % 173.82/173.85 ( 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)) % 173.82/173.85 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_strong__setprod__reindex__cong,axiom, % 173.82/173.85 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_d) % 173.82/173.85 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.85 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 173.82/173.85 => ( ! [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.85 => 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) ) % 173.82/173.85 => 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) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 173.82/173.85 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 173.82/173.85 ( ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.85 & class_Groups_Ocomm__monoid__mult(T_b) ) % 173.82/173.85 => ( V_A_2 = V_B_2 % 173.82/173.85 => ( c_Nat__Transfer_Onat__set(V_B_2) % 173.82/173.85 => ( ! [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 173.82/173.85 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 173.82/173.85 => 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) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_dom__eq__singleton__conv,axiom, % 173.82/173.85 ! [V_x_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( 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))) % 173.82/173.85 <=> ? [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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold__graph__permute__diff,axiom, % 173.82/173.85 ! [V_a_2,V_x_2,V_A_2,V_ba_2,T_b] : % 173.82/173.85 ( class_Groups_Oab__semigroup__mult(T_b) % 173.82/173.85 => ( 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)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 173.82/173.85 => 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)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold__graph__imp__finite,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 173.82/173.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_finite__dom__body,axiom, % 173.82/173.85 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold__graph_Oequations_I1_J,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold__graph_OemptyI,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_empty__fold__graphE,axiom, % 173.82/173.85 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => V_x_2 = V_z_2 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_domIff,axiom, % 173.82/173.85 ! [V_m_2,T_c,V_a_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2))) % 173.82/173.85 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_domI,axiom, % 173.82/173.85 ! [T_c,V_ba_2,T_b,V_a_2,V_m_2] : % 173.82/173.85 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_ba_2) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_insert__dom,axiom, % 173.82/173.85 ! [T_c,V_y_2,T_b,V_x_2,V_f_2] : % 173.82/173.85 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_dom__restrict,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold__graph_OinsertI,axiom, % 173.82/173.85 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 173.82/173.85 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 173.82/173.85 => 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))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_dom__empty,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_dom__eq__empty__conv,axiom, % 173.82/173.85 ! [V_f_2,T_c,T_b] : % 173.82/173.85 ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_dom__const,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_dom__minus,axiom, % 173.82/173.85 ! [V_A_2,T_c,T_b,V_x_2,V_f_2] : % 173.82/173.85 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b) % 173.82/173.85 => 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) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold__graph__insert__swap,axiom, % 173.82/173.85 ! [V_z_2,V_y_2,V_A_2,V_ba_2,T_b] : % 173.82/173.85 ( class_Groups_Oab__semigroup__mult(T_b) % 173.82/173.85 => ( 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)) % 173.82/173.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2)) % 173.82/173.85 => 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))) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Diff1__fold__graph,axiom, % 173.82/173.85 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.85 => 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))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_dom__fun__upd,axiom, % 173.82/173.85 ! [V_x_2,V_f_2,T_c,T_b,V_y_2] : % 173.82/173.85 ( ( V_y_2 = c_Option_Ooption_ONone(T_b) % 173.82/173.85 => 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)))) ) % 173.82/173.85 & ( V_y_2 != c_Option_Ooption_ONone(T_b) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold1Set_Ointros,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2)) % 173.82/173.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => 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)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_ran__restrictD,axiom, % 173.82/173.85 ! [V_A_2,V_m_2,T_c,V_y_2,T_b] : % 173.82/173.85 ( 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)))) % 173.82/173.85 => ? [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 173.82/173.85 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_accp__acc__eq,axiom, % 173.82/173.85 ! [V_x_2,V_r_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_empty__fold1SetE,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold1Set__nonempty,axiom, % 173.82/173.85 ! [V_x_2,V_A_2,V_f_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2)) % 173.82/173.85 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_acc__subset,axiom, % 173.82/173.85 ! [V_R2_2,V_R1_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold1Set__sing,axiom, % 173.82/173.85 ! [V_ba_2,V_a_2,V_f_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 <=> V_a_2 = V_ba_2 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_acc__downward,axiom, % 173.82/173.85 ! [V_a_2,V_r_2,V_ba_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 173.82/173.85 => ( 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)) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_acc_Osimps,axiom, % 173.82/173.85 ! [V_r_2,V_a_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 173.82/173.85 <=> ! [B_x] : % 173.82/173.85 ( 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)) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_max__extp_Oequations,axiom, % 173.82/173.85 ! [V_a2_2,V_a1_2,V_R_2,T_b] : % 173.82/173.85 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) % 173.82/173.85 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 173.82/173.85 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 173.82/173.85 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 & ! [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 173.82/173.85 => ? [B_xa] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 173.82/173.85 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_max__ext_Ointros,axiom, % 173.82/173.85 ! [V_R_2,V_Y_2,V_X_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) % 173.82/173.85 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( ! [B_x] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) % 173.82/173.85 => ? [B_xa] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) % 173.82/173.85 & 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)) ) ) % 173.82/173.85 => 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))) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_conseq2,axiom, % 173.82/173.85 ! [V_Q_2,V_Q_H_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] : % 173.82/173.85 ( 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)))) % 173.82/173.85 => ( ! [B_Z,B_s] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 173.82/173.85 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 173.82/173.85 => 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)))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_conseq1,axiom, % 173.82/173.85 ! [V_Pa_2,V_Q_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] : % 173.82/173.85 ( 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)))) % 173.82/173.85 => ( ! [B_Z,B_s] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) % 173.82/173.85 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 173.82/173.85 => 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)))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold1Set_Oequations,axiom, % 173.82/173.85 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 <=> ? [B_a,B_A] : % 173.82/173.85 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 173.82/173.85 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2)) % 173.82/173.85 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_insert__fold1SetE,axiom, % 173.82/173.85 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 => ~ ! [B_a,B_A] : % 173.82/173.85 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2)) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_image__split__eq__Sigma,axiom, % 173.82/173.85 ! [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))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold1__Un,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Groups_Oab__semigroup__mult(T_b) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( 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)) % 173.82/173.85 => 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)) ) ) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold1__antimono,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_b] : % 173.82/173.85 ( class_Orderings_Olinorder(T_b) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.85 => 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))) ) ) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_SigmaI,axiom, % 173.82/173.85 ! [V_B_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) % 173.82/173.85 => 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))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Sigma__Diff__distrib1,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Times__Diff__distrib1,axiom, % 173.82/173.85 ! [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))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Sigma__Diff__distrib2,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Times__eq__cancel2,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 173.82/173.85 => ( 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)) % 173.82/173.85 <=> V_A_2 = V_B_2 ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Sigma__empty1,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_card__cartesian__product,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setsum__cartesian__product,axiom, % 173.82/173.85 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__add(T_b) % 173.82/173.85 => 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Times__empty,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_c,T_b] : % 173.82/173.85 ( 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)) % 173.82/173.85 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Sigma__empty2,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Compl__Times__UNIV2,axiom, % 173.82/173.85 ! [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)))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Compl__Times__UNIV1,axiom, % 173.82/173.85 ! [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))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_setprod__cartesian__product,axiom, % 173.82/173.85 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 173.82/173.85 ( class_Groups_Ocomm__monoid__mult(T_b) % 173.82/173.85 => 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))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Sigma__Un__distrib1,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Times__Un__distrib1,axiom, % 173.82/173.85 ! [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))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Sigma__Un__distrib2,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_swap__product,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold1__singleton__def,axiom, % 173.82/173.85 ! [V_a_2,V_f_2,T_b,V_g_2] : % 173.82/173.85 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2) % 173.82/173.85 => 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 ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fold1__singleton,axiom, % 173.82/173.85 ! [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 ). % 173.82/173.85 % 173.82/173.85 fof(fact_finite__cartesian__product,axiom, % 173.82/173.85 ! [V_B_2,T_c,V_A_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 173.82/173.85 => 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)))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_equiv__type,axiom, % 173.82/173.85 ! [V_r_2,V_A_2,T_b] : % 173.82/173.85 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.85 => 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)))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Sigma__Int__distrib2,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Times__Int__distrib1,axiom, % 173.82/173.85 ! [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))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Sigma__Int__distrib1,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Id__on__subset__Times,axiom, % 173.82/173.85 ! [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)))) ). % 173.82/173.85 % 173.82/173.85 fof(fact_UNIV__Times__UNIV,axiom, % 173.82/173.85 ! [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)) ). % 173.82/173.85 % 173.82/173.85 fof(fact_SigmaE2,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.85 ( 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))) % 173.82/173.85 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_SigmaD2,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.85 ( 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))) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_SigmaD1,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.85 ( 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))) % 173.82/173.85 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_mem__Sigma__iff,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.85 ( 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))) % 173.82/173.85 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.85 & hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_folding__one_Oeq__fold,axiom, % 173.82/173.85 ! [V_A_2,V_F_2,V_f_2,T_b] : % 173.82/173.85 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 173.82/173.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.85 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_card__cartesian__product__singleton,axiom, % 173.82/173.85 ! [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) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Times__subset__cancel2,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 173.82/173.85 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 173.82/173.85 => ( 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)))) % 173.82/173.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_Image__subset,axiom, % 173.82/173.85 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 173.82/173.85 ( 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)))) % 173.82/173.85 => 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)) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_finite__cartesian__productD1,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_c,T_b] : % 173.82/173.85 ( 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)))) % 173.82/173.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 173.82/173.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_finite__cartesian__productD2,axiom, % 173.82/173.85 ! [V_B_2,V_A_2,T_c,T_b] : % 173.82/173.85 ( 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)))) % 173.82/173.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_fst__image__times,axiom, % 173.82/173.85 ! [V_A_2,T_c,T_b,V_B_2] : % 173.82/173.85 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => 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)) ) % 173.82/173.85 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => 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 ) ) ). % 173.82/173.85 % 173.82/173.85 fof(fact_snd__image__times,axiom, % 173.82/173.85 ! [V_B_2,T_c,T_b,V_A_2] : % 173.82/173.85 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => 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)) ) % 173.82/173.85 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.85 => 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 ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fold1__def,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Sup__fin_OF__eq,axiom, % 173.82/173.86 ! [V_A_2,T_b] : % 173.82/173.86 ( class_Lattices_Olattice(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => 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) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Inf__fin_OF__eq,axiom, % 173.82/173.86 ! [V_A_2,T_b] : % 173.82/173.86 ( class_Lattices_Olattice(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => 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) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Min_OF__eq,axiom, % 173.82/173.86 ! [V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => 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) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Max_OF__eq,axiom, % 173.82/173.86 ! [V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => 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) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 173.82/173.86 ! [V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => 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) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 173.82/173.86 ! [V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => 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) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_refl__on__def,axiom, % 173.82/173.86 ! [V_r_2,V_A_2,T_b] : % 173.82/173.86 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 173.82/173.86 <=> ( 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)))) % 173.82/173.86 & ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => 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)) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_insert__times__insert,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__equiv__class,axiom, % 173.82/173.86 ! [V_X_2,V_r_2,V_A_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( 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)))) % 173.82/173.86 => ( 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))) % 173.82/173.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_UN__Times__distrib,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Sigma__def,axiom, % 173.82/173.86 ! [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))))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fold1__belowI,axiom, % 173.82/173.86 ! [V_a_2,V_A_2,T_b] : % 173.82/173.86 ( class_Lattices_Osemilattice__inf(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.86 => 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)) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__quotient,axiom, % 173.82/173.86 ! [V_r_2,V_A_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( 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)))) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_below__fold1__iff,axiom, % 173.82/173.86 ! [V_x_2,V_A_2,T_b] : % 173.82/173.86 ( class_Lattices_Osemilattice__inf(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => ( 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))) % 173.82/173.86 <=> ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_min__max_Ofold1__belowI,axiom, % 173.82/173.86 ! [V_a_2,V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.86 => 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)) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fold1__insert__idem,axiom, % 173.82/173.86 ! [V_x_2,V_A_2,T_b] : % 173.82/173.86 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => 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)) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fold1__below__iff,axiom, % 173.82/173.86 ! [V_x_2,V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => ( 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)) % 173.82/173.86 <=> ? [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_min__max_Obelow__fold1__iff,axiom, % 173.82/173.86 ! [V_x_2,V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => ( 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))) % 173.82/173.86 <=> ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fold1__Un2,axiom, % 173.82/173.86 ! [V_B_2,V_A_2,T_b] : % 173.82/173.86 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.86 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => 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)) ) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_strict__below__fold1__iff,axiom, % 173.82/173.86 ! [V_x_2,V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => ( 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))) % 173.82/173.86 <=> ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fold1__strict__below__iff,axiom, % 173.82/173.86 ! [V_x_2,V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => ( 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)) % 173.82/173.86 <=> ? [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_vimage__Times,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fold1__insert,axiom, % 173.82/173.86 ! [V_x_2,V_A_2,T_b] : % 173.82/173.86 ( class_Groups_Oab__semigroup__mult(T_b) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.86 => 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)) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_semilattice__big_OF__eq,axiom, % 173.82/173.86 ! [V_A_2,V_F_2,V_f_2,T_b] : % 173.82/173.86 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 173.82/173.86 ! [V_A_2,V_I_2,T_c,T_b] : % 173.82/173.86 ? [B_f] : % 173.82/173.86 ( 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)) % 173.82/173.86 & 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_refl__onI,axiom, % 173.82/173.86 ! [V_A_2,V_r_2,T_b] : % 173.82/173.86 ( 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)))) % 173.82/173.86 => ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => 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)) ) % 173.82/173.86 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setprod__Sigma,axiom, % 173.82/173.86 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 173.82/173.86 ( class_Groups_Ocomm__monoid__mult(T_d) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 173.82/173.86 => 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)) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setsum__Sigma,axiom, % 173.82/173.86 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 173.82/173.86 ( class_Groups_Ocomm__monoid__add(T_d) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 173.82/173.86 => 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)) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fold__image__Sigma,axiom, % 173.82/173.86 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 173.82/173.86 ( class_Groups_Ocomm__monoid__mult(T_d) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 173.82/173.86 => 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)) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_card__SigmaI,axiom, % 173.82/173.86 ! [V_B_2,T_c,V_A_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 173.82/173.86 => 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) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fold1__in,axiom, % 173.82/173.86 ! [V_A_2,T_b] : % 173.82/173.86 ( class_Groups_Oab__semigroup__mult(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => ( ! [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)))))) % 173.82/173.86 => 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)) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__SigmaI,axiom, % 173.82/173.86 ! [V_B_2,T_c,V_A_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( ! [B_a] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 173.82/173.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_hom__fold1__commute,axiom, % 173.82/173.86 ! [V_N_2,V_h_2,T_b] : % 173.82/173.86 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 173.82/173.86 => ( ! [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)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 173.82/173.86 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => 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)) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_SigmaE,axiom, % 173.82/173.86 ! [V_B_2,V_A_2,V_ca_2,T_c,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ~ ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => ! [B_y] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x))) % 173.82/173.86 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_map__pair__surj,axiom, % 173.82/173.86 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_map__pair__inj__on,axiom, % 173.82/173.86 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] : % 173.82/173.86 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.86 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_map__pair__imageI,axiom, % 173.82/173.86 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fst__comp__map__pair,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_snd__comp__map__pair,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_map__pair_Ocompositionality,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_map__pair__compose,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_map__pair_Ocomp,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_snd__prod__fun,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_map__pair__ident,axiom, % 173.82/173.86 ! [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 ). % 173.82/173.86 % 173.82/173.86 fof(fact_fst__map__pair,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_map__pair__simp,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_map__pair__def,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_map__pair__surj__on,axiom, % 173.82/173.86 ! [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] : % 173.82/173.86 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 % 173.82/173.86 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2 % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_prod__fun__imageE,axiom, % 173.82/173.86 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_2,T_c,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ~ ! [B_x,B_y] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ~ 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setprod__pos__nat,axiom, % 173.82/173.86 ! [V_f_2,V_S_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.86 => ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 173.82/173.86 => 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))) ) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_folding__one__idem_Ohom__commute,axiom, % 173.82/173.86 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] : % 173.82/173.86 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 173.82/173.86 => ( ! [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)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 173.82/173.86 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => 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)) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Rep__Integ__induct,axiom, % 173.82/173.86 ! [V_Pa_2,V_y_2] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 173.82/173.86 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x))) % 173.82/173.86 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Rep__Integ__cases,axiom, % 173.82/173.86 ! [V_y_2] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 173.82/173.86 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 173.82/173.86 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 173.82/173.86 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 173.82/173.86 => ( ! [B_x] : % 173.82/173.86 ( 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))) % 173.82/173.86 => hAPP(V_g_2,B_x) = V_z_2 ) % 173.82/173.86 => 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)) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fun__left__comm__idem__remove,axiom, % 173.82/173.86 ! [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))))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_card__less__Suc,axiom, % 173.82/173.86 ! [V_i_2,V_M_2] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 173.82/173.86 => 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))))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_CollectI,axiom, % 173.82/173.86 ! [T_b,V_a_2,V_Pa_2] : % 173.82/173.86 ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__Collect__conjI,axiom, % 173.82/173.86 ! [V_Q_2,V_Pa_2,T_b] : % 173.82/173.86 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 173.82/173.86 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) % 173.82/173.86 => 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)))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__Collect__less__nat,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__Collect__le__nat,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 173.82/173.86 ! [V_x_2,V_f_2,T_c,T_b] : % 173.82/173.86 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 173.82/173.86 => 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) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Collect__split,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_SetCompr__Sigma__eq,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_vimage__Collect__eq,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Collect__neg__eq,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__Collect__disjI,axiom, % 173.82/173.86 ! [V_Q_2,V_Pa_2,T_b] : % 173.82/173.86 ( 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)))) % 173.82/173.86 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 173.82/173.86 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 173.82/173.86 ! [T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 173.82/173.86 ! [T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Collect__mem__eq,axiom, % 173.82/173.86 ! [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 ). % 173.82/173.86 % 173.82/173.86 fof(fact_mem__Collect__eq,axiom, % 173.82/173.86 ! [V_Pa_2,V_a_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 173.82/173.86 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_CollectD,axiom, % 173.82/173.86 ! [V_Pa_2,V_a_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 173.82/173.86 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_CollectE,axiom, % 173.82/173.86 ! [V_Pa_2,V_a_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 173.82/173.86 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fun__left__comm__idem,axiom, % 173.82/173.86 ! [T_b] : % 173.82/173.86 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 173.82/173.86 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fun__left__comm__idem__sup,axiom, % 173.82/173.86 ! [T_b] : % 173.82/173.86 ( class_Lattices_Osemilattice__sup(T_b) % 173.82/173.86 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Collect__disj__eq,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_empty__Collect__eq,axiom, % 173.82/173.86 ! [V_Pa_2,T_b] : % 173.82/173.86 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2) % 173.82/173.86 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Collect__empty__eq,axiom, % 173.82/173.86 ! [V_Pa_2,T_b] : % 173.82/173.86 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_empty__def,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_insert__Collect,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Collect__def,axiom, % 173.82/173.86 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ). % 173.82/173.86 % 173.82/173.86 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 173.82/173.86 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 173.82/173.86 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 173.82/173.86 => 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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 173.82/173.86 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] : % 173.82/173.86 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 173.82/173.86 => 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) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fun__left__comm__idem__insert,axiom, % 173.82/173.86 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_UNIV__def,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fun__left__comm__idem__inf,axiom, % 173.82/173.86 ! [T_b] : % 173.82/173.86 ( class_Lattices_Osemilattice__inf(T_b) % 173.82/173.86 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Collect__conj__eq,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_insert__compr,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_insert__compr__raw,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Un__def,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Int__Collect,axiom, % 173.82/173.86 ! [V_Pa_2,V_A_2,V_x_2,T_b] : % 173.82/173.86 ( 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)))) % 173.82/173.86 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.86 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Int__def,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_singleton__conv2,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_singleton__conv,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Collect__conv__if2,axiom, % 173.82/173.86 ! [T_b,V_a_2,V_Pa_2] : % 173.82/173.86 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 173.82/173.86 => 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))) ) % 173.82/173.86 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Collect__conv__if,axiom, % 173.82/173.86 ! [T_b,V_a_2,V_Pa_2] : % 173.82/173.86 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 173.82/173.86 => 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))) ) % 173.82/173.86 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_set__diff__eq,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__Collect__not,axiom, % 173.82/173.86 ! [V_Pa_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 173.82/173.86 => ( 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)))) % 173.82/173.86 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_insert__def,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Compl__eq,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_vimage__def,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Collect__imp__eq,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_dom__def,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__M__bounded__by__nat,axiom, % 173.82/173.86 ! [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))))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setsum__setsum__restrict,axiom, % 173.82/173.86 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] : % 173.82/173.86 ( class_Groups_Ocomm__monoid__add(T_d) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 173.82/173.86 => 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) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_if__image__distrib,axiom, % 173.82/173.86 ! [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))))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_dom__if,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_nat__seg__image__imp__finite,axiom, % 173.82/173.86 ! [V_n_2,V_f_2,T_b,V_A_2] : % 173.82/173.86 ( 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))) % 173.82/173.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setsum__restrict__set_H,axiom, % 173.82/173.86 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 173.82/173.86 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => 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) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setsum__image__gen,axiom, % 173.82/173.86 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] : % 173.82/173.86 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Image__singleton,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setsum__cases,axiom, % 173.82/173.86 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] : % 173.82/173.86 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => 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))))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_card__less__Suc2,axiom, % 173.82/173.86 ! [V_i_2,V_M_2] : % 173.82/173.86 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 173.82/173.86 => 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))))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_card__less,axiom, % 173.82/173.86 ! [V_i_2,V_M_2] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 173.82/173.86 => 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) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_dom__override__on,axiom, % 173.82/173.86 ! [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))))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setsum__multicount,axiom, % 173.82/173.86 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 173.82/173.86 => ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2)) % 173.82/173.86 => 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 ) % 173.82/173.86 => 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)) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__Collect__subsets,axiom, % 173.82/173.86 ! [V_A_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => 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)))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Pow__def,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_override__on__apply__in,axiom, % 173.82/173.86 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.86 => 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) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_override__on__apply__notin,axiom, % 173.82/173.86 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 173.82/173.86 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.86 => 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) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_override__on__emptyset,axiom, % 173.82/173.86 ! [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 ). % 173.82/173.86 % 173.82/173.86 fof(fact_inj__graph,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_override__on__def,axiom, % 173.82/173.86 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] : % 173.82/173.86 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.86 => 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) ) % 173.82/173.86 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 173.82/173.86 => 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) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__psubset__def,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_inv__image__def,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Nitpick_Oprod__def,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_int__ge__less__than__def,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_int__ge__less__than2__def,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_reflp__def,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Predicate_Oreflp(T_b,V_r_2) % 173.82/173.86 <=> 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_reflpE,axiom, % 173.82/173.86 ! [V_x_2,V_r_2,T_b] : % 173.82/173.86 ( c_Predicate_Oreflp(T_b,V_r_2) % 173.82/173.86 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 173.82/173.86 ! [V_B_2,V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.86 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => 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))))))) ) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 173.82/173.86 ! [V_x_2,V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => 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))))) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__Collect__bounded__ex,axiom, % 173.82/173.86 ! [V_Q_2,T_c,V_Pa_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 173.82/173.86 => ( 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))))) % 173.82/173.86 <=> ! [B_y] : % 173.82/173.86 ( hBOOL(hAPP(V_Pa_2,B_y)) % 173.82/173.86 => 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)))) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__image__set,axiom, % 173.82/173.86 ! [V_f_2,T_c,V_Pa_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 173.82/173.86 => 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))))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_ran__def,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Pow__Compl,axiom, % 173.82/173.86 ! [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))))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_add__Max__commute,axiom, % 173.82/173.86 ! [V_k_2,V_N_2,T_b] : % 173.82/173.86 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 173.82/173.86 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => 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))))) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_add__Min__commute,axiom, % 173.82/173.86 ! [V_k_2,V_N_2,T_b] : % 173.82/173.86 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 173.82/173.86 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => 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))))) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_sup__Inf2__distrib,axiom, % 173.82/173.86 ! [V_B_2,V_A_2,T_b] : % 173.82/173.86 ( class_Lattices_Odistrib__lattice(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.86 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => 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))))))) ) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_sup__Inf1__distrib,axiom, % 173.82/173.86 ! [V_x_2,V_A_2,T_b] : % 173.82/173.86 ( class_Lattices_Odistrib__lattice(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => 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))))) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_inf__Sup1__distrib,axiom, % 173.82/173.86 ! [V_x_2,V_A_2,T_b] : % 173.82/173.86 ( class_Lattices_Odistrib__lattice(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => 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))))) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_inf__Sup2__distrib,axiom, % 173.82/173.86 ! [V_B_2,V_A_2,T_b] : % 173.82/173.86 ( class_Lattices_Odistrib__lattice(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.86 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => 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))))))) ) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 173.82/173.86 ! [V_B_2,V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.86 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => 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))))))) ) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 173.82/173.86 ! [V_x_2,V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 => 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))))) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setsum__mult__setsum__if__inj,axiom, % 173.82/173.86 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : % 173.82/173.86 ( class_Rings_Osemiring__0(T_d) % 173.82/173.86 => ( 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))) % 173.82/173.86 => 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))))))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setsum__multicount__gen,axiom, % 173.82/173.86 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2)) % 173.82/173.86 => ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2)) % 173.82/173.86 => 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) ) % 173.82/173.86 => 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) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_inj__on__id,axiom, % 173.82/173.86 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ). % 173.82/173.86 % 173.82/173.86 fof(fact_map__pair_Oid,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_map__pair_Oidentity,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_id__apply,axiom, % 173.82/173.86 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 173.82/173.86 % 173.82/173.86 fof(fact_id__def,axiom, % 173.82/173.86 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 173.82/173.86 % 173.82/173.86 fof(fact_apsnd__id,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_apfst__id,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_of__int__eq__id,axiom, % 173.82/173.86 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 173.82/173.86 % 173.82/173.86 fof(fact_vimage__id,axiom, % 173.82/173.86 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ). % 173.82/173.86 % 173.82/173.86 fof(fact_o__id,axiom, % 173.82/173.86 ! [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 ). % 173.82/173.86 % 173.82/173.86 fof(fact_id__o,axiom, % 173.82/173.86 ! [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 ). % 173.82/173.86 % 173.82/173.86 fof(fact_o__eq__id__dest,axiom, % 173.82/173.86 ! [V_v_2,V_ca_2,V_ba_2,V_a_2,T_b,T_c,T_d] : % 173.82/173.86 ( 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) % 173.82/173.86 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_surj__id,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_image__id,axiom, % 173.82/173.86 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ). % 173.82/173.86 % 173.82/173.86 fof(fact_folding_Oempty,axiom, % 173.82/173.86 ! [V_F_2,V_f_2,T_c,T_b] : % 173.82/173.86 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 173.82/173.86 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_apsnd__def,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_apfst__def,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_split__Pair,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setsum__reindex__id,axiom, % 173.82/173.86 ! [V_B_2,V_f_2,T_b,T_c] : % 173.82/173.86 ( class_Groups_Ocomm__monoid__add(T_c) % 173.82/173.86 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setprod__reindex__id,axiom, % 173.82/173.86 ! [V_B_2,V_f_2,T_b,T_c] : % 173.82/173.86 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.86 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__conv__nat__seg__image,axiom, % 173.82/173.86 ! [V_A_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 <=> ? [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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__comp__def,axiom, % 173.82/173.86 ! [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))))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__compI,axiom, % 173.82/173.86 ! [V_s_2,V_ca_2,T_d,V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__comp__UNION__distrib,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__comp__UNION__distrib2,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__comp__empty1,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__comp__empty2,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__comp__distrib2,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__comp__distrib,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__comp__mono,axiom, % 173.82/173.86 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_O__assoc,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_union__comp__emptyR,axiom, % 173.82/173.86 ! [V_C_2,V_B_2,V_A_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_union__comp__emptyL,axiom, % 173.82/173.86 ! [V_B_2,V_C_2,V_A_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__comp__subset__Sigma,axiom, % 173.82/173.86 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 173.82/173.86 ( 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)))) % 173.82/173.86 => ( 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)))) % 173.82/173.86 => 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)))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_max__ext__compat,axiom, % 173.82/173.86 ! [V_S_2,V_R_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_min__ext__compat,axiom, % 173.82/173.86 ! [V_S_2,V_R_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_pred__comp__rel__comp__eq,axiom, % 173.82/173.86 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 173.82/173.86 ( 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) % 173.82/173.86 <=> 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_reduction__pairI,axiom, % 173.82/173.86 ! [V_S_2,V_R_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_R_2) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__less__than,axiom, % 173.82/173.86 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 173.82/173.86 % 173.82/173.86 fof(fact_pred__comp_Ointros,axiom, % 173.82/173.86 ! [T_d,T_c,T_b,V_ca_2,V_s_2,V_ba_2,V_a_2,V_r_2] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 173.82/173.86 => ( hBOOL(hAPP(hAPP(V_s_2,V_ba_2),V_ca_2)) % 173.82/173.86 => c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a_2,V_ca_2) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__empty,axiom, % 173.82/173.86 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__inv__image,axiom, % 173.82/173.86 ! [V_f_2,T_c,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__lex__prod,axiom, % 173.82/173.86 ! [V_rb_2,T_c,V_ra_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_ra_2) % 173.82/173.86 => ( c_Wellfounded_Owf(T_c,V_rb_2) % 173.82/173.86 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__measure,axiom, % 173.82/173.86 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__union__merge,axiom, % 173.82/173.86 ! [V_S_2,V_R_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 <=> 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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__no__loop,axiom, % 173.82/173.86 ! [V_R_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__comp__self,axiom, % 173.82/173.86 ! [V_R_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_R_2) % 173.82/173.86 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__less,axiom, % 173.82/173.86 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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__int__ge__less__than,axiom, % 173.82/173.86 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__irrefl,axiom, % 173.82/173.86 ! [V_a_2,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => ~ 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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__asym,axiom, % 173.82/173.86 ! [V_x_2,V_a_2,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => ( 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)) % 173.82/173.86 => ~ 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__not__sym,axiom, % 173.82/173.86 ! [V_x_2,V_a_2,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => ( 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)) % 173.82/173.86 => ~ 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__not__refl,axiom, % 173.82/173.86 ! [V_a_2,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => ~ 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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__Int1,axiom, % 173.82/173.86 ! [V_r_H_2,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => 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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__Int2,axiom, % 173.82/173.86 ! [V_r_H_2,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => 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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_max__ext__wf,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__pair__less,axiom, % 173.82/173.86 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__subset,axiom, % 173.82/173.86 ! [V_p_2,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => ( 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)) % 173.82/173.86 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_pred__comp_Oequations,axiom, % 173.82/173.86 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 173.82/173.86 ( c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a1_2,V_a3_2) % 173.82/173.86 <=> ? [B_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 173.82/173.86 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__finite__psubset,axiom, % 173.82/173.86 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_min__ext__wf,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__mlex,axiom, % 173.82/173.86 ! [V_f_2,V_R_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_R_2) % 173.82/173.86 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__acc__iff,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_acc__wfD,axiom, % 173.82/173.86 ! [V_x_2,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__int__ge__less__than2,axiom, % 173.82/173.86 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 <=> ~ ? [B_f] : % 173.82/173.86 ! [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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wfE__pf,axiom, % 173.82/173.86 ! [V_A_2,V_R_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_R_2) % 173.82/173.86 => ( 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))) % 173.82/173.86 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__union__compatible,axiom, % 173.82/173.86 ! [V_S_2,V_R_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_R_2) % 173.82/173.86 => ( c_Wellfounded_Owf(T_b,V_S_2) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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)) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf,axiom, % 173.82/173.86 ! [T_b] : % 173.82/173.86 ( class_Orderings_Owellorder(T_b) % 173.82/173.86 => 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)))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_reduction__pair__def,axiom, % 173.82/173.86 ! [V_Pa_2,T_b] : % 173.82/173.86 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 173.82/173.86 <=> ( 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)) % 173.82/173.86 & 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_reduction__pair__lemma,axiom, % 173.82/173.86 ! [V_S_2,V_R_2,V_Pa_2,T_b] : % 173.82/173.86 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 173.82/173.86 => ( 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))) % 173.82/173.86 => ( 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))) % 173.82/173.86 => ( c_Wellfounded_Owf(T_b,V_S_2) % 173.82/173.86 => 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)) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__map__pair__image,axiom, % 173.82/173.86 ! [V_f_2,T_c,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__lenlex,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__if__measure,axiom, % 173.82/173.86 ! [T_b,V_g_2,V_f_2,V_Pa_2] : % 173.82/173.86 ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(V_Pa_2,B_x)) % 173.82/173.86 => 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))) ) % 173.82/173.86 => 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))))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_pred__nat__def,axiom, % 173.82/173.86 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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__lex,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__pred__nat,axiom, % 173.82/173.86 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 173.82/173.86 % 173.82/173.86 fof(fact_lex__def,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__lexn,axiom, % 173.82/173.86 ! [V_n_2,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_lexn_Osimps_I1_J,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__same__fst,axiom, % 173.82/173.86 ! [T_b,V_R_2,T_c,V_Pa_2] : % 173.82/173.86 ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(V_Pa_2,B_x)) % 173.82/173.86 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) ) % 173.82/173.86 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Range__Collect__split,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_RangeI,axiom, % 173.82/173.86 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Range__Id__on,axiom, % 173.82/173.86 ! [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 ). % 173.82/173.86 % 173.82/173.86 fof(fact_Range__empty__iff,axiom, % 173.82/173.86 ! [V_r_2,T_b,T_c] : % 173.82/173.86 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Range__empty,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Range__Un__eq,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__Range,axiom, % 173.82/173.86 ! [V_r_2,T_c,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 173.82/173.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_snd__eq__Range,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Range__iff,axiom, % 173.82/173.86 ! [V_r_2,T_c,V_a_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 173.82/173.86 <=> ? [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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Range__insert,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Range__Int__subset,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Range__Diff__subset,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_RangeP__Range__eq,axiom, % 173.82/173.86 ! [V_x_2,V_r_2,T_c,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_RangeE,axiom, % 173.82/173.86 ! [V_r_2,T_c,V_ba_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 173.82/173.86 => ~ ! [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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_RangeP_Ointros,axiom, % 173.82/173.86 ! [T_c,T_b,V_ba_2,V_a_2,V_r_2] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 173.82/173.86 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_ba_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_RangeP_Oequations,axiom, % 173.82/173.86 ! [V_a2_2,V_r_2,T_c,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2)) % 173.82/173.86 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__Un,axiom, % 173.82/173.86 ! [V_s_2,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => ( c_Wellfounded_Owf(T_b,V_s_2) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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)) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wfP__def,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_OwfP(T_b,V_r_2) % 173.82/173.86 <=> 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wfP__empty,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_DomainI,axiom, % 173.82/173.86 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Domain__Id__on,axiom, % 173.82/173.86 ! [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 ). % 173.82/173.86 % 173.82/173.86 fof(fact_wfP__accp__iff,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_OwfP(T_b,V_r_2) % 173.82/173.86 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_accp__wfPD,axiom, % 173.82/173.86 ! [V_x_2,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_OwfP(T_b,V_r_2) % 173.82/173.86 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wfP__subset,axiom, % 173.82/173.86 ! [V_p_2,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_OwfP(T_b,V_r_2) % 173.82/173.86 => ( 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)) % 173.82/173.86 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Domain__empty__iff,axiom, % 173.82/173.86 ! [V_r_2,T_c,T_b] : % 173.82/173.86 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Domain__empty,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Domain__mono,axiom, % 173.82/173.86 ! [V_s_2,V_r_2,T_c,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Domain__Un__eq,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__Domain,axiom, % 173.82/173.86 ! [V_r_2,T_c,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 173.82/173.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fst__eq__Domain,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Domain__iff,axiom, % 173.82/173.86 ! [V_r_2,T_c,V_a_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 173.82/173.86 <=> ? [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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Domain__insert,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Domain__Int__subset,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Domain__Diff__subset,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Field__def,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__in__rel,axiom, % 173.82/173.86 ! [V_R_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_R_2) % 173.82/173.86 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wfP__wf__eq,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Domain__Collect__split,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_DomainP__Domain__eq,axiom, % 173.82/173.86 ! [V_x_2,V_r_2,T_c,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_DomainE,axiom, % 173.82/173.86 ! [V_r_2,T_c,V_a_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 173.82/173.86 => ~ ! [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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_DomainP_Ointros,axiom, % 173.82/173.86 ! [T_c,T_b,V_ba_2,V_a_2,V_r_2] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2)) % 173.82/173.86 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_DomainP_Oequations,axiom, % 173.82/173.86 ! [V_a1_2,V_r_2,T_c,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2)) % 173.82/173.86 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wfP__acyclicP,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_OwfP(T_b,V_r_2) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_neg__map__def,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__acyclic,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_acyclic__subset,axiom, % 173.82/173.86 ! [V_r_2,V_s_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Oacyclic(T_b,V_s_2) % 173.82/173.86 => ( 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)) % 173.82/173.86 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__acyclic__wf,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 173.82/173.86 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 173.82/173.86 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__iff__acyclic__if__finite,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 173.82/173.86 => ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_neg__single__def,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_pos__map__def,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_New__DSequence_Oneg__single__def,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_pos__single__def,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_New__DSequence_Opos__single__def,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Nitpick_Owf_H__def,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Nitpick_Owf_H(T_b,V_r_2) % 173.82/173.86 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 173.82/173.86 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 173.82/173.86 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_pigeonhole__infinite,axiom, % 173.82/173.86 ! [V_f_2,T_c,V_A_2,T_b] : % 173.82/173.86 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 173.82/173.86 => ? [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 & ~ 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)))))) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Abs__Integ__cases,axiom, % 173.82/173.86 ! [V_x_2] : % 173.82/173.86 ~ ! [B_y] : % 173.82/173.86 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 173.82/173.86 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Abs__Integ__induct,axiom, % 173.82/173.86 ! [V_x_2,V_Pa_2] : % 173.82/173.86 ( ! [B_y] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 173.82/173.86 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 173.82/173.86 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__UN__I,axiom, % 173.82/173.86 ! [V_B_2,T_c,V_A_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( ! [B_a] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 173.82/173.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_inj__on__diff__nat,axiom, % 173.82/173.86 ! [V_k_2,V_N_2] : % 173.82/173.86 ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 173.82/173.86 => 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) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wfP__SUP,axiom, % 173.82/173.86 ! [T_b,V_r_2,T_c] : % 173.82/173.86 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i)) % 173.82/173.86 => ( ! [B_i,B_j] : % 173.82/173.86 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 173.82/173.86 => 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)) ) % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__map__freshness,axiom, % 173.82/173.86 ! [V_f_2,T_c,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2))) % 173.82/173.86 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 173.82/173.86 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_mem__splitE,axiom, % 173.82/173.86 ! [V_p_2,V_ca_2,T_d,T_c,V_z_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ~ ! [B_x,B_y] : % 173.82/173.86 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) % 173.82/173.86 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_mem__splitI2,axiom, % 173.82/173.86 ! [V_ca_2,V_z_2,T_d,T_c,T_b,V_p_2] : % 173.82/173.86 ( ! [B_a,B_b] : % 173.82/173.86 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) ) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Eps__split,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_someI,axiom, % 173.82/173.86 ! [T_b,V_x_2,V_Pa_2] : % 173.82/173.86 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 173.82/173.86 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_tfl__some,axiom, % 173.82/173.86 ! [T_b,B_P] : % 173.82/173.86 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 173.82/173.86 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_someI__ex,axiom, % 173.82/173.86 ! [T_b,V_Pa_2] : % 173.82/173.86 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 173.82/173.86 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_some__eq__ex,axiom, % 173.82/173.86 ! [T_b,V_Pa_2] : % 173.82/173.86 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) % 173.82/173.86 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_some__eq__trivial,axiom, % 173.82/173.86 ! [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 ). % 173.82/173.86 % 173.82/173.86 fof(fact_some__sym__eq__trivial,axiom, % 173.82/173.86 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 173.82/173.86 % 173.82/173.86 fof(fact_exE__some,axiom, % 173.82/173.86 ! [T_b,V_ca_2,V_Pa_2] : % 173.82/173.86 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 173.82/173.86 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2) % 173.82/173.86 => hBOOL(hAPP(V_Pa_2,V_ca_2)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Eps__split__eq,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_split__paired__Eps,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wfI__pf,axiom, % 173.82/173.86 ! [V_R_2,T_b] : % 173.82/173.86 ( ! [B_A] : % 173.82/173.86 ( 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))) % 173.82/173.86 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 173.82/173.86 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Sigma__mono,axiom, % 173.82/173.86 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 173.82/173.86 => ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => 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))) ) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_acc_OaccI,axiom, % 173.82/173.86 ! [V_r_2,V_x_2,T_b] : % 173.82/173.86 ( ! [B_y] : % 173.82/173.86 ( 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)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) ) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_not__acc__down,axiom, % 173.82/173.86 ! [V_R_2,V_x_2,T_b] : % 173.82/173.86 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2))) % 173.82/173.86 => ~ ! [B_z] : % 173.82/173.86 ( 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)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fold__image__1,axiom, % 173.82/173.86 ! [V_f_2,V_S_2,T_b,T_c] : % 173.82/173.86 ( class_Groups_Ocomm__monoid__mult(T_c) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 173.82/173.86 => ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 173.82/173.86 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 173.82/173.86 => 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) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_card_Oneutral,axiom, % 173.82/173.86 ! [V_A_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 173.82/173.86 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_max__ext_Osimps,axiom, % 173.82/173.86 ! [V_R_2,V_a2_2,V_a1_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 173.82/173.86 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 173.82/173.86 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 173.82/173.86 & ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 173.82/173.86 => ? [B_xa] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 173.82/173.86 & 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)) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_fold__image__cong,axiom, % 173.82/173.86 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] : % 173.82/173.86 ( class_Groups_Oab__semigroup__mult(T_c) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 173.82/173.86 => 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) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setprod__dvd__setprod__subset2,axiom, % 173.82/173.86 ! [V_g_2,V_f_2,V_A_2,V_B_2,T_b,T_c] : % 173.82/173.86 ( class_Rings_Ocomm__semiring__1(T_c) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 173.82/173.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 173.82/173.86 => ( ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 173.82/173.86 => 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))) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Min__eqI,axiom, % 173.82/173.86 ! [V_x_2,V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( ! [B_y] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) ) % 173.82/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.86 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Max__eqI,axiom, % 173.82/173.86 ! [V_x_2,V_A_2,T_b] : % 173.82/173.86 ( class_Orderings_Olinorder(T_b) % 173.82/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 173.82/173.86 => ( ! [B_y] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) ) % 173.82/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 173.82/173.86 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__no__infinite__down__chainE,axiom, % 173.82/173.86 ! [V_f_2,V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => ~ ! [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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_setsum__reindex__cong,axiom, % 173.82/173.86 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 173.82/173.86 ( class_Groups_Ocomm__monoid__add(T_d) % 173.82/173.86 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 173.82/173.86 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 173.82/173.86 => ( ! [B_a] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 173.82/173.86 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 173.82/173.86 => 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) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_less__eq,axiom, % 173.82/173.86 ! [V_n_2,V_m_2] : % 173.82/173.86 ( 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))) % 173.82/173.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__trancl,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_less__than__def,axiom, % 173.82/173.86 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 173.82/173.86 % 173.82/173.86 fof(fact_acyclic__def,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 173.82/173.86 <=> ! [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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl_Or__into__trancl,axiom, % 173.82/173.86 ! [V_r_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__subset__Field2,axiom, % 173.82/173.86 ! [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))))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_r__into__trancl_H,axiom, % 173.82/173.86 ! [V_r_2,V_p_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__empty,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__domain,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__range,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__trancl,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 173.82/173.86 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__trans,axiom, % 173.82/173.86 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ( 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))) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 173.82/173.86 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__into__trancl2,axiom, % 173.82/173.86 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ( 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))) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_r__r__into__trancl,axiom, % 173.82/173.86 ! [V_ca_2,V_R_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__mono,axiom, % 173.82/173.86 ! [V_s_2,V_r_2,V_p_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 173.82/173.86 => ( 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)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__unfold,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__subset__Sigma,axiom, % 173.82/173.86 ! [V_A_2,V_r_2,T_b] : % 173.82/173.86 ( 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)))) % 173.82/173.86 => 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)))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__Int__subset,axiom, % 173.82/173.86 ! [V_s_2,V_r_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__insert,axiom, % 173.82/173.86 ! [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)))))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_reflcl__set__eq,axiom, % 173.82/173.86 ! [V_y_2,V_x_2,V_r_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 <=> 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)))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_r__into__rtrancl,axiom, % 173.82/173.86 ! [V_r_2,V_p_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl_Ortrancl__refl,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_IdI,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__into__rtrancl,axiom, % 173.82/173.86 ! [V_r_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__unfold__right,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__unfold__left,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_reflcl__trancl,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__reflcl,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__rtrancl__absorb,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__trancl__absorb,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_refl__rtrancl,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__idemp,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__trans,axiom, % 173.82/173.86 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ( 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))) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 173.82/173.86 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 173.82/173.86 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ( 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))) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__r__diff__Id,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_in__rtrancl__UnI,axiom, % 173.82/173.86 ! [V_S_2,V_R_2,V_x_2,T_b] : % 173.82/173.86 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 173.82/173.86 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) ) % 173.82/173.86 => 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)))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Image__closed__trancl,axiom, % 173.82/173.86 ! [V_X_2,V_r_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__Un__subset,axiom, % 173.82/173.86 ! [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)))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__reflcl,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__Un__rtrancl,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__reflcl__absorb,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__subset__rtrancl,axiom, % 173.82/173.86 ! [V_s_2,V_r_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__subset,axiom, % 173.82/173.86 ! [V_S_2,V_R_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ( 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))) % 173.82/173.86 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__mono,axiom, % 173.82/173.86 ! [V_s_2,V_r_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__Int__subset,axiom, % 173.82/173.86 ! [V_r_2,V_s_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_r__comp__rtrancl__eq,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__idemp__self__comp,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__unfold,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__empty,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Range__rtrancl,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Domain__rtrancl,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Id__O__R,axiom, % 173.82/173.86 ! [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 ). % 173.82/173.86 % 173.82/173.86 fof(fact_R__O__Id,axiom, % 173.82/173.86 ! [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 ). % 173.82/173.86 % 173.82/173.86 fof(fact_Image__Id,axiom, % 173.82/173.86 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ). % 173.82/173.86 % 173.82/173.86 fof(fact_pair__in__Id__conv,axiom, % 173.82/173.86 ! [V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 <=> V_a_2 = V_ba_2 ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__trancl__trancl,axiom, % 173.82/173.86 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ( 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))) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__rtrancl__trancl,axiom, % 173.82/173.86 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ( 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))) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__into__trancl1,axiom, % 173.82/173.86 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtranclD,axiom, % 173.82/173.86 ! [V_R_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ( V_a_2 = V_ba_2 % 173.82/173.86 | ( V_a_2 != V_ba_2 % 173.82/173.86 & 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))) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__into__trancl2,axiom, % 173.82/173.86 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ( 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))) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__eq__or__trancl,axiom, % 173.82/173.86 ! [V_R_2,V_y_2,V_x_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 <=> ( V_x_2 = V_y_2 % 173.82/173.86 | ( V_x_2 != V_y_2 % 173.82/173.86 & 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))) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Domain__Id,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Range__Id,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_refl__Id,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_pair__leq__def,axiom, % 173.82/173.86 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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Not__Domain__rtrancl,axiom, % 173.82/173.86 ! [V_y_2,V_R_2,V_x_2,T_b] : % 173.82/173.86 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2))) % 173.82/173.86 => ( 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))) % 173.82/173.86 <=> V_x_2 = V_y_2 ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_acc__downwards__aux,axiom, % 173.82/173.86 ! [V_r_2,V_a_2,V_ba_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_acc__downwards,axiom, % 173.82/173.86 ! [V_ba_2,V_r_2,V_a_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 173.82/173.86 => ( 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))) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__insert,axiom, % 173.82/173.86 ! [V_r_2,V_x_2,V_y_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 <=> ( c_Wellfounded_Owf(T_b,V_r_2) % 173.82/173.86 & ~ 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_acyclic__insert,axiom, % 173.82/173.86 ! [V_r_2,V_x_2,V_y_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 173.82/173.86 & ~ 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_refl__reflcl,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Id__def,axiom, % 173.82/173.86 ! [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))))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_irrefl__diff__Id,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_pred__nat__trancl__eq__le,axiom, % 173.82/173.86 ! [V_n_2,V_m_2] : % 173.82/173.86 ( 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))) % 173.82/173.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__subset__Sigma__aux,axiom, % 173.82/173.86 ! [V_A_2,V_r_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ( 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)))) % 173.82/173.86 => ( V_a_2 = V_ba_2 % 173.82/173.86 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_irrefl__tranclI,axiom, % 173.82/173.86 ! [V_x_2,V_r_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ~ 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_sequence__trans,axiom, % 173.82/173.86 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] : % 173.82/173.86 ( ! [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))) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__converse,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_converse__Id,axiom, % 173.82/173.86 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Range__def,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Domain__converse,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Range__converse,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_equiv__comp__eq,axiom, % 173.82/173.86 ! [V_r_2,V_A_2,T_b] : % 173.82/173.86 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 173.82/173.86 => 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 ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_converse__UNION,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_converseD,axiom, % 173.82/173.86 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => 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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_converseI,axiom, % 173.82/173.86 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_converse__iff,axiom, % 173.82/173.86 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 <=> 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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_refl__on__converse,axiom, % 173.82/173.86 ! [V_r_2,V_A_2,T_b] : % 173.82/173.86 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 173.82/173.86 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_converse__Int,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_converse__converse,axiom, % 173.82/173.86 ! [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 ). % 173.82/173.86 % 173.82/173.86 fof(fact_Field__converse,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_converse__Id__on,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_converse__inv__image,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__converse,axiom, % 173.82/173.86 ! [V_r_2,T_c,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 173.82/173.86 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_converse__Un,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_converse__rel__comp,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_acyclic__converse,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 173.82/173.86 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__converse__trancl,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 173.82/173.86 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__converse,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__converseI,axiom, % 173.82/173.86 ! [V_r_2,V_x_2,V_y_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => 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)))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__converseD,axiom, % 173.82/173.86 ! [V_r_2,V_y_2,V_x_2,T_b] : % 173.82/173.86 ( 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)))) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__converseI,axiom, % 173.82/173.86 ! [V_r_2,V_y_2,V_x_2,T_b] : % 173.82/173.86 ( 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)))) % 173.82/173.86 => 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)))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__converseD,axiom, % 173.82/173.86 ! [V_r_2,V_y_2,V_x_2,T_b] : % 173.82/173.86 ( 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)))) % 173.82/173.86 => 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)))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Image__subset__eq,axiom, % 173.82/173.86 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 <=> 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))))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_refl__on__comp__subset,axiom, % 173.82/173.86 ! [V_r_2,V_A_2,T_b] : % 173.82/173.86 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 173.82/173.86 => 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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_comp__equivI,axiom, % 173.82/173.86 ! [V_A_2,V_r_2,T_b] : % 173.82/173.86 ( 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 % 173.82/173.86 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2 % 173.82/173.86 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_finite__acyclic__wf__converse,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 173.82/173.86 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 173.82/173.86 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_converse__def,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_total__on__diff__Id,axiom, % 173.82/173.86 ! [V_r_2,V_A_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 173.82/173.86 ! [V_R_2,V_p_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 173.82/173.86 => 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)))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_relpow_Osimps_I1_J,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__power,axiom, % 173.82/173.86 ! [V_R_2,V_p_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 173.82/173.86 <=> ? [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))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__pow__imp__rtrancl,axiom, % 173.82/173.86 ! [V_R_2,V_n_2,V_p_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__pow__1,axiom, % 173.82/173.86 ! [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 ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__pow__commute,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_relpow_Osimps_I2_J,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__pow__add,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_funpow__mult,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_funpow__swap1,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_wf__exp,axiom, % 173.82/173.86 ! [V_R_2,V_n_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_comp__funpow,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_total__on__empty,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_total__on__converse,axiom, % 173.82/173.86 ! [V_r_2,V_A_2,T_b] : % 173.82/173.86 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 173.82/173.86 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__pow__0__E,axiom, % 173.82/173.86 ! [V_R_2,V_y_2,V_x_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => V_x_2 = V_y_2 ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__pow__0__I,axiom, % 173.82/173.86 ! [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))) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__pow__Suc__I2,axiom, % 173.82/173.86 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] : % 173.82/173.86 ( 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)) % 173.82/173.86 => ( 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))) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__pow__Suc__I,axiom, % 173.82/173.86 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ( 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)) % 173.82/173.86 => 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_funpow_Osimps_I2_J,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_funpow__add,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_funpow_Osimps_I1_J,axiom, % 173.82/173.86 ! [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) ). % 173.82/173.86 % 173.82/173.86 fof(fact_trancl__power,axiom, % 173.82/173.86 ! [V_R_2,V_p_2,T_b] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 173.82/173.86 <=> ? [B_n] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 173.82/173.86 & 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))) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_total__on__def,axiom, % 173.82/173.86 ! [V_r_2,V_A_2,T_b] : % 173.82/173.86 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2) % 173.82/173.86 <=> ! [B_x] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 173.82/173.86 => ! [B_xa] : % 173.82/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 173.82/173.86 => ( B_x != B_xa % 173.82/173.86 => ( 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)) % 173.82/173.86 | 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)) ) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 173.82/173.86 ! [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)) ). % 173.82/173.86 % 173.82/173.86 fof(fact_funpow__code__def,axiom, % 173.82/173.86 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__pow__E2,axiom, % 173.82/173.86 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.86 => V_x_2 != V_z_2 ) % 173.82/173.86 => ~ ! [B_y,B_m] : % 173.82/173.86 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 173.82/173.86 => ( 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)) % 173.82/173.86 => ~ 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))) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rel__pow__E,axiom, % 173.82/173.86 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 173.82/173.86 ( 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))) % 173.82/173.86 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 173.82/173.86 => V_x_2 != V_z_2 ) % 173.82/173.86 => ~ ! [B_y,B_m] : % 173.82/173.86 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 173.82/173.86 => ( 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))) % 173.82/173.86 => ~ 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)) ) ) ) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_acyclicI,axiom, % 173.82/173.86 ! [V_r_2,T_b] : % 173.82/173.86 ( ! [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))) % 173.82/173.86 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_Image__Int__eq,axiom, % 173.82/173.86 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : % 173.82/173.86 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2)) % 173.82/173.86 => 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)) ) ). % 173.82/173.86 % 173.82/173.86 fof(fact_rtrancl__Un__separator__converseE,axiom, % 173.82/173.86 ! [V_Q_2,V_Pa_2,V_ba_2,V_a_2,T_b] : % 173.82/173.86 ( 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)))) % 174.01/173.86 => ( ! [B_x] : % 174.01/173.86 ( 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))) % 174.01/173.86 => ! [B_y] : % 174.01/173.86 ( 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)) % 174.01/173.86 => B_y = B_x ) ) % 174.01/173.86 => 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))) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_single__valued__Id__on,axiom, % 174.01/173.86 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 174.01/173.86 % 174.01/173.86 fof(fact_single__valued__subset,axiom, % 174.01/173.86 ! [V_s_2,V_r_2,T_c,T_b] : % 174.01/173.86 ( 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)) % 174.01/173.86 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 174.01/173.86 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_single__valued__rel__comp,axiom, % 174.01/173.86 ! [V_s_2,T_d,V_r_2,T_c,T_b] : % 174.01/173.86 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 174.01/173.86 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2) % 174.01/173.86 => 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)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_single__valued__Id,axiom, % 174.01/173.86 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ). % 174.01/173.86 % 174.01/173.86 fof(fact_single__valued__rel__pow,axiom, % 174.01/173.86 ! [V_n_2,V_R_2,T_b] : % 174.01/173.86 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2) % 174.01/173.86 => 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)) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_single__valuedD,axiom, % 174.01/173.86 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] : % 174.01/173.86 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 174.01/173.86 => ( 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)) % 174.01/173.86 => ( 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)) % 174.01/173.86 => V_y_2 = V_z_2 ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_single__valued__def,axiom, % 174.01/173.86 ! [V_r_2,T_c,T_b] : % 174.01/173.86 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 174.01/173.86 <=> ! [B_x,B_y] : % 174.01/173.86 ( 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)) % 174.01/173.86 => ! [B_z] : % 174.01/173.86 ( 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)) % 174.01/173.86 => B_y = B_z ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_single__valued__confluent,axiom, % 174.01/173.86 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] : % 174.01/173.86 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2) % 174.01/173.86 => ( 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))) % 174.01/173.86 => ( 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))) % 174.01/173.86 => ( 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))) % 174.01/173.86 | 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))) ) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_rtrancl__Un__separatorE,axiom, % 174.01/173.86 ! [V_Q_2,V_Pa_2,V_ba_2,V_a_2,T_b] : % 174.01/173.86 ( 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)))) % 174.01/173.86 => ( ! [B_x] : % 174.01/173.86 ( 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))) % 174.01/173.86 => ! [B_y] : % 174.01/173.86 ( 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)) % 174.01/173.86 => B_x = B_y ) ) % 174.01/173.86 => 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))) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_rel__pow__Suc__E,axiom, % 174.01/173.86 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 174.01/173.86 ( 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))) % 174.01/173.86 => ~ ! [B_y] : % 174.01/173.86 ( 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))) % 174.01/173.86 => ~ 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)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_rel__pow__Suc__D2,axiom, % 174.01/173.86 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 174.01/173.86 ( 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))) % 174.01/173.86 => ? [B_y] : % 174.01/173.86 ( 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)) % 174.01/173.86 & 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))) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_rel__pow__Suc__E2,axiom, % 174.01/173.86 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] : % 174.01/173.86 ( 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))) % 174.01/173.86 => ~ ! [B_y] : % 174.01/173.86 ( 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)) % 174.01/173.86 => ~ 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))) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_tranclD2,axiom, % 174.01/173.86 ! [V_R_2,V_y_2,V_x_2,T_b] : % 174.01/173.86 ( 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))) % 174.01/173.86 => ? [B_z] : % 174.01/173.86 ( 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))) % 174.01/173.86 & 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)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_tranclD,axiom, % 174.01/173.86 ! [V_R_2,V_y_2,V_x_2,T_b] : % 174.01/173.86 ( 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))) % 174.01/173.86 => ? [B_z] : % 174.01/173.86 ( 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)) % 174.01/173.86 & 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))) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_IdE,axiom, % 174.01/173.86 ! [V_p_2,T_b] : % 174.01/173.86 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b))) % 174.01/173.86 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 174.01/173.86 ! [V_x_2,V_A_2,T_b] : % 174.01/173.86 ( class_Orderings_Olinorder(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.86 => 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) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_folding_Oeq__fold,axiom, % 174.01/173.86 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fold__image__def,axiom, % 174.01/173.86 ! [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)) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fold__empty,axiom, % 174.01/173.86 ! [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 ). % 174.01/173.86 % 174.01/173.86 fof(fact_fold__def,axiom, % 174.01/173.86 ! [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)) ). % 174.01/173.86 % 174.01/173.86 fof(fact_union__fold__insert,axiom, % 174.01/173.86 ! [V_B_2,V_A_2,T_b] : % 174.01/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fold__sup__insert,axiom, % 174.01/173.86 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 174.01/173.86 ( class_Lattices_Osemilattice__sup(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fold__inf__insert,axiom, % 174.01/173.86 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 174.01/173.86 ( class_Lattices_Osemilattice__inf(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_min__max_Ofold__inf__insert,axiom, % 174.01/173.86 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 174.01/173.86 ( class_Orderings_Olinorder(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_min__max_Ofold__sup__insert,axiom, % 174.01/173.86 ! [V_a_2,V_ba_2,V_A_2,T_b] : % 174.01/173.86 ( class_Orderings_Olinorder(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 174.01/173.86 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 174.01/173.86 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_sup__SUPR__fold__sup,axiom, % 174.01/173.86 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 174.01/173.86 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 174.01/173.86 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_sup__le__fold__sup,axiom, % 174.01/173.86 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 174.01/173.86 ( class_Lattices_Osemilattice__sup(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 174.01/173.86 => 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))) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fold__inf__le__inf,axiom, % 174.01/173.86 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 174.01/173.86 ( class_Lattices_Osemilattice__inf(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 174.01/173.86 => 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))) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 174.01/173.86 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 174.01/173.86 ( class_Orderings_Olinorder(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 174.01/173.86 => 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))) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_min__max_Osup__le__fold__sup,axiom, % 174.01/173.86 ! [V_ba_2,V_a_2,V_A_2,T_b] : % 174.01/173.86 ( class_Orderings_Olinorder(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 174.01/173.86 => 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))) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fold1__eq__fold__idem,axiom, % 174.01/173.86 ! [V_a_2,V_A_2,T_b] : % 174.01/173.86 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 174.01/173.86 ! [V_a_2,V_A_2,T_b] : % 174.01/173.86 ( class_Lattices_Olattice(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 174.01/173.86 ! [V_a_2,V_A_2,T_b] : % 174.01/173.86 ( class_Lattices_Olattice(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_Min_Oeq__fold__idem_H,axiom, % 174.01/173.86 ! [V_a_2,V_A_2,T_b] : % 174.01/173.86 ( class_Orderings_Olinorder(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_Max_Oeq__fold__idem_H,axiom, % 174.01/173.86 ! [V_a_2,V_A_2,T_b] : % 174.01/173.86 ( class_Orderings_Olinorder(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 174.01/173.86 ! [V_a_2,V_A_2,T_b] : % 174.01/173.86 ( class_Orderings_Olinorder(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 174.01/173.86 ! [V_a_2,V_A_2,T_b] : % 174.01/173.86 ( class_Orderings_Olinorder(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_minus__fold__remove,axiom, % 174.01/173.86 ! [V_B_2,V_A_2,T_b] : % 174.01/173.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_folding__one_Oeq__fold_H,axiom, % 174.01/173.86 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.86 => 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) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_SUPR__fold__sup,axiom, % 174.01/173.86 ! [V_f_2,V_A_2,T_b,T_c] : % 174.01/173.86 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fold1__eq__fold,axiom, % 174.01/173.86 ! [V_a_2,V_A_2,T_b] : % 174.01/173.86 ( class_Groups_Oab__semigroup__mult(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 174.01/173.86 => 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) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 174.01/173.86 ! [V_x_2,V_A_2,T_b] : % 174.01/173.86 ( class_Lattices_Olattice(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.86 => 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) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 174.01/173.86 ! [V_x_2,V_A_2,T_b] : % 174.01/173.86 ( class_Lattices_Olattice(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.86 => 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) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_Min_Oeq__fold_H,axiom, % 174.01/173.86 ! [V_x_2,V_A_2,T_b] : % 174.01/173.86 ( class_Orderings_Olinorder(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.86 => 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) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_Max_Oeq__fold_H,axiom, % 174.01/173.86 ! [V_x_2,V_A_2,T_b] : % 174.01/173.86 ( class_Orderings_Olinorder(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.86 => 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) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 174.01/173.86 ! [V_x_2,V_A_2,T_b] : % 174.01/173.86 ( class_Orderings_Olinorder(T_b) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.86 => 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) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm_Ofold__rec,axiom, % 174.01/173.86 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.86 => 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)))))) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 174.01/173.86 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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)))))) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 174.01/173.86 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 174.01/173.86 => 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)) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 174.01/173.86 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 174.01/173.86 => 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)) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm,axiom, % 174.01/173.86 ! [T_b] : % 174.01/173.86 ( class_Groups_Oab__semigroup__mult(T_b) % 174.01/173.86 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 174.01/173.86 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 174.01/173.86 => V_y_2 = V_x_2 ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 174.01/173.86 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 174.01/173.86 => 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)) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 174.01/173.86 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm_Ofold__equality,axiom, % 174.01/173.86 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 174.01/173.86 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 174.01/173.86 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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))) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm_Ofold__insert,axiom, % 174.01/173.86 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.86 => 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)) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 174.01/173.86 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.86 => 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) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 174.01/173.86 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 174.01/173.86 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 174.01/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 174.01/173.86 => ? [B_y_H] : % 174.01/173.86 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 174.01/173.86 & 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)) ) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INFI__fold__inf,axiom, % 174.01/173.86 ! [V_f_2,V_A_2,T_b,T_c] : % 174.01/173.86 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 174.01/173.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.86 => 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) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INT__E,axiom, % 174.01/173.86 ! [V_a_2,V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 174.01/173.86 ( 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))) % 174.01/173.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_a_2))) % 174.01/173.86 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INT__D,axiom, % 174.01/173.86 ! [V_a_2,V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 174.01/173.86 ( 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))) % 174.01/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 174.01/173.86 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INF1__E,axiom, % 174.01/173.86 ! [V_a_2,V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 174.01/173.86 ( 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)) % 174.01/173.86 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2)) % 174.01/173.86 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INF1__D,axiom, % 174.01/173.86 ! [V_a_2,V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 174.01/173.86 ( 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)) % 174.01/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 174.01/173.86 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INF2__D,axiom, % 174.01/173.86 ! [V_a_2,V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 174.01/173.86 ( 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)) % 174.01/173.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 174.01/173.86 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INF2__E,axiom, % 174.01/173.86 ! [V_a_2,V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 174.01/173.86 ( 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)) % 174.01/173.86 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2)) % 174.01/173.86 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_finite__INT,axiom, % 174.01/173.86 ! [V_A_2,T_c,V_I_2,T_b] : % 174.01/173.86 ( ? [B_x] : % 174.01/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 174.01/173.86 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) ) % 174.01/173.86 => 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))) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_UN__simps_I7_J,axiom, % 174.01/173.86 ! [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)) ). % 174.01/173.86 % 174.01/173.86 fof(fact_UN__extend__simps_I7_J,axiom, % 174.01/173.86 ! [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)) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INT__extend__simps_I9_J,axiom, % 174.01/173.86 ! [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) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INT__simps_I9_J,axiom, % 174.01/173.86 ! [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)) ). % 174.01/173.86 % 174.01/173.86 fof(fact_Compl__INT,axiom, % 174.01/173.86 ! [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)) ). % 174.01/173.86 % 174.01/173.86 fof(fact_Compl__UN,axiom, % 174.01/173.86 ! [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)) ). % 174.01/173.86 % 174.01/173.86 fof(fact_Collect__ball__eq,axiom, % 174.01/173.86 ! [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))) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INF__less__iff,axiom, % 174.01/173.86 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] : % 174.01/173.86 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.86 & class_Orderings_Olinorder(T_b) ) % 174.01/173.86 => ( 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)) % 174.01/173.86 <=> ? [B_x] : % 174.01/173.86 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 174.01/173.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INT__Int__distrib,axiom, % 174.01/173.86 ! [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)) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 174.01/173.86 ! [V_B_2,V_A_2,T_b,T_c] : % 174.01/173.86 ( 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)) % 174.01/173.86 <=> ! [B_x] : % 174.01/173.86 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 174.01/173.86 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 174.01/173.86 ! [V_B_2,V_A_2,T_c,T_b] : % 174.01/173.86 ( 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) % 174.01/173.86 <=> ! [B_x] : % 174.01/173.86 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 174.01/173.86 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_Pow__INT__eq,axiom, % 174.01/173.86 ! [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)) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INFI__apply,axiom, % 174.01/173.86 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 174.01/173.86 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.86 => 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)) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INF__commute,axiom, % 174.01/173.86 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 174.01/173.86 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.86 => 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))) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INFI__bool__eq,axiom, % 174.01/173.86 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INT__iff,axiom, % 174.01/173.86 ! [V_B_2,V_A_2,T_c,V_ba_2,T_b] : % 174.01/173.86 ( 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))) % 174.01/173.86 <=> ! [B_x] : % 174.01/173.86 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 174.01/173.86 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,B_x))) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INF__INT__eq2,axiom, % 174.01/173.86 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 174.01/173.86 ( 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)) % 174.01/173.86 <=> 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))) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INT__absorb,axiom, % 174.01/173.86 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 174.01/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 174.01/173.86 => 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) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INF__INT__eq,axiom, % 174.01/173.86 ! [V_x_2,V_r_2,T_c,T_b] : % 174.01/173.86 ( 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)) % 174.01/173.86 <=> 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))) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_vimage__INT,axiom, % 174.01/173.86 ! [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)) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INT__extend__simps_I10_J,axiom, % 174.01/173.86 ! [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) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INT__simps_I10_J,axiom, % 174.01/173.86 ! [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)) ). % 174.01/173.86 % 174.01/173.86 fof(fact_Image__INT__subset,axiom, % 174.01/173.86 ! [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)))) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INT__lower,axiom, % 174.01/173.86 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 174.01/173.86 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 174.01/173.86 => 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))) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_le__INF__iff,axiom, % 174.01/173.86 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] : % 174.01/173.86 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.86 => ( 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))) % 174.01/173.86 <=> ! [B_x] : % 174.01/173.86 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 174.01/173.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 174.01/173.86 % 174.01/173.86 fof(fact_INT__simps_I5_J,axiom, % 174.01/173.86 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__extend__simps_I5_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__subset__iff,axiom, % 174.01/173.87 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 <=> ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 174.01/173.87 => 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__insert__distrib,axiom, % 174.01/173.87 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__insert,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INF__const,axiom, % 174.01/173.87 ! [V_M_2,T_b,V_A_2,T_c] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 174.01/173.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__extend__simps_I2_J,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 174.01/173.87 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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 ) % 174.01/173.87 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__extend__simps_I1_J,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 174.01/173.87 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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 ) % 174.01/173.87 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__constant,axiom, % 174.01/173.87 ! [V_ca_2,T_c,T_b,V_A_2] : % 174.01/173.87 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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)) ) % 174.01/173.87 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__empty,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Un__INT__distrib2,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__extend__simps_I6_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Un__INT__distrib,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__extend__simps_I7_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__simps_I6_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__simps_I7_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__Un,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_converse__INTER,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INF__subset,axiom, % 174.01/173.87 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 174.01/173.87 => 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INTER__def,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__simps_I2_J,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 174.01/173.87 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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)) ) % 174.01/173.87 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__simps_I1_J,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 174.01/173.87 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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)) ) % 174.01/173.87 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__extend__simps_I3_J,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 174.01/173.87 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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) ) % 174.01/173.87 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__simps_I3_J,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 174.01/173.87 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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)) ) % 174.01/173.87 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__extend__simps_I4_J,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 174.01/173.87 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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 ) % 174.01/173.87 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INF__leI,axiom, % 174.01/173.87 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 174.01/173.87 => 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__greaterThan__UNIV,axiom, % 174.01/173.87 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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__simps_I4_J,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 174.01/173.87 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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)) ) % 174.01/173.87 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Image__INT__eq,axiom, % 174.01/173.87 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] : % 174.01/173.87 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) % 174.01/173.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_inf__INFI__fold__inf,axiom, % 174.01/173.87 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inf__fold__inf,axiom, % 174.01/173.87 ! [V_A_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Sup__fold__sup,axiom, % 174.01/173.87 ! [V_A_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_finite__Inter,axiom, % 174.01/173.87 ! [V_M_2,T_b] : % 174.01/173.87 ( ? [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) % 174.01/173.87 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) ) % 174.01/173.87 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_UnionI,axiom, % 174.01/173.87 ! [V_A_2,V_C_2,V_X_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) % 174.01/173.87 => 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_InterD,axiom, % 174.01/173.87 ! [V_X_2,V_C_2,V_A_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_InterE,axiom, % 174.01/173.87 ! [V_X_2,V_C_2,V_A_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__simps_I8_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INT__extend__simps_I8_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INF2__iff,axiom, % 174.01/173.87 ! [V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 <=> ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 174.01/173.87 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INF1__iff,axiom, % 174.01/173.87 ! [V_ba_2,V_B_2,V_A_2,T_c,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 <=> ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 174.01/173.87 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_ba_2)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inter__image__eq,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_INTER__eq__Inter__image,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Un__Inter,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inter__anti__mono,axiom, % 174.01/173.87 ! [V_A_2,V_B_2,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inter__empty,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Union__insert,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_subset__Pow__Union,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Union__disjoint,axiom, % 174.01/173.87 ! [V_A_2,V_C_2,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 <=> ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Union__empty,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Sup__le__iff,axiom, % 174.01/173.87 ! [V_ba_2,V_A_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => ( 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)) % 174.01/173.87 <=> ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_le__Inf__iff,axiom, % 174.01/173.87 ! [V_A_2,V_ba_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => ( 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))) % 174.01/173.87 <=> ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Union__upper,axiom, % 174.01/173.87 ! [V_A_2,V_B_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inter__lower,axiom, % 174.01/173.87 ! [V_A_2,V_B_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Union__mono,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Field__Union,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inf__less__iff,axiom, % 174.01/173.87 ! [V_a_2,V_S_2,T_b] : % 174.01/173.87 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 & class_Orderings_Olinorder(T_b) ) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2)) % 174.01/173.87 <=> ? [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 174.01/173.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_less__Sup__iff,axiom, % 174.01/173.87 ! [V_S_2,V_a_2,T_b] : % 174.01/173.87 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 & class_Orderings_Olinorder(T_b) ) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2))) % 174.01/173.87 <=> ? [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 174.01/173.87 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Union__Pow__eq,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_Union__quotient,axiom, % 174.01/173.87 ! [V_r_2,V_A_2,T_b] : % 174.01/173.87 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 174.01/173.87 => 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 ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inf__Sup,axiom, % 174.01/173.87 ! [V_A_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => 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))))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Sup__Inf,axiom, % 174.01/173.87 ! [V_A_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => 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)))))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_finite__UnionD,axiom, % 174.01/173.87 ! [V_A_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) % 174.01/173.87 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_image__Union,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Sigma__Union,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_vimage__Union,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Int__Union,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Int__Union2,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_UN__extend__simps_I8_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_UN__simps_I8_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Range__Union,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Domain__Union,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inter__eq,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inter__insert,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Union__Un__distrib,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Union__UNIV,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_UNION__eq__Union__image,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Union__image__eq,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Sup__upper,axiom, % 174.01/173.87 ! [V_A_2,V_x_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.87 => 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inter__UNIV,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inf__lower,axiom, % 174.01/173.87 ! [V_A_2,V_x_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inter__Un__distrib,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Sup__empty,axiom, % 174.01/173.87 ! [T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Sup__singleton,axiom, % 174.01/173.87 ! [V_a_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => 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 ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Sup__insert,axiom, % 174.01/173.87 ! [V_A_2,V_a_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Int__Inter__image,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inf__singleton,axiom, % 174.01/173.87 ! [V_a_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => 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 ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Sup__UNIV,axiom, % 174.01/173.87 ! [T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inf__empty,axiom, % 174.01/173.87 ! [T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inf__UNIV,axiom, % 174.01/173.87 ! [T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inf__insert,axiom, % 174.01/173.87 ! [V_A_2,V_a_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Un__eq__Union,axiom, % 174.01/173.87 ! [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))))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Un__Union__image,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Union__Int__subset,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Int__eq__Inter,axiom, % 174.01/173.87 ! [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))))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inter__Un__subset,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Sup__binary,axiom, % 174.01/173.87 ! [V_ba_2,V_a_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inf__binary,axiom, % 174.01/173.87 ! [V_ba_2,V_a_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_sup__Sup__fold__sup,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Sup__fin__Sup,axiom, % 174.01/173.87 ! [V_A_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_inf__Inf__fold__inf,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inf__fin__Inf,axiom, % 174.01/173.87 ! [V_A_2,T_b] : % 174.01/173.87 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_image__INT,axiom, % 174.01/173.87 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 174.01/173.87 => ( ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 174.01/173.87 => 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)) ) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2)) % 174.01/173.87 => 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)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_card__partition,axiom, % 174.01/173.87 ! [V_k_2,V_C_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 174.01/173.87 => ( ! [B_c] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2)) % 174.01/173.87 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 ) % 174.01/173.87 => ( ! [B_c1] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2)) % 174.01/173.87 => ! [B_c2] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2)) % 174.01/173.87 => ( B_c1 != B_c2 % 174.01/173.87 => 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)) ) ) ) % 174.01/173.87 => 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)) ) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inter__def,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Union__def,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_finite__Union,axiom, % 174.01/173.87 ! [V_A_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) % 174.01/173.87 => ( ! [B_M] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2)) % 174.01/173.87 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) ) % 174.01/173.87 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_insert__partition,axiom, % 174.01/173.87 ! [V_F_2,V_x_2,T_b] : % 174.01/173.87 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)) % 174.01/173.87 => ( ! [B_x] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ! [B_xa] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( B_x != B_xa % 174.01/173.87 => 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)) ) ) ) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_inj__on__Inter,axiom, % 174.01/173.87 ! [V_f_2,T_c,T_b,V_S_2] : % 174.01/173.87 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 174.01/173.87 => ( ! [B_A] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2)) % 174.01/173.87 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) ) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Inter__subset,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,T_b] : % 174.01/173.87 ( ! [B_X] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) ) % 174.01/173.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_inj__on__INTER,axiom, % 174.01/173.87 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] : % 174.01/173.87 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 => ( ! [B_i] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2)) % 174.01/173.87 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) ) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 174.01/173.87 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 174.01/173.87 => ( 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)) % 174.01/173.87 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.87 => ~ ! [B_y] : % 174.01/173.87 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 174.01/173.87 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 174.01/173.87 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => ( ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) ) % 174.01/173.87 => 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))) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 174.01/173.87 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => ( ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) ) % 174.01/173.87 => 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))) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_InterI,axiom, % 174.01/173.87 ! [V_A_2,V_C_2,T_b] : % 174.01/173.87 ( ! [B_X] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) ) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_inf__le__fold__inf,axiom, % 174.01/173.87 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 174.01/173.87 ( class_Lattices_Osemilattice__inf(T_b) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => ( ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) ) % 174.01/173.87 => 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))) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_fold__sup__le__sup,axiom, % 174.01/173.87 ! [V_ca_2,V_ba_2,V_A_2,T_b] : % 174.01/173.87 ( class_Lattices_Osemilattice__sup(T_b) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => ( ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) ) % 174.01/173.87 => 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))) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_wf__eq__minimal,axiom, % 174.01/173.87 ! [V_r_2,T_b] : % 174.01/173.87 ( c_Wellfounded_Owf(T_b,V_r_2) % 174.01/173.87 <=> ! [B_Q] : % 174.01/173.87 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 174.01/173.87 => ? [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 174.01/173.87 & ! [B_y] : % 174.01/173.87 ( 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)) % 174.01/173.87 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 174.01/173.87 => 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)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_transfer__nat__int__set__cong,axiom, % 174.01/173.87 ! [V_P_H_2,V_Pa_2] : % 174.01/173.87 ( ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 174.01/173.87 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 174.01/173.87 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_folding__image__simple__idem_Oidem,axiom, % 174.01/173.87 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 174.01/173.87 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 174.01/173.87 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 174.01/173.87 => 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) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 174.01/173.87 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 174.01/173.87 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 174.01/173.87 => 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) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Int__Collect__mono,axiom, % 174.01/173.87 ! [V_Q_2,V_Pa_2,V_B_2,V_A_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 174.01/173.87 => ( ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 174.01/173.87 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 174.01/173.87 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 174.01/173.87 => 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)))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_UnionE,axiom, % 174.01/173.87 ! [V_C_2,V_A_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ~ ! [B_X] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) % 174.01/173.87 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__upd__left,axiom, % 174.01/173.87 ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] : % 174.01/173.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2))) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_converseE,axiom, % 174.01/173.87 ! [V_r_2,V_yx_2,T_c,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ~ ! [B_x,B_y] : % 174.01/173.87 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x) % 174.01/173.87 => ~ 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__None,axiom, % 174.01/173.87 ! [V_k_2,V_n_2,V_m_2,T_b,T_c] : % 174.01/173.87 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b) % 174.01/173.87 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 174.01/173.87 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__find__right,axiom, % 174.01/173.87 ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] : % 174.01/173.87 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__assoc,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__empty,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_empty__map__add,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__def,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 174.01/173.87 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2))) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 174.01/173.87 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] : % 174.01/173.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2))) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 174.01/173.87 ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] : % 174.01/173.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2))) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_dom__map__add,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__SomeD,axiom, % 174.01/173.87 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] : % 174.01/173.87 ( 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) % 174.01/173.87 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 174.01/173.87 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 174.01/173.87 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__Some__iff,axiom, % 174.01/173.87 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] : % 174.01/173.87 ( 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) % 174.01/173.87 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) % 174.01/173.87 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 174.01/173.87 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__upd,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_inj__on__map__add__dom,axiom, % 174.01/173.87 ! [V_m_H_2,V_m_2,T_c,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 <=> 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__comm,axiom, % 174.01/173.87 ! [V_m2_2,V_m1_2,T_c,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_finite__range__map__of__map__add,axiom, % 174.01/173.87 ! [V_l_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( 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))))) % 174.01/173.87 => 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))))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rel__compE,axiom, % 174.01/173.87 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ~ ! [B_x,B_y,B_z] : % 174.01/173.87 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z) % 174.01/173.87 => ( 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)) % 174.01/173.87 => ~ 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)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_finite__dom__map__of,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_finite__range__map__of,axiom, % 174.01/173.87 ! [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))))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__map__of__foldr,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_full__small__int__def,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_small_H_Osimps,axiom, % 174.01/173.87 ! [V_f_2,V_i_2,V_d_2] : % 174.01/173.87 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 174.01/173.87 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 174.01/173.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_small_H_Opsimps,axiom, % 174.01/173.87 ! [V_i_2,V_d_2,V_f_2] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 174.01/173.87 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 174.01/173.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 174.01/173.87 => 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)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_small__int__def,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_small__prod__def,axiom, % 174.01/173.87 ! [V_d_2,V_f_2,T_b,T_c] : % 174.01/173.87 ( ( class_Smallcheck_Osmall(T_c) % 174.01/173.87 & class_Smallcheck_Osmall(T_b) ) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_small_H_Opinduct,axiom, % 174.01/173.87 ! [V_Pa_2,V_a2_2,V_a1_2,V_a0_2] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => ( ! [B_f,B_d,B_i] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 174.01/173.87 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 174.01/173.87 => 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)))) ) ) % 174.01/173.87 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,B_f),B_d),B_i)) ) ) % 174.01/173.87 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_body__def,axiom, % 174.01/173.87 c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__mapk__SomeI,axiom, % 174.01/173.87 ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] : % 174.01/173.87 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 174.01/173.87 => ( 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) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__comp__def,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_inj__mapI,axiom, % 174.01/173.87 ! [V_f_2,T_c,T_b] : % 174.01/173.87 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__comp__Some__iff,axiom, % 174.01/173.87 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] : % 174.01/173.87 ( 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) % 174.01/173.87 <=> ? [B_k_H] : % 174.01/173.87 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H) % 174.01/173.87 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__comp__simps_I2_J,axiom, % 174.01/173.87 ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] : % 174.01/173.87 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__comp__simps_I1_J,axiom, % 174.01/173.87 ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] : % 174.01/173.87 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_inj__map,axiom, % 174.01/173.87 ! [V_f_2,T_c,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_inj__map__eq__map,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 174.01/173.87 => ( 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) % 174.01/173.87 <=> V_xs_2 = V_ys_2 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_inj__mapD,axiom, % 174.01/173.87 ! [V_f_2,T_c,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__injective,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 174.01/173.87 ( 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) % 174.01/173.87 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 174.01/173.87 => V_xs_2 = V_ys_2 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__ident,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ). % 174.01/173.87 % 174.01/173.87 fof(fact_List_Omap_Oidentity,axiom, % 174.01/173.87 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_List_Omap_Oid,axiom, % 174.01/173.87 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__map,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_List_Omap_Ocompositionality,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__comp__map,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_List_Omap_Ocomp,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_foldr__map,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__comp__empty_I1_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__comp__empty_I2_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__comp__None__iff,axiom, % 174.01/173.87 ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] : % 174.01/173.87 ( 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) % 174.01/173.87 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c) % 174.01/173.87 | ? [B_k_H] : % 174.01/173.87 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H) % 174.01/173.87 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__map,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__map__keys,axiom, % 174.01/173.87 ! [V_m_2,T_c,V_xs_2,T_b] : % 174.01/173.87 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2) % 174.01/173.87 => 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 ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_finite__set,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__map,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__eq__conv,axiom, % 174.01/173.87 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] : % 174.01/173.87 ( 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) % 174.01/173.87 <=> ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 174.01/173.87 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Option_Omap_Ocomp,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Option_Omap_Ocompositionality,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_option__map__comp,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_option__map__o__sum__case,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Option_Omap_Oidentity,axiom, % 174.01/173.87 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Option_Omap_Oid,axiom, % 174.01/173.87 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_infinite__UNIV__listI,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_dom__option__map,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_option__map__Some,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_option__map__eq__Some,axiom, % 174.01/173.87 ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] : % 174.01/173.87 ( 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) % 174.01/173.87 <=> ? [B_z] : % 174.01/173.87 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z) % 174.01/173.87 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_option__map__None,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_option__map__is__None,axiom, % 174.01/173.87 ! [V_opt_2,V_f_2,T_b,T_c] : % 174.01/173.87 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b) % 174.01/173.87 <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_option__map__o__empty,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_option__map__o__map__upd,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_inj__on__map__eq__map,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( 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) % 174.01/173.87 <=> V_xs_2 = V_ys_2 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__inj__on,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 174.01/173.87 ( 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) % 174.01/173.87 => ( 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))) % 174.01/173.87 => V_xs_2 = V_ys_2 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__fun__upd,axiom, % 174.01/173.87 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] : % 174.01/173.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_inj__on__mapI,axiom, % 174.01/173.87 ! [V_A_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__eq__dom,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,T_c,T_b] : % 174.01/173.87 ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__SomeD,axiom, % 174.01/173.87 ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] : % 174.01/173.87 ( 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) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__is__SomeD,axiom, % 174.01/173.87 ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] : % 174.01/173.87 ( 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) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_dom__map__of__conv__image__fst,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__eq__None__iff,axiom, % 174.01/173.87 ! [V_x_2,V_xys_2,T_b,T_c] : % 174.01/173.87 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b) % 174.01/173.87 <=> ~ 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Option_Omap__def,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_WT__bodies__def,axiom, % 174.01/173.87 ( c_Com_OWT__bodies % 174.01/173.87 <=> ! [B_x] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__map__restrict,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_ran__distinct,axiom, % 174.01/173.87 ! [V_al_2,T_c,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__map__of__compr,axiom, % 174.01/173.87 ! [V_xs_2,T_c,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__map,axiom, % 174.01/173.87 ! [V_xs_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) % 174.01/173.87 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 174.01/173.87 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__inject__set,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,T_c,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( 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))) % 174.01/173.87 => ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2) % 174.01/173.87 <=> 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) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__is__SomeI,axiom, % 174.01/173.87 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( 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))) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__eq__Some__iff,axiom, % 174.01/173.87 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( 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) % 174.01/173.87 <=> 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Some__eq__map__of__iff,axiom, % 174.01/173.87 ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( 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) % 174.01/173.87 <=> 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_greaterThanLessThan__upto,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_weak__map__of__SomeI,axiom, % 174.01/173.87 ! [V_l_2,V_x_2,V_k_2,T_c,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ? [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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_atLeastAtMost__upto,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__upto,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__upto,axiom, % 174.01/173.87 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_atLeastLessThan__upto,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_greaterThanAtMost__upto,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nat__list__def,axiom, % 174.01/173.87 ! [V_l_2] : % 174.01/173.87 ( c_List_Onat__list(V_l_2) % 174.01/173.87 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__remove1__eq,axiom, % 174.01/173.87 ! [V_x_2,V_xs_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.87 => 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_remove1__idem,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_notin__set__remove1,axiom, % 174.01/173.87 ! [V_y_2,V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => ~ 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_in__set__remove1,axiom, % 174.01/173.87 ! [V_xs_2,T_b,V_ba_2,V_a_2] : % 174.01/173.87 ( V_a_2 != V_ba_2 % 174.01/173.87 => ( 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)))) % 174.01/173.87 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__remove1__subset,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_remove1__commute,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__remove1,axiom, % 174.01/173.87 ! [V_x,V_xs,T_a] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 174.01/173.87 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_sorted__list__of__set__remove,axiom, % 174.01/173.87 ! [V_x_2,V_A_2,T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__zip__map,axiom, % 174.01/173.87 ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => 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)) ) % 174.01/173.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__zipI2,axiom, % 174.01/173.87 ! [V_xs,T_b,V_ys,T_a] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 174.01/173.87 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__zipI1,axiom, % 174.01/173.87 ! [V_ys,T_b,V_xs,T_a] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 174.01/173.87 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__same__conv__map,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__map__fst__snd,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__zip__map2,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__zip__map,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_in__set__zipE,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__zip__rightD,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__zip__leftD,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__same,axiom, % 174.01/173.87 ! [V_xs_2,V_ba_2,V_a_2,T_b] : % 174.01/173.87 ( 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)))) % 174.01/173.87 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 & V_a_2 = V_ba_2 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__map2,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__map1,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__map__map,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_sorted__list__of__set__insert,axiom, % 174.01/173.87 ! [V_x_2,V_A_2,T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => 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)))))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__zip__upd,axiom, % 174.01/173.87 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 => ( 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) % 174.01/173.87 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) % 174.01/173.87 => ( 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)) % 174.01/173.87 => 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)) ) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__zip,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__insort,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 174.01/173.87 ( class_Orderings_Olinorder(T_c) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_insort__left__comm,axiom, % 174.01/173.87 ! [V_xs_2,V_y_2,V_x_2,T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_insort__key__left__comm,axiom, % 174.01/173.87 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__insort,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 174.01/173.87 ( class_Orderings_Olinorder(T_c) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_neq__if__length__neq,axiom, % 174.01/173.87 ! [V_ys,V_xs,T_a] : % 174.01/173.87 ( 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) % 174.01/173.87 => V_xs != V_ys ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_fun__left__comm__insort,axiom, % 174.01/173.87 ! [T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_lexn__length,axiom, % 174.01/173.87 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 % 174.01/173.87 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__map,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__eq__imp__length__eq,axiom, % 174.01/173.87 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] : % 174.01/173.87 ( 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) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_remove1__insort,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => 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 ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_card__length,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__card,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_card__distinct,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__zip__inject,axiom, % 174.01/173.87 ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 => ( 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) % 174.01/173.87 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 174.01/173.87 => ( 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)) % 174.01/173.87 => V_ys_2 = V_zs_2 ) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__fst__zip,axiom, % 174.01/173.87 ! [V_ys_2,T_c,V_xs_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 => 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 ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__snd__zip,axiom, % 174.01/173.87 ! [V_ys_2,T_c,V_xs_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 => 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 ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__insort,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 174.01/173.87 ( class_Orderings_Olinorder(T_c) % 174.01/173.87 => ( 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))) % 174.01/173.87 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__pos__if__in__set,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__eq__conv,axiom, % 174.01/173.87 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2 % 174.01/173.87 <=> ( 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 % 174.01/173.87 & 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 ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_lenlex__conv,axiom, % 174.01/173.87 ! [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)))))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_lenlex__def,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_finite__lists__length__eq,axiom, % 174.01/173.87 ! [V_n_2,V_A_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => 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))))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__eq__iff__zip__eq,axiom, % 174.01/173.87 ! [T_b,V_ys_2,V_xs_2] : % 174.01/173.87 ( V_xs_2 = V_ys_2 % 174.01/173.87 <=> ( 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) % 174.01/173.87 & ! [B_x] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__zip__is__None,axiom, % 174.01/173.87 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 => ( 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) % 174.01/173.87 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__zip__is__Some,axiom, % 174.01/173.87 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 <=> ? [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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__remove1,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => 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)) ) % 174.01/173.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_dom__map__of__zip,axiom, % 174.01/173.87 ! [V_ys_2,T_c,V_xs_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_finite__lists__length__le,axiom, % 174.01/173.87 ! [V_n_2,V_A_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => 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))))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Nitpick_Ocard_H__def,axiom, % 174.01/173.87 ! [V_A_2,T_b] : % 174.01/173.87 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => 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)))) ) % 174.01/173.87 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__iff__zip,axiom, % 174.01/173.87 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 <=> ( 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) % 174.01/173.87 & ! [B_x] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => 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)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__rtrancl__refl,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__eq__len,axiom, % 174.01/173.87 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__rtrancl__trans,axiom, % 174.01/173.87 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => ( 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)))) % 174.01/173.87 => 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)))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__mono,axiom, % 174.01/173.87 ! [V_s_2,V_r_2,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrelp__listrel__eq,axiom, % 174.01/173.87 ! [V_xa_2,V_x_2,V_r_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 <=> 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_lexn_Osimps_I2_J,axiom, % 174.01/173.87 ! [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)))))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_impossible__Cons,axiom, % 174.01/173.87 ! [V_x,V_ys,V_xs,T_a] : % 174.01/173.87 ( 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))) % 174.01/173.87 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__ConsD,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,V_y_2,T_b] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => ( V_y_2 = V_x_2 % 174.01/173.87 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__Cons__Cons,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_List_Oset_Osimps_I2_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__subset__Cons,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_foldr_Osimps_I2_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_not__Cons__self,axiom, % 174.01/173.87 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 174.01/173.87 % 174.01/173.87 fof(fact_not__Cons__self2,axiom, % 174.01/173.87 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 174.01/173.87 % 174.01/173.87 fof(fact_list_Oinject,axiom, % 174.01/173.87 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 <=> ( V_a_2 = V_a_H_2 % 174.01/173.87 & V_list_2 = V_list_H_2 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrelp_Oequations_I2_J,axiom, % 174.01/173.87 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 174.01/173.87 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrelp_OCons,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 174.01/173.87 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map_Osimps_I2_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_remove1_Osimps_I2_J,axiom, % 174.01/173.87 ! [V_xs,T_a,V_y,V_x] : % 174.01/173.87 ( ( V_x = V_y % 174.01/173.87 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 174.01/173.87 & ( V_x != V_y % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_insort__key_Osimps_I2_J,axiom, % 174.01/173.87 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => ( ( 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))) % 174.01/173.87 => 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)) ) % 174.01/173.87 & ( ~ 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))) % 174.01/173.87 => 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)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct_Osimps_I2_J,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) % 174.01/173.87 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__Cons__code_I2_J,axiom, % 174.01/173.87 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 174.01/173.87 ( ( V_l = V_k % 174.01/173.87 => 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) ) % 174.01/173.87 & ( V_l != V_k % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list_Osize_I4_J,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel_OCons,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 => ( 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))) % 174.01/173.87 => 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of_Osimps_I2_J,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Cons__in__lex,axiom, % 174.01/173.87 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 <=> ( ( 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)) % 174.01/173.87 & 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) ) % 174.01/173.87 | ( V_x_2 = V_y_2 % 174.01/173.87 & 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))) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__Cons,axiom, % 174.01/173.87 ! [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))))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__Cons__def,axiom, % 174.01/173.87 ! [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)))))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__Cons1,axiom, % 174.01/173.87 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ~ ! [B_y,B_ys] : % 174.01/173.87 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys) % 174.01/173.87 => ( 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)) % 174.01/173.87 => ~ 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))) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__Cons2,axiom, % 174.01/173.87 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ~ ! [B_x,B_xs] : % 174.01/173.87 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) % 174.01/173.87 => ( 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)) % 174.01/173.87 => ~ 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))) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__sublist,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_pick_Osimps,axiom, % 174.01/173.87 ! [V_xs,V_x,T_a,V_i] : % 174.01/173.87 ( ( 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))) % 174.01/173.87 => 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) ) % 174.01/173.87 & ( ~ 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))) % 174.01/173.87 => 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__sublistI,axiom, % 174.01/173.87 ! [V_I_2,V_xs_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.87 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_in__set__sublistD,axiom, % 174.01/173.87 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_notin__set__sublistI,axiom, % 174.01/173.87 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => ~ 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__sublist__subset,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_select__weight__cons__zero,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_pick__member,axiom, % 174.01/173.87 ! [V_xs_2,T_b,V_i_2] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__simps_I2_J,axiom, % 174.01/173.87 ! [V_xs,V_x,T_a] : % 174.01/173.87 ( class_Groups_Omonoid__add(T_a) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__subtractf,axiom, % 174.01/173.87 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( class_Groups_Oab__group__add(T_b) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__const__mult,axiom, % 174.01/173.87 ! [V_xs_2,V_f_2,V_ca_2,T_c,T_b] : % 174.01/173.87 ( class_Rings_Osemiring__0(T_b) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__mult__const,axiom, % 174.01/173.87 ! [V_xs_2,V_ca_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( class_Rings_Osemiring__0(T_b) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__addf,axiom, % 174.01/173.87 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( class_Groups_Ocomm__monoid__add(T_b) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__0,axiom, % 174.01/173.87 ! [V_xs_2,T_c,T_b] : % 174.01/173.87 ( class_Groups_Omonoid__add(T_b) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__abs,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : % 174.01/173.87 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 174.01/173.87 => 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_uminus__listsum__map,axiom, % 174.01/173.87 ! [V_xs_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( class_Groups_Oab__group__add(T_b) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__listsum__conv__Setsum,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : % 174.01/173.87 ( class_Groups_Ocomm__monoid__add(T_b) % 174.01/173.87 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_select__weight__def,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 174.01/173.87 ! [V_f_2,V_xs_2,T_b,T_c] : % 174.01/173.87 ( class_Groups_Ocomm__monoid__add(T_c) % 174.01/173.87 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 174.01/173.87 ! [V_l_2,V_k_2,V_f_2,T_b] : % 174.01/173.87 ( class_Groups_Ocomm__monoid__add(T_b) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 174.01/173.87 ! [V_j_2,V_i_2,V_f_2,T_b] : % 174.01/173.87 ( class_Groups_Ocomm__monoid__add(T_b) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__triv,axiom, % 174.01/173.87 ! [V_xs_2,V_r_2,T_c,T_b] : % 174.01/173.87 ( class_Rings_Osemiring__1(T_b) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__map__remove1,axiom, % 174.01/173.87 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] : % 174.01/173.87 ( class_Groups_Ocomm__monoid__add(T_c) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => 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)))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_select__weight__member,axiom, % 174.01/173.87 ! [V_s_2,V_xs_2,T_b] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Nitpick_Osetsum_H__def,axiom, % 174.01/173.87 ! [V_f_2,V_A_2,T_b,T_c] : % 174.01/173.87 ( class_Groups_Ocomm__monoid__add(T_c) % 174.01/173.87 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => 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))))) ) % 174.01/173.87 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.87 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_upto_Opsimps,axiom, % 174.01/173.87 ! [V_j_2,V_i_2] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 174.01/173.87 => 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)) ) % 174.01/173.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 174.01/173.87 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__Nil2,axiom, % 174.01/173.87 ! [V_r_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__Nil1,axiom, % 174.01/173.87 ! [V_r_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 174.01/173.87 ! [V_ns_2] : % 174.01/173.87 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 <=> ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 174.01/173.87 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__simps_I1_J,axiom, % 174.01/173.87 ! [T_a] : % 174.01/173.87 ( class_Groups_Omonoid__add(T_a) % 174.01/173.87 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__is__Nil__conv,axiom, % 174.01/173.87 ! [V_xs_2,V_f_2,T_b,T_c] : % 174.01/173.87 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b) % 174.01/173.87 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map_Osimps_I1_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Nil__is__map__conv,axiom, % 174.01/173.87 ! [V_xs_2,V_f_2,T_c,T_b] : % 174.01/173.87 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) % 174.01/173.87 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrelp_Oequations_I1_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrelp_ONil,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_insort__not__Nil,axiom, % 174.01/173.87 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] : % 174.01/173.87 ( class_Orderings_Olinorder(T_c) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct_Osimps_I1_J,axiom, % 174.01/173.87 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_remove1_Osimps_I1_J,axiom, % 174.01/173.87 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 174.01/173.87 % 174.01/173.87 fof(fact_foldr_Osimps_I1_J,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_upto__empty,axiom, % 174.01/173.87 ! [V_i,V_j] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 174.01/173.87 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__Nil,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip_Osimps_I1_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list_Osize_I3_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__0__conv,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : % 174.01/173.87 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_sorted__list__of__set__empty,axiom, % 174.01/173.87 ! [T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__empty,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : % 174.01/173.87 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 174.01/173.87 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__empty2,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : % 174.01/173.87 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2) % 174.01/173.87 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_List_Oset_Osimps_I1_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list_Osimps_I2_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list_Osimps_I3_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_insort__key_Osimps_I1_J,axiom, % 174.01/173.87 ! [V_x_2,V_f_2,T_b,T_c] : % 174.01/173.87 ( class_Orderings_Olinorder(T_c) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_sublist__empty,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_sublist__nil,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__greater__0__conv,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel_ONil,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Nil__notin__lex,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Nil2__notin__lex,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_upto_Osimps,axiom, % 174.01/173.87 ! [V_j,V_i] : % 174.01/173.87 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 174.01/173.87 => 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)) ) % 174.01/173.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 174.01/173.87 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_sublist__singleton,axiom, % 174.01/173.87 ! [V_x_2,T_b,V_A_2] : % 174.01/173.87 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 174.01/173.87 => 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)) ) % 174.01/173.87 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_upto__rec__number__of,axiom, % 174.01/173.87 ! [V_n,V_m] : % 174.01/173.87 ( ( 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))) % 174.01/173.87 => 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))) ) % 174.01/173.87 & ( ~ 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))) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__Nil,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__Cons__sing__Nil,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_select__weigth__select,axiom, % 174.01/173.87 ! [T_b,V_xs_2] : % 174.01/173.87 ( V_xs_2 != c_List_Olist_ONil(T_b) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_select,axiom, % 174.01/173.87 ! [V_s_2,T_b,V_xs_2] : % 174.01/173.87 ( V_xs_2 != c_List_Olist_ONil(T_b) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of_Osimps_I1_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__Cons__code_I1_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_anamorph_Osimps,axiom, % 174.01/173.87 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 174.01/173.87 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 174.01/173.87 => 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) ) % 174.01/173.87 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listset_Osimps_I1_J,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listset_Osimps_I2_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__Cons1,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__Cons,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list_Osimps_I5_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list_Osimps_I4_J,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_select__def,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_pick__same,axiom, % 174.01/173.87 ! [V_xs_2,T_b,V_l_2] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth_Osimps,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__Cons__0,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__Cons__Suc,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__map,axiom, % 174.01/173.87 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_all__set__conv__all__nth,axiom, % 174.01/173.87 ! [V_Pa_2,V_xs_2,T_b] : % 174.01/173.87 ( ! [B_x] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 174.01/173.87 <=> ! [B_i] : % 174.01/173.87 ( 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))) % 174.01/173.87 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__conv__nth,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.87 <=> ! [B_i] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ! [B_j] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( B_i != B_j % 174.01/173.87 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__eq__iff__index__eq,axiom, % 174.01/173.87 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.87 => ( 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))) % 174.01/173.87 => ( 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))) % 174.01/173.87 => ( 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) % 174.01/173.87 <=> V_i_2 = V_j_2 ) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__eq__iff__nth__eq,axiom, % 174.01/173.87 ! [T_b,V_ys_2,V_xs_2] : % 174.01/173.87 ( V_xs_2 = V_ys_2 % 174.01/173.87 <=> ( 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) % 174.01/173.87 & ! [B_i] : % 174.01/173.87 ( 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))) % 174.01/173.87 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__zip,axiom, % 174.01/173.87 ! [V_ys,T_b,V_xs,T_a,V_i] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( 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))) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_elem__le__listsum__nat,axiom, % 174.01/173.87 ! [V_ns,V_k] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__mem,axiom, % 174.01/173.87 ! [V_xs_2,T_b,V_n_2] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_in__set__conv__nth,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 <=> ? [B_i] : % 174.01/173.87 ( 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))) % 174.01/173.87 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__Cons_H,axiom, % 174.01/173.87 ! [V_xs,V_x,T_a,V_n] : % 174.01/173.87 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 174.01/173.87 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 => 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__conv__nth,axiom, % 174.01/173.87 ! [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))))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__Cons__number__of,axiom, % 174.01/173.87 ! [V_xs,V_x,T_a,V_v] : % 174.01/173.87 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 => 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 ) % 174.01/173.87 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 => 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__setsum__nth,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : % 174.01/173.87 ( class_Groups_Ocomm__monoid__add(T_b) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__sublist,axiom, % 174.01/173.87 ! [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))))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__iff__nth,axiom, % 174.01/173.87 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 <=> ( 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) % 174.01/173.87 & ! [B_n] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__zip,axiom, % 174.01/173.87 ! [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)))))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_insort__insert__insort__key,axiom, % 174.01/173.87 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => ( ~ 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)))) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__list__update,axiom, % 174.01/173.87 ! [V_i_2,V_a_2,V_xs_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.87 => ( ~ 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)))))) % 174.01/173.87 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__list__update__neq,axiom, % 174.01/173.87 ! [V_x,V_xs,T_a,V_j,V_i] : % 174.01/173.87 ( V_i != V_j % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update__id,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update__code_I1_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update_Osimps_I1_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update__nonempty,axiom, % 174.01/173.87 ! [V_x_2,V_k_2,V_xs_2,T_b] : % 174.01/173.87 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b) % 174.01/173.87 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__update,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_update__zip,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__list__update,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update__overwrite,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update__swap,axiom, % 174.01/173.87 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 174.01/173.87 ( V_i != V_i_H % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__insort__insert,axiom, % 174.01/173.87 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] : % 174.01/173.87 ( class_Orderings_Olinorder(T_c) % 174.01/173.87 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.87 => 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update__beyond,axiom, % 174.01/173.87 ! [V_x,V_i,V_xs,T_a] : % 174.01/173.87 ( 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)) % 174.01/173.87 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__update,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update__code_I3_J,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update__code_I2_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update_Osimps_I2_J,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__update__subsetI,axiom, % 174.01/173.87 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__update__subset__insert,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__list__update,axiom, % 174.01/173.87 ! [V_x,V_j,V_xs,T_a,V_i] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( ( V_i = V_j % 174.01/173.87 => 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 ) % 174.01/173.87 & ( V_i != V_j % 174.01/173.87 => 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) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update__same__conv,axiom, % 174.01/173.87 ! [V_x_2,V_xs_2,T_b,V_i_2] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 174.01/173.87 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__list__update__eq,axiom, % 174.01/173.87 ! [V_x,V_xs,T_a,V_i] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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 ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__update__memI,axiom, % 174.01/173.87 ! [V_x_2,V_xs_2,T_b,V_n_2] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_insort__insert__triv,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__insort__insert,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__update__nat,axiom, % 174.01/173.87 ! [V_n,V_ns,V_k] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_insort__insert__key__triv,axiom, % 174.01/173.87 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => ( 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)))) % 174.01/173.87 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_insort__insert__insort,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( class_Orderings_Olinorder(T_b) % 174.01/173.87 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_sublist__Cons,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_lexord__cons__cons,axiom, % 174.01/173.87 ! [V_r_2,V_y_2,V_ba_2,V_x_2,V_a_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 <=> ( 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)) % 174.01/173.87 | ( V_a_2 = V_ba_2 % 174.01/173.87 & 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))) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__append__length,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__append__length__plus,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__append,axiom, % 174.01/173.87 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 174.01/173.87 ( 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) % 174.01/173.87 => ( 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) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__append,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update__append1,axiom, % 174.01/173.87 ! [V_x,V_ys,V_xs,T_a,V_i] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update__length,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_remove1__append,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => 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) ) % 174.01/173.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__eq__Cons__conv,axiom, % 174.01/173.87 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 174.01/173.87 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) % 174.01/173.87 | ? [B_ys_H] : % 174.01/173.87 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) % 174.01/173.87 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Cons__eq__append__conv,axiom, % 174.01/173.87 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 174.01/173.87 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 ) % 174.01/173.87 | ? [B_ys_H] : % 174.01/173.87 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 % 174.01/173.87 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append1__eq__conv,axiom, % 174.01/173.87 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 <=> ( V_xs_2 = V_ys_2 % 174.01/173.87 & V_x_2 = V_y_2 ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_lexord__append__left__rightI,axiom, % 174.01/173.87 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_ba_2,V_a_2,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__Cons,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Cons__eq__appendI,axiom, % 174.01/173.87 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 174.01/173.87 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 174.01/173.87 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 174.01/173.87 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listsum__append,axiom, % 174.01/173.87 ! [V_ys,V_xs,T_a] : % 174.01/173.87 ( class_Groups_Omonoid__add(T_a) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__append,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__append,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__eq__appendI,axiom, % 174.01/173.87 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 174.01/173.87 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 174.01/173.87 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 174.01/173.87 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__same__eq,axiom, % 174.01/173.87 ! [V_zs_2,V_xs_2,V_ys_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 <=> V_ys_2 = V_zs_2 ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_same__append__eq,axiom, % 174.01/173.87 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 <=> V_ys_2 = V_zs_2 ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__eq__append__conv2,axiom, % 174.01/173.87 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 <=> ? [B_us] : % 174.01/173.87 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) % 174.01/173.87 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 ) % 174.01/173.87 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 % 174.01/173.87 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__assoc,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__of__append,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_foldr__append,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_lexord__append__leftI,axiom, % 174.01/173.87 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__Nil,axiom, % 174.01/173.87 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 174.01/173.87 % 174.01/173.87 fof(fact_Nil__is__append__conv,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 174.01/173.87 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 174.01/173.87 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__Nil2,axiom, % 174.01/173.87 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 174.01/173.87 % 174.01/173.87 fof(fact_self__append__conv,axiom, % 174.01/173.87 ! [V_ys_2,T_b,V_xs_2] : % 174.01/173.87 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 174.01/173.87 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_self__append__conv2,axiom, % 174.01/173.87 ! [V_xs_2,T_b,V_ys_2] : % 174.01/173.87 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 174.01/173.87 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__is__Nil__conv,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b) % 174.01/173.87 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 174.01/173.87 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__self__conv,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2 % 174.01/173.87 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__self__conv2,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2 % 174.01/173.87 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_eq__Nil__appendI,axiom, % 174.01/173.87 ! [T_a,V_ys,V_xs] : % 174.01/173.87 ( V_xs = V_ys % 174.01/173.87 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__append,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) % 174.01/173.87 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.87 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 174.01/173.87 & 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__append,axiom, % 174.01/173.87 ! [V_ys,V_xs,T_a,V_n] : % 174.01/173.87 ( ( 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))) % 174.01/173.87 => 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) ) % 174.01/173.87 & ( ~ 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))) % 174.01/173.87 => 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_list__update__append,axiom, % 174.01/173.87 ! [V_x,V_ys,V_xs,T_a,V_n] : % 174.01/173.87 ( ( 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))) % 174.01/173.87 => 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) ) % 174.01/173.87 & ( ~ 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))) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_lexord__Nil__right,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_sublist__append,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_lexord__lex,axiom, % 174.01/173.87 ! [V_r_2,V_y_2,V_x_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 <=> ( 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))) % 174.01/173.87 & 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__upds__append1,axiom, % 174.01/173.87 ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_lexord__take__index__conv,axiom, % 174.01/173.87 ! [V_r_2,V_y_2,V_x_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 <=> ( ( 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))) % 174.01/173.87 & 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 ) % 174.01/173.87 | ? [B_i] : % 174.01/173.87 ( 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)))) % 174.01/173.87 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2) % 174.01/173.87 & 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)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__append,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_fun__upds__append__drop,axiom, % 174.01/173.87 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_fun__upds__append2__drop,axiom, % 174.01/173.87 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__upds__Nil2,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__upds__Nil1,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__Nil,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__eq__Nil,axiom, % 174.01/173.87 ! [V_xs_2,V_n_2,T_b] : % 174.01/173.87 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 174.01/173.87 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__0,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_sublist__upt__eq__take,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__zip,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__take,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__add__upds,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__take,axiom, % 174.01/173.87 ! [V_i,V_xs,T_a] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 174.01/173.87 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__take__subset,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__take__subset__set__take,axiom, % 174.01/173.87 ! [V_xs_2,T_b,V_n_2,V_m_2] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 174.01/173.87 => 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_in__set__takeD,axiom, % 174.01/173.87 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__upds__apply__nontin,axiom, % 174.01/173.87 ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__map,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__Suc__Cons,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__1__Cons,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__upd__upds__conv__if,axiom, % 174.01/173.87 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] : % 174.01/173.87 ( ( 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)))) % 174.01/173.87 => 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) ) % 174.01/173.87 & ( ~ 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)))) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_dom__map__upds,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__all,axiom, % 174.01/173.87 ! [V_n,V_xs,T_a] : % 174.01/173.87 ( 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)) % 174.01/173.87 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__take,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__take,axiom, % 174.01/173.87 ! [V_xs,T_a,V_n,V_i] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__upds__Cons,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__Cons,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__Cons_H,axiom, % 174.01/173.87 ! [V_xs,V_x,T_a,V_n] : % 174.01/173.87 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 => 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) ) % 174.01/173.87 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__upds__list__update2__drop,axiom, % 174.01/173.87 ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 => ( 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))) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__upds__twist,axiom, % 174.01/173.87 ! [V_bs_2,V_ba_2,V_m_2,T_c,V_as_2,V_a_2,T_b] : % 174.01/173.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2))) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__Cons__number__of,axiom, % 174.01/173.87 ! [V_xs,V_x,T_a,V_v] : % 174.01/173.87 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 => 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) ) % 174.01/173.87 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 => 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)) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_restrict__map__upds,axiom, % 174.01/173.87 ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] : % 174.01/173.87 ( 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) % 174.01/173.87 => ( 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)) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__Suc__conv__app__nth,axiom, % 174.01/173.87 ! [V_xs,T_a,V_i] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_snoc__listrel1__snoc__iff,axiom, % 174.01/173.87 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 <=> ( ( 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))) % 174.01/173.87 & V_x_2 = V_y_2 ) % 174.01/173.87 | ( V_xs_2 = V_ys_2 % 174.01/173.87 & 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)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_lexord__append__leftD,axiom, % 174.01/173.87 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( ! [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)) % 174.01/173.87 => 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Cons__acc__listrel1I,axiom, % 174.01/173.87 ! [V_xs_2,V_r_2,V_x_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 174.01/173.87 => ( 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)))) % 174.01/173.87 => 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)))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel1__mono,axiom, % 174.01/173.87 ! [V_s_2,V_r_2,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel1__converse,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 174.01/173.87 ! [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)))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel1I2,axiom, % 174.01/173.87 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 174.01/173.87 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel1__eq__len,axiom, % 174.01/173.87 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rtrancl__listrel1__eq__len,axiom, % 174.01/173.87 ! [V_r_2,V_y_2,V_x_2,T_b] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_not__Nil__listrel1,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_not__listrel1__Nil,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__listrel1I,axiom, % 174.01/173.87 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( ( ( 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))) % 174.01/173.87 & V_us_2 = V_vs_2 ) % 174.01/173.87 | ( V_xs_2 = V_ys_2 % 174.01/173.87 & 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))) ) ) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_in__listrel1__converse,axiom, % 174.01/173.87 ! [V_r_2,V_y_2,V_x_2,T_b] : % 174.01/173.87 ( 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)))) % 174.01/173.87 <=> 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 174.01/173.87 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel__reflcl__if__listrel1,axiom, % 174.01/173.87 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_Cons__listrel1__Cons,axiom, % 174.01/173.87 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 <=> ( ( 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)) % 174.01/173.87 & V_xs_2 = V_ys_2 ) % 174.01/173.87 | ( V_x_2 = V_y_2 % 174.01/173.87 & 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))) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel1I1,axiom, % 174.01/173.87 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel1__subset__listrel,axiom, % 174.01/173.87 ! [V_r_H_2,V_r_2,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2) % 174.01/173.87 => 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))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel1I,axiom, % 174.01/173.87 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 174.01/173.87 ( 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)) % 174.01/173.87 => ( 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)) % 174.01/173.87 => ( 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)) % 174.01/173.87 => 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))) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 174.01/173.87 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ( 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)))) % 174.01/173.87 => 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)))) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel1__iff__update,axiom, % 174.01/173.87 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 <=> ? [B_y,B_n] : % 174.01/173.87 ( 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)) % 174.01/173.87 & 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))) % 174.01/173.87 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_listrel1E,axiom, % 174.01/173.87 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( 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))) % 174.01/173.87 => ~ ! [B_x,B_y] : % 174.01/173.87 ( 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)) % 174.01/173.87 => ! [B_us,B_vs] : % 174.01/173.87 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs)) % 174.01/173.87 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate1__def,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_upd__conv__take__nth__drop,axiom, % 174.01/173.87 ! [V_a,V_xs,T_a,V_i] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__drop__subset__set__drop,axiom, % 174.01/173.87 ! [V_xs_2,T_b,V_m_2,V_n_2] : % 174.01/173.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 174.01/173.87 => 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)))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__eq__Nil,axiom, % 174.01/173.87 ! [V_xs_2,V_n_2,T_b] : % 174.01/173.87 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 174.01/173.87 <=> 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__all,axiom, % 174.01/173.87 ! [V_n,V_xs,T_a] : % 174.01/173.87 ( 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)) % 174.01/173.87 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__via__drop,axiom, % 174.01/173.87 ! [V_ys,V_y,V_xs,V_n,T_a] : % 174.01/173.87 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 174.01/173.87 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__drop,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__rotate1,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__1__Cons,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__Suc__Cons,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__map,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_in__set__dropD,axiom, % 174.01/173.87 ! [V_xs_2,V_n_2,V_x_2,T_b] : % 174.01/173.87 ( 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)))) % 174.01/173.87 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__rotate1,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__drop__subset,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct1__rotate,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2))) % 174.01/173.87 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__drop,axiom, % 174.01/173.87 ! [V_i,V_xs,T_a] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 174.01/173.87 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__drop,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__0,axiom, % 174.01/173.87 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__zip,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__Nil,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate1__is__Nil__conv,axiom, % 174.01/173.87 ! [V_xs_2,T_b] : % 174.01/173.87 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 174.01/173.87 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__append,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__drop,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__take,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__take__drop__id,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__eq__conv__conj,axiom, % 174.01/173.87 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.87 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2 % 174.01/173.87 <=> ( 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) % 174.01/173.87 & 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__Cons,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__Cons_H,axiom, % 174.01/173.87 ! [V_xs,V_x,T_a,V_n] : % 174.01/173.87 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 => 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) ) % 174.01/173.87 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__drop,axiom, % 174.01/173.87 ! [V_xs,T_a,V_i,V_n] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_append__eq__append__conv__if,axiom, % 174.01/173.87 ! [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] : % 174.01/173.87 ( 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) % 174.01/173.87 <=> ( ( 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))) % 174.01/173.87 => ( 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) % 174.01/173.87 & 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) ) ) % 174.01/173.87 & ( ~ 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))) % 174.01/173.87 => ( 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 % 174.01/173.87 & 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 ) ) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_nth__drop_H,axiom, % 174.01/173.87 ! [V_xs,T_a,V_i] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate__simps,axiom, % 174.01/173.87 ! [V_xs,V_x,T_b,T_a] : % 174.01/173.87 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 174.01/173.87 & 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__Cons__number__of,axiom, % 174.01/173.87 ! [V_xs,V_x,T_a,V_v] : % 174.01/173.87 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 => 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) ) % 174.01/173.87 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__add,axiom, % 174.01/173.87 ! [V_xs,T_a,V_j,V_i] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate1__length01,axiom, % 174.01/173.87 ! [V_xs,T_a] : % 174.01/173.87 ( 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))) % 174.01/173.87 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__append1,axiom, % 174.01/173.87 ! [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))) ). % 174.01/173.87 % 174.01/173.87 fof(fact_zip__append2,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_id__take__nth__drop,axiom, % 174.01/173.87 ! [V_xs,T_a,V_i] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__hd__drop,axiom, % 174.01/173.87 ! [V_xs,T_a,V_n] : % 174.01/173.87 ( 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))) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_hd__drop__conv__nth,axiom, % 174.01/173.87 ! [V_n,T_a,V_xs] : % 174.01/173.87 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.87 => ( 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))) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_hd__map,axiom, % 174.01/173.87 ! [V_f_2,T_c,T_b,V_xs_2] : % 174.01/173.87 ( V_xs_2 != c_List_Olist_ONil(T_b) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_hd_Osimps,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_hd__append2,axiom, % 174.01/173.87 ! [V_ys,T_a,V_xs] : % 174.01/173.87 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_hd__append,axiom, % 174.01/173.87 ! [V_ys,T_a,V_xs] : % 174.01/173.87 ( ( V_xs = c_List_Olist_ONil(T_a) % 174.01/173.87 => 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) ) % 174.01/173.87 & ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.87 => 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) ) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_hd__in__set,axiom, % 174.01/173.87 ! [T_b,V_xs_2] : % 174.01/173.87 ( V_xs_2 != c_List_Olist_ONil(T_b) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_hd__conv__nth,axiom, % 174.01/173.87 ! [T_a,V_xs] : % 174.01/173.87 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.87 => 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)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate1__hd__tl,axiom, % 174.01/173.87 ! [T_a,V_xs] : % 174.01/173.87 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_hd__rotate__conv__nth,axiom, % 174.01/173.87 ! [V_n,T_a,V_xs] : % 174.01/173.87 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.87 => 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))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__Suc,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_drop__tl,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_tl__drop,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_tl__append2,axiom, % 174.01/173.87 ! [V_ys,T_a,V_xs] : % 174.01/173.87 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.87 => 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) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__rotate,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate__conv__mod,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_tl_Osimps_I2_J,axiom, % 174.01/173.87 ! [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 ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate__map,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_map__tl,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_set__rotate,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__rotate,axiom, % 174.01/173.87 ! [V_xs_2,V_n_2,T_b] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2))) % 174.01/173.87 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_distinct__tl,axiom, % 174.01/173.87 ! [V_xs,T_a] : % 174.01/173.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 174.01/173.87 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate__rotate,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_tl_Osimps_I1_J,axiom, % 174.01/173.87 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate__is__Nil__conv,axiom, % 174.01/173.87 ! [V_xs_2,V_n_2,T_b] : % 174.01/173.87 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) % 174.01/173.87 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__tl,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate__def,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate__Suc,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate1__rotate__swap,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_tl__append,axiom, % 174.01/173.87 ! [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) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate0,axiom, % 174.01/173.87 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate__add,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate__id,axiom, % 174.01/173.87 ! [V_xs,T_a,V_n] : % 174.01/173.87 ( 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) % 174.01/173.87 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_rotate__length01,axiom, % 174.01/173.87 ! [V_n,V_xs,T_a] : % 174.01/173.87 ( 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))) % 174.01/173.87 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 174.01/173.87 % 174.01/173.87 fof(fact_length__tl,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_tl__take,axiom, % 174.01/173.87 ! [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)) ). % 174.01/173.87 % 174.01/173.87 fof(fact_take__Suc,axiom, % 174.01/173.87 ! [V_n,T_a,V_xs] : % 174.01/173.87 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.87 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rotate__drop__take,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_fold1__set,axiom, % 174.01/173.88 ! [V_xs_2,T_b] : % 174.01/173.88 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 174.01/173.88 => ( V_xs_2 != c_List_Olist_ONil(T_b) % 174.01/173.88 => 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)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_list_Osize_I2_J,axiom, % 174.01/173.88 ! [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))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_foldl__Nil,axiom, % 174.01/173.88 ! [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 ). % 174.01/173.88 % 174.01/173.88 fof(fact_foldr__conv__foldl,axiom, % 174.01/173.88 ! [V_a_2,V_xs_2,T_b] : % 174.01/173.88 ( class_Groups_Oab__semigroup__add(T_b) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_foldl__absorb0,axiom, % 174.01/173.88 ! [V_zs_2,V_x_2,T_b] : % 174.01/173.88 ( class_Groups_Omonoid__add(T_b) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_foldl__assoc,axiom, % 174.01/173.88 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 174.01/173.88 ( class_Groups_Osemigroup__add(T_b) % 174.01/173.88 => 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)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_start__le__sum,axiom, % 174.01/173.88 ! [V_ns_2,V_n_2,V_m_2] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 174.01/173.88 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_foldl__map,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_list__size__map,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_foldl__Cons,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_foldl__append,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_listsum__foldl,axiom, % 174.01/173.88 ! [T_b] : % 174.01/173.88 ( class_Groups_Omonoid__add(T_b) % 174.01/173.88 => 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)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_foldl__foldr1,axiom, % 174.01/173.88 ! [V_xs_2,T_b] : % 174.01/173.88 ( class_Groups_Omonoid__add(T_b) % 174.01/173.88 => 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)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_foldl__foldr1__lemma,axiom, % 174.01/173.88 ! [V_xs_2,V_a_2,T_b] : % 174.01/173.88 ( class_Groups_Omonoid__add(T_b) % 174.01/173.88 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sum__eq__0__conv,axiom, % 174.01/173.88 ! [V_ns_2,V_m_2] : % 174.01/173.88 ( 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) % 174.01/173.88 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.88 & ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 174.01/173.88 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_list_Osize_I1_J,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 174.01/173.88 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] : % 174.01/173.88 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_Sup__set__fold,axiom, % 174.01/173.88 ! [V_xs_2,T_b] : % 174.01/173.88 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_Inf__set__fold,axiom, % 174.01/173.88 ! [V_xs_2,T_b] : % 174.01/173.88 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_Sup__fin__set__fold,axiom, % 174.01/173.88 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( class_Lattices_Olattice(T_b) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_Inf__fin__set__fold,axiom, % 174.01/173.88 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( class_Lattices_Olattice(T_b) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_Min__fin__set__fold,axiom, % 174.01/173.88 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_Max__fin__set__fold,axiom, % 174.01/173.88 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_min__max_OInf__fin__set__fold,axiom, % 174.01/173.88 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_min__max_OSup__fin__set__fold,axiom, % 174.01/173.88 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_SUPR__set__fold,axiom, % 174.01/173.88 ! [V_f_2,V_xs_2,T_c,T_b] : % 174.01/173.88 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_INFI__set__fold,axiom, % 174.01/173.88 ! [V_f_2,V_xs_2,T_c,T_b] : % 174.01/173.88 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_list__size__estimation,axiom, % 174.01/173.88 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 174.01/173.88 => 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))) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_list__size__estimation_H,axiom, % 174.01/173.88 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 174.01/173.88 => 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))) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_map__upds__fold__map__upd,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_elem__le__sum,axiom, % 174.01/173.88 ! [V_ns_2,V_n_2] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 174.01/173.88 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_list__size__conv__listsum,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_listrel__subset,axiom, % 174.01/173.88 ! [V_A_2,V_r_2,T_b] : % 174.01/173.88 ( 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)))) % 174.01/173.88 => 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))))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_lists__accI,axiom, % 174.01/173.88 ! [V_r_2,V_xs_2,T_b] : % 174.01/173.88 ( 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)))) % 174.01/173.88 => 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)))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_lists_ONil,axiom, % 174.01/173.88 ! [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))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_equiv__listrel,axiom, % 174.01/173.88 ! [V_r_2,V_A_2,T_b] : % 174.01/173.88 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 174.01/173.88 => 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)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_listrel__refl__on,axiom, % 174.01/173.88 ! [V_r_2,V_A_2,T_b] : % 174.01/173.88 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 174.01/173.88 => 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)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_lists__UNIV,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_append__in__lists__conv,axiom, % 174.01/173.88 ! [V_A_2,V_ys_2,V_xs_2,T_b] : % 174.01/173.88 ( 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))) % 174.01/173.88 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 174.01/173.88 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_lists__mono,axiom, % 174.01/173.88 ! [V_B_2,V_A_2,T_b] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 174.01/173.88 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_Cons__in__lists__iff,axiom, % 174.01/173.88 ! [V_A_2,V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( 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))) % 174.01/173.88 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 174.01/173.88 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_in__lists__conv__set,axiom, % 174.01/173.88 ! [V_A_2,V_xs_2,T_b] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 174.01/173.88 <=> ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_lists__eq__set,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_lists__empty,axiom, % 174.01/173.88 ! [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))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_lists__accD,axiom, % 174.01/173.88 ! [V_r_2,V_xs_2,T_b] : % 174.01/173.88 ( 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)))) % 174.01/173.88 => 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)))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_lexord__append__rightI,axiom, % 174.01/173.88 ! [V_r_2,V_x_2,T_b,V_y_2] : % 174.01/173.88 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z) % 174.01/173.88 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_lexord__Nil__left,axiom, % 174.01/173.88 ! [V_r_2,V_y_2,T_b] : % 174.01/173.88 ( 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))) % 174.01/173.88 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_last__list__update,axiom, % 174.01/173.88 ! [V_x,V_k,T_a,V_xs] : % 174.01/173.88 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.88 => ( ( 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)) % 174.01/173.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 174.01/173.88 & ( 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)) % 174.01/173.88 => 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) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_listsum__mono,axiom, % 174.01/173.88 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] : % 174.01/173.88 ( ( class_Groups_Omonoid__add(T_c) % 174.01/173.88 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 174.01/173.88 => ( ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 174.01/173.88 => 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)))) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_last__append,axiom, % 174.01/173.88 ! [V_xs,T_a,V_ys] : % 174.01/173.88 ( ( V_ys = c_List_Olist_ONil(T_a) % 174.01/173.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 174.01/173.88 & ( V_ys != c_List_Olist_ONil(T_a) % 174.01/173.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_last__appendR,axiom, % 174.01/173.88 ! [V_xs,T_a,V_ys] : % 174.01/173.88 ( V_ys != c_List_Olist_ONil(T_a) % 174.01/173.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_last__appendL,axiom, % 174.01/173.88 ! [V_xs,T_a,V_ys] : % 174.01/173.88 ( V_ys = c_List_Olist_ONil(T_a) % 174.01/173.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_last_Osimps,axiom, % 174.01/173.88 ! [V_x,T_a,V_xs] : % 174.01/173.88 ( ( V_xs = c_List_Olist_ONil(T_a) % 174.01/173.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 174.01/173.88 & ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_last__ConsR,axiom, % 174.01/173.88 ! [V_x,T_a,V_xs] : % 174.01/173.88 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_last__ConsL,axiom, % 174.01/173.88 ! [V_x,T_a,V_xs] : % 174.01/173.88 ( V_xs = c_List_Olist_ONil(T_a) % 174.01/173.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_last__map,axiom, % 174.01/173.88 ! [V_f_2,T_c,T_b,V_xs_2] : % 174.01/173.88 ( V_xs_2 != c_List_Olist_ONil(T_b) % 174.01/173.88 => 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)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_last__in__set,axiom, % 174.01/173.88 ! [T_b,V_as_2] : % 174.01/173.88 ( V_as_2 != c_List_Olist_ONil(T_b) % 174.01/173.88 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_last__snoc,axiom, % 174.01/173.88 ! [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 ). % 174.01/173.88 % 174.01/173.88 fof(fact_last__drop,axiom, % 174.01/173.88 ! [V_xs,T_a,V_n] : % 174.01/173.88 ( 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))) % 174.01/173.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_last__conv__nth,axiom, % 174.01/173.88 ! [T_a,V_xs] : % 174.01/173.88 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.88 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_lexord__linear,axiom, % 174.01/173.88 ! [V_y_2,V_x_2,V_r_2,T_b] : % 174.01/173.88 ( ! [B_a,B_b] : % 174.01/173.88 ( 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)) % 174.01/173.88 | B_a = B_b % 174.01/173.88 | 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)) ) % 174.01/173.88 => ( 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))) % 174.01/173.88 | V_x_2 = V_y_2 % 174.01/173.88 | 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))) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_lexord__irreflexive,axiom, % 174.01/173.88 ! [V_y_2,V_r_2,T_b] : % 174.01/173.88 ( ! [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)) % 174.01/173.88 => ~ 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_lists_Osimps,axiom, % 174.01/173.88 ! [V_A_2,V_a_2,T_b] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2))) % 174.01/173.88 <=> ( V_a_2 = c_List_Olist_ONil(T_b) % 174.01/173.88 | ? [B_a,B_l] : % 174.01/173.88 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) % 174.01/173.88 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 174.01/173.88 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_list__size__pointwise,axiom, % 174.01/173.88 ! [V_g_2,V_f_2,V_xs_2,T_b] : % 174.01/173.88 ( ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 174.01/173.88 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_butlast__take,axiom, % 174.01/173.88 ! [V_xs,T_a,V_n] : % 174.01/173.88 ( 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))) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_nth__take__lemma,axiom, % 174.01/173.88 ! [V_ys,V_xs,T_a,V_k] : % 174.01/173.88 ( 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))) % 174.01/173.88 => ( 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))) % 174.01/173.88 => ( ! [B_i] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 174.01/173.88 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 174.01/173.88 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_map__butlast,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_distinct__butlast,axiom, % 174.01/173.88 ! [T_a,V_xs] : % 174.01/173.88 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.88 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 174.01/173.88 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_butlast_Osimps_I1_J,axiom, % 174.01/173.88 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 174.01/173.88 % 174.01/173.88 fof(fact_in__set__butlastD,axiom, % 174.01/173.88 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 174.01/173.88 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_butlast_Osimps_I2_J,axiom, % 174.01/173.88 ! [V_x,T_a,V_xs] : % 174.01/173.88 ( ( V_xs = c_List_Olist_ONil(T_a) % 174.01/173.88 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 174.01/173.88 & ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.88 => 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)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_butlast__append,axiom, % 174.01/173.88 ! [V_xs,T_a,V_ys] : % 174.01/173.88 ( ( V_ys = c_List_Olist_ONil(T_a) % 174.01/173.88 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 174.01/173.88 & ( V_ys != c_List_Olist_ONil(T_a) % 174.01/173.88 => 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)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_butlast__drop,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_drop__butlast,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_in__set__butlast__appendI,axiom, % 174.01/173.88 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 174.01/173.88 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) ) % 174.01/173.88 => 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))))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_butlast__snoc,axiom, % 174.01/173.88 ! [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 ). % 174.01/173.88 % 174.01/173.88 fof(fact_take__butlast,axiom, % 174.01/173.88 ! [V_xs,T_a,V_n] : % 174.01/173.88 ( 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))) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_length__butlast,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_butlast__conv__take,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_butlast__list__update,axiom, % 174.01/173.88 ! [V_x,V_xs,T_a,V_k] : % 174.01/173.88 ( ( 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)) % 174.01/173.88 => 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) ) % 174.01/173.88 & ( 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)) % 174.01/173.88 => 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) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_append__butlast__last__id,axiom, % 174.01/173.88 ! [T_a,V_xs] : % 174.01/173.88 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.88 => 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 ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_snoc__eq__iff__butlast,axiom, % 174.01/173.88 ! [V_ys_2,V_x_2,V_xs_2,T_b] : % 174.01/173.88 ( 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 % 174.01/173.88 <=> ( V_ys_2 != c_List_Olist_ONil(T_b) % 174.01/173.88 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2 % 174.01/173.88 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose__aux__max,axiom, % 174.01/173.88 ! [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)))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_partition__set,axiom, % 174.01/173.88 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 174.01/173.88 ( 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) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter__is__subset,axiom, % 174.01/173.88 ! [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))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_length__filter__le,axiom, % 174.01/173.88 ! [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))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_set__filter,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter__append,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sum__length__filter__compl,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter_Osimps_I2_J,axiom, % 174.01/173.88 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 174.01/173.88 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 174.01/173.88 => 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)) ) % 174.01/173.88 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 174.01/173.88 => 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) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter__id__conv,axiom, % 174.01/173.88 ! [V_xs_2,V_Pa_2,T_b] : % 174.01/173.88 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2 % 174.01/173.88 <=> ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter__insort__triv,axiom, % 174.01/173.88 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] : % 174.01/173.88 ( class_Orderings_Olinorder(T_c) % 174.01/173.88 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 174.01/173.88 => 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) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_distinct__filter,axiom, % 174.01/173.88 ! [V_Pa_2,V_xs_2,T_b] : % 174.01/173.88 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.88 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter__remove1,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_remove1__filter__not,axiom, % 174.01/173.88 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 174.01/173.88 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter__filter,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_partition__filter1,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter__empty__conv,axiom, % 174.01/173.88 ! [V_xs_2,V_Pa_2,T_b] : % 174.01/173.88 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b) % 174.01/173.88 <=> ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter_Osimps_I1_J,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_partition__filter__conv,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_partition__filter2,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter__map,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_length__filter__map,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_length__filter__less,axiom, % 174.01/173.88 ! [V_Pa_2,V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 174.01/173.88 => 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))) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_set__minus__filter__out,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_partition__P,axiom, % 174.01/173.88 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 174.01/173.88 ( 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) % 174.01/173.88 => ( ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2))) % 174.01/173.88 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 174.01/173.88 & ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2))) % 174.01/173.88 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_partition_Osimps_I1_J,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter__in__sublist,axiom, % 174.01/173.88 ! [V_s_2,V_xs_2,T_b] : % 174.01/173.88 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_partition_Osimps_I2_J,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_length__filter__conv__card,axiom, % 174.01/173.88 ! [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))))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_map__filter__def,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose__max__length,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_map__of__filter__in,axiom, % 174.01/173.88 ! [V_Pa_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] : % 174.01/173.88 ( 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) % 174.01/173.88 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_k_2),V_z_2)) % 174.01/173.88 => 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) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose__map__map,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_map__filter__simps_I1_J,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_map__filter__simps_I2_J,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose_Osimps_I1_J,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose__empty,axiom, % 174.01/173.88 ! [V_xs_2,T_b] : % 174.01/173.88 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b)) % 174.01/173.88 <=> ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 174.01/173.88 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose_Osimps_I2_J,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sublist__shift__lemma__Suc,axiom, % 174.01/173.88 ! [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)))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_select__weigth__drop__zero,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_pick__drop__zero,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_nth__transpose,axiom, % 174.01/173.88 ! [V_xs_2,T_b,V_i_2] : % 174.01/173.88 ( 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)))) % 174.01/173.88 => 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)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_length__transpose,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_map__filter__map__filter,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_insort__key__remove1,axiom, % 174.01/173.88 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] : % 174.01/173.88 ( class_Orderings_Olinorder(T_c) % 174.01/173.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 174.01/173.88 => ( 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 % 174.01/173.88 => 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 ) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sublist__def,axiom, % 174.01/173.88 ! [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))))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted_ONil,axiom, % 174.01/173.88 ! [T_a] : % 174.01/173.88 ( class_Orderings_Olinorder(T_a) % 174.01/173.88 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__single,axiom, % 174.01/173.88 ! [V_x,T_a] : % 174.01/173.88 ( class_Orderings_Olinorder(T_a) % 174.01/173.88 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__same,axiom, % 174.01/173.88 ! [V_xs_2,V_g_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => 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)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__map__same,axiom, % 174.01/173.88 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__filter,axiom, % 174.01/173.88 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 174.01/173.88 => 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))) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_length__upt,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_last__upt,axiom, % 174.01/173.88 ! [V_j,V_i] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 174.01/173.88 => 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)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__butlast,axiom, % 174.01/173.88 ! [V_xs,T_a] : % 174.01/173.88 ( class_Orderings_Olinorder(T_a) % 174.01/173.88 => ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 174.01/173.88 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_take__upt,axiom, % 174.01/173.88 ! [V_n,V_m,V_i] : % 174.01/173.88 ( 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)) % 174.01/173.88 => 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)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_upt__conv__Nil,axiom, % 174.01/173.88 ! [V_i,V_j] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 174.01/173.88 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_upt__eq__Nil__conv,axiom, % 174.01/173.88 ! [V_j_2,V_i_2] : % 174.01/173.88 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 174.01/173.88 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 174.01/173.88 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__many__eq,axiom, % 174.01/173.88 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( 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))) % 174.01/173.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 174.01/173.88 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__many,axiom, % 174.01/173.88 ! [V_zs,V_y,V_x,T_a] : % 174.01/173.88 ( class_Orderings_Olinorder(T_a) % 174.01/173.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 174.01/173.88 => 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))) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_upt__add__eq__append,axiom, % 174.01/173.88 ! [V_k,V_j,V_i] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 174.01/173.88 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_upt__Suc__append,axiom, % 174.01/173.88 ! [V_j,V_i] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 174.01/173.88 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_upt__Suc,axiom, % 174.01/173.88 ! [V_j,V_i] : % 174.01/173.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 174.01/173.88 => 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))) ) % 174.01/173.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 174.01/173.88 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__Cons,axiom, % 174.01/173.88 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 174.01/173.88 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 174.01/173.88 & ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__append,axiom, % 174.01/173.88 ! [V_ys_2,V_xs_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 174.01/173.88 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 174.01/173.88 & c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 174.01/173.88 & ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => ! [B_xa] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2))) % 174.01/173.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_drop__upt,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__drop,axiom, % 174.01/173.88 ! [V_n,V_xs,T_a] : % 174.01/173.88 ( class_Orderings_Olinorder(T_a) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 174.01/173.88 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_hd__upt,axiom, % 174.01/173.88 ! [V_j,V_i] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 174.01/173.88 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__insort__insert,axiom, % 174.01/173.88 ! [V_x_2,V_xs_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 174.01/173.88 => 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)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_upt__rec,axiom, % 174.01/173.88 ! [V_j,V_i] : % 174.01/173.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 174.01/173.88 => 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)) ) % 174.01/173.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 174.01/173.88 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_upt__conv__Cons,axiom, % 174.01/173.88 ! [V_j,V_i] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 174.01/173.88 => 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)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_atLeastLessThan__upt,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_set__upt,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__distinct__set__unique,axiom, % 174.01/173.88 ! [V_ys_2,V_xs_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 174.01/173.88 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 174.01/173.88 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 174.01/173.88 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 174.01/173.88 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__insort,axiom, % 174.01/173.88 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( 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)) % 174.01/173.88 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_distinct__upt,axiom, % 174.01/173.88 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__remove1,axiom, % 174.01/173.88 ! [V_a,V_xs,T_a] : % 174.01/173.88 ( class_Orderings_Olinorder(T_a) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 174.01/173.88 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__upt,axiom, % 174.01/173.88 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__upto,axiom, % 174.01/173.88 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__list__of__set__range,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_upt__0,axiom, % 174.01/173.88 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted_Oequations_I1_J,axiom, % 174.01/173.88 ! [T_a] : % 174.01/173.88 ( class_Orderings_Olinorder(T_a) % 174.01/173.88 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__take,axiom, % 174.01/173.88 ! [V_n,V_xs,T_a] : % 174.01/173.88 ( class_Orderings_Olinorder(T_a) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 174.01/173.88 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__tl,axiom, % 174.01/173.88 ! [V_xs,T_a] : % 174.01/173.88 ( class_Orderings_Olinorder(T_a) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 174.01/173.88 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_upt__rec__number__of,axiom, % 174.01/173.88 ! [V_n,V_m] : % 174.01/173.88 ( ( 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))) % 174.01/173.88 => 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))) ) % 174.01/173.88 & ( ~ 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))) % 174.01/173.88 => 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) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__insort__key,axiom, % 174.01/173.88 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( 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))) % 174.01/173.88 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__map__remove1,axiom, % 174.01/173.88 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 174.01/173.88 => 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))) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_map__Suc__upt,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__insort__insert__key,axiom, % 174.01/173.88 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 174.01/173.88 => 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))) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_upt__eq__Cons__conv,axiom, % 174.01/173.88 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 174.01/173.88 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 174.01/173.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 174.01/173.88 & V_i_2 = V_x_2 % 174.01/173.88 & 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 ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter__insort,axiom, % 174.01/173.88 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 174.01/173.88 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 174.01/173.88 => 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)) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_map__nth,axiom, % 174.01/173.88 ! [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 ). % 174.01/173.88 % 174.01/173.88 fof(fact_atLeastAtMost__upt,axiom, % 174.01/173.88 ! [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))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_atLeast__upt,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 174.01/173.88 ! [V_n_2,V_m_2,V_f_2,T_b] : % 174.01/173.88 ( class_Groups_Ocomm__monoid__add(T_b) % 174.01/173.88 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 174.01/173.88 ! [V_n_2,V_m_2,V_f_2,T_b] : % 174.01/173.88 ( class_Groups_Ocomm__monoid__add(T_b) % 174.01/173.88 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_nth__upt,axiom, % 174.01/173.88 ! [V_j,V_k,V_i] : % 174.01/173.88 ( 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)) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_greaterThanAtMost__upt,axiom, % 174.01/173.88 ! [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))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted_Oequations_I2_J,axiom, % 174.01/173.88 ! [V_a1_2,V_a2_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2)) % 174.01/173.88 <=> ( ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2))) % 174.01/173.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) % 174.01/173.88 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_greaterThanLessThan__upt,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_nth__map__upt,axiom, % 174.01/173.88 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] : % 174.01/173.88 ( 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))) % 174.01/173.88 => 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)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__list__of__set,axiom, % 174.01/173.88 ! [V_A_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 174.01/173.88 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 % 174.01/173.88 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) % 174.01/173.88 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_atMost__upto,axiom, % 174.01/173.88 ! [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))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_insort__remove1,axiom, % 174.01/173.88 ! [V_xs_2,V_a_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 174.01/173.88 => 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 ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__nth__mono,axiom, % 174.01/173.88 ! [V_j,V_i,V_xs,T_a] : % 174.01/173.88 ( class_Orderings_Olinorder(T_a) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 174.01/173.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 174.01/173.88 => ( 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))) % 174.01/173.88 => 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))) ) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__equals__nth__mono,axiom, % 174.01/173.88 ! [V_xs_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 174.01/173.88 <=> ! [B_j] : % 174.01/173.88 ( 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))) % 174.01/173.88 => ! [B_i] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 174.01/173.88 => 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))) ) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_map__sorted__distinct__set__unique,axiom, % 174.01/173.88 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 174.01/173.88 ( class_Orderings_Olinorder(T_c) % 174.01/173.88 => ( 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))) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 174.01/173.88 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)) % 174.01/173.88 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))) % 174.01/173.88 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 174.01/173.88 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sublist__shift__lemma,axiom, % 174.01/173.88 ! [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))))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose__rectangle,axiom, % 174.01/173.88 ! [V_n_2,T_b,V_xs_2] : % 174.01/173.88 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 174.01/173.88 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 174.01/173.88 => ( ! [B_i] : % 174.01/173.88 ( 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))) % 174.01/173.88 => 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 ) % 174.01/173.88 => 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)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose_Opsimps_I2_J,axiom, % 174.01/173.88 ! [V_xss_2,T_b] : % 174.01/173.88 ( 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))) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose_Opsimps_I1_J,axiom, % 174.01/173.88 ! [T_b] : % 174.01/173.88 ( 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)))) % 174.01/173.88 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose__column,axiom, % 174.01/173.88 ! [V_i_2,V_xs_2,T_b] : % 174.01/173.88 ( 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))) % 174.01/173.88 => ( 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))) % 174.01/173.88 => 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) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose__aux__filter__head,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_inj__on__rev,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter__concat,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_length__concat,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__eq__Cons__iff,axiom, % 174.01/173.88 ! [V_ys_2,V_y_2,V_xs_2,T_b] : % 174.01/173.88 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) % 174.01/173.88 <=> 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev_Osimps_I2_J,axiom, % 174.01/173.88 ! [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))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_concat_Osimps_I2_J,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__singleton__conv,axiom, % 174.01/173.88 ! [V_x_2,V_xs_2,T_b] : % 174.01/173.88 ( 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)) % 174.01/173.88 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_singleton__rev__conv,axiom, % 174.01/173.88 ! [V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( 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) % 174.01/173.88 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_concat__eq__Nil__conv,axiom, % 174.01/173.88 ! [V_xss_2,T_b] : % 174.01/173.88 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b) % 174.01/173.88 <=> ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 174.01/173.88 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_Nil__eq__concat__conv,axiom, % 174.01/173.88 ! [V_xss_2,T_b] : % 174.01/173.88 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2) % 174.01/173.88 <=> ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 174.01/173.88 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev_Osimps_I1_J,axiom, % 174.01/173.88 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 174.01/173.88 % 174.01/173.88 fof(fact_concat_Osimps_I1_J,axiom, % 174.01/173.88 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 174.01/173.88 % 174.01/173.88 fof(fact_Nil__is__rev__conv,axiom, % 174.01/173.88 ! [V_xs_2,T_b] : % 174.01/173.88 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2) % 174.01/173.88 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__is__Nil__conv,axiom, % 174.01/173.88 ! [V_xs_2,T_b] : % 174.01/173.88 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 174.01/173.88 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__concat,axiom, % 174.01/173.88 ! [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))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__map,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_map__concat,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_concat__conv__foldl,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__foldl__cons,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_foldl__conv__concat,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_distinct__rev,axiom, % 174.01/173.88 ! [V_xs_2,T_b] : % 174.01/173.88 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2))) % 174.01/173.88 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__append,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_concat__append,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_set__concat,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_length__rev,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_listsum__rev,axiom, % 174.01/173.88 ! [V_xs,T_a] : % 174.01/173.88 ( class_Groups_Ocomm__monoid__add(T_a) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__is__rev__conv,axiom, % 174.01/173.88 ! [V_ys_2,V_xs_2,T_b] : % 174.01/173.88 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2) % 174.01/173.88 <=> V_xs_2 = V_ys_2 ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__swap,axiom, % 174.01/173.88 ! [V_ys_2,V_xs_2,T_b] : % 174.01/173.88 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2 % 174.01/173.88 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__rev__ident,axiom, % 174.01/173.88 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 174.01/173.88 % 174.01/173.88 fof(fact_foldr__foldl,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_foldl__foldr,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_set__rev,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_zip__rev,axiom, % 174.01/173.88 ! [V_ys,T_b,V_xs,T_a] : % 174.01/173.88 ( 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) % 174.01/173.88 => 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)) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__filter,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_last__rev,axiom, % 174.01/173.88 ! [T_a,V_xs] : % 174.01/173.88 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.88 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_hd__rev,axiom, % 174.01/173.88 ! [T_a,V_xs] : % 174.01/173.88 ( V_xs != c_List_Olist_ONil(T_a) % 174.01/173.88 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__transpose,axiom, % 174.01/173.88 ! [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)))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__take,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__drop,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rotate__rev,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose_Osimps_I3_J,axiom, % 174.01/173.88 ! [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))))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__nth,axiom, % 174.01/173.88 ! [V_xs,T_a,V_n] : % 174.01/173.88 ( 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))) % 174.01/173.88 => 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))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_concat__injective,axiom, % 174.01/173.88 ! [V_ys_2,V_xs_2,T_b] : % 174.01/173.88 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 174.01/173.88 => ( 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) % 174.01/173.88 => ( ! [B_x] : % 174.01/173.88 ( 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)))) % 174.01/173.88 => 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)) ) % 174.01/173.88 => V_xs_2 = V_ys_2 ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_concat__eq__concat__iff,axiom, % 174.01/173.88 ! [V_ys_2,V_xs_2,T_b] : % 174.01/173.88 ( ! [B_x] : % 174.01/173.88 ( 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)))) % 174.01/173.88 => 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)) ) % 174.01/173.88 => ( 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) % 174.01/173.88 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 174.01/173.88 <=> V_xs_2 = V_ys_2 ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_rev__update,axiom, % 174.01/173.88 ! [V_y,V_xs,T_a,V_k] : % 174.01/173.88 ( 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))) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_concat__map__singleton,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__rev__nth__mono,axiom, % 174.01/173.88 ! [V_j,V_i,V_xs,T_a] : % 174.01/173.88 ( class_Orderings_Olinorder(T_a) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 174.01/173.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 174.01/173.88 => ( 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))) % 174.01/173.88 => 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))) ) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_foldr__max__sorted,axiom, % 174.01/173.88 ! [V_y_2,V_xs_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2)) % 174.01/173.88 => ( ( V_xs_2 = c_List_Olist_ONil(T_b) % 174.01/173.88 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 ) % 174.01/173.88 & ( V_xs_2 != c_List_Olist_ONil(T_b) % 174.01/173.88 => 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) ) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose_Opsimps_I3_J,axiom, % 174.01/173.88 ! [V_xss_2,V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( 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))) % 174.01/173.88 => 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))))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_length__transpose__sorted,axiom, % 174.01/173.88 ! [V_xs_2,T_b] : % 174.01/173.88 ( 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))) % 174.01/173.88 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 174.01/173.88 => 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) ) % 174.01/173.88 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b)) % 174.01/173.88 => 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))) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose__column__length,axiom, % 174.01/173.88 ! [V_i_2,V_xs_2,T_b] : % 174.01/173.88 ( 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))) % 174.01/173.88 => ( 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))) % 174.01/173.88 => 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)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose__aux__filter__tail,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_nth__nth__transpose__sorted,axiom, % 174.01/173.88 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 174.01/173.88 ( 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))) % 174.01/173.88 => ( 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)))) % 174.01/173.88 => ( 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)))) % 174.01/173.88 => 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) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transpose__transpose,axiom, % 174.01/173.88 ! [V_xs_2,T_b] : % 174.01/173.88 ( 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))) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 174.01/173.88 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_takeWhile__map,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_return__list__def,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_zip__takeWhile__snd,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_zip__takeWhile__fst,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(fact_set__takeWhileD,axiom, % 174.01/173.88 ! [V_xs_2,V_Pa_2,V_x_2,T_b] : % 174.01/173.88 ( 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)))) % 174.01/173.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_takeWhile__eq__all__conv,axiom, % 174.01/173.88 ! [V_xs_2,V_Pa_2,T_b] : % 174.01/173.88 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2 % 174.01/173.88 <=> ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_length__takeWhile__le,axiom, % 174.01/173.88 ! [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))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_takeWhile__eq__take,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_distinct__takeWhile,axiom, % 174.01/173.88 ! [V_Pa_2,V_xs_2,T_b] : % 174.01/173.88 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.88 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_takeWhile_Osimps_I1_J,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(fact_sorted__takeWhile,axiom, % 174.01/173.88 ! [V_Pa_2,V_xs_2,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 174.01/173.88 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_takeWhile_Osimps_I2_J,axiom, % 174.01/173.88 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 174.01/173.88 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 174.01/173.88 => 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)) ) % 174.01/173.88 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 174.01/173.88 => 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) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_takeWhile__tail,axiom, % 174.01/173.88 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] : % 174.01/173.88 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_takeWhile__append1,axiom, % 174.01/173.88 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 174.01/173.88 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 174.01/173.88 => 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) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_nth__length__takeWhile,axiom, % 174.01/173.88 ! [V_xs_2,V_Pa_2,T_b] : % 174.01/173.88 ( 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))) % 174.01/173.88 => ~ 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))))) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_takeWhile__nth,axiom, % 174.01/173.88 ! [V_xs_2,V_Pa_2,T_b,V_j_2] : % 174.01/173.88 ( 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)))) % 174.01/173.88 => 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) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_map__upds__def,axiom, % 174.01/173.88 ! [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)))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_takeWhile__not__last,axiom, % 174.01/173.88 ! [T_b,V_xs_2] : % 174.01/173.88 ( V_xs_2 != c_List_Olist_ONil(T_b) % 174.01/173.88 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 174.01/173.88 => 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) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 174.01/173.88 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] : % 174.01/173.88 ( class_Orderings_Olinorder(T_b) % 174.01/173.88 => ( 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))) % 174.01/173.88 => 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) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_transfer__nat__int__list__return__embed,axiom, % 174.01/173.88 ! [V_l] : % 174.01/173.88 ( c_List_Onat__list(V_l) % 174.01/173.88 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 174.01/173.88 % 174.01/173.88 fof(fact_length__remdups__concat,axiom, % 174.01/173.88 ! [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))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_distinct__remdups,axiom, % 174.01/173.88 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 174.01/173.88 % 174.01/173.88 fof(fact_length__remdups__leq,axiom, % 174.01/173.88 ! [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))) ). % 174.01/173.88 % 174.01/173.88 %----Arity declarations (201) % 174.01/173.88 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 174.01/173.88 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Lattices_Obounded__lattice(T_1) % 174.01/173.88 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 174.01/173.88 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Lattices_Obounded__lattice(T_1) % 174.01/173.88 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Lattices_Obounded__lattice(T_1) % 174.01/173.88 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Lattices_Olattice(T_1) % 174.01/173.88 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Lattices_Olattice(T_1) % 174.01/173.88 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Lattices_Odistrib__lattice(T_1) % 174.01/173.88 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Lattices_Oboolean__algebra(T_1) % 174.01/173.88 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Orderings_Opreorder,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Orderings_Opreorder(T_1) % 174.01/173.88 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Finite__Set_Ofinite,axiom, % 174.01/173.88 ! [T_1,T_2] : % 174.01/173.88 ( ( class_Finite__Set_Ofinite(T_2) % 174.01/173.88 & class_Finite__Set_Ofinite(T_1) ) % 174.01/173.88 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Lattices_Olattice,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Lattices_Olattice(T_1) % 174.01/173.88 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Orderings_Oorder,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Orderings_Oorder(T_1) % 174.01/173.88 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Orderings_Otop,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Orderings_Otop(T_1) % 174.01/173.88 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Orderings_Oord,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Orderings_Oord(T_1) % 174.01/173.88 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Orderings_Obot,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Orderings_Obot(T_1) % 174.01/173.88 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Groups_Ouminus,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Groups_Ouminus(T_1) % 174.01/173.88 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_fun__Groups_Ominus,axiom, % 174.01/173.88 ! [T_2,T_1] : % 174.01/173.88 ( class_Groups_Ominus(T_1) % 174.01/173.88 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 174.01/173.88 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 174.01/173.88 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 174.01/173.88 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 174.01/173.88 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 174.01/173.88 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 174.01/173.88 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 174.01/173.88 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 174.01/173.88 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 174.01/173.88 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 174.01/173.88 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 174.01/173.88 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 174.01/173.88 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 174.01/173.88 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 174.01/173.88 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 174.01/173.88 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 174.01/173.88 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 174.01/173.88 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 174.01/173.88 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 174.01/173.88 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 174.01/173.88 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 174.01/173.88 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 174.01/173.88 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 174.01/173.88 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 174.01/173.88 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 174.01/173.88 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 174.01/173.88 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 174.01/173.88 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 174.01/173.88 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 174.01/173.88 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 174.01/173.88 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 174.01/173.88 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 174.01/173.88 class_Divides_Osemiring__div(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 174.01/173.88 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 174.01/173.88 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 174.01/173.88 class_Groups_Oab__group__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 174.01/173.88 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 174.01/173.88 class_Rings_Oordered__ring(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 174.01/173.88 class_Orderings_Opreorder(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 174.01/173.88 class_Orderings_Olinorder(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 174.01/173.88 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 174.01/173.88 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 174.01/173.88 class_Groups_Omonoid__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 174.01/173.88 class_Smallcheck_Osmall(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 174.01/173.88 class_Rings_Osemiring__1(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 174.01/173.88 class_Rings_Osemiring__0(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 174.01/173.88 class_Lattices_Olattice(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 174.01/173.88 class_Groups_Ogroup__add(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 174.01/173.88 class_Divides_Oring__div(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 174.01/173.88 class_Rings_Omult__zero(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom, % 174.01/173.88 class_Rings_Ocomm__ring(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 174.01/173.88 class_Orderings_Oorder(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 174.01/173.88 class_Int_Oring__char__0(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 174.01/173.88 class_Int_Onumber__ring(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 174.01/173.88 class_Rings_Osemiring(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Orderings_Oord,axiom, % 174.01/173.88 class_Orderings_Oord(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 174.01/173.88 class_Groups_Ouminus(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 174.01/173.88 class_Groups_Osgn__if(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 174.01/173.88 class_Groups_Oabs__if(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 174.01/173.88 class_Rings_Oring__1(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Ominus,axiom, % 174.01/173.88 class_Groups_Ominus(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Power_Opower,axiom, % 174.01/173.88 class_Power_Opower(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Ozero,axiom, % 174.01/173.88 class_Groups_Ozero(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Oring,axiom, % 174.01/173.88 class_Rings_Oring(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Oidom,axiom, % 174.01/173.88 class_Rings_Oidom(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Int_Onumber,axiom, % 174.01/173.88 class_Int_Onumber(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Groups_Oone,axiom, % 174.01/173.88 class_Groups_Oone(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Int__Oint__Rings_Odvd,axiom, % 174.01/173.88 class_Rings_Odvd(tc_Int_Oint) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 174.01/173.88 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 174.01/173.88 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 174.01/173.88 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 174.01/173.88 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 174.01/173.88 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 174.01/173.88 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 174.01/173.88 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 174.01/173.88 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 174.01/173.88 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 174.01/173.88 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 174.01/173.88 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 174.01/173.88 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 174.01/173.88 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 174.01/173.88 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 174.01/173.88 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 174.01/173.88 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 174.01/173.88 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 174.01/173.88 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 174.01/173.88 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 174.01/173.88 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 174.01/173.88 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 174.01/173.88 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 174.01/173.88 class_Orderings_Owellorder(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 174.01/173.88 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 174.01/173.88 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 174.01/173.88 class_Orderings_Opreorder(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 174.01/173.88 class_Orderings_Olinorder(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 174.01/173.88 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 174.01/173.88 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 174.01/173.88 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 174.01/173.88 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 174.01/173.88 class_Lattices_Olattice(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 174.01/173.88 class_Rings_Omult__zero(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 174.01/173.88 class_Orderings_Oorder(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 174.01/173.88 class_Rings_Osemiring(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 174.01/173.88 class_Orderings_Oord(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 174.01/173.88 class_Orderings_Obot(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 174.01/173.88 class_Groups_Ominus(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Power_Opower,axiom, % 174.01/173.88 class_Power_Opower(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 174.01/173.88 class_Groups_Ozero(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Int_Onumber,axiom, % 174.01/173.88 class_Int_Onumber(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Groups_Oone,axiom, % 174.01/173.88 class_Groups_Oone(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Nat__Onat__Rings_Odvd,axiom, % 174.01/173.88 class_Rings_Odvd(tc_Nat_Onat) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 174.01/173.88 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 174.01/173.88 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 174.01/173.88 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 174.01/173.88 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 174.01/173.88 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 174.01/173.88 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 174.01/173.88 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 174.01/173.88 class_Orderings_Opreorder(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 174.01/173.88 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 174.01/173.88 class_Lattices_Olattice(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 174.01/173.88 class_Orderings_Oorder(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 174.01/173.88 class_Orderings_Otop(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 174.01/173.88 class_Orderings_Oord(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 174.01/173.88 class_Orderings_Obot(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 174.01/173.88 class_Groups_Ouminus(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 174.01/173.88 class_Groups_Ominus(tc_HOL_Obool) ). % 174.01/173.88 % 174.01/173.88 fof(arity_sum__Finite__Set_Ofinite,axiom, % 174.01/173.88 ! [T_1,T_2] : % 174.01/173.88 ( ( class_Finite__Set_Ofinite(T_2) % 174.01/173.88 & class_Finite__Set_Ofinite(T_1) ) % 174.01/173.88 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 174.01/173.88 ! [T_1] : % 174.01/173.88 ( class_Finite__Set_Ofinite(T_1) % 174.01/173.88 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_prod__Finite__Set_Ofinite,axiom, % 174.01/173.88 ! [T_1,T_2] : % 174.01/173.88 ( ( class_Finite__Set_Ofinite(T_2) % 174.01/173.88 & class_Finite__Set_Ofinite(T_1) ) % 174.01/173.88 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_prod__Smallcheck_Osmall,axiom, % 174.01/173.88 ! [T_1,T_2] : % 174.01/173.88 ( ( class_Smallcheck_Osmall(T_2) % 174.01/173.88 & class_Smallcheck_Osmall(T_1) ) % 174.01/173.88 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 174.01/173.88 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 174.01/173.88 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 174.01/173.88 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 174.01/173.88 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 174.01/173.88 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 174.01/173.88 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 174.01/173.88 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 174.01/173.88 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 174.01/173.88 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 174.01/173.88 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 174.01/173.88 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 174.01/173.88 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 174.01/173.88 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 174.01/173.88 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 174.01/173.88 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 174.01/173.88 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 174.01/173.88 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 174.01/173.88 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 174.01/173.88 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 174.01/173.88 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 174.01/173.88 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 174.01/173.88 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 174.01/173.88 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 174.01/173.88 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 174.01/173.88 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 174.01/173.88 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 174.01/173.88 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 174.01/173.88 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 174.01/173.88 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 174.01/173.88 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 174.01/173.88 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 174.01/173.88 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 174.01/173.88 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 174.01/173.88 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 174.01/173.88 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 174.01/173.88 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 174.01/173.88 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 174.01/173.88 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom, % 174.01/173.88 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ). % 174.01/173.88 % 174.01/173.88 %----Helper facts (20) % 174.01/173.88 fof(help_c__COMBI__1,axiom, % 174.01/173.88 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 174.01/173.88 % 174.01/173.88 fof(help_c__COMBK__1,axiom, % 174.01/173.88 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 174.01/173.88 % 174.01/173.88 fof(help_c__COMBB__1,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__COMBC__1,axiom, % 174.01/173.88 ! [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) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__COMBS__1,axiom, % 174.01/173.88 ! [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)) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fequal__1,axiom, % 174.01/173.88 ! [V_y_2,V_x_2] : % 174.01/173.88 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 174.01/173.88 | V_x_2 = V_y_2 ) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fequal__2,axiom, % 174.01/173.88 ! [V_y_2,V_x_2] : % 174.01/173.88 ( V_x_2 != V_y_2 % 174.01/173.88 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fFalse__1,axiom, % 174.01/173.88 ~ hBOOL(c_fFalse) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fTrue__1,axiom, % 174.01/173.88 hBOOL(c_fTrue) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fNot__1,axiom, % 174.01/173.88 ! [V_Pa_2] : % 174.01/173.88 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2)) % 174.01/173.88 | ~ hBOOL(V_Pa_2) ) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fNot__2,axiom, % 174.01/173.88 ! [V_Pa_2] : % 174.01/173.88 ( ~ ~ hBOOL(V_Pa_2) % 174.01/173.88 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fconj__1,axiom, % 174.01/173.88 ! [V_Q_2,V_Pa_2] : % 174.01/173.88 ( ~ hBOOL(V_Pa_2) % 174.01/173.88 | ~ hBOOL(V_Q_2) % 174.01/173.88 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) ) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fconj__2,axiom, % 174.01/173.88 ! [V_Q_2,V_Pa_2] : % 174.01/173.88 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) % 174.01/173.88 | hBOOL(V_Pa_2) ) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fconj__3,axiom, % 174.01/173.88 ! [V_Q_2,V_Pa_2] : % 174.01/173.88 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) % 174.01/173.88 | hBOOL(V_Q_2) ) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fdisj__1,axiom, % 174.01/173.88 ! [V_Q_2,V_Pa_2] : % 174.01/173.88 ( ~ hBOOL(V_Pa_2) % 174.01/173.88 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fdisj__2,axiom, % 174.01/173.88 ! [V_Pa_2,V_Q_2] : % 174.01/173.88 ( ~ hBOOL(V_Q_2) % 174.01/173.88 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fdisj__3,axiom, % 174.01/173.88 ! [V_Q_2,V_Pa_2] : % 174.01/173.88 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) % 174.01/173.88 | hBOOL(V_Pa_2) % 174.01/173.88 | hBOOL(V_Q_2) ) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fimplies__1,axiom, % 174.01/173.88 ! [V_Q_2,V_Pa_2] : % 174.01/173.88 ( hBOOL(V_Pa_2) % 174.01/173.88 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fimplies__2,axiom, % 174.01/173.88 ! [V_Pa_2,V_Q_2] : % 174.01/173.88 ( ~ hBOOL(V_Q_2) % 174.01/173.88 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ). % 174.01/173.88 % 174.01/173.88 fof(help_c__fimplies__3,axiom, % 174.01/173.88 ! [V_Q_2,V_Pa_2] : % 174.01/173.88 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) % 174.01/173.88 | ~ hBOOL(V_Pa_2) % 174.01/173.88 | hBOOL(V_Q_2) ) ). % 174.01/173.88 % 174.01/173.88 %----Conjectures (7) % 174.01/173.88 fof(conj_0,hypothesis, % 174.01/173.88 ! [B_n] : % 174.01/173.88 ( ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) % 174.01/173.88 => c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) % 174.01/173.88 => ! [B_Z,B_s] : % 174.01/173.88 ( ( v_P(B_Z,B_s) % 174.01/173.88 & hBOOL(hAPP(v_b,B_s)) ) % 174.01/173.88 => ! [B_s_H] : % 174.01/173.88 ( c_Natural_Oevaln(v_c,B_s,B_n,B_s_H) % 174.01/173.88 => v_P(B_Z,B_s_H) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(conj_1,hypothesis, % 174.01/173.88 hBOOL(hAPP(v_ba,v_s0)) ). % 174.01/173.88 % 174.01/173.88 fof(conj_2,hypothesis, % 174.01/173.88 c_Natural_Oevaln(v_ca,v_s0,v_na,v_s1) ). % 174.01/173.88 % 174.01/173.88 fof(conj_3,hypothesis, % 174.01/173.88 ( v_ca = c_Com_Ocom_OWhile(v_b,v_c) % 174.01/173.88 => ( ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) % 174.01/173.88 => c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,B_x) ) % 174.01/173.88 => ! [B_Z] : % 174.01/173.88 ( v_P(B_Z,v_s0) % 174.01/173.88 => ( v_P(B_Z,v_s1) % 174.01/173.88 & ~ hBOOL(hAPP(v_b,v_s1)) ) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(conj_4,hypothesis, % 174.01/173.88 c_Natural_Oevaln(c_Com_Ocom_OWhile(v_ba,v_ca),v_s1,v_na,v_s2) ). % 174.01/173.88 % 174.01/173.88 fof(conj_5,hypothesis, % 174.01/173.88 ( c_Com_Ocom_OWhile(v_ba,v_ca) = c_Com_Ocom_OWhile(v_b,v_c) % 174.01/173.88 => ( ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) % 174.01/173.88 => c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,B_x) ) % 174.01/173.88 => ! [B_Z] : % 174.01/173.88 ( v_P(B_Z,v_s1) % 174.01/173.88 => ( v_P(B_Z,v_s2) % 174.01/173.88 & ~ hBOOL(hAPP(v_b,v_s2)) ) ) ) ) ). % 174.01/173.88 % 174.01/173.88 fof(conj_6,conjecture, % 174.01/173.88 ( ( v_ba = v_b % 174.01/173.88 & v_ca = v_c ) % 174.01/173.88 => ( ! [B_x] : % 174.01/173.88 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) % 174.01/173.88 => c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,B_x) ) % 174.01/173.88 => ! [B_Z] : % 174.01/173.88 ( v_P(B_Z,v_s0) % 174.01/173.88 => ( v_P(B_Z,v_s2) % 174.01/173.88 & ~ hBOOL(hAPP(v_b,v_s2)) ) ) ) ) ). % 174.01/173.88 % 174.01/173.88 %------------------------------------------------------------------------------ % 174.01/173.88 %------------------------------------------- % 174.01/173.88 % Proof found % 174.01/173.88 % SZS status Theorem for theBenchmark % 174.01/173.88 % SZS output start Proof % 174.01/173.88 %ClaNum:10047(EqnAxiom:2803) % 174.01/173.88 %VarNum:68143(SingletonVarNum:20223) % 174.01/173.88 %MaxLitNum:8 % 174.01/173.88 %MaxfuncDepth:13 % 174.01/173.88 %SharedTerms:1083 % 174.01/173.88 %goalClause: 2804 2805 3003 4567 5474 % 174.01/173.88 %singleGoalClaCount:3 % 174.01/173.88 [2804]E(a1,a2) % 174.01/173.88 [2805]E(a861,a862) % 174.01/173.88 [2809]P1(a179) % 174.01/173.88 [2810]P2(a851) % 174.01/173.88 [2811]P2(a3) % 174.01/173.88 [2812]P2(a103) % 174.01/173.88 [2813]P3(a851) % 174.01/173.88 [2814]P3(a3) % 174.01/173.88 [2815]P3(a103) % 174.01/173.88 [2816]P4(a851) % 174.01/173.88 [2817]P4(a3) % 174.01/173.88 [2818]P4(a103) % 174.01/173.88 [2819]P5(a851) % 174.01/173.88 [2820]P5(a3) % 174.01/173.88 [2821]P5(a103) % 174.01/173.88 [2822]P66(a851) % 174.01/173.88 [2823]P66(a3) % 174.01/173.88 [2824]P66(a103) % 174.01/173.88 [2825]P67(a851) % 174.01/173.88 [2826]P67(a3) % 174.01/173.88 [2827]P67(a103) % 174.01/173.88 [2828]P68(a3) % 174.01/173.88 [2829]P73(a851) % 174.01/173.88 [2830]P73(a3) % 174.01/173.88 [2831]P73(a103) % 174.01/173.88 [2832]P137(a851) % 174.01/173.88 [2833]P137(a3) % 174.01/173.88 [2834]P85(a851) % 174.01/173.88 [2835]P85(a3) % 174.01/173.88 [2836]P85(a103) % 174.01/173.88 [2837]P74(a851) % 174.01/173.88 [2838]P74(a3) % 174.01/173.88 [2839]P74(a103) % 174.01/173.88 [2840]P80(a851) % 174.01/173.88 [2841]P80(a3) % 174.01/173.88 [2842]P80(a103) % 174.01/173.88 [2843]P110(a3) % 174.01/173.88 [2844]P81(a851) % 174.01/173.88 [2845]P81(a3) % 174.01/173.88 [2846]P81(a103) % 174.01/173.88 [2847]P117(a851) % 174.01/173.88 [2848]P117(a3) % 174.01/173.88 [2849]P117(a103) % 174.01/173.88 [2850]P86(a851) % 174.01/173.88 [2851]P86(a3) % 174.01/173.88 [2852]P86(a103) % 174.01/173.88 [2853]P99(a851) % 174.01/173.88 [2854]P99(a845) % 174.01/173.88 [2855]P99(a3) % 174.01/173.88 [2856]P99(a103) % 174.01/173.88 [2857]P103(a851) % 174.01/173.88 [2858]P103(a845) % 174.01/173.88 [2859]P103(a3) % 174.01/173.88 [2860]P103(a103) % 174.01/173.88 [2861]P100(a851) % 174.01/173.88 [2862]P100(a3) % 174.01/173.88 [2863]P100(a103) % 174.01/173.88 [2864]P102(a851) % 174.01/173.88 [2865]P102(a845) % 174.01/173.88 [2866]P102(a3) % 174.01/173.88 [2867]P102(a103) % 174.01/173.88 [2868]P111(a3) % 174.01/173.88 [2869]P120(a3) % 174.01/173.88 [2870]P121(a3) % 174.01/173.88 [2871]P64(a851) % 174.01/173.88 [2872]P64(a3) % 174.01/173.88 [2873]P64(a103) % 174.01/173.88 [2874]P69(a3) % 174.01/173.88 [2875]P70(a851) % 174.01/173.88 [2876]P70(a3) % 174.01/173.88 [2877]P70(a103) % 174.01/173.88 [2878]P75(a851) % 174.01/173.88 [2879]P75(a3) % 174.01/173.88 [2880]P75(a103) % 174.01/173.88 [2881]P76(a851) % 174.01/173.88 [2882]P76(a3) % 174.01/173.88 [2883]P76(a103) % 174.01/173.88 [2884]P87(a3) % 174.01/173.88 [2885]P133(a3) % 174.01/173.88 [2886]P104(a3) % 174.01/173.88 [2887]P77(a3) % 174.01/173.88 [2888]P6(a3) % 174.01/173.88 [2889]P122(a851) % 174.01/173.88 [2890]P122(a3) % 174.01/173.88 [2891]P122(a103) % 174.01/173.88 [2892]P134(a3) % 174.01/173.88 [2893]P127(a851) % 174.01/173.88 [2894]P127(a3) % 174.01/173.88 [2895]P127(a103) % 174.01/173.88 [2896]P138(a851) % 174.01/173.88 [2897]P138(a3) % 174.01/173.88 [2898]P138(a103) % 174.01/173.88 [2899]P109(a851) % 174.01/173.88 [2900]P109(a3) % 174.01/173.88 [2901]P109(a103) % 174.01/173.88 [2902]P135(a851) % 174.01/173.88 [2903]P135(a3) % 174.01/173.88 [2904]P135(a103) % 174.01/173.88 [2905]P118(a3) % 174.01/173.88 [2906]P119(a3) % 174.01/173.88 [2907]P123(a851) % 174.01/173.88 [2908]P123(a3) % 174.01/173.88 [2909]P123(a103) % 174.01/173.88 [2910]P115(a851) % 174.01/173.88 [2911]P115(a3) % 174.01/173.88 [2912]P115(a103) % 174.01/173.88 [2913]P82(a3) % 174.01/173.88 [2914]P124(a3) % 174.01/173.88 [2915]P78(a851) % 174.01/173.88 [2916]P78(a3) % 174.01/173.88 [2917]P78(a103) % 174.01/173.88 [2918]P128(a851) % 174.01/173.88 [2919]P128(a3) % 174.01/173.88 [2920]P128(a103) % 174.01/173.88 [2921]P129(a3) % 174.01/173.88 [2922]P131(a851) % 174.01/173.88 [2923]P131(a3) % 174.01/173.88 [2924]P131(a103) % 174.01/173.88 [2925]P130(a851) % 174.01/173.88 [2926]P130(a3) % 174.01/173.88 [2927]P130(a103) % 174.01/173.88 [2928]P125(a851) % 174.01/173.88 [2929]P125(a3) % 174.01/173.88 [2930]P125(a103) % 174.01/173.88 [2931]P126(a3) % 174.01/173.88 [2932]P90(a845) % 174.01/173.88 [2933]P7(a851) % 174.01/173.88 [2934]P7(a3) % 174.01/173.88 [2935]P7(a103) % 174.01/173.88 [2936]P8(a3) % 174.01/173.88 [2937]P84(a845) % 174.01/173.88 [2938]P84(a3) % 174.01/173.88 [2939]P71(a851) % 174.01/173.88 [2940]P71(a845) % 174.01/173.88 [2941]P71(a3) % 174.01/173.88 [2942]P71(a103) % 174.01/173.88 [2943]P88(a3) % 174.01/173.88 [2944]P79(a3) % 174.01/173.88 [2945]P89(a851) % 174.01/173.88 [2946]P89(a3) % 174.01/173.88 [2947]P89(a103) % 174.01/173.88 [2948]P132(a3) % 174.01/173.88 [2949]P65(a3) % 174.01/173.88 [2950]P105(a851) % 174.01/173.88 [2951]P105(a3) % 174.01/173.88 [2952]P105(a103) % 174.01/173.88 [2953]P136(a851) % 174.01/173.88 [2954]P136(a3) % 174.01/173.88 [2955]P136(a103) % 174.01/173.88 [2956]P112(a851) % 174.01/173.88 [2957]P112(a3) % 174.01/173.88 [2958]P112(a103) % 174.01/173.88 [2959]P108(a3) % 174.01/173.88 [2960]P92(a851) % 174.01/173.88 [2961]P92(a845) % 174.01/173.88 [2962]P92(a3) % 174.01/173.88 [2963]P93(a851) % 174.01/173.88 [2964]P93(a845) % 174.01/173.88 [2965]P93(a3) % 174.01/173.88 [2966]P9(a845) % 174.01/173.88 [2967]P106(a845) % 174.01/173.88 [2968]P94(a845) % 174.01/173.88 [2969]P59(a845) % 174.01/173.88 [2970]P59(a854) % 174.01/173.88 [2971]P101(a851) % 174.01/173.88 [2972]P101(a845) % 174.01/173.88 [2973]P95(a845) % 174.01/173.88 [2974]P97(a851) % 174.01/173.88 [2975]P97(a845) % 174.01/173.88 [2976]P97(a3) % 174.01/173.88 [2977]P98(a851) % 174.01/173.88 [2978]P98(a845) % 174.01/173.88 [2979]P98(a3) % 174.01/173.88 [2980]P72(a851) % 174.01/173.88 [2981]P72(a3) % 174.01/173.88 [2982]P72(a103) % 174.01/173.88 [2983]P107(a851) % 174.01/173.88 [2984]P139(a3) % 174.01/173.88 [2985]P139(a854) % 174.01/173.88 [2986]P83(a851) % 174.01/173.88 [2987]P83(a3) % 174.01/173.88 [2988]P83(a103) % 174.01/173.88 [2989]P96(a845) % 174.01/173.88 [3001]P36(a851,a239) % 174.01/173.88 [3002]P36(a851,a325) % 174.01/173.88 [3003]P142(a331,a863) % 174.01/173.88 [3393]P39(a862,a863,a864,a865) % 174.01/173.88 [4361]~E(a101,a87) % 174.01/173.88 [4362]~P1(a180) % 174.01/173.88 [2806]E(f4(a3),a87) % 174.01/173.88 [2807]E(f5(a103),a6) % 174.01/173.88 [2808]E(f104(a103),a7) % 174.01/173.88 [2990]E(f36(a27),f4(a851)) % 174.01/173.88 [2991]E(f88(a179),f4(a851)) % 174.01/173.88 [2992]E(f88(a180),f4(a851)) % 174.01/173.88 [2993]E(f181(a851),f105(a851)) % 174.01/173.88 [2994]E(f182(a851),f4(a851)) % 174.01/173.88 [2995]E(f238(a851),f106(a851)) % 174.01/173.88 [2996]E(f107(a3),f41(a3)) % 174.01/173.88 [2997]P10(f4(a3)) % 174.01/173.88 [2998]P10(f82(a3)) % 174.01/173.88 [3041]P1(f777(a28,a27)) % 174.01/173.88 [3042]P1(f777(a1,a863)) % 174.01/173.88 [3051]P36(f857(a851,a851),a42) % 174.01/173.88 [3080]E(f168(a847,a846,a31),a32) % 174.01/173.88 [3392]E(f327(a851,a851,a239,a239),a42) % 174.01/173.88 [3442]P39(f37(a1,a862),a865,a864,a866) % 174.01/173.88 [4363]~E(f82(a3),f4(a3)) % 174.01/173.88 [2999]E(f115(f4(a851)),f4(a851)) % 174.01/173.88 [3000]E(f8(f4(a103)),f4(a851)) % 174.01/173.88 [3005]E(f777(f83(a3),a87),a87) % 174.01/173.88 [3009]E(f777(a7,f4(a851)),f4(a103)) % 174.01/173.88 [3010]E(f777(a116,f4(a851)),f82(a851)) % 174.01/173.88 [3011]E(f777(a109,f82(a3)),f82(a851)) % 174.01/173.88 [3012]E(f777(a7,f82(a851)),f82(a103)) % 174.01/173.88 [3014]E(f777(f108(a3),a87),f4(a3)) % 174.01/173.88 [3015]E(f777(f108(a103),a87),f4(a103)) % 174.01/173.88 [3016]E(f777(a109,f4(a3)),f4(a851)) % 174.01/173.88 [3017]E(f777(f183(a846),a27),f4(a851)) % 174.01/173.88 [3018]E(f777(f183(a845),a179),f4(a851)) % 174.01/173.88 [3019]E(f777(f183(a845),a180),f4(a851)) % 174.01/173.88 [3020]E(f777(f108(a851),a87),f4(a851)) % 174.01/173.88 [3026]E(f777(f83(a3),f82(a3)),a101) % 174.01/173.88 [3034]E(f777(f183(a103),f4(a103)),f4(a851)) % 174.01/173.88 [3035]E(f777(f104(a3),f4(a851)),f4(a3)) % 174.01/173.88 [3036]E(f777(f104(a3),f82(a851)),f82(a3)) % 174.01/173.88 [3037]E(f777(f83(a3),f4(a3)),f4(a3)) % 174.01/173.88 [3047]E(f777(a109,f82(a3)),f777(a116,f4(a851))) % 174.01/173.88 [3049]E(f326(f857(a851,a851),a42),a43) % 174.01/173.88 [3050]E(f328(f857(a851,a851),a42),a72) % 174.01/173.88 [3071]E(f777(f259(a851),f4(a851)),f182(f858(a851,a845))) % 174.01/173.88 [3072]E(f777(f260(a851),f4(a851)),f241(f858(a851,a845))) % 174.01/173.88 [3082]P38(f182(f858(a3,a845))) % 174.01/173.88 [3117]E(f777(f777(f5(a103),f4(a103)),f82(a103)),f4(a103)) % 174.01/173.88 [3189]P1(f777(f777(f235(a3),a101),f4(a3))) % 174.01/173.88 [3214]P1(f777(f777(f235(a3),f4(a3)),f82(a3))) % 174.01/173.88 [3216]P1(f777(f777(f234(a3),f4(a3)),f82(a3))) % 174.01/173.88 [3383]P1(f777(f65(a847),f171(a847,a846,a32))) % 174.01/173.88 [3426]E(f777(f777(f283(a851,a851,a851),a325),f302(a851,a325)),a239) % 174.01/173.88 [3464]P40(a3,a851,a109,f777(f234(a3),f4(a3))) % 174.01/173.88 [3467]E(f777(f777(f48(a851,f858(a851,a845)),f241(f858(a851,a845))),f259(a851)),f241(f858(a851,a845))) % 174.01/173.88 [3468]E(f777(f777(f48(a851,f858(a851,a845)),f241(f858(a851,a845))),f295(a851)),f241(f858(a851,a845))) % 174.01/173.88 [3469]E(f777(f777(f48(a851,f858(a851,a845)),f241(f858(a851,a845))),f260(a851)),f241(f858(a851,a845))) % 174.01/173.88 [3470]E(f777(f777(f49(a851,f858(a851,a845)),f241(f858(a851,a845))),f298(a851)),f182(f858(a851,a845))) % 174.01/173.88 [3486]P29(a851,a3,f104(a3),f241(f858(a851,a845))) % 174.01/173.88 [3499]P40(a851,a3,f104(a3),f777(f20(a845,a851),a179)) % 174.01/173.88 [3630]E(f777(f77(a851,a103,a3,a7),a109),f108(a103)) % 174.01/173.88 [3848]P55(a103,a851,a24,a7,f241(f858(a851,a845))) % 174.01/173.88 [3856]P55(a3,f858(f857(a851,a851),a845),a111,a93,a102) % 174.01/173.88 [4125]E(f254(a3,a3,a3,a3,f41(a3),f83(a3)),a60) % 174.01/173.88 [4394]~E(f777(f108(a3),a101),f777(f108(a3),a87)) % 174.01/173.88 [4395]~P1(f777(a188,f4(a3))) % 174.01/173.88 [4396]~P1(f777(a188,f82(a3))) % 174.01/173.88 [4452]~P1(f777(f777(f235(a3),a87),f4(a3))) % 174.01/173.88 [3065]E(f777(f777(f5(a3),a101),a101),a87) % 174.01/173.88 [3079]E(f777(f104(a3),f777(a116,f4(a851))),f82(a3)) % 174.01/173.88 [3141]E(f777(f44(a854),f241(f858(a854,a845))),f82(a851)) % 174.01/173.88 [3163]P1(f777(a188,f777(f108(a3),a101))) % 174.01/173.88 [3164]P1(f777(f777(f235(a3),a101),a87)) % 174.01/173.88 [3166]P1(f777(f777(f234(a3),a101),a87)) % 174.01/173.88 [3225]E(f777(f777(f304(a851),f4(a851)),f182(f858(a851,a845))),f777(f295(a851),f4(a851))) % 174.01/173.88 [3281]P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),a87))) % 174.01/173.88 [3292]E(f777(f305(a851,a851,a116),f241(f858(a851,a845))),f777(f298(a851),f4(a851))) % 174.01/173.88 [3330]P12(f857(a851,a851),f241(f858(f857(a851,a851),a845)),a113) % 174.01/173.88 [3637]E(f777(f77(a851,a3,a103,f104(a3)),a24),a25) % 174.01/173.88 [3697]P36(a851,f777(f258(f857(a851,a851)),f777(f253(a851,a851,a845),f235(a851)))) % 174.01/173.88 [4443]~P1(f777(a188,f777(f108(a3),a87))) % 174.01/173.88 [4444]~P1(f777(f777(f235(a3),a101),a101)) % 174.01/173.88 [4445]~P1(f777(f777(f235(a3),a87),a101)) % 174.01/173.88 [4446]~P1(f777(f777(f235(a3),a87),a87)) % 174.01/173.88 [4447]~P1(f777(f777(f234(a3),a87),a101)) % 174.01/173.88 [4462]~P1(f777(f65(a851),f241(f858(a851,a845)))) % 174.01/173.88 [4463]~P1(f777(f65(a3),f241(f858(a3,a845)))) % 174.01/173.88 [4290]E(f777(f253(a3,a3,a845),f777(f777(f12(f858(a3,a845),f858(a3,a845),a3),f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f235(a3),f4(a3))))),f777(f777(f11(a3,a3,f858(a3,a845)),f777(f777(f12(f858(a3,f858(a3,a845)),f858(a3,f858(a3,a845)),a3),f11(a3,a3,a845)),f777(f777(f12(f858(a3,a3),f858(a3,f858(a3,a845)),a3),f777(f12(a3,f858(a3,a845),a3),a332)),a214))),f82(a3)))),a210) % 174.01/173.88 [3365]E(f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101),f777(f83(a3),a101)) % 174.01/173.88 [3408]E(f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101),f777(f777(f5(a3),a87),a101)) % 174.01/173.88 [3562]E(f777(f777(f63(f857(a851,a851)),f241(f858(f857(a851,a851),a845))),a113),a102) % 174.01/173.88 [3592]E(f777(f108(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f82(a3)) % 174.01/173.88 [3593]E(f777(f108(a103),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f82(a103)) % 174.01/173.88 [3594]E(f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f82(a851)) % 174.01/173.88 [3597]E(f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(a116,f4(a851))) % 174.01/173.88 [3986]E(f777(f777(f105(f858(f857(f857(a851,a851),f857(a851,a851)),a845)),a42),f302(f857(a851,a851),f182(f858(f857(f857(a851,a851),f857(a851,a851)),a845)))),a74) % 174.01/173.88 [4057]E(f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),f4(a851)),f4(a851))),f182(f858(f857(a851,a851),a845))))),f4(a3)) % 174.01/173.88 [4058]E(f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),f82(a851)),f4(a851))),f182(f858(f857(a851,a851),a845))))),f82(a3)) % 174.01/173.88 [4072]E(f777(f258(f857(a851,a851)),f777(f253(a851,a851,a845),f777(f777(f12(a851,f858(a851,a845),a851),f777(f11(a851,a851,a845),a332)),a116))),a325) % 174.01/173.88 [4041]E(f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),f777(a116,f777(a116,f4(a851)))) % 174.01/173.88 [4044]E(f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),f777(f777(f84(a851),f82(a851)),f82(a851))) % 174.01/173.88 [4045]E(f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),f777(f44(a845),f241(f858(a845,a845)))) % 174.01/173.88 [4110]P10(f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))) % 174.01/173.88 [4184]P30(f858(f857(a851,a851),a845),f777(f777(f243(f858(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),a845),f858(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),a845)),a43),a73)) % 174.01/173.88 [4185]P30(f858(f857(a851,a851),a845),f777(f777(f243(f858(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),a845),f858(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),a845)),a72),a75)) % 174.01/173.88 [4222]E(f777(f777(f105(f858(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),a845)),f328(f857(a851,a851),a74)),f777(f777(f304(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),f182(f858(f857(a851,a851),a845))),f182(f858(f857(a851,a851),a845)))),f182(f858(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),a845)))),a75) % 174.01/173.88 [4223]E(f777(f777(f105(f858(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),a845)),f326(f857(a851,a851),a74)),f777(f777(f304(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),f182(f858(f857(a851,a851),a845))),f182(f858(f857(a851,a851),a845)))),f182(f858(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),a845)))),a73) % 174.01/173.88 [4112]E(f777(a109,f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(a116,f777(a116,f4(a851)))) % 174.01/173.88 [4161]E(f777(f104(a3),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))) % 174.01/173.88 [4194]P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))) % 174.01/173.88 [4195]E(f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),a101)),f777(a116,f777(a116,f777(a116,f4(a851))))) % 174.01/173.88 [4235]P10(f777(f108(a3),f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),a101))) % 174.01/173.88 [4262]E(f777(f104(a3),f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),a101))),f777(f108(a3),f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),a101))) % 174.01/173.88 [4276]P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),a101)))) % 174.01/173.88 [3004]P11(x30041,a332) % 174.01/173.88 [3394]P29(a851,a851,a116,x33941) % 174.01/173.88 [3021]P36(a3,f110(x30211)) % 174.01/173.88 [3022]P36(a3,f112(x30221)) % 174.01/173.88 [3025]P37(x30251,f185(x30251)) % 174.01/173.88 [3068]P36(f858(x30681,a845),f301(x30681)) % 174.01/173.88 [3108]E(f54(a3,x31081,x31081),f4(a3)) % 174.01/173.88 [3160]P19(x31601,f858(x31601,a845),f304(x31601)) % 174.01/173.88 [4365]~E(f777(a29,x43651),a27) % 174.01/173.88 [4367]~E(f777(a116,x43671),x43671) % 174.01/173.88 [4379]~E(f777(a116,x43791),f4(a851)) % 174.01/173.88 [3006]E(f777(f183(a851),x30061),x30061) % 174.01/173.88 [3007]E(f777(f108(a3),x30071),x30071) % 174.01/173.88 [3023]E(f777(a93,f335(x30231)),x30231) % 174.01/173.88 [3024]E(f240(x30241,f4(a103)),f4(a103)) % 174.01/173.88 [3038]E(f118(x30381,f117(x30381)),f117(x30381)) % 174.01/173.88 [3043]E(f36(f777(a29,x30431)),f4(a851)) % 174.01/173.88 [3044]E(f777(f143(x30441),f117(x30441)),f117(x30441)) % 174.01/173.88 [3045]E(f777(f159(x30451),f117(x30451)),f117(x30451)) % 174.01/173.88 [3046]E(f777(f144(x30461),f117(x30461)),f117(x30461)) % 174.01/173.88 [3052]E(f777(f108(a3),x30521),f777(f107(a3),x30521)) % 174.01/173.88 [3054]E(f777(a7,f777(a24,x30541)),x30541) % 174.01/173.88 [3055]E(f777(a24,f777(a7,x30551)),x30551) % 174.01/173.88 [3056]E(f777(a93,f777(a111,x30561)),x30561) % 174.01/173.88 [3057]P10(f777(f104(a3),x30571)) % 174.01/173.88 [3061]E(f777(f183(f855(x30611)),f185(x30611)),f4(a851)) % 174.01/173.88 [3062]E(f777(f183(f852(x30621)),f117(x30621)),f4(a851)) % 174.01/173.88 [3067]E(f777(f183(a846),f777(a29,x30671)),f4(a851)) % 174.01/173.88 [3077]E(f228(x30771,f185(x30771)),f182(f858(x30771,a845))) % 174.01/173.88 [3085]E(f777(f777(f84(a851),x30851),f4(a851)),x30851) % 174.01/173.88 [3086]E(f777(f777(f84(a3),x30861),f4(a3)),x30861) % 174.01/173.88 [3087]E(f777(f777(f85(a851),x30871),f82(a851)),x30871) % 174.01/173.88 [3088]E(f777(f777(f85(a3),x30881),f82(a3)),x30881) % 174.01/173.88 [3089]E(f777(f777(f5(a851),x30891),f4(a851)),x30891) % 174.01/173.88 [3090]E(f777(f777(f181(a851),x30901),f4(a851)),x30901) % 174.01/173.88 [3091]E(f777(f777(f85(a851),x30911),f4(a851)),f4(a851)) % 174.01/173.88 [3092]E(f777(f777(f45(a3),x30921),f4(a3)),f4(a3)) % 174.01/173.88 [3093]E(f777(f777(f238(a851),x30931),f4(a851)),f4(a851)) % 174.01/173.88 [3099]E(f777(f160(x30991),f117(x30991)),f182(f858(x30991,a845))) % 174.01/173.88 [3103]P1(f777(f129(x31031),f117(x31031))) % 174.01/173.88 [3109]E(f777(f145(x31091,x31091),f9(x31091)),f41(f852(x31091))) % 174.01/173.88 [3110]E(f777(f145(x31101,x31101),f41(x31101)),f41(f852(x31101))) % 174.01/173.88 [3111]E(f777(f198(x31111,x31111),f9(x31111)),f41(f855(x31111))) % 174.01/173.88 [3112]E(f777(f198(x31121,x31121),f41(x31121)),f41(f855(x31121))) % 174.01/173.88 [3113]E(f54(a3,x31131,f4(a3)),x31131) % 174.01/173.88 [3114]E(f777(f234(a851),f777(a116,x31141)),f777(f235(a851),x31141)) % 174.01/173.88 [3115]E(f777(f259(a851),f777(a116,x31151)),f777(f295(a851),x31151)) % 174.01/173.88 [3116]E(f777(f260(a851),f777(a116,x31161)),f777(f298(a851),x31161)) % 174.01/173.88 [3118]E(f54(a3,f4(a3),x31181),f4(a3)) % 174.01/173.88 [3125]E(f777(f777(f84(a851),x31251),f82(a851)),f777(a116,x31251)) % 174.01/173.88 [3135]E(f777(f296(a851,x31351),f4(a851)),f182(f858(a851,a845))) % 174.01/173.88 [3146]E(f297(a851,f4(a851),x31461),f777(f295(a851),x31461)) % 174.01/173.88 [3192]E(f777(f777(f5(a851),f777(a116,x31921)),f82(a851)),x31921) % 174.01/173.88 [3205]E(f56(f4(a3),x32051),f777(f777(f243(a3,a3),f4(a3)),f4(a3))) % 174.01/173.88 [3255]P1(f777(f777(f235(a851),x32551),f777(a116,x32551))) % 174.01/173.88 [3269]P1(f777(f777(f235(a851),f4(a851)),f777(a116,x32691))) % 174.01/173.88 [3549]E(f777(f777(f5(a103),f777(a7,f777(a116,f777(a24,x35491)))),f82(a103)),x35491) % 174.01/173.88 [3619]P1(f777(f777(f234(a3),f777(f83(a3),f777(f104(a3),x36191))),f4(a3))) % 174.01/173.88 [3772]P1(f777(f777(f235(a3),f777(f83(a3),f777(f104(a3),f777(a116,x37721)))),f4(a3))) % 174.01/173.88 [4402]~E(f241(f858(x44021,a845)),f182(f858(x44021,a845))) % 174.01/173.88 [4455]~P1(f777(f777(f235(a851),x44551),f4(a851))) % 174.01/173.88 [4471]~P1(f777(f777(f235(a3),f777(f104(a3),x44711)),f4(a3))) % 174.01/173.88 [3066]E(f166(x30661,f117(f852(x30661))),f117(f852(x30661))) % 174.01/173.88 [3069]E(f777(f777(f85(a3),a87),x30691),a87) % 174.01/173.88 [3070]E(f777(f777(f84(a3),a87),x30701),x30701) % 174.01/173.88 [3073]E(f777(a109,f777(f104(a3),x30731)),x30731) % 174.01/173.88 [3074]E(f777(f777(f84(a3),x30741),a87),x30741) % 174.01/173.88 [3075]E(f777(f777(f5(a3),x30751),a87),x30751) % 174.01/173.88 [3078]E(f777(f777(f5(a851),x30781),x30781),f4(a851)) % 174.01/173.88 [3083]E(f777(f83(a3),f777(f83(a3),x30831)),x30831) % 174.01/173.88 [3084]E(f777(f44(a851),f777(f259(a851),x30841)),x30841) % 174.01/173.88 [3094]E(f777(f777(f84(a851),f4(a851)),x30941),x30941) % 174.01/173.88 [3095]E(f777(f777(f84(a3),f4(a3)),x30951),x30951) % 174.01/173.88 [3096]E(f777(f777(f85(a851),f82(a851)),x30961),x30961) % 174.01/173.88 [3097]E(f777(f777(f85(a3),f82(a3)),x30971),x30971) % 174.01/173.88 [3098]E(f777(f777(f181(a851),f4(a851)),x30981),x30981) % 174.01/173.88 [3104]E(f777(f777(f85(a851),f4(a851)),x31041),f4(a851)) % 174.01/173.88 [3105]E(f777(f777(f45(a3),f4(a3)),x31051),f4(a3)) % 174.01/173.88 [3106]E(f777(f777(f5(a851),f4(a851)),x31061),f4(a851)) % 174.01/173.88 [3107]E(f777(f777(f238(a851),f4(a851)),x31071),f4(a851)) % 174.01/173.88 [3123]E(f777(f296(a851,f4(a851)),x31231),f777(f259(a851),x31231)) % 174.01/173.88 [3124]E(f777(f777(f85(a3),a101),x31241),f777(f83(a3),x31241)) % 174.01/173.88 [3127]E(f777(a109,f777(f108(a3),x31271)),f777(f108(a851),x31271)) % 174.01/173.88 [3128]E(f777(a24,f777(f108(a103),x31281)),f777(f108(a851),x31281)) % 174.01/173.88 [3129]E(f777(f44(a851),f777(f295(a851),x31291)),f777(a116,x31291)) % 174.01/173.88 [3139]E(f777(f777(f84(a851),f82(a851)),x31391),f777(a116,x31391)) % 174.01/173.88 [3142]E(f777(f107(a3),f777(f104(a3),x31421)),f777(f104(a3),x31421)) % 174.01/173.88 [3143]E(f777(f79(a3),f777(f104(a3),x31431)),f777(f104(a3),x31431)) % 174.01/173.88 [3148]E(f777(f44(x31481),f182(f858(x31481,a845))),f4(a851)) % 174.01/173.88 [3150]E(f777(f777(f45(a851),x31501),f777(a116,f4(a851))),x31501) % 174.01/173.88 [3161]E(f54(a851,x31611,f777(a116,f4(a851))),f4(a851)) % 174.01/173.88 [3162]E(f54(a3,x31621,f777(f108(a3),a101)),f4(a3)) % 174.01/173.88 [3176]E(f777(f777(f45(a3),x31761),f777(f108(a3),a101)),f777(f83(a3),x31761)) % 174.01/173.88 [3180]E(f132(a851,f777(f296(a851,x31801),f4(a851))),f117(a851)) % 174.01/173.88 [3181]E(f777(f777(f5(a3),x31811),f82(a3)),f777(f777(f84(a3),x31811),a101)) % 174.01/173.88 [3182]E(f777(f777(f84(a3),x31821),f82(a3)),f777(f777(f5(a3),x31821),a101)) % 174.01/173.88 [3185]P1(f777(f777(f189(a27),x31851),x31851)) % 174.01/173.88 [3186]P1(f777(f777(f234(a851),x31861),x31861)) % 174.01/173.88 [3187]P1(f777(f777(f234(a3),x31871),x31871)) % 174.01/173.88 [3188]P1(f777(f777(f281(a851),x31881),x31881)) % 174.01/173.88 [3193]E(f777(f83(a3),f777(f108(a3),x31931)),f777(f108(a3),f777(f83(a3),x31931))) % 174.01/173.88 [3194]P1(f777(f65(a851),f777(f259(a851),x31941))) % 174.01/173.88 [3195]P1(f777(f65(a851),f777(f295(a851),x31951))) % 174.01/173.88 [3203]E(f151(x32031,f241(f858(x32031,a845))),f241(f858(f852(x32031),a845))) % 174.01/173.88 [3208]P1(f777(f777(f234(a851),f4(a851)),x32081)) % 174.01/173.88 [3219]E(f777(f777(f84(a851),f115(x32191)),f777(a116,f4(a851))),f115(f777(a116,x32191))) % 174.01/173.88 [3220]E(f777(f258(x32201),f777(f20(a845,x32201),a179)),f241(f858(x32201,a845))) % 174.01/173.88 [3221]E(f777(f258(x32211),f777(f20(a845,x32211),a180)),f182(f858(x32211,a845))) % 174.01/173.88 [3224]E(f777(f777(f304(a851),x32241),f777(f259(a851),x32241)),f777(f259(a851),f777(a116,x32241))) % 174.01/173.88 [3235]E(f777(f777(f84(a3),f82(a3)),f777(f104(a3),x32351)),f777(f104(a3),f777(a116,x32351))) % 174.01/173.88 [3258]E(f182(f858(f857(x32581,x32581),a845)),f262(x32581,f182(f858(x32581,a845)))) % 174.01/173.88 [3259]E(f777(f303(x32591),f241(f858(x32591,a845))),f241(f858(f858(x32591,a845),a845))) % 174.01/173.88 [3260]E(f777(f83(f858(x32601,a845)),f241(f858(x32601,a845))),f182(f858(x32601,a845))) % 174.01/173.88 [3261]E(f777(f83(f858(x32611,a845)),f182(f858(x32611,a845))),f241(f858(x32611,a845))) % 174.01/173.88 [3263]P1(f777(f65(x32631),f182(f858(x32631,a845)))) % 174.01/173.88 [3265]E(f777(f296(a851,x32651),f777(a116,x32651)),f777(f777(f304(a851),x32651),f182(f858(a851,a845)))) % 174.01/173.88 [3266]E(f89(f857(a851,a851),f57(x32661,f4(a851))),f777(f777(f243(a851,a851),f4(a851)),x32661)) % 174.01/173.88 [3280]E(f777(f777(f304(a851),f777(a116,x32801)),f777(f295(a851),x32801)),f777(f295(a851),f777(a116,x32801))) % 174.01/173.88 [3283]P36(x32831,f182(f858(f857(x32831,x32831),a845))) % 174.01/173.88 [3286]P1(f777(f777(f234(a3),f4(a3)),f777(f104(a3),x32861))) % 174.01/173.88 [3294]E(f777(f777(f84(a851),f777(f183(a851),x32941)),f777(a116,f4(a851))),f777(f183(a851),f777(a116,x32941))) % 174.01/173.88 [3401]P38(f777(f305(a851,a3,f104(a3)),x34011)) % 174.01/173.88 [3441]P47(x34411,f182(f858(x34411,a845)),f182(f858(f857(x34411,x34411),a845))) % 174.01/173.88 [3461]E(f777(f777(f243(a3,a3),f777(f108(a3),a101)),f777(f777(f5(a3),x34611),f82(a3))),f59(f777(f108(a3),a101),x34611)) % 174.01/173.88 [3511]P58(x35111,f777(f20(f858(x35111,a845),x35111),f777(f20(a845,x35111),a180))) % 174.01/173.88 [3520]E(f284(a851,f281(a851),x35201,x35201),f777(f777(f304(a851),x35201),f182(f858(a851,a845)))) % 174.01/173.88 [3711]P1(f777(f777(f336(f858(f857(a851,a851),a845)),f335(x37111)),a102)) % 174.01/173.88 [3736]P1(f777(f777(f336(f858(f857(a851,a851),a845)),f777(a111,x37361)),a102)) % 174.01/173.88 [3866]P29(x38661,f858(x38661,a845),f777(f777(f11(x38661,f858(x38661,a845),f858(x38661,a845)),f304(x38661)),f182(f858(x38661,a845))),f241(f858(x38661,a845))) % 174.01/173.88 [4398]~E(f777(f777(f84(a3),x43981),x43981),a101) % 174.01/173.88 [4442]~E(f777(a7,f777(a116,f777(a24,x44421))),f4(a103)) % 174.01/173.88 [4448]~P1(f777(a188,f777(f104(a3),x44481))) % 174.01/173.88 [4451]~P1(f777(f777(f235(a851),x44511),x44511)) % 174.01/173.88 [4464]~P1(f777(f777(f234(a851),f777(a116,x44641)),x44641)) % 174.01/173.88 [3210]E(f777(a109,f777(f83(a3),f777(f104(a3),x32101))),f4(a851)) % 174.01/173.88 [3213]E(f777(f777(f84(a3),f777(f83(a3),x32131)),x32131),f4(a3)) % 174.01/173.88 [3218]E(f777(f44(a3),f777(f296(a3,f4(a3)),x32181)),f777(a109,x32181)) % 174.01/173.88 [3228]E(f777(f777(f244(a851),f777(a116,f4(a851))),x32281),f777(a116,f4(a851))) % 174.01/173.88 [3327]E(f777(f278(x33271),f182(f858(f857(x33271,x33271),a845))),f182(f858(x33271,a845))) % 174.01/173.88 [3335]E(f47(f858(x33351,a845),f241(f858(f858(x33351,a845),a845))),f182(f858(x33351,a845))) % 174.01/173.88 [3336]E(f47(f858(x33361,a845),f182(f858(f858(x33361,a845),a845))),f241(f858(x33361,a845))) % 174.01/173.88 [3337]E(f46(f858(x33371,a845),f241(f858(f858(x33371,a845),a845))),f241(f858(x33371,a845))) % 174.01/173.88 [3338]E(f46(f858(x33381,a845),f182(f858(f858(x33381,a845),a845))),f182(f858(x33381,a845))) % 174.01/173.88 [3343]P1(f777(f777(f281(a851),f777(a116,f4(a851))),x33431)) % 174.01/173.88 [3381]E(f777(f777(f304(f852(x33811)),f117(x33811)),f182(f858(f852(x33811),a845))),f152(x33811,f117(f858(x33811,a845)))) % 174.01/173.88 [3382]E(f777(f777(f304(f852(x33821)),f117(x33821)),f182(f858(f852(x33821),a845))),f151(x33821,f182(f858(x33821,a845)))) % 174.01/173.88 [3425]E(f777(f777(f84(a851),f8(x34251)),f777(a116,f4(a851))),f8(f777(a7,f777(a116,f777(a24,x34251))))) % 174.01/173.88 [3453]E(f777(f44(a3),f777(f305(a851,a3,f104(a3)),x34531)),f777(f44(a851),x34531)) % 174.01/173.88 [3456]P1(f777(f777(f234(a851),x34561),f777(f777(f85(a851),x34561),x34561))) % 174.01/173.88 [3492]E(f777(f305(a3,a851,a109),f297(a3,f4(a3),f777(f104(a3),x34921))),f777(f295(a851),x34921)) % 174.01/173.88 [3506]E(f777(f777(f45(a851),f777(a116,f4(a851))),f777(f108(a851),x35061)),f777(a109,f777(f777(f45(a3),f82(a3)),f777(f108(a3),x35061)))) % 174.01/173.88 [3508]E(f777(f160(a851),f132(a851,f777(f296(a851,f4(a851)),f777(a116,x35081)))),f777(f295(a851),x35081)) % 174.01/173.88 [3509]E(f777(f777(f84(a851),f777(f183(a103),x35091)),f777(a116,f4(a851))),f777(f183(a103),f777(a7,f777(a116,f777(a24,x35091))))) % 174.01/173.88 [3525]E(f777(f305(a3,a851,a109),f777(f305(a851,a3,f104(a3)),x35251)),x35251) % 174.01/173.88 [3554]E(f777(f777(f304(a851),f4(a851)),f777(f305(a851,a851,a116),f777(f259(a851),x35541))),f777(f259(a851),f777(a116,x35541))) % 174.01/173.88 [3561]P53(x35611,x35611,f302(x35611,f182(f858(f857(x35611,x35611),a845)))) % 174.01/173.88 [3567]P1(f777(a188,f777(f83(a3),f777(f104(a3),f777(a116,x35671))))) % 174.01/173.88 [3578]E(f777(f777(f5(f858(a851,a845)),f777(f260(a851),x35781)),f777(f777(f304(a851),x35781),f182(f858(a851,a845)))),f777(f260(a851),f777(a116,x35781))) % 174.01/173.88 [3595]E(f777(f777(f84(a3),f777(f777(f5(a3),a87),x35951)),f777(f777(f5(a3),a87),x35951)),f777(f777(f5(a3),a87),f777(f777(f84(a3),x35951),x35951))) % 174.01/173.88 [3609]E(f777(f777(f304(f858(x36091,a845)),f182(f858(x36091,a845))),f182(f858(f858(x36091,a845),a845))),f777(f303(x36091),f182(f858(x36091,a845)))) % 174.01/173.88 [3638]E(f777(f777(f5(f858(a851,a845)),f777(f298(a851),x36381)),f777(f777(f304(a851),f777(a116,x36381)),f182(f858(a851,a845)))),f777(f298(a851),f777(a116,x36381))) % 174.01/173.88 [3647]E(f777(f777(f304(f855(x36471)),f185(x36471)),f777(f305(x36471,f855(x36471),f229(x36471)),f241(f858(x36471,a845)))),f241(f858(f855(x36471),a845))) % 174.01/173.88 [3748]E(f777(f108(a851),f777(f777(f84(a3),x37481),x37481)),f777(f777(f90(a851,a851),f777(f108(a851),x37481)),f777(f777(f22(a851,a851,a851),f84(a851)),f9(a851)))) % 174.01/173.88 [4136]P19(x41361,f858(x41361,a845),f777(f777(f12(f858(x41361,a845),f858(f858(x41361,a845),f858(x41361,a845)),x41361),f777(f11(f858(x41361,a845),f858(x41361,a845),f858(x41361,a845)),f5(f858(x41361,a845)))),f777(f777(f11(x41361,f858(x41361,a845),f858(x41361,a845)),f304(x41361)),f182(f858(x41361,a845))))) % 174.01/173.88 [4221]E(f777(f258(f857(a3,a3)),f777(f253(a3,a3,a845),f777(f777(f12(f858(a3,a845),f858(a3,a845),a3),f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f234(a3),x42211)))),f235(a3)))),f112(x42211)) % 174.01/173.88 [4253]E(f777(f258(f857(a3,a3)),f777(f253(a3,a3,a845),f777(f777(f22(a3,f858(a3,a845),f858(a3,a845)),f777(f777(f12(f858(a845,a845),f858(f858(a3,a845),f858(a3,a845)),a3),f12(a845,a845,a3)),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f234(a3),x42531)))),f235(a3)))),f110(x42531)) % 174.01/173.88 [4305]E(f777(f258(f857(f858(x43051,a845),f858(x43051,a845))),f777(f253(f858(x43051,a845),f858(x43051,a845),a845),f777(f777(f11(f858(x43051,a845),f858(f858(x43051,a845),a845),f858(f858(x43051,a845),a845)),f777(f777(f12(f858(f858(x43051,a845),f858(a845,a845)),f858(f858(f858(x43051,a845),a845),f858(f858(x43051,a845),a845)),f858(x43051,a845)),f22(f858(x43051,a845),a845,a845)),f777(f777(f12(f858(f858(x43051,a845),a845),f858(f858(x43051,a845),f858(a845,a845)),f858(x43051,a845)),f777(f12(a845,f858(a845,a845),f858(x43051,a845)),a333)),f235(f858(x43051,a845))))),f65(x43051)))),f301(x43051)) % 174.01/173.88 [4468]~P1(f777(f65(f852(x44681)),f241(f858(f852(x44681),a845)))) % 174.01/173.88 [4481]~P1(f777(f777(f234(a3),f4(a3)),f777(f83(a3),f777(f104(a3),f777(a116,x44811))))) % 174.01/173.88 [3359]E(f777(f777(f5(a3),f777(f777(f84(a3),x33591),a101)),a101),x33591) % 174.01/173.88 [3375]E(f777(f160(a851),f132(a851,f777(f296(a851,f4(a851)),x33751))),f777(f259(a851),x33751)) % 174.01/173.88 [3615]E(f777(f777(f84(a3),f777(f777(f84(a3),f82(a3)),x36151)),x36151),f777(f777(f5(a3),f777(f777(f84(a3),x36151),x36151)),a101)) % 174.01/173.88 [3665]E(f777(f280(x36651,x36651),f302(x36651,f182(f858(f857(x36651,x36651),a845)))),f302(x36651,f182(f858(f857(x36651,x36651),a845)))) % 174.01/173.88 [3714]P1(f777(f777(f234(a851),x37141),f777(f777(f85(a851),x37141),f777(f777(f85(a851),x37141),x37141)))) % 174.01/173.88 [3990]P1(f777(f65(a851),f777(f258(a851),f777(f777(f11(a851,a851,a845),f235(a851)),x39901)))) % 174.01/173.88 [3991]P1(f777(f65(a851),f777(f258(a851),f777(f777(f11(a851,a851,a845),f234(a851)),x39911)))) % 174.01/173.88 [4272]E(f777(f258(f857(x42721,x42721)),f777(f777(f12(f858(x42721,a845),a845,f857(x42721,x42721)),f91(x42721)),f777(f777(f11(f857(x42721,x42721),f858(x42721,f857(x42721,x42721)),f858(x42721,a845)),f777(f777(f12(f858(f857(x42721,x42721),a845),f858(f858(x42721,f857(x42721,x42721)),f858(x42721,a845)),f857(x42721,x42721)),f12(f857(x42721,x42721),a845,x42721)),a332)),f777(f777(f22(x42721,x42721,f857(x42721,x42721)),f243(x42721,x42721)),f9(x42721))))),f302(x42721,f182(f858(f857(x42721,x42721),a845)))) % 174.01/173.88 [4470]~E(f777(f777(f5(a3),f777(f777(f84(a3),x44701),x44701)),a101),a87) % 174.01/173.88 [4472]~E(f777(f777(f84(a3),f777(f777(f84(a3),f82(a3)),x44721)),x44721),f4(a3)) % 174.01/173.88 [3760]E(f777(f777(f84(a3),f777(f777(f5(a3),a101),x37601)),f777(f777(f5(a3),a101),x37601)),f777(f777(f5(a3),a101),f777(f777(f5(a3),f777(f777(f84(a3),x37601),x37601)),a101))) % 174.01/173.88 [3874]E(f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),a101),x38741)),f777(f777(f5(a3),a101),x38741))),a101),f777(f777(f5(a3),a101),f777(f777(f84(a3),x38741),x38741))) % 174.01/173.88 [3910]E(f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f84(a3),x39101),a101)),f777(f777(f84(a3),x39101),a101))),a101),f777(f777(f84(a3),f777(f777(f84(a3),x39101),x39101)),a101)) % 174.01/173.88 [3949]E(f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),a101),x39491)),f777(f777(f5(a3),a101),x39491))),a101),f777(f777(f5(a3),a87),f777(f777(f5(a3),f777(f777(f84(a3),x39491),x39491)),a101))) % 174.01/173.88 [4053]E(f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x40531),f4(a851))),f182(f858(f857(a851,a851),a845))))),f777(f104(a3),x40531)) % 174.01/173.88 [4063]E(f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),f339(x40631)),f492(x40631))),f182(f858(f857(a851,a851),a845))))),x40631) % 174.01/173.88 [4093]E(f777(f258(a3),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f234(a3),f4(a3)))),x40931)),f777(f305(a851,a3,f104(a3)),f777(f258(a851),f777(f777(f12(a3,a845,a851),x40931),f104(a3))))) % 174.01/173.88 [4144]P38(f777(f258(a3),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f234(a3),f4(a3)))),x41441))) % 174.01/173.88 [4164]P1(f777(f777(f336(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),x41641),f182(f858(f857(a851,a851),a845)))),a75)) % 174.01/173.88 [4170]E(f777(f305(a3,a851,a109),f777(f258(a3),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f234(a3),f4(a3)))),f777(f777(f12(a851,a845,a3),x41701),a109)))),f777(f258(a851),x41701)) % 174.01/173.88 [4319]E(f308(a851,f777(f777(f48(f857(a851,a851),f858(a851,a845)),f777(a111,x43191)),f777(f253(a851,a851,f858(a851,a845)),f777(f777(f11(a851,f858(a851,a845),f858(a851,f858(a851,a845))),f777(f777(f12(f858(a851,f858(f858(a851,a845),f858(a851,a845))),f858(f858(a851,a845),f858(a851,f858(a851,a845))),a851),f11(a851,f858(a851,a845),f858(a851,a845))),f777(f777(f12(f858(a851,a851),f858(a851,f858(f858(a851,a845),f858(a851,a845))),a851),f777(f12(a851,f858(f858(a851,a845),f858(a851,a845)),a851),f304(a851))),f5(a851)))),f182(f858(a851,a845)))))),f777(a109,x43191)) % 174.01/173.88 [3803]E(f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),x38031),x38031)),a101)),a101),f777(f777(f84(a3),x38031),x38031)) % 174.01/173.88 [3849]E(f777(f777(f5(a3),f777(f777(f5(a3),f777(f777(f84(a3),x38491),x38491)),a101)),a101),f777(f777(f84(a3),f777(f777(f5(a3),x38491),a101)),f777(f777(f5(a3),x38491),a101))) % 174.01/173.88 [4070]E(f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f84(a3),f777(f83(a3),x40701)),a101)),f777(f777(f84(a3),f777(f83(a3),x40701)),a101))),a101),f777(f83(a3),f777(f777(f5(a3),f777(f777(f84(a3),x40701),x40701)),a101))) % 174.01/173.88 [4113]E(f777(f777(f84(a851),x41131),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(a116,f777(a116,x41131))) % 174.01/173.88 [4114]E(f777(f777(f85(a851),x41141),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(f777(f84(a851),x41141),x41141)) % 174.01/173.88 [4115]E(f777(f777(f45(a851),f777(f777(f84(a851),x41151),x41151)),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x41151) % 174.01/173.88 [4197]E(f54(a851,f777(a116,f777(a116,x41971)),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f54(a851,x41971,f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))) % 174.01/173.88 [4336]E(f777(a93,f777(f777(f48(f857(a851,a851),f858(f857(a851,a851),a845)),f777(a111,x43361)),f777(f253(a851,a851,f858(f857(a851,a851),a845)),f777(f777(f12(f858(a851,f858(f857(a851,a851),a845)),f858(a851,f858(f857(a851,a851),a845)),a851),f777(f12(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845),a851),f279(f857(a851,a851),f857(a851,a851),a113))),f777(f777(f11(a851,f858(f857(a851,a851),a845),f858(a851,f858(f857(a851,a851),a845))),f777(f777(f12(f858(a851,f858(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f858(f858(f857(a851,a851),a845),f858(a851,f858(f857(a851,a851),a845))),a851),f11(a851,f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f12(f858(a851,f857(a851,a851)),f858(a851,f858(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),a851),f777(f12(f857(a851,a851),f858(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),a851),f304(f857(a851,a851)))),f777(f11(a851,a851,f857(a851,a851)),f243(a851,a851))))),f182(f858(f857(a851,a851),a845))))))),f777(f83(a3),x43361)) % 174.01/173.88 [4192]E(f777(f777(f84(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x41921),f777(a116,f777(a116,x41921))) % 174.01/173.88 [4193]E(f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x41931),f777(f777(f84(a851),x41931),x41931)) % 174.01/173.88 [4226]E(f777(f777(f45(a851),f777(a116,f777(a116,x42261))),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(a116,f777(f777(f45(a851),x42261),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))) % 174.01/173.88 [4277]E(f777(f777(f84(a851),f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),a101))),x42771),f777(a116,f777(a116,f777(a116,x42771)))) % 174.01/173.88 [4357]E(f777(f253(a3,a3,f857(a3,a3)),f777(f777(f22(a3,f858(a3,f857(a3,a3)),f858(a3,f857(a3,a3))),f777(f777(f12(f858(a3,f858(f857(a3,a3),f857(a3,a3))),f858(f858(a3,f857(a3,a3)),f858(a3,f857(a3,a3))),a3),f22(a3,f857(a3,a3),f857(a3,a3))),f777(f777(f12(f858(a3,f857(a3,a3)),f858(a3,f858(f857(a3,a3),f857(a3,a3))),a3),f777(f22(a3,f857(a3,a3),f858(f857(a3,a3),f857(a3,a3))),f777(f777(f12(a845,f858(f857(a3,a3),f858(f857(a3,a3),f857(a3,a3))),a3),f100(f857(a3,a3))),f777(f777(f12(a3,a845,a3),f777(f234(a3),f4(a3))),f777(f777(f11(a3,a3,a3),f5(a3)),x43571))))),f777(f777(f11(a3,f858(a3,a3),f858(a3,f857(a3,a3))),f777(f777(f12(f858(a3,f857(a3,a3)),f858(f858(a3,a3),f858(a3,f857(a3,a3))),a3),f12(a3,f857(a3,a3),a3)),f777(f777(f12(a3,f858(a3,f857(a3,a3)),a3),f243(a3,a3)),f777(f777(f11(a3,a3,a3),f777(f777(f12(a3,f858(a3,a3),a3),f84(a3)),f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))),f82(a3))))),f777(f777(f11(a3,a3,a3),f5(a3)),x43571))))),f777(f777(f12(a3,f858(a3,f857(a3,a3)),a3),f243(a3,a3)),f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))))),f52(x43571)) % 174.01/173.88 [3404]P39(a27,x34041,x34042,x34041) % 174.01/173.88 [3060]P18(a3,f165(x30601,x30602)) % 174.01/173.88 [3156]P47(x31561,x31562,f262(x31561,x31562)) % 174.01/173.88 [3157]P53(x31571,x31571,f262(x31571,x31572)) % 174.01/173.88 [3428]P29(x34281,x34281,f9(x34281),x34282) % 174.01/173.88 [3429]P29(x34291,x34291,f41(x34291),x34292) % 174.01/173.88 [3436]P34(x34361,x34362,f117(x34361),f117(x34361)) % 174.01/173.88 [3437]P29(x34371,f855(x34371),f229(x34371),x34372) % 174.01/173.88 [3447]P29(f852(x34471),f852(x34471),f144(x34471),x34472) % 174.01/173.88 [4371]~E(f37(x43711,x43712),a27) % 174.01/173.88 [4372]~E(f38(x43721,x43722),a27) % 174.01/173.88 [4373]~E(f30(x43731,x43732),a27) % 174.01/173.88 [3027]E(f777(f9(x30271),x30272),x30272) % 174.01/173.88 [3028]E(f777(f258(x30281),x30282),x30282) % 174.01/173.88 [3030]E(f777(f41(x30301),x30302),x30302) % 174.01/173.88 [3039]E(f777(f186(x30391),x30392),f119(x30391)) % 174.01/173.88 [3048]E(f36(f30(x30481,x30482)),f4(a851)) % 174.01/173.88 [3058]E(f89(x30581,f777(a332,x30582)),x30582) % 174.01/173.88 [3059]E(f94(x30591,f777(a332,x30592)),x30592) % 174.01/173.88 [3076]E(f777(f183(a846),f30(x30761,x30762)),f4(a851)) % 174.01/173.88 [3081]E(f777(f128(x30811,x30812),f117(x30811)),f117(x30811)) % 174.01/173.88 [3100]E(f302(x31001,f302(x31001,x31002)),f302(x31001,x31002)) % 174.01/173.88 [3121]E(f777(f777(f127(x31211),x31212),f117(x31211)),x31212) % 174.01/173.88 [3130]E(f777(f777(f161(x31301),x31302),f117(x31301)),f117(x31301)) % 174.01/173.88 [3131]E(f777(f777(f130(x31311),x31312),f117(x31311)),f117(x31311)) % 174.01/173.88 [3133]E(f230(x31331,x31332,f185(x31331)),f4(a851)) % 174.01/173.88 [3134]E(f146(x31341,x31342,f117(x31341)),f4(a851)) % 174.01/173.88 [3136]E(f153(x31361,x31362,f117(x31361)),f117(x31361)) % 174.01/173.88 [3137]E(f164(x31371,x31372,f117(x31371)),f117(x31371)) % 174.01/173.88 [3138]E(f162(x31381,f117(x31381),x31382),f117(x31381)) % 174.01/173.88 [3144]E(f777(f261(x31441,x31441),f262(x31441,x31442)),x31442) % 174.01/173.88 [3145]E(f777(f263(x31451,x31451),f262(x31451,x31452)),x31452) % 174.01/173.88 [3154]P1(f777(a28,f30(x31541,x31542))) % 174.01/173.88 [3155]E(f777(f280(x31551,x31551),f262(x31551,x31552)),f262(x31551,x31552)) % 174.01/173.88 [3168]E(f302(f852(x31681),f148(x31681,x31682)),f149(x31681,f302(x31681,x31682))) % 174.01/173.88 [3170]P1(f777(f129(a3),f165(x31701,x31702))) % 174.01/173.88 [3178]E(f777(f261(x31781,x31781),f302(x31781,x31782)),f241(f858(x31781,a845))) % 174.01/173.88 [3179]E(f777(f263(x31791,x31791),f302(x31791,x31792)),f241(f858(x31791,a845))) % 174.01/173.88 [3183]P1(f777(f129(x31831),f154(x31831,x31832))) % 174.01/173.88 [3191]E(f777(f160(a3),f165(x31911,x31912)),f297(a3,x31911,x31912)) % 174.01/173.88 [3206]P54(x32061,f182(f858(x32061,a845)),x32062) % 174.01/173.88 [3211]E(f777(f252(a3,a3),f55(x32111,x32112)),f54(a3,x32111,x32112)) % 174.01/173.88 [3212]E(f777(f296(a851,x32121),f777(a116,x32122)),f297(a851,x32121,x32122)) % 174.01/173.88 [3239]E(f297(a851,f777(a116,x32391),x32392),f299(a851,x32391,x32392)) % 174.01/173.88 [3242]P47(x32421,f241(f858(x32421,a845)),f302(x32421,x32422)) % 174.01/173.88 [3305]E(f777(f777(f5(a851),x33051),f777(a116,x33052)),f777(f44(a851),f300(a851,x33052,x33051))) % 174.01/173.88 [3360]E(f158(x33601,x33602,f117(x33601)),f777(f777(f243(f852(x33601),f852(x33601)),f117(x33601)),f117(x33601))) % 174.01/173.88 [3379]E(f777(f253(x33791,x33792,f857(x33791,x33792)),f243(x33791,x33792)),f41(f857(x33791,x33792))) % 174.01/173.88 [3384]P1(f777(f777(f336(f852(x33841)),f117(x33841)),f151(x33841,x33842))) % 174.01/173.88 [3385]E(f777(f183(f852(x33851)),f118(x33851,x33852)),f777(f777(f5(a851),f777(f183(f852(x33851)),x33852)),f82(a851))) % 174.01/173.88 [3395]P1(f777(f65(a851),f297(a851,x33951,x33952))) % 174.01/173.88 [3396]P1(f777(f65(a851),f299(a851,x33961,x33962))) % 174.01/173.88 [3397]P1(f777(f65(a851),f300(a851,x33971,x33972))) % 174.01/173.88 [3398]P1(f777(f65(a3),f297(a3,x33981,x33982))) % 174.01/173.88 [3399]P1(f777(f65(a3),f299(a3,x33991,x33992))) % 174.01/173.88 [3400]P1(f777(f65(a3),f300(a3,x34001,x34002))) % 174.01/173.88 [3505]E(f777(f305(a851,a851,a116),f297(a851,x35051,x35052)),f297(a851,f777(a116,x35051),f777(a116,x35052))) % 174.01/173.88 [3522]E(f777(f777(f283(x35221,x35221,x35221),f302(x35221,x35222)),f302(x35221,x35222)),f302(x35221,x35222)) % 174.01/173.88 [3552]E(f777(f777(f243(a3,a3),f777(f777(f45(a3),x35521),x35522)),f54(a3,x35521,x35522)),f55(x35521,x35522)) % 174.01/173.88 [3553]E(f777(f777(f243(a103,a103),f777(f777(f45(a103),x35531),x35532)),f54(a103,x35531,x35532)),f26(x35531,x35532)) % 174.01/173.88 [3582]E(f777(f777(f243(a851,a851),f777(f777(f45(a851),x35821),x35822)),f54(a851,x35821,x35822)),f89(f857(a851,a851),f57(x35821,x35822))) % 174.01/173.88 [3634]P1(f777(f777(f235(a851),f777(f777(f5(a851),x36341),x36342)),f777(a116,x36341))) % 174.01/173.88 [3735]E(f777(f777(f84(a3),f777(f777(f85(a3),x37351),f777(f777(f45(a3),x37352),x37351))),f54(a3,x37352,x37351)),x37352) % 174.01/173.88 [3739]E(f777(f777(f48(a851,f858(f857(f852(x37391),f852(x37391)),a845)),f241(f858(a851,a845))),f135(x37391,x37392)),f137(x37391,x37392)) % 174.01/173.88 [3964]P1(f777(f777(f336(f857(f852(x39641),f852(x39641))),f777(f777(f243(f852(x39641),f852(x39641)),f117(x39641)),f117(x39641))),f149(x39641,x39642))) % 174.01/173.88 [4127]E(f254(x41271,x41271,x41272,x41272,f9(x41271),f9(x41272)),f41(f857(x41271,x41272))) % 174.01/173.88 [4129]E(f254(x41291,x41291,x41292,x41292,f41(x41291),f41(x41292)),f41(f857(x41291,x41292))) % 174.01/173.88 [4381]~E(f777(f229(x43811),x43812),f185(x43811)) % 174.01/173.88 [4399]~P37(x43991,f777(f229(x43991),x43992)) % 174.01/173.88 [3119]E(f777(f233(x31191),f777(f229(x31191),x31192)),x31192) % 174.01/173.88 [3120]E(f777(f144(x31201),f777(f144(x31201),x31202)),x31202) % 174.01/173.88 [3122]E(f777(f777(f130(x31221),f4(a851)),x31222),x31222) % 174.01/173.88 [3132]E(f777(f777(f161(x31321),f4(a851)),x31322),f117(x31321)) % 174.01/173.88 [3140]E(f777(f777(f127(x31401),f117(x31401)),x31402),x31402) % 174.01/173.88 [3147]E(f777(f183(f855(x31471)),f777(f229(x31471),x31472)),f4(a851)) % 174.01/173.88 [3149]E(f46(f858(x31491,a845),f777(f303(x31491),x31492)),x31492) % 174.01/173.88 [3151]E(f777(f160(x31511),f777(f143(x31511),x31512)),f777(f160(x31511),x31512)) % 174.01/173.88 [3152]E(f777(f160(x31521),f777(f144(x31521),x31522)),f777(f160(x31521),x31522)) % 174.01/173.88 [3159]E(f777(f777(f5(a103),x31591),x31592),f777(f777(a6,x31591),x31592)) % 174.01/173.88 [3172]E(f777(f777(f84(a851),x31721),x31722),f777(f777(f84(a851),x31722),x31721)) % 174.01/173.88 [3173]E(f777(f777(f84(a3),x31731),x31732),f777(f777(f84(a3),x31732),x31731)) % 174.01/173.88 [3174]E(f777(f777(f85(a851),x31741),x31742),f777(f777(f85(a851),x31742),x31741)) % 174.01/173.88 [3175]E(f777(f777(f85(a3),x31751),x31752),f777(f777(f85(a3),x31752),x31751)) % 174.01/173.88 [3198]E(f777(f777(f175(x31981,x31981),f4(a851)),x31982),f41(x31981)) % 174.01/173.88 [3199]E(f777(f183(f852(x31991)),f777(f143(x31991),x31992)),f777(f183(f852(x31991)),x31992)) % 174.01/173.88 [3200]E(f777(f183(f852(x32001)),f777(f144(x32001),x32002)),f777(f183(f852(x32001)),x32002)) % 174.01/173.88 [3201]E(f162(x32011,x32012,f182(f858(a851,a845))),f117(x32011)) % 174.01/173.88 [3202]E(f777(f777(f145(x32021,x32021),f9(x32021)),x32022),x32022) % 174.01/173.88 [3204]E(f777(f242(a3,a3),f55(x32041,x32042)),f777(f777(f45(a3),x32041),x32042)) % 174.01/173.88 [3222]E(f36(f37(x32221,x32222)),f777(f777(f84(a851),f36(x32222)),f777(a116,f4(a851)))) % 174.01/173.88 [3223]E(f777(f278(x32231),f777(f280(x32231,x32231),x32232)),f777(f278(x32231),x32232)) % 174.01/173.88 [3227]P1(f777(f65(x32271),f777(f160(x32271),x32272))) % 174.01/173.88 [3234]E(f777(f777(f84(a3),x32341),f777(f83(a3),x32342)),f777(f777(f5(a3),x32341),x32342)) % 174.01/173.88 [3241]P28(x32411,x32412,f182(f858(f850(x32411),a845))) % 174.01/173.88 [3245]E(f777(f305(x32451,x32451,f9(x32451)),x32452),x32452) % 174.01/173.88 [3246]E(f777(f305(x32461,x32461,f41(x32461)),x32462),x32462) % 174.01/173.88 [3247]E(f777(f307(x32471,x32471,f9(x32471)),x32472),x32472) % 174.01/173.88 [3248]E(f777(f307(x32481,x32481,f41(x32481)),x32482),x32482) % 174.01/173.88 [3249]P1(f777(f241(f858(x32491,a845)),x32492)) % 174.01/173.88 [3251]E(f777(f44(a851),f777(f296(a851,x32511),x32512)),f777(f777(f5(a851),x32512),x32511)) % 174.01/173.88 [3252]E(f777(f296(a851,f777(a116,x32521)),x32522),f300(a851,x32521,x32522)) % 174.01/173.88 [3264]E(f777(f777(f304(x32641),x32642),f182(f858(x32641,a845))),f777(f258(x32641),f777(a332,x32642))) % 174.01/173.88 [3270]E(f777(f777(f304(x32701),x32702),f182(f858(x32701,a845))),f228(x32701,f777(f229(x32701),x32702))) % 174.01/173.88 [3272]E(f302(x32721,f777(f280(x32721,x32721),x32722)),f777(f280(x32721,x32721),f302(x32721,x32722))) % 174.01/173.88 [3276]E(f777(f777(f84(a851),f777(a116,x32761)),x32762),f777(f777(f84(a851),x32761),f777(a116,x32762))) % 174.01/173.88 [3277]E(f777(f777(f5(a851),f777(a116,x32771)),f777(a116,x32772)),f777(f777(f5(a851),x32771),x32772)) % 174.01/173.88 [3282]E(f777(f44(a851),f299(a851,x32821,x32822)),f777(f777(f5(a851),x32822),x32821)) % 174.01/173.88 [3291]P36(x32911,f777(f777(f282(a851,x32911),a239),x32912)) % 174.01/173.88 [3293]P18(a851,f132(a851,f777(f296(a851,x32931),x32932))) % 174.01/173.88 [3295]P1(f777(f65(a851),f777(f296(a851,x32951),x32952))) % 174.01/173.88 [3296]P1(f777(f65(a3),f777(f296(a3,x32961),x32962))) % 174.01/173.88 [3298]E(f777(f280(f852(x32981),f852(x32981)),f148(x32981,x32982)),f148(x32981,f777(f280(x32981,x32981),x32982))) % 174.01/173.88 [3299]E(f777(f183(a846),f37(x32991,x32992)),f777(f777(f84(a851),f777(f183(a846),x32992)),f777(a116,f4(a851)))) % 174.01/173.88 [3301]E(f777(f296(a3,x33011),f777(f777(f84(a3),x33012),f82(a3))),f297(a3,x33011,x33012)) % 174.01/173.88 [3304]E(f777(f777(f45(a3),f777(f83(a3),x33041)),f777(f83(a3),x33042)),f777(f777(f45(a3),x33041),x33042)) % 174.01/173.88 [3312]E(f173(x33121,x33122,f777(f20(f855(x33122),x33121),f185(x33122))),f182(f858(x33122,a845))) % 174.01/173.88 [3313]E(f171(x33131,x33132,f777(f20(f855(x33132),x33131),f185(x33132))),f182(f858(x33131,a845))) % 174.01/173.88 [3314]E(f777(f777(f175(f857(x33141,x33141),a845),f82(a851)),x33142),x33142) % 174.01/173.88 [3316]E(f777(f777(f5(f858(x33161,a845)),x33162),f182(f858(x33161,a845))),x33162) % 174.01/173.88 [3317]E(f777(f777(f105(f858(x33171,a845)),x33172),f182(f858(x33171,a845))),x33172) % 174.01/173.88 [3318]E(f777(f777(f106(f858(x33181,a845)),x33182),f241(f858(x33181,a845))),x33182) % 174.01/173.88 [3319]E(f777(f242(a851,a851),f89(f857(a851,a851),f57(x33191,x33192))),f777(f777(f45(a851),x33191),x33192)) % 174.01/173.88 [3325]E(f309(x33251,f777(a25,x33252),f777(f83(a3),f777(a25,x33252))),f777(f777(f312(a3),x33251),x33252)) % 174.01/173.88 [3326]E(f297(a3,f777(f777(f84(a3),x33261),f82(a3)),x33262),f299(a3,x33261,x33262)) % 174.01/173.88 [3331]E(f777(f252(a851,a851),f89(f857(a851,a851),f57(x33311,x33312))),f54(a851,x33311,x33312)) % 174.01/173.88 [3339]E(f310(x33391,f777(a25,x33392),f777(f83(a3),f777(a25,x33392))),f311(a3,x33391,x33392)) % 174.01/173.88 [3342]P1(f777(f777(f336(x33421),x33422),f241(f858(x33421,a845)))) % 174.01/173.88 [3346]E(f777(f777(f5(a851),f777(a116,x33461)),x33462),f777(f44(a851),f297(a851,x33462,x33461))) % 174.01/173.88 [3371]E(f777(f777(f5(f858(x33711,a845)),x33712),f241(f858(x33711,a845))),f182(f858(x33711,a845))) % 174.01/173.88 [3372]E(f777(f777(f105(f858(x33721,a845)),x33722),f241(f858(x33721,a845))),f241(f858(x33721,a845))) % 174.01/173.88 [3373]E(f777(f777(f106(f858(x33731,a845)),x33732),f182(f858(x33731,a845))),f182(f858(x33731,a845))) % 174.01/173.88 [3387]E(f54(a3,f777(f104(a3),x33871),f777(f104(a3),x33872)),f777(f104(a3),f54(a851,x33871,x33872))) % 174.01/173.88 [3388]E(f54(a3,f777(f83(a3),x33881),f777(f83(a3),x33882)),f777(f83(a3),f54(a3,x33881,x33882))) % 174.01/173.88 [3402]E(f777(f183(f852(x34021)),f777(f159(x34021),x34022)),f777(f777(f5(a851),f777(f183(f852(x34021)),x34022)),f82(a851))) % 174.01/173.88 [3430]E(f777(f777(f45(a3),f54(a3,x34301,x34302)),x34302),f4(a3)) % 174.01/173.88 [3439]E(f777(a7,f54(a851,f777(a24,x34391),f777(a24,x34392))),f54(a103,x34391,x34392)) % 174.01/173.88 [3472]E(f777(a7,f777(f777(f84(a851),f777(a24,x34721)),f777(a24,x34722))),f777(f777(f84(a103),x34721),x34722)) % 174.01/173.88 [3473]E(f777(a7,f777(f777(f85(a851),f777(a24,x34731)),f777(a24,x34732))),f777(f777(f85(a103),x34731),x34732)) % 174.01/173.88 [3474]E(f777(a7,f777(f777(f45(a851),f777(a24,x34741)),f777(a24,x34742))),f777(f777(f45(a103),x34741),x34742)) % 174.01/173.88 [3475]E(f777(a7,f777(f777(f5(a851),f777(a24,x34751)),f777(a24,x34752))),f777(f777(f5(a103),x34751),x34752)) % 174.01/173.88 [3484]E(f777(f305(a851,a851,a116),f777(f296(a851,x34841),x34842)),f777(f296(a851,f777(a116,x34841)),f777(a116,x34842))) % 174.01/173.88 [3510]P1(f777(f57(x35101,x35102),f89(f857(a851,a851),f57(x35101,x35102)))) % 174.01/173.88 [3527]E(f777(f777(f84(a851),f777(f777(f84(a851),f36(x35271)),f36(x35272))),f777(a116,f4(a851))),f36(f38(x35271,x35272))) % 174.01/173.88 [3528]E(f54(a851,f777(a116,f54(a851,x35281,x35282)),x35282),f54(a851,f777(a116,x35281),x35282)) % 174.01/173.88 [3542]E(f777(f777(f49(f858(x35421,a845),f858(x35421,a845)),x35422),f9(f858(x35421,a845))),f47(f858(x35421,a845),x35422)) % 174.01/173.88 [3543]E(f777(f777(f48(f858(x35431,a845),f858(x35431,a845)),x35432),f9(f858(x35431,a845))),f46(f858(x35431,a845),x35432)) % 174.01/173.88 [3546]P1(f777(f777(f336(f858(x35461,a845)),x35462),f777(f303(x35461),x35462))) % 174.01/173.88 [3551]E(f54(a3,f777(f83(a3),f54(a3,x35511,x35512)),x35512),f54(a3,f777(f83(a3),x35511),x35512)) % 174.01/173.88 [3563]P1(f777(f777(f234(f858(x35631,a845)),x35632),f241(f858(x35631,a845)))) % 174.01/173.88 [3565]E(f777(f777(f283(x35651,x35651,x35651),f302(x35651,x35652)),f302(x35651,f302(x35651,x35652))),f302(x35651,x35652)) % 174.01/173.88 [3566]E(f777(f777(f105(f858(x35661,a845)),f777(f263(x35661,x35661),x35662)),f777(f261(x35661,x35661),x35662)),f777(f278(x35661),x35662)) % 174.01/173.88 [3588]E(f316(x35881,x35882,f241(f858(x35881,a845)),f241(f858(x35882,a845))),f241(f858(f859(x35881,x35882),a845))) % 174.01/173.88 [3639]P1(f777(f777(f234(a851),f54(a851,x36391,x36392)),x36391)) % 174.01/173.88 [3663]P1(f777(f777(f234(a3),f777(f83(a3),f777(f104(a3),x36631))),f777(f104(a3),x36632))) % 174.01/173.88 [3688]P1(f777(f777(f336(f858(x36881,a845)),f182(f858(x36881,a845))),f777(f303(x36881),x36882))) % 174.01/173.88 [3693]E(f302(x36931,f777(f777(f283(x36931,x36931,x36931),x36932),f302(x36931,x36932))),f302(x36931,x36932)) % 174.01/173.88 [3696]E(f777(f777(f283(x36961,x36961,x36961),f302(x36961,x36962)),x36962),f777(f777(f283(x36961,x36961,x36961),x36962),f302(x36961,x36962))) % 174.01/173.88 [3698]E(f777(a109,f777(f777(f84(a3),f777(f777(f5(a3),x36981),x36982)),f82(a3))),f777(f44(a3),f297(a3,x36982,x36981))) % 174.01/173.88 [3715]E(f777(f261(x37151,x37151),f777(f777(f283(x37151,x37151,x37151),x37152),f302(x37151,x37152))),f777(f261(x37151,x37151),x37152)) % 174.01/173.88 [3716]E(f777(f263(x37161,x37161),f777(f777(f283(x37161,x37161,x37161),x37162),f302(x37161,x37162))),f777(f263(x37161,x37161),x37162)) % 174.01/173.88 [3731]E(f777(f777(f84(a851),f777(f777(f84(a851),f777(f183(a846),x37311)),f777(f183(a846),x37312))),f777(a116,f4(a851))),f777(f183(a846),f38(x37311,x37312))) % 174.01/173.88 [3743]P29(a851,a851,f777(f777(f11(a851,a851,a851),f84(a851)),x37431),x37432) % 174.01/173.88 [3745]P18(a851,f777(f144(a851),f777(f777(f145(f852(x37451),a851),f183(f852(x37451))),f166(x37451,x37452)))) % 174.01/173.88 [3792]P1(f777(f777(f235(a3),f777(f83(a3),f777(f104(a3),f777(a116,x37921)))),f777(f104(a3),x37922))) % 174.01/173.88 [3832]E(f777(f134(f852(x38321),x38321,f777(f11(x38321,f852(x38321),f852(x38321)),f142(x38321)),f117(x38321)),x38322),f777(f144(x38321),x38322)) % 174.01/173.88 [3881]P1(f777(f777(f234(f858(f857(f852(x38811),f852(x38811)),a845)),f149(x38811,x38812)),f302(f852(x38811),f148(x38811,x38812)))) % 174.01/173.88 [3914]P1(f777(f57(x39141,x39142),f777(f777(f243(a851,a851),f777(f777(f45(a851),x39141),x39142)),f54(a851,x39141,x39142)))) % 174.01/173.88 [3925]P1(f777(f777(f234(f858(f857(f852(x39251),f852(x39251)),a845)),f148(x39251,f302(x39251,x39252))),f302(f852(x39251),f148(x39251,x39252)))) % 174.01/173.88 [4156]E(f777(f777(f255(f857(a103,a103),a103,f857(a103,a103),f857(x41561,f857(a103,a103))),f266(f777(f157(a103),f777(f777(f145(f857(a103,x41561),a103),f242(a103,x41561)),x41562)))),f777(f777(f12(x41561,f858(f857(a103,a103),f857(x41561,f857(a103,a103))),a103),f243(x41561,f857(a103,a103))),f267(x41561,x41562))),f265(x41561,x41562)) % 174.01/173.88 [4335]E(f777(f253(f858(f857(x43351,x43351),a845),f858(f857(x43351,x43351),a845),f858(f858(x43352,x43351),f857(f858(f857(x43352,x43352),a845),f858(f857(x43352,x43352),a845)))),f777(f777(f11(f858(f857(x43351,x43351),a845),f858(f858(f857(x43351,x43351),a845),f858(f858(x43352,x43351),f858(f857(x43352,x43352),a845))),f858(f858(f857(x43351,x43351),a845),f858(f858(x43352,x43351),f857(f858(f857(x43352,x43352),a845),f858(f857(x43352,x43352),a845))))),f777(f777(f12(f858(f858(f858(x43352,x43351),f858(f857(x43352,x43352),a845)),f858(f858(x43352,x43351),f857(f858(f857(x43352,x43352),a845),f858(f857(x43352,x43352),a845)))),f858(f858(f858(f857(x43351,x43351),a845),f858(f858(x43352,x43351),f858(f857(x43352,x43352),a845))),f858(f858(f857(x43351,x43351),a845),f858(f858(x43352,x43351),f857(f858(f857(x43352,x43352),a845),f858(f857(x43352,x43352),a845))))),f858(f857(x43351,x43351),a845)),f12(f858(f858(x43352,x43351),f858(f857(x43352,x43352),a845)),f858(f858(x43352,x43351),f857(f858(f857(x43352,x43352),a845),f858(f857(x43352,x43352),a845))),f858(f857(x43351,x43351),a845))),f777(f777(f12(f858(f858(x43352,x43351),f858(f858(f857(x43352,x43352),a845),f857(f858(f857(x43352,x43352),a845),f858(f857(x43352,x43352),a845)))),f858(f858(f858(x43352,x43351),f858(f857(x43352,x43352),a845)),f858(f858(x43352,x43351),f857(f858(f857(x43352,x43352),a845),f858(f857(x43352,x43352),a845)))),f858(f857(x43351,x43351),a845)),f22(f858(x43352,x43351),f858(f857(x43352,x43352),a845),f857(f858(f857(x43352,x43352),a845),f858(f857(x43352,x43352),a845)))),f777(f777(f12(f858(f858(x43352,x43351),f858(f857(x43352,x43352),a845)),f858(f858(x43352,x43351),f858(f858(f857(x43352,x43352),a845),f857(f858(f857(x43352,x43352),a845),f858(f857(x43352,x43352),a845)))),f858(f857(x43351,x43351),a845)),f777(f12(f858(f857(x43352,x43352),a845),f858(f858(f857(x43352,x43352),a845),f857(f858(f857(x43352,x43352),a845),f858(f857(x43352,x43352),a845))),f858(x43352,x43351)),f243(f858(f857(x43352,x43352),a845),f858(f857(x43352,x43352),a845)))),f282(x43351,x43352))))),f282(x43351,x43352))),f78(x43351,x43352)) % 174.01/173.88 [4449]~E(f777(f303(x44491),x44492),f182(f858(f858(x44491,a845),a845))) % 174.01/173.88 [4467]~P1(f777(f777(f336(x44671),x44672),f182(f858(x44671,a845)))) % 174.01/173.88 [4476]~P1(f777(f777(f235(f858(x44761,a845)),x44762),f182(f858(x44761,a845)))) % 174.01/173.88 [3254]E(f777(f777(f5(a851),x32541),f777(f777(f84(a851),x32541),x32542)),f4(a851)) % 174.01/173.88 [3256]E(f777(f777(f105(f858(x32561,a845)),x32562),x32562),x32562) % 174.01/173.88 [3257]E(f777(f777(f106(f858(x32571,a845)),x32572),x32572),x32572) % 174.01/173.88 [3284]E(f777(f777(f5(f858(x32841,a845)),x32842),x32842),f182(f858(x32841,a845))) % 174.01/173.88 [3287]E(f777(f135(x32871,x32872),f4(a851)),f182(f858(f857(f852(x32871),f852(x32871)),a845))) % 174.01/173.88 [3288]E(f777(f777(f84(a851),x32881),f777(a116,x32882)),f777(a116,f777(f777(f84(a851),x32881),x32882))) % 174.01/173.88 [3300]E(f190(f777(f104(a3),x33001),f777(f104(a3),x33002)),f777(f104(a3),f777(f777(f5(a851),x33001),x33002))) % 174.01/173.88 [3303]E(f777(f777(f45(a3),f777(f83(a3),x33031)),x33032),f777(f777(f45(a3),x33031),f777(f83(a3),x33032))) % 174.01/173.88 [3307]E(f777(f44(a3),f777(f296(a3,x33071),x33072)),f777(a109,f777(f777(f5(a3),x33072),x33071))) % 174.01/173.88 [3310]E(f777(f777(f84(a851),f777(a116,x33101)),x33102),f777(a116,f777(f777(f84(a851),x33101),x33102))) % 174.01/173.88 [3315]E(f777(f83(f858(x33151,a845)),f777(f83(f858(x33151,a845)),x33152)),x33152) % 174.01/173.88 [3328]E(f166(x33281,f777(f777(f142(f852(x33281)),f117(x33281)),x33282)),f166(x33281,x33282)) % 174.01/173.88 [3332]E(f777(f777(f84(a851),x33321),f777(f777(f85(a851),x33321),x33322)),f777(f777(f85(a851),x33321),f777(a116,x33322))) % 174.01/173.88 [3340]E(f777(f777(a6,f777(a7,x33401)),f777(a7,x33402)),f777(a7,f777(f777(f5(a851),x33401),x33402))) % 174.01/173.88 [3351]E(f777(f777(f85(a3),f777(f83(a3),x33511)),x33512),f777(f83(a3),f777(f777(f85(a3),x33511),x33512))) % 174.01/173.88 [3353]E(f777(f777(f244(a3),f777(f104(a3),x33531)),x33532),f777(f104(a3),f777(f777(f244(a851),x33531),x33532))) % 174.01/173.88 [3354]E(f777(f777(f84(a103),f777(a7,x33541)),f777(a7,x33542)),f777(a7,f777(f777(f84(a851),x33541),x33542))) % 174.01/173.88 [3355]E(f777(f777(f85(a103),f777(a7,x33551)),f777(a7,x33552)),f777(a7,f777(f777(f85(a851),x33551),x33552))) % 174.01/173.88 [3356]E(f777(f777(f238(a851),f777(a116,x33561)),f777(a116,x33562)),f777(a116,f777(f777(f238(a851),x33561),x33562))) % 174.01/173.88 [3357]E(f777(f777(f181(a851),f777(a116,x33571)),f777(a116,x33572)),f777(a116,f777(f777(f181(a851),x33571),x33572))) % 174.01/173.88 [3363]E(f777(f160(a851),f132(a851,f777(f296(a851,x33631),x33632))),f777(f296(a851,x33631),x33632)) % 174.01/173.88 [3364]E(f308(x33641,f777(f777(f304(x33641),x33642),f182(f858(x33641,a845)))),x33642) % 174.01/173.88 [3369]E(f777(f261(x33691,x33692),f182(f858(f857(x33691,x33692),a845))),f182(f858(x33692,a845))) % 174.01/173.88 [3370]E(f777(f263(x33701,x33702),f182(f858(f857(x33701,x33702),a845))),f182(f858(x33701,a845))) % 174.01/173.88 [3374]E(f777(a109,f777(f777(f5(a3),x33741),x33742)),f777(f44(a3),f299(a3,x33742,x33741))) % 174.01/173.88 [3378]E(f777(f777(f84(a851),x33781),f777(f777(f85(a851),x33782),x33781)),f777(f777(f85(a851),f777(a116,x33782)),x33781)) % 174.01/173.88 [3380]E(f777(f777(f63(x33801),f182(f858(x33801,a845))),x33802),f182(f858(f858(x33801,a845),a845))) % 174.01/173.88 [3389]E(f777(f183(f852(a851)),f132(a851,f777(f296(a851,x33891),x33892))),f777(f777(f5(a851),x33892),x33891)) % 174.01/173.88 [3409]E(f777(f777(f105(f858(x34091,a845)),f182(f858(x34091,a845))),x34092),x34092) % 174.01/173.88 [3410]E(f777(f777(f106(f858(x34101,a845)),f241(f858(x34101,a845))),x34102),x34102) % 174.01/173.88 [3413]E(f777(f777(f84(a3),f777(f83(a3),x34131)),f777(f83(a3),x34132)),f777(f83(a3),f777(f777(f84(a3),x34131),x34132))) % 174.01/173.88 [3416]E(f777(f777(f84(a3),f777(f104(a3),x34161)),f777(f104(a3),x34162)),f777(f104(a3),f777(f777(f84(a851),x34161),x34162))) % 174.01/173.88 [3417]E(f777(f777(f84(a3),f777(f108(a3),x34171)),f777(f108(a3),x34172)),f777(f108(a3),f777(f777(f84(a3),x34171),x34172))) % 174.01/173.88 [3419]E(f777(f777(f85(a3),f777(f104(a3),x34191)),f777(f104(a3),x34192)),f777(f104(a3),f777(f777(f85(a851),x34191),x34192))) % 174.01/173.88 [3420]E(f777(f777(f85(a3),f777(f108(a3),x34201)),f777(f108(a3),x34202)),f777(f108(a3),f777(f777(f85(a3),x34201),x34202))) % 174.01/173.88 [3421]E(f777(f777(f45(a3),f777(f104(a3),x34211)),f777(f104(a3),x34212)),f777(f104(a3),f777(f777(f45(a851),x34211),x34212))) % 174.01/173.88 [3440]E(f777(f777(f10(x34401,a851),f777(f20(a851,x34401),f82(a851))),x34402),f777(f44(x34401),x34402)) % 174.01/173.88 [3448]E(f777(f83(a3),f54(a3,f777(f83(a3),x34481),x34482)),f54(a3,x34481,f777(f83(a3),x34482))) % 174.01/173.88 [3450]E(f777(f160(a3),f165(x34501,f777(f777(f5(a3),x34502),f82(a3)))),f777(f296(a3,x34501),x34502)) % 174.01/173.88 [3454]P1(f777(f777(f234(a851),x34541),f777(f777(f84(a851),x34542),x34541))) % 174.01/173.88 [3455]P1(f777(f777(f234(a851),x34551),f777(f777(f84(a851),x34551),x34552))) % 174.01/173.88 [3458]E(f777(f777(f5(f858(x34581,a845)),f182(f858(x34581,a845))),x34582),f182(f858(x34581,a845))) % 174.01/173.88 [3459]E(f777(f777(f105(f858(x34591,a845)),f241(f858(x34591,a845))),x34592),f241(f858(x34591,a845))) % 174.01/173.88 [3460]E(f777(f777(f106(f858(x34601,a845)),f182(f858(x34601,a845))),x34602),f182(f858(x34601,a845))) % 174.01/173.88 [3465]E(f777(f777(f243(a3,a3),x34651),f777(f83(a3),x34652)),f777(a60,f777(f777(f243(a3,a3),x34651),x34652))) % 174.01/173.88 [3466]E(f777(f296(a3,f777(f777(f84(a3),x34661),f82(a3))),x34662),f300(a3,x34661,x34662)) % 174.01/173.88 [3476]E(f777(f777(f85(a851),x34761),f777(f777(f45(a851),x34762),x34761)),f777(f777(f5(a851),x34762),f54(a851,x34762,x34761))) % 174.01/173.88 [3477]E(f777(f777(f85(a3),x34771),f777(f777(f45(a3),x34772),x34771)),f777(f777(f5(a3),x34772),f54(a3,x34772,x34771))) % 174.01/173.88 [3481]E(f777(f160(a3),f165(f777(f777(f84(a3),x34811),f82(a3)),x34812)),f299(a3,x34811,x34812)) % 174.01/173.88 [3485]P1(f777(f777(f234(f858(x34851,a845)),x34852),x34852)) % 174.01/173.88 [3490]E(f777(f777(f105(f858(x34901,a845)),x34902),f777(f83(f858(x34901,a845)),x34902)),f241(f858(x34901,a845))) % 174.01/173.88 [3491]E(f777(f777(f106(f858(x34911,a845)),x34912),f777(f83(f858(x34911,a845)),x34912)),f182(f858(x34911,a845))) % 174.01/173.88 [3497]E(f777(f777(f5(a851),f777(f777(f5(a851),x34971),f82(a851))),x34972),f777(f777(f5(a851),x34971),f777(a116,x34972))) % 174.01/173.88 [3502]E(f777(f777(f5(f858(x35021,a845)),f241(f858(x35021,a845))),x35022),f777(f83(f858(x35021,a845)),x35022)) % 174.01/173.88 [3503]E(f777(f777(f5(a3),f777(f108(a3),x35031)),f777(f108(a3),x35032)),f777(f108(a3),f777(f777(f84(a3),x35031),f777(f83(a3),x35032)))) % 174.01/173.88 [3515]E(f777(f160(a851),f132(a851,f777(f296(a851,x35151),f777(a116,x35152)))),f297(a851,x35151,x35152)) % 174.01/173.88 [3544]E(f777(f777(f175(f857(x35441,x35441),a845),f4(a851)),x35442),f302(x35441,f182(f858(f857(x35441,x35441),a845)))) % 174.01/173.88 [3548]P1(f777(f129(a851),f132(a851,f777(f296(a851,x35481),x35482)))) % 174.01/173.88 [3564]E(f777(f305(a3,a851,a109),f297(a3,f777(f104(a3),x35641),f777(f104(a3),x35642))),f297(a851,x35641,x35642)) % 174.01/173.88 [3574]E(f177(a851,f4(a851),f9(a851),f777(f777(f5(a851),x35741),x35742)),f777(f777(f5(a851),x35741),f777(a116,x35742))) % 174.01/173.88 [3575]E(f777(a109,f777(f777(f5(a3),x35751),f777(f777(f84(a3),x35752),f82(a3)))),f777(f44(a3),f300(a3,x35752,x35751))) % 174.01/173.88 [3610]E(f777(f777(f145(a851,a851),a116),f132(a851,f777(f296(a851,x36101),x36102))),f132(a851,f777(f296(a851,f777(a116,x36101)),f777(a116,x36102)))) % 174.01/173.88 [3617]E(f777(f160(a3),f165(f777(f777(f84(a3),x36171),f82(a3)),f777(f777(f5(a3),x36172),f82(a3)))),f300(a3,x36171,x36172)) % 174.01/173.88 [3631]P1(f777(f777(f234(f858(x36311,a845)),f182(f858(x36311,a845))),x36312)) % 174.01/173.88 [3635]E(f89(x36351,f777(f777(f11(x36351,x36351,a845),a332),x36352)),x36352) % 174.01/173.88 [3636]E(f94(x36361,f777(f777(f11(x36361,x36361,a845),a332),x36362)),x36362) % 174.01/173.89 [3640]E(f777(f160(a851),f132(a851,f777(f296(a851,f777(a116,x36401)),f777(a116,x36402)))),f299(a851,x36401,x36402)) % 174.01/173.89 [3666]E(f777(f777(f250(x36661,x36662),f241(f858(x36661,a845))),f777(f20(f858(x36662,a845),x36661),f241(f858(x36662,a845)))),f241(f858(f857(x36661,x36662),a845))) % 174.01/173.89 [3702]E(f777(f258(x37021),f777(f777(f12(a845,a845,x37021),a330),x37022)),f777(f83(f858(x37021,a845)),f777(f258(x37021),x37022))) % 174.01/173.89 [3705]E(f777(f258(x37051),f777(f777(f11(x37051,x37051,a845),a332),x37052)),f777(f777(f304(x37051),x37052),f182(f858(x37051,a845)))) % 174.01/173.89 [3712]E(f777(f777(f84(a3),f777(f777(f84(a3),x37121),x37121)),f777(f777(f84(a3),x37122),x37122)),f777(f777(f84(a3),f777(f777(f84(a3),x37121),x37122)),f777(f777(f84(a3),x37121),x37122))) % 174.01/173.89 [3713]E(f777(f777(f5(a3),f777(f777(f84(a3),x37131),x37131)),f777(f777(f84(a3),x37132),x37132)),f777(f777(f84(a3),f777(f777(f5(a3),x37131),x37132)),f777(f777(f5(a3),x37131),x37132))) % 174.01/173.89 [3728]P1(f777(f777(f234(a851),f777(f44(x37281),f777(f160(x37281),x37282))),f777(f183(f852(x37281)),x37282))) % 174.01/173.89 [3729]P1(f777(f777(f234(a851),f777(f183(f852(x37291)),f154(x37291,x37292))),f777(f183(f852(x37291)),x37292))) % 174.01/173.89 [3740]E(f777(f258(x37401),f777(f777(f11(x37401,f858(x37401,a845),a845),f336(x37401)),x37402)),x37402) % 174.01/173.89 [3756]E(f777(f777(f161(x37561),f777(f777(f5(a851),f777(f183(f852(x37561)),x37562)),f82(a851))),x37562),f118(x37561,x37562)) % 174.01/173.89 [3779]E(f177(a851,f4(a851),f777(f777(f12(a851,a851,a851),a116),f777(f238(a851),x37791)),x37792),f777(f777(f238(a851),f777(a116,x37791)),x37792)) % 174.01/173.89 [3783]E(f46(f858(x37831,a845),f777(f305(f858(f857(x37831,x37831),a845),f858(x37831,a845),f278(x37831)),x37832)),f777(f278(x37831),f46(f858(f857(x37831,x37831),a845),x37832))) % 174.01/173.89 [3784]E(f177(a851,f777(a116,x37841),f777(f777(f12(a851,a851,a851),a116),f777(f181(a851),x37841)),x37842),f777(f777(f181(a851),f777(a116,x37841)),x37842)) % 174.01/173.89 [3786]E(f777(f777(f243(a3,a3),f777(f777(f45(a3),f777(f79(a3),x37861)),f777(f79(a3),x37862))),f54(a3,f777(f79(a3),x37861),f777(f79(a3),x37862))),f62(x37861,x37862)) % 174.01/173.89 [3806]P1(f777(f777(f234(f858(f858(x38061,a845),a845)),x38062),f777(f303(x38061),f46(f858(x38061,a845),x38062)))) % 174.01/173.89 [3837]E(f777(f777(f48(x38371,f858(x38371,a845)),x38372),f777(f777(f11(x38371,f858(x38371,a845),f858(x38371,a845)),f304(x38371)),f182(f858(x38371,a845)))),x38372) % 174.01/173.89 [3838]E(f777(f777(f283(x38381,x38381,x38381),f777(f280(x38381,x38381),x38382)),f302(x38381,f777(f280(x38381,x38381),x38382))),f777(f280(x38381,x38381),f777(f777(f283(x38381,x38381,x38381),x38382),f302(x38381,x38382)))) % 174.01/173.89 [3906]E(f777(f160(x39061),f777(f134(f852(x39061),f852(x39061),f127(x39061),f117(x39061)),x39062)),f777(f777(f48(f852(x39061),f858(x39061,a845)),f777(f160(f852(x39061)),x39062)),f160(x39061))) % 174.01/173.89 [3937]E(f777(f777(f105(f858(f857(x39371,x39371),a845)),f302(x39371,f182(f858(f857(x39371,x39371),a845)))),f777(f777(f283(x39371,x39371,x39371),f302(x39371,x39372)),x39372)),f302(x39371,x39372)) % 174.01/173.89 [3975]E(f777(f777(f169(x39751,x39751),x39752),x39752),f777(f777(f145(x39751,f857(x39751,x39751)),f777(f777(f22(x39751,x39751,f857(x39751,x39751)),f243(x39751,x39751)),f9(x39751))),x39752)) % 174.01/173.89 [4089]E(f777(f134(a851,f852(x40891),f777(f11(f852(x40891),a851,a851),f777(f777(f12(a851,f858(a851,a851),f852(x40891)),f181(a851)),f183(f852(x40891)))),f4(a851)),f777(f144(f852(x40891)),x40892)),f777(f183(f852(f852(x40891))),f166(x40891,x40892))) % 174.01/173.89 [4169]E(f777(f777(f282(f857(a851,f852(x41691)),f852(x41691)),f327(a851,f852(x41691),a239,f137(x41691,x41692))),f777(f777(f22(f852(x41691),f852(x41691),f857(a851,f852(x41691))),f777(f777(f12(a851,f858(f852(x41691),f857(a851,f852(x41691))),f852(x41691)),f243(a851,f852(x41691))),f183(f852(x41691)))),f9(f852(x41691)))),f138(x41691,x41692)) % 174.01/173.89 [4292]E(f777(f258(x42921),f777(f777(f12(f858(f858(x42921,a845),a845),a845,x42921),f92(f858(x42921,a845))),f777(f777(f12(f858(f858(x42921,a845),a845),f858(f858(x42921,a845),a845),x42921),f777(f22(f858(x42921,a845),a845,a845),f777(f777(f12(a845,f858(a845,a845),f858(x42921,a845)),a337),f777(f777(f11(f858(x42921,a845),f858(f858(x42921,a845),a845),a845),f336(f858(x42921,a845))),x42922)))),f336(x42921)))),f47(f858(x42921,a845),x42922)) % 174.01/173.89 [4477]~P1(f777(f777(f235(a3),f777(f104(a3),x44771)),f777(f83(a3),f777(f104(a3),x44772)))) % 174.01/173.89 [3376]E(f777(f777(f5(a851),f777(f777(f84(a851),x33761),x33762)),x33762),x33761) % 174.01/173.89 [3377]E(f777(f777(f5(a851),f777(f777(f84(a851),x33771),x33772)),x33771),x33772) % 174.01/173.89 [3449]E(f777(f777(f84(a851),f777(f777(f5(a851),x34491),x34492)),x34492),f777(f777(f181(a851),x34491),x34492)) % 174.01/173.89 [3550]E(f777(f777(f85(a851),f777(f777(f45(a851),x35501),x35502)),x35502),f777(f777(f5(a851),x35501),f54(a851,x35501,x35502))) % 174.01/173.89 [3579]E(f777(f160(a851),f132(a851,f777(f296(a851,f777(a116,x35791)),x35792))),f300(a851,x35791,x35792)) % 174.01/173.89 [3587]E(f777(f104(a3),f213(f777(a109,f777(f79(a3),x35871)),f777(a109,f777(f79(a3),x35872)))),f777(f777(a214,x35871),x35872)) % 174.01/173.89 [3589]E(f777(f777(f105(f858(x35891,a845)),f777(f83(f858(x35891,a845)),x35892)),x35892),f241(f858(x35891,a845))) % 174.01/173.89 [3590]E(f777(f777(f106(f858(x35901,a845)),f777(f83(f858(x35901,a845)),x35902)),x35902),f182(f858(x35901,a845))) % 174.01/173.89 [3606]P1(f777(f777(f234(a851),f777(f777(f45(a851),x36061),x36062)),x36061)) % 174.01/173.89 [3607]P1(f777(f777(f234(a851),f777(f777(f5(a851),x36071),x36072)),x36071)) % 174.01/173.89 [3632]P1(f777(f777(f235(a851),x36321),f777(a116,f777(f777(f84(a851),x36322),x36321)))) % 174.01/173.89 [3633]P1(f777(f777(f235(a851),x36331),f777(a116,f777(f777(f84(a851),x36331),x36332)))) % 174.01/173.89 [3652]E(f777(f777(f85(a851),f777(a109,f777(f79(a3),x36521))),f777(a109,f777(f79(a3),x36522))),f777(a109,f777(f79(a3),f777(f777(f85(a3),x36521),x36522)))) % 174.01/173.89 [3662]P1(f777(f777(f234(a3),f4(a3)),f777(f777(f244(a3),f777(f79(a3),x36621)),x36622))) % 174.01/173.89 [3734]E(f777(f279(f852(x37341),f852(x37341),f149(x37341,x37342)),f777(f777(f304(f852(x37341)),f117(x37341)),f182(f858(f852(x37341),a845)))),f777(f777(f304(f852(x37341)),f117(x37341)),f182(f858(f852(x37341),a845)))) % 174.01/173.89 [3752]E(f777(f777(f105(f858(f857(x37521,x37521),a845)),f302(x37521,x37522)),f302(x37521,f182(f858(f857(x37521,x37521),a845)))),f302(x37521,x37522)) % 174.01/173.89 [3768]E(f777(f777(f45(a3),f777(f108(a3),f777(f777(f84(a3),x37681),x37681))),f777(f108(a3),f777(f777(f84(a3),x37682),x37682))),f777(f777(f45(a3),f777(f108(a3),x37681)),f777(f108(a3),x37682))) % 174.01/173.89 [3827]E(f777(f777(f244(a3),x38271),f777(f108(a851),f777(f777(f84(a3),x38272),x38272))),f777(f777(f90(a3,a3),f777(f777(f244(a3),x38271),f777(f108(a851),x38272))),f777(f777(f22(a3,a3,a3),f85(a3)),f9(a3)))) % 174.01/173.89 [3833]E(f777(f258(f858(x38331,a845)),f777(f777(f11(f858(x38331,a845),f858(x38331,a845),a845),f234(f858(x38331,a845))),x38332)),f777(f303(x38331),x38332)) % 174.01/173.89 [3880]E(f777(f305(a3,a3,f777(f777(f11(a3,a3,a3),f84(a3)),x38801)),f777(f296(a3,f4(a3)),f777(f777(f5(a3),x38802),x38801))),f777(f296(a3,x38801),x38802)) % 174.01/173.89 [3883]P48(x38831,f777(f777(f5(f858(f857(x38831,x38831),a845)),x38832),f302(x38831,f182(f858(f857(x38831,x38831),a845))))) % 174.01/173.89 [3903]E(f777(f183(f852(x39031)),f777(f134(f852(x39031),f852(x39031),f127(x39031),f117(x39031)),x39032)),f777(f157(a851),f777(f777(f145(f852(x39031),a851),f183(f852(x39031))),x39032))) % 174.01/173.89 [3908]P47(x39081,f241(f858(x39081,a845)),f777(f777(f105(f858(f857(x39081,x39081),a845)),x39082),f302(x39081,f182(f858(f857(x39081,x39081),a845))))) % 174.01/173.89 [3954]E(f177(a851,f4(a851),f777(f777(f12(a851,a851,a851),a116),f777(f777(f11(a851,a851,a851),f238(a851)),x39541)),x39542),f777(f777(f238(a851),x39542),f777(a116,x39541))) % 174.01/173.89 [3957]E(f177(a851,f777(a116,x39571),f777(f777(f12(a851,a851,a851),a116),f777(f777(f11(a851,a851,a851),f181(a851)),x39571)),x39572),f777(f777(f181(a851),x39572),f777(a116,x39571))) % 174.01/173.89 [3960]E(f777(f305(x39601,f852(x39601),f777(f777(f11(x39601,f852(x39601),f852(x39601)),f142(x39601)),f117(x39601))),x39602),f163(x39601,x39602,f777(f777(f304(f852(x39601)),f117(x39601)),f182(f858(f852(x39601),a845))))) % 174.01/173.89 [3961]E(f777(f777(f105(f858(f857(x39611,x39611),a845)),f777(f777(f283(x39611,x39611,x39611),x39612),f302(x39611,x39612))),f302(x39611,f182(f858(f857(x39611,x39611),a845)))),f302(x39611,x39612)) % 174.01/173.89 [3969]P1(f777(f777(f234(f858(f857(x39691,x39691),a845)),f262(x39691,x39692)),f777(f777(f250(x39691,x39691),x39692),f777(f20(f858(x39691,a845),x39691),x39692)))) % 174.01/173.89 [3973]E(f777(f305(a3,a851,a109),f777(f777(f105(f858(a3,a845)),f777(f305(a851,a3,f104(a3)),x39731)),f777(f305(a851,a3,f104(a3)),x39732))),f777(f777(f105(f858(a851,a845)),x39731),x39732)) % 174.01/173.89 [3974]E(f777(f305(a3,a851,a109),f777(f777(f106(f858(a3,a845)),f777(f305(a851,a3,f104(a3)),x39741)),f777(f305(a851,a3,f104(a3)),x39742))),f777(f777(f106(f858(a851,a845)),x39741),x39742)) % 174.01/173.89 [3978]E(f777(f258(x39781),f777(f777(f12(a845,a845,x39781),a330),f777(f777(f11(x39781,f858(x39781,a845),a845),f336(x39781)),x39782))),f777(f83(f858(x39781,a845)),x39782)) % 174.01/173.89 [4005]E(f777(f134(f852(x40051),f852(x40051),f127(x40051),f117(x40051)),f777(f777(f145(f852(x40051),f852(x40051)),f144(x40051)),f777(f144(f852(x40051)),x40052))),f777(f144(x40051),f777(f134(f852(x40051),f852(x40051),f127(x40051),f117(x40051)),x40052))) % 174.01/173.89 [4032]E(f777(f777(f48(a851,f858(f857(x40321,x40321),a845)),f241(f858(a851,a845))),f777(f777(f11(a851,f858(f857(x40321,x40321),a845),f858(f857(x40321,x40321),a845)),f175(f857(x40321,x40321),a845)),x40322)),f302(x40321,x40322)) % 174.01/173.89 [4054]E(f89(x40541,f777(f777(f12(f858(x40541,a845),a845,x40541),f777(a332,x40542)),f777(f777(f11(x40541,f858(x40541,a845),f858(x40541,a845)),f304(x40541)),f182(f858(x40541,a845))))),f308(x40541,x40542)) % 174.01/173.89 [4062]E(f777(f183(f852(x40621)),f154(x40621,f777(f134(f852(x40621),f852(x40621),f127(x40621),f117(x40621)),x40622))),f777(f44(x40621),f777(f777(f48(f852(x40621),f858(x40621,a845)),f777(f160(f852(x40621)),x40622)),f160(x40621)))) % 174.01/173.89 [4077]E(f777(f777(f105(f858(f857(x40771,x40771),a845)),x40772),f777(f777(f283(x40771,x40771,x40771),f777(f777(f283(x40771,x40771,x40771),x40772),f302(x40771,x40772))),x40772)),f777(f777(f283(x40771,x40771,x40771),x40772),f302(x40771,x40772))) % 174.01/173.89 [4098]P1(f777(f777(f234(f858(f857(x40981,x40981),a845)),f777(f777(f283(x40981,x40981,x40981),x40982),f302(x40981,x40982))),f777(f777(f250(x40981,x40981),f777(f278(x40981),x40982)),f777(f20(f858(x40981,a845),x40981),f777(f278(x40981),x40982))))) % 174.01/173.89 [4145]E(f777(f258(f852(x41451)),f777(f777(f11(f852(x41451),f858(x41451,a845),a845),f777(f777(f12(f858(x41451,a845),f858(f858(x41451,a845),a845),f852(x41451)),f234(f858(x41451,a845))),f160(x41451))),x41452)),f151(x41451,x41452)) % 174.01/173.89 [4157]E(f777(f147(f852(x41571),x41571,f117(x41571),f777(f777(f12(f852(x41571),f858(f852(x41571),f852(x41571)),x41571),f777(f11(f852(x41571),f852(x41571),f852(x41571)),f127(x41571))),f777(f777(f11(x41571,f852(x41571),f852(x41571)),f142(x41571)),f117(x41571)))),x41572),f777(f143(x41571),x41572)) % 174.01/173.89 [4196]P29(f858(x41961,x41962),f858(f857(x41961,x41962),a845),f777(f777(f12(f858(f857(x41961,x41962),a845),f858(f857(x41961,x41962),a845),f858(x41961,x41962)),f258(f857(x41961,x41962))),f777(f777(f12(f858(x41961,f858(x41962,a845)),f858(f857(x41961,x41962),a845),f858(x41961,x41962)),f253(x41961,x41962,a845)),f777(f12(x41962,f858(x41962,a845),x41961),f777(f11(x41962,x41962,a845),a332)))),f241(f858(f858(x41961,x41962),a845))) % 174.01/173.89 [4201]E(f54(a3,f777(f108(a3),f777(f777(f84(a3),x42011),x42011)),f777(f108(a3),f777(f777(f84(a3),x42012),x42012))),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f54(a3,f777(f108(a3),x42011),f777(f108(a3),x42012)))) % 174.01/173.89 [4242]E(f777(f777(f48(x42421,f858(f857(x42421,x42421),a845)),x42422),f777(f777(f11(x42421,f858(f857(x42421,x42421),a845),f858(f857(x42421,x42421),a845)),f777(f777(f12(f857(x42421,x42421),f858(f858(f857(x42421,x42421),a845),f858(f857(x42421,x42421),a845)),x42421),f304(f857(x42421,x42421))),f777(f777(f22(x42421,x42421,f857(x42421,x42421)),f243(x42421,x42421)),f9(x42421)))),f182(f858(f857(x42421,x42421),a845)))),f262(x42421,x42422)) % 174.01/173.89 [4250]E(f200(x42501,f777(f777(f243(a3,a3),f777(f83(a3),f777(f777(f77(f857(a3,a3),a3,x42501,f242(a3,a3)),f209(x42501)),x42502))),f777(f777(f77(f857(a3,a3),a3,x42501,f252(a3,a3)),f209(x42501)),x42502))),f223(x42501,x42502)) % 174.01/173.89 [4330]E(f777(f258(f858(x43301,a845)),f777(f777(f12(f858(f858(x43301,a845),a845),a845,f858(x43301,a845)),f91(f858(x43301,a845))),f777(f777(f11(f858(x43301,a845),f858(f858(x43301,a845),a845),f858(f858(x43301,a845),a845)),f777(f777(f12(f858(f858(x43301,a845),f858(a845,a845)),f858(f858(f858(x43301,a845),a845),f858(f858(x43301,a845),a845)),f858(x43301,a845)),f22(f858(x43301,a845),a845,a845)),f777(f777(f12(f858(f858(x43301,a845),a845),f858(f858(x43301,a845),f858(a845,a845)),f858(x43301,a845)),f777(f12(a845,f858(a845,a845),f858(x43301,a845)),a333)),f777(f777(f11(f858(x43301,a845),f858(f858(x43301,a845),f858(x43301,a845)),f858(f858(x43301,a845),a845)),f777(f777(f12(f858(f858(x43301,a845),a845),f858(f858(f858(x43301,a845),f858(x43301,a845)),f858(f858(x43301,a845),a845)),f858(x43301,a845)),f12(f858(x43301,a845),a845,f858(x43301,a845))),a332)),f83(f858(x43301,a845)))))),f777(f777(f12(f858(f858(x43301,a845),a845),a845,f858(x43301,a845)),f777(f336(f858(x43301,a845)),x43302)),f303(x43301))))),f777(f303(x43301),f777(f83(f858(x43301,a845)),x43302))) % 174.01/173.89 [4474]~E(f777(f777(f84(a3),x44741),x44741),f777(f777(f5(a3),f777(f777(f84(a3),x44742),x44742)),a101)) % 174.01/173.89 [4479]~P1(f777(f777(f235(a851),f777(f777(f84(a851),x44791),x44792)),x44792)) % 174.01/173.89 [4480]~P1(f777(f777(f235(a851),f777(f777(f84(a851),x44801),x44802)),x44801)) % 174.01/173.89 [3667]E(f777(f777(f5(a851),x36671),f777(f777(f85(a851),f777(f777(f45(a851),x36671),x36672)),x36672)),f54(a851,x36671,x36672)) % 174.01/173.89 [3668]E(f777(f777(f5(a3),x36681),f777(f777(f85(a3),f777(f777(f45(a3),x36681),x36682)),x36682)),f54(a3,x36681,x36682)) % 174.01/173.89 [3703]E(f777(f777(f145(a851,x37031),f777(f155(x37031),x37032)),f132(a851,f777(f296(a851,f4(a851)),f777(f183(f852(x37031)),x37032)))),x37032) % 174.01/173.89 [3764]E(f777(f279(x37641,x37641,f302(x37641,f182(f858(f857(x37641,x37641),a845)))),x37642),x37642) % 174.01/173.89 [3884]E(f302(x38841,f777(f777(f5(f858(f857(x38841,x38841),a845)),x38842),f302(x38841,f182(f858(f857(x38841,x38841),a845))))),f302(x38841,x38842)) % 174.01/173.89 [3885]E(f302(x38851,f777(f777(f105(f858(f857(x38851,x38851),a845)),x38852),f302(x38851,f182(f858(f857(x38851,x38851),a845))))),f302(x38851,x38852)) % 174.01/173.89 [3941]E(f777(f777(f5(a3),f777(f777(f5(a3),f777(f777(f84(a3),x39411),x39411)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),x39412),x39412)),a101)),f777(f777(f84(a3),f777(f777(f5(a3),x39411),x39412)),f777(f777(f5(a3),x39411),x39412))) % 174.01/173.89 [3983]E(f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f84(a3),x39831),x39832)),f777(f777(f84(a3),x39831),x39832))),a101),f777(f777(f84(a3),f777(f777(f84(a3),x39831),x39831)),f777(f777(f5(a3),f777(f777(f84(a3),x39832),x39832)),a101))) % 174.01/173.89 [4009]E(f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),x40091),x40091)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),x40092),x40092)),a101)),f777(f777(f84(a3),f777(f777(f84(a3),x40091),f777(f777(f5(a3),x40092),a101))),f777(f777(f84(a3),x40091),f777(f777(f5(a3),x40092),a101)))) % 174.01/173.89 [4020]E(f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f84(a3),x40201),x40202)),f777(f777(f84(a3),x40201),x40202))),a101),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),x40201),x40201)),a101)),f777(f777(f84(a3),x40202),x40202))) % 174.01/173.89 [4021]E(f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),x40211),x40212)),f777(f777(f5(a3),x40211),x40212))),a101),f777(f777(f5(a3),f777(f777(f5(a3),f777(f777(f84(a3),x40211),x40211)),a101)),f777(f777(f84(a3),x40212),x40212))) % 174.01/173.89 [4074]E(f777(f104(a3),f777(f777(f45(a851),f777(f777(f85(a851),f777(a109,f777(f79(a3),x40741))),f777(a109,f777(f79(a3),x40742)))),f213(f777(a109,f777(f79(a3),x40741)),f777(a109,f777(f79(a3),x40742))))),f215(x40741,x40742)) % 174.01/173.89 [4119]E(f777(f777(f255(f857(a103,a103),a103,f857(a103,a103),f857(x41191,f857(a103,a103))),f266(f777(a7,f777(f183(f852(x41191)),x41192)))),f777(f777(f12(x41191,f858(f857(a103,a103),f857(x41191,f857(a103,a103))),a103),f243(x41191,f857(a103,a103))),f777(f777(f12(a851,x41191,a103),f777(f155(x41191),x41192)),a24))),f272(x41191,x41192)) % 174.01/173.89 [4202]E(f777(f134(a851,f852(x42021),f777(f11(f852(x42021),a851,a851),f777(f777(f12(a851,f858(a851,a851),f852(x42021)),f181(a851)),f183(f852(x42021)))),f4(a851)),f777(f144(f852(x42021)),f166(x42021,x42022))),f777(f183(f852(f852(x42021))),f777(f128(f852(x42021),f777(f777(f12(a845,a845,f852(x42021)),a330),f777(f777(f11(f852(x42021),f852(x42021),a845),a332),f117(x42021)))),x42022))) % 174.01/173.89 [4208]E(f777(f777(f48(a851,f858(x42081,a845)),f241(f858(a851,a845))),f777(f777(f11(a851,f858(a851,f858(x42081,a845)),f858(x42081,a845)),f777(f777(f12(f858(a851,a845),f858(f858(a851,f858(x42081,a845)),f858(x42081,a845)),a851),f48(a851,f858(x42081,a845))),f296(a851,f4(a851)))),x42082)),f777(f777(f48(a851,f858(x42081,a845)),f241(f858(a851,a845))),x42082)) % 174.01/173.89 [4227]P1(f777(f65(a851),f777(f258(a851),f777(f777(f22(a851,a845,a845),f777(f777(f12(a845,f858(a845,a845),a851),a333),x42271)),f777(f777(f11(a851,a851,a845),f235(a851)),x42272))))) % 174.01/173.89 [4340]E(f777(f258(f857(f852(x43401),f852(x43401))),f777(f253(f852(x43401),f852(x43401),a845),f777(f777(f22(f852(x43401),f858(f852(x43401),a845),f858(f852(x43401),a845)),f777(f777(f12(f858(f852(x43401),f858(a845,a845)),f858(f858(f852(x43401),a845),f858(f852(x43401),a845)),f852(x43401)),f22(f852(x43401),a845,a845)),f777(f777(f12(f858(f852(x43401),a845),f858(f852(x43401),f858(a845,a845)),f852(x43401)),f777(f12(a845,f858(a845,a845),f852(x43401)),a334)),f777(f777(f11(f852(x43401),f858(f852(x43401),a851),f858(f852(x43401),a845)),f777(f777(f12(f858(a851,a845),f858(f858(f852(x43401),a851),f858(f852(x43401),a845)),f852(x43401)),f12(a851,a845,f852(x43401))),f777(f777(f12(a851,f858(a851,a845),f852(x43401)),f235(a851)),f183(f852(x43401))))),f183(f852(x43401)))))),f777(f777(f22(f852(x43401),f858(f852(x43401),a845),f858(f852(x43401),a845)),f777(f777(f12(f858(f852(x43401),f858(a845,a845)),f858(f858(f852(x43401),a845),f858(f852(x43401),a845)),f852(x43401)),f22(f852(x43401),a845,a845)),f777(f777(f12(f858(f852(x43401),a845),f858(f852(x43401),f858(a845,a845)),f852(x43401)),f777(f12(a845,f858(a845,a845),f852(x43401)),a333)),f777(f777(f11(f852(x43401),f858(f852(x43401),a851),f858(f852(x43401),a845)),f777(f777(f12(f858(a851,a845),f858(f858(f852(x43401),a851),f858(f852(x43401),a845)),f852(x43401)),f12(a851,a845,f852(x43401))),f777(f777(f12(a851,f858(a851,a845),f852(x43401)),a332),f183(f852(x43401))))),f183(f852(x43401)))))),f777(f777(f11(f852(x43401),f858(f857(f852(x43401),f852(x43401)),a845),f858(f852(x43401),a845)),f777(f777(f12(f858(f852(x43401),f858(f858(f857(f852(x43401),f852(x43401)),a845),a845)),f858(f858(f857(f852(x43401),f852(x43401)),a845),f858(f852(x43401),a845)),f852(x43401)),f11(f852(x43401),f858(f857(f852(x43401),f852(x43401)),a845),a845)),f777(f777(f12(f858(f852(x43401),f857(f852(x43401),f852(x43401))),f858(f852(x43401),f858(f858(f857(f852(x43401),f852(x43401)),a845),a845)),f852(x43401)),f777(f12(f857(f852(x43401),f852(x43401)),f858(f858(f857(f852(x43401),f852(x43401)),a845),a845),f852(x43401)),f336(f857(f852(x43401),f852(x43401))))),f243(f852(x43401),f852(x43401))))),f137(x43401,x43402)))))),f138(x43401,x43402)) % 174.01/173.89 [4012]E(f777(f777(f84(a3),f777(f777(f84(a3),f777(f777(f85(a3),x40121),x40122)),f777(f777(f85(a3),x40121),x40122))),x40122),f777(f777(f85(a3),f777(f777(f5(a3),f777(f777(f84(a3),x40121),x40121)),a101)),x40122)) % 174.01/173.89 [4117]E(f777(a109,f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x41171),x41172)),f182(f858(f857(a851,a851),a845)))))),f777(f777(f5(a851),x41171),x41172)) % 174.01/173.89 [4123]E(f777(f777(f283(x41231,x41231,x41231),f777(f777(f105(f858(f857(x41231,x41231),a845)),x41232),f302(x41231,f182(f858(f857(x41231,x41231),a845))))),f302(x41231,f777(f777(f105(f858(f857(x41231,x41231),a845)),x41232),f302(x41231,f182(f858(f857(x41231,x41231),a845)))))),f302(x41231,x41232)) % 174.01/173.89 [4162]E(f267(x41621,f777(f128(f857(a103,x41621),f777(f253(a103,x41621,a845),f777(f777(f12(a845,f858(x41621,a845),a103),f20(a845,x41621)),f777(f235(a103),f4(a103))))),x41622)),f267(x41621,x41622)) % 174.01/173.89 [4163]E(f265(x41631,f777(f128(f857(a103,x41631),f777(f253(a103,x41631,a845),f777(f777(f12(a845,f858(x41631,a845),a103),f20(a845,x41631)),f777(f235(a103),f4(a103))))),x41632)),f265(x41631,x41632)) % 174.01/173.89 [4165]E(f777(f83(a3),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x41651),x41652)),f182(f858(f857(a851,a851),a845)))))),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x41652),x41651)),f182(f858(f857(a851,a851),a845)))))) % 174.01/173.89 [4239]E(f777(f777(f90(a3,a851),f777(f108(a3),f777(f777(f84(a3),x42391),a101))),f777(f777(f22(a3,a851,a851),f777(f777(f11(a3,a851,f858(a851,a851)),f777(f777(f12(a845,f858(a851,f858(a851,a851)),a3),f100(a851)),a188)),f4(a851))),f777(f777(f12(a851,a851,a3),a116),f777(f777(f12(a851,a851,a3),f777(f238(a851),x42392)),a109)))),f777(f777(f238(a851),f777(a116,x42392)),f777(f108(a851),x42391))) % 174.01/173.89 [4240]E(f777(f777(f90(a3,a851),f777(f108(a3),f777(f777(f84(a3),x42401),a101))),f777(f777(f22(a3,a851,a851),f777(f777(f11(a3,a851,f858(a851,a851)),f777(f777(f12(a845,f858(a851,f858(a851,a851)),a3),f100(a851)),a188)),f777(a116,x42402))),f777(f777(f12(a851,a851,a3),a116),f777(f777(f12(a851,a851,a3),f777(f181(a851),x42402)),a109)))),f777(f777(f181(a851),f777(a116,x42402)),f777(f108(a851),x42401))) % 174.01/173.89 [4260]E(f777(f134(f852(x42601),f852(x42601),f127(x42601),f117(x42601)),f777(f777(f145(f852(x42601),f852(x42601)),f147(f852(x42601),x42601,f117(x42601),f777(f777(f12(f852(x42601),f858(f852(x42601),f852(x42601)),x42601),f20(f852(x42601),f852(x42601))),f777(f777(f11(x42601,f852(x42601),f852(x42601)),f142(x42601)),f117(x42601))))),x42602)),f777(f777(f145(f852(x42601),x42601),f133(x42601)),f777(f128(f852(x42601),f777(f777(f12(a845,a845,f852(x42601)),a330),f777(f777(f11(f852(x42601),f852(x42601),a845),a332),f117(x42601)))),x42602))) % 174.01/173.89 [4320]E(f777(f253(a3,a3,a845),f777(f777(f11(a3,f858(a3,a845),f858(a3,a845)),f777(f777(f12(f858(a3,f858(a845,a845)),f858(f858(a3,a845),f858(a3,a845)),a3),f22(a3,a845,a845)),f777(f777(f12(f858(a3,a845),f858(a3,f858(a845,a845)),a3),f777(f12(a845,f858(a845,a845),a3),a333)),f777(f777(f12(f858(a3,a3),f858(a3,a845),a3),f777(f12(a3,a845,a3),f777(a332,x43201))),f777(f777(f12(a3,f858(a3,a3),a3),f84(a3)),f777(f85(a3),x43202)))))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f777(f12(a845,a845,a3),f777(a337,f777(f777(f235(a3),f4(a3)),x43202))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f234(a3),f4(a3)))),f777(f777(f11(a3,a3,a845),f235(a3)),x43202))))),f777(f777(f12(a845,a845,a3),f777(a337,f777(a330,f777(f777(f235(a3),f4(a3)),x43202)))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f235(a3),x43202))),f777(f777(f11(a3,a3,a845),f234(a3)),f4(a3))))))),f58(x43201,x43202)) % 174.01/173.89 [4322]E(f777(f258(x43221),f777(f777(f12(f858(a851,a845),a845,x43221),f91(a851)),f777(f777(f11(x43221,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),x43221),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),x43221),f777(f12(a845,f858(a845,a845),a851),a333)),f777(f777(f11(x43221,f858(a851,x43221),f858(a851,a845)),f777(f777(f12(f858(x43221,a845),f858(f858(a851,x43221),f858(a851,a845)),x43221),f12(x43221,a845,a851)),a332)),f777(f155(x43221),x43222))))),f777(f777(f11(a851,a851,a845),f235(a851)),f777(f183(f852(x43221)),x43222))))),f777(f160(x43221),x43222)) % 174.01/173.89 [4135]E(f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),x41351),a101)),x41352)),f777(f777(f5(a3),f777(f777(f84(a3),x41351),a101)),x41352))),a101),f777(f777(f5(a3),f777(f777(f84(a3),x41351),x41351)),f777(f777(f5(a3),f777(f777(f84(a3),x41352),x41352)),a101))) % 174.01/173.89 [4255]E(f777(f134(f852(f852(x42551)),f852(f852(x42551)),f127(f852(x42551)),f117(f852(x42551))),f777(f777(f145(f852(x42551),f852(f852(x42551))),f147(f852(f852(x42551)),x42551,f117(f852(x42551)),f777(f20(f858(f852(x42551),f852(f852(x42551))),x42551),f777(f777(f11(f852(x42551),f852(f852(x42551)),f852(f852(x42551))),f142(f852(x42551))),f117(f852(x42551)))))),x42552)),f777(f777(f145(f852(x42551),f852(x42551)),f159(x42551)),f777(f128(f852(x42551),f777(f777(f12(a845,a845,f852(x42551)),a330),f777(f777(f11(f852(x42551),f852(x42551),a845),a332),f117(x42551)))),x42552))) % 174.01/173.89 [4265]E(f777(f777(f90(a3,a851),f777(f108(a3),f777(f777(f84(a3),x42651),a101))),f777(f777(f22(a3,a851,a851),f777(f777(f11(a3,a851,f858(a851,a851)),f777(f777(f12(a845,f858(a851,f858(a851,a851)),a3),f100(a851)),a188)),f4(a851))),f777(f777(f12(a851,a851,a3),a116),f777(f777(f11(a3,a851,a851),f777(f777(f12(a851,f858(a851,a851),a3),f238(a851)),a109)),x42652)))),f777(f777(f238(a851),f777(f108(a851),x42651)),f777(a116,x42652))) % 174.01/173.89 [4266]E(f777(f777(f90(a3,a851),f777(f108(a3),f777(f777(f84(a3),x42661),a101))),f777(f777(f22(a3,a851,a851),f777(f777(f11(a3,a851,f858(a851,a851)),f777(f777(f12(a845,f858(a851,f858(a851,a851)),a3),f100(a851)),a188)),f777(a116,x42662))),f777(f777(f12(a851,a851,a3),a116),f777(f777(f11(a3,a851,a851),f777(f777(f12(a851,f858(a851,a851),a3),f181(a851)),a109)),x42662)))),f777(f777(f181(a851),f777(f108(a851),x42661)),f777(a116,x42662))) % 174.01/173.89 [4254]E(f777(f253(x42541,x42541,a845),f777(f777(f22(x42541,a845,f858(x42541,a845)),f777(f777(f12(f858(x42541,f858(a845,a845)),f858(a845,f858(x42541,a845)),x42541),f11(x42541,a845,a845)),f777(f777(f12(f858(x42541,a845),f858(x42541,f858(a845,a845)),x42541),f777(f12(a845,f858(a845,a845),x42541),a333)),a332))),x42542)),f262(x42541,x42542)) % 174.01/173.89 [4298]E(f777(f777(f45(a851),x42981),f777(f777(f84(a851),f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),a101))),x42982)),f777(f777(f45(a851),x42981),f777(a116,f777(a116,f777(a116,x42982))))) % 174.01/173.89 [4299]E(f54(a851,x42991,f777(f777(f84(a851),f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),a101))),x42992)),f54(a851,x42991,f777(a116,f777(a116,f777(a116,x42992))))) % 174.01/173.89 [4300]E(f54(a851,f777(f777(f84(a851),f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),a101))),x43001),x43002),f54(a851,f777(a116,f777(a116,f777(a116,x43001))),x43002)) % 174.01/173.89 [4313]E(f124(f777(x43131,f777(f777(f85(a103),f777(f108(a103),f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),a101))),x43132))),f777(f197(x43131),x43132)) % 174.01/173.89 [4314]E(f777(f777(f45(a851),f777(f777(f84(a851),f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),a101))),x43141)),x43142),f777(f777(f45(a851),f777(a116,f777(a116,f777(a116,x43141)))),x43142)) % 174.01/173.89 [3488]P29(x34881,f859(x34882,x34881),f315(x34881,x34882),x34883) % 174.01/173.89 [3489]P29(x34891,f859(x34891,x34892),f306(x34891,x34892),x34893) % 174.01/173.89 [4382]~E(f37(x43821,x43822),f777(a29,x43823)) % 174.01/173.89 [4383]~E(f38(x43831,x43832),f777(a29,x43833)) % 174.01/173.89 [4384]~E(f30(x43841,x43842),f777(a29,x43843)) % 174.01/173.89 [4385]~E(f777(a29,x43851),f37(x43852,x43853)) % 174.01/173.89 [4386]~E(f777(a29,x43861),f38(x43862,x43863)) % 174.01/173.89 [4387]~E(f777(a29,x43871),f30(x43872,x43873)) % 174.01/173.89 [4406]~E(f35(x44061,x44062,x44063),a27) % 174.01/173.89 [4407]~E(f34(x44071,x44072,x44073),a27) % 174.01/173.89 [4408]~E(f33(x44081,x44082,x44083),a27) % 174.01/173.89 [3101]E(f777(f187(x31011,x31012),x31013),f122(x31011,x31012)) % 174.01/173.89 [3102]E(f777(f196(x31021,x31022),x31023),f125(x31021,x31022)) % 174.01/173.89 [3196]E(f777(f777(f145(x31961,x31962),x31963),f117(x31961)),f117(x31962)) % 174.01/173.89 [3197]E(f777(f777(f198(x31971,x31972),x31973),f185(x31971)),f185(x31972)) % 174.01/173.89 [3217]E(f36(f33(x32171,x32172,x32173)),f4(a851)) % 174.01/173.89 [3236]E(f777(f176(x32361,x32362,x32363),f4(a851)),x32362) % 174.01/173.89 [3237]E(f777(f183(a846),f33(x32371,x32372,x32373)),f4(a851)) % 174.01/173.89 [3238]E(f777(f777(f169(x32381,x32382),x32383),f117(x32382)),f117(f857(x32381,x32382))) % 174.01/173.89 [3275]E(f89(x32751,f66(x32751,x32752,x32753)),f777(f67(x32751,x32752),x32753)) % 174.01/173.89 [3344]E(f777(f242(f852(x33441),f852(x33441)),f158(x33441,x33442,x33443)),f777(f128(x33441,x33442),x33443)) % 174.01/173.89 [3422]E(f177(x34221,x34222,x34223,f4(a851)),x34222) % 174.01/173.89 [3423]E(f21(x34231,x34232,x34233,f4(a103)),x34232) % 174.01/173.89 [3424]E(f23(x34241,x34242,x34243,f4(a103)),x34242) % 174.01/173.89 [3431]E(f156(x34311,x34312,x34313,f117(x34311)),f117(x34312)) % 174.01/173.89 [3438]E(f777(f777(f155(x34381),f777(f777(f142(x34381),x34382),x34383)),f4(a851)),x34382) % 174.01/173.89 [3487]P29(x34871,x34872,x34873,f182(f858(x34871,a845))) % 174.01/173.89 [3583]E(f264(x35831,x35832,x35833),f777(f243(f858(a103,f858(a845,f855(f853(x35831)))),f857(a103,a103)),f50(x35831))) % 174.01/173.89 [3642]E(f777(f77(x36421,x36422,x36421,x36423),f41(x36421)),x36423) % 174.01/173.89 [3818]P1(f777(f777(f336(f857(x38181,x38181)),f777(f777(f243(x38181,x38181),x38182),x38182)),f302(x38181,x38183))) % 174.01/173.89 [4483]~P1(f777(f777(f336(f857(f852(x44831),f852(x44831))),f777(f777(f243(f852(x44831),f852(x44831)),x44832),f117(x44831))),f137(x44831,x44833))) % 174.01/173.89 [4484]~P1(f777(f777(f336(f857(f852(x44841),f852(x44841))),f777(f777(f243(f852(x44841),f852(x44841)),x44842),f117(x44841))),f139(x44841,x44843))) % 174.01/173.89 [4485]~P1(f777(f777(f336(f857(f852(x44851),f852(x44851))),f777(f777(f243(f852(x44851),f852(x44851)),x44852),f117(x44851))),f148(x44851,x44853))) % 174.01/173.89 [4486]~P1(f777(f777(f336(f857(f852(x44861),f852(x44861))),f777(f777(f243(f852(x44861),f852(x44861)),f117(x44861)),x44862)),f137(x44861,x44863))) % 174.01/173.89 [4487]~P1(f777(f777(f336(f857(f852(x44871),f852(x44871))),f777(f777(f243(f852(x44871),f852(x44871)),f117(x44871)),x44872)),f148(x44871,x44873))) % 174.01/173.89 [3171]E(f777(f777(f199(x31711),x31712),x31713),f200(x31711,f212(x31712,x31713))) % 174.01/173.89 [3226]E(f777(f280(x32261,x32262),f777(f280(x32262,x32261),x32263)),x32263) % 174.01/173.89 [3243]E(f314(x32431,x32432,f777(f306(x32431,x32432),x32433)),x32433) % 174.01/173.89 [3244]E(f317(x32441,x32442,f777(f315(x32442,x32441),x32443)),x32443) % 174.01/173.89 [3250]E(f777(f777(f169(x32501,x32502),f117(x32501)),x32503),f117(f857(x32501,x32502))) % 174.01/173.89 [3253]E(f162(x32531,x32532,f777(f259(a851),x32533)),f777(f777(f161(x32531),x32533),x32532)) % 174.01/173.89 [3267]E(f777(f183(f859(x32671,x32672)),f777(f306(x32671,x32672),x32673)),f4(a851)) % 174.01/173.89 [3268]E(f777(f183(f859(x32681,x32682)),f777(f315(x32682,x32681),x32683)),f4(a851)) % 174.01/173.89 [3273]E(f777(f261(x32731,x32732),f777(f280(x32732,x32731),x32733)),f777(f263(x32732,x32731),x32733)) % 174.01/173.89 [3274]E(f777(f263(x32741,x32742),f777(f280(x32742,x32741),x32743)),f777(f261(x32742,x32741),x32743)) % 174.01/173.89 [3289]E(f777(f128(x32891,x32892),f777(f144(x32891),x32893)),f777(f144(x32891),f777(f128(x32891,x32892),x32893))) % 174.01/173.89 [3302]E(f777(f777(f130(x33021),x33022),f777(f159(x33021),x33023)),f777(f777(f130(x33021),f777(a116,x33022)),x33023)) % 174.01/173.89 [3320]E(f36(f34(x33201,x33202,x33203)),f777(f777(f84(a851),f36(x33203)),f777(a116,f4(a851)))) % 174.01/173.89 [3321]E(f777(f305(x33211,x33212,x33213),f182(f858(x33211,a845))),f182(f858(x33212,a845))) % 174.01/173.89 [3322]E(f777(f279(x33221,x33222,x33223),f182(f858(x33221,a845))),f182(f858(x33222,a845))) % 174.01/173.89 [3323]E(f777(f307(x33231,x33232,x33233),f241(f858(x33232,a845))),f241(f858(x33231,a845))) % 174.01/173.89 [3324]E(f777(f307(x33241,x33242,x33243),f182(f858(x33242,a845))),f182(f858(x33241,a845))) % 174.01/173.89 [3361]E(f230(x33611,x33612,f777(f229(x33611),x33613)),f777(f777(f84(a851),f777(x33612,x33613)),f777(a116,f4(a851)))) % 174.01/173.89 [3443]E(f777(f183(a846),f34(x34431,x34432,x34433)),f777(f777(f84(a851),f777(f183(a846),x34433)),f777(a116,f4(a851)))) % 174.01/173.89 [3444]E(f777(f305(f857(x34441,x34442),x34442,f252(x34441,x34442)),x34443),f777(f261(x34441,x34442),x34443)) % 174.01/173.89 [3445]E(f777(f305(f857(x34451,x34452),x34451,f242(x34451,x34452)),x34453),f777(f263(x34451,x34452),x34453)) % 174.01/173.89 [3514]E(f777(f777(f243(x35141,x35142),f777(f242(x35141,x35142),x35143)),f777(f252(x35141,x35142),x35143)),x35143) % 174.01/173.89 [3521]E(f777(f777(f253(x35211,x35212,x35211),f20(x35211,x35212)),x35213),f777(f242(x35211,x35212),x35213)) % 174.01/173.89 [3540]E(f172(x35401,x35402,x35403,f777(f20(f855(x35402),x35401),f185(x35402))),x35403) % 174.01/173.89 [3541]E(f172(x35411,x35412,f777(f20(f855(x35412),x35411),f185(x35412)),x35413),x35413) % 174.01/173.89 [3596]E(f36(f35(x35961,x35962,x35963)),f777(f777(f84(a851),f777(f777(f84(a851),f36(x35962)),f36(x35963))),f777(a116,f4(a851)))) % 174.01/173.89 [3646]E(f777(f77(x36461,x36461,x36462,f41(x36461)),x36463),x36463) % 174.01/173.89 [3732]P1(f777(f65(x37321),f171(x37321,x37322,f168(x37321,x37322,x37323)))) % 174.01/173.89 [3755]P1(f777(f777(f189(f30(x37551,x37552)),x37553),f777(f777(f777(a191,x37553),x37551),f777(x37552,x37553)))) % 174.01/173.89 [3757]E(f777(f183(a846),f35(x37571,x37572,x37573)),f777(f777(f84(a851),f777(f777(f84(a851),f777(f183(a846),x37572)),f777(f183(a846),x37573))),f777(a116,f4(a851)))) % 174.01/173.89 [3828]P1(f777(f777(f234(f858(x38281,a845)),f777(f160(x38281),f777(f128(x38281,x38282),x38283))),f777(f160(x38281),x38283))) % 174.01/173.89 [3871]P1(f777(f777(f234(f858(x38711,a845)),f777(f160(x38711),f777(f777(f161(x38711),x38712),x38713))),f777(f160(x38711),x38713))) % 174.01/173.89 [3872]P1(f777(f777(f234(f858(x38721,a845)),f777(f160(x38721),f777(f777(f130(x38721),x38722),x38723))),f777(f160(x38721),x38723))) % 174.01/173.89 [3876]P1(f777(f777(f234(f858(x38761,a845)),f777(f160(x38761),f153(x38761,x38762,x38763))),f777(f160(x38761),x38763))) % 174.01/173.89 [3877]P1(f777(f777(f234(f858(x38771,a845)),f777(f160(x38771),f162(x38771,x38772,x38773))),f777(f160(x38771),x38772))) % 174.01/173.89 [3901]P29(f857(x39011,x39012),f857(x39012,x39011),f777(f253(x39011,x39012,f857(x39012,x39011)),f777(f11(x39012,x39011,f857(x39012,x39011)),f243(x39012,x39011))),x39013) % 174.01/173.89 [3913]E(f777(f777(f777(f175(f852(x39131),f852(x39131)),f54(a851,x39132,f777(f183(f852(x39131)),x39133))),f143(x39131)),x39133),f777(f777(f777(f175(f852(x39131),f852(x39131)),x39132),f143(x39131)),x39133)) % 174.01/173.89 [3958]P1(f777(f777(f336(f857(f852(x39581),f852(x39581))),f777(f777(f243(f852(x39581),f852(x39581)),x39582),x39582)),f149(x39581,f302(x39581,x39583)))) % 174.01/173.89 [4102]E(f89(f857(x41021,x41022),f777(f777(f22(f857(x41021,x41022),x41022,a845),f777(f777(f12(x41021,f858(x41022,a845),f857(x41021,x41022)),x41023),f242(x41021,x41022))),f252(x41021,x41022))),f89(f857(x41021,x41022),f777(f253(x41021,x41022,a845),x41023))) % 174.01/173.89 [4103]E(f94(f857(x41031,x41032),f777(f777(f22(f857(x41031,x41032),x41032,a845),f777(f777(f12(x41031,f858(x41032,a845),f857(x41031,x41032)),x41033),f242(x41031,x41032))),f252(x41031,x41032))),f94(f857(x41031,x41032),f777(f253(x41031,x41032,a845),x41033))) % 174.01/173.89 [4142]E(f777(f777(f282(f857(a851,x41421),x41421),f327(a851,x41421,a239,x41422)),f777(f777(f22(x41421,x41421,f857(a851,x41421)),f777(f777(f12(a851,f858(x41421,f857(a851,x41421)),x41421),f243(a851,x41421)),x41423)),f9(x41421))),f329(x41421,x41423,x41422)) % 174.01/173.89 [4204]E(f777(f254(x42041,x42041,x42042,x42042,f9(x42041),f9(x42042)),x42043),x42043) % 174.01/173.89 [4339]E(f777(f777(f90(a3,x43391),f215(f777(f777(f77(f857(a3,a3),a3,x43391,f252(a3,a3)),f209(x43391)),x43392),f777(f777(f77(f857(a3,a3),a3,x43391,f252(a3,a3)),f209(x43391)),x43393))),f777(f777(f22(a3,a3,x43391),f777(f777(f12(a3,f858(a3,x43391),a3),f199(x43391)),f777(f777(f22(a3,a3,a3),f777(f777(f12(a3,f858(a3,a3),a3),f84(a3)),f777(f777(f12(a3,a3,a3),f777(f85(a3),f777(f777(f77(f857(a3,a3),a3,x43391,f242(a3,a3)),f209(x43391)),x43392))),f777(f777(f11(a3,a3,a3),f45(a3)),f777(f777(f77(f857(a3,a3),a3,x43391,f252(a3,a3)),f209(x43391)),x43392))))),f777(f777(f12(a3,a3,a3),f777(f85(a3),f777(f777(f77(f857(a3,a3),a3,x43391,f242(a3,a3)),f209(x43391)),x43393))),f777(f777(f11(a3,a3,a3),f45(a3)),f777(f777(f77(f857(a3,a3),a3,x43391,f252(a3,a3)),f209(x43391)),x43393)))))),f9(a3))),f226(x43391,x43392,x43393)) % 174.01/173.89 [4401]~E(f777(f777(f142(x44011),x44012),x44013),x44013) % 174.01/173.89 [4410]~E(f777(f777(f142(x44101),x44102),x44103),f117(x44101)) % 174.01/173.89 [4436]~E(f777(f777(f304(x44361),x44362),x44363),f182(f858(x44361,a845))) % 174.01/173.89 [4465]~E(f777(f305(x44651,f858(x44651,a845),x44652),x44653),f777(f303(x44651),x44653)) % 174.01/173.89 [3230]E(f777(f777(f150(x32301,f117(x32301)),x32302),x32303),f117(x32301)) % 174.01/173.89 [3231]E(f777(f133(x32311),f777(f777(f142(x32311),x32312),x32313)),x32312) % 174.01/173.89 [3232]E(f777(f159(x32321),f777(f777(f142(x32321),x32322),x32323)),x32323) % 174.01/173.89 [3278]E(f777(f777(f130(x32781),f82(a851)),f777(f777(f142(x32781),x32782),x32783)),x32783) % 174.01/173.89 [3309]E(f118(x33091,f777(f777(f130(x33091),x33092),x33093)),f777(f777(f130(x33091),x33092),f118(x33091,x33093))) % 174.01/173.89 [3311]E(f777(f777(f150(x33111,x33112),x33113),f777(f777(f155(x33111),x33112),x33113)),x33112) % 174.01/173.89 [3334]E(f777(f777(f304(x33341),x33342),f777(f777(f304(x33341),x33342),x33343)),f777(f777(f304(x33341),x33342),x33343)) % 174.01/173.89 [3347]E(f777(f777(f304(x33471),x33472),f777(f160(x33471),x33473)),f777(f160(x33471),f777(f777(f142(x33471),x33472),x33473))) % 174.01/173.89 [3349]E(f777(f777(f130(x33491),x33492),f777(f159(x33491),x33493)),f777(f159(x33491),f777(f777(f130(x33491),x33492),x33493))) % 174.01/173.89 [3358]E(f777(f777(f161(x33581),f82(a851)),f777(f777(f142(x33581),x33582),x33583)),f777(f777(f142(x33581),x33582),f117(x33581))) % 174.01/173.89 [3391]E(f777(f168(x33911,x33912,f117(f857(x33911,x33912))),x33913),f185(x33912)) % 174.01/173.89 [3407]E(f777(f67(x34071,x34072),f777(f777(f304(x34071),x34073),f182(f858(x34071,a845)))),x34073) % 174.01/173.89 [3451]E(f777(f777(f84(a851),x34511),f777(f777(f84(a851),x34512),x34513)),f777(f777(f84(a851),x34512),f777(f777(f84(a851),x34511),x34513))) % 174.01/173.89 [3452]E(f777(f777(f84(a3),x34521),f777(f777(f84(a3),x34522),x34523)),f777(f777(f84(a3),x34522),f777(f777(f84(a3),x34521),x34523))) % 174.01/173.89 [3457]E(f777(f777(f250(x34571,x34572),f182(f858(x34571,a845))),x34573),f182(f858(f857(x34571,x34572),a845))) % 174.01/173.89 [3479]E(f777(f777(f105(f858(x34791,a845)),x34792),x34793),f777(f777(f105(f858(x34791,a845)),x34793),x34792)) % 174.01/173.89 [3480]E(f777(f777(f106(f858(x34801,a845)),x34802),x34803),f777(f777(f106(f858(x34801,a845)),x34803),x34802)) % 174.01/173.89 [3482]E(f777(f777(f127(x34821),x34822),f777(f777(f142(x34821),x34823),f117(x34821))),f777(f143(x34821),f777(f777(f142(x34821),x34823),x34822))) % 174.01/173.89 [3483]E(f777(f777(f127(x34831),f777(f144(x34831),x34832)),f777(f144(x34831),x34833)),f777(f144(x34831),f777(f777(f127(x34831),x34833),x34832))) % 174.01/173.89 [3493]E(f777(f159(x34931),f777(f777(f161(x34931),f777(a116,x34932)),x34933)),f777(f777(f161(x34931),x34932),f777(f159(x34931),x34933))) % 174.01/173.89 [3500]P1(f777(f777(f336(x35001),x35002),f777(f777(f304(x35001),x35002),x35003))) % 174.01/173.89 [3504]E(f777(f777(f49(x35041,f858(x35042,a845)),f182(f858(x35041,a845))),x35043),f241(f858(x35042,a845))) % 174.01/173.89 [3507]E(f777(f279(x35071,x35071,f262(x35071,x35072)),x35073),f777(f777(f106(f858(x35071,a845)),x35072),x35073)) % 174.01/173.89 [3519]E(f777(f183(f852(x35191)),f777(f777(f142(x35191),x35192),x35193)),f777(f777(f84(a851),f777(f183(f852(x35191)),x35193)),f777(a116,f4(a851)))) % 174.01/173.89 [3523]E(f136(x35231,f777(f777(f127(x35231),x35232),f777(f777(f142(x35231),x35233),f117(x35231)))),x35233) % 174.01/173.89 [3524]E(f118(x35241,f777(f777(f127(x35241),x35242),f777(f777(f142(x35241),x35243),f117(x35241)))),x35242) % 174.01/173.89 [3529]E(f777(f777(f127(x35291),f777(f777(f161(x35291),x35292),x35293)),f777(f777(f130(x35291),x35292),x35293)),x35293) % 174.01/173.89 [3538]E(f777(f777(f5(a851),f777(f777(f84(a851),x35381),x35382)),f777(f777(f84(a851),x35383),x35382)),f777(f777(f5(a851),x35381),x35383)) % 174.01/173.89 [3539]E(f777(f777(f5(a851),f777(f777(f84(a851),x35391),x35392)),f777(f777(f84(a851),x35391),x35393)),f777(f777(f5(a851),x35392),x35393)) % 174.01/173.89 [3545]E(f777(f777(f127(x35451),f777(f144(x35451),x35452)),f777(f777(f142(x35451),x35453),f117(x35451))),f777(f144(x35451),f777(f777(f142(x35451),x35453),x35452))) % 174.01/173.89 [3547]E(f777(f777(f84(a851),f777(f183(f852(x35471)),x35472)),f777(f183(f852(x35471)),x35473)),f777(f183(f852(x35471)),f777(f777(f127(x35471),x35472),x35473))) % 174.01/173.89 [3557]E(f777(f777(f105(f858(x35571,a845)),f777(f160(x35571),x35572)),f777(f160(x35571),x35573)),f777(f160(x35571),f777(f777(f127(x35571),x35572),x35573))) % 174.01/173.89 [3558]E(f54(a851,f777(f777(f85(a851),x35581),x35582),f777(f777(f85(a851),x35581),x35583)),f777(f777(f85(a851),x35581),f54(a851,x35582,x35583))) % 174.01/173.89 [3571]E(f777(f777(f161(x35711),f777(f777(f5(a851),x35712),f82(a851))),f777(f159(x35711),x35713)),f777(f159(x35711),f777(f777(f161(x35711),x35712),x35713))) % 174.01/173.89 [3576]E(f777(f777(f106(f858(x35761,a845)),x35762),f777(f83(f858(x35761,a845)),x35763)),f777(f777(f5(f858(x35761,a845)),x35762),x35763)) % 174.01/173.89 [3577]E(f777(f777(f5(f858(x35771,a845)),x35772),f777(f83(f858(x35771,a845)),x35773)),f777(f777(f106(f858(x35771,a845)),x35772),x35773)) % 174.01/173.89 [3599]E(f777(f777(f250(x35991,x35992),x35993),f777(f20(f858(x35992,a845),x35991),f182(f858(x35992,a845)))),f182(f858(f857(x35991,x35992),a845))) % 174.01/173.89 [3601]E(f777(f777(f84(a851),f777(f777(f85(a851),x36011),x36012)),f777(f777(f85(a851),x36011),x36013)),f777(f777(f85(a851),x36011),f777(f777(f84(a851),x36012),x36013))) % 174.01/173.89 [3602]E(f777(f777(f5(a851),f777(f777(f85(a851),x36021),x36022)),f777(f777(f85(a851),x36021),x36023)),f777(f777(f85(a851),x36021),f777(f777(f5(a851),x36022),x36023))) % 174.01/173.89 [3603]E(f777(f777(f84(a3),f777(f777(f85(a3),x36031),x36032)),f777(f777(f85(a3),x36031),x36033)),f777(f777(f85(a3),x36031),f777(f777(f84(a3),x36032),x36033))) % 174.01/173.89 [3604]E(f777(f777(f5(a3),f777(f777(f85(a3),x36041),x36042)),f777(f777(f85(a3),x36041),x36043)),f777(f777(f85(a3),x36041),f777(f777(f5(a3),x36042),x36043))) % 174.01/173.89 [3605]E(f777(f777(f85(a3),f777(f777(f244(a3),x36051),x36052)),f777(f777(f244(a3),x36051),x36053)),f777(f777(f244(a3),x36051),f777(f777(f84(a851),x36052),x36053))) % 174.01/173.89 [3618]E(f777(f777(f48(x36181,f858(x36182,a845)),x36183),f777(f20(f858(x36182,a845),x36181),f182(f858(x36182,a845)))),f182(f858(x36182,a845))) % 174.01/173.89 [3620]E(f54(a851,f777(f777(f85(a851),x36201),x36202),f777(f777(f85(a851),x36203),x36202)),f777(f777(f85(a851),f54(a851,x36201,x36203)),x36202)) % 174.01/173.89 [3625]E(f54(a3,f777(f777(f85(a3),x36251),f54(a3,x36252,x36253)),x36253),f54(a3,f777(f777(f85(a3),x36251),x36252),x36253)) % 174.01/173.89 [3626]E(f54(a3,f777(f777(f5(a3),x36261),f54(a3,x36262,x36263)),x36263),f54(a3,f777(f777(f5(a3),x36261),x36262),x36263)) % 174.01/173.89 [3627]P1(f777(f777(f234(f858(x36271,a845)),x36272),f777(f777(f304(x36271),x36273),x36272))) % 174.01/173.89 [3651]E(f777(f305(f857(x36511,x36512),x36511,f242(x36511,x36512)),f777(f160(f857(x36511,x36512)),x36513)),f171(x36511,x36512,f168(x36511,x36512,x36513))) % 174.01/173.89 [3708]E(f777(f777(f49(f858(x37081,a845),f858(x37081,a845)),x37082),f777(f105(f858(x37081,a845)),x37083)),f777(f777(f105(f858(x37081,a845)),x37083),f47(f858(x37081,a845),x37082))) % 174.01/173.89 [3709]E(f777(f777(f48(f858(x37091,a845),f858(x37091,a845)),x37092),f777(f106(f858(x37091,a845)),x37093)),f777(f777(f106(f858(x37091,a845)),x37093),f46(f858(x37091,a845),x37092))) % 174.01/173.89 [3719]E(f777(f160(x37191),f777(f777(f777(f175(f852(x37191),f852(x37191)),x37192),f143(x37191)),x37193)),f777(f160(x37191),x37193)) % 174.01/173.89 [3723]E(f777(f777(f161(x37231),f777(f183(f852(x37231)),f164(x37231,x37232,x37233))),x37233),f164(x37231,x37232,x37233)) % 174.01/173.89 [3724]E(f171(x37241,x37242,f777(f777(f12(x37242,f855(x37242),x37241),f229(x37242)),x37243)),f241(f858(x37241,a845))) % 174.01/173.89 [3727]E(f777(f183(f852(x37271)),f777(f777(f777(f175(f852(x37271),f852(x37271)),x37272),f143(x37271)),x37273)),f777(f183(f852(x37271)),x37273)) % 174.01/173.89 [3730]E(f777(f777(f253(x37301,x37302,x37302),f777(f20(f858(x37302,x37302),x37301),f9(x37302))),x37303),f777(f252(x37301,x37302),x37303)) % 174.01/173.89 [3737]E(f54(a3,f777(f777(f5(a3),f54(a3,x37371,x37372)),x37373),x37372),f54(a3,f777(f777(f5(a3),x37371),x37373),x37372)) % 174.01/173.89 [3738]E(f54(a3,f777(f777(f244(a3),f54(a3,x37381,x37382)),x37383),x37382),f54(a3,f777(f777(f244(a3),x37381),x37383),x37382)) % 174.01/173.89 [3741]E(f777(f777(f48(f858(f857(x37411,x37412),a845),f858(x37412,a845)),x37413),f261(x37411,x37412)),f777(f261(x37411,x37412),f46(f858(f857(x37411,x37412),a845),x37413))) % 174.01/173.89 [3742]E(f777(f777(f48(f858(f857(x37421,x37422),a845),f858(x37421,a845)),x37423),f263(x37421,x37422)),f777(f263(x37421,x37422),f46(f858(f857(x37421,x37422),a845),x37423))) % 174.01/173.89 [3770]E(f777(f77(x37701,x37701,x37701,x37702),f777(f777(f175(x37701,x37701),x37703),x37702)),f777(f777(f175(x37701,x37701),f777(a116,x37703)),x37702)) % 174.01/173.89 [3780]E(f231(f855(x37801),x37802,f185(x37801),f777(f777(f12(x37801,f855(x37801),x37802),f229(x37801)),x37803)),f777(f198(x37802,x37801),x37803)) % 174.01/173.89 [3787]E(f777(f777(f130(x37871),f777(f777(f5(a851),f777(f183(f852(x37871)),x37872)),x37873)),f777(f144(x37871),x37872)),f777(f144(x37871),f777(f777(f161(x37871),x37873),x37872))) % 174.01/173.89 [3788]E(f777(f777(f161(x37881),f777(f777(f5(a851),f777(f183(f852(x37881)),x37882)),x37883)),f777(f144(x37881),x37882)),f777(f144(x37881),f777(f777(f130(x37881),x37883),x37882))) % 174.01/173.89 [3791]E(f777(f777(f84(a851),f777(f157(a851),f777(f777(f145(x37911,a851),x37912),x37913))),f777(f183(f852(x37911)),x37913)),f146(x37911,x37912,x37913)) % 174.01/173.89 [3807]E(f777(f143(x38071),f777(f777(f777(f175(f852(x38071),f852(x38071)),x38072),f143(x38071)),x38073)),f777(f777(f777(f175(f852(x38071),f852(x38071)),f777(a116,x38072)),f143(x38071)),x38073)) % 174.01/173.89 [3819]P1(f777(f777(f234(a851),f777(f183(f852(x38191)),f777(f128(x38191,x38192),x38193))),f777(f183(f852(x38191)),x38193))) % 174.01/173.89 [3836]E(f777(f777(f105(f858(f858(x38361,a845),a845)),f777(f303(x38361),x38362)),f777(f305(f858(x38361,a845),f858(x38361,a845),f777(f304(x38361),x38363)),f777(f303(x38361),x38362))),f777(f303(x38361),f777(f777(f304(x38361),x38363),x38362))) % 174.01/173.89 [3852]P28(x38521,x38522,f777(f777(f304(f850(x38521)),f777(f777(f777(f95(x38521),x38523),a27),x38523)),f182(f858(f850(x38521),a845)))) % 174.01/173.89 [3868]P1(f777(f777(f234(a851),f777(f183(f852(x38681)),f164(x38681,x38682,x38683))),f777(f183(f852(x38681)),x38683))) % 174.01/173.89 [3875]E(f777(f263(x38751,x38752),f777(f258(f857(x38751,x38752)),f777(f253(x38751,x38752,a845),x38753))),f777(f258(x38751),f777(f777(f12(f858(x38752,a845),a845,x38751),f91(x38752)),x38753))) % 174.01/173.89 [3888]E(f777(f305(a851,a851,f777(f777(f11(a851,a851,a851),f84(a851)),x38881)),f297(a851,x38882,x38883)),f297(a851,f777(f777(f84(a851),x38882),x38881),f777(f777(f84(a851),x38883),x38881))) % 174.01/173.89 [3904]E(f777(f305(a851,a851,f777(f777(f11(a851,a851,a851),f84(a851)),x39041)),f777(f296(a851,x39042),x39043)),f777(f296(a851,f777(f777(f84(a851),x39042),x39041)),f777(f777(f84(a851),x39043),x39041))) % 174.01/173.89 [3922]E(f777(f777(f169(x39221,x39222),f777(f777(f145(f857(x39221,x39222),x39221),f242(x39221,x39222)),x39223)),f777(f777(f145(f857(x39221,x39222),x39222),f252(x39221,x39222)),x39223)),x39223) % 174.01/173.89 [3927]E(f777(f777(f84(a851),f777(f777(f85(a851),x39271),f54(a851,f777(f777(f45(a851),x39272),x39271),x39273))),f54(a851,x39272,x39271)),f54(a851,x39272,f777(f777(f85(a851),x39271),x39273))) % 174.01/173.89 [3938]P1(f777(f65(f855(x39381)),f777(f305(x39382,f855(x39381),f168(x39382,x39381,x39383)),f241(f858(x39382,a845))))) % 174.01/173.89 [3942]E(f777(f777(f127(x39421),x39422),f777(f134(f852(x39421),f852(x39421),f127(x39421),f117(x39421)),x39423)),f777(f134(f852(x39421),f852(x39421),f127(x39421),x39422),x39423)) % 174.01/173.89 [3962]P1(f777(f777(f336(f857(x39621,x39621)),f777(f777(f243(x39621,x39621),x39622),x39622)),f777(f777(f175(f857(x39621,x39621),a845),f4(a851)),x39623))) % 174.01/173.89 [3968]E(f777(f258(x39681),f777(f777(f12(f858(x39682,a845),a845,x39681),f91(x39682)),f777(f11(x39682,x39681,a845),x39683))),f777(f261(x39682,x39681),f777(f258(f857(x39682,x39681)),f777(f253(x39682,x39681,a845),x39683)))) % 174.01/173.89 [3987]E(f777(f777(f105(f858(x39871,a845)),f777(f777(f48(a851,f858(x39871,a845)),f297(a851,f82(a851),x39872)),x39873)),f777(x39873,f4(a851))),f777(f777(f48(a851,f858(x39871,a845)),f777(f295(a851),x39872)),x39873)) % 174.01/173.89 [4002]E(f777(f134(f852(x40021),f852(x40021),f127(x40021),f117(x40021)),f777(f777(f145(f852(x40021),f852(x40021)),f128(x40021,x40022)),x40023)),f777(f128(x40021,x40022),f777(f134(f852(x40021),f852(x40021),f127(x40021),f117(x40021)),x40023))) % 174.01/173.89 [4007]E(f777(f252(f852(x40071),f852(x40071)),f158(x40071,x40072,x40073)),f777(f128(x40071,f777(f77(a845,a845,x40071,a330),x40072)),x40073)) % 174.01/173.89 [4056]E(f777(f777(f84(a3),f777(f777(f84(a3),f777(f777(f85(a3),x40561),f777(f777(f45(a3),x40562),x40561))),f54(a3,x40562,x40561))),x40563),f777(f777(f84(a3),x40562),x40563)) % 174.01/173.89 [4090]E(f777(f777(f84(a3),f777(f777(f84(a3),f777(f777(f85(a3),f777(f777(f45(a3),x40901),x40902)),x40902)),f54(a3,x40901,x40902))),x40903),f777(f777(f84(a3),x40901),x40903)) % 174.01/173.89 [4120]E(f89(f857(x41201,x41202),f777(f253(x41201,x41202,a845),f777(f777(f12(f858(x41202,f857(x41201,x41202)),f858(x41202,a845),x41201),f777(f12(f857(x41201,x41202),a845,x41202),x41203)),f243(x41201,x41202)))),f89(f857(x41201,x41202),x41203)) % 174.01/173.89 [4121]E(f94(f857(x41211,x41212),f777(f253(x41211,x41212,a845),f777(f777(f12(f858(x41212,f857(x41211,x41212)),f858(x41212,a845),x41211),f777(f12(f857(x41211,x41212),a845,x41212),x41213)),f243(x41211,x41212)))),f94(f857(x41211,x41212),x41213)) % 174.01/173.89 [4153]P1(f777(f777(f234(f858(x41531,a845)),f46(f858(x41531,a845),f777(f777(f106(f858(f858(x41531,a845),a845)),x41532),x41533))),f777(f777(f106(f858(x41531,a845)),f46(f858(x41531,a845),x41532)),f46(f858(x41531,a845),x41533)))) % 174.01/173.89 [4154]E(f777(f144(x41541),f777(f777(f777(f175(f852(x41541),f852(x41541)),f777(f777(f5(a851),f777(f183(f852(x41541)),x41542)),f54(a851,x41543,f777(f183(f852(x41541)),x41542)))),f143(x41541)),x41542)),f777(f777(f777(f175(f852(x41541),f852(x41541)),x41543),f143(x41541)),f777(f144(x41541),x41542))) % 174.01/173.89 [4166]E(f777(f258(x41661),f777(f777(f12(a845,a845,x41661),a330),f777(f777(f11(x41661,f855(x41662),a845),f777(f777(f12(f855(x41662),f858(f855(x41662),a845),x41661),a332),x41663)),f185(x41662)))),f171(x41661,x41662,x41663)) % 174.01/173.89 [4229]E(f777(f258(x42291),f777(f777(f12(f858(x42292,a845),a845,x42291),f91(x42292)),f777(f777(f12(f855(x42291),f858(x42292,a845),x42291),f777(f11(x42292,f855(x42291),a845),f777(f777(f12(f855(x42291),f858(f855(x42291),a845),x42292),a332),x42293))),f229(x42291)))),f173(x42292,x42291,x42293)) % 174.01/173.89 [4478]~P1(f777(f66(x44781,x44782,f182(f858(x44781,a845))),x44783)) % 174.01/173.89 [3494]E(f777(f183(f852(x34941)),f777(f777(f161(x34941),x34942),x34943)),f777(f777(f238(a851),f777(f183(f852(x34941)),x34943)),x34942)) % 174.01/173.89 [3495]E(f777(f183(f852(x34951)),f777(f777(f130(x34951),x34952),x34953)),f777(f777(f5(a851),f777(f183(f852(x34951)),x34953)),x34952)) % 174.01/173.89 [3531]E(f777(f777(f45(a851),f777(f777(f45(a851),x35311),x35312)),x35313),f777(f777(f45(a851),x35311),f777(f777(f85(a851),x35312),x35313))) % 174.01/173.89 [3532]E(f777(f777(f84(a851),f777(f777(f84(a851),x35321),x35322)),x35323),f777(f777(f84(a851),x35321),f777(f777(f84(a851),x35322),x35323))) % 174.01/173.89 [3533]E(f777(f777(f84(a3),f777(f777(f84(a3),x35331),x35332)),x35333),f777(f777(f84(a3),x35331),f777(f777(f84(a3),x35332),x35333))) % 174.01/173.89 [3534]E(f777(f777(f85(a851),f777(f777(f85(a851),x35341),x35342)),x35343),f777(f777(f85(a851),x35341),f777(f777(f85(a851),x35342),x35343))) % 174.01/173.89 [3535]E(f777(f777(f85(a3),f777(f777(f85(a3),x35351),x35352)),x35353),f777(f777(f85(a3),x35351),f777(f777(f85(a3),x35352),x35353))) % 174.01/173.89 [3536]E(f777(f777(f5(a851),f777(f777(f5(a851),x35361),x35362)),x35363),f777(f777(f5(a851),x35361),f777(f777(f84(a851),x35362),x35363))) % 174.01/173.89 [3537]E(f777(f777(f244(a3),f777(f777(f244(a3),x35371),x35372)),x35373),f777(f777(f244(a3),x35371),f777(f777(f85(a851),x35372),x35373))) % 174.01/173.89 [3555]E(f152(x35551,f777(f777(f142(f858(x35551,a845)),x35552),x35553)),f163(x35551,x35552,f152(x35551,x35553))) % 174.01/173.89 [3600]E(f777(f777(f5(a851),f777(f777(f5(a851),x36001),x36002)),x36003),f777(f777(f5(a851),f777(f777(f5(a851),x36001),x36003)),x36002)) % 174.01/173.89 [3608]E(f777(f777(f106(f858(x36081,a845)),x36082),f777(f777(f5(f858(x36081,a845)),x36083),x36082)),f182(f858(x36081,a845))) % 174.01/173.89 [3653]E(f47(f858(x36531,a845),f777(f777(f304(f858(x36531,a845)),x36532),x36533)),f777(f777(f106(f858(x36531,a845)),x36532),f47(f858(x36531,a845),x36533))) % 174.01/173.89 [3654]E(f46(f858(x36541,a845),f777(f777(f304(f858(x36541,a845)),x36542),x36543)),f777(f777(f105(f858(x36541,a845)),x36542),f46(f858(x36541,a845),x36543))) % 174.01/173.89 [3656]E(f777(f777(f84(a851),f777(f777(f85(a851),x36561),x36562)),f777(f777(f85(a851),x36563),x36562)),f777(f777(f85(a851),f777(f777(f84(a851),x36561),x36563)),x36562)) % 174.01/173.89 [3657]E(f777(f777(f5(a851),f777(f777(f85(a851),x36571),x36572)),f777(f777(f85(a851),x36573),x36572)),f777(f777(f85(a851),f777(f777(f5(a851),x36571),x36573)),x36572)) % 174.01/173.89 [3658]E(f777(f777(f84(a3),f777(f777(f85(a3),x36581),x36582)),f777(f777(f85(a3),x36583),x36582)),f777(f777(f85(a3),f777(f777(f84(a3),x36581),x36583)),x36582)) % 174.01/173.89 [3660]E(f777(f777(f5(a3),f777(f777(f85(a3),x36601),x36602)),f777(f777(f85(a3),x36603),x36602)),f777(f777(f85(a3),f777(f777(f5(a3),x36601),x36603)),x36602)) % 174.01/173.89 [3661]E(f777(f777(f238(a851),f777(f777(f5(a851),x36611),x36612)),f777(f777(f5(a851),x36613),x36612)),f777(f777(f5(a851),f777(f777(f238(a851),x36611),x36613)),x36612)) % 174.01/173.89 [3685]E(f777(f777(f105(f858(x36851,a845)),x36852),f777(f777(f5(f858(x36851,a845)),x36853),x36852)),f777(f777(f105(f858(x36851,a845)),x36852),x36853)) % 174.01/173.89 [3686]E(f777(f777(f105(f858(x36861,a845)),x36862),f777(f777(f105(f858(x36861,a845)),x36862),x36863)),f777(f777(f105(f858(x36861,a845)),x36862),x36863)) % 174.01/173.89 [3687]E(f777(f777(f106(f858(x36871,a845)),x36872),f777(f777(f106(f858(x36871,a845)),x36872),x36873)),f777(f777(f106(f858(x36871,a845)),x36872),x36873)) % 174.01/173.89 [3699]E(f777(f777(f283(x36991,x36992,x36992),x36993),f302(x36992,f182(f858(f857(x36992,x36992),a845)))),x36993) % 174.01/173.89 [3704]E(f777(f777(f105(f858(x37041,a845)),f777(f777(f304(x37041),x37042),f182(f858(x37041,a845)))),x37043),f777(f777(f304(x37041),x37042),x37043)) % 174.01/173.89 [3722]E(f777(f777(f5(a851),f777(f777(f5(a851),f777(a116,x37221)),x37222)),f777(a116,x37223)),f777(f777(f5(a851),f777(f777(f5(a851),x37221),x37222)),x37223)) % 174.01/173.89 [3750]E(f777(f777(f106(f858(f858(x37501,a845),a845)),f777(f303(x37501),x37502)),f777(f303(x37501),x37503)),f777(f303(x37501),f777(f777(f106(f858(x37501,a845)),x37502),x37503))) % 174.01/173.89 [3753]E(f777(f777(f105(f858(x37531,a845)),f777(f83(f858(x37531,a845)),x37532)),x37533),f777(f83(f858(x37531,a845)),f777(f777(f5(f858(x37531,a845)),x37532),x37533))) % 174.01/173.89 [3766]E(f777(f777(f304(x37661),x37662),f777(f777(f5(f858(x37661,a845)),x37663),f777(f777(f304(x37661),x37662),f182(f858(x37661,a845))))),f777(f777(f304(x37661),x37662),x37663)) % 174.01/173.89 [3777]P1(f777(f777(f234(f858(x37771,a845)),x37772),f777(f777(f105(f858(x37771,a845)),x37773),x37772))) % 174.01/173.89 [3778]P1(f777(f777(f234(f858(x37781,a845)),x37782),f777(f777(f105(f858(x37781,a845)),x37782),x37783))) % 174.01/173.89 [3781]E(f777(f777(f106(f858(x37811,a845)),f777(f83(f858(x37811,a845)),x37812)),f777(f83(f858(x37811,a845)),x37813)),f777(f83(f858(x37811,a845)),f777(f777(f105(f858(x37811,a845)),x37812),x37813))) % 174.01/173.89 [3782]E(f777(f777(f105(f858(x37821,a845)),f777(f83(f858(x37821,a845)),x37822)),f777(f83(f858(x37821,a845)),x37823)),f777(f83(f858(x37821,a845)),f777(f777(f106(f858(x37821,a845)),x37822),x37823))) % 174.01/173.89 [3795]P1(f777(f777(f234(f858(x37951,a845)),f777(f160(x37951),x37952)),f777(f160(x37951),f777(f777(f142(x37951),x37953),x37952)))) % 174.01/173.89 [3804]E(f777(f777(f105(f858(x38041,a845)),f777(f777(f5(f858(x38041,a845)),x38042),x38043)),f777(f777(f106(f858(x38041,a845)),x38042),x38043)),x38042) % 174.01/173.89 [3854]E(f777(f777(f10(x38541,a3),f777(f777(f12(a851,a3,x38541),f104(a3)),x38542)),x38543),f777(f104(a3),f777(f777(f10(x38541,a851),x38542),x38543))) % 174.01/173.89 [3855]E(f777(f777(f13(x38551,a3),f777(f777(f12(a851,a3,x38551),f104(a3)),x38552)),x38553),f777(f104(a3),f777(f777(f13(x38551,a851),x38552),x38553))) % 174.01/173.89 [3911]E(f777(f83(f858(f857(x39111,x39112),a845)),f777(f777(f250(x39111,x39112),x39113),f777(f20(f858(x39112,a845),x39111),f241(f858(x39112,a845))))),f777(f777(f250(x39111,x39112),f777(f83(f858(x39111,a845)),x39113)),f777(f20(f858(x39112,a845),x39111),f241(f858(x39112,a845))))) % 174.01/173.89 [3912]E(f777(f83(f858(f857(x39121,x39122),a845)),f777(f777(f250(x39121,x39122),f241(f858(x39121,a845))),f777(f20(f858(x39122,a845),x39121),x39123))),f777(f777(f250(x39121,x39122),f241(f858(x39121,a845))),f777(f20(f858(x39122,a845),x39121),f777(f83(f858(x39122,a845)),x39123)))) % 174.01/173.89 [3963]E(f777(f777(f48(f858(x39631,a845),f858(x39631,a845)),x39632),f777(f777(f11(f858(x39631,a845),f858(x39631,a845),f858(x39631,a845)),f106(f858(x39631,a845))),x39633)),f777(f777(f106(f858(x39631,a845)),f46(f858(x39631,a845),x39632)),x39633)) % 174.01/173.89 [3970]E(f777(f134(f852(x39701),f852(x39701),f127(x39701),f117(x39701)),f777(f777(f142(f852(x39701)),x39702),x39703)),f777(f777(f127(x39701),x39702),f777(f134(f852(x39701),f852(x39701),f127(x39701),f117(x39701)),x39703))) % 174.01/173.89 [3993]E(f777(f777(f304(f858(x39931,a845)),f777(f279(x39931,x39931,x39932),f777(f777(f304(x39931),x39933),f182(f858(x39931,a845))))),f182(f858(f858(x39931,a845),a845))),f777(f777(f63(x39931),f777(f777(f304(x39931),x39933),f182(f858(x39931,a845)))),x39932)) % 174.01/173.89 [4003]E(f777(f777(f84(a851),f777(f777(f85(a851),x40031),f777(f777(f45(a851),x40032),x40033))),f777(f777(f45(a851),f777(f777(f85(a851),x40031),f54(a851,x40032,x40033))),x40033)),f777(f777(f45(a851),f777(f777(f85(a851),x40031),x40032)),x40033)) % 174.01/173.89 [4004]E(f777(f777(f84(a3),f777(f777(f85(a3),x40041),f777(f777(f45(a3),x40042),x40043))),f777(f777(f45(a3),f777(f777(f85(a3),x40041),f54(a3,x40042,x40043))),x40043)),f777(f777(f45(a3),f777(f777(f85(a3),x40041),x40042)),x40043)) % 174.01/173.89 [4088]E(f777(f777(f127(x40881),f777(f134(f852(x40881),f852(x40881),f127(x40881),f117(x40881)),x40882)),f777(f134(f852(x40881),f852(x40881),f127(x40881),f117(x40881)),x40883)),f777(f134(f852(x40881),f852(x40881),f127(x40881),f117(x40881)),f777(f777(f127(f852(x40881)),x40882),x40883))) % 174.01/173.89 [4091]E(f777(f777(f243(f852(x40911),f852(x40911)),f777(f128(x40911,x40912),x40913)),f777(f128(x40911,f777(f77(a845,a845,x40911,a330),x40912)),x40913)),f158(x40911,x40912,x40913)) % 174.01/173.89 [4094]E(f777(f777(f84(a851),f777(f777(f84(a851),f777(f777(f45(a851),x40941),x40942)),f777(f777(f45(a851),x40943),x40942))),f777(f777(f45(a851),f777(f777(f84(a851),f54(a851,x40941,x40942)),f54(a851,x40943,x40942))),x40942)),f777(f777(f45(a851),f777(f777(f84(a851),x40941),x40943)),x40942)) % 174.01/173.89 [4095]E(f777(f777(f84(a3),f777(f777(f84(a3),f777(f777(f45(a3),x40951),x40952)),f777(f777(f45(a3),x40953),x40952))),f777(f777(f45(a3),f777(f777(f84(a3),f54(a3,x40951,x40952)),f54(a3,x40953,x40952))),x40952)),f777(f777(f45(a3),f777(f777(f84(a3),x40951),x40953)),x40952)) % 174.01/173.89 [4168]E(f777(f258(x41681),f777(f777(f22(x41681,a845,a845),f777(f777(f12(a845,f858(a845,a845),x41681),a334),f777(f777(f11(x41681,x41681,a845),a332),x41682))),f777(f777(f11(x41681,f858(x41681,a845),a845),f336(x41681)),x41683))),f777(f777(f304(x41681),x41682),x41683)) % 174.01/173.89 [4190]E(f777(f258(x41901),f777(f777(f22(x41901,a845,a845),f777(f777(f12(a845,f858(a845,a845),x41901),a334),f777(f777(f11(x41901,f858(x41901,a845),a845),f336(x41901)),x41902))),f777(f777(f11(x41901,f858(x41901,a845),a845),f336(x41901)),x41903))),f777(f777(f105(f858(x41901,a845)),x41902),x41903)) % 174.01/173.89 [4191]E(f777(f258(x41911),f777(f777(f22(x41911,a845,a845),f777(f777(f12(a845,f858(a845,a845),x41911),a333),f777(f777(f11(x41911,f858(x41911,a845),a845),f336(x41911)),x41912))),f777(f777(f11(x41911,f858(x41911,a845),a845),f336(x41911)),x41913))),f777(f777(f106(f858(x41911,a845)),x41912),x41913)) % 174.01/173.89 [4278]E(f777(f777(f48(x42781,f858(f858(x42781,a845),a845)),x42782),f777(f777(f11(x42781,f858(f858(x42781,a845),a845),f858(f858(x42781,a845),a845)),f777(f777(f12(f858(x42781,a845),f858(f858(f858(x42781,a845),a845),f858(f858(x42781,a845),a845)),x42781),f304(f858(x42781,a845))),f777(f777(f12(f858(x42781,a845),f858(x42781,a845),x42781),f279(x42781,x42781,x42783)),f777(f777(f11(x42781,f858(x42781,a845),f858(x42781,a845)),f304(x42781)),f182(f858(x42781,a845)))))),f182(f858(f858(x42781,a845),a845)))),f777(f777(f63(x42781),x42782),x42783)) % 174.01/173.89 [4280]E(f777(f777(f199(x42801),f777(f777(f85(a3),f777(f777(f77(f857(a3,a3),a3,x42801,f242(a3,a3)),f209(x42801)),x42802)),f777(f777(f77(f857(a3,a3),a3,x42801,f242(a3,a3)),f209(x42801)),x42803))),f777(f777(f85(a3),f777(f777(f77(f857(a3,a3),a3,x42801,f252(a3,a3)),f209(x42801)),x42802)),f777(f777(f77(f857(a3,a3),a3,x42801,f252(a3,a3)),f209(x42801)),x42803))),f224(x42801,x42802,x42803)) % 174.01/173.89 [3674]E(f54(a851,f777(f777(f84(a851),f777(f777(f85(a851),x36741),x36742)),x36743),x36742),f54(a851,x36743,x36742)) % 174.01/173.89 [3721]E(f132(a851,f777(f296(a851,f777(f777(f84(a851),x37211),x37212)),x37213)),f777(f777(f130(a851),x37212),f132(a851,f777(f296(a851,x37211),x37213)))) % 174.01/173.89 [3765]E(f777(f777(f84(a3),f777(f104(a3),x37651)),f777(f777(f84(a3),f777(f104(a3),x37652)),x37653)),f777(f777(f84(a3),f777(f104(a3),f777(f777(f84(a851),x37651),x37652))),x37653)) % 174.01/173.89 [3773]E(f777(f777(f5(f858(x37731,a845)),f777(f777(f5(f858(x37731,a845)),x37732),x37733)),x37733),f777(f777(f5(f858(x37731,a845)),x37732),x37733)) % 174.01/173.89 [3774]E(f777(f777(f105(f858(x37741,a845)),f777(f777(f5(f858(x37741,a845)),x37742),x37743)),x37743),f777(f777(f105(f858(x37741,a845)),x37742),x37743)) % 174.01/173.89 [3796]E(f777(f777(f283(x37961,x37961,x37962),f302(x37961,f182(f858(f857(x37961,x37961),a845)))),x37963),x37963) % 174.01/173.89 [3801]E(f777(f777(f105(f858(x38011,a845)),f777(f278(x38011),x38012)),f777(f278(x38011),x38013)),f777(f278(x38011),f777(f777(f105(f858(f857(x38011,x38011),a845)),x38012),x38013))) % 174.01/173.89 [3810]E(f265(x38101,f777(f777(f142(f857(a103,x38101)),f777(f777(f243(a103,x38101),f4(a103)),x38102)),x38103)),f265(x38101,x38103)) % 174.01/173.89 [3813]E(f777(f777(f106(f858(x38131,a845)),f47(f858(x38131,a845),x38132)),f47(f858(x38131,a845),x38133)),f47(f858(x38131,a845),f777(f777(f105(f858(f858(x38131,a845),a845)),x38132),x38133))) % 174.01/173.89 [3814]E(f777(f777(f105(f858(x38141,a845)),f46(f858(x38141,a845),x38142)),f46(f858(x38141,a845),x38143)),f46(f858(x38141,a845),f777(f777(f105(f858(f858(x38141,a845),a845)),x38142),x38143))) % 174.01/173.89 [3847]E(f777(f777(f283(x38471,x38471,x38471),f777(f777(f175(f857(x38471,x38471),a845),x38472),x38473)),x38473),f777(f777(f175(f857(x38471,x38471),a845),f777(a116,x38472)),x38473)) % 174.01/173.89 [3897]P1(f777(f777(f234(f858(x38971,a845)),f777(f777(f5(f858(x38971,a845)),x38972),x38973)),x38972)) % 174.01/173.89 [3898]P1(f777(f777(f234(f858(x38981,a845)),f777(f777(f106(f858(x38981,a845)),x38982),x38983)),x38983)) % 174.01/173.89 [3899]P1(f777(f777(f234(f858(x38991,a845)),f777(f777(f106(f858(x38991,a845)),x38992),x38993)),x38992)) % 174.01/173.89 [3924]E(f302(x39241,f777(f777(f105(f858(f857(x39241,x39241),a845)),f302(x39241,x39242)),f302(x39241,x39243))),f302(x39241,f777(f777(f105(f858(f857(x39241,x39241),a845)),x39242),x39243))) % 174.01/173.89 [3928]E(f46(f858(x39281,a845),f777(f777(f304(f858(x39281,a845)),x39282),f777(f777(f304(f858(x39281,a845)),x39283),f182(f858(f858(x39281,a845),a845))))),f777(f777(f105(f858(x39281,a845)),x39282),x39283)) % 174.01/173.89 [3929]E(f47(f858(x39291,a845),f777(f777(f304(f858(x39291,a845)),x39292),f777(f777(f304(f858(x39291,a845)),x39293),f182(f858(f858(x39291,a845),a845))))),f777(f777(f106(f858(x39291,a845)),x39292),x39293)) % 174.01/173.89 [3935]E(f777(f777(f283(x39351,x39351,x39351),f777(f777(f175(f857(x39351,x39351),a845),x39352),x39353)),x39353),f777(f777(f283(x39351,x39351,x39351),x39353),f777(f777(f175(f857(x39351,x39351),a845),x39352),x39353))) % 174.01/173.89 [4008]E(f777(f777(f105(f858(x40081,a845)),f777(f258(x40081),f777(f777(f11(x40081,x40081,a845),a332),x40082))),x40083),f777(f777(f304(x40081),x40082),x40083)) % 174.01/173.89 [4010]E(f777(a109,f777(f777(f10(x40101,a3),f777(f777(f12(a851,a3,x40101),f104(a3)),x40102)),x40103)),f777(f777(f10(x40101,a851),x40102),x40103)) % 174.01/173.89 [4011]E(f777(a109,f777(f777(f13(x40111,a3),f777(f777(f12(a851,a3,x40111),f104(a3)),x40112)),x40113)),f777(f777(f13(x40111,a851),x40112),x40113)) % 174.01/173.89 [4085]E(f777(f147(f852(x40851),x40851,f777(f159(x40851),x40852),f777(f20(f858(f852(x40851),f852(x40851)),x40851),f777(f777(f11(f852(x40851),f852(x40851),f852(x40851)),f127(x40851)),x40852))),x40853),f777(f159(x40851),f777(f777(f127(x40851),x40853),x40852))) % 174.01/173.89 [4116]P1(f777(f777(f234(f858(f858(x41161,a845),a845)),f777(f777(f105(f858(f858(x41161,a845),a845)),f777(f303(x41161),x41162)),f777(f303(x41161),x41163))),f777(f303(x41161),f777(f777(f105(f858(x41161,a845)),x41162),x41163)))) % 174.01/173.89 [4209]E(f777(f258(x42091),f777(f777(f22(x42091,a845,a845),f777(f777(f12(a845,f858(a845,a845),x42091),a333),f777(f777(f11(x42091,f858(x42091,a845),a845),f336(x42091)),x42092))),f777(f777(f12(a845,a845,x42091),a330),f777(f777(f11(x42091,f858(x42091,a845),a845),f336(x42091)),x42093)))),f777(f777(f5(f858(x42091,a845)),x42092),x42093)) % 174.01/173.89 [4230]E(f777(f44(a851),f777(f258(a851),f777(f777(f22(a851,a845,a845),f777(f777(f12(a845,f858(a845,a845),a851),a333),f777(f777(f11(a851,a851,a845),f235(a851)),f777(f183(f852(x42301)),x42302)))),f777(f777(f12(x42301,a845,a851),x42303),f777(f155(x42301),x42302))))),f777(f183(f852(x42301)),f777(f128(x42301,x42303),x42302))) % 174.01/173.89 [4232]E(f777(f183(f852(x42321)),f162(x42321,x42322,x42323)),f777(f44(a851),f777(f258(a851),f777(f777(f22(a851,a845,a845),f777(f777(f12(a845,f858(a845,a845),a851),a333),f777(f777(f11(a851,a851,a845),f235(a851)),f777(f183(f852(x42321)),x42322)))),f777(f777(f11(a851,f858(a851,a845),a845),f336(a851)),x42323))))) % 174.01/173.89 [4325]E(f777(f777(f106(f858(f857(f852(x43251),f852(x43251)),a845)),f777(f305(f857(f857(x43251,f852(x43251)),f857(x43251,f852(x43251))),f857(f852(x43251),f852(x43251)),f254(f857(x43251,f852(x43251)),f852(x43251),f857(x43251,f852(x43251)),f852(x43251),f777(f253(x43251,f852(x43251),f852(x43251)),f142(x43251)),f777(f253(x43251,f852(x43251),f852(x43251)),f142(x43251)))),f327(x43251,f852(x43251),x43252,f777(f135(x43251,x43252),x43253)))),f777(f258(f857(f852(x43251),f852(x43251))),f777(f253(f852(x43251),f852(x43251),a845),f777(f777(f11(f852(x43251),f858(f852(x43251),a845),f858(f852(x43251),a845)),f777(f777(f12(f858(a845,a845),f858(f858(f852(x43251),a845),f858(f852(x43251),a845)),f852(x43251)),f12(a845,a845,f852(x43251))),f777(f777(f12(a845,f858(a845,a845),f852(x43251)),a333),f777(f777(f11(f852(x43251),a851,a845),f777(f777(f12(a851,f858(a851,a845),f852(x43251)),a332),f183(f852(x43251)))),f777(a116,x43253))))),f777(f777(f11(f852(x43251),a851,a845),f777(f777(f12(a851,f858(a851,a845),f852(x43251)),a332),f183(f852(x43251)))),f777(a116,x43253)))))),f777(f135(x43251,x43252),f777(a116,x43253))) % 174.01/173.89 [3815]E(f54(a851,f777(a116,f777(f777(f84(a851),f777(f777(f85(a851),x38151),x38152)),x38153)),x38152),f54(a851,f777(a116,x38153),x38152)) % 174.01/173.89 [4075]E(f777(f258(x40751),f777(f777(f22(x40751,a845,a845),f777(f777(f12(a845,f858(a845,a845),x40751),a333),x40752)),x40753)),f777(f777(f106(f858(x40751,a845)),f777(f258(x40751),x40752)),f777(f258(x40751),x40753))) % 174.01/173.89 [4076]E(f777(f258(x40761),f777(f777(f22(x40761,a845,a845),f777(f777(f12(a845,f858(a845,a845),x40761),a334),x40762)),x40763)),f777(f777(f105(f858(x40761,a845)),f777(f258(x40761),x40762)),f777(f258(x40761),x40763))) % 174.01/173.89 [4078]E(f777(f777(f127(x40781),f777(f777(f130(x40781),f54(a851,x40782,f777(f183(f852(x40781)),x40783))),x40783)),f777(f777(f161(x40781),f54(a851,x40782,f777(f183(f852(x40781)),x40783))),x40783)),f777(f777(f777(f175(f852(x40781),f852(x40781)),x40782),f143(x40781)),x40783)) % 174.01/173.89 [4083]E(f777(f258(x40831),f777(f777(f22(x40831,a845,a845),f777(f777(f12(a845,f858(a845,a845),x40831),a337),x40832)),x40833)),f777(f777(f105(f858(x40831,a845)),f777(f83(f858(x40831,a845)),f777(f258(x40831),x40832))),f777(f258(x40831),x40833))) % 174.01/173.89 [4097]E(f777(f777(f84(a851),f777(f183(f852(x40971)),f777(f128(x40971,x40972),x40973))),f777(f183(f852(x40971)),f777(f128(x40971,f777(f777(f12(a845,a845,x40971),a330),x40972)),x40973))),f777(f183(f852(x40971)),x40973)) % 174.01/173.89 [4124]P1(f777(f777(f234(f858(x41241,a845)),f777(f777(f105(f858(x41241,a845)),f47(f858(x41241,a845),x41242)),f47(f858(x41241,a845),x41243))),f47(f858(x41241,a845),f777(f777(f106(f858(f858(x41241,a845),a845)),x41242),x41243)))) % 174.01/173.89 [4140]E(f777(f160(x41401),f777(f128(x41401,f777(f777(f12(a845,a845,x41401),a330),f777(f777(f11(x41401,x41401,a845),a332),x41402))),x41403)),f777(f777(f5(f858(x41401,a845)),f777(f160(x41401),x41403)),f777(f777(f304(x41401),x41402),f182(f858(x41401,a845))))) % 174.01/173.89 [4149]P1(f777(f777(f234(f858(f857(x41491,x41491),a845)),f777(f777(f105(f858(f857(x41491,x41491),a845)),f302(x41491,x41492)),f302(x41491,x41493))),f302(x41491,f777(f777(f105(f858(f857(x41491,x41491),a845)),x41492),x41493)))) % 174.01/173.89 [4173]E(f777(f777(f85(a851),f777(a116,f777(a116,f4(a851)))),f777(f777(f10(a851,a851),f777(f777(f12(a851,a851,a851),f777(f84(a851),x41731)),f777(f777(f11(a851,a851,a851),f85(a851)),x41732))),f777(f259(a851),x41733))),f777(f777(f85(a851),x41733),f777(f777(f84(a851),x41731),f777(f777(f84(a851),x41731),f777(f777(f85(a851),f777(f777(f5(a851),x41733),f82(a851))),x41732))))) % 174.01/173.89 [4183]E(f777(f258(x41831),f777(f777(f22(x41831,a845,a845),f777(f777(f12(a845,f858(a845,a845),x41831),a333),f777(f777(f11(x41831,f858(x41831,a845),a845),f336(x41831)),f777(f160(x41831),x41832)))),x41833)),f777(f160(x41831),f777(f128(x41831,x41833),x41832))) % 174.01/173.89 [4324]E(f777(f258(x43241),f777(f777(f12(f858(a851,a845),a845,x43241),f91(a851)),f777(f777(f11(x43241,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),x43241),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),x43241),f777(f12(a845,f858(a845,a845),a851),a333)),f777(f777(f11(x43241,f858(a851,x43241),f858(a851,a845)),f777(f777(f12(f858(x43241,a845),f858(f858(a851,x43241),f858(a851,a845)),x43241),f12(x43241,a845,a851)),a332)),f777(f155(x43241),x43242))))),f777(f777(f22(a851,a845,a845),f777(f777(f12(a845,f858(a845,a845),a851),a333),f777(f777(f11(a851,a851,a845),f235(a851)),f777(f183(f852(x43241)),x43242)))),f777(f777(f11(a851,f858(a851,a845),a845),f336(a851)),x43243))))),f777(f160(x43241),f162(x43241,x43242,x43243))) % 174.01/173.89 [4220]E(f777(f258(x42201),f777(f777(f22(x42201,a845,a845),f777(f777(f12(a845,f858(a845,a845),x42201),a337),f777(f777(f12(a845,a845,x42201),a330),f777(f777(f11(x42201,x42201,a845),a332),x42202)))),x42203)),f777(f777(f304(x42201),x42202),f777(f258(x42201),x42203))) % 174.01/173.89 [4251]E(f777(f777(f145(f857(x42511,a851),x42511),f242(x42511,a851)),f777(f128(f857(x42511,a851),f777(f777(f11(f857(x42511,a851),f858(a851,a845),a845),f777(f777(f12(a851,f858(f858(a851,a845),a845),f857(x42511,a851)),f336(a851)),f252(x42511,a851))),x42512)),f777(f777(f169(x42511,a851),x42513),f132(a851,f777(f296(a851,f4(a851)),f777(f183(f852(x42511)),x42513)))))),f162(x42511,x42513,x42512)) % 174.01/173.89 [4279]E(f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(f777(f10(a851,a3),f777(f777(f12(a3,a3,a851),f777(f84(a3),x42791)),f777(f777(f11(a851,a3,a3),f777(f777(f12(a3,f858(a3,a3),a851),f85(a3)),f104(a3))),x42792))),f777(f259(a851),x42793))),f777(f777(f85(a3),f777(f104(a3),x42793)),f777(f777(f84(a3),x42791),f777(f777(f84(a3),x42791),f777(f777(f85(a3),f777(f104(a3),f777(f777(f5(a851),x42793),f82(a851)))),x42792))))) % 174.01/173.89 [4318]E(f777(f258(f857(x43181,x43182)),f777(f253(x43181,x43182,a845),f777(f777(f11(x43181,f858(f857(x43182,x43181),a845),f858(x43182,a845)),f777(f777(f12(f858(x43182,f858(f858(f857(x43182,x43181),a845),a845)),f858(f858(f857(x43182,x43181),a845),f858(x43182,a845)),x43181),f11(x43182,f858(f857(x43182,x43181),a845),a845)),f777(f777(f12(f858(x43182,f857(x43182,x43181)),f858(x43182,f858(f858(f857(x43182,x43181),a845),a845)),x43181),f777(f12(f857(x43182,x43181),f858(f858(f857(x43182,x43181),a845),a845),x43182),f336(f857(x43182,x43181)))),f777(f11(x43182,x43181,f857(x43182,x43181)),f243(x43182,x43181))))),x43183))),f777(f280(x43182,x43181),x43183)) % 174.01/173.89 [4353]E(f777(f258(f852(x43531)),f777(f777(f12(f858(x43531,a845),a845,f852(x43531)),f91(x43531)),f777(f777(f12(f858(x43531,f858(f852(x43531),a845)),f858(x43531,a845),f852(x43531)),f777(f12(f858(f852(x43531),a845),a845,x43531),f91(f852(x43531)))),f777(f777(f11(f852(x43531),f858(x43531,f858(f852(x43531),a845)),f858(x43531,f858(f852(x43531),a845))),f777(f777(f12(f858(x43531,f858(f858(f852(x43531),a845),f858(f852(x43531),a845))),f858(f858(x43531,f858(f852(x43531),a845)),f858(x43531,f858(f852(x43531),a845))),f852(x43531)),f22(x43531,f858(f852(x43531),a845),f858(f852(x43531),a845))),f777(f777(f12(f858(x43531,f858(f852(x43531),f858(a845,a845))),f858(x43531,f858(f858(f852(x43531),a845),f858(f852(x43531),a845))),f852(x43531)),f777(f12(f858(f852(x43531),f858(a845,a845)),f858(f858(f852(x43531),a845),f858(f852(x43531),a845)),x43531),f22(f852(x43531),a845,a845))),f777(f777(f12(f858(x43531,f858(f852(x43531),a845)),f858(x43531,f858(f852(x43531),f858(a845,a845))),f852(x43531)),f777(f12(f858(f852(x43531),a845),f858(f852(x43531),f858(a845,a845)),x43531),f777(f12(a845,f858(a845,a845),f852(x43531)),a333))),f777(f777(f11(f852(x43531),f858(x43531,f858(f852(x43531),f852(x43531))),f858(x43531,f858(f852(x43531),a845))),f777(f777(f12(f858(f858(f852(x43531),f852(x43531)),f858(f852(x43531),a845)),f858(f858(x43531,f858(f852(x43531),f852(x43531))),f858(x43531,f858(f852(x43531),a845))),f852(x43531)),f12(f858(f852(x43531),f852(x43531)),f858(f852(x43531),a845),x43531)),f777(f777(f12(f858(f852(x43531),a845),f858(f858(f852(x43531),f852(x43531)),f858(f852(x43531),a845)),f852(x43531)),f12(f852(x43531),a845,f852(x43531))),a332))),f142(x43531)))))),f777(f777(f11(x43531,f858(f852(x43531),a845),f858(f852(x43531),a845)),f777(f777(f12(f858(a845,a845),f858(f858(f852(x43531),a845),f858(f852(x43531),a845)),x43531),f12(a845,a845,f852(x43531))),f777(f777(f12(a845,f858(a845,a845),x43531),a333),f777(f777(f11(x43531,f858(x43531,a845),a845),f336(x43531)),x43532)))),f777(f777(f11(f852(x43531),f858(f852(x43531),a845),a845),f336(f852(x43531))),x43533)))))),f163(x43531,x43532,x43533)) % 174.01/173.89 [4338]E(f777(f777(f90(a3,f857(a3,a3)),f777(f777(f5(a3),x43381),x43382)),f777(f777(f11(a3,f857(a3,a3),f857(a3,a3)),f777(f777(f22(a3,f857(a3,a3),f858(f857(a3,a3),f857(a3,a3))),f777(f777(f12(a845,f858(f857(a3,a3),f858(f857(a3,a3),f857(a3,a3))),a3),f100(f857(a3,a3))),f777(f234(a3),f4(a3)))),f777(f243(a3,a3),f777(f777(f84(a3),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x43383)),f82(a3))))),f777(f777(f243(a3,a3),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x43383)),x43381))),f777(f52(x43382),f777(f777(f243(a3,a3),x43383),x43381))) % 174.01/173.89 [4389]~E(f38(x43891,x43892),f37(x43893,x43894)) % 174.01/173.89 [4392]~E(f30(x43921,x43922),f37(x43923,x43924)) % 174.01/173.89 [4393]~E(f30(x43931,x43932),f38(x43933,x43934)) % 174.01/173.89 [4411]~E(f777(a29,x44111),f35(x44112,x44113,x44114)) % 174.01/173.89 [4412]~E(f777(a29,x44121),f34(x44122,x44123,x44124)) % 174.01/173.89 [4413]~E(f777(a29,x44131),f33(x44132,x44133,x44134)) % 174.01/173.89 [4414]~E(f35(x44141,x44142,x44143),f777(a29,x44144)) % 174.01/173.89 [4415]~E(f34(x44151,x44152,x44153),f777(a29,x44154)) % 174.01/173.89 [4416]~E(f33(x44161,x44162,x44163),f777(a29,x44164)) % 174.01/173.89 [3368]E(f777(f777(f777(f76(x33681,x33682),x33683),x33684),f777(x33683,x33684)),x33683) % 174.01/173.89 [3432]E(f777(f777(f245(x34321,x34322,x34323),x34324),f4(a851)),x34322) % 174.01/173.89 [3471]E(f177(x34711,x34712,x34713,f777(a116,x34714)),f777(x34713,x34714)) % 174.01/173.89 [3512]E(f153(x35121,x35122,f153(x35121,x35123,x35124)),f153(x35121,x35123,f153(x35121,x35122,x35124))) % 174.01/173.89 [3629]P39(f30(x36291,x36292),x36293,x36294,f777(f777(f777(a191,x36293),x36291),f777(x36292,x36293))) % 174.01/173.89 [3641]E(f777(f231(x36411,x36412,x36413,x36414),f185(x36412)),x36413) % 174.01/173.89 [3643]E(f777(f147(x36431,x36432,x36433,x36434),f117(x36432)),x36433) % 174.01/173.89 [3644]E(f777(f134(x36441,x36442,x36443,x36444),f117(x36442)),x36444) % 174.01/173.89 [3681]E(f777(f183(f856(x36811,x36812)),f217(x36811,x36812,x36813,x36814)),f4(a851)) % 174.01/173.89 [3706]E(f777(f253(x37061,x37062,x37063),f251(x37061,x37062,x37063,x37064)),x37064) % 174.01/173.89 [3762]E(f777(f231(f855(x37621),x37622,f185(x37621),f777(f20(f855(x37621),x37622),f185(x37621))),f777(x37623,x37624)),f185(x37621)) % 174.01/173.89 [3805]E(f777(f777(f105(f858(x38051,a845)),f171(x38051,x38052,x38053)),f171(x38051,x38052,x38054)),f171(x38051,x38052,f172(x38051,x38052,x38054,x38053))) % 174.01/173.89 [3834]E(f777(f777(f255(x38341,x38342,x38343,f857(x38342,x38343)),x38344),f243(x38342,x38343)),x38344) % 174.01/173.89 [3843]E(f232(x38431,x38432,x38433,x38434,f185(x38432)),x38433) % 174.01/173.89 [4131]P41(x41311,x41312,x41313,x41314,f182(f858(x41311,a845)),x41314) % 174.01/173.89 [4440]~E(f777(f315(x44401,x44402),x44403),f777(f306(x44402,x44401),x44404)) % 174.01/173.89 [3177]E(f777(f777(f20(x31771,x31772),x31773),x31774),x31773) % 174.01/173.89 [3290]E(f777(f777(f198(x32901,x32902),x32903),f777(f229(x32901),x32904)),f777(f229(x32902),f777(x32903,x32904))) % 174.01/173.89 [3463]E(f153(x34631,x34632,f777(f128(x34631,x34633),x34634)),f777(f128(x34631,x34633),f153(x34631,x34632,x34634))) % 174.01/173.89 [3496]E(f777(f777(f68(x34961,x34962,x34963),x34964),f182(f858(x34961,a845))),x34964) % 174.01/173.89 [3518]E(f777(f777(f155(x35181),f777(f777(f142(x35181),x35182),x35183)),f777(a116,x35184)),f777(f777(f155(x35181),x35183),x35184)) % 174.01/173.89 [3556]P31(x35561,f4(a851),f777(f777(f777(f95(x35561),x35562),f777(a29,x35563)),x35564)) % 174.01/173.89 [3581]E(f777(f777(x35811,x35812),f777(f176(x35813,x35814,x35811),x35812)),f777(f176(x35813,x35814,x35811),f777(a116,x35812))) % 174.01/173.89 [3621]E(f251(x36211,x36212,x36213,f777(f253(x36211,x36212,x36213),x36214)),x36214) % 174.01/173.89 [3679]E(f777(f777(f150(x36791,f777(f777(f142(x36791),x36792),x36793)),f4(a851)),x36794),f777(f777(f142(x36791),x36794),x36793)) % 174.01/173.89 [3689]E(f777(f777(f48(f858(x36891,a845),f858(x36892,a845)),x36893),f305(x36891,x36892,x36894)),f777(f305(x36891,x36892,x36894),f46(f858(x36891,a845),x36893))) % 174.01/173.89 [3690]E(f777(f777(f48(f858(x36901,a845),f858(x36902,a845)),x36903),f307(x36902,x36901,x36904)),f777(f307(x36902,x36901,x36904),f46(f858(x36901,a845),x36903))) % 174.01/173.89 [3790]E(f171(x37901,x37902,f174(x37901,x37902,x37903,x37904)),f777(f777(f106(f858(x37901,a845)),f171(x37901,x37902,x37903)),x37904)) % 174.01/173.89 [3809]E(f777(f134(x38091,x38092,f777(f11(x38092,x38091,x38091),x38093),x38094),f777(f144(x38092),f117(x38092))),x38094) % 174.01/173.89 [3853]E(f80(x38531,x38532,x38533,x38534,f182(f858(x38531,a845))),x38533) % 174.01/173.89 [3900]E(f777(f777(f777(f777(f76(x39001,f855(x39002)),f777(f20(f855(x39002),x39001),f185(x39002))),x39003),f185(x39002)),x39004),f185(x39002)) % 174.01/173.89 [4049]E(f321(x40491,x40492,x40493,f777(f777(f12(f859(x40491,x40493),x40492,x40491),x40494),f306(x40491,x40493)),f777(f777(f12(f859(x40491,x40493),x40492,x40493),x40494),f315(x40493,x40491))),x40494) % 174.01/173.89 [4059]E(f777(f253(x40591,x40592,x40593),f777(f777(f12(f858(x40592,f857(x40591,x40592)),f858(x40592,x40593),x40591),f777(f12(f857(x40591,x40592),x40593,x40592),x40594)),f243(x40591,x40592))),x40594) % 174.01/173.89 [3366]E(f777(f252(x33661,x33662),f777(f777(f243(x33661,x33662),x33663),x33664)),x33664) % 174.01/173.89 [3367]E(f777(f242(x33671,x33672),f777(f777(f243(x33671,x33672),x33673),x33674)),x33673) % 174.01/173.89 [3405]E(f777(f183(f852(x34051)),f777(f777(f145(x34052,x34051),x34053),x34054)),f777(f183(f852(x34052)),x34054)) % 174.01/173.89 [3406]E(f777(f183(f852(x34061)),f777(f777(f150(x34061,x34062),x34063),x34064)),f777(f183(f852(x34061)),x34062)) % 174.01/173.89 [3427]E(f777(f777(f130(x34271),f777(a116,x34272)),f777(f777(f142(x34271),x34273),x34274)),f777(f777(f130(x34271),x34272),x34274)) % 174.01/173.89 [3498]E(f777(f777(f304(x34981),x34982),f777(f777(f304(x34981),x34983),x34984)),f777(f777(f304(x34981),x34983),f777(f777(f304(x34981),x34982),x34984))) % 174.01/173.89 [3501]E(f777(f777(f145(x35011,x35012),x35013),f118(x35011,x35014)),f118(x35012,f777(f777(f145(x35011,x35012),x35013),x35014))) % 174.01/173.89 [3516]E(f777(f144(x35161),f777(f777(f145(x35162,x35161),x35163),x35164)),f777(f777(f145(x35162,x35161),x35163),f777(f144(x35162),x35164))) % 174.01/173.89 [3517]E(f777(f777(f145(x35171,x35172),x35173),f777(f159(x35171),x35174)),f777(f159(x35172),f777(f777(f145(x35171,x35172),x35173),x35174))) % 174.01/173.89 [3526]E(f777(f777(f161(x35261),f777(a116,x35262)),f777(f777(f142(x35261),x35263),x35264)),f777(f777(f142(x35261),x35263),f777(f777(f161(x35261),x35262),x35264))) % 174.01/173.89 [3530]E(f777(f160(x35301),f777(f777(f145(x35302,x35301),x35303),x35304)),f777(f305(x35302,x35301,x35303),f777(f160(x35302),x35304))) % 174.01/173.89 [3580]E(f21(x35801,x35802,x35803,f777(a7,f777(a116,f777(a24,x35804)))),f777(x35803,x35804)) % 174.01/173.89 [3584]E(f777(f777(f127(x35841),f777(f128(x35841,x35842),x35843)),f777(f128(x35841,x35842),x35844)),f777(f128(x35841,x35842),f777(f777(f127(x35841),x35843),x35844))) % 174.01/173.89 [3611]E(f777(f280(x36111,x36111),f777(f777(f282(x36112,x36111),x36113),x36114)),f777(f777(f282(x36112,x36111),f777(f280(x36112,x36112),x36113)),x36114)) % 174.01/173.89 [3622]E(f777(f777(f283(x36221,x36222,x36223),x36224),f182(f858(f857(x36222,x36223),a845))),f182(f858(f857(x36221,x36223),a845))) % 174.01/173.89 [3623]E(f777(f777(f161(x36231),f777(f777(f5(a851),x36232),x36233)),f777(f777(f130(x36231),x36233),x36234)),f777(f777(f130(x36231),x36233),f777(f777(f161(x36231),x36232),x36234))) % 174.01/173.89 [3645]E(f777(f777(f777(f275(x36451),x36452),x36453),x36454),f777(f243(f858(a103,f858(a845,f855(f853(x36451)))),f857(a103,a103)),f777(f51(x36451),x36452))) % 174.01/173.89 [3671]E(f47(f858(x36711,a845),f777(f305(x36712,f858(x36711,a845),x36713),x36714)),f777(f777(f49(x36712,f858(x36711,a845)),x36714),x36713)) % 174.01/173.89 [3672]E(f46(f858(x36721,a845),f777(f305(x36722,f858(x36721,a845),x36723),x36724)),f777(f777(f48(x36722,f858(x36721,a845)),x36724),x36723)) % 174.01/173.89 [3673]E(f777(f183(f852(f857(x36731,x36732))),f777(f777(f169(x36731,x36732),x36733),x36734)),f777(f777(f238(a851),f777(f183(f852(x36731)),x36733)),f777(f183(f852(x36732)),x36734))) % 174.01/173.89 [3675]E(f777(f307(x36751,x36752,x36753),f777(f83(f858(x36752,a845)),x36754)),f777(f83(f858(x36751,a845)),f777(f307(x36751,x36752,x36753),x36754))) % 174.01/173.89 [3707]E(f777(f174(x37071,x37072,x37073,f182(f858(x37071,a845))),x37074),f185(x37072)) % 174.01/173.89 [3726]E(f777(f307(x37261,x37262,x37263),f777(f258(x37262),x37264)),f777(f258(x37261),f777(f777(f12(x37262,a845,x37261),x37264),x37263))) % 174.01/173.89 [3744]E(f777(f777(f155(x37441),f777(f777(f127(x37441),x37442),f777(f777(f142(x37441),x37443),x37444))),f777(f183(f852(x37441)),x37442)),x37443) % 174.01/173.89 [3749]E(f777(f174(x37491,x37492,f777(f20(f855(x37492),x37491),f185(x37492)),x37493),x37494),f185(x37492)) % 174.01/173.89 [3771]E(f777(f305(x37711,x37712,x37713),f777(f307(x37711,x37712,x37713),x37714)),f777(f777(f106(f858(x37712,a845)),x37714),f777(f305(x37711,x37712,x37713),f241(f858(x37711,a845))))) % 174.01/173.89 [3789]P1(f777(f777(f336(x37891),f777(x37892,x37893)),f777(f305(x37894,x37891,x37892),f241(f858(x37894,a845))))) % 174.01/173.89 [3797]E(f23(x37971,x37972,x37973,f777(a7,f777(a116,f777(a24,x37974)))),f777(f777(x37973,x37974),f23(x37971,x37972,x37973,x37974))) % 174.01/173.89 [3812]E(f146(x38121,x38122,f777(f777(f142(x38121),x38123),x38124)),f777(f777(f84(a851),f777(f777(f84(a851),f777(x38122,x38123)),f146(x38121,x38122,x38124))),f777(a116,f4(a851)))) % 174.01/173.89 [3825]E(f177(f852(x38251),f777(f777(f142(x38251),x38252),x38253),f777(f777(f11(a851,f852(x38251),f852(x38251)),f130(x38251)),x38253),x38254),f777(f777(f130(x38251),x38254),f777(f777(f142(x38251),x38252),x38253))) % 174.01/173.89 [3826]P29(x38261,f857(x38262,x38261),f338(x38263,x38264,x38262,x38261),f777(f777(f48(x38262,f858(x38261,a845)),x38264),x38263)) % 174.01/173.89 [3835]E(f777(f777(f5(f858(x38351,a845)),f777(f777(f5(f858(x38351,a845)),x38352),x38353)),f777(f777(f304(x38351),x38354),f182(f858(x38351,a845)))),f777(f777(f5(f858(x38351,a845)),x38352),f777(f777(f304(x38351),x38354),x38353))) % 174.01/173.89 [3846]E(f777(f777(f175(f858(x38461,x38462),f858(x38461,x38462)),x38463),f77(x38462,x38462,x38461,x38464)),f77(x38462,x38462,x38461,f777(f777(f175(x38462,x38462),x38463),x38464))) % 174.01/173.89 [3923]E(f777(f777(f777(f175(f852(x39231),f852(x39231)),x39232),f143(x39231)),f777(f777(f777(f175(f852(x39231),f852(x39231)),x39233),f143(x39231)),x39234)),f777(f777(f777(f175(f852(x39231),f852(x39231)),f777(f777(f84(a851),x39232),x39233)),f143(x39231)),x39234)) % 174.01/173.89 [3972]E(f777(f777(f105(f858(f859(x39721,x39722),a845)),f777(f305(x39721,f859(x39721,x39722),f306(x39721,x39722)),x39723)),f777(f305(x39722,f859(x39721,x39722),f315(x39722,x39721)),x39724)),f316(x39721,x39722,x39723,x39724)) % 174.01/173.89 [4013]P1(f777(f777(f234(f858(x40131,a845)),f777(f160(x40131),f777(f777(f150(x40131,x40132),x40133),x40134))),f777(f777(f304(x40131),x40134),f777(f160(x40131),x40132)))) % 174.01/173.89 [4047]E(f777(f777(f48(f858(x40471,a845),f858(f857(x40471,x40472),a845)),x40473),f777(f777(f11(f858(x40471,a845),f858(x40471,f858(x40472,a845)),f858(f857(x40471,x40472),a845)),f250(x40471,x40472)),x40474)),f777(f777(f250(x40471,x40472),f46(f858(x40471,a845),x40473)),x40474)) % 174.01/173.89 [4084]E(f206(x40841,x40842,x40843,f777(f77(x40842,f858(a103,f858(a103,f858(f857(a103,a103),f858(a103,f853(x40842))))),x40841,f205(x40842)),x40844)),f207(x40841,x40842,x40844,x40843)) % 174.01/173.89 [4100]E(f202(x41001,x41002,x41003,f777(f77(x41002,f858(a103,f858(a103,f858(f857(a103,a103),f858(a103,f853(f855(x41002)))))),x41001,f201(x41002)),x41004)),f203(x41001,x41002,x41004,x41003)) % 174.01/173.89 [4105]P1(f777(f70(x41051,x41052,x41053,x41054,f182(f858(x41051,a845))),x41054)) % 174.01/173.89 [4152]E(f777(f777(f48(x41521,f858(x41522,a845)),x41523),f777(f777(f11(x41521,f858(x41522,a845),f858(x41522,a845)),f777(f777(f12(x41522,f858(f858(x41522,a845),f858(x41522,a845)),x41521),f304(x41522)),x41524)),f182(f858(x41522,a845)))),f777(f305(x41521,x41522,x41524),x41523)) % 174.01/173.89 [4158]P1(f777(f777(f234(f858(x41581,a845)),f777(f261(x41582,x41581),f777(f777(f106(f858(f857(x41582,x41581),a845)),x41583),x41584))),f777(f777(f106(f858(x41581,a845)),f777(f261(x41582,x41581),x41583)),f777(f261(x41582,x41581),x41584)))) % 174.01/173.89 [4159]P1(f777(f777(f234(f858(x41591,a845)),f777(f263(x41591,x41592),f777(f777(f106(f858(f857(x41591,x41592),a845)),x41593),x41594))),f777(f777(f106(f858(x41591,a845)),f777(f263(x41591,x41592),x41593)),f777(f263(x41591,x41592),x41594)))) % 174.01/173.89 [4218]P1(f777(f777(f234(f858(f857(x42181,x42182),a845)),f777(f305(x42182,f857(x42181,x42182),f338(x42183,x42184,x42181,x42182)),f777(f777(f48(x42181,f858(x42182,a845)),x42184),x42183))),f777(f777(f250(x42181,x42182),x42184),x42183))) % 174.01/173.89 [4219]E(f273(x42191,x42192,x42193,f777(f77(x42192,f858(a103,f858(a103,f858(f857(a103,a103),f857(f858(a103,f858(a845,f855(f853(x42192)))),f857(a103,a103))))),x42191,f275(x42192)),x42194)),f276(x42191,x42192,x42194,x42193)) % 174.01/173.89 [4257]E(f89(f857(x42571,x42572),f777(f253(x42571,x42572,a845),f777(f777(f11(x42571,f858(x42572,a845),f858(x42572,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x42572,a845),f858(x42572,a845)),x42571),f12(a845,a845,x42572)),f777(f777(f12(a845,f858(a845,a845),x42571),a333),f777(a332,x42573)))),f777(a332,x42574)))),f777(f777(f243(x42571,x42572),x42573),x42574)) % 174.01/173.89 [4258]E(f94(f857(x42581,x42582),f777(f253(x42581,x42582,a845),f777(f777(f11(x42581,f858(x42582,a845),f858(x42582,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x42582,a845),f858(x42582,a845)),x42581),f12(a845,a845,x42582)),f777(f777(f12(a845,f858(a845,a845),x42581),a333),f777(a332,x42583)))),f777(a332,x42584)))),f777(f777(f243(x42581,x42582),x42583),x42584)) % 174.01/173.89 [4328]E(f777(f777(f253(f852(x43281),f852(x43281),f857(f852(x43281),f852(x43281))),f777(f777(f22(f852(x43281),f858(f852(x43281),f857(f852(x43281),f852(x43281))),f858(f852(x43281),f857(f852(x43281),f852(x43281)))),f777(f777(f12(f858(f852(x43281),f858(f857(f852(x43281),f852(x43281)),f857(f852(x43281),f852(x43281)))),f858(f858(f852(x43281),f857(f852(x43281),f852(x43281))),f858(f852(x43281),f857(f852(x43281),f852(x43281)))),f852(x43281)),f22(f852(x43281),f857(f852(x43281),f852(x43281)),f857(f852(x43281),f852(x43281)))),f777(f777(f12(f858(f852(x43281),f857(f852(x43281),f852(x43281))),f858(f852(x43281),f858(f857(f852(x43281),f852(x43281)),f857(f852(x43281),f852(x43281)))),f852(x43281)),f777(f12(f857(f852(x43281),f852(x43281)),f858(f857(f852(x43281),f852(x43281)),f857(f852(x43281),f852(x43281))),f852(x43281)),f777(f100(f857(f852(x43281),f852(x43281))),f777(x43282,x43283)))),f777(f777(f12(f852(x43281),f858(f852(x43281),f857(f852(x43281),f852(x43281))),f852(x43281)),f243(f852(x43281),f852(x43281))),f777(f142(x43281),x43283))))),f777(f777(f11(f852(x43281),f858(f852(x43281),f852(x43281)),f858(f852(x43281),f857(f852(x43281),f852(x43281)))),f777(f777(f12(f858(f852(x43281),f857(f852(x43281),f852(x43281))),f858(f858(f852(x43281),f852(x43281)),f858(f852(x43281),f857(f852(x43281),f852(x43281)))),f852(x43281)),f12(f852(x43281),f857(f852(x43281),f852(x43281)),f852(x43281))),f243(f852(x43281),f852(x43281)))),f777(f142(x43281),x43283)))),f158(x43281,x43282,x43284)),f158(x43281,x43282,f777(f777(f142(x43281),x43283),x43284))) % 174.01/173.89 [4334]E(f777(f134(f858(x43341,f855(x43342)),f857(x43341,x43342),f777(f11(f857(x43341,x43342),f858(x43341,f855(x43342)),f858(x43341,f855(x43342))),f777(f253(x43341,x43342,f858(f858(x43341,f855(x43342)),f858(x43341,f855(x43342)))),f777(f777(f11(x43341,f858(x43342,f855(x43342)),f858(x43342,f858(f858(x43341,f855(x43342)),f858(x43341,f855(x43342))))),f777(f777(f12(f858(f855(x43342),f858(f858(x43341,f855(x43342)),f858(x43341,f855(x43342)))),f858(f858(x43342,f855(x43342)),f858(x43342,f858(f858(x43341,f855(x43342)),f858(x43341,f855(x43342))))),x43341),f12(f855(x43342),f858(f858(x43341,f855(x43342)),f858(x43341,f855(x43342))),x43342)),f777(f777(f12(f858(f858(x43341,f855(x43342)),f858(f855(x43342),f858(x43341,f855(x43342)))),f858(f855(x43342),f858(f858(x43341,f855(x43342)),f858(x43341,f855(x43342)))),x43341),f11(f858(x43341,f855(x43342)),f855(x43342),f858(x43341,f855(x43342)))),f777(f11(f858(x43341,f855(x43342)),x43341,f858(f855(x43342),f858(x43341,f855(x43342)))),f76(x43341,f855(x43342)))))),f229(x43342)))),x43343),f777(f144(f857(x43341,x43342)),x43344)),f172(x43341,x43342,x43343,f168(x43341,x43342,x43344))) % 174.01/173.89 [3446]E(f777(f183(f850(x34461)),f777(f777(f777(f95(x34461),x34462),x34463),x34464)),f4(a851)) % 174.01/173.89 [3559]E(f777(f777(f161(x35591),x35592),f777(f777(f161(x35591),x35593),x35594)),f777(f777(f161(x35591),f777(f777(f238(a851),x35592),x35593)),x35594)) % 174.01/173.89 [3560]E(f777(f777(f130(x35601),x35602),f777(f777(f130(x35601),x35603),x35604)),f777(f777(f130(x35601),f777(f777(f84(a851),x35602),x35603)),x35604)) % 174.01/173.89 [3572]E(f777(f777(f127(x35721),f777(f777(f142(x35721),x35722),x35723)),x35724),f777(f777(f142(x35721),x35722),f777(f777(f127(x35721),x35723),x35724))) % 174.01/173.89 [3573]E(f777(f777(f127(x35731),f777(f777(f127(x35731),x35732),x35733)),x35734),f777(f777(f127(x35731),x35732),f777(f777(f127(x35731),x35733),x35734))) % 174.01/173.89 [3655]E(f777(f777(f155(x36551),f777(f777(f142(x36551),x36552),x36553)),x36554),f177(x36551,x36552,f777(f155(x36551),x36553),x36554)) % 174.01/173.89 [3664]E(f777(f777(f175(x36641,x36641),x36642),f777(f777(f175(x36641,x36641),x36643),x36644)),f777(f777(f175(x36641,x36641),f777(f777(f85(a851),x36643),x36642)),x36644)) % 174.01/173.89 [3692]E(f777(f777(f105(f858(x36921,a845)),x36922),f777(f777(f304(x36921),x36923),x36924)),f777(f777(f304(x36921),x36923),f777(f777(f105(f858(x36921,a845)),x36922),x36924))) % 174.01/173.89 [3710]E(f777(f777(f777(f175(x37101,x37101),x37102),x37103),f777(x37103,x37104)),f777(x37103,f777(f777(f777(f175(x37101,x37101),x37102),x37103),x37104))) % 174.01/173.89 [3717]E(f777(f777(f283(x37171,x37172,x37173),f182(f858(f857(x37171,x37172),a845))),x37174),f182(f858(f857(x37171,x37173),a845))) % 174.01/173.89 [3733]E(f777(f777(f105(f858(x37331,a845)),f777(f777(f304(x37331),x37332),x37333)),x37334),f777(f777(f304(x37331),x37332),f777(f777(f105(f858(x37331,a845)),x37333),x37334))) % 174.01/173.89 [3751]E(f777(f44(f857(x37511,x37512)),f777(f777(f250(x37511,x37512),x37513),f777(f20(f858(x37512,a845),x37511),x37514))),f777(f777(f85(a851),f777(f44(x37511),x37513)),f777(f44(x37512),x37514))) % 174.01/173.89 [3759]E(f777(f777(f106(f858(x37591,a845)),f777(f777(f304(x37591),x37592),x37593)),f777(f777(f304(x37591),x37592),x37594)),f777(f777(f304(x37591),x37592),f777(f777(f106(f858(x37591,a845)),x37593),x37594))) % 174.01/173.89 [3769]E(f172(x37691,x37692,f168(x37691,x37692,x37693),f168(x37691,x37692,x37694)),f168(x37691,x37692,f777(f777(f127(f857(x37691,x37692)),x37694),x37693))) % 174.01/173.89 [3775]E(f777(f777(f105(f858(x37751,a845)),x37752),f777(f777(f105(f858(x37751,a845)),x37753),x37754)),f777(f777(f105(f858(x37751,a845)),x37753),f777(f777(f105(f858(x37751,a845)),x37752),x37754))) % 174.01/173.89 [3776]E(f777(f777(f106(f858(x37761,a845)),x37762),f777(f777(f106(f858(x37761,a845)),x37763),x37764)),f777(f777(f106(f858(x37761,a845)),x37763),f777(f777(f106(f858(x37761,a845)),x37762),x37764))) % 174.01/173.89 [3785]E(f68(x37851,x37852,f777(f777(f12(x37852,f858(x37852,x37852),x37851),x37853),x37854)),f777(f69(x37852,x37851,x37853),x37854)) % 174.01/173.89 [3794]E(f166(x37941,f777(f777(f145(f852(x37942),f852(x37941)),f777(f145(x37942,x37941),x37943)),x37944)),f777(f777(f145(f852(x37942),f852(x37941)),f777(f145(x37942,x37941),x37943)),f166(x37942,x37944))) % 174.01/173.89 [3811]E(f174(x38111,x38112,x38113,f777(f83(f858(x38111,a845)),f777(f777(f304(x38111),x38114),f182(f858(x38111,a845))))),f777(f777(f777(f76(x38111,f855(x38112)),x38113),x38114),f185(x38112))) % 174.01/173.89 [3867]E(f777(f77(x38671,x38671,x38671,f777(f777(f175(x38671,x38671),x38672),x38673)),f777(f777(f175(x38671,x38671),x38674),x38673)),f777(f777(f175(x38671,x38671),f777(f777(f84(a851),x38672),x38674)),x38673)) % 174.01/173.89 [3882]E(f777(f777(f777(f76(x38821,f855(x38822)),f168(x38821,x38822,x38823)),f777(f242(x38821,x38822),x38824)),f777(f229(x38822),f777(f252(x38821,x38822),x38824))),f168(x38821,x38822,f777(f777(f142(f857(x38821,x38822)),x38824),x38823))) % 174.01/173.89 [3889]E(f172(x38891,x38892,x38893,f168(x38891,x38892,f777(f144(f857(x38891,x38892)),f777(f777(f169(x38891,x38892),x38894),f117(x38892))))),x38893) % 174.01/173.89 [3892]E(f777(f777(f106(f858(x38921,a845)),f777(f777(f5(f858(x38921,a845)),x38922),x38923)),f777(f777(f5(f858(x38921,a845)),x38922),x38924)),f777(f777(f5(f858(x38921,a845)),x38922),f777(f777(f105(f858(x38921,a845)),x38923),x38924))) % 174.01/173.89 [3893]E(f777(f777(f105(f858(x38931,a845)),f777(f777(f5(f858(x38931,a845)),x38932),x38933)),f777(f777(f5(f858(x38931,a845)),x38932),x38934)),f777(f777(f5(f858(x38931,a845)),x38932),f777(f777(f106(f858(x38931,a845)),x38933),x38934))) % 174.01/173.89 [3894]E(f777(f777(f106(f858(x38941,a845)),f777(f777(f105(f858(x38941,a845)),x38942),x38943)),f777(f777(f105(f858(x38941,a845)),x38942),x38944)),f777(f777(f105(f858(x38941,a845)),x38942),f777(f777(f106(f858(x38941,a845)),x38943),x38944))) % 174.01/173.89 [3895]E(f777(f777(f5(f858(x38951,a845)),f777(f777(f106(f858(x38951,a845)),x38952),x38953)),f777(f777(f106(f858(x38951,a845)),x38952),x38954)),f777(f777(f106(f858(x38951,a845)),x38952),f777(f777(f5(f858(x38951,a845)),x38953),x38954))) % 174.01/173.89 [3896]E(f777(f777(f105(f858(x38961,a845)),f777(f777(f106(f858(x38961,a845)),x38962),x38963)),f777(f777(f106(f858(x38961,a845)),x38962),x38964)),f777(f777(f106(f858(x38961,a845)),x38962),f777(f777(f105(f858(x38961,a845)),x38963),x38964))) % 174.01/173.89 [3902]E(f777(f44(f857(x39021,x39022)),f777(f777(f250(x39021,x39022),f777(f777(f304(x39021),x39023),f182(f858(x39021,a845)))),f777(f20(f858(x39022,a845),x39021),x39024))),f777(f44(x39022),x39024)) % 174.01/173.89 [3939]E(f777(f777(f49(x39391,f858(x39392,a845)),x39393),f777(f777(f12(f858(x39392,a845),f858(x39392,a845),x39391),f83(f858(x39392,a845))),x39394)),f777(f83(f858(x39392,a845)),f777(f777(f48(x39391,f858(x39392,a845)),x39393),x39394))) % 174.01/173.89 [3940]E(f777(f777(f48(x39401,f858(x39402,a845)),x39403),f777(f777(f12(f858(x39402,a845),f858(x39402,a845),x39401),f83(f858(x39402,a845))),x39404)),f777(f83(f858(x39402,a845)),f777(f777(f49(x39401,f858(x39402,a845)),x39403),x39404))) % 174.01/173.89 [3956]E(f777(f777(f283(x39561,x39561,x39561),f777(f777(f175(f857(x39561,x39561),a845),x39562),x39563)),f777(f777(f175(f857(x39561,x39561),a845),x39564),x39563)),f777(f777(f175(f857(x39561,x39561),a845),f777(f777(f84(a851),x39562),x39564)),x39563)) % 174.01/173.89 [3988]E(f777(f777(f49(x39881,f858(f858(x39882,a845),a845)),x39883),f777(f777(f12(f858(x39882,a845),f858(f858(x39882,a845),a845),x39881),f303(x39882)),x39884)),f777(f303(x39882),f777(f777(f49(x39881,f858(x39882,a845)),x39883),x39884))) % 174.01/173.89 [4018]E(f777(f777(f48(f858(x40181,a845),f858(x40182,a845)),x40183),f777(f777(f11(f858(x40181,a845),f858(x40181,f858(x40182,a845)),f858(x40182,a845)),f48(x40181,f858(x40182,a845))),x40184)),f777(f777(f48(x40181,f858(x40182,a845)),f46(f858(x40181,a845),x40183)),x40184)) % 174.01/173.89 [4019]E(f777(f777(f49(f858(x40191,a845),f858(x40192,a845)),x40193),f777(f777(f11(f858(x40191,a845),f858(x40191,f858(x40192,a845)),f858(x40192,a845)),f49(x40191,f858(x40192,a845))),x40194)),f777(f777(f49(x40191,f858(x40192,a845)),f46(f858(x40191,a845),x40193)),x40194)) % 174.01/173.89 [4024]E(f777(f777(f145(x40241,x40242),x40243),f777(f134(f852(x40241),f852(x40241),f127(x40241),f117(x40241)),x40244)),f777(f134(f852(x40242),f852(x40242),f127(x40242),f117(x40242)),f777(f777(f145(f852(x40241),f852(x40242)),f777(f145(x40241,x40242),x40243)),x40244))) % 174.01/173.89 [4026]E(f177(f852(x40261),f117(x40261),f777(f777(f12(f852(x40261),f852(x40261),a851),f777(f142(x40261),x40262)),f777(f777(f11(a851,f852(x40261),f852(x40261)),f161(x40261)),x40263)),x40264),f777(f777(f161(x40261),x40264),f777(f777(f142(x40261),x40262),x40263))) % 174.01/173.89 [4069]P1(f777(f777(f234(f858(x40691,a845)),f777(f305(x40692,x40691,x40693),f777(f307(x40692,x40691,x40693),x40694))),x40694)) % 174.01/173.89 [4071]E(f777(f305(f857(x40711,x40712),f857(x40712,x40711),f777(f253(x40711,x40712,f857(x40712,x40711)),f777(f11(x40712,x40711,f857(x40712,x40711)),f243(x40712,x40711)))),f777(f777(f250(x40711,x40712),x40713),f777(f20(f858(x40712,a845),x40711),x40714))),f777(f777(f250(x40712,x40711),x40714),f777(f20(f858(x40711,a845),x40712),x40713))) % 174.01/173.89 [4080]E(f777(f777(f48(x40801,f858(x40802,a845)),x40803),f777(f777(f12(f858(x40801,a845),f858(x40802,a845),x40801),f279(x40801,x40802,x40804)),f777(f777(f11(x40801,f858(x40801,a845),f858(x40801,a845)),f304(x40801)),f182(f858(x40801,a845))))),f777(f279(x40801,x40802,x40804),x40803)) % 174.01/173.89 [4081]E(f777(f777(f48(x40811,f858(x40812,a845)),x40813),f777(f777(f12(f858(x40811,a845),f858(x40812,a845),x40811),f307(x40812,x40811,x40814)),f777(f777(f11(x40811,f858(x40811,a845),f858(x40811,a845)),f304(x40811)),f182(f858(x40811,a845))))),f777(f307(x40812,x40811,x40814),x40813)) % 174.01/173.89 [4172]E(f777(f777(f106(f858(x41721,a845)),f777(f777(f106(f858(x41721,a845)),f777(f777(f105(f858(x41721,a845)),x41722),x41723)),f777(f777(f105(f858(x41721,a845)),x41723),x41724))),f777(f777(f105(f858(x41721,a845)),x41724),x41722)),f777(f777(f105(f858(x41721,a845)),f777(f777(f105(f858(x41721,a845)),f777(f777(f106(f858(x41721,a845)),x41722),x41723)),f777(f777(f106(f858(x41721,a845)),x41723),x41724))),f777(f777(f106(f858(x41721,a845)),x41724),x41722))) % 174.01/173.89 [4231]E(f777(f134(f852(x42311),f852(x42311),f127(x42311),f117(x42311)),f777(f777(f145(x42312,f852(x42311)),f777(f777(f11(x42312,f852(x42311),f852(x42311)),f777(f777(f12(x42311,f858(f852(x42311),f852(x42311)),x42312),f142(x42311)),x42313)),f117(x42311))),x42314)),f777(f777(f145(x42312,x42311),x42313),x42314)) % 174.01/173.89 [4241]E(f777(f777(f90(a3,x42411),f777(f108(a3),f777(f777(f84(a3),x42412),a101))),f777(f777(f22(a3,x42411,x42411),f777(f777(f11(a3,x42411,f858(x42411,x42411)),f777(f777(f12(a845,f858(x42411,f858(x42411,x42411)),a3),f100(x42411)),a188)),x42413)),f777(f777(f12(a851,x42411,a3),x42414),a109))),f177(x42411,x42413,x42414,f777(f108(a851),x42412))) % 174.01/173.89 [4482]~P1(f777(f777(f182(f858(x44821,f858(x44822,a845))),x44823),x44824)) % 174.01/173.89 [3720]E(f777(f777(f155(x37201),f777(f777(f127(x37201),x37202),x37203)),f777(f777(f84(a851),f777(f183(f852(x37201)),x37202)),x37204)),f777(f777(f155(x37201),x37203),x37204)) % 174.01/173.89 [3725]E(f777(f777(f130(x37251),x37252),f777(f777(f161(x37251),f777(f777(f84(a851),x37253),x37252)),x37254)),f777(f777(f161(x37251),x37253),f777(f777(f130(x37251),x37252),x37254))) % 174.01/173.89 [3823]E(f777(f777(f105(f858(x38231,a845)),f777(f261(x38232,x38231),x38233)),f777(f261(x38232,x38231),x38234)),f777(f261(x38232,x38231),f777(f777(f105(f858(f857(x38232,x38231),a845)),x38233),x38234))) % 174.01/173.89 [3824]E(f777(f777(f105(f858(x38241,a845)),f777(f263(x38241,x38242),x38243)),f777(f263(x38241,x38242),x38244)),f777(f263(x38241,x38242),f777(f777(f105(f858(f857(x38241,x38242),a845)),x38243),x38244))) % 174.01/173.89 [3829]E(f777(f777(f5(f858(x38291,a845)),f777(f777(f106(f858(x38291,a845)),x38292),x38293)),x38294),f777(f777(f106(f858(x38291,a845)),x38292),f777(f777(f5(f858(x38291,a845)),x38293),x38294))) % 174.01/173.89 [3830]E(f777(f777(f105(f858(x38301,a845)),f777(f777(f105(f858(x38301,a845)),x38302),x38303)),x38304),f777(f777(f105(f858(x38301,a845)),x38302),f777(f777(f105(f858(x38301,a845)),x38303),x38304))) % 174.01/173.89 [3831]E(f777(f777(f106(f858(x38311,a845)),f777(f777(f106(f858(x38311,a845)),x38312),x38313)),x38314),f777(f777(f106(f858(x38311,a845)),x38312),f777(f777(f106(f858(x38311,a845)),x38313),x38314))) % 174.01/173.89 [3869]E(f777(f777(f105(f858(f857(x38691,x38692),a845)),f777(f280(x38692,x38691),x38693)),f777(f280(x38692,x38691),x38694)),f777(f280(x38692,x38691),f777(f777(f105(f858(f857(x38692,x38691),a845)),x38693),x38694))) % 174.01/173.89 [3870]E(f777(f777(f106(f858(f857(x38701,x38702),a845)),f777(f280(x38702,x38701),x38703)),f777(f280(x38702,x38701),x38704)),f777(f280(x38702,x38701),f777(f777(f106(f858(f857(x38702,x38701),a845)),x38703),x38704))) % 174.01/173.89 [3905]E(f172(x39051,x39052,x39053,f168(x39051,x39052,f777(f144(f857(x39051,x39052)),f777(f777(f169(x39051,x39052),f117(x39051)),x39054)))),x39053) % 174.01/173.89 [3943]E(f777(f777(f105(f858(x39431,a845)),f777(f777(f5(f858(x39431,a845)),x39432),x39433)),f777(f777(f5(f858(x39431,a845)),x39434),x39433)),f777(f777(f5(f858(x39431,a845)),f777(f777(f105(f858(x39431,a845)),x39432),x39434)),x39433)) % 174.01/173.89 [3944]E(f777(f777(f106(f858(x39441,a845)),f777(f777(f105(f858(x39441,a845)),x39442),x39443)),f777(f777(f105(f858(x39441,a845)),x39444),x39443)),f777(f777(f105(f858(x39441,a845)),f777(f777(f106(f858(x39441,a845)),x39442),x39444)),x39443)) % 174.01/173.89 [3945]E(f777(f777(f5(f858(x39451,a845)),f777(f777(f106(f858(x39451,a845)),x39452),x39453)),f777(f777(f106(f858(x39451,a845)),x39454),x39453)),f777(f777(f106(f858(x39451,a845)),f777(f777(f5(f858(x39451,a845)),x39452),x39454)),x39453)) % 174.01/173.89 [3946]E(f777(f777(f105(f858(x39461,a845)),f777(f777(f106(f858(x39461,a845)),x39462),x39463)),f777(f777(f106(f858(x39461,a845)),x39464),x39463)),f777(f777(f106(f858(x39461,a845)),f777(f777(f105(f858(x39461,a845)),x39462),x39464)),x39463)) % 174.01/173.89 [3947]E(f777(f777(f5(f858(x39471,a845)),f777(f777(f106(f858(x39471,a845)),x39472),x39473)),f777(f777(f106(f858(x39471,a845)),x39474),x39473)),f777(f777(f5(f858(x39471,a845)),f777(f777(f106(f858(x39471,a845)),x39472),x39473)),x39474)) % 174.01/173.89 [3959]E(f777(f777(f5(f858(x39591,a845)),f777(f777(f5(f858(x39591,a845)),x39592),f777(f777(f304(x39591),x39593),f182(f858(x39591,a845))))),x39594),f777(f777(f5(f858(x39591,a845)),x39592),f777(f777(f304(x39591),x39593),x39594))) % 174.01/173.89 [4015]E(f777(f777(f105(f858(x40151,a845)),f777(f777(f304(x40151),x40152),f777(f777(f304(x40151),x40153),f182(f858(x40151,a845))))),f777(f278(x40151),x40154)),f777(f278(x40151),f777(f777(f304(f857(x40151,x40151)),f777(f777(f243(x40151,x40151),x40152),x40153)),x40154))) % 174.01/173.89 [4042]E(f777(f777(f48(a851,f858(x40421,a845)),f777(f295(a851),x40422)),f777(f777(f12(a851,f858(x40421,a845),a851),x40423),f777(f777(f11(a851,a851,a851),f84(a851)),x40424))),f777(f777(f48(a851,f858(x40421,a845)),f297(a851,x40424,f777(f777(f84(a851),x40422),x40424))),x40423)) % 174.01/173.89 [4043]E(f163(x40431,f777(f279(x40431,x40431,x40432),f777(f777(f304(x40431),x40433),f182(f858(x40431,a845)))),f777(f279(f852(x40431),f852(x40431),f149(x40431,x40432)),f777(f777(f304(f852(x40431)),x40434),f182(f858(f852(x40431),a845))))),f777(f279(f852(x40431),f852(x40431),f149(x40431,x40432)),f777(f777(f304(f852(x40431)),f777(f777(f142(x40431),x40433),x40434)),f182(f858(f852(x40431),a845))))) % 174.01/173.89 [4106]E(f168(x41061,x41062,f777(f777(f145(x41061,f857(x41061,x41062)),f777(f777(f22(x41061,x41062,f857(x41061,x41062)),f243(x41061,x41062)),x41063)),x41064)),f174(x41061,x41062,f777(f77(x41062,f855(x41062),x41061,f229(x41062)),x41063),f777(f160(x41061),x41064))) % 174.01/173.89 [4109]E(f777(f258(x41091),f777(f777(f11(x41091,f858(x41092,a845),a845),f777(f777(f12(x41092,f858(f858(x41092,a845),a845),x41091),f336(x41092)),x41093)),x41094)),f777(f307(x41091,x41092,x41093),x41094)) % 174.01/173.89 [4203]E(f777(f258(x42031),f777(f777(f11(x42031,f858(f857(x42032,x42031),a845),a845),f777(f777(f12(f857(x42032,x42031),f858(f858(f857(x42032,x42031),a845),a845),x42031),f336(f857(x42032,x42031))),f777(f243(x42032,x42031),x42033))),x42034)),f777(f279(x42032,x42031,x42034),f777(f777(f304(x42032),x42033),f182(f858(x42032,a845))))) % 174.01/173.89 [4217]E(f777(f777(f145(f857(x42171,a851),x42171),f242(x42171,a851)),f777(f128(f857(x42171,a851),f777(f777(f12(a851,a845,f857(x42171,a851)),x42172),f777(f777(f12(a851,a851,f857(x42171,a851)),a116),f252(x42171,a851)))),f777(f777(f169(x42171,a851),x42173),x42174))),f777(f777(f145(f857(x42171,a851),x42171),f242(x42171,a851)),f777(f128(f857(x42171,a851),f777(f777(f12(a851,a845,f857(x42171,a851)),x42172),f252(x42171,a851))),f777(f777(f169(x42171,a851),x42173),f777(f777(f145(a851,a851),a116),x42174))))) % 174.01/173.89 [4224]P1(f777(f777(f234(f858(f858(x42241,a845),a845)),f777(f777(f48(x42242,f858(f858(x42241,a845),a845)),x42243),f777(f777(f12(f858(x42241,a845),f858(f858(x42241,a845),a845),x42242),f303(x42241)),x42244))),f777(f303(x42241),f777(f777(f48(x42242,f858(x42241,a845)),x42243),x42244)))) % 174.01/173.89 [4264]E(f777(f777(f90(a3,x42641),f777(f108(a3),f777(f777(f84(a3),x42642),a101))),f777(f777(f22(a3,x42641,x42641),f777(f777(f11(a3,x42641,f858(x42641,x42641)),f777(f777(f12(a845,f858(x42641,f858(x42641,x42641)),a3),f100(x42641)),a188)),x42643)),f777(f777(f22(a3,x42641,x42641),f777(f777(f12(a851,f858(x42641,x42641),a3),x42644),a109)),f777(f777(f12(a851,x42641,a3),f176(x42641,x42643,x42644)),a109)))),f777(f176(x42641,x42643,x42644),f777(f108(a851),x42642))) % 174.01/173.89 [4267]E(f777(f777(f145(x42671,x42672),f777(f77(f855(x42672),x42672,x42671,f233(x42672)),x42673)),f777(f128(x42671,f777(f777(f12(a845,a845,x42671),a330),f777(f777(f11(x42671,f855(x42672),a845),f777(f777(f12(f855(x42672),f858(f855(x42672),a845),x42671),a332),x42673)),f185(x42672)))),x42674)),f156(x42671,x42672,x42673,x42674)) % 174.01/173.89 [4288]E(f777(f258(f857(x42881,x42882)),f777(f253(x42881,x42882,a845),f777(f777(f11(x42881,f858(x42882,a845),f858(x42882,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x42882,a845),f858(x42882,a845)),x42881),f12(a845,a845,x42882)),f777(f777(f12(a845,f858(a845,a845),x42881),a333),f777(f777(f11(x42881,f858(x42881,a845),a845),f336(x42881)),x42883)))),f777(f777(f11(x42882,f858(x42882,a845),a845),f336(x42882)),x42884)))),f225(x42881,x42882,x42883,x42884)) % 174.01/173.89 [4321]E(f777(f777(f48(x43211,f858(f857(x43211,x43212),a845)),x43213),f777(f777(f22(x43211,f858(x43212,f858(f857(x43211,x43212),a845)),f858(f857(x43211,x43212),a845)),f777(f777(f12(f858(x43212,a845),f858(f858(x43212,f858(f857(x43211,x43212),a845)),f858(f857(x43211,x43212),a845)),x43211),f48(x43212,f858(f857(x43211,x43212),a845))),x43214)),f777(f777(f11(x43211,f858(f857(x43211,x43212),a845),f858(x43212,f858(f857(x43211,x43212),a845))),f777(f777(f12(f858(x43212,f858(f858(f857(x43211,x43212),a845),f858(f857(x43211,x43212),a845))),f858(f858(f857(x43211,x43212),a845),f858(x43212,f858(f857(x43211,x43212),a845))),x43211),f11(x43212,f858(f857(x43211,x43212),a845),f858(f857(x43211,x43212),a845))),f777(f777(f12(f858(x43212,f857(x43211,x43212)),f858(x43212,f858(f858(f857(x43211,x43212),a845),f858(f857(x43211,x43212),a845))),x43211),f777(f12(f857(x43211,x43212),f858(f858(f857(x43211,x43212),a845),f858(f857(x43211,x43212),a845)),x43212),f304(f857(x43211,x43212)))),f243(x43211,x43212)))),f182(f858(f857(x43211,x43212),a845))))),f777(f777(f250(x43211,x43212),x43213),x43214)) % 174.01/173.89 [3878]E(f777(f777(f127(x38781),f777(f777(f161(x38781),x38782),x38783)),f777(f777(f161(x38781),f777(f777(f5(a851),x38782),f777(f183(f852(x38781)),x38783))),x38784)),f777(f777(f161(x38781),x38782),f777(f777(f127(x38781),x38783),x38784))) % 174.01/173.89 [3879]E(f777(f777(f127(x38791),f777(f777(f130(x38791),x38792),x38793)),f777(f777(f130(x38791),f777(f777(f5(a851),x38792),f777(f183(f852(x38791)),x38793))),x38794)),f777(f777(f130(x38791),x38792),f777(f777(f127(x38791),x38793),x38794))) % 174.01/173.89 [3932]E(f777(f777(f84(a851),f777(f777(f85(a851),x39321),x39322)),f777(f777(f84(a851),f777(f777(f85(a851),x39323),x39322)),x39324)),f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f84(a851),x39321),x39323)),x39322)),x39324)) % 174.01/173.89 [4137]P1(f777(f777(f234(f858(x41371,a845)),f777(f777(f5(f858(x41371,a845)),f777(f261(x41372,x41371),x41373)),f777(f261(x41372,x41371),x41374))),f777(f261(x41372,x41371),f777(f777(f5(f858(f857(x41372,x41371),a845)),x41373),x41374)))) % 174.01/173.89 [4138]P1(f777(f777(f234(f858(x41381,a845)),f777(f777(f5(f858(x41381,a845)),f777(f263(x41381,x41382),x41383)),f777(f263(x41381,x41382),x41384))),f777(f263(x41381,x41382),f777(f777(f5(f858(f857(x41381,x41382),a845)),x41383),x41384)))) % 174.01/173.89 [4243]E(f777(f777(f84(a3),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x42431),x42432)),f182(f858(f857(a851,a851),a845)))))),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x42433),x42434)),f182(f858(f857(a851,a851),a845)))))),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),f777(f777(f84(a851),x42431),x42433)),f777(f777(f84(a851),x42432),x42434))),f182(f858(f857(a851,a851),a845)))))) % 174.01/173.89 [4283]E(f777(f777(f85(a3),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x42831),x42832)),f182(f858(f857(a851,a851),a845)))))),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x42833),x42834)),f182(f858(f857(a851,a851),a845)))))),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),f777(f777(f84(a851),f777(f777(f85(a851),x42831),x42833)),f777(f777(f85(a851),x42832),x42834))),f777(f777(f84(a851),f777(f777(f85(a851),x42831),x42834)),f777(f777(f85(a851),x42832),x42833)))),f182(f858(f857(a851,a851),a845)))))) % 174.01/173.89 [4303]E(f777(f258(x43031),f777(f777(f12(f858(x43032,a845),a845,x43031),f92(x43032)),f777(f777(f12(f858(x43032,a845),f858(x43032,a845),x43031),f777(f22(x43032,a845,a845),f777(f777(f12(a845,f858(a845,a845),x43032),a337),f777(f777(f11(x43032,f858(x43032,a845),a845),f336(x43032)),x43033)))),f777(f777(f11(x43031,f858(x43032,f858(x43031,a845)),f858(x43032,a845)),f777(f777(f12(f858(f858(x43031,a845),a845),f858(f858(x43032,f858(x43031,a845)),f858(x43032,a845)),x43031),f12(f858(x43031,a845),a845,x43032)),f336(x43031))),x43034)))),f777(f777(f49(x43032,f858(x43031,a845)),x43033),x43034)) % 174.01/173.89 [4337]E(f777(f777(f283(x43371,x43371,x43371),f777(f777(f304(f857(x43371,x43371)),f777(f777(f243(x43371,x43371),x43372),x43373)),x43374)),f302(x43371,f777(f777(f304(f857(x43371,x43371)),f777(f777(f243(x43371,x43371),x43372),x43373)),x43374))),f777(f777(f105(f858(f857(x43371,x43371),a845)),f777(f777(f283(x43371,x43371,x43371),x43374),f302(x43371,x43374))),f777(f258(f857(x43371,x43371)),f777(f253(x43371,x43371,a845),f777(f777(f11(x43371,f858(x43371,a845),f858(x43371,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x43371,a845),f858(x43371,a845)),x43371),f12(a845,a845,x43371)),f777(f777(f12(a845,f858(a845,a845),x43371),a333),f777(f777(f11(x43371,f858(f857(x43371,x43371),a845),a845),f777(f777(f12(f857(x43371,x43371),f858(f858(f857(x43371,x43371),a845),a845),x43371),f336(f857(x43371,x43371))),f777(f777(f11(x43371,x43371,f857(x43371,x43371)),f243(x43371,x43371)),x43372))),f302(x43371,x43374))))),f777(f777(f11(x43371,f858(f857(x43371,x43371),a845),a845),f777(f777(f12(f857(x43371,x43371),f858(f858(f857(x43371,x43371),a845),a845),x43371),f336(f857(x43371,x43371))),f777(f243(x43371,x43371),x43373))),f302(x43371,x43374))))))) % 174.01/173.89 [4139]E(f777(f128(x41391,f777(f777(f22(x41391,a845,a845),f777(f777(f12(a845,f858(a845,a845),x41391),a333),x41392)),x41393)),x41394),f777(f128(x41391,x41393),f777(f128(x41391,x41392),x41394))) % 174.01/173.89 [4237]E(f777(f777(f127(x42371),f777(f777(f777(f100(f852(x42371)),f777(f777(f336(a851),f4(a851)),x42372)),f777(f777(f142(x42371),x42373),f117(x42371))),f117(x42371))),f162(x42371,x42374,f777(f258(a851),f777(f777(f11(a851,f858(a851,a845),a845),f777(f777(f12(a851,f858(f858(a851,a845),a845),a851),f336(a851)),a116)),x42372)))),f162(x42371,f777(f777(f142(x42371),x42373),x42374),x42372)) % 174.01/173.89 [4332]E(f777(f258(f857(x43321,x43322)),f777(f777(f12(f858(a851,a845),a845,f857(x43321,x43322)),f91(a851)),f777(f777(f11(f857(x43321,x43322),f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),f857(x43321,x43322)),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),f857(x43321,x43322)),f777(f12(a845,f858(a845,a845),a851),a333)),f777(f777(f11(f857(x43321,x43322),f858(a851,f857(x43321,x43322)),f858(a851,a845)),f777(f777(f12(f858(f857(x43321,x43322),a845),f858(f858(a851,f857(x43321,x43322)),f858(a851,a845)),f857(x43321,x43322)),f12(f857(x43321,x43322),a845,a851)),a332)),f777(f777(f22(a851,x43322,f857(x43321,x43322)),f777(f777(f12(x43321,f858(x43322,f857(x43321,x43322)),a851),f243(x43321,x43322)),f777(f155(x43321),x43323))),f777(f155(x43322),x43324)))))),f777(f777(f11(a851,a851,a845),f235(a851)),f777(f777(f238(a851),f777(f183(f852(x43321)),x43323)),f777(f183(f852(x43322)),x43324)))))),f777(f160(f857(x43321,x43322)),f777(f777(f169(x43321,x43322),x43323),x43324))) % 174.01/173.89 [4256]E(f777(f258(f857(x42561,x42562)),f777(f253(x42561,x42562,a845),f777(f777(f11(x42561,f858(x42562,a845),f858(x42562,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x42562,a845),f858(x42562,a845)),x42561),f12(a845,a845,x42562)),f777(f777(f12(a845,f858(a845,a845),x42561),a333),x42563))),x42564))),f777(f777(f250(x42561,x42562),f777(f258(x42561),x42563)),f777(f20(f858(x42562,a845),x42561),f777(f258(x42562),x42564)))) % 174.01/173.89 [4259]E(f777(f258(f857(x42591,x42592)),f777(f253(x42591,x42592,a845),f777(f777(f22(x42591,f858(x42592,a845),f858(x42592,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x42592,a845),f858(x42592,a845)),x42591),f12(a845,a845,x42592)),f777(f777(f12(a845,f858(a845,a845),x42591),a333),x42593))),x42594))),f777(f777(f250(x42591,x42592),f777(f258(x42591),x42593)),f777(f777(f12(f858(x42592,a845),f858(x42592,a845),x42591),f258(x42592)),x42594))) % 174.01/173.89 [4274]E(f777(f258(x42741),f777(f777(f12(f858(x42742,a845),a845,x42741),f92(x42742)),f777(f777(f12(f858(x42742,a845),f858(x42742,a845),x42741),f777(f22(x42742,a845,a845),f777(f777(f12(a845,f858(a845,a845),x42742),a337),f777(f777(f11(x42742,f858(x42742,a845),a845),f336(x42742)),x42743)))),x42744))),f777(f777(f49(x42742,f858(x42741,a845)),x42743),f777(f777(f12(f858(x42741,a845),f858(x42741,a845),x42742),f258(x42741)),f777(f11(x42741,x42742,a845),x42744)))) % 174.01/173.89 [4316]E(f777(f777(f145(f857(x43161,a851),x43161),f242(x43161,a851)),f777(f128(f857(x43161,a851),f777(f777(f11(f857(x43161,a851),f858(a851,a845),a845),f777(f777(f12(a851,f858(f858(a851,a845),a845),f857(x43161,a851)),f336(a851)),f252(x43161,a851))),x43162)),f777(f777(f169(x43161,a851),x43163),f132(a851,f777(f296(a851,x43164),f777(f777(f84(a851),x43164),f777(f183(f852(x43161)),x43163))))))),f777(f777(f145(f857(x43161,a851),x43161),f242(x43161,a851)),f777(f128(f857(x43161,a851),f777(f777(f11(f857(x43161,a851),f858(a851,a845),a845),f777(f777(f12(a851,f858(f858(a851,a845),a845),f857(x43161,a851)),f336(a851)),f777(f777(f11(f857(x43161,a851),a851,a851),f777(f777(f12(a851,f858(a851,a851),f857(x43161,a851)),f84(a851)),f252(x43161,a851))),x43164))),x43162)),f777(f777(f169(x43161,a851),x43163),f132(a851,f777(f296(a851,f4(a851)),f777(f183(f852(x43161)),x43163))))))) % 174.01/173.89 [4317]E(f777(a116,f777(f777(f181(a851),f777(f183(f852(x43171)),x43172)),f777(f134(a851,f852(x43173),f777(f11(f852(x43173),a851,a851),f777(f777(f12(a851,f858(a851,a851),f852(x43173)),f181(a851)),f777(f777(f11(f852(x43173),a851,a851),f777(f777(f12(a851,f858(a851,a851),f852(x43173)),f5(a851)),f183(f852(x43173)))),f777(a116,f4(a851))))),f4(a851)),f777(f144(f852(x43173)),f777(f128(f852(x43173),f777(f777(f12(a845,a845,f852(x43173)),a330),f777(f777(f11(f852(x43173),f852(x43173),a845),a332),f117(x43173)))),x43174))))),f777(f777(f181(a851),f777(a116,f777(f183(f852(x43171)),x43172))),f777(f134(a851,f852(x43173),f777(f11(f852(x43173),a851,a851),f777(f777(f12(a851,f858(a851,a851),f852(x43173)),f181(a851)),f183(f852(x43173)))),f4(a851)),f777(f144(f852(x43173)),x43174)))) % 174.01/173.89 [4273]E(f777(f777(f127(x42731),f162(x42731,x42732,x42733)),f162(x42731,x42734,f777(f258(a851),f777(f777(f11(a851,f858(a851,a845),a845),f777(f777(f12(a851,f858(f858(a851,a845),a845),a851),f336(a851)),f777(f777(f11(a851,a851,a851),f84(a851)),f777(f183(f852(x42731)),x42732)))),x42733)))),f162(x42731,f777(f777(f127(x42731),x42732),x42734),x42733)) % 174.01/173.89 [4323]E(f777(f777(f142(f852(x43231)),f777(f777(f142(x43231),x43232),f777(f134(f852(x43231),f852(x43231),f127(x43231),f117(x43231)),f777(f777(f145(f852(x43231),f852(x43231)),f147(f852(x43231),x43231,f117(x43231),f777(f777(f12(f852(x43231),f858(f852(x43231),f852(x43231)),x43231),f20(f852(x43231),f852(x43231))),f777(f777(f11(x43231,f852(x43231),f852(x43231)),f142(x43231)),f117(x43231))))),x43233)))),f166(x43231,f777(f777(f142(f852(x43231)),x43234),f777(f134(f852(f852(x43231)),f852(f852(x43231)),f127(f852(x43231)),f117(f852(x43231))),f777(f777(f145(f852(x43231),f852(f852(x43231))),f147(f852(f852(x43231)),x43231,f117(f852(x43231)),f777(f20(f858(f852(x43231),f852(f852(x43231))),x43231),f777(f777(f11(f852(x43231),f852(f852(x43231)),f852(f852(x43231))),f142(f852(x43231))),f117(f852(x43231)))))),x43233))))),f166(x43231,f777(f777(f142(f852(x43231)),f777(f777(f142(x43231),x43232),x43234)),x43233))) % 174.01/173.89 [4333]E(f777(f258(f857(x43331,x43331)),f777(f253(x43331,x43331,a845),f777(f777(f11(x43331,f858(f857(x43332,x43332),a845),f858(x43331,a845)),f777(f777(f12(f858(x43331,f858(f858(f857(x43332,x43332),a845),a845)),f858(f858(f857(x43332,x43332),a845),f858(x43331,a845)),x43331),f11(x43331,f858(f857(x43332,x43332),a845),a845)),f777(f777(f12(f858(x43331,f857(x43332,x43332)),f858(x43331,f858(f858(f857(x43332,x43332),a845),a845)),x43331),f777(f12(f857(x43332,x43332),f858(f858(f857(x43332,x43332),a845),a845),x43331),f336(f857(x43332,x43332)))),f777(f777(f11(x43331,f858(x43331,x43332),f858(x43331,f857(x43332,x43332))),f777(f777(f12(f858(x43332,f857(x43332,x43332)),f858(f858(x43331,x43332),f858(x43331,f857(x43332,x43332))),x43331),f12(x43332,f857(x43332,x43332),x43331)),f777(f777(f12(x43332,f858(x43332,f857(x43332,x43332)),x43331),f243(x43332,x43332)),x43333))),x43333)))),x43334))),f777(f777(f282(x43332,x43331),x43334),x43333)) % 174.01/173.89 [4417]~E(f37(x44171,x44172),f35(x44173,x44174,x44175)) % 174.01/173.89 [4418]~E(f37(x44181,x44182),f34(x44183,x44184,x44185)) % 174.01/173.89 [4419]~E(f37(x44191,x44192),f33(x44193,x44194,x44195)) % 174.01/173.89 [4420]~E(f38(x44201,x44202),f35(x44203,x44204,x44205)) % 174.01/173.89 [4421]~E(f38(x44211,x44212),f34(x44213,x44214,x44215)) % 174.01/173.89 [4422]~E(f38(x44221,x44222),f33(x44223,x44224,x44225)) % 174.01/173.89 [4423]~E(f30(x44231,x44232),f35(x44233,x44234,x44235)) % 174.01/173.89 [4424]~E(f30(x44241,x44242),f34(x44243,x44244,x44245)) % 174.01/173.89 [4425]~E(f30(x44251,x44252),f33(x44253,x44254,x44255)) % 174.01/173.89 [4426]~E(f35(x44261,x44262,x44263),f37(x44264,x44265)) % 174.01/173.89 [4427]~E(f35(x44271,x44272,x44273),f38(x44274,x44275)) % 174.01/173.89 [4428]~E(f35(x44281,x44282,x44283),f30(x44284,x44285)) % 174.01/173.89 [4429]~E(f34(x44291,x44292,x44293),f37(x44294,x44295)) % 174.01/173.89 [4430]~E(f34(x44301,x44302,x44303),f38(x44304,x44305)) % 174.01/173.89 [4431]~E(f34(x44311,x44312,x44313),f30(x44314,x44315)) % 174.01/173.89 [4432]~E(f33(x44321,x44322,x44323),f37(x44324,x44325)) % 174.01/173.89 [4433]~E(f33(x44331,x44332,x44333),f38(x44334,x44335)) % 174.01/173.89 [4434]~E(f33(x44341,x44342,x44343),f30(x44344,x44345)) % 174.01/173.89 [3821]E(f777(f172(x38211,x38212,x38213,x38214),x38215),f777(f231(f855(x38212),x38212,f777(x38213,x38215),f229(x38212)),f777(x38214,x38215))) % 174.01/173.89 [3907]E(f172(x39071,x39072,f172(x39071,x39072,x39073,x39074),x39075),f172(x39071,x39072,x39073,f172(x39071,x39072,x39074,x39075))) % 174.01/173.89 [3650]E(f777(f777(f253(x36501,x36502,x36503),x36504),x36505),f777(f777(x36504,f777(f242(x36501,x36502),x36505)),f777(f252(x36501,x36502),x36505))) % 174.01/173.89 [3676]E(f777(f231(x36761,x36762,x36763,x36764),f777(f229(x36762),x36765)),f777(x36764,x36765)) % 174.01/173.89 [3684]E(f777(f777(f777(f69(x36841,x36842,x36843),x36844),x36845),f182(f858(x36842,a845))),x36845) % 174.01/173.89 [3700]E(f777(f318(x37001,x37002,x37003,x37004),f777(f306(x37001,x37003),x37005)),f777(x37004,x37005)) % 174.01/173.89 [3701]E(f777(f319(x37011,x37012,x37013,x37014),f777(f315(x37011,x37013),x37015)),f777(x37014,x37015)) % 174.01/173.89 [3850]E(f232(x38501,x38502,x38503,x38504,f777(f229(x38502),x38505)),f777(x38504,x38505)) % 174.01/173.89 [3886]E(f320(x38861,x38862,x38863,x38864,f777(f306(x38861,x38862),x38865)),f777(f777(f84(a851),f777(x38863,x38865)),f777(a116,f4(a851)))) % 174.01/173.89 [3887]E(f320(x38871,x38872,x38873,x38874,f777(f315(x38872,x38871),x38875)),f777(f777(f84(a851),f777(x38874,x38875)),f777(a116,f4(a851)))) % 174.01/173.89 [3965]E(f777(f77(f855(x39651),f855(x39652),f855(x39653),f777(f198(x39651,x39652),x39654)),f777(f198(x39653,x39651),x39655)),f777(f198(x39653,x39652),f777(f77(x39651,x39652,x39653,x39654),x39655))) % 174.01/173.89 [3967]E(f777(f77(f852(x39671),f852(x39672),f852(x39673),f777(f145(x39671,x39672),x39674)),f777(f145(x39673,x39671),x39675)),f777(f145(x39673,x39672),f777(f77(x39671,x39672,x39673,x39674),x39675))) % 174.01/173.89 [4046]E(f89(x40461,f70(x40462,x40461,x40463,x40464,x40465)),f777(f777(f68(x40462,x40461,x40463),x40464),x40465)) % 174.01/173.89 [4082]E(f777(f777(f84(a851),f777(f777(f84(a851),f777(x40821,f777(f242(x40822,x40823),x40824))),f777(x40825,f777(f252(x40822,x40823),x40824)))),f777(a116,f4(a851))),f257(x40822,x40823,x40821,x40825,x40824)) % 174.01/173.89 [4269]E(f156(x42691,x42692,f777(f777(f11(x42691,f855(x42692),f855(x42692)),f777(f777(f22(x42691,f855(x42692),f858(f855(x42692),f855(x42692))),f777(f777(f12(a845,f858(f855(x42692),f858(f855(x42692),f855(x42692))),x42691),f100(f855(x42692))),x42693)),f777(f777(f12(x42692,f855(x42692),x42691),f229(x42692)),x42694))),f185(x42692)),x42695),f777(f777(f145(x42691,x42692),x42694),f777(f128(x42691,x42693),x42695))) % 174.01/173.89 [4475]~E(f777(f777(f777(f76(x44751,f855(x44752)),x44753),x44754),f777(f229(x44752),x44755)),f777(f20(f855(x44752),x44751),f185(x44752))) % 174.01/173.89 [3585]E(f777(f777(f161(x35851),x35852),f777(f777(f145(x35853,x35851),x35854),x35855)),f777(f777(f145(x35853,x35851),x35854),f777(f777(f161(x35853),x35852),x35855))) % 174.01/173.89 [3586]E(f777(f777(f130(x35861),x35862),f777(f777(f145(x35863,x35861),x35864),x35865)),f777(f777(f145(x35863,x35861),x35864),f777(f777(f130(x35863),x35862),x35865))) % 174.01/173.89 [3616]E(f777(f777(f145(x36161,x36162),x36163),f777(f777(f142(x36161),x36164),x36165)),f777(f777(f142(x36162),f777(x36163,x36164)),f777(f777(f145(x36161,x36162),x36163),x36165))) % 174.01/173.89 [3680]E(f777(f305(x36801,x36802,x36803),f777(f777(f304(x36801),x36804),x36805)),f777(f777(f304(x36802),f777(x36803,x36804)),f777(f305(x36801,x36802,x36803),x36805))) % 174.01/173.89 [3746]E(f777(f777(f169(x37461,x37462),f777(f777(f161(x37461),x37463),x37464)),f777(f777(f161(x37462),x37463),x37465)),f777(f777(f161(f857(x37461,x37462)),x37463),f777(f777(f169(x37461,x37462),x37464),x37465))) % 174.01/173.89 [3747]E(f777(f777(f169(x37471,x37472),f777(f777(f130(x37471),x37473),x37474)),f777(f777(f130(x37472),x37473),x37475)),f777(f777(f130(f857(x37471,x37472)),x37473),f777(f777(f169(x37471,x37472),x37474),x37475))) % 174.01/173.89 [3758]E(f777(f777(f150(x37581,f777(f777(f142(x37581),x37582),x37583)),f777(a116,x37584)),x37585),f777(f777(f142(x37581),x37582),f777(f777(f150(x37581,x37583),x37584),x37585))) % 174.01/173.89 [3761]E(f777(f231(f855(x37611),x37612,f185(x37611),x37613),f777(f777(f20(f855(x37612),x37614),f185(x37612)),x37615)),f185(x37611)) % 174.01/173.89 [3763]E(f777(f777(f127(x37631),f777(f777(f145(x37632,x37631),x37633),x37634)),f777(f777(f145(x37632,x37631),x37633),x37635)),f777(f777(f145(x37632,x37631),x37633),f777(f777(f127(x37632),x37634),x37635))) % 174.01/173.89 [3767]E(f777(f777(x37671,x37672),f777(f777(f245(x37673,x37674,x37671),x37672),x37675)),f777(f777(f245(x37673,x37674,x37671),x37672),f777(a116,x37675))) % 174.01/173.89 [3808]E(f777(f777(f283(x38081,x38082,x38083),f777(f280(x38082,x38081),x38084)),f777(f280(x38083,x38082),x38085)),f777(f280(x38083,x38081),f777(f777(f283(x38083,x38082,x38081),x38085),x38084))) % 174.01/173.89 [3839]E(f777(f777(f777(f175(f852(x38391),f852(x38391)),x38392),f143(x38391)),f777(f777(f145(x38393,x38391),x38394),x38395)),f777(f777(f145(x38393,x38391),x38394),f777(f777(f777(f175(f852(x38393),f852(x38393)),x38392),f143(x38393)),x38395))) % 174.01/173.89 [3840]E(f777(f777(f255(x38401,x38402,x38401,x38403),f777(f243(x38402,x38401),x38404)),x38405),f777(x38405,x38404)) % 174.01/173.89 [3864]E(f146(x38641,x38642,f777(f777(f145(x38643,x38641),x38644),x38645)),f146(x38643,f777(f77(x38641,a851,x38643,x38642),x38644),x38645)) % 174.01/173.89 [3930]E(f777(f777(f77(f855(x39301),f855(x39302),x39303,f777(f198(x39301,x39302),x39304)),f777(f20(f855(x39301),x39303),f185(x39301))),x39305),f185(x39302)) % 174.01/173.89 [3931]E(f164(f857(x39311,x39312),f777(f77(x39312,a845,f857(x39311,x39312),x39313),f252(x39311,x39312)),f777(f777(f169(x39311,x39312),x39314),x39315)),f777(f777(f169(x39311,x39312),x39314),f164(x39312,x39313,x39315))) % 174.01/173.89 [3936]E(f777(f305(x39361,x39362,f777(f777(f12(x39363,x39362,x39361),x39364),x39365)),f241(f858(x39361,a845))),f777(f305(x39363,x39362,x39364),f777(f305(x39361,x39363,x39365),f241(f858(x39361,a845))))) % 174.01/173.89 [3950]E(f164(f857(x39501,x39502),f777(f77(x39501,a845,f857(x39501,x39502),x39503),f242(x39501,x39502)),f777(f777(f169(x39501,x39502),x39504),x39505)),f777(f777(f169(x39501,x39502),f164(x39501,x39503,x39504)),x39505)) % 174.01/173.89 [3971]E(f777(f777(f105(f858(x39711,a845)),f777(f307(x39711,x39712,x39713),f777(f777(f304(x39712),x39714),f182(f858(x39712,a845))))),f777(f307(x39711,x39712,x39713),x39715)),f777(f307(x39711,x39712,x39713),f777(f777(f304(x39712),x39714),x39715))) % 174.01/173.89 [4031]E(f777(f777(f145(x40311,x40312),x40313),f164(x40311,f777(f77(x40312,a845,x40311,x40314),x40313),x40315)),f164(x40312,x40314,f777(f777(f145(x40311,x40312),x40313),x40315))) % 174.01/173.89 [4038]E(f777(f134(x40381,x40382,f777(f11(x40382,x40381,x40381),f777(f11(x40381,x40382,x40381),x40383)),x40384),f777(f144(x40382),f777(f144(x40382),x40385))),f777(f134(x40381,x40382,x40383,x40384),x40385)) % 174.01/173.89 [4039]E(f777(f777(f777(f76(x40391,f855(x40392)),f174(x40391,x40392,x40393,x40394)),x40395),f777(x40393,x40395)),f174(x40391,x40392,x40393,f777(f777(f304(x40391),x40395),x40394))) % 174.01/173.89 [4048]E(f777(f321(x40481,x40482,x40483,f777(f20(x40482,x40481),x40484),f777(f20(x40482,x40483),x40484)),x40485),x40484) % 174.01/173.89 [4107]E(f777(f231(f852(x41071),x41071,f156(x41072,x41071,x41073,x41074),f777(f777(f11(x41071,f852(x41071),f852(x41071)),f142(x41071)),f156(x41072,x41071,x41073,x41074))),f777(x41073,x41075)),f156(x41072,x41071,x41073,f777(f777(f142(x41072),x41075),x41074))) % 174.01/173.89 [4147]P1(f777(f777(f234(f858(x41471,a845)),f777(f305(x41472,x41471,x41473),f777(f777(f106(f858(x41472,a845)),x41474),x41475))),f777(f777(f106(f858(x41471,a845)),f777(f305(x41472,x41471,x41473),x41474)),f777(f305(x41472,x41471,x41473),x41475)))) % 174.01/173.89 [4148]P1(f777(f777(f234(f858(x41481,a845)),f777(f279(x41482,x41481,x41483),f777(f777(f106(f858(x41482,a845)),x41484),x41485))),f777(f777(f106(f858(x41481,a845)),f777(f279(x41482,x41481,x41483),x41484)),f777(f279(x41482,x41481,x41483),x41485)))) % 174.01/173.89 [4244]E(f777(f252(x42441,x42442),f777(f254(x42443,x42441,x42442,x42442,x42444,f41(x42442)),x42445)),f777(f252(x42443,x42442),x42445)) % 174.01/173.89 [4245]E(f777(f242(x42451,x42452),f777(f254(x42451,x42451,x42453,x42452,f41(x42451),x42454),x42455)),f777(f242(x42451,x42453),x42455)) % 174.01/173.89 [4327]P28(x43271,x43272,f777(f777(f304(f850(x43271)),f777(f777(f777(f95(x43271),f777(f777(f11(x43271,f858(a848,a848),f858(a848,a845)),f777(f777(f12(f858(a848,a845),f858(f858(a848,a848),f858(a848,a845)),x43271),f12(a848,a845,a848)),x43273)),f777(f777(f22(a848,a851,a848),f777(f777(f11(a848,a849,f858(a851,a848)),a191),x43274)),x43275))),f30(x43274,x43275)),x43273)),f182(f858(f850(x43271),a845)))) % 174.01/173.89 [4331]P28(x43311,x43312,f777(f777(f304(f850(x43311)),f777(f777(f777(f95(x43311),f777(f777(f11(x43311,f858(a848,a845),f858(a848,a845)),f777(f777(f12(f858(a848,f858(a845,a845)),f858(f858(a848,a845),f858(a848,a845)),x43311),f22(a848,a845,a845)),f777(f777(f12(f858(a848,a845),f858(a848,f858(a845,a845)),x43311),f777(f12(a845,f858(a845,a845),a848),a333)),x43313))),f777(f777(f12(a845,a845,a848),a330),x43314))),f37(x43314,x43315)),x43313)),f182(f858(f850(x43311),a845)))) % 174.01/173.89 [3433]E(f777(f777(f777(f777(f201(x34331),x34332),x34333),x34334),x34335),f187(x34331,x34332)) % 174.01/173.89 [3434]E(f777(f777(f777(f777(f205(x34341),x34342),x34343),x34344),x34345),f196(x34341,x34342)) % 174.01/173.89 [3478]E(f97(x34781,x34782,f777(f777(f777(f95(x34781),x34783),x34784),x34785)),f4(a851)) % 174.01/173.89 [3568]E(f777(f777(f777(f777(f76(x35681,x35682),x35683),x35684),x35685),x35684),x35685) % 174.01/173.89 [3798]E(f777(f777(f48(x37981,f858(x37982,a845)),f777(f777(f304(x37981),x37983),x37984)),x37985),f777(f777(f105(f858(x37982,a845)),f777(x37985,x37983)),f777(f777(f48(x37981,f858(x37982,a845)),x37984),x37985))) % 174.01/173.89 [3799]E(f777(f777(f49(x37991,f858(x37992,a845)),f777(f777(f304(x37991),x37993),x37994)),x37995),f777(f777(f106(f858(x37992,a845)),f777(x37995,x37993)),f777(f777(f49(x37991,f858(x37992,a845)),x37994),x37995))) % 174.01/173.89 [3857]E(f777(f777(f105(f858(x38571,a845)),f777(f305(x38572,x38571,x38573),x38574)),f777(f305(x38572,x38571,x38573),x38575)),f777(f305(x38572,x38571,x38573),f777(f777(f105(f858(x38572,a845)),x38574),x38575))) % 174.01/173.89 [3858]E(f777(f777(f105(f858(x38581,a845)),f777(f279(x38582,x38581,x38583),x38584)),f777(f279(x38582,x38581,x38583),x38585)),f777(f279(x38582,x38581,x38583),f777(f777(f105(f858(x38582,a845)),x38584),x38585))) % 174.01/173.89 [3859]E(f777(f777(f5(f858(x38591,a845)),f777(f307(x38591,x38592,x38593),x38594)),f777(f307(x38591,x38592,x38593),x38595)),f777(f307(x38591,x38592,x38593),f777(f777(f5(f858(x38592,a845)),x38594),x38595))) % 174.01/173.89 [3860]E(f777(f777(f105(f858(x38601,a845)),f777(f307(x38601,x38602,x38603),x38604)),f777(f307(x38601,x38602,x38603),x38605)),f777(f307(x38601,x38602,x38603),f777(f777(f105(f858(x38602,a845)),x38604),x38605))) % 174.01/173.89 [3861]E(f777(f777(f106(f858(x38611,a845)),f777(f307(x38611,x38612,x38613),x38614)),f777(f307(x38611,x38612,x38613),x38615)),f777(f307(x38611,x38612,x38613),f777(f777(f106(f858(x38612,a845)),x38614),x38615))) % 174.01/173.89 [3863]E(f174(x38631,x38632,f174(x38631,x38632,x38633,x38634),x38635),f174(x38631,x38632,x38633,f777(f777(f106(f858(x38631,a845)),x38634),x38635))) % 174.01/173.89 [3865]E(f120(x38651,x38652,f777(x38653,x38654),f777(f777(f11(x38651,a103,f853(x38652)),x38655),x38654)),f777(f194(x38651,x38652,x38653,x38655),x38654)) % 174.01/173.89 [3926]E(f777(f777(f150(x39261,f777(f777(f127(x39261),x39262),f777(f777(f142(x39261),x39263),x39264))),f777(f183(f852(x39261)),x39262)),x39265),f777(f777(f127(x39261),x39262),f777(f777(f142(x39261),x39265),x39264))) % 174.01/173.89 [3934]E(f777(f777(f49(x39341,f858(x39342,a845)),x39343),f777(f777(f12(f858(x39342,a845),f858(x39342,a845),x39341),f777(f304(x39342),x39344)),x39345)),f777(f777(f304(x39342),x39344),f777(f777(f49(x39341,f858(x39342,a845)),x39343),x39345))) % 174.01/173.89 [4006]E(f174(x40061,x40062,f777(f777(f777(f76(x40061,f855(x40062)),x40063),x40064),f777(f229(x40062),x40065)),f777(f83(f858(x40061,a845)),f777(f777(f304(x40061),x40064),f182(f858(x40061,a845))))),f174(x40061,x40062,x40063,f777(f83(f858(x40061,a845)),f777(f777(f304(x40061),x40064),f182(f858(x40061,a845)))))) % 174.01/173.89 [4092]E(f777(f777(f145(x40921,x40922),x40923),f777(f128(x40921,f777(f77(x40922,a845,x40921,x40924),x40923)),x40925)),f777(f128(x40922,x40924),f777(f777(f145(x40921,x40922),x40923),x40925))) % 174.01/173.89 [4099]E(f777(f183(f852(x40991)),f777(f128(x40991,x40992),f777(f777(f145(x40993,x40991),x40994),x40995))),f777(f183(f852(x40993)),f777(f128(x40993,f777(f77(x40991,a845,x40993,x40992),x40994)),x40995))) % 174.01/173.89 [4236]E(f777(f777(f105(f858(x42361,a845)),f777(f777(f5(f858(x42361,a845)),f171(x42361,x42362,x42363)),f777(f258(x42361),f777(f777(f11(x42361,f858(x42361,a845),a845),f336(x42361)),f777(f777(f5(f858(x42361,a845)),x42364),f171(x42361,x42362,x42365)))))),f777(f258(x42361),f777(f777(f11(x42361,f858(x42361,a845),a845),f336(x42361)),f777(f777(f106(f858(x42361,a845)),x42364),f171(x42361,x42362,x42365))))),f171(x42361,x42362,f80(x42361,f855(x42362),x42363,x42365,x42364))) % 174.01/173.89 [4308]E(f777(f147(f852(f857(x43081,x43082)),x43082,f117(f857(x43081,x43082)),f777(f777(f11(x43082,f858(f852(x43082),f852(f857(x43081,x43082))),f858(f852(x43082),f852(f857(x43081,x43082)))),f777(f777(f12(f858(f852(f857(x43081,x43082)),f852(f857(x43081,x43082))),f858(f858(f852(x43082),f852(f857(x43081,x43082))),f858(f852(x43082),f852(f857(x43081,x43082)))),x43082),f12(f852(f857(x43081,x43082)),f852(f857(x43081,x43082)),f852(x43082))),f777(f777(f12(f857(x43081,x43082),f858(f852(f857(x43081,x43082)),f852(f857(x43081,x43082))),x43082),f142(f857(x43081,x43082))),f777(f243(x43081,x43082),x43083)))),f777(f169(x43081,x43082),x43084))),x43085),f777(f777(f169(x43081,x43082),f777(f777(f142(x43081),x43083),x43084)),x43085)) % 174.01/173.89 [3793]E(f777(f777(f150(x37931,f777(f777(f150(x37931,x37932),x37933),x37934)),x37933),x37935),f777(f777(f150(x37931,x37932),x37933),x37935)) % 174.01/173.89 [3841]E(f777(f261(x38411,x38412),f777(f777(f304(f857(x38411,x38412)),f777(f777(f243(x38411,x38412),x38413),x38414)),x38415)),f777(f777(f304(x38412),x38414),f777(f261(x38411,x38412),x38415))) % 174.01/173.89 [3842]E(f777(f263(x38421,x38422),f777(f777(f304(f857(x38421,x38422)),f777(f777(f243(x38421,x38422),x38423),x38424)),x38425)),f777(f777(f304(x38421),x38423),f777(f263(x38421,x38422),x38425))) % 174.01/173.89 [3890]E(f123(x38901,x38902,f777(x38903,x38904),f777(f777(f11(x38901,a103,f853(f855(x38902))),x38905),x38904)),f777(f192(x38901,x38902,x38903,x38905),x38904)) % 174.01/173.89 [3919]E(f777(f777(f5(f858(f857(x39191,x39192),a845)),f777(f777(f250(x39191,x39192),x39193),x39194)),f777(f777(f250(x39191,x39192),x39195),x39194)),f777(f777(f250(x39191,x39192),f777(f777(f5(f858(x39191,a845)),x39193),x39195)),x39194)) % 174.01/173.89 [3920]E(f777(f777(f105(f858(f857(x39201,x39202),a845)),f777(f777(f250(x39201,x39202),x39203),x39204)),f777(f777(f250(x39201,x39202),x39205),x39204)),f777(f777(f250(x39201,x39202),f777(f777(f105(f858(x39201,a845)),x39203),x39205)),x39204)) % 174.01/173.89 [3921]E(f777(f777(f106(f858(f857(x39211,x39212),a845)),f777(f777(f250(x39211,x39212),x39213),x39214)),f777(f777(f250(x39211,x39212),x39215),x39214)),f777(f777(f250(x39211,x39212),f777(f777(f106(f858(x39211,a845)),x39213),x39215)),x39214)) % 174.01/173.89 [3984]E(f777(f777(f105(f858(x39841,a845)),f777(f777(f48(x39842,f858(x39841,a845)),x39843),x39844)),f777(f777(f48(x39842,f858(x39841,a845)),x39845),x39844)),f777(f777(f48(x39842,f858(x39841,a845)),f777(f777(f105(f858(x39842,a845)),x39843),x39845)),x39844)) % 174.01/173.89 [3985]E(f777(f777(f106(f858(x39851,a845)),f777(f777(f49(x39852,f858(x39851,a845)),x39853),x39854)),f777(f777(f49(x39852,f858(x39851,a845)),x39855),x39854)),f777(f777(f49(x39852,f858(x39851,a845)),f777(f777(f105(f858(x39852,a845)),x39853),x39855)),x39854)) % 174.01/173.89 [3999]E(f777(f777(f48(x39991,f858(x39992,a845)),x39993),f777(f777(f12(f858(x39992,a845),f858(x39992,a845),x39991),f777(f5(f858(x39992,a845)),x39994)),x39995)),f777(f777(f5(f858(x39992,a845)),x39994),f777(f777(f49(x39991,f858(x39992,a845)),x39993),x39995))) % 174.01/173.89 [4000]E(f777(f777(f48(x40001,f858(x40002,a845)),x40003),f777(f777(f12(f858(x40002,a845),f858(x40002,a845),x40001),f777(f106(f858(x40002,a845)),x40004)),x40005)),f777(f777(f106(f858(x40002,a845)),x40004),f777(f777(f48(x40001,f858(x40002,a845)),x40003),x40005))) % 174.01/173.89 [4001]E(f777(f777(f49(x40011,f858(x40012,a845)),x40013),f777(f777(f12(f858(x40012,a845),f858(x40012,a845),x40011),f777(f105(f858(x40012,a845)),x40014)),x40015)),f777(f777(f105(f858(x40012,a845)),x40014),f777(f777(f49(x40011,f858(x40012,a845)),x40013),x40015))) % 174.01/173.89 [4060]E(f177(f852(x40601),f777(f777(f142(x40601),x40602),x40603),f777(f777(f12(f852(x40601),f852(x40601),a851),f777(f142(x40601),x40604)),f777(f777(f11(a851,x40601,f852(x40601)),f150(x40601,x40603)),x40602)),x40605),f777(f777(f150(x40601,f777(f777(f142(x40601),x40604),x40603)),x40605),x40602)) % 174.01/173.89 [4064]E(f777(f777(f48(x40641,f858(f857(x40642,x40643),a845)),x40644),f777(f777(f12(f858(f857(x40643,x40642),a845),f858(f857(x40642,x40643),a845),x40641),f280(x40643,x40642)),x40645)),f777(f280(x40643,x40642),f777(f777(f48(x40641,f858(f857(x40643,x40642),a845)),x40644),x40645))) % 174.01/173.89 [4065]E(f777(f777(f49(x40651,f858(f857(x40652,x40653),a845)),x40654),f777(f777(f12(f858(f857(x40653,x40652),a845),f858(f857(x40652,x40653),a845),x40651),f280(x40653,x40652)),x40655)),f777(f280(x40653,x40652),f777(f777(f49(x40651,f858(f857(x40653,x40652),a845)),x40654),x40655))) % 174.01/173.89 [4118]E(f171(x41181,x41182,f777(f777(f22(x41181,f855(x41183),f855(x41182)),f777(f777(f12(f858(x41183,x41182),f858(f855(x41183),f855(x41182)),x41181),f198(x41183,x41182)),x41184)),x41185)),f171(x41181,x41183,x41185)) % 174.01/173.89 [4171]P1(f777(f777(f234(f858(x41711,a845)),f777(f777(f5(f858(x41711,a845)),f777(f305(x41712,x41711,x41713),x41714)),f777(f305(x41712,x41711,x41713),x41715))),f777(f305(x41712,x41711,x41713),f777(f777(f5(f858(x41712,a845)),x41714),x41715)))) % 174.01/173.89 [4312]E(f777(f147(f852(f857(x43121,x43122)),x43121,f117(f857(x43121,x43122)),f777(f777(f11(x43121,f858(f852(x43121),f852(f857(x43121,x43122))),f858(f852(x43121),f852(f857(x43121,x43122)))),f777(f777(f12(f858(f852(f857(x43121,x43122)),f852(f857(x43121,x43122))),f858(f858(f852(x43121),f852(f857(x43121,x43122))),f858(f852(x43121),f852(f857(x43121,x43122)))),x43121),f12(f852(f857(x43121,x43122)),f852(f857(x43121,x43122)),f852(x43121))),f777(f777(f12(f857(x43121,x43122),f858(f852(f857(x43121,x43122)),f852(f857(x43121,x43122))),x43121),f142(f857(x43121,x43122))),f777(f777(f11(x43121,x43122,f857(x43121,x43122)),f243(x43121,x43122)),x43123)))),f777(f777(f11(f852(x43121),f852(x43122),f852(f857(x43121,x43122))),f169(x43121,x43122)),x43124))),x43125),f777(f777(f169(x43121,x43122),x43125),f777(f777(f142(x43122),x43123),x43124))) % 174.01/173.89 [4329]E(f777(f134(f858(x43291,f855(x43292)),f857(x43291,x43292),f777(f777(f12(f858(x43291,f858(x43292,f858(x43291,f855(x43292)))),f858(f857(x43291,x43292),f858(x43291,f855(x43292))),f858(x43291,f855(x43292))),f253(x43291,x43292,f858(x43291,f855(x43292)))),f777(f777(f11(f858(x43291,f855(x43292)),f858(x43292,f855(x43292)),f858(x43291,f858(x43292,f858(x43291,f855(x43292))))),f777(f777(f12(f858(x43291,f858(f858(x43292,f855(x43292)),f858(x43292,f858(x43291,f855(x43292))))),f858(f858(x43292,f855(x43292)),f858(x43291,f858(x43292,f858(x43291,f855(x43292))))),f858(x43291,f855(x43292))),f11(x43291,f858(x43292,f855(x43292)),f858(x43292,f858(x43291,f855(x43292))))),f777(f777(f12(f858(x43291,f858(f855(x43292),f858(x43291,f855(x43292)))),f858(x43291,f858(f858(x43292,f855(x43292)),f858(x43292,f858(x43291,f855(x43292))))),f858(x43291,f855(x43292))),f777(f12(f858(f855(x43292),f858(x43291,f855(x43292))),f858(f858(x43292,f855(x43292)),f858(x43292,f858(x43291,f855(x43292)))),x43291),f12(f855(x43292),f858(x43291,f855(x43292)),x43292))),f76(x43291,f855(x43292))))),f229(x43292))),x43293),f777(f777(f169(x43291,x43292),x43294),x43295)),f172(x43291,x43292,x43293,f168(x43291,x43292,f777(f144(f857(x43291,x43292)),f777(f777(f169(x43291,x43292),x43294),x43295))))) % 174.01/173.89 [4025]E(f777(f777(f105(f858(x40251,a845)),f777(f279(x40252,x40251,x40253),x40254)),f777(f279(x40252,x40251,x40255),x40254)),f777(f279(x40252,x40251,f777(f777(f105(f858(f857(x40252,x40251),a845)),x40253),x40255)),x40254)) % 174.01/173.89 [4067]E(f777(f777(f127(f857(x40671,x40672)),f777(f777(f169(x40671,x40672),x40673),f777(f777(f161(x40672),f777(f183(f852(x40671)),x40673)),x40674))),f777(f777(f169(x40671,x40672),x40675),f777(f777(f130(x40672),f777(f183(f852(x40671)),x40673)),x40674))),f777(f777(f169(x40671,x40672),f777(f777(f127(x40671),x40673),x40675)),x40674)) % 174.01/173.89 [4096]E(f171(x40961,x40962,f172(x40961,x40962,x40963,f168(x40961,x40962,f777(f144(f857(x40961,x40962)),f777(f777(f169(x40961,x40962),x40964),x40965))))),f777(f777(f105(f858(x40961,a845)),f777(f160(x40961),f777(f777(f161(x40961),f777(f183(f852(x40962)),x40965)),x40964))),f171(x40961,x40962,x40963))) % 174.01/173.89 [4174]E(f777(f777(f250(x41741,x41742),x41743),f777(f777(f22(x41741,f858(x41742,a845),f858(x41742,a845)),f777(f777(f12(f858(x41742,a845),f858(f858(x41742,a845),f858(x41742,a845)),x41741),f5(f858(x41742,a845))),x41744)),x41745)),f777(f777(f5(f858(f857(x41741,x41742),a845)),f777(f777(f250(x41741,x41742),x41743),x41744)),f777(f777(f250(x41741,x41742),x41743),x41745))) % 174.01/173.89 [4175]E(f777(f777(f250(x41751,x41752),x41753),f777(f777(f22(x41751,f858(x41752,a845),f858(x41752,a845)),f777(f777(f12(f858(x41752,a845),f858(f858(x41752,a845),f858(x41752,a845)),x41751),f105(f858(x41752,a845))),x41754)),x41755)),f777(f777(f105(f858(f857(x41751,x41752),a845)),f777(f777(f250(x41751,x41752),x41753),x41754)),f777(f777(f250(x41751,x41752),x41753),x41755))) % 174.01/173.89 [4176]E(f777(f777(f250(x41761,x41762),x41763),f777(f777(f22(x41761,f858(x41762,a845),f858(x41762,a845)),f777(f777(f12(f858(x41762,a845),f858(f858(x41762,a845),f858(x41762,a845)),x41761),f106(f858(x41762,a845))),x41764)),x41765)),f777(f777(f106(f858(f857(x41761,x41762),a845)),f777(f777(f250(x41761,x41762),x41763),x41764)),f777(f777(f250(x41761,x41762),x41763),x41765))) % 174.01/173.89 [4180]E(f777(f777(f48(x41801,f858(x41802,a845)),x41803),f777(f777(f11(x41801,f858(x41802,a845),f858(x41802,a845)),f777(f777(f12(f858(x41802,a845),f858(f858(x41802,a845),f858(x41802,a845)),x41801),f5(f858(x41802,a845))),x41804)),x41805)),f777(f777(f5(f858(x41802,a845)),f777(f777(f48(x41801,f858(x41802,a845)),x41803),x41804)),x41805)) % 174.01/173.89 [4181]E(f777(f777(f48(x41811,f858(x41812,a845)),x41813),f777(f777(f11(x41811,f858(x41812,a845),f858(x41812,a845)),f777(f777(f12(f858(x41812,a845),f858(f858(x41812,a845),f858(x41812,a845)),x41811),f106(f858(x41812,a845))),x41814)),x41815)),f777(f777(f106(f858(x41812,a845)),f777(f777(f48(x41811,f858(x41812,a845)),x41813),x41814)),x41815)) % 174.01/173.89 [4182]E(f777(f777(f49(x41821,f858(x41822,a845)),x41823),f777(f777(f11(x41821,f858(x41822,a845),f858(x41822,a845)),f777(f777(f12(f858(x41822,a845),f858(f858(x41822,a845),f858(x41822,a845)),x41821),f105(f858(x41822,a845))),x41824)),x41825)),f777(f777(f105(f858(x41822,a845)),f777(f777(f49(x41821,f858(x41822,a845)),x41823),x41824)),x41825)) % 174.01/173.89 [4186]E(f777(f777(f48(x41861,f858(x41862,a845)),x41863),f777(f777(f22(x41861,f858(x41862,a845),f858(x41862,a845)),f777(f777(f12(f858(x41862,a845),f858(f858(x41862,a845),f858(x41862,a845)),x41861),f105(f858(x41862,a845))),x41864)),x41865)),f777(f777(f105(f858(x41862,a845)),f777(f777(f48(x41861,f858(x41862,a845)),x41863),x41864)),f777(f777(f48(x41861,f858(x41862,a845)),x41863),x41865))) % 174.01/173.89 [4187]E(f777(f777(f49(x41871,f858(x41872,a845)),x41873),f777(f777(f22(x41871,f858(x41872,a845),f858(x41872,a845)),f777(f777(f12(f858(x41872,a845),f858(f858(x41872,a845),f858(x41872,a845)),x41871),f106(f858(x41872,a845))),x41874)),x41875)),f777(f777(f106(f858(x41872,a845)),f777(f777(f49(x41871,f858(x41872,a845)),x41873),x41874)),f777(f777(f49(x41871,f858(x41872,a845)),x41873),x41875))) % 174.01/173.89 [4199]E(f777(f777(f48(x41991,f858(x41992,a845)),x41993),f777(f777(f22(x41991,f858(x41992,a845),f858(x41992,a845)),f777(f777(f12(f858(x41992,a845),f858(f858(x41992,a845),f858(x41992,a845)),x41991),f105(f858(x41992,a845))),x41994)),x41995)),f777(f777(f105(f858(x41992,a845)),f46(f858(x41992,a845),f777(f305(x41991,f858(x41992,a845),x41994),x41993))),f46(f858(x41992,a845),f777(f305(x41991,f858(x41992,a845),x41995),x41993)))) % 174.01/173.89 [4200]E(f777(f777(f49(x42001,f858(x42002,a845)),x42003),f777(f777(f22(x42001,f858(x42002,a845),f858(x42002,a845)),f777(f777(f12(f858(x42002,a845),f858(f858(x42002,a845),f858(x42002,a845)),x42001),f106(f858(x42002,a845))),x42004)),x42005)),f777(f777(f106(f858(x42002,a845)),f47(f858(x42002,a845),f777(f305(x42001,f858(x42002,a845),x42004),x42003))),f47(f858(x42002,a845),f777(f305(x42001,f858(x42002,a845),x42005),x42003)))) % 174.01/173.89 [4108]E(f777(f777(f127(f857(x41081,x41082)),f777(f777(f169(x41081,x41082),f777(f777(f161(x41081),f777(f183(f852(x41082)),x41083)),x41084)),x41083)),f777(f777(f169(x41081,x41082),f777(f777(f130(x41081),f777(f183(f852(x41082)),x41083)),x41084)),x41085)),f777(f777(f169(x41081,x41082),x41084),f777(f777(f127(x41082),x41083),x41085))) % 174.01/173.89 [4225]E(f89(x42251,f777(f777(f22(x42251,a845,a845),f777(f777(f12(a845,f858(a845,a845),x42251),a333),f777(f777(f11(x42251,f858(x42251,a845),a845),f336(x42251)),x42252))),f777(f777(f11(x42251,x42253,a845),f777(f777(f12(x42253,f858(x42253,a845),x42251),a332),x42254)),x42255))),f777(f81(x42251,x42253,x42252,x42254),x42255)) % 174.01/173.89 [4275]E(f777(f777(f90(a3,x42751),f777(f108(a3),f777(f777(f84(a3),x42752),a101))),f777(f777(f22(a3,x42751,x42751),f777(f777(f11(a3,x42751,f858(x42751,x42751)),f777(f777(f12(a845,f858(x42751,f858(x42751,x42751)),a3),f100(x42751)),a188)),f177(x42751,x42753,x42754,x42755))),f777(f777(f12(a851,x42751,a3),x42754),f777(f777(f11(a3,a851,a851),f777(f777(f12(a851,f858(a851,a851),a3),f84(a851)),a109)),x42755)))),f177(x42751,x42753,x42754,f777(f777(f84(a851),f777(f108(a851),x42752)),x42755))) % 174.01/173.89 [4309]E(f168(x43091,x43092,f777(f777(f145(f857(x43091,x43093),f857(x43091,x43092)),f777(f253(x43091,x43093,f857(x43091,x43092)),f777(f777(f11(x43091,f858(x43093,x43092),f858(x43093,f857(x43091,x43092))),f777(f777(f12(f858(x43092,f857(x43091,x43092)),f858(f858(x43093,x43092),f858(x43093,f857(x43091,x43092))),x43091),f12(x43092,f857(x43091,x43092),x43093)),f243(x43091,x43092))),x43094))),x43095)),f777(f77(f855(x43093),f855(x43092),x43091,f777(f198(x43093,x43092),x43094)),f168(x43091,x43093,x43095))) % 174.01/173.89 [4268]E(f171(x42681,x42682,f777(f777(f22(x42681,f855(x42682),f855(x42682)),f777(f777(f22(x42681,f855(x42682),f858(f855(x42682),f855(x42682))),f777(f777(f12(a845,f858(f855(x42682),f858(f855(x42682),f855(x42682))),x42681),f100(f855(x42682))),x42683)),x42684)),x42685)),f777(f777(f105(f858(x42681,a845)),f777(f777(f106(f858(x42681,a845)),f171(x42681,x42682,x42684)),f777(f258(x42681),x42683))),f777(f777(f106(f858(x42681,a845)),f171(x42681,x42682,x42685)),f777(f258(x42681),f777(f777(f12(a845,a845,x42681),a330),x42683))))) % 174.01/173.89 [4307]E(f777(f777(f90(a3,x43071),f777(f108(a3),f777(f777(f84(a3),x43072),a101))),f777(f777(f22(a3,x43071,x43071),f777(f777(f11(a3,x43071,f858(x43071,x43071)),f777(f777(f12(a845,f858(x43071,f858(x43071,x43071)),a3),f100(x43071)),a188)),f777(f176(x43071,x43073,x43074),x43075))),f777(f777(f22(a3,x43071,x43071),f777(f777(f12(a851,f858(x43071,x43071),a3),x43074),f777(f777(f11(a3,a851,a851),f777(f777(f12(a851,f858(a851,a851),a3),f84(a851)),a109)),x43075))),f777(f777(f12(a851,x43071,a3),f176(x43071,x43073,x43074)),f777(f777(f11(a3,a851,a851),f777(f777(f12(a851,f858(a851,a851),a3),f84(a851)),a109)),x43075))))),f777(f176(x43071,x43073,x43074),f777(f777(f84(a851),f777(f108(a851),x43072)),x43075))) % 174.01/173.89 [4356]E(f777(f258(f857(x43561,x43562)),f777(f253(x43561,x43562,a845),f777(f777(f12(f858(x43562,f858(x43563,a845)),f858(x43562,a845),x43561),f777(f12(f858(x43563,a845),a845,x43562),f91(x43563))),f777(f777(f11(x43561,f858(x43562,f858(x43563,a845)),f858(x43562,f858(x43563,a845))),f777(f777(f12(f858(f858(x43563,a845),f858(x43563,a845)),f858(f858(x43562,f858(x43563,a845)),f858(x43562,f858(x43563,a845))),x43561),f12(f858(x43563,a845),f858(x43563,a845),x43562)),f777(f777(f12(f858(x43563,f858(a845,a845)),f858(f858(x43563,a845),f858(x43563,a845)),x43561),f22(x43563,a845,a845)),f777(f777(f12(f858(x43563,a845),f858(x43563,f858(a845,a845)),x43561),f777(f12(a845,f858(a845,a845),x43563),a333)),f777(f777(f11(x43561,f858(f857(x43561,x43563),a845),f858(x43563,a845)),f777(f777(f12(f858(x43563,f858(f858(f857(x43561,x43563),a845),a845)),f858(f858(f857(x43561,x43563),a845),f858(x43563,a845)),x43561),f11(x43563,f858(f857(x43561,x43563),a845),a845)),f777(f777(f12(f858(x43563,f857(x43561,x43563)),f858(x43563,f858(f858(f857(x43561,x43563),a845),a845)),x43561),f777(f12(f857(x43561,x43563),f858(f858(f857(x43561,x43563),a845),a845),x43563),f336(f857(x43561,x43563)))),f243(x43561,x43563)))),x43564))))),f777(f777(f11(x43562,f858(f857(x43563,x43562),a845),f858(x43563,a845)),f777(f777(f12(f858(x43563,f858(f858(f857(x43563,x43562),a845),a845)),f858(f858(f857(x43563,x43562),a845),f858(x43563,a845)),x43562),f11(x43563,f858(f857(x43563,x43562),a845),a845)),f777(f777(f12(f858(x43563,f857(x43563,x43562)),f858(x43563,f858(f858(f857(x43563,x43562),a845),a845)),x43562),f777(f12(f857(x43563,x43562),f858(f858(f857(x43563,x43562),a845),a845),x43563),f336(f857(x43563,x43562)))),f777(f11(x43563,x43562,f857(x43563,x43562)),f243(x43563,x43562))))),x43565))))),f777(f777(f283(x43561,x43563,x43562),x43564),x43565)) % 174.01/173.89 [4457]~E(f34(x44571,x44572,x44573),f35(x44574,x44575,x44576)) % 174.01/173.89 [4460]~E(f33(x44601,x44602,x44603),f35(x44604,x44605,x44606)) % 174.01/173.89 [4461]~E(f33(x44611,x44612,x44613),f34(x44614,x44615,x44616)) % 174.01/173.89 [3951]E(f220(x39511,x39512,x39513,x39514,f217(x39511,x39512,x39515,x39516)),f777(f777(x39514,x39515),x39516)) % 174.01/173.89 [3952]E(f221(x39521,x39522,x39523,x39524,f217(x39521,x39522,x39525,x39526)),f777(f777(x39524,x39525),x39526)) % 174.01/173.89 [4215]E(f777(f77(f857(x42151,x42152),x42152,f857(x42153,x42154),f252(x42151,x42152)),f254(x42153,x42151,x42154,x42152,x42155,x42156)),f777(f77(x42154,x42152,f857(x42153,x42154),x42156),f252(x42153,x42154))) % 174.01/173.89 [4216]E(f777(f77(f857(x42161,x42162),x42161,f857(x42163,x42164),f242(x42161,x42162)),f254(x42163,x42161,x42164,x42162,x42165,x42166)),f777(f77(x42163,x42161,f857(x42163,x42164),x42165),f242(x42163,x42164))) % 174.01/173.89 [3817]E(f777(f777(f77(x38171,x38172,x38173,x38174),x38175),x38176),f777(x38174,f777(x38175,x38176))) % 174.01/173.89 [4014]E(f222(x40141,x40142,x40143,x40144,f217(x40141,x40142,x40145,x40146)),f777(f777(f84(a851),f777(f777(f84(a851),f777(x40143,x40145)),f777(x40144,x40146))),f777(a116,f4(a851)))) % 174.01/173.89 [4036]E(f777(f321(x40361,x40362,x40363,x40364,x40365),f777(f306(x40361,x40363),x40366)),f777(x40364,x40366)) % 174.01/173.89 [4037]E(f777(f321(x40371,x40372,x40373,x40374,x40375),f777(f315(x40373,x40371),x40376)),f777(x40375,x40376)) % 174.01/173.89 [4132]E(f322(x41321,x41322,x41323,x41324,x41325,f777(f306(x41321,x41323),x41326)),f777(x41324,x41326)) % 174.01/173.89 [4133]E(f322(x41331,x41332,x41333,x41334,x41335,f777(f315(x41333,x41331),x41336)),f777(x41335,x41336)) % 174.01/173.89 [3614]E(f777(f777(f253(x36141,x36142,x36143),x36144),f777(f777(f243(x36141,x36142),x36145),x36146)),f777(f777(x36144,x36145),x36146)) % 174.01/173.89 [3677]E(f777(f777(f777(f12(x36771,x36772,x36773),x36774),x36775),x36776),f777(x36774,f777(x36775,x36776))) % 174.01/173.89 [3678]E(f777(f777(f777(f11(x36781,x36782,x36783),x36784),x36785),x36786),f777(f777(x36784,x36786),x36785)) % 174.01/173.89 [3694]E(f777(f777(f777(f22(x36941,x36942,x36943),x36944),x36945),x36946),f777(f777(x36944,x36946),f777(x36945,x36946))) % 174.01/173.89 [3718]E(f777(f147(x37181,x37182,x37183,x37184),f777(f777(f142(x37182),x37185),x37186)),f777(f777(x37184,x37185),x37186)) % 174.01/173.89 [3820]E(f777(f777(f142(f857(x38201,x38202)),f777(f777(f243(x38201,x38202),x38203),x38204)),f777(f777(f169(x38201,x38202),x38205),x38206)),f777(f777(f169(x38201,x38202),f777(f777(f142(x38201),x38203),x38205)),f777(f777(f142(x38202),x38204),x38206))) % 174.01/173.89 [3822]E(f777(f777(f145(x38221,x38222),x38223),f777(f777(f150(x38221,x38224),x38225),x38226)),f777(f777(f150(x38222,f777(f777(f145(x38221,x38222),x38223),x38224)),x38225),f777(x38223,x38226))) % 174.01/173.89 [3845]E(f777(f777(f251(x38451,x38452,x38453,x38454),x38455),x38456),f777(x38454,f777(f777(f243(x38451,x38452),x38455),x38456))) % 174.01/173.89 [3862]E(f777(f134(x38621,x38622,x38623,x38624),f777(f777(f142(x38622),x38625),x38626)),f777(f134(x38621,x38622,x38623,f777(f777(x38623,x38624),x38625)),x38626)) % 174.01/173.89 [3891]E(f256(x38911,x38912,x38913,x38914,f777(f777(f243(x38911,x38912),x38915),x38916)),f777(f777(x38914,x38915),x38916)) % 174.01/173.89 [3977]E(f777(f777(f48(x39771,f858(x39772,a845)),x39773),f777(f77(x39774,f858(x39772,a845),x39771,x39775),x39776)),f777(f777(f48(x39774,f858(x39772,a845)),f777(f305(x39771,x39774,x39776),x39773)),x39775)) % 174.01/173.89 [4028]E(f777(f777(f145(x40281,x40282),x40283),f777(f777(f145(x40284,x40281),x40285),x40286)),f777(f777(f145(x40284,x40282),f777(f77(x40281,x40282,x40284,x40283),x40285)),x40286)) % 174.01/173.89 [4030]E(f777(f777(f198(x40301,x40302),x40303),f777(f777(f198(x40304,x40301),x40305),x40306)),f777(f777(f198(x40304,x40302),f777(f77(x40301,x40302,x40304,x40303),x40305)),x40306)) % 174.01/173.89 [4034]E(f777(f305(x40341,x40342,f777(f77(x40343,x40342,x40341,x40344),x40345)),x40346),f777(f305(x40343,x40342,x40344),f777(f305(x40341,x40343,x40345),x40346))) % 174.01/173.89 [4035]E(f777(f307(x40351,x40352,f777(f77(x40353,x40352,x40351,x40354),x40355)),x40356),f777(f307(x40351,x40353,x40355),f777(f307(x40353,x40352,x40354),x40356))) % 174.01/173.89 [4066]E(f172(x40661,x40662,x40663,f777(f777(f777(f76(x40661,f855(x40662)),x40664),x40665),f777(f229(x40662),x40666))),f777(f777(f777(f76(x40661,f855(x40662)),f172(x40661,x40662,x40663,x40664)),x40665),f777(f229(x40662),x40666))) % 174.01/173.89 [4068]E(f777(f134(x40681,x40682,x40683,f777(f134(x40681,x40682,x40683,x40684),x40685)),x40686),f777(f134(x40681,x40682,x40683,x40684),f777(f777(f127(x40682),x40685),x40686))) % 174.01/173.89 [4205]E(f777(f254(x42051,x42051,x42052,x42053,f41(x42051),x42054),f777(f777(f243(x42051,x42052),x42055),x42056)),f777(f777(f243(x42051,x42053),x42055),f777(x42054,x42056))) % 174.01/173.89 [4206]E(f777(f254(x42061,x42062,x42063,x42063,x42064,f41(x42063)),f777(f777(f243(x42061,x42063),x42065),x42066)),f777(f777(f243(x42062,x42063),f777(x42064,x42065)),x42066)) % 174.01/173.89 [4291]E(f777(f777(f145(f857(x42911,x42912),f857(x42911,x42913)),f777(f253(x42911,x42912,f857(x42911,x42913)),f777(f777(f11(x42911,f858(x42912,x42913),f858(x42912,f857(x42911,x42913))),f777(f777(f12(f858(x42913,f857(x42911,x42913)),f858(f858(x42912,x42913),f858(x42912,f857(x42911,x42913))),x42911),f12(x42913,f857(x42911,x42913),x42912)),f243(x42911,x42913))),x42914))),f777(f777(f169(x42911,x42912),x42915),x42916)),f777(f777(f169(x42911,x42913),x42915),f777(f777(f145(x42912,x42913),x42914),x42916))) % 174.01/173.89 [3682]E(f98(x36821,x36822,x36823,f777(f777(f777(f95(x36821),x36824),x36825),x36826)),f777(f777(f777(x36823,x36824),x36825),x36826)) % 174.01/173.89 [3683]E(f99(x36831,x36832,x36833,f777(f777(f777(f95(x36831),x36834),x36835),x36836)),f777(f777(f777(x36833,x36834),x36835),x36836)) % 174.01/173.89 [3873]E(f777(f777(f77(x38731,x38732,x38733,f777(f20(x38732,x38731),x38734)),x38735),x38736),x38734) % 174.01/173.89 [3909]E(f777(f305(x39091,x39092,x39093),f777(f305(x39094,x39091,x39095),x39096)),f777(f305(x39094,x39092,f777(f777(f12(x39091,x39092,x39094),x39093),x39095)),x39096)) % 174.01/173.89 [3915]E(f777(f777(f48(x39151,f858(x39152,a845)),f777(f305(x39153,x39151,x39154),x39155)),x39156),f777(f777(f48(x39153,f858(x39152,a845)),x39155),f777(f777(f12(x39151,f858(x39152,a845),x39153),x39156),x39154))) % 174.01/173.89 [3916]E(f777(f777(f49(x39161,f858(x39162,a845)),f777(f305(x39163,x39161,x39164),x39165)),x39166),f777(f777(f49(x39163,f858(x39162,a845)),x39165),f777(f777(f12(x39161,f858(x39162,a845),x39163),x39166),x39164))) % 174.01/173.89 [3917]E(f777(f777(f48(x39171,f858(x39172,a845)),x39173),f777(f777(f12(x39174,f858(x39172,a845),x39171),x39175),x39176)),f777(f777(f48(x39174,f858(x39172,a845)),f777(f305(x39171,x39174,x39176),x39173)),x39175)) % 174.01/173.89 [3918]E(f777(f777(f49(x39181,f858(x39182,a845)),x39183),f777(f777(f12(x39184,f858(x39182,a845),x39181),x39185),x39186)),f777(f777(f49(x39184,f858(x39182,a845)),f777(f305(x39181,x39184,x39186),x39183)),x39185)) % 174.01/173.89 [3979]E(f777(f777(f48(x39791,f858(x39792,a845)),x39793),f777(f777(f12(f858(x39794,a845),f858(x39792,a845),x39791),f305(x39794,x39792,x39795)),x39796)),f777(f305(x39794,x39792,x39795),f777(f777(f48(x39791,f858(x39794,a845)),x39793),x39796))) % 174.01/173.89 [3980]E(f777(f777(f48(x39801,f858(x39802,a845)),x39803),f777(f777(f12(f858(x39804,a845),f858(x39802,a845),x39801),f279(x39804,x39802,x39805)),x39806)),f777(f279(x39804,x39802,x39805),f777(f777(f48(x39801,f858(x39804,a845)),x39803),x39806))) % 174.01/173.89 [3981]E(f777(f777(f48(x39811,f858(x39812,a845)),x39813),f777(f777(f12(f858(x39814,a845),f858(x39812,a845),x39811),f307(x39812,x39814,x39815)),x39816)),f777(f307(x39812,x39814,x39815),f777(f777(f48(x39811,f858(x39814,a845)),x39813),x39816))) % 174.01/173.89 [3982]E(f777(f777(f49(x39821,f858(x39822,a845)),x39823),f777(f777(f12(f858(x39824,a845),f858(x39822,a845),x39821),f307(x39822,x39824,x39825)),x39826)),f777(f307(x39822,x39824,x39825),f777(f777(f49(x39821,f858(x39824,a845)),x39823),x39826))) % 174.01/173.89 [4073]E(f777(f134(x40731,x40732,f777(f11(x40732,x40731,x40731),x40733),x40734),f777(f144(x40732),f777(f777(f142(x40732),x40735),x40736))),f777(f777(x40733,x40735),f777(f134(x40731,x40732,f777(f11(x40732,x40731,x40731),x40733),x40734),f777(f144(x40732),x40736)))) % 174.01/173.89 [4134]E(f777(f777(f22(f857(x41341,x41342),x41342,x41343),f777(f777(f12(x41344,f858(x41342,x41343),f857(x41341,x41342)),x41345),f777(f777(f12(x41341,x41344,f857(x41341,x41342)),x41346),f242(x41341,x41342)))),f252(x41341,x41342)),f777(f253(x41341,x41342,x41343),f777(f777(f12(x41344,f858(x41342,x41343),x41341),x41345),x41346))) % 174.01/173.89 [4141]E(f777(f134(x41411,x41412,f777(f11(x41412,x41411,x41411),x41413),f777(f134(x41411,x41412,f777(f11(x41412,x41411,x41411),x41413),x41414),f777(f144(x41412),x41415))),f777(f144(x41412),x41416)),f777(f134(x41411,x41412,f777(f11(x41412,x41411,x41411),x41413),x41414),f777(f144(x41412),f777(f777(f127(x41412),x41416),x41415)))) % 174.01/173.89 [4143]E(f777(f777(f145(f857(x41431,x41432),f857(x41433,x41432)),f777(f253(x41431,x41432,f857(x41433,x41432)),f777(f777(f12(x41433,f858(x41432,f857(x41433,x41432)),x41431),f243(x41433,x41432)),x41434))),f777(f777(f169(x41431,x41432),x41435),x41436)),f777(f777(f169(x41433,x41432),f777(f777(f145(x41431,x41433),x41434),x41435)),x41436)) % 174.01/173.89 [4189]P1(f777(f777(f234(f858(x41891,a845)),f777(f279(x41892,x41891,x41893),f777(f777(f49(x41894,f858(x41892,a845)),x41895),x41896))),f777(f777(f49(x41894,f858(x41891,a845)),x41895),f777(f777(f12(f858(x41892,a845),f858(x41891,a845),x41894),f279(x41892,x41891,x41893)),x41896)))) % 174.01/173.89 [3992]E(f777(f777(f169(x39921,x39922),f777(f777(f150(x39921,x39923),x39924),f777(f242(x39921,x39922),x39925))),f777(f777(f150(x39922,x39926),x39924),f777(f252(x39921,x39922),x39925))),f777(f777(f150(f857(x39921,x39922),f777(f777(f169(x39921,x39922),x39923),x39926)),x39924),x39925)) % 174.01/173.89 [4055]E(f777(f777(f105(f858(f857(x40551,x40552),a845)),f777(f777(f283(x40551,x40553,x40552),x40554),x40555)),f777(f777(f283(x40551,x40553,x40552),x40554),x40556)),f777(f777(f283(x40551,x40553,x40552),x40554),f777(f777(f105(f858(f857(x40553,x40552),a845)),x40555),x40556))) % 174.01/173.89 [4155]E(f777(f777(f304(f857(x41551,x41552)),f777(f777(f243(x41551,x41552),x41553),x41554)),f777(f777(f105(f858(f857(x41551,x41552),a845)),f777(f777(f250(x41551,x41552),x41555),f777(f20(f858(x41552,a845),x41551),f777(f777(f304(x41552),x41554),x41556)))),f777(f777(f250(x41551,x41552),f777(f777(f304(x41551),x41553),x41555)),f777(f20(f858(x41552,a845),x41551),x41556)))),f777(f777(f250(x41551,x41552),f777(f777(f304(x41551),x41553),x41555)),f777(f20(f858(x41552,a845),x41551),f777(f777(f304(x41552),x41554),x41556)))) % 174.01/173.89 [4228]E(f777(f777(f106(f858(x42281,a845)),f777(f307(x42281,x42282,f777(f77(f857(x42282,x42283),x42282,x42281,f242(x42282,x42283)),x42284)),x42285)),f777(f307(x42281,x42283,f777(f77(f857(x42282,x42283),x42283,x42281,f252(x42282,x42283)),x42284)),x42286)),f777(f307(x42281,f857(x42282,x42283),x42284),f777(f777(f250(x42282,x42283),x42285),f777(f20(f858(x42283,a845),x42282),x42286)))) % 174.01/173.89 [3976]E(f777(f777(f777(f76(x39761,x39762),f777(f777(f777(f76(x39761,x39762),x39763),x39764),x39765)),x39764),x39766),f777(f777(f777(f76(x39761,x39762),x39763),x39764),x39766)) % 174.01/173.89 [4079]E(f777(f777(f105(f858(f857(x40791,x40792),a845)),f777(f777(f283(x40791,x40793,x40792),x40794),x40795)),f777(f777(f283(x40791,x40793,x40792),x40796),x40795)),f777(f777(f283(x40791,x40793,x40792),f777(f777(f105(f858(f857(x40791,x40793),a845)),x40794),x40796)),x40795)) % 174.01/173.89 [4213]E(f777(f777(f48(x42131,f858(x42132,a845)),x42133),f777(f777(f11(x42131,f858(x42134,f858(x42132,a845)),f858(x42132,a845)),f777(f777(f12(f858(x42134,a845),f858(f858(x42134,f858(x42132,a845)),f858(x42132,a845)),x42131),f48(x42134,f858(x42132,a845))),x42135)),x42136)),f777(f777(f48(x42134,f858(x42132,a845)),f777(f777(f48(x42131,f858(x42134,a845)),x42133),x42135)),x42136)) % 174.01/173.89 [4214]E(f777(f777(f49(x42141,f858(x42142,a845)),x42143),f777(f777(f11(x42141,f858(x42144,f858(x42142,a845)),f858(x42142,a845)),f777(f777(f12(f858(x42144,a845),f858(f858(x42144,f858(x42142,a845)),f858(x42142,a845)),x42141),f49(x42144,f858(x42142,a845))),x42145)),x42146)),f777(f777(f49(x42144,f858(x42142,a845)),f777(f777(f48(x42141,f858(x42144,a845)),x42143),x42145)),x42146)) % 174.01/173.89 [4263]E(f777(f253(x42631,x42632,f857(x42633,x42634)),f777(f777(f11(x42631,f858(x42632,x42634),f858(x42632,f857(x42633,x42634))),f777(f777(f12(f858(x42634,f857(x42633,x42634)),f858(f858(x42632,x42634),f858(x42632,f857(x42633,x42634))),x42631),f12(x42634,f857(x42633,x42634),x42632)),f777(f777(f12(x42633,f858(x42634,f857(x42633,x42634)),x42631),f243(x42633,x42634)),x42635))),x42636)),f254(x42631,x42633,x42632,x42634,x42635,x42636)) % 174.01/173.89 [4188]E(f777(f777(f777(f76(x41881,f855(x41882)),f174(x41881,x41882,x41883,f777(f777(f5(f858(x41881,a845)),x41884),f777(f777(f304(x41881),x41885),f182(f858(x41881,a845)))))),x41885),x41886),f777(f777(f777(f76(x41881,f855(x41882)),f174(x41881,x41882,x41883,x41884)),x41885),x41886)) % 174.01/173.89 [4286]E(f777(f305(x42861,x42862,f777(f777(f22(x42861,x42862,x42862),f777(f777(f22(x42861,x42862,f858(x42862,x42862)),f777(f777(f12(a845,f858(x42862,f858(x42862,x42862)),x42861),f100(x42862)),x42863)),x42864)),x42865)),x42866),f777(f777(f105(f858(x42862,a845)),f777(f305(x42861,x42862,x42864),f777(f777(f106(f858(x42861,a845)),x42866),f777(f258(x42861),x42863)))),f777(f305(x42861,x42862,x42865),f777(f777(f106(f858(x42861,a845)),x42866),f777(f258(x42861),f777(f777(f12(a845,a845,x42861),a330),x42863)))))) % 174.01/173.89 [4297]E(f777(f305(x42971,f857(x42972,x42973),f777(f777(f22(x42971,x42973,f857(x42972,x42973)),f777(f777(f12(x42972,f858(x42973,f857(x42972,x42973)),x42971),f243(x42972,x42973)),x42974)),x42975)),x42976),f777(f777(f250(x42972,x42973),f777(f305(x42971,x42972,x42974),x42976)),f777(f777(f12(f858(x42971,a845),f858(x42973,a845),x42972),f305(x42971,x42973,x42975)),f777(f777(f11(x42972,f858(x42971,a845),f858(x42971,a845)),f777(f777(f12(f858(x42971,a845),f858(f858(x42971,a845),f858(x42971,a845)),x42972),f106(f858(x42971,a845))),f777(f777(f12(f858(x42972,a845),f858(x42971,a845),x42972),f307(x42971,x42972,x42974)),f777(f777(f11(x42972,f858(x42972,a845),f858(x42972,a845)),f304(x42972)),f182(f858(x42972,a845)))))),x42976)))) % 174.01/173.89 [4246]E(f777(f252(x42461,x42462),f777(f254(x42463,x42461,x42464,x42462,x42465,x42466),x42467)),f777(x42466,f777(f252(x42463,x42464),x42467))) % 174.01/173.89 [4247]E(f777(f242(x42471,x42472),f777(f254(x42473,x42471,x42474,x42472,x42475,x42476),x42477)),f777(x42475,f777(f242(x42473,x42474),x42477))) % 174.01/173.89 [3953]E(f777(f777(f169(x39531,x39532),f777(f777(f150(x39531,x39533),x39534),x39535)),f777(f777(f150(x39532,x39536),x39534),x39537)),f777(f777(f150(f857(x39531,x39532),f777(f777(f169(x39531,x39532),x39533),x39536)),x39534),f777(f777(f243(x39531,x39532),x39535),x39537))) % 174.01/173.89 [4023]E(f777(f777(f777(f255(x40231,x40232,x40233,x40234),x40235),x40236),x40237),f777(f777(f253(x40232,x40233,x40234),x40236),f777(x40235,x40237))) % 174.01/173.89 [4033]E(f777(f777(f777(f255(x40331,x40332,x40333,x40334),x40335),x40336),x40337),f777(f777(x40336,f777(f242(x40332,x40333),f777(x40335,x40337))),f777(f252(x40332,x40333),f777(x40335,x40337)))) % 174.01/173.89 [4086]E(f777(f77(x40861,x40862,x40863,x40864),f777(f77(x40865,x40861,x40863,x40866),x40867)),f777(f77(x40865,x40862,x40863,f777(f77(x40861,x40862,x40865,x40864),x40866)),x40867)) % 174.01/173.89 [4150]E(f777(f77(f855(x41501),f855(x41502),x41503,f777(f198(x41501,x41502),x41504)),f777(f777(f777(f76(x41503,f855(x41501)),x41505),x41506),f777(f229(x41501),x41507))),f777(f777(f777(f76(x41503,f855(x41502)),f777(f77(f855(x41501),f855(x41502),x41503,f777(f198(x41501,x41502),x41504)),x41505)),x41506),f777(f229(x41502),f777(x41504,x41507)))) % 174.01/173.89 [4270]E(f777(f254(x42701,x42702,x42703,x42703,x42704,f41(x42703)),f777(f254(x42701,x42701,x42705,x42703,f41(x42701),x42706),x42707)),f777(f777(f243(x42702,x42703),f777(x42704,f777(f242(x42701,x42705),x42707))),f777(x42706,f777(f252(x42701,x42705),x42707)))) % 174.01/173.89 [4271]E(f777(f254(x42711,x42711,x42712,x42713,f41(x42711),x42714),f777(f254(x42715,x42711,x42712,x42712,x42716,f41(x42712)),x42717)),f777(f777(f243(x42711,x42713),f777(x42716,f777(f242(x42715,x42712),x42717))),f777(x42714,f777(f252(x42715,x42712),x42717)))) % 174.01/173.89 [4284]E(f777(f254(x42841,x42842,x42843,x42843,x42844,f41(x42843)),f777(f254(x42845,x42841,x42843,x42843,x42846,f41(x42843)),x42847)),f777(f254(x42845,x42842,x42843,x42843,f777(f77(x42841,x42842,x42845,x42844),x42846),f41(x42843)),x42847)) % 174.01/173.89 [4285]E(f777(f254(x42851,x42851,x42852,x42853,f41(x42851),x42854),f777(f254(x42851,x42851,x42855,x42852,f41(x42851),x42856),x42857)),f777(f254(x42851,x42851,x42855,x42853,f41(x42851),f777(f77(x42852,x42853,x42855,x42854),x42856)),x42857)) % 174.01/173.89 [4294]E(f777(f254(x42941,x42942,x42943,x42943,x42944,f41(x42943)),f777(f254(x42941,x42941,x42945,x42943,f41(x42941),x42946),x42947)),f777(f254(x42942,x42942,x42945,x42943,f41(x42942),x42946),f777(f254(x42941,x42942,x42945,x42945,x42944,f41(x42945)),x42947))) % 174.01/173.89 [3989]E(f777(f777(f283(x39891,x39892,x39893),f777(f777(f283(x39891,x39894,x39892),x39895),x39896)),x39897),f777(f777(f283(x39891,x39894,x39893),x39895),f777(f777(f283(x39894,x39892,x39893),x39896),x39897))) % 174.01/173.89 [4061]E(f777(f777(f253(x40611,x40612,x40613),f777(f77(x40614,f858(x40612,x40613),x40611,x40615),x40616)),x40617),f777(f777(x40615,f777(x40616,f777(f242(x40611,x40612),x40617))),f777(f252(x40611,x40612),x40617))) % 174.01/173.89 [4111]E(f777(f77(x41111,x41112,x41113,x41114),f777(f777(f777(f76(x41113,x41111),x41115),x41116),x41117)),f777(f777(f777(f76(x41113,x41112),f777(f77(x41111,x41112,x41113,x41114),x41115)),x41116),f777(x41114,x41117))) % 174.01/173.89 [4146]E(f777(f134(x41461,x41462,f777(f11(x41462,x41461,x41461),x41463),x41464),f777(f144(x41462),f777(f777(f145(x41465,x41462),x41466),x41467))),f777(f134(x41461,x41465,f777(f11(x41465,x41461,x41461),f777(f77(x41462,f858(x41461,x41461),x41465,x41463),x41466)),x41464),f777(f144(x41465),x41467))) % 174.01/173.89 [4151]E(f321(x41511,f855(x41512),x41513,f777(f77(f855(x41514),f855(x41512),x41511,f777(f198(x41514,x41512),x41515)),x41516),f777(f77(f855(x41514),f855(x41512),x41513,f777(f198(x41514,x41512),x41515)),x41517)),f777(f77(f855(x41514),f855(x41512),f859(x41511,x41513),f777(f198(x41514,x41512),x41515)),f321(x41511,f855(x41514),x41513,x41516,x41517))) % 174.01/173.89 [4087]E(f777(f777(f48(x40871,f858(f857(x40872,x40873),a845)),x40874),f777(f777(f12(f858(f857(x40875,x40873),a845),f858(f857(x40872,x40873),a845),x40871),f777(f283(x40872,x40875,x40873),x40876)),x40877)),f777(f777(f283(x40872,x40875,x40873),x40876),f777(f777(f48(x40871,f858(f857(x40875,x40873),a845)),x40874),x40877))) % 174.01/173.89 [4122]E(f172(x41221,x41222,f777(f777(f777(f76(x41221,f855(x41222)),x41223),x41224),f777(f229(x41222),x41225)),f168(x41221,x41222,f777(f144(f857(x41221,x41222)),f777(f777(f169(x41221,x41222),x41226),x41227)))),f172(x41221,x41222,x41223,f168(x41221,x41222,f777(f144(f857(x41221,x41222)),f777(f777(f169(x41221,x41222),f777(f777(f142(x41221),x41224),x41226)),f777(f777(f142(x41222),x41225),x41227)))))) % 174.01/173.89 [4233]E(f777(f777(f48(x42331,f858(f857(x42332,x42333),a845)),x42334),f777(f777(f11(x42331,f858(f857(x42335,x42333),a845),f858(f857(x42332,x42333),a845)),f777(f777(f12(f858(f857(x42332,x42335),a845),f858(f858(f857(x42335,x42333),a845),f858(f857(x42332,x42333),a845)),x42331),f283(x42332,x42335,x42333)),x42336)),x42337)),f777(f777(f283(x42332,x42335,x42333),f777(f777(f48(x42331,f858(f857(x42332,x42335),a845)),x42334),x42336)),x42337)) % 174.01/173.89 [4234]E(f777(f134(x42341,x42342,f777(f777(f11(x42341,f858(x42342,x42343),f858(x42342,x42341)),f777(f777(f12(f858(x42343,x42341),f858(f858(x42342,x42343),f858(x42342,x42341)),x42341),f12(x42343,x42341,x42342)),x42344)),x42345),x42346),x42347),f777(f134(x42341,x42343,x42344,x42346),f777(f777(f145(x42342,x42343),x42345),x42347))) % 174.01/173.89 [4295]E(f777(f777(f49(x42951,f858(x42952,a845)),x42953),f777(f777(f12(f858(x42954,f858(x42952,a845)),f858(x42952,a845),x42951),f777(f49(x42954,f858(x42952,a845)),x42955)),f777(f777(f11(x42951,f858(x42954,f858(x42952,a845)),f858(x42954,f858(x42952,a845))),f777(f777(f12(f858(f858(x42952,a845),f858(x42952,a845)),f858(f858(x42954,f858(x42952,a845)),f858(x42954,f858(x42952,a845))),x42951),f12(f858(x42952,a845),f858(x42952,a845),x42954)),f777(f777(f12(f858(x42952,a845),f858(f858(x42952,a845),f858(x42952,a845)),x42951),f105(f858(x42952,a845))),x42956))),x42957))),f777(f777(f105(f858(x42952,a845)),f777(f777(f49(x42951,f858(x42952,a845)),x42953),x42956)),f777(f777(f49(x42954,f858(x42952,a845)),x42955),x42957))) % 174.01/173.89 [4296]E(f777(f777(f48(x42961,f858(x42962,a845)),x42963),f777(f777(f12(f858(x42964,f858(x42962,a845)),f858(x42962,a845),x42961),f777(f48(x42964,f858(x42962,a845)),x42965)),f777(f777(f11(x42961,f858(x42964,f858(x42962,a845)),f858(x42964,f858(x42962,a845))),f777(f777(f12(f858(f858(x42962,a845),f858(x42962,a845)),f858(f858(x42964,f858(x42962,a845)),f858(x42964,f858(x42962,a845))),x42961),f12(f858(x42962,a845),f858(x42962,a845),x42964)),f777(f777(f12(f858(x42962,a845),f858(f858(x42962,a845),f858(x42962,a845)),x42961),f106(f858(x42962,a845))),x42966))),x42967))),f777(f777(f106(f858(x42962,a845)),f777(f777(f48(x42961,f858(x42962,a845)),x42963),x42966)),f777(f777(f48(x42964,f858(x42962,a845)),x42965),x42967))) % 174.01/173.89 [4289]E(f194(x42891,x42892,f777(f777(f777(x42893,x42894),x42895),x42896),f777(f777(f11(x42891,f857(a103,a103),f858(a103,f853(x42892))),f777(f777(f11(x42891,a103,f858(f857(a103,a103),f858(a103,f853(x42892)))),f777(f777(f11(x42891,a103,f858(a103,f858(f857(a103,a103),f858(a103,f853(x42892))))),x42897),x42894)),x42895)),x42896)),f777(f777(f777(f206(x42891,x42892,x42893,x42897),x42894),x42895),x42896)) % 174.01/173.89 [4302]E(f195(x43021,x43022,f777(f777(f777(x43023,x43024),x43025),x43026),f777(f777(f11(x43021,f857(a103,a103),f858(a103,f853(x43022))),f777(f777(f11(x43021,a103,f858(f857(a103,a103),f858(a103,f853(x43022)))),f777(f777(f11(x43021,a103,f858(a103,f858(f857(a103,a103),f858(a103,f853(x43022))))),x43027),x43024)),x43025)),x43026)),f208(x43021,x43022,x43023,x43027,x43024,x43025,x43026)) % 174.01/173.89 [4293]E(f192(x42931,x42932,f777(f777(f777(x42933,x42934),x42935),x42936),f777(f777(f11(x42931,f857(a103,a103),f858(a103,f853(f855(x42932)))),f777(f777(f11(x42931,a103,f858(f857(a103,a103),f858(a103,f853(f855(x42932))))),f777(f777(f11(x42931,a103,f858(a103,f858(f857(a103,a103),f858(a103,f853(f855(x42932)))))),x42937),x42934)),x42935)),x42936)),f777(f777(f777(f202(x42931,x42932,x42933,x42937),x42934),x42935),x42936)) % 174.01/173.89 [4304]E(f193(x43041,x43042,f777(f777(f777(x43043,x43044),x43045),x43046),f777(f777(f11(x43041,f857(a103,a103),f858(a103,f853(f855(x43042)))),f777(f777(f11(x43041,a103,f858(f857(a103,a103),f858(a103,f853(f855(x43042))))),f777(f777(f11(x43041,a103,f858(a103,f858(f857(a103,a103),f858(a103,f853(f855(x43042)))))),x43047),x43044)),x43045)),x43046)),f204(x43041,x43042,x43043,x43047,x43044,x43045,x43046)) % 174.01/173.89 [4207]E(f777(f254(x42071,x42072,x42073,x42074,x42075,x42076),f777(f777(f243(x42071,x42073),x42077),x42078)),f777(f777(f243(x42072,x42074),f777(x42075,x42077)),f777(x42076,x42078))) % 174.01/173.89 [4306]E(f777(f777(f145(f857(x43061,x43062),f857(x43063,x43064)),f777(f253(x43061,x43062,f857(x43063,x43064)),f777(f777(f11(x43061,f858(x43062,x43064),f858(x43062,f857(x43063,x43064))),f777(f777(f12(f858(x43064,f857(x43063,x43064)),f858(f858(x43062,x43064),f858(x43062,f857(x43063,x43064))),x43061),f12(x43064,f857(x43063,x43064),x43062)),f777(f777(f12(x43063,f858(x43064,f857(x43063,x43064)),x43061),f243(x43063,x43064)),x43065))),x43066))),f777(f777(f169(x43061,x43062),x43067),x43068)),f777(f777(f169(x43063,x43064),f777(f777(f145(x43061,x43063),x43065),x43067)),f777(f777(f145(x43062,x43064),x43066),x43068))) % 174.01/173.89 [4310]E(f777(f777(f145(f857(x43101,x43102),x43103),f777(f253(x43101,x43102,x43103),f777(f777(f12(f858(x43102,f857(x43101,x43104)),f858(x43102,x43103),x43101),f777(f12(f857(x43101,x43104),x43103,x43102),x43105)),f777(f777(f11(x43101,f858(x43102,x43104),f858(x43102,f857(x43101,x43104))),f777(f777(f12(f858(x43104,f857(x43101,x43104)),f858(f858(x43102,x43104),f858(x43102,f857(x43101,x43104))),x43101),f12(x43104,f857(x43101,x43104),x43102)),f243(x43101,x43104))),x43106)))),f777(f777(f169(x43101,x43102),x43107),x43108)),f777(f777(f145(f857(x43101,x43104),x43103),x43105),f777(f777(f169(x43101,x43104),x43107),f777(f777(f145(x43102,x43104),x43106),x43108)))) % 174.01/173.89 [4238]E(f777(f777(f145(f857(x42381,x42382),x42383),f777(f253(x42381,x42382,x42383),f777(f777(f12(f858(x42382,f857(x42384,x42382)),f858(x42382,x42383),x42381),f777(f12(f857(x42384,x42382),x42383,x42382),x42385)),f777(f777(f12(x42384,f858(x42382,f857(x42384,x42382)),x42381),f243(x42384,x42382)),x42386)))),f777(f777(f169(x42381,x42382),x42387),x42388)),f777(f777(f145(f857(x42384,x42382),x42383),x42385),f777(f777(f169(x42384,x42382),f777(f777(f145(x42381,x42384),x42386),x42387)),x42388))) % 174.01/173.89 [4198]E(f777(f777(f253(x41981,x41982,x41983),f777(f777(f12(f858(x41982,f857(x41984,x41985)),f858(x41982,x41983),x41981),f777(f12(f857(x41984,x41985),x41983,x41982),f777(f253(x41984,x41985,x41983),x41986))),x41987)),x41988),f777(f777(f253(x41984,x41985,x41983),x41986),f777(f777(f253(x41981,x41982,f857(x41984,x41985)),x41987),x41988))) % 174.01/173.89 [4311]E(f777(f777(f48(f857(x43111,x43112),f858(f857(x43113,x43114),a845)),f777(f777(f250(x43111,x43112),x43115),f777(f20(f858(x43112,a845),x43111),x43116))),f777(f253(x43111,x43112,f858(f857(x43113,x43114),a845)),f777(f777(f11(x43111,f858(x43112,f858(x43113,f858(x43114,a845))),f858(x43112,f858(f857(x43113,x43114),a845))),f777(f777(f12(f858(f858(x43113,f858(x43114,a845)),f858(f857(x43113,x43114),a845)),f858(f858(x43112,f858(x43113,f858(x43114,a845))),f858(x43112,f858(f857(x43113,x43114),a845))),x43111),f12(f858(x43113,f858(x43114,a845)),f858(f857(x43113,x43114),a845),x43112)),f777(f777(f12(f858(x43113,a845),f858(f858(x43113,f858(x43114,a845)),f858(f857(x43113,x43114),a845)),x43111),f250(x43113,x43114)),x43117))),f777(f777(f12(f858(x43114,a845),f858(x43113,f858(x43114,a845)),x43112),f20(f858(x43114,a845),x43113)),x43118)))),f777(f777(f250(x43113,x43114),f777(f777(f48(x43111,f858(x43113,a845)),x43115),x43117)),f777(f20(f858(x43114,a845),x43113),f777(f777(f48(x43112,f858(x43114,a845)),x43116),x43118)))) % 174.01/173.89 [4341]E(f39(x43411,x43412,x43413,x43414,x43415,x43416,x43417,x43418,x43419,a27),x43412) % 174.01/173.89 [4342]E(f40(x43421,x43422,x43423,x43424,x43425,x43426,x43427,x43428,x43429,a27),x43422) % 174.01/173.89 [4252]E(f777(f777(f255(x42521,x42522,x42523,x42524),f777(f777(f255(x42521,x42525,x42526,f857(x42522,x42523)),x42527),x42528)),x42529),f777(f777(f255(x42521,x42525,x42526,x42524),x42527),f777(f777(f11(x42525,f858(x42522,f858(x42523,x42524)),f858(x42526,x42524)),f777(f777(f12(f858(x42526,f857(x42522,x42523)),f858(f858(x42522,f858(x42523,x42524)),f858(x42526,x42524)),x42525),f255(x42526,x42522,x42523,x42524)),x42528)),x42529))) % 174.01/173.89 [4343]E(f39(x43431,x43432,x43433,x43434,x43435,x43436,x43437,x43438,x43439,f777(a29,x434310)),f777(x43438,x434310)) % 174.01/173.89 [4344]E(f40(x43441,x43442,x43443,x43444,x43445,x43446,x43447,x43448,x43449,f777(a29,x434410)),f777(x43448,x434410)) % 174.01/173.89 [4282]E(f777(f77(f857(x42821,x42822),f857(x42823,x42824),f857(x42825,x42826),f254(x42821,x42823,x42822,x42824,x42827,x42828)),f254(x42825,x42821,x42826,x42822,x42829,x428210)),f254(x42825,x42823,x42826,x42824,f777(f77(x42821,x42823,x42825,x42827),x42829),f777(f77(x42822,x42824,x42826,x42828),x428210))) % 174.01/173.89 [4345]E(f39(x43451,x43452,x43453,x43454,x43455,x43456,x43457,x43458,x43459,f37(x434510,x434511)),f777(f777(x43457,x434510),x434511)) % 174.01/173.89 [4346]E(f39(x43461,x43462,x43463,x43464,x43465,x43466,x43467,x43468,x43469,f38(x434610,x434611)),f777(f777(x43465,x434610),x434611)) % 174.01/173.89 [4347]E(f39(x43471,x43472,x43473,x43474,x43475,x43476,x43477,x43478,x43479,f30(x434710,x434711)),f777(f777(x43473,x434710),x434711)) % 174.01/173.89 [4348]E(f40(x43481,x43482,x43483,x43484,x43485,x43486,x43487,x43488,x43489,f30(x434810,x434811)),f777(f777(x43483,x434810),x434811)) % 174.01/173.89 [4354]E(f777(f777(f777(x43541,x43542),x43543),f40(x43544,x43545,x43546,x43547,x43548,x43549,x43541,x435410,x435411,x43543)),f40(x43544,x43545,x43546,x43547,x43548,x43549,x43541,x435410,x435411,f37(x43542,x43543))) % 174.01/173.89 [4358]E(f777(f777(f777(f777(x43581,x43582),x43583),f40(x43584,x43585,x43586,x43587,x43581,x43588,x43589,x435810,x435811,x43582)),f40(x43584,x43585,x43586,x43587,x43581,x43588,x43589,x435810,x435811,x43583)),f40(x43584,x43585,x43586,x43587,x43581,x43588,x43589,x435810,x435811,f38(x43582,x43583))) % 174.01/173.89 [4287]E(f777(f254(x42871,x42872,x42873,x42874,x42875,x42876),f777(f254(x42877,x42871,x42878,x42873,x42879,x428710),x428711)),f777(f254(x42877,x42872,x42878,x42874,f777(f77(x42871,x42872,x42877,x42875),x42879),f777(f77(x42873,x42874,x42878,x42876),x428710)),x428711)) % 174.01/173.89 [4355]E(f777(f777(f777(f777(x43551,x43552),x43553),x43554),f40(x43555,x43556,x43557,x43551,x43558,x43559,x435510,x435511,x435512,x43554)),f40(x43555,x43556,x43557,x43551,x43558,x43559,x435510,x435511,x435512,f34(x43552,x43553,x43554))) % 174.01/173.89 [4359]E(f777(f777(f777(f777(f777(x43591,x43592),x43593),x43594),f40(x43595,x43596,x43597,x43598,x43599,x43591,x435910,x435911,x435912,x43593)),f40(x43595,x43596,x43597,x43598,x43599,x43591,x435910,x435911,x435912,x43594)),f40(x43595,x43596,x43597,x43598,x43599,x43591,x435910,x435911,x435912,f35(x43592,x43593,x43594))) % 174.01/173.89 [4349]E(f39(x43491,x43492,x43493,x43494,x43495,x43496,x43497,x43498,x43499,f35(x434910,x434911,x434912)),f777(f777(f777(x43496,x434910),x434911),x434912)) % 174.01/173.89 [4350]E(f39(x43501,x43502,x43503,x43504,x43505,x43506,x43507,x43508,x43509,f34(x435010,x435011,x435012)),f777(f777(f777(x43504,x435010),x435011),x435012)) % 174.01/173.89 [4351]E(f39(x43511,x43512,x43513,x43514,x43515,x43516,x43517,x43518,x43519,f33(x435110,x435111,x435112)),f777(f777(f777(x43519,x435110),x435111),x435112)) % 174.01/173.89 [4352]E(f40(x43521,x43522,x43523,x43524,x43525,x43526,x43527,x43528,x43529,f33(x435210,x435211,x435212)),f777(f777(f777(x43529,x435210),x435211),x435212)) % 174.01/173.89 [4567]~P142(a331,a866)+P1(f777(a2,a866)) % 174.01/173.89 [6368]P13(a5000)+P1(f777(f777(f336(f857(a847,a846)),a697),f777(f160(f857(a847,a846)),a31))) % 174.01/173.89 [8411]P13(a5000)+~P1(f777(f777(f253(a847,a846,a845),f777(f20(f858(a846,a845),a847),a28)),a697)) % 174.01/173.89 [4488]~P59(x44881)+P59(f855(x44881)) % 174.01/173.89 [4491]~P138(x44911)+~E(f82(x44911),f4(x44911)) % 174.01/173.89 [4493]~E(x44931,f4(a103))+E(f777(a25,x44931),f4(a3)) % 174.01/173.89 [4494]~E(x44941,f4(a3))+E(f86(a3,x44941),f4(a3)) % 174.01/173.89 [4500]~P2(x45001)+P33(x45001,f4(x45001)) % 174.01/173.89 [4502]~P100(x45021)+P18(x45021,f117(x45021)) % 174.01/173.89 [4511]P1(x45111)+P1(f777(a330,x45111)) % 174.01/173.89 [4552]~P2(x45521)+~P33(x45521,f82(x45521)) % 174.01/173.89 [4597]~P1(x45971)+~P1(f777(a330,x45971)) % 174.01/173.89 [4621]E(f777(a109,x46211),f4(a851))+~P1(f777(a188,x46211)) % 174.01/173.89 [4681]~P91(x46811)+P19(x46811,x46811,f85(x46811)) % 174.01/173.89 [4682]~P100(x46821)+P19(x46821,x46821,f238(x46821)) % 174.01/173.89 [4683]~P100(x46831)+P19(x46831,x46831,f181(x46831)) % 174.01/173.89 [4684]~P92(x46841)+P19(x46841,x46841,f105(x46841)) % 174.01/173.89 [4685]~P98(x46851)+P19(x46851,x46851,f106(x46851)) % 174.01/173.89 [4686]~P64(x46861)+P20(x46861,x46861,f85(x46861)) % 174.01/173.89 [4498]E(x44981,f4(a851))+E(f777(a116,f556(x44981)),x44981) % 174.01/173.89 [4499]~E(x44991,f4(a851))+E(f777(f104(a3),x44991),f4(a3)) % 174.01/173.89 [4505]~P88(x45051)+E(f777(f108(x45051),a87),f4(x45051)) % 174.01/173.89 [4507]~E(f602(x45071),f4(a851))+E(f777(f157(a851),x45071),f4(a851)) % 174.01/173.89 [4508]~P102(x45081)+E(f236(x45081,f234(x45081)),f238(x45081)) % 174.01/173.89 [4509]~P102(x45091)+E(f237(x45091,f234(x45091)),f181(x45091)) % 174.01/173.89 [4510]~P82(x45101)+E(f86(x45101,f4(x45101)),f4(x45101)) % 174.01/173.89 [4517]~P2(x45171)+E(f777(f104(x45171),f4(a851)),f4(x45171)) % 174.01/173.89 [4518]~P2(x45181)+E(f777(f104(x45181),f82(a851)),f82(x45181)) % 174.01/173.89 [4519]~P133(x45191)+E(f777(f107(x45191),f4(a3)),f4(x45191)) % 174.01/173.89 [4520]~P133(x45201)+E(f777(f107(x45201),f82(a3)),f82(x45201)) % 174.01/173.89 [4521]E(x45211,f4(a851))+~E(f777(f104(a3),x45211),f4(a3)) % 174.01/173.89 [4546]~P69(x45461)+E(f777(f83(x45461),f4(x45461)),f4(x45461)) % 174.01/173.89 [4547]~P90(x45471)+E(f777(f83(x45471),f241(x45471)),f182(x45471)) % 174.01/173.89 [4548]~P90(x45481)+E(f777(f83(x45481),f182(x45481)),f241(x45481)) % 174.01/173.89 [4549]~P79(x45491)+E(f777(f79(x45491),f4(x45491)),f4(x45491)) % 174.01/173.89 [4550]~P110(x45501)+E(f777(f79(x45501),f82(x45501)),f82(x45501)) % 174.01/173.89 [4551]~P67(x45511)+E(f777(f157(x45511),f117(x45511)),f4(x45511)) % 174.01/173.89 [4573]~P35(x45731)+P38(f777(f160(a3),x45731)) % 174.01/173.89 [4602]~P88(x46021)+E(f777(f83(x46021),f82(x46021)),f777(f108(x46021),a101)) % 174.01/173.89 [4620]~P88(x46201)+P33(x46201,f777(f108(x46201),a87)) % 174.01/173.89 [4645]P35(x46451)+~P38(f777(f160(a3),x46451)) % 174.01/173.89 [4687]E(f777(f104(a3),f777(a109,x46871)),x46871)+P1(f777(a188,x46871)) % 174.01/173.89 [4753]~P105(x47531)+E(f245(x47531,f82(x47531),f85(x47531)),f244(x47531)) % 174.01/173.89 [4781]~P88(x47811)+~P33(x47811,f777(f108(x47811),a101)) % 174.01/173.89 [4791]E(f777(a32,x47911),f185(a846))+P1(f777(a28,f777(a29,x47911))) % 174.01/173.89 [4921]E(f777(f79(a3),x49211),x49211)+P1(f777(f777(f235(a3),x49211),f4(a3))) % 174.01/173.89 [4941]~E(f777(a109,x49411),f4(a851))+P1(f777(f777(f234(a3),x49411),f4(a3))) % 174.01/173.89 [4977]~E(f777(f79(a3),x49771),f82(a3))+P1(f777(f777(f281(a3),x49771),f82(a3))) % 174.01/173.89 [5007]~P1(f777(a188,x50071))+P1(f777(f777(f235(a3),x50071),f4(a3))) % 174.01/173.89 [5048]~P2(x50481)+P1(f777(f777(f336(x50481),f4(x50481)),f178(x50481))) % 174.01/173.89 [5049]~P133(x50491)+P1(f777(f777(f336(x50491),f4(x50491)),f114(x50491))) % 174.01/173.89 [5050]~P2(x50501)+P1(f777(f777(f336(x50501),f82(x50501)),f178(x50501))) % 174.01/173.89 [5051]~P133(x50511)+P1(f777(f777(f336(x50511),f82(x50511)),f114(x50511))) % 174.01/173.89 [5052]~P117(x50521)+P1(f777(f777(f235(x50521),f4(x50521)),f82(x50521))) % 174.01/173.89 [5053]~P117(x50531)+P1(f777(f777(f234(x50531),f4(x50531)),f82(x50531))) % 174.01/173.89 [5056]E(f777(f229(a846),f451(x50561)),f777(a32,x50561))+~P1(f777(a28,f777(a29,x50561))) % 174.01/173.89 [5057]E(f777(f229(a846),f473(x50571)),f777(a32,x50571))+~P1(f777(a28,f777(a29,x50571))) % 174.01/173.89 [5108]E(x51081,f4(a851))+~P1(f777(f777(f234(a851),x51081),f4(a851))) % 174.01/173.89 [5109]E(x51091,f82(a851))+~P1(f777(f777(f281(a851),x51091),f82(a851))) % 174.01/173.89 [5153]E(f777(a109,x51531),f4(a851))+~P1(f777(f777(f234(a3),x51531),f4(a3))) % 174.01/173.89 [5181]E(f777(f79(a3),x51811),f82(a3))+~P1(f777(f777(f281(a3),x51811),f82(a3))) % 174.01/173.89 [5208]P1(f777(a188,x52081))+~P1(f777(f777(f235(a3),x52081),f4(a3))) % 174.01/173.89 [5213]~P100(x52131)+P20(x52131,f852(x52131),f140(x52131,x52131,f9(x52131))) % 174.01/173.89 [5232]P38(x52321)+~P1(f777(f777(f234(a3),f4(a3)),f340(x52321))) % 174.01/173.89 [5238]E(f777(f79(a3),x52381),f777(f83(a3),x52381))+~P1(f777(f777(f235(a3),x52381),f4(a3))) % 174.01/173.89 [5409]~P117(x54091)+~P1(f777(f777(f235(x54091),f82(x54091)),f4(x54091))) % 174.01/173.89 [5410]~P117(x54101)+~P1(f777(f777(f234(x54101),f82(x54101)),f4(x54101))) % 174.01/173.89 [5422]~E(x54221,f4(a3))+P1(f777(f777(f235(a3),f777(f79(a3),x54221)),f82(a3))) % 174.01/173.89 [5423]~E(x54231,f4(a851))+P1(f777(f777(f234(a3),f777(f104(a3),x54231)),f4(a3))) % 174.01/173.89 [5537]~P67(x55371)+E(f134(x55371,x55371,f84(x55371),f4(x55371)),f157(x55371)) % 174.01/173.89 [5712]~P86(x57121)+P29(a851,x57121,f104(x57121),f241(f858(a851,a845))) % 174.01/173.89 [5909]E(x59091,f4(a851))+~P1(f777(f777(f234(a3),f777(f104(a3),x59091)),f4(a3))) % 174.01/173.89 [5910]E(x59101,f4(a3))+~P1(f777(f777(f235(a3),f777(f79(a3),x59101)),f82(a3))) % 174.01/173.89 [6741]~P1(f777(f777(f235(a3),x67411),f4(a3)))+P1(f777(f777(f235(a3),f777(f777(f84(a3),x67411),x67411)),f4(a3))) % 174.01/173.89 [7316]P1(f777(f777(f235(a3),x73161),f4(a3)))+~P1(f777(f777(f235(a3),f777(f777(f84(a3),x73161),x73161)),f4(a3))) % 174.01/173.89 [7881]E(x78811,f777(a7,f4(a851)))+P1(f777(f777(f235(a851),f777(f777(f5(a851),f777(a24,x78811)),f777(a116,f4(a851)))),f777(a24,x78811))) % 174.01/173.89 [8623]~P1(f777(f777(f235(a3),x86231),f4(a3)))+P1(f777(f777(f235(a3),f777(f777(f5(a3),f777(f777(f84(a3),x86231),x86231)),a101)),f4(a3))) % 174.01/173.89 [8707]~P1(f777(f777(f235(a3),x87071),f4(a3)))+P1(f777(f777(f235(a3),f777(f777(f84(a3),f777(f777(f84(a3),f82(a3)),x87071)),x87071)),f4(a3))) % 174.01/173.89 [8991]P1(f777(f777(f235(a3),x89911),f4(a3)))+~P1(f777(f777(f235(a3),f777(f777(f5(a3),f777(f777(f84(a3),x89911),x89911)),a101)),f4(a3))) % 174.01/173.89 [9055]P1(f777(f777(f235(a3),x90551),f4(a3)))+~P1(f777(f777(f235(a3),f777(f777(f84(a3),f777(f777(f84(a3),f82(a3)),x90551)),x90551)),f4(a3))) % 174.01/173.89 [4590]~E(a87,x45901)+E(f777(f777(f84(a3),x45901),x45901),a87) % 174.01/173.89 [4591]~E(x45911,a87)+E(f777(f777(f84(a3),x45911),x45911),a87) % 174.01/173.89 [4606]E(x46061,f4(a3))+E(f777(f777(f45(a3),x46061),x46061),f82(a3)) % 174.01/173.89 [4731]E(x47311,a87)+~E(f777(f777(f84(a3),x47311),x47311),a87) % 174.01/173.89 [4732]E(a87,x47321)+~E(f777(f777(f84(a3),x47321),x47321),a87) % 174.01/173.89 [4743]~P9(x47431)+E(f47(x47431,f241(f858(x47431,a845))),f182(x47431)) % 174.01/173.89 [4744]~P9(x47441)+E(f47(x47441,f182(f858(x47441,a845))),f241(x47441)) % 174.01/173.89 [4745]~P9(x47451)+E(f46(x47451,f241(f858(x47451,a845))),f241(x47451)) % 174.01/173.89 [4746]~P9(x47461)+E(f46(x47461,f182(f858(x47461,a845))),f182(x47461)) % 174.01/173.89 [4747]~P100(x47471)+E(f132(x47471,f182(f858(x47471,a845))),f117(x47471)) % 174.01/173.89 [4881]E(x48811,f4(a851))+P1(f777(f777(f235(a851),f4(a851)),x48811)) % 174.01/173.89 [4901]~P10(x49011)+P1(f777(f777(f234(a3),f4(a3)),x49011)) % 174.01/173.89 [4932]~E(f777(f108(a851),x49321),f4(a851))+P1(f777(f777(f234(a3),x49321),a87)) % 174.01/173.89 [4937]P38(x49371)+P1(f777(f777(f336(a3),f340(x49371)),x49371)) % 174.01/173.89 [4938]E(x49381,f777(a7,f4(a851)))+P1(f777(f777(f234(a103),f82(a103)),x49381)) % 174.01/173.89 [4982]P1(f777(a188,x49821))+P1(f777(f777(f234(a3),f4(a3)),x49821)) % 174.01/173.89 [5030]E(f777(f104(a3),f777(a109,x50301)),f4(a3))+P1(f777(f777(f234(a3),f4(a3)),x50301)) % 174.01/173.89 [5096]E(f777(f104(a3),f777(f108(a851),x50961)),f777(f108(a3),x50961))+P1(f777(a188,f777(f108(a3),x50961))) % 174.01/173.89 [5116]E(f777(f108(a851),x51161),f4(a851))+~P1(f777(a188,f777(f108(a3),x51161))) % 174.01/173.89 [5117]E(f777(f108(a851),x51171),f4(a851))+~P1(f777(f777(f234(a3),x51171),a87)) % 174.01/173.89 [5148]P10(x51481)+~P1(f777(f777(f234(a3),f4(a3)),x51481)) % 174.01/173.89 [5216]E(f777(a116,f581(x52161)),x52161)+~P1(f777(f777(f235(a851),f4(a851)),x52161)) % 174.01/173.89 [5217]E(f777(a116,f619(x52171)),x52171)+~P1(f777(f777(f235(a851),f4(a851)),x52171)) % 174.01/173.89 [5226]E(f777(a116,f777(f108(a851),x52261)),f82(a851))+~P1(f777(a188,f777(f108(a3),x52261))) % 174.01/173.89 [5234]E(f777(f104(a3),f627(x52341)),x52341)+~P1(f777(f777(f235(a3),f4(a3)),x52341)) % 174.01/173.89 [5241]~E(x52411,f777(a7,f4(a851)))+~P1(f777(f777(f234(a103),f82(a103)),x52411)) % 174.01/173.89 [5248]E(f777(f104(a3),f777(f108(a851),x52481)),f4(a3))+~P1(f777(a188,f777(f108(a3),x52481))) % 174.01/173.89 [5273]E(f777(f157(a851),x52731),f4(a851))+P1(f777(f777(f336(a851),f602(x52731)),f777(f160(a851),x52731))) % 174.01/173.89 [5293]E(f777(f104(a3),f777(a109,x52931)),x52931)+~P1(f777(f777(f234(a3),f4(a3)),x52931)) % 174.01/173.89 [5302]~P1(f777(a188,x53021))+~P1(f777(f777(f234(a3),f4(a3)),x53021)) % 174.01/173.89 [5402]E(f777(f777(f84(a851),f82(a851)),f777(f108(a851),x54021)),f82(a851))+~P1(f777(f777(f235(a3),x54021),a87)) % 174.01/173.89 [5459]E(x54591,f4(a851))+~P1(f777(f777(f235(a851),x54591),f777(a116,f4(a851)))) % 174.01/173.89 [5480]E(x54801,f777(a116,f4(a851)))+~P1(f777(f777(f281(a851),x54801),f777(a116,f4(a851)))) % 174.01/173.89 [5498]E(f777(f777(f84(a851),f777(f108(a851),x54981)),f82(a851)),f82(a851))+~P1(f777(f777(f235(a3),x54981),a87)) % 174.01/173.89 [5499]E(f777(f777(f5(a851),f777(f108(a851),x54991)),f82(a851)),f4(a851))+~P1(f777(f777(f234(a3),x54991),a87)) % 174.01/173.89 [5509]~P38(x55091)+E(f777(f44(a851),f777(f305(a3,a851,a109),x55091)),f777(f44(a3),x55091)) % 174.01/173.89 [5538]~P100(x55381)+E(f236(x55381,f777(f11(x55381,x55381,a845),f234(x55381))),f181(x55381)) % 174.01/173.89 [5539]~P100(x55391)+E(f237(x55391,f777(f11(x55391,x55391,a845),f234(x55391))),f238(x55391)) % 174.01/173.89 [5548]E(f54(a851,f777(a116,f4(a851)),f777(f108(a851),x55481)),f777(a116,f4(a851)))+~P1(f777(a188,f777(f108(a3),x55481))) % 174.01/173.89 [5556]P1(f777(f777(f235(a3),f4(a3)),x55561))+~P1(f777(f777(f234(a3),f82(a3)),x55561)) % 174.01/173.89 [5557]~P1(f777(f777(f235(a3),f4(a3)),x55571))+P1(f777(f777(f234(a3),f82(a3)),x55571)) % 174.01/173.89 [5567]E(f777(a116,f777(f777(f5(a851),x55671),f82(a851))),x55671)+~P1(f777(f777(f235(a851),f4(a851)),x55671)) % 174.01/173.89 [5625]P1(f777(f777(f235(a851),f4(a851)),f627(x56251)))+~P1(f777(f777(f235(a3),f4(a3)),x56251)) % 174.01/173.89 [5682]E(f54(a3,f777(f108(a3),a101),x56821),f777(f777(f5(a3),x56821),f82(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x56821)) % 174.01/173.89 [5727]~P1(f777(f777(f235(a3),a87),x57271))+P1(f777(f777(f235(a851),f4(a851)),f777(f108(a851),x57271))) % 174.01/173.89 [5781]P1(f777(f777(f235(a851),f4(a851)),f777(a109,x57811)))+~P1(f777(f777(f235(a3),f4(a3)),x57811)) % 174.01/173.89 [5828]~P1(f777(f777(f235(a851),f4(a851)),x58281))+P1(f777(f777(f235(a3),f4(a3)),f777(f104(a3),x58281))) % 174.01/173.89 [5863]~P1(f777(f777(f235(a851),f4(a851)),f777(a109,x58631)))+P1(f777(f777(f235(a3),f4(a3)),x58631)) % 174.01/173.89 [5878]~P38(x58781)+E(f777(f305(a851,a3,f104(a3)),f777(f305(a3,a851,a109),x58781)),x58781) % 174.01/173.89 [5889]P1(f777(f777(f235(a3),a87),x58891))+~P1(f777(f777(f235(a851),f4(a851)),f777(f108(a851),x58891))) % 174.01/173.89 [5951]P1(f777(f777(f235(a851),f4(a851)),x59511))+~P1(f777(f777(f235(a3),f4(a3)),f777(f104(a3),x59511))) % 174.01/173.89 [6067]E(f777(f305(a851,a3,f104(a3)),f777(f259(a851),f777(a109,x60671))),f777(f296(a3,f4(a3)),x60671))+~P1(f777(f777(f234(a3),f4(a3)),x60671)) % 174.01/173.89 [6083]~P117(x60831)+P1(f777(f777(f235(x60831),f4(x60831)),f777(f777(f84(x60831),f82(x60831)),f82(x60831)))) % 174.01/173.89 [6134]P1(f777(f777(f235(a851),f777(a116,f4(a851))),f777(a109,x61341)))+~P1(f777(f777(f235(a3),f82(a3)),x61341)) % 174.01/173.89 [6231]E(x62311,f4(a3))+P1(f777(f58(f4(a3),x62311),f777(f777(f243(a3,a3),f4(a3)),f4(a3)))) % 174.01/173.89 [6411]~P1(f777(f777(f235(a851),f777(a116,f4(a851))),f777(a109,x64111)))+P1(f777(f777(f235(a3),f82(a3)),x64111)) % 174.01/173.89 [6863]~P107(x68631)+P36(x68631,f777(f258(f857(x68631,x68631)),f777(f253(x68631,x68631,a845),f235(x68631)))) % 174.01/173.89 [5114]~P35(x51141)+E(f131(f777(f777(f145(a3,a851),a109),x51141)),x51141) % 174.01/173.89 [5449]E(f777(f108(a851),f777(f777(f5(a3),x54491),a101)),f777(a116,f777(f108(a851),x54491)))+P1(f777(a188,f777(f108(a3),x54491))) % 174.01/173.89 [5474]P31(a843,a864,x54741)+~P1(f777(f777(f336(f850(a843)),x54741),a860)) % 174.01/173.89 [5573]E(f777(f83(a3),f777(f104(a3),f777(a116,f685(x55731)))),x55731)+~P1(f777(f777(f235(a3),x55731),f4(a3))) % 174.01/173.89 [5583]E(f777(f777(f84(a851),f82(a851)),f777(f108(a851),x55831)),f777(f108(a851),f777(f777(f5(a3),x55831),a101)))+P1(f777(f777(f235(a3),x55831),a87)) % 174.01/173.89 [5627]E(f777(f777(f45(a3),f777(f108(a3),a101)),x56271),f777(f108(a3),a101))+~P1(f777(f777(f235(a3),f4(a3)),x56271)) % 174.01/173.89 [5723]E(f777(f777(f84(a851),f777(f108(a851),x57231)),f82(a851)),f777(f108(a851),f777(f777(f5(a3),x57231),a101)))+P1(f777(f777(f235(a3),x57231),a87)) % 174.01/173.89 [5724]E(f777(f777(f5(a851),f777(f108(a851),x57241)),f82(a851)),f777(f108(a851),f777(f777(f84(a3),x57241),a101)))+P1(f777(f777(f234(a3),x57241),a87)) % 174.01/173.89 [5767]E(f777(a109,f777(f777(f84(a3),f82(a3)),x57671)),f777(a116,f777(a109,x57671)))+~P1(f777(f777(f234(a3),f4(a3)),x57671)) % 174.01/173.89 [5805]E(f777(a116,f777(f777(f5(a851),x58051),f777(a116,f4(a851)))),x58051)+~P1(f777(f777(f235(a851),f4(a851)),x58051)) % 174.01/173.89 [6012]E(f54(a851,f777(a116,f4(a851)),f777(f108(a851),x60121)),f777(a109,f54(a3,f82(a3),f777(f108(a3),x60121))))+P1(f777(a188,f777(f108(a3),x60121))) % 174.01/173.89 [6058]~P1(f777(f777(f235(a3),a101),x60581))+P1(f777(f777(f235(a3),a101),f777(f777(f84(a3),x60581),x60581))) % 174.01/173.89 [6059]~P1(f777(f777(f235(a3),a87),x60591))+P1(f777(f777(f235(a3),a87),f777(f777(f84(a3),x60591),x60591))) % 174.01/173.89 [6060]~P1(f777(f777(f235(a3),a101),x60601))+P1(f777(f777(f234(a3),a101),f777(f777(f84(a3),x60601),x60601))) % 174.01/173.89 [6061]~P1(f777(f777(f234(a3),a87),x60611))+P1(f777(f777(f234(a3),a87),f777(f777(f84(a3),x60611),x60611))) % 174.01/173.89 [6245]~P1(f777(f65(x62451),f241(f858(x62451,a845))))+P1(f777(f65(f855(x62451)),f241(f858(f855(x62451),a845)))) % 174.01/173.89 [6336]~P1(f777(f777(f234(a3),f4(a3)),x63361))+P1(f777(f777(f235(a3),f4(a3)),f777(f777(f84(a3),f82(a3)),x63361))) % 174.01/173.89 [6342]E(f777(f242(a3,a3),f56(f82(a3),f777(f108(a3),x63421))),f777(f777(f45(a3),f82(a3)),f777(f108(a3),x63421)))+~P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x63421))) % 174.01/173.89 [6367]E(f777(f252(a3,a3),f56(f82(a3),f777(f108(a3),x63671))),f54(a3,f82(a3),f777(f108(a3),x63671)))+~P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x63671))) % 174.01/173.89 [6380]P1(f777(f65(x63801),f241(f858(x63801,a845))))+~P1(f777(f65(f855(x63801)),f241(f858(f855(x63801),a845)))) % 174.01/173.89 [6412]P1(f777(f777(f235(a3),a101),x64121))+~P1(f777(f777(f235(a3),a101),f777(f777(f84(a3),x64121),x64121))) % 174.01/173.89 [6413]P1(f777(f777(f235(a3),a101),x64131))+~P1(f777(f777(f234(a3),a101),f777(f777(f84(a3),x64131),x64131))) % 174.01/173.89 [6414]P1(f777(f777(f235(a3),a87),x64141))+~P1(f777(f777(f235(a3),a87),f777(f777(f84(a3),x64141),x64141))) % 174.01/173.89 [6415]P1(f777(f777(f234(a3),a87),x64151))+~P1(f777(f777(f234(a3),a87),f777(f777(f84(a3),x64151),x64151))) % 174.01/173.89 [6747]~P1(f777(f65(x67471),f241(f858(x67471,a845))))+P1(f777(f777(f235(a851),f4(a851)),f777(f44(x67471),f241(f858(x67471,a845))))) % 174.01/173.89 [7361]P1(f777(f65(a851),x73611))+~P1(f777(f65(a3),f777(f305(a851,a3,f104(a3)),x73611))) % 174.01/173.89 [5377]~E(a101,x53771)+E(f777(f777(f5(a3),f777(f777(f84(a3),x53771),x53771)),a101),a101) % 174.01/173.89 [5378]~E(x53781,a101)+E(f777(f777(f5(a3),f777(f777(f84(a3),x53781),x53781)),a101),a101) % 174.01/173.89 [5883]E(x58831,a101)+~E(f777(f777(f5(a3),f777(f777(f84(a3),x58831),x58831)),a101),a101) % 174.01/173.89 [5884]E(a101,x58841)+~E(f777(f777(f5(a3),f777(f777(f84(a3),x58841),x58841)),a101),a101) % 174.01/173.89 [6305]~E(f777(f108(a851),x63051),f4(a851))+P1(f777(a188,f777(f108(a3),f777(f777(f84(a3),x63051),a101)))) % 174.01/173.89 [6671]~P1(f777(a188,f777(f108(a3),x66711)))+P1(f777(a188,f777(f108(a3),f777(f777(f84(a3),x66711),x66711)))) % 174.01/173.89 [6672]~P1(f777(f777(f234(a3),x66721),a101))+P1(f777(f777(f235(a3),f777(f777(f84(a3),x66721),x66721)),a101)) % 174.01/173.89 [6673]~P1(f777(f777(f235(a3),x66731),a87))+P1(f777(f777(f235(a3),f777(f777(f84(a3),x66731),x66731)),a87)) % 174.01/173.89 [6674]~P1(f777(f777(f234(a3),x66741),a101))+P1(f777(f777(f234(a3),f777(f777(f84(a3),x66741),x66741)),a101)) % 174.01/173.89 [6675]~P1(f777(f777(f234(a3),x66751),a87))+P1(f777(f777(f234(a3),f777(f777(f84(a3),x66751),x66751)),a87)) % 174.01/173.89 [7005]E(f777(f108(a851),x70051),f4(a851))+~P1(f777(a188,f777(f108(a3),f777(f777(f84(a3),x70051),a101)))) % 174.01/173.89 [7264]~P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x72641)))+P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),f777(f777(f84(a3),x72641),x72641)))) % 174.01/173.89 [7265]P1(f777(a188,f777(f108(a3),x72651)))+~P1(f777(a188,f777(f108(a3),f777(f777(f84(a3),x72651),x72651)))) % 174.01/173.89 [7266]P1(f777(f777(f235(a3),x72661),a87))+~P1(f777(f777(f235(a3),f777(f777(f84(a3),x72661),x72661)),a87)) % 174.01/173.89 [7267]P1(f777(f777(f234(a3),x72671),a101))+~P1(f777(f777(f235(a3),f777(f777(f84(a3),x72671),x72671)),a101)) % 174.01/173.89 [7268]P1(f777(f777(f234(a3),x72681),a101))+~P1(f777(f777(f234(a3),f777(f777(f84(a3),x72681),x72681)),a101)) % 174.01/173.89 [7269]P1(f777(f777(f234(a3),x72691),a87))+~P1(f777(f777(f234(a3),f777(f777(f84(a3),x72691),x72691)),a87)) % 174.01/173.89 [7648]E(f777(a111,f573(x76481)),x76481)+~P1(f777(f777(f336(f858(f857(a851,a851),a845)),x76481),a102)) % 174.01/173.89 [6218]~P88(x62181)+E(f777(f108(x62181),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f82(x62181)) % 174.01/173.89 [6725]~P1(f777(a188,f777(f108(a3),x67251)))+E(f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),x67251),x67251)),a101)),f4(a851)) % 174.01/173.89 [7827]~P1(f777(f777(f235(a3),f777(f108(a3),x78271)),f4(a3)))+E(f777(f242(a3,a3),f777(a60,f59(f777(f83(a3),f82(a3)),f777(f83(a3),f777(f108(a3),x78271))))),f777(f777(f45(a3),f82(a3)),f777(f108(a3),x78271))) % 174.01/173.89 [7840]~P1(f777(f777(f235(a3),f777(f108(a3),x78401)),f4(a3)))+E(f777(f252(a3,a3),f777(a60,f59(f777(f83(a3),f82(a3)),f777(f83(a3),f777(f108(a3),x78401))))),f54(a3,f82(a3),f777(f108(a3),x78401))) % 174.01/173.89 [7887]~P1(f777(f777(f235(a3),a101),x78871))+P1(f777(f777(f235(a3),a101),f777(f777(f5(a3),f777(f777(f84(a3),x78871),x78871)),a101))) % 174.01/173.89 [7888]~P1(f777(f777(f234(a3),a87),x78881))+P1(f777(f777(f235(a3),a87),f777(f777(f5(a3),f777(f777(f84(a3),x78881),x78881)),a101))) % 174.01/173.89 [7889]~P1(f777(f777(f234(a3),a101),x78891))+P1(f777(f777(f234(a3),a101),f777(f777(f5(a3),f777(f777(f84(a3),x78891),x78891)),a101))) % 174.01/173.89 [7890]~P1(f777(f777(f234(a3),a87),x78901))+P1(f777(f777(f234(a3),a87),f777(f777(f5(a3),f777(f777(f84(a3),x78901),x78901)),a101))) % 174.01/173.89 [8187]~P88(x81871)+~P33(x81871,f777(f108(x81871),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))) % 174.01/173.89 [8367]P1(f777(f777(f235(a3),a101),x83671))+~P1(f777(f777(f235(a3),a101),f777(f777(f5(a3),f777(f777(f84(a3),x83671),x83671)),a101))) % 174.01/173.89 [8368]P1(f777(f777(f234(a3),a101),x83681))+~P1(f777(f777(f234(a3),a101),f777(f777(f5(a3),f777(f777(f84(a3),x83681),x83681)),a101))) % 174.01/173.89 [8369]P1(f777(f777(f234(a3),a87),x83691))+~P1(f777(f777(f235(a3),a87),f777(f777(f5(a3),f777(f777(f84(a3),x83691),x83691)),a101))) % 174.01/173.89 [8370]P1(f777(f777(f234(a3),a87),x83701))+~P1(f777(f777(f234(a3),a87),f777(f777(f5(a3),f777(f777(f84(a3),x83701),x83701)),a101))) % 174.01/173.89 [8666]E(f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),x86661),x86661)),a101)),f777(f777(f90(a851,a851),f777(f108(a851),x86661)),f777(f777(f12(a851,a851,a851),a116),f777(f777(f22(a851,a851,a851),f84(a851)),f9(a851)))))+P1(f777(a188,f777(f108(a3),x86661))) % 174.01/173.89 [9439]E(x94391,f182(f858(f857(a851,a851),a845)))+P1(f777(f777(f336(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),x94391),f182(f858(f857(a851,a851),a845)))),a72)) % 174.01/173.89 [8600]~P1(f777(a188,f777(f108(a3),x86001)))+P1(f777(a188,f777(f108(a3),f777(f777(f5(a3),f777(f777(f84(a3),x86001),x86001)),a101)))) % 174.01/173.89 [8601]~P1(f777(f777(f235(a3),x86011),a101))+P1(f777(f777(f235(a3),f777(f777(f5(a3),f777(f777(f84(a3),x86011),x86011)),a101)),a101)) % 174.01/173.89 [8602]~P1(f777(f777(f235(a3),x86021),a87))+P1(f777(f777(f235(a3),f777(f777(f5(a3),f777(f777(f84(a3),x86021),x86021)),a101)),a87)) % 174.01/173.89 [8603]~P1(f777(f777(f234(a3),x86031),a101))+P1(f777(f777(f234(a3),f777(f777(f5(a3),f777(f777(f84(a3),x86031),x86031)),a101)),a101)) % 174.01/173.89 [8604]~P1(f777(f777(f235(a3),x86041),a87))+P1(f777(f777(f234(a3),f777(f777(f5(a3),f777(f777(f84(a3),x86041),x86041)),a101)),a87)) % 174.01/173.89 [8700]~P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x87001)))+P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),f777(f777(f5(a3),f777(f777(f84(a3),x87001),x87001)),a101)))) % 174.01/173.89 [8830]~P88(x88301)+E(f777(f777(f84(x88301),f82(x88301)),f82(x88301)),f777(f108(x88301),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))) % 174.01/173.89 [8977]P1(f777(a188,f777(f108(a3),x89771)))+~P1(f777(a188,f777(f108(a3),f777(f777(f5(a3),f777(f777(f84(a3),x89771),x89771)),a101)))) % 174.01/173.89 [8978]P1(f777(f777(f235(a3),x89781),a101))+~P1(f777(f777(f235(a3),f777(f777(f5(a3),f777(f777(f84(a3),x89781),x89781)),a101)),a101)) % 174.01/173.89 [8979]P1(f777(f777(f235(a3),x89791),a87))+~P1(f777(f777(f235(a3),f777(f777(f5(a3),f777(f777(f84(a3),x89791),x89791)),a101)),a87)) % 174.01/173.89 [8980]P1(f777(f777(f235(a3),x89801),a87))+~P1(f777(f777(f234(a3),f777(f777(f5(a3),f777(f777(f84(a3),x89801),x89801)),a101)),a87)) % 174.01/173.89 [8981]P1(f777(f777(f234(a3),x89811),a101))+~P1(f777(f777(f234(a3),f777(f777(f5(a3),f777(f777(f84(a3),x89811),x89811)),a101)),a101)) % 174.01/173.89 [9487]~P1(f777(f65(f857(a851,a851)),x94871))+P1(f777(f777(f336(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),f182(f858(f857(a851,a851),a845))),x94871)),a73)) % 174.01/173.89 [9273]~P2(x92731)+E(f777(f777(f244(x92731),f4(x92731)),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f4(x92731)) % 174.01/173.89 [9274]~P2(x92741)+E(f777(f777(f244(x92741),f82(x92741)),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f82(x92741)) % 174.01/173.89 [9684]~P1(f777(f777(f235(a851),f82(a851)),x96841))+P1(f777(f777(f235(a851),f4(a851)),f777(f777(f45(a851),x96841),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))) % 174.01/173.89 [9690]~P1(f777(f777(f235(a851),f4(a851)),x96901))+P1(f777(f777(f235(a851),f4(a851)),f777(f777(f45(a851),f777(f777(f84(a851),x96901),f82(a851))),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))) % 174.01/173.89 [9729]~E(f54(a851,x97291,f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f82(a851))+P1(f777(f777(f235(a851),f4(a851)),f54(a851,x97291,f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))) % 174.01/173.89 [9764]E(f54(a851,x97641,f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f82(a851))+~P1(f777(f777(f235(a851),f4(a851)),f54(a851,x97641,f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))) % 174.01/173.89 [4525]~P36(x45251,x45252)+P56(x45251,x45252) % 174.01/173.89 [4526]~P42(x45261,x45262)+P56(x45261,x45262) % 174.01/173.89 [4489]~E(x44891,x44892)+E(f268(x44891,x44892),f82(a103)) % 174.01/173.89 [4492]E(f213(x44921,x44922),x44921)+~E(x44922,f4(a851)) % 174.01/173.89 [4497]P37(x44971,x44972)+~E(x44972,f185(x44971)) % 174.01/173.89 [4503]~P37(x45032,x45031)+E(x45031,f185(x45032)) % 174.01/173.89 [4530]~P99(x45302)+P99(f858(x45301,x45302)) % 174.01/173.89 [4531]~P103(x45312)+P103(f858(x45311,x45312)) % 174.01/173.89 [4532]~P102(x45322)+P102(f858(x45321,x45322)) % 174.01/173.89 [4533]~P90(x45332)+P90(f858(x45331,x45332)) % 174.01/173.89 [4534]~P84(x45342)+P84(f858(x45341,x45342)) % 174.01/173.89 [4535]~P71(x45352)+P71(f858(x45351,x45352)) % 174.01/173.89 [4536]~P93(x45362)+P92(f858(x45361,x45362)) % 174.01/173.89 [4537]~P93(x45372)+P93(f858(x45371,x45372)) % 174.01/173.89 [4538]~P9(x45382)+P9(f858(x45381,x45382)) % 174.01/173.89 [4539]~P106(x45392)+P106(f858(x45391,x45392)) % 174.01/173.89 [4540]~P96(x45402)+P94(f858(x45401,x45402)) % 174.01/173.89 [4541]~P101(x45412)+P101(f858(x45411,x45412)) % 174.01/173.89 [4542]~P96(x45422)+P95(f858(x45421,x45422)) % 174.01/173.89 [4543]~P97(x45432)+P97(f858(x45431,x45432)) % 174.01/173.89 [4544]~P93(x45442)+P98(f858(x45441,x45442)) % 174.01/173.89 [4545]~P96(x45452)+P96(f858(x45451,x45452)) % 174.01/173.89 [4558]E(x45581,x45582)+~E(f777(a116,x45581),f777(a116,x45582)) % 174.01/173.89 [4559]E(x45591,x45592)+~E(f777(a29,x45591),f777(a29,x45592)) % 174.01/173.89 [4560]E(x45601,x45602)+~E(f777(a7,x45601),f777(a7,x45602)) % 174.01/173.89 [4562]E(x45621,x45622)+~E(f777(a24,x45621),f777(a24,x45622)) % 174.01/173.89 [4563]E(x45631,x45632)+~E(f777(a111,x45631),f777(a111,x45632)) % 174.01/173.89 [4661]~P7(x46611)+E(f54(x46611,x46612,x46612),f4(x46611)) % 174.01/173.89 [4694]~P36(x46941,x46942)+P36(f852(x46941),f138(x46941,x46942)) % 174.01/173.89 [4695]~P36(x46951,x46952)+P36(f852(x46951),f137(x46951,x46952)) % 174.01/173.89 [4786]~P36(x47861,x47862)+P36(f858(x47861,a845),f328(x47861,x47862)) % 174.01/173.89 [4787]~P36(x47871,x47872)+P36(f858(x47871,a845),f326(x47871,x47872)) % 174.01/173.89 [4906]~P10(x49061)+P38(f297(a3,x49061,x49062)) % 174.01/173.89 [5010]~P36(x50101,x50102)+P58(x50101,f71(x50101,x50101,x50102)) % 174.01/173.89 [5503]~P77(x55031)+P29(x55031,x55031,f83(x55031),x55032) % 174.01/173.89 [4513]~E(x45132,f117(x45131))+E(f777(f143(x45131),x45132),f117(x45131)) % 174.01/173.89 [4514]~E(x45142,f117(x45141))+E(f777(f144(x45141),x45142),f117(x45141)) % 174.01/173.89 [4568]E(x45681,f777(a109,x45682))+~E(f777(f104(a3),x45681),x45682) % 174.01/173.89 [4571]E(x45711,f117(x45712))+~E(f777(f143(x45712),x45711),f117(x45712)) % 174.01/173.89 [4572]E(x45721,f117(x45722))+~E(f777(f144(x45722),x45721),f117(x45722)) % 174.01/173.89 [4587]~P88(x45871)+E(f777(f108(x45871),x45872),f777(f107(x45871),x45872)) % 174.01/173.89 [4594]~E(x45942,f185(x45941))+E(f228(x45941,x45942),f182(f858(x45941,a845))) % 174.01/173.89 [4596]~P59(x45961)+P1(f777(f65(x45961),x45962)) % 174.01/173.89 [4603]E(x46031,f185(x46032))+E(f777(f229(x46032),f493(x46032,x46031)),x46031) % 174.01/173.89 [4604]E(x46041,f185(x46042))+E(f777(f229(x46042),f494(x46042,x46041)),x46041) % 174.01/173.89 [4605]E(x46051,f185(x46052))+E(f777(f229(x46052),f505(x46052,x46051)),x46051) % 174.01/173.89 [4607]~E(f723(x46072,x46071),f117(x46071))+E(f166(x46071,x46072),f117(f852(x46071))) % 174.01/173.89 [4616]~E(x46162,f117(x46161))+E(f777(f160(x46161),x46162),f182(f858(x46161,a845))) % 174.01/173.89 [4617]~E(x46172,f117(x46171))+E(f182(f858(x46171,a845)),f777(f160(x46171),x46172)) % 174.01/173.89 [4619]E(x46191,x46192)+~E(f777(f104(a3),x46191),f777(f104(a3),x46192)) % 174.01/173.89 [4622]E(f211(x46221,x46222),f4(a851))+P1(f777(f65(x46221),x46222)) % 174.01/173.89 [4640]~P110(x46401)+E(f86(x46401,f86(x46401,x46402)),f86(x46401,x46402)) % 174.01/173.89 [4652]~P85(x46521)+E(f777(f777(f244(x46521),x46522),f82(a851)),x46522) % 174.01/173.89 [4653]~P75(x46531)+E(f777(f777(f244(x46531),x46532),f82(a851)),x46532) % 174.01/173.89 [4655]E(x46551,x46552)+E(f268(x46551,x46552),f777(f777(f84(a103),x46552),f82(a103))) % 174.01/173.89 [4658]E(f777(f44(x46581),x46582),f4(a851))+P1(f777(f65(x46581),x46582)) % 174.01/173.89 [4664]~P66(x46641)+E(f777(f777(f84(x46641),x46642),f4(x46641)),x46642) % 174.01/173.89 [4665]~P67(x46651)+E(f777(f777(f84(x46651),x46652),f4(x46651)),x46652) % 174.01/173.89 [4666]~P85(x46661)+E(f777(f777(f84(x46661),x46662),f4(x46661)),x46662) % 174.01/173.89 [4667]~P85(x46671)+E(f777(f777(f85(x46671),x46672),f82(x46671)),x46672) % 174.01/173.89 [4668]~P70(x46681)+E(f777(f777(f85(x46681),x46682),f82(x46681)),x46682) % 174.01/173.89 [4669]~P75(x46691)+E(f777(f777(f85(x46691),x46692),f82(x46691)),x46692) % 174.01/173.89 [4670]~P7(x46701)+E(f777(f777(f45(x46701),x46702),f82(x46701)),x46702) % 174.01/173.89 [4671]~P69(x46711)+E(f777(f777(f5(x46711),x46712),f4(x46711)),x46712) % 174.01/173.89 [4672]~P113(x46721)+E(f777(f777(f285(x46721),x46722),f82(x46721)),x46722) % 174.01/173.89 [4673]~P95(x46731)+E(f777(f777(f105(x46731),x46732),f182(x46731)),x46732) % 174.01/173.89 [4674]~P94(x46741)+E(f777(f777(f106(x46741),x46742),f241(x46741)),x46742) % 174.01/173.89 [4675]~P85(x46751)+E(f777(f777(f244(x46751),x46752),f4(a851)),f82(x46751)) % 174.01/173.89 [4676]~P105(x46761)+E(f777(f777(f244(x46761),x46762),f4(a851)),f82(x46761)) % 174.01/173.89 [4677]~E(x46772,f182(f858(x46771,a845)))+E(f777(f44(x46771),x46772),f4(a851)) % 174.01/173.89 [4688]~P7(x46881)+E(f54(x46881,x46882,f4(x46881)),x46882) % 174.01/173.89 [4696]~P85(x46961)+E(f777(f777(f85(x46961),x46962),f4(x46961)),f4(x46961)) % 174.01/173.89 [4697]~P122(x46971)+E(f777(f777(f85(x46971),x46972),f4(x46971)),f4(x46971)) % 174.01/173.89 [4698]~P7(x46981)+E(f777(f777(f45(x46981),x46982),f4(x46981)),f4(x46981)) % 174.01/173.89 [4699]~P114(x46991)+E(f777(f777(f285(x46991),x46992),f4(x46991)),f4(x46991)) % 174.01/173.89 [4700]~P94(x47001)+E(f777(f777(f105(x47001),x47002),f241(x47001)),f241(x47001)) % 174.01/173.89 [4701]~P95(x47011)+E(f777(f777(f106(x47011),x47012),f182(x47011)),f182(x47011)) % 174.01/173.89 [4702]E(x47021,f185(x47022))+~E(f228(x47022,x47021),f182(f858(x47022,a845))) % 174.01/173.89 [4703]~P7(x47031)+E(f54(x47031,x47032,f82(x47031)),f4(x47031)) % 174.01/173.89 [4704]~P7(x47041)+E(f54(x47041,f4(x47041),x47042),f4(x47041)) % 174.01/173.89 [4755]P36(x47551,x47552)+~E(f603(x47552,x47551),f182(f858(x47551,a845))) % 174.01/173.89 [4756]E(x47561,f117(x47562))+~E(f777(f160(x47562),x47561),f182(f858(x47562,a845))) % 174.01/173.89 [4757]E(x47571,f117(x47572))+~E(f182(f858(x47572,a845)),f777(f160(x47572),x47571)) % 174.01/173.89 [4760]~E(x47601,x47602)+P1(f777(f777(a332,x47601),x47602)) % 174.01/173.89 [4770]P1(x47701)+P1(f777(f777(a337,x47701),x47702)) % 174.01/173.89 [4771]E(x47711,f117(x47712))+E(f777(f777(f155(x47712),x47711),f4(a851)),f777(f133(x47712),x47711)) % 174.01/173.89 [4777]~P1(x47772)+P1(f777(f777(a337,x47771),x47772)) % 174.01/173.89 [4778]~P1(x47782)+P1(f777(f777(a334,x47781),x47782)) % 174.01/173.89 [4779]~P1(x47791)+P1(f777(f777(a334,x47791),x47792)) % 174.01/173.89 [4789]~E(f724(x47892,x47891),f728(x47892,x47891))+P1(f777(f129(x47891),x47892)) % 174.01/173.89 [4797]E(f777(f258(x47971),x47972),f182(f858(x47971,a845)))+P1(f777(x47972,f559(x47972))) % 174.01/173.89 [4798]E(f182(f858(x47981,a845)),f777(f258(x47981),x47982))+P1(f777(x47982,f560(x47982))) % 174.01/173.89 [4862]~P110(x48621)+E(f777(f777(f85(x48621),x48622),f86(x48621,x48622)),f777(f79(x48621),x48622)) % 174.01/173.89 [4874]~E(x48741,f4(a3))+E(f55(x48741,x48742),f777(f777(f243(a3,a3),f4(a3)),f4(a3))) % 174.01/173.89 [4905]~P56(x49051,x49052)+P56(x49051,f777(f280(x49051,x49051),x49052)) % 174.01/173.89 [4922]~E(f777(a32,x49221),f777(f229(a846),x49222))+P1(f777(a28,f777(a29,x49221))) % 174.01/173.89 [4926]E(x49261,x49262)+~P1(f777(f777(a332,x49261),x49262)) % 174.01/173.89 [4930]~P1(f777(a28,x49302))+P1(f777(a28,f37(x49301,x49302))) % 174.01/173.89 [4939]P1(x49391)+~P1(f777(f777(a333,x49392),x49391)) % 174.01/173.89 [4940]P1(x49401)+~P1(f777(f777(a333,x49401),x49402)) % 174.01/173.89 [4944]~P106(x49441)+P1(f777(f777(f234(x49441),x49442),f241(x49441))) % 174.01/173.89 [4945]~P85(x49451)+P1(f777(f777(f281(x49451),x49452),f4(x49451))) % 174.01/173.89 [4949]E(x49491,x49492)+~E(f777(x49491,f375(x49492,x49491)),f777(x49492,f375(x49492,x49491))) % 174.01/173.89 [4984]E(x49841,f4(a851))+E(f213(x49841,f54(a851,x49842,x49841)),f213(x49842,x49841)) % 174.01/173.89 [4989]~P100(x49891)+P18(x49891,f777(f777(f142(x49891),x49892),f117(x49891))) % 174.01/173.89 [4991]E(x49911,f4(a3))+P1(f777(f58(x49912,x49911),f55(x49912,x49911))) % 174.01/173.89 [5008]~E(x50081,x50082)+P1(f777(f777(f235(a851),x50081),f777(a116,x50082))) % 174.01/173.89 [5018]~E(x50181,f4(a851))+P1(f777(f777(f235(a851),x50181),f777(a116,x50182))) % 174.01/173.89 [5029]P1(f777(x50291,x50292))+P1(f777(f777(f234(a3),f4(a3)),f778(x50291))) % 174.01/173.89 [5066]P1(f777(a28,x50661))+~P1(f777(a28,f37(x50662,x50661))) % 174.01/173.89 [5068]P1(f777(a28,x50681))+~P1(f777(a28,f38(x50682,x50681))) % 174.01/173.89 [5070]P1(f777(a28,x50701))+~P1(f777(a28,f38(x50701,x50702))) % 174.01/173.89 [5099]P56(x50991,x50992)+~P56(x50991,f777(f280(x50991,x50991),x50992)) % 174.01/173.89 [5101]~E(f54(a851,x51012,x51011),f4(a851))+E(f777(f777(f85(a851),x51011),f790(x51011,x51012)),x51012) % 174.01/173.89 [5102]~E(f54(a3,x51022,x51021),f4(a3))+E(f777(f777(f85(a3),x51021),f791(x51021,x51022)),x51022) % 174.01/173.89 [5129]~P1(f777(x51291,x51292))+P1(f777(f777(f234(a3),f4(a3)),f762(x51291))) % 174.01/173.89 [5140]E(f777(f777(f5(a851),f777(a109,x51401)),f777(a109,x51402)),f777(a109,x51401))+~P1(f777(a188,x51402)) % 174.01/173.89 [5170]E(f269(x51701,x51702),f82(a103))+~P1(f777(f777(f234(a103),x51701),f82(a103))) % 174.01/173.89 [5261]E(f777(f777(f155(x52611),x52612),f724(x52612,x52611)),f777(f777(f155(x52611),x52612),f728(x52612,x52611)))+P1(f777(f129(x52611),x52612)) % 174.01/173.89 [5303]~P1(f777(x53031,f94(x53032,x53031)))+P1(f777(x53031,f604(x53032,x53031))) % 174.01/173.89 [5367]P58(x53671,x53672)+~P1(f777(f323(x53671,x53672),f582(x53672,x53671))) % 174.01/173.89 [5510]~E(f777(a116,f54(a851,x55101,x55102)),x55102)+E(f54(a851,f777(a116,x55101),x55102),f4(a851)) % 174.01/173.89 [5563]P36(x55631,x55632)+P1(f777(f777(f336(x55631),f683(x55632,x55631)),f684(x55632,x55631))) % 174.01/173.89 [5569]~P2(x55691)+P1(f777(f777(f336(x55691),f777(f104(x55691),x55692)),f178(x55691))) % 174.01/173.89 [5570]~P133(x55701)+P1(f777(f777(f336(x55701),f777(f104(x55701),x55702)),f114(x55701))) % 174.01/173.89 [5571]~P133(x55711)+P1(f777(f777(f336(x55711),f777(f107(x55711),x55712)),f114(x55711))) % 174.01/173.89 [5572]~P88(x55721)+P1(f777(f777(f336(x55721),f777(f108(x55721),x55722)),f114(x55721))) % 174.01/173.89 [5726]E(f777(a116,f54(a851,x57261,x57262)),x57262)+E(f54(a851,f777(a116,x57261),x57262),f777(a116,f54(a851,x57261,x57262))) % 174.01/173.89 [6147]P36(x61471,x61472)+~P1(f777(f777(f336(x61471),f584(x61472,x61471)),f324(x61471,x61472))) % 174.01/173.89 [6181]~P117(x61811)+~P1(f777(f777(f235(x61811),f777(f104(x61811),x61812)),f4(x61811))) % 174.01/173.89 [6182]~P79(x61821)+~P1(f777(f777(f235(x61821),f777(f79(x61821),x61822)),f4(x61821))) % 174.01/173.89 [6274]P1(f777(f777(f235(a3),x62741),f54(a3,x62742,x62741)))+~P1(f777(f777(f235(a3),x62741),f4(a3))) % 174.01/173.89 [6382]E(f777(f777(f304(a851),f777(a116,x63821)),f297(a851,x63822,x63821)),f297(a851,x63822,f777(a116,x63821)))+~P1(f777(f777(f234(a851),x63822),f777(a116,x63821))) % 174.01/173.89 [6609]E(f777(f143(x66091),x66092),x66092)+~P1(f777(f777(f234(a851),f777(f183(f852(x66091)),x66092)),f82(a851))) % 174.01/173.89 [6632]~P79(x66321)+P1(f777(f777(f234(x66321),f777(f83(x66321),f777(f79(x66321),x66322))),f4(x66321))) % 174.01/173.89 [6668]~P36(x66681,x66682)+P36(x66681,f777(f777(f283(x66681,x66681,x66681),x66682),f302(x66681,x66682))) % 174.01/173.89 [6900]~P1(f777(f777(f235(a3),x69002),f4(a3)))+P1(f777(f777(f234(a3),f54(a3,x69001,x69002)),f4(a3))) % 174.01/173.89 [7311]~P2(x73111)+E(f184(x73111,f777(f777(f11(x73111,x73111,x73111),f84(x73111)),f82(x73111)),x73112,f4(x73111)),f777(f104(x73111),x73112)) % 174.01/173.89 [7344]~P118(x73441)+~P1(f777(f777(f235(x73441),f777(f777(f85(x73441),x73442),x73442)),f4(x73441))) % 174.01/173.89 [9859]~P110(x98591)+~P1(f777(f777(f235(x98591),f777(f777(f244(x98591),x98592),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f4(x98591))) % 174.01/173.89 [4569]~E(x45692,f117(x45691))+E(f777(f183(f852(x45691)),x45692),f4(a851)) % 174.01/173.89 [4608]~E(x46081,f4(a851))+E(f777(f777(f84(a851),x46081),x46082),x46082) % 174.01/173.89 [4609]~E(x46092,f4(a851))+E(f777(f777(f85(a851),x46091),x46092),f4(a851)) % 174.01/173.89 [4611]~E(x46111,f4(a851))+E(f777(f777(f85(a851),x46111),x46112),f4(a851)) % 174.01/173.89 [4612]~E(x46122,f4(a3))+E(f777(f777(f45(a3),x46121),x46122),f4(a3)) % 174.01/173.89 [4613]~E(x46132,f4(a851))+E(f777(f777(f244(a851),x46131),x46132),f82(a851)) % 174.01/173.89 [4623]E(x46231,f117(x46232))+~E(f777(f183(f852(x46232)),x46231),f4(a851)) % 174.01/173.89 [4625]~P91(x46251)+E(f777(f777(f85(x46251),x46252),x46252),x46252) % 174.01/173.89 [4627]~P100(x46271)+E(f777(f777(f238(x46271),x46272),x46272),x46272) % 174.01/173.89 [4629]~P100(x46291)+E(f777(f777(f181(x46291),x46292),x46292),x46292) % 174.01/173.89 [4631]~P92(x46311)+E(f777(f777(f105(x46311),x46312),x46312),x46312) % 174.01/173.89 [4632]~P93(x46321)+E(f777(f777(f105(x46321),x46322),x46322),x46322) % 174.01/173.89 [4633]~P93(x46331)+E(f777(f777(f106(x46331),x46332),x46332),x46332) % 174.01/173.89 [4635]~P98(x46351)+E(f777(f777(f106(x46351),x46352),x46352),x46352) % 174.01/173.89 [4651]~P69(x46511)+E(f777(f777(f5(x46511),x46512),x46512),f4(x46511)) % 174.01/173.89 [4662]~P69(x46621)+E(f777(f83(x46621),f777(f83(x46621),x46622)),x46622) % 174.01/173.89 [4663]~P90(x46631)+E(f777(f83(x46631),f777(f83(x46631),x46632)),x46632) % 174.01/173.89 [4680]~E(x46802,f4(a851))+E(f777(f777(f244(a851),x46801),x46802),f777(a116,f4(a851))) % 174.01/173.89 [4712]~P66(x47121)+E(f777(f777(f84(x47121),f4(x47121)),x47122),x47122) % 174.01/173.89 [4713]~P67(x47131)+E(f777(f777(f84(x47131),f4(x47131)),x47132),x47132) % 174.01/173.89 [4714]~P85(x47141)+E(f777(f777(f84(x47141),f4(x47141)),x47142),x47142) % 174.01/173.89 [4715]~P85(x47151)+E(f777(f777(f85(x47151),f82(x47151)),x47152),x47152) % 174.01/173.89 [4716]~P70(x47161)+E(f777(f777(f85(x47161),f82(x47161)),x47162),x47162) % 174.01/173.89 [4717]~P75(x47171)+E(f777(f777(f85(x47171),f82(x47171)),x47172),x47172) % 174.01/173.89 [4718]~P95(x47181)+E(f777(f777(f105(x47181),f182(x47181)),x47182),x47182) % 174.01/173.89 [4719]~P94(x47191)+E(f777(f777(f106(x47191),f241(x47191)),x47192),x47192) % 174.01/173.89 [4736]~P85(x47361)+E(f777(f777(f85(x47361),f4(x47361)),x47362),f4(x47361)) % 174.01/173.89 [4737]~P122(x47371)+E(f777(f777(f85(x47371),f4(x47371)),x47372),f4(x47371)) % 174.01/173.89 [4738]~P7(x47381)+E(f777(f777(f45(x47381),f4(x47381)),x47382),f4(x47381)) % 174.01/173.89 [4739]~P75(x47391)+E(f777(f777(f244(x47391),f82(x47391)),x47392),f82(x47391)) % 174.01/173.89 [4740]~P113(x47401)+E(f777(f777(f285(x47401),f4(x47401)),x47402),f4(x47401)) % 174.01/173.89 [4741]~P94(x47411)+E(f777(f777(f105(x47411),f241(x47411)),x47412),f241(x47411)) % 174.01/173.89 [4742]~P95(x47421)+E(f777(f777(f106(x47421),f182(x47421)),x47422),f182(x47421)) % 174.01/173.89 [4750]E(x47501,f117(x47502))+E(f136(x47502,f777(f144(x47502),x47501)),f777(f133(x47502),x47501)) % 174.01/173.89 [4751]E(x47511,f117(x47512))+E(f777(f133(x47512),f777(f144(x47512),x47511)),f136(x47512,x47511)) % 174.01/173.89 [4752]E(x47521,f4(a851))+~E(f777(f777(f84(a851),x47522),x47521),x47522) % 174.01/173.89 [4758]~P133(x47581)+E(f777(f107(x47581),f777(f104(a3),x47582)),f777(f104(x47581),x47582)) % 174.01/173.89 [4759]~P88(x47591)+E(f777(f107(x47591),f777(f108(a3),x47592)),f777(f108(x47591),x47592)) % 174.01/173.89 [4766]E(x47661,f4(a851))+~E(f777(f777(f84(a851),x47662),x47661),f4(a851)) % 174.01/173.89 [4767]E(x47671,f4(a851))+~E(f777(f777(f84(a851),x47671),x47672),f4(a851)) % 174.01/173.89 [4768]E(x47681,f82(a851))+~E(f777(f777(f85(a851),x47682),x47681),f82(a851)) % 174.01/173.89 [4769]E(x47691,f82(a851))+~E(f777(f777(f85(a851),x47691),x47692),f82(a851)) % 174.01/173.89 [4782]~P110(x47821)+E(f777(f79(x47821),f777(f104(x47821),x47822)),f777(f104(x47821),x47822)) % 174.01/173.89 [4783]~P79(x47831)+E(f777(f79(x47831),f777(f83(x47831),x47832)),f777(f79(x47831),x47832)) % 174.01/173.89 [4784]~P79(x47841)+E(f777(f79(x47841),f777(f79(x47841),x47842)),f777(f79(x47841),x47842)) % 174.01/173.89 [4785]~P66(x47851)+E(f777(f157(x47851),f777(f144(x47851),x47852)),f777(f157(x47851),x47852)) % 174.01/173.89 [4790]~E(x47901,f777(a116,f4(a851)))+E(f777(f777(f244(a851),x47901),x47902),f777(a116,f4(a851))) % 174.01/173.89 [4800]~P69(x48001)+E(f777(f777(f5(x48001),f4(x48001)),x48002),f777(f83(x48001),x48002)) % 174.01/173.89 [4801]~E(x48012,f4(a851))+E(f132(a851,f777(f296(a851,x48011),x48012)),f117(a851)) % 174.01/173.89 [4810]~P88(x48101)+E(f777(f777(f84(x48101),x48102),f777(f108(x48101),a87)),x48102) % 174.01/173.89 [4811]E(x48111,f4(a3))+E(f56(f777(f79(a3),x48112),f777(f79(a3),x48111)),f62(x48112,x48111)) % 174.01/173.89 [4823]~E(x48231,x48232)+P1(f777(f777(f234(a851),x48231),x48232)) % 174.01/173.89 [4827]~E(x48271,x48272)+P1(f777(f777(f281(a851),x48271),x48272)) % 174.01/173.89 [4834]~E(x48341,f4(a103))+E(f777(f777(f84(a851),f777(a24,x48341)),x48342),x48342) % 174.01/173.89 [4835]~E(f777(f108(a3),x48352),f777(f104(a3),x48351))+E(x48351,f777(a109,f777(f108(a3),x48352))) % 174.01/173.89 [4844]~P10(x48441)+P10(f777(f777(f244(a3),x48441),x48442)) % 174.01/173.89 [4845]~P69(x48451)+E(f777(f777(f84(x48451),x48452),f777(f83(x48451),x48452)),f4(x48451)) % 174.01/173.89 [4846]~P90(x48461)+E(f777(f777(f105(x48461),x48462),f777(f83(x48461),x48462)),f241(x48461)) % 174.01/173.89 [4847]~P90(x48471)+E(f777(f777(f106(x48471),x48472),f777(f83(x48471),x48472)),f182(x48471)) % 174.01/173.89 [4871]E(x48711,f4(a851))+~E(f777(f83(a3),f777(f104(a3),x48712)),f777(f104(a3),x48711)) % 174.01/173.89 [4872]E(x48721,f4(a851))+~E(f777(f83(a3),f777(f104(a3),x48721)),f777(f104(a3),x48722)) % 174.01/173.89 [4882]E(f190(x48821,x48822),f4(a3))+P1(f777(f777(f234(a3),x48822),x48821)) % 174.01/173.89 [4883]E(f240(x48831,x48832),f4(a103))+P1(f777(f777(f235(a103),x48831),x48832)) % 174.01/173.89 [4884]E(f165(x48841,x48842),f117(a3))+P1(f777(f777(f234(a3),x48841),x48842)) % 174.01/173.89 [4897]E(x48971,f777(a116,f4(a851)))+~E(f777(f777(f85(a851),x48972),x48971),f777(a116,f4(a851))) % 174.01/173.89 [4898]E(x48981,f777(a116,f4(a851)))+~E(f777(f777(f85(a851),x48981),x48982),f777(a116,f4(a851))) % 174.01/173.89 [4899]~P103(x48991)+P1(f777(f777(f234(x48991),x48992),x48992)) % 174.01/173.89 [4900]~P85(x49001)+P1(f777(f777(f281(x49001),x49002),x49002)) % 174.01/173.89 [4903]~P88(x49031)+E(f777(f777(f85(x49031),x49032),f777(f108(x49031),a101)),f777(f83(x49031),x49032)) % 174.01/173.89 [4919]~P133(x49191)+E(f777(f83(x49191),f777(f107(x49191),x49192)),f777(f107(x49191),f777(f83(a3),x49192))) % 174.01/173.89 [4920]~P88(x49201)+E(f777(f83(x49201),f777(f108(x49201),x49202)),f777(f108(x49201),f777(f83(a3),x49202))) % 174.01/173.89 [4954]~E(x49541,f777(a116,x49542))+P1(f777(f777(f235(a851),f4(a851)),x49541)) % 174.01/173.89 [4972]~P100(x49721)+E(f777(f83(f858(x49721,a845)),f777(f259(x49721),x49722)),f777(f260(x49721),x49722)) % 174.01/173.89 [4973]~P100(x49731)+E(f777(f83(f858(x49731,a845)),f777(f298(x49731),x49732)),f777(f295(x49731),x49732)) % 174.01/173.89 [4974]~P100(x49741)+E(f777(f83(f858(x49741,a845)),f777(f295(x49741),x49742)),f777(f298(x49741),x49742)) % 174.01/173.89 [4975]~P100(x49751)+E(f777(f83(f858(x49751,a845)),f777(f260(x49751),x49752)),f777(f259(x49751),x49752)) % 174.01/173.89 [4983]~E(f777(f104(a3),x49832),x49831)+P1(f777(f777(f234(a3),f4(a3)),x49831)) % 174.01/173.89 [4990]~E(x49902,f4(a3))+E(f62(x49901,x49902),f777(f777(f243(a3,a3),f4(a3)),f777(f79(a3),x49901))) % 174.01/173.89 [4992]~P101(x49921)+P1(f777(f777(f234(x49921),f182(x49921)),x49922)) % 174.01/173.89 [4993]~P85(x49931)+P1(f777(f777(f281(x49931),f82(x49931)),x49932)) % 174.01/173.89 [5024]E(x50241,x50242)+~E(f777(f777(f84(a3),x50241),x50241),f777(f777(f84(a3),x50242),x50242)) % 174.01/173.89 [5028]~P1(f777(x50281,x50282))+P1(f777(x50281,f777(a109,f762(x50281)))) % 174.01/173.89 [5054]~P110(x50541)+E(f777(f777(f85(x50541),f86(x50541,x50542)),f777(f79(x50541),x50542)),x50542) % 174.01/173.89 [5055]E(x50551,x50552)+~P1(f777(f777(f189(a27),x50551),x50552)) % 174.01/173.89 [5064]~E(x50642,f4(a851))+E(f89(f857(a851,a851),f57(x50641,x50642)),f777(f777(f243(a851,a851),f4(a851)),x50641)) % 174.01/173.89 [5075]~E(x50751,x50752)+~P1(f777(f777(f235(a851),x50751),x50752)) % 174.01/173.89 [5076]~E(x50761,x50762)+~P1(f777(f777(f235(a3),x50761),x50762)) % 174.01/173.89 [5079]~P2(x50791)+E(f777(f777(f84(x50791),f82(x50791)),f777(f104(x50791),x50792)),f777(f104(x50791),f777(a116,x50792))) % 174.01/173.89 [5083]~E(x50831,f4(a851))+~P1(f777(f777(f235(a851),x50832),x50831)) % 174.01/173.89 [5097]E(f777(f44(x50971),f777(f160(x50971),x50972)),f777(f183(f852(x50971)),x50972))+~P1(f777(f129(x50971),x50972)) % 174.01/173.89 [5106]~P1(f777(x51061,f729(x51061)))+P1(f777(x51061,f777(f104(a3),x51062))) % 174.01/173.89 [5118]E(f240(x51181,x51182),x51182)+~P1(f777(f777(f235(a103),x51181),x51182)) % 174.01/173.89 [5120]E(f269(x51201,x51202),f82(a103))+~P1(f777(f777(f235(a103),x51202),x51201)) % 174.01/173.89 [5121]E(f165(x51211,x51212),f117(a3))+~P1(f777(f777(f235(a3),x51212),x51211)) % 174.01/173.89 [5124]~P99(x51241)+E(f297(x51241,x51242,x51242),f777(f777(f304(x51241),x51242),f182(f858(x51241,a845)))) % 174.01/173.89 [5143]~E(f777(f777(f5(a851),x51431),x51432),f4(a851))+P1(f777(f777(f234(a851),x51431),x51432)) % 174.01/173.89 [5171]~P103(x51711)+~P1(f777(f777(f235(x51711),x51712),x51712)) % 174.01/173.89 [5174]~E(f54(a3,x51741,x51742),f4(a3))+E(f54(a3,x51741,f777(f83(a3),x51742)),f4(a3)) % 174.01/173.89 [5176]~E(f54(a3,x51761,x51762),f4(a3))+E(f54(a3,f777(f83(a3),x51761),x51762),f4(a3)) % 174.01/173.89 [5183]E(f777(f296(a851,x51831),f777(a116,x51832)),f182(f858(a851,a845)))+P1(f777(f777(f234(a851),x51831),x51832)) % 174.01/173.89 [5200]E(f132(a851,f777(f296(a851,x52001),x52002)),f117(a851))+P1(f777(f777(f235(a851),x52001),x52002)) % 174.01/173.89 [5205]~E(f777(f44(x52051),f777(f160(x52051),x52052)),f777(f183(f852(x52051)),x52052))+P1(f777(f129(x52051),x52052)) % 174.01/173.89 [5209]~P1(f777(f129(x52091),x52092))+P1(f777(f129(x52091),f777(f143(x52091),x52092))) % 174.01/173.89 [5210]~P1(f777(f129(x52101),x52102))+P1(f777(f129(x52101),f777(f159(x52101),x52102))) % 174.01/173.89 [5211]~P1(f777(f129(x52111),x52112))+P1(f777(f129(x52111),f777(f144(x52111),x52112))) % 174.01/173.89 [5219]P1(f777(x52191,x52192))+~P1(f777(x52191,f777(a109,f778(x52191)))) % 174.01/173.89 [5220]P1(f777(f777(f234(a851),x52202),x52201))+P1(f777(f777(f234(a851),x52201),x52202)) % 174.01/173.89 [5221]P1(f777(f777(f234(a3),x52212),x52211))+P1(f777(f777(f234(a3),x52211),x52212)) % 174.01/173.89 [5224]~P79(x52241)+P1(f777(f777(f234(x52241),x52242),f777(f79(x52241),x52242))) % 174.01/173.89 [5227]P1(f777(x52271,f730(x52271)))+~P1(f777(x52271,f777(f104(a3),x52272))) % 174.01/173.89 [5251]E(f777(f777(f45(a851),x52511),x52512),f4(a851))+~P1(f777(f777(f235(a851),x52511),x52512)) % 174.01/173.89 [5253]E(f777(f777(f5(a851),x52531),x52532),f4(a851))+~P1(f777(f777(f234(a851),x52531),x52532)) % 174.01/173.89 [5271]E(f54(a851,x52711,x52712),x52711)+~P1(f777(f777(f235(a851),x52711),x52712)) % 174.01/173.89 [5278]E(f54(a3,x52781,f777(f83(a3),x52782)),f286(x52781,x52782))+P1(f777(f777(f234(a3),f4(a3)),x52782)) % 174.01/173.89 [5291]E(f777(f777(f5(a3),x52911),x52912),f190(x52911,x52912))+~P1(f777(f777(f234(a3),x52912),x52911)) % 174.01/173.89 [5309]P1(f777(f777(f234(a3),f4(a3)),f729(x53091)))+P1(f777(x53091,f777(f104(a3),x53092))) % 174.01/173.89 [5322]~P117(x53221)+P1(f777(f777(f234(x53221),f4(x53221)),f777(f104(x53221),x53222))) % 174.01/173.89 [5323]~P79(x53231)+P1(f777(f777(f234(x53231),f4(x53231)),f777(f79(x53231),x53232))) % 174.01/173.89 [5352]E(f777(f777(f84(a851),x53521),f682(x53522,x53521)),x53522)+~P1(f777(f777(f234(a851),x53521),x53522)) % 174.01/173.89 [5353]E(f777(f777(f84(a851),x53531),f605(x53532,x53531)),x53532)+~P1(f777(f777(f235(a851),x53531),x53532)) % 174.01/173.89 [5365]~E(f777(f108(a3),x53651),f777(f104(a3),x53652))+P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x53651))) % 174.01/173.89 [5368]E(f297(a3,x53681,x53682),f182(f858(a3,a845)))+~P1(f777(f777(f235(a3),x53682),x53681)) % 174.01/173.89 [5371]~P110(x53711)+E(f777(f777(f85(x53711),f777(f79(x53711),x53712)),f777(f79(x53711),x53712)),f777(f777(f85(x53711),x53712),x53712)) % 174.01/173.89 [5376]E(f132(a851,f777(f296(a851,x53761),f777(a116,x53762))),f117(a851))+P1(f777(f777(f234(a851),x53761),x53762)) % 174.01/173.89 [5380]E(f777(f777(f45(a3),x53801),x53802),f287(x53801,x53802))+~P1(f777(f777(f234(a3),f4(a3)),x53802)) % 174.01/173.89 [5400]P1(f777(f129(x54001),x54002))+~P1(f777(f129(x54001),f777(f143(x54001),x54002))) % 174.01/173.89 [5401]P1(f777(f129(x54011),x54012))+~P1(f777(f129(x54011),f777(f144(x54011),x54012))) % 174.01/173.89 [5424]P1(f777(f65(a851),x54241))+P1(f777(f777(f336(a851),f377(x54241,x54242)),x54241)) % 174.01/173.89 [5425]P1(f777(f65(a851),x54251))+P1(f777(f777(f336(a851),f402(x54251,x54252)),x54251)) % 174.01/173.89 [5426]P1(f777(f777(f235(a851),x54262),f777(a116,x54261)))+P1(f777(f777(f235(a851),x54261),x54262)) % 174.01/173.89 [5427]E(f54(a3,x54271,x54272),f286(x54271,x54272))+~P1(f777(f777(f234(a3),f4(a3)),x54272)) % 174.01/173.89 [5430]E(f132(a851,f777(f296(a851,x54301),x54302)),f117(a851))+~P1(f777(f777(f234(a851),x54302),x54301)) % 174.01/173.89 [5431]~P77(x54311)+E(f777(f305(x54311,x54311,f83(x54311)),f777(f259(x54311),x54312)),f777(f298(x54311),f777(f83(x54311),x54312))) % 174.01/173.89 [5432]~P77(x54321)+E(f777(f305(x54321,x54321,f83(x54321)),f777(f298(x54321),x54322)),f777(f259(x54321),f777(f83(x54321),x54322))) % 174.01/173.89 [5433]~P77(x54331)+E(f777(f305(x54331,x54331,f83(x54331)),f777(f295(x54331),x54332)),f777(f260(x54331),f777(f83(x54331),x54332))) % 174.01/173.89 [5434]~P77(x54341)+E(f777(f305(x54341,x54341,f83(x54341)),f777(f260(x54341),x54342)),f777(f295(x54341),f777(f83(x54341),x54342))) % 174.01/173.89 [5445]E(x54451,f182(f858(x54452,a845)))+P1(f777(f777(f336(x54452),f404(x54451,x54452)),x54451)) % 174.01/173.89 [5446]E(x54461,f182(f858(x54462,a845)))+P1(f777(f777(f336(x54462),f405(x54461,x54462)),x54461)) % 174.01/173.89 [5457]~P1(f777(f777(f235(a851),x54571),x54572))+P1(f777(f777(f234(a851),x54571),x54572)) % 174.01/173.89 [5458]~P1(f777(f777(f235(a3),x54581),x54582))+P1(f777(f777(f234(a3),x54581),x54582)) % 174.01/173.89 [5470]E(f56(x54701,x54702),f777(f777(f243(a3,a3),f4(a3)),x54701))+~P1(f777(f777(f235(a3),x54701),x54702)) % 174.01/173.89 [5471]E(f212(f777(f83(a3),x54711),f777(f83(a3),x54712)),f212(x54711,x54712))+~P1(f777(f777(f235(a3),x54712),f4(a3))) % 174.01/173.89 [5484]E(x54841,x54842)+~E(f777(a7,f777(a116,f777(a24,x54841))),f777(a7,f777(a116,f777(a24,x54842)))) % 174.01/173.89 [5489]E(f56(x54891,x54892),f777(f777(f243(a3,a3),f4(a3)),x54891))+~P1(f777(f777(f234(a3),x54892),f4(a3))) % 174.01/173.89 [5516]E(f54(a851,f777(f108(a851),x55161),f777(f108(a851),x55162)),f4(a851))+~P1(f777(a188,f777(f108(a3),x55161))) % 174.01/173.89 [5530]P1(f777(f777(f234(a3),f4(a3)),f730(x55301)))+~P1(f777(x55301,f777(f104(a3),x55302))) % 174.01/173.89 [5561]P38(f297(a3,x55611,x55612))+~P1(f777(f777(f234(a3),f4(a3)),x55611)) % 174.01/173.89 [5565]~P1(f777(f65(x55651),x55652))+P1(f777(f65(f858(x55651,a845)),f777(f303(x55651),x55652))) % 174.01/173.89 [5578]E(f777(f777(f84(a3),x55781),f777(f104(a3),f792(x55782,x55781))),x55782)+~P1(f777(f777(f234(a3),x55781),x55782)) % 174.01/173.89 [5586]P1(f777(f777(f234(a851),x55861),x55862))+P1(f777(f777(f234(a851),f777(a116,x55862)),x55861)) % 174.01/173.89 [5631]E(f777(f777(f45(a851),f777(f108(a851),x56311)),f777(f108(a851),x56312)),f4(a851))+~P1(f777(a188,f777(f108(a3),x56311))) % 174.01/173.89 [5632]E(f777(f777(f85(a851),f777(f108(a851),x56321)),f777(f108(a851),x56322)),f4(a851))+~P1(f777(f777(f235(a3),x56321),a87)) % 174.01/173.89 [5634]P1(f777(f777(f235(a851),x56341),f777(a116,x56342)))+~P1(f777(f777(f235(a851),x56341),x56342)) % 174.01/173.89 [5636]P1(f777(f777(f235(a851),x56361),f777(a116,x56362)))+~P1(f777(f777(f234(a851),x56361),x56362)) % 174.01/173.89 [5638]P1(f777(f777(f234(a851),x56381),f777(a116,x56382)))+~P1(f777(f777(f234(a851),x56381),x56382)) % 174.01/173.89 [5639]~E(x56391,x56392)+P1(f777(f777(f235(a3),x56391),f777(f777(f84(a3),x56392),f82(a3)))) % 174.01/173.89 [5642]E(f54(a3,x56421,x56422),f4(a3))+E(f777(f777(f5(a3),x56422),f54(a3,x56421,x56422)),f54(a3,f777(f83(a3),x56421),x56422)) % 174.01/173.89 [5650]E(x56501,f117(x56502))+P1(f777(f777(f336(x56502),f136(x56502,x56501)),f777(f160(x56502),x56501))) % 174.01/173.89 [5662]E(f89(f857(a851,a851),f57(x56621,x56622)),f777(f777(f243(a851,a851),f4(a851)),x56621))+~P1(f777(f777(f235(a851),x56621),x56622)) % 174.01/173.89 [5702]E(f777(f777(f84(a851),f777(f108(a851),x57021)),f777(f108(a851),x57022)),f777(f108(a851),x57022))+~P1(f777(f777(f235(a3),x57021),a87)) % 174.01/173.89 [5703]E(f777(f777(f5(a851),f777(f108(a851),x57031)),f777(f108(a851),x57032)),f777(f108(a851),x57031))+~P1(f777(f777(f235(a3),x57032),a87)) % 174.01/173.89 [5708]E(f777(a116,f777(f777(f84(a851),x57081),f583(x57082,x57081))),x57082)+~P1(f777(f777(f235(a851),x57081),x57082)) % 174.01/173.89 [5709]E(f777(a116,f777(f777(f84(a851),x57091),f606(x57092,x57091))),x57092)+~P1(f777(f777(f235(a851),x57091),x57092)) % 174.01/173.89 [5716]~P1(f777(f777(f281(a3),x57161),x57162))+P1(f777(f777(f281(a3),x57161),f777(f83(a3),x57162))) % 174.01/173.89 [5717]P1(f777(f777(f235(a851),f4(a851)),f605(x57171,x57172)))+~P1(f777(f777(f235(a851),x57172),x57171)) % 174.01/173.89 [5736]P1(f777(x57361,x57362))+~P1(f777(x57361,f777(a93,f607(x57362,x57361)))) % 174.01/173.89 [5744]~P1(f777(f777(f235(a851),x57441),f777(a116,x57442)))+P1(f777(f777(f234(a851),x57441),x57442)) % 174.01/173.89 [5793]E(f777(f777(f304(a851),x57931),f777(f296(a851,x57932),x57931)),f777(f296(a851,x57932),f777(a116,x57931)))+~P1(f777(f777(f234(a851),x57932),x57931)) % 174.01/173.89 [5798]E(x57981,f117(x57982))+E(f777(f777(f127(x57982),f118(x57982,x57981)),f777(f777(f142(x57982),f136(x57982,x57981)),f117(x57982))),x57981) % 174.01/173.89 [5809]P1(f777(f65(x58091),x58092))+~P1(f777(f777(f235(a851),f4(a851)),f777(f44(x58091),x58092))) % 174.01/173.89 [5813]~E(x58131,f182(f858(x58132,a845)))+~P1(f777(f777(f235(a851),f4(a851)),f777(f44(x58132),x58131))) % 174.01/173.89 [5823]~P1(f777(f777(f235(a851),x58231),x58232))+P1(f777(f777(f234(a851),f777(a116,x58231)),x58232)) % 174.01/173.89 [5831]E(x58311,f117(x58312))+P1(f777(f777(f336(x58312),f777(f133(x58312),x58311)),f777(f160(x58312),x58311))) % 174.01/173.89 [5837]~P117(x58371)+P1(f777(f777(f235(x58371),x58372),f777(f777(f84(x58371),x58372),f82(x58371)))) % 174.01/173.89 [5839]~P79(x58391)+P1(f777(f777(f234(x58391),f777(f83(x58391),x58392)),f777(f79(x58391),x58392))) % 174.01/173.89 [5851]P1(f777(f777(f281(a3),x58511),x58512))+~P1(f777(f777(f281(a3),x58511),f777(f83(a3),x58512))) % 174.01/173.89 [5852]~E(x58521,x58522)+E(f284(a851,f281(a851),x58521,x58522),f777(f777(f304(a851),x58521),f182(f858(a851,a845)))) % 174.01/173.89 [5870]P1(f777(f65(a851),x58701))+~P1(f777(f777(f235(a851),f402(x58701,x58702)),x58702)) % 174.01/173.89 [5871]P1(f777(f65(a851),x58711))+~P1(f777(f777(f234(a851),f377(x58711,x58712)),x58712)) % 174.01/173.89 [5875]~P1(f777(f65(f857(x58751,x58751)),x58752))+P1(f777(f65(x58751),f777(f278(x58751),x58752))) % 174.01/173.89 [5926]E(f284(a851,f281(a851),x59261,x59262),f182(f858(a851,a845)))+P1(f777(f777(f281(a851),x59261),x59262)) % 174.01/173.89 [5932]~P1(f777(f777(f235(a851),x59322),f777(a116,x59321)))+~P1(f777(f777(f235(a851),x59321),x59322)) % 174.01/173.89 [5933]~P99(x59331)+E(f777(f777(f106(f858(x59331,a845)),f777(f295(x59331),x59332)),f777(f260(x59331),x59332)),f777(f777(f304(x59331),x59332),f182(f858(x59331,a845)))) % 174.01/173.89 [5946]P1(f777(f65(x59461),x59462))+~P1(f777(f65(f858(x59461,a845)),f777(f303(x59461),x59462))) % 174.01/173.89 [5970]P1(f777(f777(f235(a851),f777(a116,x59701)),f777(a116,x59702)))+~P1(f777(f777(f235(a851),x59701),x59702)) % 174.01/173.89 [5971]P1(f777(f777(f235(a851),f777(a24,x59711)),f777(a24,x59712)))+~P1(f777(f777(f235(a103),x59711),x59712)) % 174.01/173.89 [5972]P1(f777(f777(f235(a103),f777(a7,x59721)),f777(a7,x59722)))+~P1(f777(f777(f235(a851),x59721),x59722)) % 174.01/173.89 [5973]P1(f777(f777(f234(a851),f777(a116,x59731)),f777(a116,x59732)))+~P1(f777(f777(f234(a851),x59731),x59732)) % 174.01/173.89 [5974]P1(f777(f777(f234(a851),f777(a24,x59741)),f777(a24,x59742)))+~P1(f777(f777(f234(a103),x59741),x59742)) % 174.01/173.89 [5975]P1(f777(f777(f234(a103),f777(a7,x59751)),f777(a7,x59752)))+~P1(f777(f777(f234(a851),x59751),x59752)) % 174.01/173.89 [5978]E(x59781,x59782)+~E(f777(f305(a851,a3,f104(a3)),x59781),f777(f305(a851,a3,f104(a3)),x59782)) % 174.01/173.89 [5994]P1(f777(f777(f235(a851),x59941),x59942))+~P1(f777(f777(f235(a851),f777(a116,x59941)),x59942)) % 174.01/173.89 [5997]P1(f777(f777(f235(a851),x59971),x59972))+~P1(f777(f777(f234(a851),f777(a116,x59971)),x59972)) % 174.01/173.89 [5998]P1(f777(f777(f234(a851),x59981),x59982))+~P1(f777(f777(f234(a851),f777(a116,x59981)),x59982)) % 174.01/173.89 [6015]E(f54(a3,x60151,x60152),f4(a3))+E(f777(f777(f5(a3),f54(a3,x60151,x60152)),x60152),f54(a3,x60151,f777(f83(a3),x60152))) % 174.01/173.89 [6086]E(f777(f44(f858(x60861,a845)),f777(f303(x60861),x60862)),f777(f777(f244(a851),f777(a116,f777(a116,f4(a851)))),f777(f44(x60861),x60862)))+~P1(f777(f65(x60861),x60862)) % 174.01/173.89 [6089]E(x60891,f117(x60892))+E(f777(f777(f155(x60892),x60891),f777(f777(f5(a851),f777(f183(f852(x60892)),x60891)),f82(a851))),f136(x60892,x60891)) % 174.01/173.89 [6113]E(x61131,f117(x61132))+E(f777(f777(f127(x61132),f777(f159(x61132),x61131)),f777(f777(f142(x61132),f777(f133(x61132),x61131)),f117(x61132))),f777(f143(x61132),x61131)) % 174.01/173.89 [6144]~P1(f777(f65(x61441),f46(f858(x61441,a845),x61442)))+P1(f777(f65(f858(x61441,a845)),x61442)) % 174.01/173.89 [6165]P1(f777(f777(f234(a851),f777(f108(a851),x61651)),f777(f108(a851),x61652)))+~P1(f777(f777(f234(a3),x61651),a87)) % 174.01/173.89 [6185]~P1(f777(f777(f235(a3),x61851),x61852))+P1(f777(f777(f235(a3),x61851),f777(f777(f84(a3),x61852),f82(a3)))) % 174.01/173.89 [6186]~P1(f777(f777(f234(a3),x61861),x61862))+P1(f777(f777(f235(a3),x61861),f777(f777(f84(a3),x61862),f82(a3)))) % 174.01/173.89 [6187]~P1(f777(f777(f235(a3),x61871),x61872))+P1(f777(f777(f234(a3),x61871),f777(f777(f5(a3),x61872),f82(a3)))) % 174.01/173.89 [6190]~P1(f777(f777(f235(a851),x61901),x61902))+P1(f777(f777(f235(a3),f777(f104(a3),x61901)),f777(f104(a3),x61902))) % 174.01/173.89 [6191]~P1(f777(f777(f235(a3),x61911),x61912))+P1(f777(f777(f235(a3),f777(f108(a3),x61911)),f777(f108(a3),x61912))) % 174.01/173.89 [6192]~P1(f777(f777(f234(a3),x61921),x61922))+P1(f777(f777(f234(a851),f777(f108(a851),x61921)),f777(f108(a851),x61922))) % 174.01/173.89 [6194]~P1(f777(f777(f234(a851),x61941),x61942))+P1(f777(f777(f234(a3),f777(f104(a3),x61941)),f777(f104(a3),x61942))) % 174.01/173.89 [6195]~P1(f777(f777(f234(a3),x61951),x61952))+P1(f777(f777(f234(a3),f777(f108(a3),x61951)),f777(f108(a3),x61952))) % 174.01/173.89 [6197]~P1(f777(f777(f281(a851),x61971),x61972))+P1(f777(f777(f281(a3),f777(f104(a3),x61971)),f777(f104(a3),x61972))) % 174.01/173.89 [6213]~P1(f777(f777(f234(a851),x62131),x62132))+~P1(f777(f777(f234(a851),f777(a116,x62132)),x62131)) % 174.01/173.89 [6261]~P1(f777(f777(f235(a851),f777(a116,x62611)),f777(a116,x62612)))+P1(f777(f777(f235(a851),x62611),x62612)) % 174.01/173.89 [6262]~P1(f777(f777(f235(a103),f777(a7,x62621)),f777(a7,x62622)))+P1(f777(f777(f235(a851),x62621),x62622)) % 174.01/173.89 [6263]~P1(f777(f777(f235(a851),f777(a109,x62631)),f777(a109,x62632)))+P1(f777(f777(f235(a3),x62631),x62632)) % 174.01/173.89 [6264]~P1(f777(f777(f235(a851),f777(a24,x62641)),f777(a24,x62642)))+P1(f777(f777(f235(a103),x62641),x62642)) % 174.01/173.89 [6265]~P1(f777(f777(f234(a851),f777(a116,x62651)),f777(a116,x62652)))+P1(f777(f777(f234(a851),x62651),x62652)) % 174.01/173.89 [6266]~P1(f777(f777(f234(a103),f777(a7,x62661)),f777(a7,x62662)))+P1(f777(f777(f234(a851),x62661),x62662)) % 174.01/173.89 [6267]~P1(f777(f777(f234(a851),f777(a24,x62671)),f777(a24,x62672)))+P1(f777(f777(f234(a103),x62671),x62672)) % 174.01/173.89 [6311]~P1(f777(f777(f235(a851),f777(a109,x63112)),f777(a109,x63111)))+P1(f777(f777(f235(a3),f4(a3)),x63111)) % 174.01/173.89 [6322]~E(f54(a3,f777(f108(a3),x63222),f777(f108(a3),x63221)),f4(a3))+P1(f777(f777(f281(a3),f777(f108(a3),x63221)),f777(f108(a3),x63222))) % 174.01/173.89 [6341]P1(f777(f777(f234(a3),f4(a3)),f54(a3,x63411,x63412)))+~P1(f777(f777(f235(a3),f4(a3)),x63412)) % 174.01/173.89 [6510]P36(x65101,x65102)+~E(f777(f777(f283(x65101,x65101,x65101),x65102),x65102),f182(f858(f857(x65101,x65101),a845))) % 174.01/173.89 [6526]~P36(x65261,x65262)+P36(x65261,f777(f777(f283(x65261,x65261,x65261),x65262),x65262)) % 174.01/173.89 [6538]P1(f777(f777(f235(a3),x65381),x65382))+~P1(f777(f777(f234(a3),x65381),f777(f777(f5(a3),x65382),f82(a3)))) % 174.01/173.89 [6539]P1(f777(f777(f234(a3),x65391),x65392))+~P1(f777(f777(f235(a3),x65391),f777(f777(f84(a3),x65392),f82(a3)))) % 174.01/173.89 [6542]P1(f777(f777(f235(a851),x65421),x65422))+~P1(f777(f777(f235(a3),f777(f104(a3),x65421)),f777(f104(a3),x65422))) % 174.01/173.89 [6543]P1(f777(f777(f235(a3),x65431),x65432))+~P1(f777(f777(f235(a851),f777(f108(a851),x65431)),f777(f108(a851),x65432))) % 174.01/173.89 [6544]P1(f777(f777(f235(a3),x65441),x65442))+~P1(f777(f777(f235(a3),f777(f108(a3),x65441)),f777(f108(a3),x65442))) % 174.01/173.89 [6546]P1(f777(f777(f234(a851),x65461),x65462))+~P1(f777(f777(f234(a3),f777(f104(a3),x65461)),f777(f104(a3),x65462))) % 174.01/173.89 [6547]P1(f777(f777(f234(a3),x65471),x65472))+~P1(f777(f777(f234(a3),f777(f108(a3),x65471)),f777(f108(a3),x65472))) % 174.01/173.89 [6549]P1(f777(f777(f281(a851),x65491),x65492))+~P1(f777(f777(f281(a3),f777(f104(a3),x65491)),f777(f104(a3),x65492))) % 174.01/173.89 [6605]E(f54(a3,f777(f108(a3),x66051),f777(f108(a3),x66052)),f4(a3))+~P1(f777(f777(f281(a3),f777(f108(a3),x66052)),f777(f108(a3),x66051))) % 174.01/173.89 [6620]~E(f284(a851,f281(a851),x66201,x66202),f182(f858(a851,a845)))+~P1(f777(f777(f281(a851),x66201),x66202)) % 174.01/173.89 [6648]~E(f771(x66482,x66481),f117(x66481))+E(f777(f134(f852(x66481),f852(x66481),f127(x66481),f117(x66481)),x66482),f117(x66481)) % 174.01/173.89 [6649]~E(f772(x66492,x66491),f117(x66491))+E(f777(f134(f852(x66491),f852(x66491),f127(x66491),f117(x66491)),x66492),f117(x66491)) % 174.01/173.89 [6656]~P9(x66561)+E(f777(f134(x66561,x66561,f106(x66561),f241(x66561)),x66562),f47(x66561,f777(f160(x66561),x66562))) % 174.01/173.89 [6657]~P9(x66571)+E(f777(f134(x66571,x66571,f105(x66571),f182(x66571)),x66572),f46(x66571,f777(f160(x66571),x66572))) % 174.01/173.89 [6669]E(x66691,f4(a103))+E(f777(f777(f84(a851),f777(a24,f777(f777(f5(a103),x66691),f82(a103)))),f777(a116,x66692)),f777(f777(f84(a851),f777(a24,x66691)),x66692)) % 174.01/173.89 [6721]P1(f777(f777(f235(a3),f777(f777(f5(a3),x67211),x67212)),f4(a3)))+~P1(f777(f777(f235(a3),x67211),x67212)) % 174.01/173.89 [6749]~P100(x67491)+E(f777(f777(f105(f858(x67491,a845)),f777(f777(f304(x67491),x67492),f182(f858(x67491,a845)))),f777(f298(x67491),x67492)),f777(f260(x67491),x67492)) % 174.01/173.89 [6831]~P58(x68311,x68312)+P36(x68311,f777(f258(f857(x68311,x68311)),f777(f253(x68311,x68311,a845),x68312))) % 174.01/173.89 [6832]~P58(x68321,x68322)+P56(x68321,f777(f258(f857(x68321,x68321)),f777(f253(x68321,x68321,a845),x68322))) % 174.01/173.89 [6833]E(x68331,f182(f858(x68332,a845)))+~P1(f777(f777(f234(f858(x68332,a845)),x68331),f182(f858(x68332,a845)))) % 174.01/173.89 [6918]~P1(f777(f777(f235(a851),f4(a851)),x69182))+P1(f777(f777(f235(a851),f54(a851,x69181,x69182)),x69182)) % 174.01/173.89 [6920]~P1(f777(f777(f235(a3),f4(a3)),x69202))+P1(f777(f777(f235(a3),f54(a3,x69201,x69202)),x69202)) % 174.01/173.89 [6921]~P1(f777(f777(f235(a851),f4(a851)),x69212))+P1(f777(f777(f234(a851),f54(a851,x69211,x69212)),x69212)) % 174.01/173.89 [6922]~P1(f777(f777(f234(a3),f4(a3)),x69221))+P1(f777(f777(f234(a3),f54(a3,x69221,x69222)),x69221)) % 174.01/173.89 [6994]~P99(x69941)+E(f777(f777(f5(f858(x69941,a845)),f777(f777(f304(x69941),x69942),f182(f858(x69941,a845)))),f777(f259(x69941),x69942)),f777(f777(f304(x69941),x69942),f182(f858(x69941,a845)))) % 174.01/173.89 [7072]~P49(x70721,x70722)+P47(x70721,f241(f858(x70721,a845)),f777(f258(f857(x70721,x70721)),f777(f253(x70721,x70721,a845),x70722))) % 174.01/173.89 [7073]P1(f777(x70731,x70732))+P1(f777(f777(f336(f858(f857(a851,a851),a845)),f607(x70732,x70731)),a102)) % 174.01/173.89 [7116]E(f777(f777(f127(a851),f132(a851,f777(f296(a851,x71161),x71162))),f777(f777(f142(a851),x71162),f117(a851))),f132(a851,f777(f296(a851,x71161),f777(a116,x71162))))+~P1(f777(f777(f234(a851),x71161),x71162)) % 174.01/173.89 [7273]E(x72731,f4(a851))+~E(f777(f134(a851,a851,f84(a851),x72731),x72732),f4(a851)) % 174.01/173.89 [7302]~P1(f777(f777(f235(a3),f777(f777(f5(a3),x73021),x73022)),f4(a3)))+P1(f777(f777(f235(a3),x73021),x73022)) % 174.01/173.89 [7332]P36(x73321,x73322)+~P36(x73321,f777(f777(f283(x73321,x73321,x73321),x73322),x73322)) % 174.01/173.89 [7364]~P1(f777(f777(f234(a851),f777(a116,x73641)),x73642))+P1(f177(a845,a180,f777(f234(a851),x73641),x73642)) % 174.01/173.89 [7524]P29(a851,a851,f777(f777(f11(a851,a851,a851),f5(a851)),x75241),x75242)+P1(f777(f777(f336(a851),f609(x75241,x75242)),x75242)) % 174.01/173.89 [7583]E(f777(f777(f777(f69(a851,x75831,f84(a851)),f777(f20(a851,x75831),f82(a851))),f4(a851)),x75832),f777(f44(x75831),x75832))+~P1(f777(f65(x75831),x75832)) % 174.01/173.89 [7626]P29(a851,a851,f777(f777(f11(a851,a851,a851),f5(a851)),x76261),x76262)+~P1(f777(f777(f234(a851),x76261),f609(x76261,x76262))) % 174.01/173.89 [7683]P36(x76831,x76832)+P1(f777(f777(f234(f858(x76831,a845)),f603(x76832,x76831)),f777(f279(x76831,x76831,x76832),f603(x76832,x76831)))) % 174.01/173.89 [7687]P58(x76871,x76872)+~P36(x76871,f777(f258(f857(x76871,x76871)),f777(f253(x76871,x76871,a845),x76872))) % 174.01/173.89 [7759]P1(f777(f777(f234(a851),f777(a116,x77591)),x77592))+~P1(f177(a845,a180,f777(f234(a851),x77591),x77592)) % 174.01/173.89 [7815]P1(f777(f777(f336(f857(a851,a851)),f777(f777(f243(a851,a851),x78151),x78152)),f302(a851,a325)))+~P1(f777(f777(f234(a851),x78151),x78152)) % 174.01/173.89 [7909]P49(x79091,x79092)+~P47(x79091,f241(f858(x79091,a845)),f777(f258(f857(x79091,x79091)),f777(f253(x79091,x79091,a845),x79092))) % 174.01/173.89 [8165]~P36(x81651,f777(f280(x81651,x81651),x81652))+P36(x81651,f777(f280(x81651,x81651),f777(f777(f283(x81651,x81651,x81651),x81652),f302(x81651,x81652)))) % 174.01/173.89 [8282]P1(f777(f65(f857(x82821,x82821)),f777(f777(f283(x82821,x82821,x82821),x82822),f302(x82821,x82822))))+~P1(f777(f65(f857(x82821,x82821)),x82822)) % 174.01/173.89 [8312]E(x83121,f4(a3))+P1(f777(f58(x83122,x83121),f777(f777(f243(a3,a3),f777(f777(f45(a3),x83122),x83121)),f54(a3,x83122,x83121)))) % 174.01/173.89 [8326]~P1(f777(f777(f336(f857(a851,a851)),f777(f777(f243(a851,a851),x83261),x83262)),f302(a851,a325)))+P1(f777(f777(f234(a851),x83261),x83262)) % 174.01/173.89 [8347]~P67(x83471)+E(f777(f134(x83471,x83471,f777(f11(x83471,x83471,x83471),f84(x83471)),f4(x83471)),f777(f144(x83471),x83472)),f777(f134(x83471,x83471,f84(x83471),f4(x83471)),x83472)) % 174.01/173.89 [8622]P1(f777(f777(f336(f857(a851,a851)),f777(f777(f243(a851,a851),x86221),x86222)),f777(f777(f283(a851,a851,a851),a325),f302(a851,a325))))+~P1(f777(f777(f235(a851),x86221),x86222)) % 174.01/173.89 [8664]~P1(f777(f65(f857(x86641,x86641)),f777(f777(f283(x86641,x86641,x86641),x86642),f302(x86641,x86642))))+P1(f777(f65(f857(x86641,x86641)),x86642)) % 174.01/173.89 [8884]P56(x88841,x88842)+P1(f777(f777(f336(f857(x88841,x88841)),f777(f777(f243(x88841,x88841),f636(x88842,x88841)),f636(x88842,x88841))),f777(f777(f283(x88841,x88841,x88841),x88842),f302(x88841,x88842)))) % 174.01/173.89 [8885]P56(x88851,x88852)+P1(f777(f777(f336(f857(x88851,x88851)),f777(f777(f243(x88851,x88851),f643(x88852,x88851)),f643(x88852,x88851))),f777(f777(f283(x88851,x88851,x88851),x88852),f302(x88851,x88852)))) % 174.01/173.89 [8994]~P1(f777(f777(f336(f857(a851,a851)),f777(f777(f243(a851,a851),x89941),x89942)),f777(f777(f283(a851,a851,a851),a325),f302(a851,a325))))+P1(f777(f777(f235(a851),x89941),x89942)) % 174.01/173.89 [4968]~P88(x49681)+E(f777(f777(f84(x49681),f777(f108(x49681),a87)),x49682),x49682) % 174.01/173.89 [4998]~P69(x49981)+E(f777(f777(f84(x49981),f777(f83(x49981),x49982)),x49982),f4(x49981)) % 174.01/173.89 [4999]~P6(x49991)+E(f777(f777(f84(x49991),f777(f83(x49991),x49992)),x49992),f4(x49991)) % 174.01/173.89 [5000]~P90(x50001)+E(f777(f777(f105(x50001),f777(f83(x50001),x50002)),x50002),f241(x50001)) % 174.01/173.89 [5001]~P90(x50011)+E(f777(f777(f106(x50011),f777(f83(x50011),x50012)),x50012),f182(x50011)) % 174.01/173.89 [5032]~P88(x50321)+E(f777(f777(f85(x50321),f777(f108(x50321),a101)),x50322),f777(f83(x50321),x50322)) % 174.01/173.89 [5194]~P104(x51941)+E(f777(f777(f85(x51941),f777(f83(x51941),f82(x51941))),x51942),f777(f83(x51941),x51942)) % 174.01/173.89 [5237]E(f777(f79(a3),x52371),f82(a3))+~E(f777(f79(a3),f777(f777(f85(a3),x52371),x52372)),f82(a3)) % 174.01/173.89 [5326]~P88(x53261)+E(f777(f777(f84(x53261),f82(x53261)),f777(f108(x53261),x53262)),f777(f108(x53261),f777(f777(f5(a3),x53262),a101))) % 174.01/173.89 [5381]~P93(x53811)+E(f17(x53811,f777(f777(f304(x53811),x53812),f182(f858(x53811,a845)))),x53812) % 174.01/173.89 [5382]~P100(x53821)+E(f18(x53821,f777(f777(f304(x53821),x53822),f182(f858(x53821,a845)))),x53822) % 174.01/173.89 [5383]~P100(x53831)+E(f19(x53831,f777(f777(f304(x53831),x53832),f182(f858(x53831,a845)))),x53832) % 174.01/173.89 [5384]~P93(x53841)+E(f14(x53841,f777(f777(f304(x53841),x53842),f182(f858(x53841,a845)))),x53842) % 174.01/173.89 [5385]~P9(x53851)+E(f47(x53851,f777(f777(f304(x53851),x53852),f182(f858(x53851,a845)))),x53852) % 174.01/173.89 [5386]~P9(x53861)+E(f46(x53861,f777(f777(f304(x53861),x53862),f182(f858(x53861,a845)))),x53862) % 174.01/173.89 [5408]E(f777(f777(f84(a851),x54081),f777(f777(f5(a851),x54082),x54081)),x54082)+P1(f777(f777(f235(a851),x54082),x54081)) % 174.01/173.89 [5440]E(x54401,f117(x54402))+P1(f777(f777(f235(a851),f4(a851)),f777(f183(f852(x54402)),x54401))) % 174.01/173.89 [5558]~P100(x55581)+E(f15(x55581,f181(x55581),f777(f777(f304(x55581),x55582),f182(f858(x55581,a845)))),x55582) % 174.01/173.89 [5559]~P100(x55591)+E(f16(x55591,f238(x55591),f777(f777(f304(x55591),x55592),f182(f858(x55591,a845)))),x55592) % 174.01/173.89 [5620]E(f777(f777(f84(a851),x56201),f777(f777(f5(a851),x56202),x56201)),x56202)+~P1(f777(f777(f234(a851),x56201),x56202)) % 174.01/173.89 [5621]E(f777(f777(f85(a3),x56211),f777(f777(f45(a3),x56212),x56211)),x56212)+~P1(f777(f777(f281(a3),x56211),x56212)) % 174.01/173.89 [5622]E(f777(f777(f5(a851),x56221),f777(f777(f5(a851),x56221),x56222)),x56222)+~P1(f777(f777(f234(a851),x56222),x56221)) % 174.01/173.89 [5641]E(f54(a851,f777(f777(f5(a851),x56411),x56412),x56412),f54(a851,x56411,x56412))+P1(f777(f777(f235(a851),x56411),x56412)) % 174.01/173.89 [5651]E(f777(f83(a3),f777(f777(f45(a3),x56511),f777(f83(a3),x56512))),f287(x56511,x56512))+P1(f777(f777(f234(a3),f4(a3)),x56512)) % 174.01/173.89 [5653]~E(x56532,f4(a851))+P1(f777(f777(f235(a851),f4(a851)),f777(f777(f244(a851),x56531),x56532))) % 174.01/173.89 [5713]~P88(x57131)+E(f777(f777(f84(x57131),f777(f83(x57131),f82(x57131))),f777(f108(x57131),x57132)),f777(f108(x57131),f777(f777(f84(a3),x57132),a101))) % 174.01/173.89 [5714]E(f777(f777(f244(a851),f777(f108(a851),x57141)),x57142),f777(f777(f244(a851),f4(a851)),x57142))+~P1(f777(a188,f777(f108(a3),x57141))) % 174.01/173.89 [5815]E(f777(f133(a851),f132(a851,f777(f296(a851,x58151),x58152))),x58151)+~P1(f777(f777(f235(a851),x58151),x58152)) % 174.01/173.89 [5832]E(f777(f777(f85(a851),f777(f108(a851),x58321)),f777(f108(a851),x58322)),f777(f108(a851),f777(f777(f85(a3),x58321),x58322)))+P1(f777(f777(f235(a3),x58321),a87)) % 174.01/173.89 [5838]~P118(x58381)+P1(f777(f777(f234(x58381),f4(x58381)),f777(f777(f85(x58381),x58382),x58382))) % 174.01/173.89 [5850]E(f777(f777(f5(a851),f777(a116,x58501)),x58502),f777(a116,f777(f777(f5(a851),x58501),x58502)))+~P1(f777(f777(f234(a851),x58502),x58501)) % 174.01/173.89 [5853]E(f54(a851,f777(f777(f5(a851),x58531),x58532),x58532),f54(a851,x58531,x58532))+~P1(f777(f777(f234(a851),x58532),x58531)) % 174.01/173.89 [5905]E(f777(f777(f244(a851),f777(a109,x59051)),x59052),f777(a109,f777(f777(f244(a3),x59051),x59052)))+~P1(f777(f777(f234(a3),f4(a3)),x59051)) % 174.01/173.89 [5921]P1(f777(f129(x59211),x59212))+P1(f777(f777(f235(a851),f724(x59212,x59211)),f777(f183(f852(x59211)),x59212))) % 174.01/173.89 [5922]P1(f777(f129(x59221),x59222))+P1(f777(f777(f235(a851),f728(x59222,x59221)),f777(f183(f852(x59221)),x59222))) % 174.01/173.89 [5937]~P1(f777(f777(f281(a3),x59371),x59372))+P1(f777(f777(f281(a3),f777(f83(a3),x59371)),x59372)) % 174.01/173.89 [5940]~E(x59401,f117(x59402))+~P1(f777(f777(f235(a851),f4(a851)),f777(f183(f852(x59402)),x59401))) % 174.01/173.89 [5953]E(f136(a851,f132(a851,f777(f296(a851,x59531),x59532))),f777(f777(f5(a851),x59532),f82(a851)))+~P1(f777(f777(f235(a851),x59531),x59532)) % 174.01/173.89 [5956]E(f777(f777(f84(a3),x59561),f777(f104(a3),f777(a116,f630(x59562,x59561)))),x59562)+~P1(f777(f777(f235(a3),x59561),x59562)) % 174.01/173.89 [5962]E(x59621,f4(a851))+E(f777(f777(f85(a851),x59622),f777(f777(f244(a851),x59622),f777(f777(f5(a851),x59621),f82(a851)))),f777(f777(f244(a851),x59622),x59621)) % 174.01/173.89 [5988]E(f777(f777(f85(a851),f777(a109,x59881)),f777(a109,x59882)),f777(a109,f777(f777(f85(a3),x59881),x59882)))+~P1(f777(f777(f234(a3),f4(a3)),x59881)) % 174.01/173.89 [5989]E(f777(f777(f45(a851),f777(a109,x59891)),f777(a109,x59892)),f777(a109,f777(f777(f45(a3),x59891),x59892)))+~P1(f777(f777(f234(a3),f4(a3)),x59891)) % 174.01/173.89 [6003]~P85(x60031)+E(f777(f777(f84(x60031),x60032),x60032),f777(f777(f85(x60031),f777(f777(f84(x60031),f82(x60031)),f82(x60031))),x60032)) % 174.01/173.89 [6022]E(f777(f777(f45(a3),f777(f79(a3),x60221)),f777(f79(a3),x60222)),f777(f79(a3),f777(f777(f45(a3),x60221),x60222)))+~P1(f777(f777(f281(a3),x60222),x60221)) % 174.01/173.89 [6023]E(f777(f777(f5(a3),f777(f104(a3),x60231)),f777(f104(a3),x60232)),f777(f104(a3),f777(f777(f5(a851),x60231),x60232)))+~P1(f777(f777(f234(a851),x60232),x60231)) % 174.01/173.89 [6025]E(f777(f777(f243(a3,a3),f777(f108(a3),a101)),f777(f777(f84(a3),x60251),x60252)),f59(x60251,x60252))+~P1(f777(f777(f234(a3),x60252),f4(a3))) % 174.01/173.89 [6064]E(f166(x60641,x60642),f117(f852(x60641)))+P1(f777(f777(f336(f852(x60641)),f723(x60642,x60641)),f777(f160(f852(x60641)),x60642))) % 174.01/173.89 [6128]~P1(f777(f777(f281(a851),x61281),x61282))+P1(f777(f777(f281(a851),x61281),f777(f777(f84(a851),x61282),x61281))) % 174.01/173.89 [6150]E(f777(f777(f142(a3),x61501),f165(f777(f777(f84(a3),x61501),f82(a3)),x61502)),f165(x61501,x61502))+~P1(f777(f777(f234(a3),x61501),x61502)) % 174.01/173.89 [6188]~P1(f777(f777(f235(a851),x61882),x61881))+P1(f777(f777(f235(a851),f4(a851)),f777(f777(f5(a851),x61881),x61882))) % 174.01/173.89 [6220]~P1(f777(f777(f235(a851),x62201),f777(a109,x62202)))+P1(f777(f777(f235(a3),f777(f104(a3),x62201)),x62202)) % 174.01/173.89 [6221]P1(f777(f777(f281(a3),x62211),x62212))+~P1(f777(f777(f281(a3),f777(f83(a3),x62211)),x62212)) % 174.01/173.89 [6251]~P100(x62511)+E(f777(f777(f105(f858(x62511,a845)),f777(f259(x62511),x62512)),f777(f777(f304(x62511),x62512),f182(f858(x62511,a845)))),f777(f295(x62511),x62512)) % 174.01/173.89 [6254]~P1(f777(f777(f235(a851),f4(a851)),x62541))+P1(f777(f777(f235(a851),f4(a851)),f777(f777(f244(a851),x62541),x62542))) % 174.01/173.89 [6255]~P1(f777(f777(f234(a3),f4(a3)),x62551))+P1(f777(f777(f234(a3),f4(a3)),f777(f777(f244(a3),x62551),x62552))) % 174.01/173.89 [6283]~E(f777(x62831,f4(a851)),f4(a851))+E(f777(f777(f10(a851,a851),x62831),f297(a851,f777(a116,f4(a851)),x62832)),f777(f777(f10(a851,a851),x62831),f297(a851,f4(a851),x62832))) % 174.01/173.89 [6349]~P88(x63491)+E(f777(f777(f85(x63491),f777(f777(f84(x63491),f82(x63491)),f82(x63491))),f777(f108(x63491),x63492)),f777(f108(x63491),f777(f777(f84(a3),x63492),x63492))) % 174.01/173.89 [6371]E(f777(f777(f304(a3),x63711),f297(a3,f777(f777(f84(a3),x63711),f82(a3)),x63712)),f297(a3,x63711,x63712))+P1(f777(f777(f235(a3),x63712),x63711)) % 174.01/173.89 [6372]P1(f777(f777(f235(a851),x63721),f777(a109,x63722)))+~P1(f777(f777(f235(a3),f777(f104(a3),x63721)),x63722)) % 174.01/173.89 [6474]P1(f777(f777(f281(a851),x64741),x64742))+~P1(f777(f777(f281(a851),x64741),f777(f777(f84(a851),x64742),x64741))) % 174.01/173.89 [6480]E(f777(a109,f777(f777(f45(a3),f777(f108(a3),x64801)),f777(f108(a3),x64802))),f777(f777(f45(a851),f777(f108(a851),x64801)),f777(f108(a851),x64802)))+P1(f777(a188,f777(f108(a3),x64801))) % 174.01/173.89 [6540]P1(f777(f777(f235(a851),x65401),x65402))+~P1(f777(f777(f235(a851),f4(a851)),f777(f777(f5(a851),x65402),x65401))) % 174.01/173.89 [6583]P1(f777(f777(f235(a851),f4(a851)),x65831))+~P1(f777(f777(f235(a851),f4(a851)),f777(f777(f85(a851),x65832),x65831))) % 174.01/173.89 [6584]P1(f777(f777(f235(a851),f4(a851)),x65841))+~P1(f777(f777(f235(a851),f4(a851)),f777(f777(f85(a851),x65841),x65842))) % 174.01/173.89 [6601]~P1(f777(f777(f234(a3),x66011),f4(a3)))+E(f777(f777(f85(a851),f777(a109,f777(f83(a3),x66011))),f777(a109,f777(f83(a3),x66012))),f777(a109,f777(f777(f85(a3),x66011),x66012))) % 174.01/173.89 [6667]~E(x66672,f182(f858(x66671,a845)))+P1(f777(f777(f234(f858(x66671,a845)),x66672),f777(f83(f858(x66671,a845)),x66672))) % 174.01/173.89 [6730]~P88(x67301)+E(f777(f777(f84(x67301),f777(f777(f84(x67301),f4(x67301)),f777(f108(x67301),x67302))),f777(f108(x67301),x67302)),f777(f108(x67301),f777(f777(f84(a3),x67302),x67302))) % 174.01/173.89 [6739]~P1(f777(f777(f281(a3),f777(f104(a3),x67391)),x67392))+P1(f777(f777(f281(a851),x67391),f777(a109,f777(f79(a3),x67392)))) % 174.01/173.89 [6791]~P1(f777(f777(f235(a3),x67911),x67912))+P1(f777(f777(f234(a3),f777(f777(f84(a3),x67911),f82(a3))),x67912)) % 174.01/173.89 [6830]P1(f777(f777(f281(a3),f777(f104(a3),x68301)),x68302))+~P1(f777(f777(f281(a851),x68301),f777(a109,f777(f79(a3),x68302)))) % 174.01/173.89 [6864]E(x68641,f4(a851))+~P1(f777(f777(f234(a3),f777(f104(a3),x68642)),f777(f83(a3),f777(f104(a3),x68641)))) % 174.01/173.89 [6865]E(x68651,f4(a851))+~P1(f777(f777(f234(a3),f777(f104(a3),x68651)),f777(f83(a3),f777(f104(a3),x68652)))) % 174.01/173.89 [6970]E(f777(f777(f243(a3,a3),f777(f108(a3),a101)),f777(f777(f84(a3),x69701),x69702)),f59(x69701,x69702))+~P1(f777(f777(f234(a3),f4(a3)),f777(f777(f84(a3),x69701),x69702))) % 174.01/173.89 [7007]~P30(x70071,x70072)+P36(x70071,f777(f242(f858(f857(x70071,x70071),a845),f858(f857(x70071,x70071),a845)),x70072)) % 174.01/173.89 [7028]~P1(f777(f777(f234(a851),f777(a116,f4(a851))),x70281))+P1(f777(f777(f234(a851),f777(a116,f4(a851))),f777(f777(f244(a851),x70281),x70282))) % 174.01/173.89 [7198]~P1(f777(f777(f235(a3),x71981),x71982))+P1(f777(f777(f235(a3),f777(f777(f84(a3),x71981),x71981)),f777(f777(f84(a3),x71982),x71982))) % 174.01/173.89 [7210]~P1(f777(f777(f234(a3),x72101),x72102))+P1(f777(f777(f234(a3),f777(f777(f84(a3),x72101),x72101)),f777(f777(f84(a3),x72102),x72102))) % 174.01/173.89 [7277]~P1(f777(f777(f235(a851),f4(a851)),x72771))+P1(f777(f777(f235(a851),f777(f777(f5(a851),x72771),f777(a116,x72772))),x72771)) % 174.01/173.89 [7314]P1(f777(f777(f234(a851),f777(a116,f4(a851))),x73141))+~P1(f777(f777(f234(a851),f777(a116,f4(a851))),f777(f777(f85(a851),x73142),x73141))) % 174.01/173.89 [7315]P1(f777(f777(f234(a851),f777(a116,f4(a851))),x73151))+~P1(f777(f777(f234(a851),f777(a116,f4(a851))),f777(f777(f85(a851),x73151),x73152))) % 174.01/173.89 [7319]P1(f777(f777(f234(a851),f777(f777(f155(a851),x73191),x73192)),f777(f157(a851),x73191)))+~P1(f777(f777(f235(a851),x73192),f777(f183(f852(a851)),x73191))) % 174.01/173.89 [7363]P1(f777(f777(f235(a3),x73631),x73632))+~P1(f777(f777(f234(a3),f777(f777(f84(a3),x73631),f82(a3))),x73632)) % 174.01/173.89 [7409]P1(f777(f65(x74091),f241(f858(x74091,a845))))+~P1(f777(f65(f858(x74092,x74091)),f241(f858(f858(x74092,x74091),a845)))) % 174.01/173.89 [7410]P1(f777(f65(x74101),f241(f858(x74101,a845))))+~P1(f777(f65(f859(x74102,x74101)),f241(f858(f859(x74102,x74101),a845)))) % 174.01/173.89 [7411]P1(f777(f65(x74111),f241(f858(x74111,a845))))+~P1(f777(f65(f859(x74111,x74112)),f241(f858(f859(x74111,x74112),a845)))) % 174.01/173.89 [7450]E(x74501,f182(f858(x74502,a845)))+~P1(f777(f777(f234(f858(x74502,a845)),x74501),f777(f83(f858(x74502,a845)),x74501))) % 174.01/173.89 [7593]E(f777(f134(f852(x75931),f852(x75931),f127(x75931),f117(x75931)),x75932),f117(x75931))+P1(f777(f777(f336(f852(x75931)),f771(x75932,x75931)),f777(f160(f852(x75931)),x75932))) % 174.01/173.89 [7594]E(f777(f134(f852(x75941),f852(x75941),f127(x75941),f117(x75941)),x75942),f117(x75941))+P1(f777(f777(f336(f852(x75941)),f772(x75942,x75941)),f777(f160(f852(x75941)),x75942))) % 174.01/173.89 [7835]P1(f777(f777(f235(a3),x78351),x78352))+~P1(f777(f777(f235(a3),f777(f777(f84(a3),x78351),x78351)),f777(f777(f84(a3),x78352),x78352))) % 174.01/173.89 [7838]P1(f777(f777(f234(a3),x78381),x78382))+~P1(f777(f777(f234(a3),f777(f777(f84(a3),x78381),x78381)),f777(f777(f84(a3),x78382),x78382))) % 174.01/173.89 [7930]~P85(x79301)+E(f777(f777(f85(x79301),f777(f777(f84(x79301),f82(x79301)),f82(x79301))),f777(f777(f10(a851,x79301),f104(x79301)),f297(a851,f82(a851),x79302))),f777(f777(f85(x79301),f777(f104(x79301),x79302)),f777(f777(f84(x79301),f777(f104(x79301),x79302)),f82(x79301)))) % 174.01/173.89 [7986]P1(f777(f777(f336(a851),x79861),x79862))+~P1(f777(f777(f336(a3),f777(f104(a3),x79861)),f777(f305(a851,a3,f104(a3)),x79862))) % 174.01/173.89 [8136]~P1(f777(f65(x81361),x81362))+E(f777(f305(a851,x81361,f585(x81362,x81361)),f777(f258(a851),f777(f777(f11(a851,a851,a845),f235(a851)),f586(x81362,x81361)))),x81362) % 174.01/173.89 [8420]P48(x84201,x84202)+P1(f777(f777(f336(f857(x84201,x84201)),f777(f777(f243(x84201,x84201),f475(x84202,x84201)),f475(x84202,x84201))),x84202)) % 174.01/173.89 [8556]~P88(x85561)+E(f777(f777(f5(x85561),f82(x85561)),f777(f108(x85561),x85562)),f777(f108(x85561),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f83(a3),x85562)))) % 174.01/173.89 [8660]~P1(f777(f777(f235(f858(a851,a845)),x86601),x86602))+P1(f777(f777(f235(f858(a3,a845)),f777(f305(a851,a3,f104(a3)),x86601)),f777(f305(a851,a3,f104(a3)),x86602))) % 174.01/173.89 [8687]~P1(f777(f777(f235(a3),x86871),x86872))+P1(f777(f777(f235(a3),f777(f777(f5(a3),f777(f777(f84(a3),x86871),x86871)),a101)),f777(f777(f84(a3),x86872),x86872))) % 174.01/173.89 [8689]~P1(f777(f777(f235(a3),x86891),x86892))+P1(f777(f777(f234(a3),f777(f777(f5(a3),f777(f777(f84(a3),x86891),x86891)),a101)),f777(f777(f84(a3),x86892),x86892))) % 174.01/173.89 [8756]~P1(f777(f777(f336(a851),x87561),f777(f160(a851),x87562)))+P1(f777(f777(f234(a851),x87561),f777(f134(a851,a851,f84(a851),f4(a851)),x87562))) % 174.01/173.89 [8828]P44(x88281,x88282)+~P1(f777(f777(f336(f857(x88281,x88281)),f777(f777(f243(x88281,x88281),f429(x88282,x88281)),f429(x88282,x88281))),x88282)) % 174.01/173.89 [8961]~P1(f777(f777(f235(f858(a3,a845)),f777(f305(a851,a3,f104(a3)),x89611)),f777(f305(a851,a3,f104(a3)),x89612)))+P1(f777(f777(f235(f858(a851,a845)),x89611),x89612)) % 174.01/173.89 [8962]~P1(f777(f777(f234(f858(a3,a845)),f777(f305(a851,a3,f104(a3)),x89621)),f777(f305(a851,a3,f104(a3)),x89622)))+P1(f777(f777(f234(f858(a851,a845)),x89621),x89622)) % 174.01/173.89 [9044]P1(f777(f777(f235(a3),x90441),x90442))+~P1(f777(f777(f235(a3),f777(f777(f5(a3),f777(f777(f84(a3),x90441),x90441)),a101)),f777(f777(f84(a3),x90442),x90442))) % 174.01/173.89 [9046]P1(f777(f777(f235(a3),x90461),x90462))+~P1(f777(f777(f234(a3),f777(f777(f5(a3),f777(f777(f84(a3),x90461),x90461)),a101)),f777(f777(f84(a3),x90462),x90462))) % 174.01/173.89 [9899]~P1(f777(f65(x98991),x98992))+E(f777(f183(f852(x98991)),f94(f852(x98991),f777(f777(f22(f852(x98991),a845,a845),f777(f777(f12(a845,f858(a845,a845),f852(x98991)),a333),f777(f777(f11(f852(x98991),f858(x98991,a845),a845),f777(f777(f12(f858(x98991,a845),f858(f858(x98991,a845),a845),f852(x98991)),a332),f160(x98991))),x98992))),f129(x98991)))),f211(x98991,x98992)) % 174.01/173.89 [5952]E(f777(f777(f84(a851),f777(f777(f5(a851),x59521),x59522)),x59522),x59521)+~P1(f777(f777(f234(a851),x59522),x59521)) % 174.01/173.89 [6018]E(f777(f777(f45(a851),f777(f777(f85(a851),x60181),x60182)),x60182),x60181)+~P1(f777(f777(f235(a851),f4(a851)),x60182)) % 174.01/173.89 [6019]E(f777(f777(f45(a851),f777(f777(f85(a851),x60191),x60192)),x60191),x60192)+~P1(f777(f777(f235(a851),f4(a851)),x60191)) % 174.01/173.89 [6024]~P66(x60241)+E(f777(f777(f10(a851,x60241),f777(f155(x60241),x60242)),f777(f296(a851,f4(a851)),f777(f183(f852(x60241)),x60242))),f777(f157(x60241),x60242)) % 174.01/173.89 [6142]E(f54(a851,f777(a116,f777(f777(f85(a851),x61421),x61422)),x61421),f82(a851))+~P1(f777(f777(f235(a851),f82(a851)),x61421)) % 174.01/173.89 [6148]E(f777(a116,f777(f777(f84(a851),f777(f108(a851),x61481)),x61482)),f777(f777(f84(a851),f82(a851)),x61482))+~P1(f777(a188,f777(f108(a3),x61481))) % 174.01/173.89 [6174]E(f777(a109,f777(f777(f244(a3),f777(f108(a3),x61741)),x61742)),f777(f777(f244(a851),f777(f108(a851),x61741)),x61742))+P1(f777(a188,f777(f108(a3),x61741))) % 174.01/173.89 [6427]E(f777(f777(f5(a851),x64271),f777(f108(a851),f777(f777(f84(a3),x64272),a101))),f777(f777(f5(a851),f777(a116,x64271)),f777(f108(a851),x64272)))+~P1(f777(f777(f235(a3),a87),x64272)) % 174.01/173.89 [6509]E(x65091,f4(a851))+E(f777(a116,f777(f777(f84(a851),f777(f777(f5(a851),x65091),f82(a851))),x65092)),f777(f777(f84(a851),x65091),x65092)) % 174.01/173.89 [6554]E(x65541,f4(a3))+P1(f777(f777(f235(a3),f4(a3)),f777(f777(f244(a3),f777(f79(a3),x65541)),x65542))) % 174.01/173.89 [6569]~E(x65692,f4(a851))+P1(f777(f777(f235(a3),f4(a3)),f777(f777(f244(a3),f777(f79(a3),x65691)),x65692))) % 174.01/173.89 [6606]E(x66061,f4(a851))+E(f777(f777(f84(a851),x66062),f777(f777(f85(a851),f777(f777(f5(a851),x66061),f82(a851))),x66062)),f777(f777(f85(a851),x66061),x66062)) % 174.01/173.89 [6661]~P1(f777(f777(f234(a3),x66611),x66612))+P1(f777(f777(f235(a3),f777(f777(f84(a3),x66611),a101)),x66612)) % 174.01/173.89 [6795]E(f777(f777(f142(a851),x67951),f132(a851,f777(f296(a851,f777(a116,x67951)),x67952))),f132(a851,f777(f296(a851,x67951),x67952)))+~P1(f777(f777(f235(a851),x67951),x67952)) % 174.01/173.89 [6964]~P1(f777(f777(f281(a3),x69641),f777(f104(a3),x69642)))+P1(f777(f777(f281(a851),f777(a109,f777(f79(a3),x69641))),x69642)) % 174.01/173.89 [6998]E(x69981,x69982)+~E(f777(f777(f5(a3),f777(f777(f84(a3),x69981),x69981)),a101),f777(f777(f5(a3),f777(f777(f84(a3),x69982),x69982)),a101)) % 174.01/173.89 [7001]E(x70011,f117(x70012))+E(f265(x70012,f777(f777(f145(x70012,f857(a103,x70012)),f777(f243(a103,x70012),f82(a103))),x70011)),f272(x70012,x70011)) % 174.01/173.89 [7240]P1(f777(f777(f234(a3),x72401),x72402))+~P1(f777(f777(f235(a3),f777(f777(f84(a3),x72401),a101)),x72402)) % 174.01/173.89 [7382]P1(f777(f777(f281(a3),x73821),f777(f104(a3),x73822)))+~P1(f777(f777(f281(a851),f777(a109,f777(f79(a3),x73821))),x73822)) % 174.01/173.89 [7732]~P1(f777(f777(f235(a851),x77321),x77322))+P1(f777(f777(f336(f857(a851,a851)),f777(f777(f243(a851,a851),x77321),x77322)),a239)) % 174.01/173.89 [7960]~P1(f777(f777(f235(a103),f4(a103)),x79601))+P1(f777(f777(f235(a103),f777(f242(a103,f857(a103,a103)),f777(f266(x79601),x79602))),x79601)) % 174.01/173.89 [8261]~P79(x82611)+P1(f777(f777(f234(x82611),f777(f79(x82611),f777(f157(x82611),x82612))),f777(f157(x82611),f777(f777(f145(x82611,x82611),f79(x82611)),x82612)))) % 174.01/173.89 [8284]P1(f777(f777(f235(a851),x82841),x82842))+~P1(f777(f777(f336(f857(a851,a851)),f777(f777(f243(a851,a851),x82841),x82842)),a239)) % 174.01/173.89 [8444]E(f777(f777(f243(x84441,x84441),f655(x84442,x84441)),f655(x84442,x84441)),x84442)+~P1(f777(f777(f336(f857(x84441,x84441)),x84442),f302(x84441,f182(f858(f857(x84441,x84441),a845))))) % 174.01/173.89 [8489]E(f777(f296(a851,x84891),f777(f777(f84(a851),x84891),f777(f44(a851),x84892))),x84892)+~P1(f777(f777(f234(f858(a851,a845)),x84892),f777(f296(a851,x84891),f777(f777(f84(a851),x84891),f777(f44(a851),x84892))))) % 174.01/173.89 [8789]E(f777(f777(f45(a3),f777(f108(a3),f777(f777(f5(a3),f777(f777(f84(a3),x87891),x87891)),a101))),f777(f108(a3),f777(f777(f84(a3),x87892),x87892))),f777(f777(f45(a3),f777(f108(a3),x87891)),f777(f108(a3),x87892)))+~P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x87892))) % 174.01/173.89 [8894]E(f164(f852(x88941),f777(f777(f12(a845,a845,f852(x88941)),a330),f777(f777(f11(f852(x88941),f852(x88941),a845),a332),f117(x88941))),x88942),f166(x88941,f166(x88941,x88942)))+~P18(a851,f777(f144(a851),f777(f777(f145(f852(x88941),a851),f183(f852(x88941))),x88942))) % 174.01/173.89 [8897]E(f777(f777(f45(a3),f777(f108(a3),f777(f777(f5(a3),f777(f777(f84(a3),x88971),x88971)),a101))),f777(f108(a3),f777(f777(f84(a3),x88972),x88972))),f777(f777(f45(a3),f777(f777(f84(a3),f777(f108(a3),x88971)),f82(a3))),f777(f108(a3),x88972)))+P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x88972))) % 174.01/173.89 [9669]P1(f777(a188,x96692))+E(f777(f777(f90(a3,a851),f777(f777(f5(a3),x96691),x96692)),f777(f777(f22(a3,a851,a851),f777(f777(f11(a3,a851,f858(a851,a851)),f777(f777(f12(a845,f858(a851,f858(a851,a851)),a3),f100(a851)),a188)),f4(a851))),a109)),f777(f777(f5(a851),f777(a109,x96691)),f777(a109,x96692))) % 174.01/173.89 [9673]E(f777(f777(f90(a3,a851),f777(f108(a3),f777(f777(f84(a3),x96731),f777(f83(a3),x96732)))),f777(f777(f22(a3,a851,a851),f777(f777(f11(a3,a851,f858(a851,a851)),f777(f777(f12(a845,f858(a851,f858(a851,a851)),a3),f100(a851)),a188)),f4(a851))),a109)),f777(f777(f5(a851),f777(f108(a851),x96731)),f777(f108(a851),x96732)))+P1(f777(f777(f235(a3),x96732),a87)) % 174.01/173.89 [9674]~P30(x96741,x96742)+P1(f777(f777(f234(f858(f857(x96741,x96741),a845)),f777(f777(f283(x96741,x96741,x96741),f777(f242(f858(f857(x96741,x96741),a845),f858(f857(x96741,x96741),a845)),x96742)),f777(f252(f858(f857(x96741,x96741),a845),f858(f857(x96741,x96741),a845)),x96742))),f777(f242(f858(f857(x96741,x96741),a845),f858(f857(x96741,x96741),a845)),x96742))) % 174.01/173.89 [9730]~E(f777(f44(a851),f777(f258(a851),f777(f777(f22(a851,a845,a845),f777(f777(f12(a845,f858(a845,a845),a851),a333),f777(f777(f11(a851,f858(a851,a845),a845),f336(a851)),x97301))),f777(f777(f11(a851,a851,a845),f235(a851)),f777(a116,x97302))))),f4(a851))+~P1(f777(f777(f336(a851),f4(a851)),x97301)) % 174.01/173.89 [9743]E(f293(a851,f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x97431,x97432),f182(f858(a851,a845)))+~P1(f777(f777(f281(a851),x97432),x97431)) % 174.01/173.89 [9751]E(f294(a851,f281(a851),f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x97511,x97512),f182(f858(a851,a845)))+P1(f777(f777(f281(a851),x97511),x97512)) % 174.01/173.89 [9752]E(f291(a851,f281(a851),f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x97521,x97522),f182(f858(a851,a845)))+P1(f777(f777(f281(a851),x97521),x97522)) % 174.01/173.89 [9756]E(f294(a851,f281(a851),f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x97561,x97562),f182(f858(a851,a845)))+~P1(f777(f777(f281(a851),x97562),x97561)) % 174.01/173.89 [9758]E(f291(a851,f281(a851),f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x97581,x97582),f182(f858(a851,a845)))+~P1(f777(f777(f281(a851),x97582),x97581)) % 174.01/173.89 [9801]E(f54(a3,f777(f108(a3),f777(f777(f5(a3),f777(f777(f84(a3),x98011),x98011)),a101)),f777(f108(a3),f777(f777(f84(a3),x98012),x98012))),f777(f777(f84(a3),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f54(a3,f777(f108(a3),x98011),f777(f108(a3),x98012)))),f82(a3)))+~P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x98012))) % 174.01/173.89 [9810]E(f54(a3,f777(f108(a3),f777(f777(f5(a3),f777(f777(f84(a3),x98101),x98101)),a101)),f777(f108(a3),f777(f777(f84(a3),x98102),x98102))),f777(f777(f5(a3),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f54(a3,f777(f777(f84(a3),f777(f108(a3),x98101)),f82(a3)),f777(f108(a3),x98102)))),f82(a3)))+P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x98102))) % 174.01/173.89 [9868]~P9(x98681)+E(f46(x98681,f777(f258(x98681),f777(f777(f12(f858(x98681,a845),a845,x98681),f92(x98681)),f777(f777(f12(f858(x98681,a845),f858(x98681,a845),x98681),f777(f22(x98681,a845,a845),f777(f777(f12(a845,f858(a845,a845),x98681),a337),f777(f777(f11(x98681,f858(x98681,a845),a845),f336(x98681)),x98682)))),f234(x98681))))),f47(x98681,x98682)) % 174.01/173.89 [9892]~P36(x98921,x98922)+P58(x98921,f777(f777(f11(x98921,f858(f857(x98921,x98921),a845),f858(x98921,a845)),f777(f777(f12(f858(x98921,f858(f858(f857(x98921,x98921),a845),a845)),f858(f858(f857(x98921,x98921),a845),f858(x98921,a845)),x98921),f11(x98921,f858(f857(x98921,x98921),a845),a845)),f777(f777(f12(f858(x98921,f857(x98921,x98921)),f858(x98921,f858(f858(f857(x98921,x98921),a845),a845)),x98921),f777(f12(f857(x98921,x98921),f858(f858(f857(x98921,x98921),a845),a845),x98921),f336(f857(x98921,x98921)))),f243(x98921,x98921)))),x98922)) % 174.01/173.89 [9893]~P12(x98931,f241(f858(x98931,a845)),x98932)+P11(x98931,f777(f777(f11(x98931,f858(f857(x98931,x98931),a845),f858(x98931,a845)),f777(f777(f12(f858(x98931,f858(f858(f857(x98931,x98931),a845),a845)),f858(f858(f857(x98931,x98931),a845),f858(x98931,a845)),x98931),f11(x98931,f858(f857(x98931,x98931),a845),a845)),f777(f777(f12(f858(x98931,f857(x98931,x98931)),f858(x98931,f858(f858(f857(x98931,x98931),a845),a845)),x98931),f777(f12(f857(x98931,x98931),f858(f858(f857(x98931,x98931),a845),a845),x98931),f336(f857(x98931,x98931)))),f243(x98931,x98931)))),x98932)) % 174.01/173.89 [9930]P36(x99301,x99302)+~P58(x99301,f777(f777(f11(x99301,f858(f857(x99301,x99301),a845),f858(x99301,a845)),f777(f777(f12(f858(x99301,f858(f858(f857(x99301,x99301),a845),a845)),f858(f858(f857(x99301,x99301),a845),f858(x99301,a845)),x99301),f11(x99301,f858(f857(x99301,x99301),a845),a845)),f777(f777(f12(f858(x99301,f857(x99301,x99301)),f858(x99301,f858(f858(f857(x99301,x99301),a845),a845)),x99301),f777(f12(f857(x99301,x99301),f858(f858(f857(x99301,x99301),a845),a845),x99301),f336(f857(x99301,x99301)))),f243(x99301,x99301)))),x99302)) % 174.01/173.89 [9931]P12(x99311,f241(f858(x99311,a845)),x99312)+~P11(x99311,f777(f777(f11(x99311,f858(f857(x99311,x99311),a845),f858(x99311,a845)),f777(f777(f12(f858(x99311,f858(f858(f857(x99311,x99311),a845),a845)),f858(f858(f857(x99311,x99311),a845),f858(x99311,a845)),x99311),f11(x99311,f858(f857(x99311,x99311),a845),a845)),f777(f777(f12(f858(x99311,f857(x99311,x99311)),f858(x99311,f858(f858(f857(x99311,x99311),a845),a845)),x99311),f777(f12(f857(x99311,x99311),f858(f858(f857(x99311,x99311),a845),a845),x99311),f336(f857(x99311,x99311)))),f243(x99311,x99311)))),x99312)) % 174.01/173.89 [7186]E(f777(f777(f84(a851),f777(f108(a851),f777(f777(f5(a3),x71861),a101))),x71862),f777(a116,f777(f777(f84(a851),f777(f108(a851),x71861)),x71862)))+P1(f777(a188,f777(f108(a3),x71861))) % 174.01/173.89 [7651]~P88(x76511)+E(f777(f777(f84(x76511),f777(f777(f84(x76511),f82(x76511)),f777(f108(x76511),x76512))),f777(f108(x76511),x76512)),f777(f108(x76511),f777(f777(f5(a3),f777(f777(f84(a3),x76512),x76512)),a101))) % 174.01/173.89 [8286]~P1(f777(f777(f234(a3),x82861),x82862))+P1(f777(f777(f235(a3),f777(f777(f84(a3),x82861),x82861)),f777(f777(f5(a3),f777(f777(f84(a3),x82862),x82862)),a101))) % 174.01/173.89 [8288]~P1(f777(f777(f234(a3),x82881),x82882))+P1(f777(f777(f234(a3),f777(f777(f84(a3),x82881),x82881)),f777(f777(f5(a3),f777(f777(f84(a3),x82882),x82882)),a101))) % 174.01/173.89 [8691]P1(f777(f777(f234(a3),x86911),x86912))+~P1(f777(f777(f235(a3),f777(f777(f84(a3),x86911),x86911)),f777(f777(f5(a3),f777(f777(f84(a3),x86912),x86912)),a101))) % 174.01/173.89 [8693]P1(f777(f777(f234(a3),x86931),x86932))+~P1(f777(f777(f234(a3),f777(f777(f84(a3),x86931),x86931)),f777(f777(f5(a3),f777(f777(f84(a3),x86932),x86932)),a101))) % 174.01/173.89 [8952]~P1(f777(f777(f235(a3),x89521),x89522))+P1(f777(f777(f235(a3),f777(f777(f5(a3),f777(f777(f84(a3),x89521),x89521)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),x89522),x89522)),a101))) % 174.01/173.89 [8954]~P1(f777(f777(f234(a3),x89541),x89542))+P1(f777(f777(f234(a3),f777(f777(f5(a3),f777(f777(f84(a3),x89541),x89541)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),x89542),x89542)),a101))) % 174.01/173.89 [9188]P1(f777(f777(f235(a3),x91881),x91882))+~P1(f777(f777(f235(a3),f777(f777(f5(a3),f777(f777(f84(a3),x91881),x91881)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),x91882),x91882)),a101))) % 174.01/173.89 [9190]P1(f777(f777(f234(a3),x91901),x91902))+~P1(f777(f777(f234(a3),f777(f777(f5(a3),f777(f777(f84(a3),x91901),x91901)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),x91902),x91902)),a101))) % 174.01/173.89 [9221]~P1(f777(f65(x92211),x92212))+P1(f777(f65(f858(x92211,a845)),f777(f258(f858(x92211,a845)),f777(f777(f11(f858(x92211,a845),f858(x92211,a845),a845),f234(f858(x92211,a845))),x92212)))) % 174.01/173.89 [9268]~E(f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),x92681),f182(f858(f857(a851,a851),a845)))),f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),x92682),f182(f858(f857(a851,a851),a845)))))+P1(f777(f777(f336(f857(f857(a851,a851),f857(a851,a851))),f777(f777(f243(f857(a851,a851),f857(a851,a851)),x92681),x92682)),a113)) % 174.01/173.89 [9354]E(f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),x93541),f182(f858(f857(a851,a851),a845)))),f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),x93542),f182(f858(f857(a851,a851),a845)))))+~P1(f777(f777(f336(f857(f857(a851,a851),f857(a851,a851))),f777(f777(f243(f857(a851,a851),f857(a851,a851)),x93541),x93542)),a113)) % 174.01/173.89 [9388]P1(f777(f777(f234(a3),f4(a3)),f700(x93881,x93882)))+E(f777(f258(a3),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f234(a3),f4(a3)))),x93881)),f777(f258(a3),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f234(a3),f4(a3)))),x93882))) % 174.01/173.89 [9878]~P9(x98781)+E(f47(x98781,f777(f258(x98781),f777(f777(f12(f858(x98781,a845),a845,x98781),f92(x98781)),f777(f777(f12(f858(x98781,a845),f858(x98781,a845),x98781),f777(f22(x98781,a845,a845),f777(f777(f12(a845,f858(a845,a845),x98781),a337),f777(f777(f11(x98781,f858(x98781,a845),a845),f336(x98781)),x98782)))),f777(f11(x98781,x98781,a845),f234(x98781)))))),f46(x98781,x98782)) % 174.01/173.89 [9898]P1(f777(f777(f336(a851),f4(a851)),x98981))+E(f777(f44(a851),f777(f258(a851),f777(f777(f22(a851,a845,a845),f777(f777(f12(a845,f858(a845,a845),a851),a333),f777(f777(f11(a851,f858(a851,a845),a845),f777(f777(f12(a851,f858(f858(a851,a845),a845),a851),f336(a851)),a116)),x98981))),f777(f777(f11(a851,a851,a845),f235(a851)),x98982)))),f777(f44(a851),f777(f258(a851),f777(f777(f22(a851,a845,a845),f777(f777(f12(a845,f858(a845,a845),a851),a333),f777(f777(f11(a851,f858(a851,a845),a845),f336(a851)),x98981))),f777(f777(f11(a851,a851,a845),f235(a851)),f777(a116,x98982)))))) % 174.01/173.89 [9945]P1(f777(f777(f281(a851),x99451),x99452))+~P1(f777(f777(f336(a851),x99452),f289(a851,f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x99451))) % 174.01/173.89 [9946]P1(f777(f777(f281(a851),x99461),x99462))+~P1(f777(f777(f336(a851),x99461),f292(a851,f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x99462))) % 174.01/173.89 [9947]~P1(f777(f777(f281(a851),x99471),x99472))+~P1(f777(f777(f336(a851),x99472),f292(a851,f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x99471))) % 174.01/173.89 [9948]~P1(f777(f777(f281(a851),x99481),x99482))+~P1(f777(f777(f336(a851),x99481),f289(a851,f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x99482))) % 174.01/173.89 [7518]~P88(x75181)+E(f777(f777(f85(x75181),x75182),f777(f108(x75181),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),x75182) % 174.01/173.89 [7785]~P88(x77851)+E(f777(f777(f84(x77851),f777(f108(x77851),x77852)),f82(x77851)),f777(f108(x77851),f777(f777(f84(a3),x77852),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))) % 174.01/173.89 [7929]P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x79292)))+E(f777(f777(f244(a3),x79291),f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),x79292),x79292)),a101))),f82(a3)) % 174.01/173.89 [9245]~P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x92452)))+E(f777(f777(f244(a3),x92451),f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),x92452),x92452)),a101))),f777(f777(f90(a3,a3),f777(f777(f244(a3),x92451),f777(f108(a851),x92452))),f777(f777(f22(a3,a3,a3),f777(f777(f12(a3,f858(a3,a3),a3),f85(a3)),f777(f85(a3),x92451))),f9(a3)))) % 174.01/173.89 [9720]~P1(f777(f777(f235(a851),f777(f108(a851),x97201)),f777(a116,x97202)))+P1(f777(f777(f90(a3,a845),f777(f108(a3),f777(f777(f84(a3),x97201),a101))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a337),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f11(a3,a851,a845),f777(f777(f12(a851,f858(a851,a845),a3),f235(a851)),a109)),x97202)))) % 174.01/173.89 [9721]~P1(f777(f777(f234(a851),f777(f108(a851),x97211)),f777(a116,x97212)))+P1(f777(f777(f90(a3,a845),f777(f108(a3),f777(f777(f84(a3),x97211),a101))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a337),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f11(a3,a851,a845),f777(f777(f12(a851,f858(a851,a845),a3),f234(a851)),a109)),x97212)))) % 174.01/173.89 [9785]P1(f777(f777(f235(a851),f777(f108(a851),x97851)),f777(a116,x97852)))+~P1(f777(f777(f90(a3,a845),f777(f108(a3),f777(f777(f84(a3),x97851),a101))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a337),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f11(a3,a851,a845),f777(f777(f12(a851,f858(a851,a845),a3),f235(a851)),a109)),x97852)))) % 174.01/173.89 [9786]P1(f777(f777(f234(a851),f777(f108(a851),x97861)),f777(a116,x97862)))+~P1(f777(f777(f90(a3,a845),f777(f108(a3),f777(f777(f84(a3),x97861),a101))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a337),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f11(a3,a851,a845),f777(f777(f12(a851,f858(a851,a845),a3),f234(a851)),a109)),x97862)))) % 174.01/173.89 [9816]~P1(f777(f777(f235(a851),f777(a116,x98162)),f777(f108(a851),x98161)))+P1(f777(f777(f90(a3,a845),f777(f108(a3),f777(f777(f84(a3),x98161),a101))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a337),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f12(a851,a845,a3),f777(f235(a851),x98162)),a109))))) % 174.01/173.89 [9817]~P1(f777(f777(f234(a851),f777(a116,x98172)),f777(f108(a851),x98171)))+P1(f777(f777(f90(a3,a845),f777(f108(a3),f777(f777(f84(a3),x98171),a101))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a337),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f12(a851,a845,a3),f777(f234(a851),x98172)),a109))))) % 174.01/173.89 [9866]P1(f777(f777(f235(a851),f777(a116,x98661)),f777(f108(a851),x98662)))+~P1(f777(f777(f90(a3,a845),f777(f108(a3),f777(f777(f84(a3),x98662),a101))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a337),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f12(a851,a845,a3),f777(f235(a851),x98661)),a109))))) % 174.01/173.89 [9867]P1(f777(f777(f234(a851),f777(a116,x98671)),f777(f108(a851),x98672)))+~P1(f777(f777(f90(a3,a845),f777(f108(a3),f777(f777(f84(a3),x98672),a101))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a337),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f12(a851,a845,a3),f777(f234(a851),x98671)),a109))))) % 174.01/173.89 [9938]~P1(f777(f777(f336(a851),f4(a851)),x99381))+E(f777(a116,f777(f44(a851),f777(f258(a851),f777(f777(f22(a851,a845,a845),f777(f777(f12(a845,f858(a845,a845),a851),a333),f777(f777(f11(a851,f858(a851,a845),a845),f777(f777(f12(a851,f858(f858(a851,a845),a845),a851),f336(a851)),a116)),x99381))),f777(f777(f11(a851,a851,a845),f235(a851)),x99382))))),f777(f44(a851),f777(f258(a851),f777(f777(f22(a851,a845,a845),f777(f777(f12(a845,f858(a845,a845),a851),a333),f777(f777(f11(a851,f858(a851,a845),a845),f336(a851)),x99381))),f777(f777(f11(a851,a851,a845),f235(a851)),f777(a116,x99382)))))) % 174.01/173.89 [8470]~P88(x84701)+E(f777(f777(f85(x84701),f777(f108(x84701),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),x84702),x84702) % 174.01/173.89 [8530]~P88(x85301)+E(f777(f777(f84(x85301),f82(x85301)),f777(f108(x85301),x85302)),f777(f108(x85301),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),x85302))) % 174.01/173.89 [8576]~P88(x85761)+E(f777(f777(f5(x85761),f777(f108(x85761),x85762)),f82(x85761)),f777(f108(x85761),f777(f777(f84(a3),x85762),f777(f83(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))) % 174.01/173.89 [8709]~P1(f777(f777(f235(a851),f777(f108(a851),a87)),x87092))+E(f777(f777(f5(a851),x87091),f777(f777(f5(a851),x87092),f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(f777(f5(a851),f777(a116,x87091)),x87092)) % 174.01/173.89 [9284]~P85(x92841)+E(f777(f777(f85(x92841),x92842),x92842),f777(f777(f244(x92841),x92842),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))) % 174.01/173.89 [9285]~P75(x92851)+E(f777(f777(f244(x92851),x92852),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(f777(f85(x92851),x92852),x92852)) % 174.01/173.89 [9287]~P88(x92871)+E(f777(f777(f85(x92871),x92872),f777(f108(x92871),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(f777(f84(x92871),x92872),x92872)) % 174.01/173.89 [9520]~P133(x95201)+E(f777(f777(f244(x95201),f777(f83(x95201),x95202)),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(f777(f244(x95201),x95202),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))) % 174.01/173.89 [9521]~P110(x95211)+E(f777(f777(f244(x95211),f777(f79(x95211),x95212)),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(f777(f244(x95211),x95212),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))) % 174.01/173.89 [9517]~P88(x95171)+E(f777(f777(f85(x95171),f777(f108(x95171),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x95172),f777(f777(f84(x95171),x95172),x95172)) % 174.01/173.89 [9631]~P110(x96311)+E(f777(f79(x96311),f777(f777(f244(x96311),x96312),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x96311),x96312),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))) % 174.01/173.89 [9681]~P110(x96811)+P1(f777(f777(f234(x96811),f4(x96811)),f777(f777(f244(x96811),x96812),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))) % 174.01/173.89 [9857]~E(f777(a116,x98572),f777(f108(a851),x98571))+P1(f777(f777(f90(a3,a845),f777(f108(a3),f777(f777(f84(a3),x98571),a101))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a337),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f11(a3,a851,a845),f777(f777(f12(a851,f858(a851,a845),a3),a332),a109)),x98572))))) % 174.01/173.89 [9858]~E(f777(f108(a851),x98581),f777(a116,x98582))+P1(f777(f777(f90(a3,a845),f777(f108(a3),f777(f777(f84(a3),x98581),a101))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a337),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f11(a3,a851,a845),f777(f777(f12(a851,f858(a851,a845),a3),a332),a109)),x98582))))) % 174.01/173.89 [9901]E(f777(a116,x99011),f777(f108(a851),x99012))+~P1(f777(f777(f90(a3,a845),f777(f108(a3),f777(f777(f84(a3),x99012),a101))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a337),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f11(a3,a851,a845),f777(f777(f12(a851,f858(a851,a845),a3),a332),a109)),x99011))))) % 174.01/173.89 [9902]E(f777(f108(a851),x99021),f777(a116,x99022))+~P1(f777(f777(f90(a3,a845),f777(f108(a3),f777(f777(f84(a3),x99021),a101))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a337),f777(f777(f12(a845,a845,a3),a330),a188))),f777(f777(f11(a3,a851,a845),f777(f777(f12(a851,f858(a851,a845),a3),a332),a109)),x99022))))) % 174.01/173.89 [9679]~P88(x96791)+E(f777(f777(f244(x96791),f777(f108(x96791),a101)),f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x96792)),f82(x96791)) % 174.01/173.89 [9680]~P133(x96801)+E(f777(f777(f244(x96801),f777(f83(x96801),f82(x96801))),f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x96802)),f82(x96801)) % 174.01/173.89 [9683]~P75(x96831)+E(f777(f777(f244(x96831),x96832),f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),a101))),f777(f777(f85(x96831),f777(f777(f85(x96831),x96832),x96832)),x96832)) % 174.01/173.89 [9881]~P1(f777(f777(f234(a3),f4(a3)),x98812))+E(f54(a3,f777(f777(f84(a3),f82(a3)),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x98811)),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x98812)),f777(f777(f84(a3),f82(a3)),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f54(a3,x98811,x98812)))) % 174.01/173.89 [9904]~P1(f777(f777(f234(a3),f4(a3)),x99042))+E(f777(f777(f45(a3),f777(f777(f84(a3),f82(a3)),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x99041))),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x99042)),f777(f777(f45(a3),x99041),x99042)) % 174.01/173.89 [9906]~P1(f777(f777(f234(a3),x99062),f4(a3)))+E(f777(f777(f45(a3),f777(f777(f84(a3),f82(a3)),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x99061))),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x99062)),f777(f777(f45(a3),f777(f777(f84(a3),x99061),f82(a3))),x99062)) % 174.01/173.89 [9907]~P1(f777(f777(f234(a3),x99072),f4(a3)))+E(f54(a3,f777(f777(f84(a3),f82(a3)),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x99071)),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x99072)),f777(f777(f5(a3),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f54(a3,f777(f777(f84(a3),x99071),f82(a3)),x99072))),f82(a3))) % 174.01/173.89 [9776]~P88(x97761)+E(f777(f777(f244(x97761),f777(f108(x97761),a101)),f777(a116,f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x97762))),f777(f108(x97761),a101)) % 174.01/173.89 [9778]~P133(x97781)+E(f777(f777(f244(x97781),f777(f83(x97781),f82(x97781))),f777(a116,f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x97782))),f777(f83(x97781),f82(x97781))) % 174.01/173.89 [6004]E(x60041,x60042)+~P39(a27,x60041,x60043,x60042) % 174.01/173.89 [5009]~P36(x50091,x50093)+P36(x50091,f329(x50091,x50092,x50093)) % 174.01/173.89 [5177]P31(x51771,x51772,x51773)+~P31(x51771,f777(a116,x51772),x51773) % 174.01/173.89 [5262]~P12(x52621,x52622,x52623)+P12(f852(x52621),f151(x52621,x52622),f149(x52621,x52623)) % 174.01/173.89 [5263]~P47(x52631,x52632,x52633)+P47(f852(x52631),f151(x52631,x52632),f149(x52631,x52633)) % 174.01/173.89 [5373]P54(x53731,x53732,x53733)+~E(f628(x53733,x53732,x53731),f629(x53733,x53732,x53731)) % 174.01/173.89 [5374]P53(x53741,x53742,x53743)+~E(f641(x53743,x53742,x53741),f642(x53743,x53742,x53741)) % 174.01/173.89 [6326]P32(x63261,x63262,x63263)+~P31(x63261,f671(x63263,x63262,x63261),f783(x63263,x63262,x63261)) % 174.01/173.89 [4565]~E(x45651,f185(x45652))+~E(x45651,f777(f229(x45652),x45653)) % 174.01/173.89 [4614]~E(f777(f144(x46142),x46141),x46143)+E(x46141,f777(f144(x46142),x46143)) % 174.01/173.89 [4615]~E(x46152,f777(f144(x46151),x46153))+E(f777(f144(x46151),x46152),x46153) % 174.01/173.89 [4659]E(x46591,x46592)+~E(f777(f229(x46593),x46591),f777(f229(x46593),x46592)) % 174.01/173.89 [4660]E(x46601,x46602)+~E(f777(f144(x46603),x46601),f777(f144(x46603),x46602)) % 174.01/173.89 [4858]~P11(x48583,x48581)+P1(f777(f777(x48581,x48582),x48582)) % 174.01/173.89 [4859]~P49(x48593,x48591)+P1(f777(f777(x48591,x48592),x48592)) % 174.01/173.89 [4861]~P58(x48611,x48612)+P1(f777(f323(x48611,x48612),x48613)) % 174.01/173.89 [4923]~P36(x49231,x49232)+P36(f852(x49231),f777(f135(x49231,x49232),x49233)) % 174.01/173.89 [4927]~P1(f777(x49272,x49273))+~E(f777(f258(x49271),x49272),f182(f858(x49271,a845))) % 174.01/173.89 [4928]~P1(f777(x49282,x49283))+~E(f182(f858(x49281,a845)),f777(f258(x49281),x49282)) % 174.01/173.89 [4964]~P1(f777(x49641,x49643))+P1(f777(x49641,f94(x49642,x49641))) % 174.01/173.89 [5091]~E(x50912,x50913)+P1(f777(f777(f336(x50911),x50912),f777(a332,x50913))) % 174.01/173.89 [5144]E(f777(f144(x51441),x51442),f777(f777(f142(x51441),x51443),f117(x51441)))+~E(x51442,f777(f777(f142(x51441),x51443),f117(x51441))) % 174.01/173.89 [5145]~E(x51453,f777(f777(f142(x51451),x51452),f117(x51451)))+E(f777(f777(f142(x51451),x51452),f117(x51451)),f777(f144(x51451),x51453)) % 174.01/173.89 [5172]~E(x51723,f777(f20(f855(x51722),x51721),f185(x51722)))+E(f171(x51721,x51722,x51723),f182(f858(x51721,a845))) % 174.01/173.89 [5193]E(f777(f44(x51931),f376(x51932,x51933,x51931)),x51932)+~E(f777(f44(x51931),x51933),f777(a116,x51932)) % 174.01/173.89 [5199]~P36(x51991,x51993)+P1(f777(f777(f336(x51991),x51992),f324(x51991,x51993))) % 174.01/173.89 [5202]~E(f777(f144(x52022),x52021),f777(f777(f142(x52022),x52023),f117(x52022)))+E(x52021,f777(f777(f142(x52022),x52023),f117(x52022))) % 174.01/173.89 [5203]~E(f777(f777(f142(x52032),x52033),f117(x52032)),f777(f144(x52032),x52031))+E(x52031,f777(f777(f142(x52032),x52033),f117(x52032))) % 174.01/173.89 [5218]E(x52181,f777(f20(f855(x52182),x52183),f185(x52182)))+~E(f171(x52183,x52182,x52181),f182(f858(x52183,a845))) % 174.01/173.89 [5225]E(f89(f857(a851,a851),f57(x52251,x52252)),x52253)+~P1(f777(f57(x52251,x52252),x52253)) % 174.01/173.89 [5233]~E(x52333,f777(f229(x52331),x52332))+P1(f777(f777(f336(x52331),x52332),f228(x52331,x52333))) % 174.01/173.89 [5325]~E(x53252,f117(x53251))+P1(f777(f777(f336(f852(x53251)),x53252),f151(x53251,x53253))) % 174.01/173.89 [5333]~P47(x53331,x53332,x53333)+P47(x53331,x53332,f777(f280(x53331,x53331),x53333)) % 174.01/173.89 [5334]~P54(x53341,x53342,x53343)+P54(x53341,x53342,f777(f280(x53341,x53341),x53343)) % 174.01/173.89 [5354]~P7(x53541)+E(f54(x53541,f54(x53541,x53542,x53543),x53543),f54(x53541,x53542,x53543)) % 174.01/173.89 [5451]E(x54511,x54512)+~P1(f777(f777(f336(x54513),x54511),f777(a332,x54512))) % 174.01/173.89 [5494]~P2(x54941)+E(f184(x54941,x54942,f4(a851),x54943),x54943) % 174.01/173.89 [5514]P47(x55141,x55142,x55143)+~P47(x55141,x55142,f777(f280(x55141,x55141),x55143)) % 174.01/173.89 [5515]P54(x55151,x55152,x55153)+~P54(x55151,x55152,f777(f280(x55151,x55151),x55153)) % 174.01/173.89 [5536]E(x55361,f777(f229(x55362),x55363))+~P1(f777(f777(f336(x55362),x55363),f228(x55362,x55361))) % 174.01/173.89 [5618]~P1(f777(a28,x56183))+P1(f777(a28,f34(x56181,x56182,x56183))) % 174.01/173.89 [5630]E(f777(f128(x56301,x56302),x56303),f117(x56301))+P1(f777(x56302,f748(x56303,x56302,x56301))) % 174.01/173.89 [5786]~P1(f777(f129(x57861),x57863))+P1(f777(f129(x57861),f153(x57861,x57862,x57863))) % 174.01/173.89 [5787]~P1(f777(f129(x57871),x57872))+P1(f777(f129(x57871),f162(x57871,x57872,x57873))) % 174.01/173.89 [5788]~P1(f777(f129(x57881),x57883))+P1(f777(f129(x57881),f164(x57881,x57882,x57883))) % 174.01/173.89 [5789]~P140(x57891,x57893,x57892)+P1(f777(x57891,f54(a3,x57892,x57893))) % 174.01/173.89 [5888]P1(f777(a28,f33(x58881,x58882,x58883)))+~P1(f777(a28,f777(a29,x58882))) % 174.01/173.89 [5900]~P99(x59001)+E(f777(f777(f106(f858(x59001,a845)),f777(f259(x59001),x59002)),f297(x59001,x59002,x59003)),f182(f858(x59001,a845))) % 174.01/173.89 [5901]~P99(x59011)+E(f777(f777(f106(f858(x59011,a845)),f777(f295(x59011),x59012)),f299(x59011,x59012,x59013)),f182(f858(x59011,a845))) % 174.01/173.89 [5902]~P99(x59021)+E(f777(f777(f106(f858(x59021,a845)),f777(f295(x59021),x59022)),f300(x59021,x59022,x59023)),f182(f858(x59021,a845))) % 174.01/173.89 [6053]P1(f777(a28,x60531))+~P1(f777(a28,f34(x60532,x60533,x60531))) % 174.01/173.89 [6055]P1(f777(a28,x60551))+~P1(f777(a28,f35(x60552,x60553,x60551))) % 174.01/173.89 [6057]P1(f777(a28,x60571))+~P1(f777(a28,f35(x60572,x60571,x60573))) % 174.01/173.89 [6137]E(f777(f128(x61371,x61372),x61373),x61373)+~P1(f777(x61372,f760(x61373,x61372,x61371))) % 174.01/173.89 [6139]E(f777(f777(f304(x61391),f416(x61392,x61393,x61391)),f376(x61392,x61393,x61391)),x61393)+~E(f777(f44(x61391),x61393),f777(a116,x61392)) % 174.01/173.89 [6154]P140(x61541,x61542,x61543)+~P1(f777(x61541,f54(a3,x61543,x61542))) % 174.01/173.89 [6206]E(f164(x62061,x62062,x62063),x62063)+~P1(f777(x62062,f770(x62063,x62062,x62061))) % 174.01/173.89 [6247]~P1(f777(a28,f33(x62472,x62471,x62473)))+P1(f777(a28,f777(a29,x62471))) % 174.01/173.89 [6295]~P1(f777(x62952,f821(x62953,x62952,x62951)))+P1(f777(f247(x62951,x62952),x62953)) % 174.01/173.89 [6555]~P1(f777(f323(x65551,x65552),f822(x65553,x65552,x65551)))+P1(f777(f323(x65551,x65552),x65553)) % 174.01/173.89 [6556]~P1(f777(f323(x65561,x65562),f823(x65563,x65562,x65561)))+P1(f777(f323(x65561,x65562),x65563)) % 174.01/173.89 [7187]~P7(x71871)+E(f777(f777(f84(x71871),f777(f777(f85(x71871),x71872),f777(f777(f45(x71871),x71873),x71872))),f54(x71871,x71873,x71872)),x71873) % 174.01/173.89 [7675]E(f777(f777(f243(x76751,x76751),f474(x76752,x76753,x76751)),f474(x76752,x76753,x76751)),x76753)+~P1(f777(f777(f336(f857(x76751,x76751)),x76753),f262(x76751,x76752))) % 174.01/173.89 [7794]~P1(f777(f777(f336(x77941),f528(x77943,x77942,x77941)),f324(x77941,x77943)))+P1(f777(f777(f336(x77941),x77942),f324(x77941,x77943))) % 174.01/173.89 [7795]~P1(f777(f777(f336(x77951),f621(x77953,x77952,x77951)),f324(x77951,x77953)))+P1(f777(f777(f336(x77951),x77952),f324(x77951,x77953))) % 174.01/173.89 [7796]~P1(f777(f777(f336(x77961),f623(x77963,x77962,x77961)),f324(x77961,x77963)))+P1(f777(f777(f336(x77961),x77962),f324(x77961,x77963))) % 174.01/173.89 [7982]~P7(x79821)+E(f777(f777(f84(x79821),f777(f777(f85(x79821),f777(f777(f45(x79821),x79822),x79823)),x79823)),f54(x79821,x79822,x79823)),x79822) % 174.01/173.89 [8023]~E(f777(f44(x80231),x80232),f777(a116,x80233))+~P1(f777(f777(f336(x80231),f416(x80233,x80232,x80231)),f376(x80233,x80232,x80231))) % 174.01/173.89 [8624]P1(f777(f777(f234(f858(f857(x86241,x86241),a845)),f302(x86241,x86242)),f302(x86241,x86243)))+~P1(f777(f777(f234(f858(f857(x86241,x86241),a845)),x86242),f302(x86241,x86243))) % 174.01/173.89 [8862]E(x88621,f117(x88622))+~P1(f777(f777(f336(f857(f852(x88622),f852(x88622))),f777(f777(f243(f852(x88622),f852(x88622)),x88621),f117(x88622))),f149(x88622,x88623))) % 174.01/173.89 [8888]E(x88881,f117(x88882))+~P1(f777(f777(f336(f857(f852(x88882),f852(x88882))),f777(f777(f243(f852(x88882),f852(x88882)),f117(x88882)),x88881)),f149(x88882,x88883))) % 174.01/173.89 [9015]E(f777(f777(f142(x90151),f751(x90152,x90153,x90151)),f752(x90152,x90153,x90151)),x90153)+~P1(f777(f777(f336(f857(f852(x90151),f852(x90151))),f777(f777(f243(f852(x90151),f852(x90151)),f117(x90151)),x90153)),f139(x90151,x90152))) % 174.01/173.89 [9214]~P118(x92141)+~P1(f777(f777(f235(x92141),f777(f777(f84(x92141),f777(f777(f85(x92141),x92142),x92142)),f777(f777(f85(x92141),x92143),x92143))),f4(x92141))) % 174.01/173.89 [9263]P1(f777(f65(x92631),x92632))+~P1(f777(f777(f336(f857(f858(x92631,a845),f858(x92631,a845))),f777(f777(f243(f858(x92631,a845),f858(x92631,a845)),x92633),x92632)),f301(x92631))) % 174.01/173.89 [9541]~P45(x95411,x95412,x95413)+P1(f777(f777(f235(a3),f777(f777(f77(f857(a3,a3),a3,x95411,f242(a3,a3)),f209(x95411)),f226(x95411,x95412,f223(x95411,x95413)))),f4(a3))) % 174.01/173.89 [9542]~P46(x95421,x95422,x95423)+P1(f777(f777(f234(a3),f777(f777(f77(f857(a3,a3),a3,x95421,f242(a3,a3)),f209(x95421)),f226(x95421,x95422,f223(x95421,x95423)))),f4(a3))) % 174.01/173.89 [9656]P45(x96561,x96562,x96563)+~P1(f777(f777(f235(a3),f777(f777(f77(f857(a3,a3),a3,x96561,f242(a3,a3)),f209(x96561)),f226(x96561,x96562,f223(x96561,x96563)))),f4(a3))) % 174.01/173.89 [9657]P46(x96571,x96572,x96573)+~P1(f777(f777(f234(a3),f777(f777(f77(f857(a3,a3),a3,x96571,f242(a3,a3)),f209(x96571)),f226(x96571,x96572,f223(x96571,x96573)))),f4(a3))) % 174.01/173.89 [9987]~P110(x99871)+~P1(f777(f777(f235(x99871),f777(f777(f84(x99871),f777(f777(f244(x99871),x99872),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x99871),x99873),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))),f4(x99871))) % 174.01/173.89 [4643]~E(x46433,f117(x46431))+E(f777(f777(f127(x46431),x46432),x46433),x46432) % 174.01/173.89 [4644]~E(x46442,f117(x46441))+E(f777(f777(f127(x46441),x46442),x46443),x46443) % 174.01/173.89 [4650]~E(x46502,f4(a851))+E(f777(f777(f161(x46501),x46502),x46503),f117(x46501)) % 174.01/173.89 [4654]~E(x46543,f117(x46541))+E(f777(f777(f161(x46541),x46542),x46543),f117(x46541)) % 174.01/173.89 [4693]~E(x46931,x46933)+E(x46931,f777(f777(f127(x46932),f117(x46932)),x46933)) % 174.01/173.89 [4774]~P106(x47742)+E(f777(f241(f858(x47741,x47742)),x47743),f241(x47742)) % 174.01/173.89 [4776]~P101(x47762)+E(f777(f182(f858(x47761,x47762)),x47763),f182(x47762)) % 174.01/173.89 [4795]E(x47951,f117(x47952))+~E(f777(f777(f127(x47952),x47953),x47951),x47953) % 174.01/173.89 [4796]E(x47961,f117(x47962))+~E(f777(f777(f127(x47962),x47961),x47963),x47963) % 174.01/173.89 [4804]E(x48041,f117(x48042))+~E(f777(f777(f127(x48042),x48043),x48041),f117(x48042)) % 174.01/173.89 [4805]E(x48051,f117(x48052))+~E(f777(f777(f127(x48052),x48051),x48053),f117(x48052)) % 174.01/173.89 [4830]~E(x48302,f4(a851))+E(f777(f777(f85(a851),x48301),x48302),f777(f777(f85(a851),x48303),x48302)) % 174.01/173.89 [4832]~E(x48321,f4(a851))+E(f777(f777(f85(a851),x48321),x48322),f777(f777(f85(a851),x48321),x48323)) % 174.01/173.89 [4885]~P85(x48851)+E(f777(f777(f84(x48851),x48852),x48853),f777(f777(f84(x48851),x48853),x48852)) % 174.01/173.89 [4886]~P85(x48861)+E(f777(f777(f85(x48861),x48862),x48863),f777(f777(f85(x48861),x48863),x48862)) % 174.01/173.89 [4888]~P100(x48881)+E(f777(f777(f238(x48881),x48882),x48883),f777(f777(f238(x48881),x48883),x48882)) % 174.01/173.89 [4890]~P100(x48901)+E(f777(f777(f181(x48901),x48902),x48903),f777(f777(f181(x48901),x48903),x48902)) % 174.01/173.89 [4892]~P92(x48921)+E(f777(f777(f105(x48921),x48922),x48923),f777(f777(f105(x48921),x48923),x48922)) % 174.01/173.89 [4893]~P93(x48931)+E(f777(f777(f105(x48931),x48932),x48933),f777(f777(f105(x48931),x48933),x48932)) % 174.01/173.89 [4894]~P93(x48941)+E(f777(f777(f106(x48941),x48942),x48943),f777(f777(f106(x48941),x48943),x48942)) % 174.01/173.89 [4896]~P98(x48961)+E(f777(f777(f106(x48961),x48962),x48963),f777(f777(f106(x48961),x48963),x48962)) % 174.01/173.89 [4959]E(f54(a851,x49591,x49592),f4(a851))+~E(x49591,f777(f777(f85(a851),x49592),x49593)) % 174.01/173.89 [4960]E(f54(a3,x49601,x49602),f4(a3))+~E(x49601,f777(f777(f85(a3),x49602),x49603)) % 174.01/173.89 [5022]E(x50221,x50222)+~E(f777(f777(f84(a851),x50223),x50221),f777(f777(f84(a851),x50223),x50222)) % 174.01/173.89 [5023]E(x50231,x50232)+~E(f777(f777(f84(a851),x50231),x50233),f777(f777(f84(a851),x50232),x50233)) % 174.01/173.89 [5033]~P69(x50331)+E(f777(f777(f84(x50331),x50332),f777(f83(x50331),x50333)),f777(f777(f5(x50331),x50332),x50333)) % 174.01/173.89 [5034]~P104(x50341)+E(f777(f777(f84(x50341),x50342),f777(f83(x50341),x50343)),f777(f777(f5(x50341),x50342),x50343)) % 174.01/173.89 [5035]~P6(x50351)+E(f777(f777(f84(x50351),x50352),f777(f83(x50351),x50353)),f777(f777(f5(x50351),x50352),x50353)) % 174.01/173.89 [5036]~P90(x50361)+E(f777(f777(f106(x50361),x50362),f777(f83(x50361),x50363)),f777(f777(f5(x50361),x50362),x50363)) % 174.01/173.89 [5037]~P69(x50371)+E(f777(f777(f5(x50371),x50372),f777(f83(x50371),x50373)),f777(f777(f84(x50371),x50372),x50373)) % 174.01/173.89 [5084]~P1(f777(x50843,x50842))+P1(f777(f777(f336(x50841),x50842),x50843)) % 174.01/173.89 [5086]~P66(x50862)+E(f777(f777(f10(x50861,x50862),x50863),f182(f858(x50861,a845))),f4(x50862)) % 174.01/173.89 [5088]~P70(x50882)+E(f777(f777(f13(x50881,x50882),x50883),f182(f858(x50881,a845))),f82(x50882)) % 174.01/173.89 [5134]~E(x51342,f777(f777(f84(a851),x51341),x51343))+P1(f777(f777(f234(a851),x51341),x51342)) % 174.01/173.89 [5136]~E(x51362,f182(f858(x51361,a845)))+E(f777(f777(f63(x51361),x51362),x51363),f182(f858(f858(x51361,a845),a845))) % 174.01/173.89 [5137]~E(x51372,f182(f858(x51371,a845)))+E(f182(f858(f858(x51371,a845),a845)),f777(f777(f63(x51371),x51372),x51373)) % 174.01/173.89 [5206]~E(f777(f261(x52062,x52063),x52061),f182(f858(x52063,a845)))+E(x52061,f182(f858(f857(x52062,x52063),a845))) % 174.01/173.89 [5207]~E(f777(f263(x52072,x52073),x52071),f182(f858(x52072,a845)))+E(x52071,f182(f858(f857(x52072,x52073),a845))) % 174.01/173.89 [5239]E(f777(f261(x52391,x52392),x52393),f182(f858(x52392,a845)))+~E(x52393,f182(f858(f857(x52391,x52392),a845))) % 174.01/173.89 [5240]E(f777(f263(x52401,x52402),x52403),f182(f858(x52401,a845)))+~E(x52403,f182(f858(f857(x52401,x52402),a845))) % 174.01/173.89 [5243]E(f271(x52431,x52432,x52433),f777(f777(f5(a103),x52432),x52433))+P1(f777(f777(f235(a103),x52432),x52433)) % 174.01/173.89 [5259]P1(f777(x52591,x52592))+~P1(f777(f777(f336(x52593),x52592),x52591)) % 174.01/173.89 [5296]E(x52961,x52962)+~E(f777(f83(f858(x52963,a845)),x52961),f777(f83(f858(x52963,a845)),x52962)) % 174.01/173.89 [5301]E(f309(x53011,x53012,x53013),f185(f852(a844)))+~P1(f777(f777(f235(a3),x53012),x53013)) % 174.01/173.89 [5306]~E(x53061,f182(f858(x53062,a845)))+~P1(f777(f777(f336(x53062),x53063),x53061)) % 174.01/173.89 [5335]~E(x53352,f777(f777(f84(a3),x53351),f777(f104(a3),x53353)))+P1(f777(f777(f234(a3),x53351),x53352)) % 174.01/173.89 [5351]E(f777(f777(f304(x53511),x53512),x53513),x53513)+~P1(f777(f777(f336(x53511),x53512),x53513)) % 174.01/173.89 [5363]E(x53631,f182(f858(x53632,a845)))+~E(f777(f777(f63(x53632),x53631),x53633),f182(f858(f858(x53632,a845),a845))) % 174.01/173.89 [5364]E(x53641,f182(f858(x53642,a845)))+~E(f182(f858(f858(x53642,a845),a845)),f777(f777(f63(x53642),x53641),x53643)) % 174.01/173.89 [5370]~P121(x53701)+E(f777(f777(f85(x53701),f777(f83(x53701),x53702)),f777(f83(x53701),x53703)),f777(f777(f85(x53701),x53702),x53703)) % 174.01/173.89 [5372]~P60(x53721)+E(f777(f777(f285(x53721),f777(f83(x53721),x53722)),f777(f83(x53721),x53723)),f777(f777(f285(x53721),x53722),x53723)) % 174.01/173.89 [5404]~P1(f777(x54043,x54042))+P1(f777(f777(f336(x54041),x54042),f777(f258(x54041),x54043))) % 174.01/173.89 [5444]E(f153(x54441,x54442,x54443),x54443)+P1(f777(f777(f336(x54441),x54442),f777(f160(x54441),x54443))) % 174.01/173.89 [5522]~P1(f777(f129(x55221),x55223))+P1(f777(f129(x55221),f777(f128(x55221,x55222),x55223))) % 174.01/173.89 [5564]~P7(x55641)+E(f777(f777(f45(x55641),f54(x55641,x55642,x55643)),x55643),f4(x55641)) % 174.01/173.89 [5582]E(f162(x55821,f777(f777(f142(x55821),x55822),f117(x55821)),x55823),f117(x55821))+P1(f777(f777(f336(a851),f4(a851)),x55823)) % 174.01/173.89 [5647]E(x56471,x56472)+~E(f777(f777(f85(a851),f777(a116,x56473)),x56471),f777(f777(f85(a851),f777(a116,x56473)),x56472)) % 174.01/173.89 [5648]~E(x56482,f777(f777(f84(a3),x56481),f777(f104(a3),f777(a116,x56483))))+P1(f777(f777(f235(a3),x56481),x56482)) % 174.01/173.89 [5766]~E(x57663,f117(x57661))+E(f777(f777(f777(f175(f852(x57661),f852(x57661)),x57662),f143(x57661)),x57663),f117(x57661)) % 174.01/173.89 [5770]P1(f777(x57701,x57702))+~P1(f777(f777(f336(x57703),x57702),f777(f258(x57703),x57701))) % 174.01/173.89 [5804]E(x58041,x58042)+~E(f777(f777(f304(x58043),x58041),f182(f858(x58043,a845))),f777(f777(f304(x58043),x58042),f182(f858(x58043,a845)))) % 174.01/173.89 [5814]~P99(x58141)+E(f777(f777(f106(f858(x58141,a845)),f777(f259(x58141),x58142)),f777(f296(x58141,x58142),x58143)),f182(f858(x58141,a845))) % 174.01/173.89 [5874]~P77(x58741)+E(f777(f305(x58741,x58741,f83(x58741)),f777(f296(x58741,x58742),x58743)),f299(x58741,f777(f83(x58741),x58743),f777(f83(x58741),x58742))) % 174.01/173.89 [5882]E(f777(f183(f852(x58821)),f153(x58821,x58822,x58823)),f777(f183(f852(x58821)),x58823))+P1(f777(f777(f336(x58821),x58822),f777(f160(x58821),x58823))) % 174.01/173.89 [5939]~P99(x59391)+E(f777(f777(f106(f858(x59391,a845)),f777(f296(x59391,x59392),x59393)),f777(f260(x59391),x59393)),f182(f858(x59391,a845))) % 174.01/173.89 [5960]~P77(x59601)+E(f777(f305(x59601,x59601,f83(x59601)),f297(x59601,x59602,x59603)),f297(x59601,f777(f83(x59601),x59603),f777(f83(x59601),x59602))) % 174.01/173.89 [5961]~P77(x59611)+E(f777(f305(x59611,x59611,f83(x59611)),f300(x59611,x59612,x59613)),f300(x59611,f777(f83(x59611),x59613),f777(f83(x59611),x59612))) % 174.01/173.89 [6020]E(f162(x60201,f777(f777(f142(x60201),x60202),f117(x60201)),x60203),f777(f777(f142(x60201),x60202),f117(x60201)))+~P1(f777(f777(f336(a851),f4(a851)),x60203)) % 174.01/173.89 [6028]~P77(x60281)+E(f777(f305(x60281,x60281,f83(x60281)),f299(x60281,x60282,x60283)),f777(f296(x60281,f777(f83(x60281),x60283)),f777(f83(x60281),x60282))) % 174.01/173.89 [6048]~P8(x60481)+E(f54(x60481,f777(f83(x60481),f54(x60481,x60482,x60483)),x60483),f54(x60481,f777(f83(x60481),x60482),x60483)) % 174.01/173.89 [6152]~P1(f777(f65(f857(x61522,x61521)),x61523))+P1(f777(f65(x61521),f777(f261(x61522,x61521),x61523))) % 174.01/173.89 [6153]~P1(f777(f65(f857(x61531,x61532)),x61533))+P1(f777(f65(x61531),f777(f263(x61531,x61532),x61533))) % 174.01/173.89 [6158]~P99(x61581)+E(f777(f777(f106(f858(x61581,a845)),f297(x61581,x61582,x61583)),f777(f298(x61581),x61583)),f182(f858(x61581,a845))) % 174.01/173.89 [6159]~P99(x61591)+E(f777(f777(f106(f858(x61591,a845)),f299(x61591,x61592,x61593)),f777(f298(x61591),x61593)),f182(f858(x61591,a845))) % 174.01/173.89 [6160]~P99(x61601)+E(f777(f777(f106(f858(x61601,a845)),f300(x61601,x61602,x61603)),f777(f260(x61601),x61603)),f182(f858(x61601,a845))) % 174.01/173.89 [6229]E(f777(f777(f155(x62291),x62292),f731(x62292,x62293,x62291)),x62293)+~P1(f777(f777(f336(x62291),x62293),f777(f160(x62291),x62292))) % 174.01/173.89 [6381]E(x63811,f117(x63812))+~E(f777(f777(f777(f175(f852(x63812),f852(x63812)),x63813),f143(x63812)),x63811),f117(x63812)) % 174.01/173.89 [6460]P39(x64601,x64602,f409(x64603,x64602,x64601),x64603)+~P1(f777(f777(f189(x64601),x64602),x64603)) % 174.01/173.89 [6461]P39(x64611,x64612,f523(x64613,x64612,x64611),x64613)+~P1(f777(f777(f189(x64611),x64612),x64613)) % 174.01/173.89 [6491]~P1(f777(f65(f857(x64912,x64911)),x64913))+P1(f777(f65(f857(x64911,x64912)),f777(f280(x64912,x64911),x64913))) % 174.01/173.89 [6513]E(x65131,x65132)+~E(f284(a851,f281(a851),x65133,x65131),f777(f777(f304(a851),x65132),f182(f858(a851,a845)))) % 174.01/173.89 [6514]E(x65141,x65142)+~E(f284(a851,f281(a851),x65141,x65142),f777(f777(f304(a851),x65143),f182(f858(a851,a845)))) % 174.01/173.89 [6650]P54(x66501,x66502,x66503)+P1(f777(f777(f336(x66501),f629(x66503,x66502,x66501)),x66502)) % 174.01/173.89 [6651]P54(x66511,x66512,x66513)+P1(f777(f777(f336(x66511),f628(x66513,x66512,x66511)),x66512)) % 174.01/173.89 [6663]P1(f777(f323(x66631,x66632),x66633))+P1(f777(f777(x66632,f822(x66633,x66632,x66631)),x66633)) % 174.01/173.89 [6664]P1(f777(f323(x66641,x66642),x66643))+P1(f777(f777(x66642,f823(x66643,x66642,x66641)),x66643)) % 174.01/173.89 [6695]E(f777(f183(f852(x66951)),f153(x66951,x66952,x66953)),f777(f777(f5(a851),f777(f183(f852(x66951)),x66953)),f82(a851)))+~P1(f777(f777(f336(x66951),x66952),f777(f160(x66951),x66953))) % 174.01/173.89 [6735]P1(f777(f247(x67351,x67352),x67353))+P1(f777(f777(f336(x67351),f821(x67353,x67352,x67351)),x67353)) % 174.01/173.89 [6748]~P1(f777(f65(f857(x67482,x67481)),f777(f280(x67481,x67482),x67483)))+P1(f777(f65(f857(x67481,x67482)),x67483)) % 174.01/173.89 [6809]~P1(f777(f777(f336(x68091),x68092),f777(f160(x68091),f118(x68091,x68093))))+P1(f777(f777(f336(x68091),x68092),f777(f160(x68091),x68093))) % 174.01/173.89 [6816]P32(x68161,x68162,x68163)+P1(f777(f777(f336(f850(x68161)),f783(x68163,x68162,x68161)),x68163)) % 174.01/173.89 [6845]E(f777(f128(x68451,x68452),x68453),x68453)+P1(f777(f777(f336(x68451),f760(x68453,x68452,x68451)),f777(f160(x68451),x68453))) % 174.01/173.89 [6862]E(f777(f128(x68621,x68622),x68623),f117(x68621))+P1(f777(f777(f336(x68621),f748(x68623,x68622,x68621)),f777(f160(x68621),x68623))) % 174.01/173.89 [6890]E(f164(x68901,x68902,x68903),x68903)+P1(f777(f777(f336(x68901),f770(x68903,x68902,x68901)),f777(f160(x68901),x68903))) % 174.01/173.89 [7011]P1(f777(f777(f336(x70111),x70112),f698(x70113,x70112,x70111)))+~P1(f777(f777(f336(x70111),x70112),f46(f858(x70111,a845),x70113))) % 174.01/173.89 [7013]~P66(x70131)+E(f777(f777(f84(x70131),f777(f777(f10(a851,x70131),x70132),f777(f259(a851),x70133))),f777(x70132,x70133)),f777(f777(f10(a851,x70131),x70132),f777(f259(a851),f777(a116,x70133)))) % 174.01/173.89 [7117]~P1(f777(f777(f336(x71171),x71172),f687(x71172,x71173,x71171)))+P1(f777(f777(f336(x71171),x71172),f47(f858(x71171,a845),x71173))) % 174.01/173.89 [7146]~P66(x71461)+E(f777(f777(f84(x71461),f777(f777(f10(a851,x71461),x71462),f777(f295(a851),x71463))),f777(x71462,f777(a116,x71463))),f777(f777(f10(a851,x71461),x71462),f777(f295(a851),f777(a116,x71463)))) % 174.01/173.89 [7300]P1(f777(f777(f336(f852(x73001)),x73002),f151(x73001,x73003)))+P1(f777(f777(f336(x73001),f747(x73003,x73002,x73001)),f777(f160(x73001),x73002))) % 174.01/173.89 [7317]~P1(f777(f777(f336(f852(x73171)),x73172),f151(x73171,f324(x73171,x73173))))+P1(f777(f777(f336(f852(x73171)),x73172),f324(f852(x73171),f148(x73171,x73173)))) % 174.01/173.89 [7345]~P1(f777(f777(f336(f852(x73451)),x73452),f324(f852(x73451),f148(x73451,x73453))))+P1(f777(f777(f336(f852(x73451)),x73452),f151(x73451,f324(x73451,x73453)))) % 174.01/173.89 [7385]E(f777(f777(f777(f175(f852(x73851),f852(x73851)),x73852),f143(x73851)),x73853),x73853)+~P1(f777(f777(f234(a851),f777(f183(f852(x73851)),x73853)),f82(a851))) % 174.01/173.89 [7439]~P29(x74391,x74392,x74393,f241(f858(x74391,a845)))+P29(f852(x74391),f852(x74392),f777(f145(x74391,x74392),x74393),f241(f858(f852(x74391),a845))) % 174.01/173.89 [7596]E(x75961,f777(f777(f84(a851),f777(f777(f85(a851),f777(f242(a851,a851),x75962)),x75963)),f777(f252(a851,a851),x75962)))+~P1(f777(f57(x75961,x75963),x75962)) % 174.01/173.89 [7604]P29(x76041,x76042,x76043,f241(f858(x76041,a845)))+~P29(f852(x76041),f852(x76042),f777(f145(x76041,x76042),x76043),f241(f858(f852(x76041),a845))) % 174.01/173.89 [7647]P1(f777(f777(f336(f858(x76471,a845)),f687(x76472,x76473,x76471)),x76473))+P1(f777(f777(f336(x76471),x76472),f47(f858(x76471,a845),x76473))) % 174.01/173.89 [7736]P1(f777(f777(f336(f852(x77361)),x77362),f151(x77361,x77363)))+~P1(f777(f777(f336(x77361),f747(x77363,x77362,x77361)),x77363)) % 174.01/173.89 [7867]E(x78671,x78672)+~E(f777(f777(f11(x78673,f858(x78673,a845),a845),f336(x78673)),x78671),f777(f777(f11(x78673,f858(x78673,a845),a845),f336(x78673)),x78672)) % 174.01/173.89 [7873]~P1(f777(f777(f336(f857(x78731,x78731)),x78733),f262(x78731,x78732)))+P1(f777(f777(f336(x78731),f474(x78732,x78733,x78731)),x78732)) % 174.01/173.89 [7875]~P1(f777(f777(f336(x78751),x78753),f46(f858(x78751,a845),x78752)))+P1(f777(f777(f336(f858(x78751,a845)),f698(x78752,x78753,x78751)),x78752)) % 174.01/173.89 [8135]E(f777(f231(f855(f852(a844)),f852(a844),f309(x81351,x81352,f777(f777(f84(a3),x81353),f82(a3))),f229(f852(a844))),f777(x81351,x81353)),f309(x81351,x81352,x81353))+P1(f777(f777(f235(a3),x81352),x81353)) % 174.01/173.89 [8234]E(x82341,f117(x82342))+P1(f777(f777(f336(x82342),f777(f242(x82342,f857(a103,a103)),f777(f272(x82342,x82341),x82343))),f777(f160(x82342),x82341))) % 174.01/173.89 [8332]~P5(x83321)+E(f777(f134(x83321,x83321,f777(f11(x83321,x83321,x83321),f84(x83321)),x83322),f777(f144(x83321),x83323)),f777(f134(x83321,x83321,f84(x83321),x83322),x83323)) % 174.01/173.89 [8793]~P100(x87931)+E(f777(f160(x87931),f141(x87931,x87931,f9(x87931),x87932,x87933)),f777(f777(f304(x87931),x87932),f777(f160(x87931),x87933))) % 174.01/173.89 [8802]P1(f777(f777(f235(a851),f4(a851)),f640(x88021,x88022,x88023)))+~P1(f777(f777(f336(f857(x88023,x88023)),x88022),f777(f777(f283(x88023,x88023,x88023),x88021),f302(x88023,x88021)))) % 174.01/173.89 [9065]~P56(x90651,x90652)+~P1(f777(f777(f336(f857(x90651,x90651)),f777(f777(f243(x90651,x90651),x90653),x90653)),f777(f777(f283(x90651,x90651,x90651),x90652),f302(x90651,x90652)))) % 174.01/173.89 [9176]~E(f777(f777(f106(f858(f857(x91761,x91761),a845)),f777(f280(x91761,x91761),x91762)),f302(x91761,x91762)),f182(f858(f857(x91761,x91761),a845)))+~P1(f777(f777(f336(f857(x91761,x91761)),f777(f777(f243(x91761,x91761),x91763),x91763)),f777(f777(f283(x91761,x91761,x91761),x91762),f302(x91761,x91762)))) % 174.01/173.89 [9350]~P1(f777(f65(x93501),x93502))+P1(f777(f777(f234(a851),f777(f44(x93501),f777(f777(f5(f858(x93501,a845)),x93502),f777(f777(f304(x93501),x93503),f182(f858(x93501,a845)))))),f777(f44(x93501),x93502))) % 174.01/173.89 [4943]~E(x49433,f117(x49431))+E(f136(x49431,f777(f777(f142(x49431),x49432),x49433)),x49432) % 174.01/173.89 [4956]~E(x49563,f117(x49561))+E(f118(x49561,f777(f777(f142(x49561),x49562),x49563)),f117(x49561)) % 174.01/173.89 [4986]E(x49861,f117(x49862))+E(f136(x49862,f777(f777(f142(x49862),x49863),x49861)),f136(x49862,x49861)) % 174.01/173.89 [4988]E(x49881,f117(x49882))+E(f136(x49882,f777(f777(f127(x49882),x49883),x49881)),f136(x49882,x49881)) % 174.01/173.89 [4995]~E(x49953,f117(x49951))+E(f136(x49951,f777(f777(f127(x49951),x49952),x49953)),f136(x49951,x49952)) % 174.01/173.89 [4996]~E(x49963,f117(x49961))+E(f118(x49961,f777(f777(f127(x49961),x49962),x49963)),f118(x49961,x49962)) % 174.01/173.89 [5027]E(x50271,f117(x50272))+E(f777(f133(x50272),f777(f777(f127(x50272),x50271),x50273)),f777(f133(x50272),x50271)) % 174.01/173.89 [5058]~E(x50582,f117(x50581))+E(f777(f133(x50581),f777(f777(f127(x50581),x50582),x50583)),f777(f133(x50581),x50583)) % 174.01/173.89 [5110]~P100(x51101)+E(f777(f777(f238(x51101),x51102),f777(f777(f181(x51101),x51102),x51103)),x51102) % 174.01/173.89 [5111]~P100(x51111)+E(f777(f777(f181(x51111),x51112),f777(f777(f238(x51111),x51112),x51113)),x51112) % 174.01/173.89 [5112]~P93(x51121)+E(f777(f777(f105(x51121),x51122),f777(f777(f106(x51121),x51122),x51123)),x51122) % 174.01/173.89 [5113]~P93(x51131)+E(f777(f777(f106(x51131),x51132),f777(f777(f105(x51131),x51132),x51133)),x51132) % 174.01/173.89 [5132]~P7(x51321)+E(f54(x51321,f777(f777(f85(x51321),x51322),x51323),x51323),f4(x51321)) % 174.01/173.89 [5133]~P7(x51331)+E(f54(x51331,f777(f777(f85(x51331),x51332),x51333),x51332),f4(x51331)) % 174.01/173.89 [5201]~P6(x52011)+E(f777(f83(x52011),f777(f777(f5(x52011),x52012),x52013)),f777(f777(f5(x52011),x52013),x52012)) % 174.01/173.89 [5264]E(x52641,f117(x52642))+E(f118(x52642,f777(f777(f142(x52642),x52643),x52641)),f777(f777(f142(x52642),x52643),f118(x52642,x52641))) % 174.01/173.89 [5265]E(x52651,f117(x52652))+E(f118(x52652,f777(f777(f127(x52652),x52653),x52651)),f777(f777(f127(x52652),x52653),f118(x52652,x52651))) % 174.01/173.89 [5266]~P9(x52661)+E(f47(x52661,f777(f777(f304(x52661),x52662),x52663)),f777(f777(f106(x52661),x52662),f47(x52661,x52663))) % 174.01/173.89 [5267]~P9(x52671)+E(f46(x52671,f777(f777(f304(x52671),x52672),x52673)),f777(f777(f105(x52671),x52672),f46(x52671,x52673))) % 174.01/173.89 [5310]~P91(x53101)+E(f777(f777(f85(x53101),x53102),f777(f777(f85(x53101),x53102),x53103)),f777(f777(f85(x53101),x53102),x53103)) % 174.01/173.89 [5312]~P100(x53121)+E(f777(f777(f238(x53121),x53122),f777(f777(f238(x53121),x53122),x53123)),f777(f777(f238(x53121),x53122),x53123)) % 174.01/173.89 [5314]~P100(x53141)+E(f777(f777(f181(x53141),x53142),f777(f777(f181(x53141),x53142),x53143)),f777(f777(f181(x53141),x53142),x53143)) % 174.01/173.89 [5316]~P92(x53161)+E(f777(f777(f105(x53161),x53162),f777(f777(f105(x53161),x53162),x53163)),f777(f777(f105(x53161),x53162),x53163)) % 174.01/173.89 [5317]~P93(x53171)+E(f777(f777(f105(x53171),x53172),f777(f777(f105(x53171),x53172),x53173)),f777(f777(f105(x53171),x53172),x53173)) % 174.01/173.89 [5318]~P93(x53181)+E(f777(f777(f106(x53181),x53182),f777(f777(f106(x53181),x53182),x53183)),f777(f777(f106(x53181),x53182),x53183)) % 174.01/173.89 [5320]~P98(x53201)+E(f777(f777(f106(x53201),x53202),f777(f777(f106(x53201),x53202),x53203)),f777(f777(f106(x53201),x53202),x53203)) % 174.01/173.89 [5328]~P7(x53281)+E(f54(x53281,f777(f777(f84(x53281),x53282),x53283),x53283),f54(x53281,x53282,x53283)) % 174.01/173.89 [5329]~P7(x53291)+E(f54(x53291,f777(f777(f84(x53291),x53292),x53293),x53292),f54(x53291,x53293,x53292)) % 174.01/173.89 [5336]~P121(x53361)+E(f777(f777(f85(x53361),x53362),f777(f83(x53361),x53363)),f777(f83(x53361),f777(f777(f85(x53361),x53362),x53363))) % 174.01/173.89 [5337]~P60(x53371)+E(f777(f777(f285(x53371),x53372),f777(f83(x53371),x53373)),f777(f83(x53371),f777(f777(f285(x53371),x53372),x53373))) % 174.01/173.89 [5338]~P67(x53381)+E(f777(f777(f84(x53381),x53382),f777(f157(x53381),x53383)),f777(f157(x53381),f777(f777(f142(x53381),x53382),x53383))) % 174.01/173.89 [5369]~P121(x53691)+E(f777(f777(f85(x53691),f777(f83(x53691),x53692)),x53693),f777(f777(f85(x53691),x53692),f777(f83(x53691),x53693))) % 174.01/173.89 [5375]~P12(x53751,x53752,x53753)+E(f46(f858(x53751,a845),f777(f777(f63(x53751),x53752),x53753)),x53752) % 174.01/173.89 [5436]~P105(x54361)+E(f777(f777(f85(x54361),x54362),f777(f777(f244(x54361),x54362),x54363)),f777(f777(f244(x54361),x54362),f777(a116,x54363))) % 174.01/173.89 [5437]~P85(x54371)+E(f777(f777(f85(x54371),x54372),f777(f777(f244(x54371),x54372),x54373)),f777(f777(f244(x54371),x54372),f777(a116,x54373))) % 174.01/173.89 [5447]~P69(x54471)+E(f777(f777(f84(x54471),f777(f83(x54471),x54472)),f777(f777(f84(x54471),x54472),x54473)),x54473) % 174.01/173.89 [5466]~P2(x54661)+E(f777(f777(f244(x54661),f777(f104(x54661),x54662)),x54663),f777(f104(x54661),f777(f777(f244(a851),x54662),x54663))) % 174.01/173.89 [5467]~P133(x54671)+E(f777(f777(f244(x54671),f777(f107(x54671),x54672)),x54673),f777(f107(x54671),f777(f777(f244(a3),x54672),x54673))) % 174.01/173.89 [5472]~P79(x54721)+E(f777(f79(x54721),f777(f777(f5(x54721),x54722),x54723)),f777(f79(x54721),f777(f777(f5(x54721),x54723),x54722))) % 174.01/173.89 [5475]~P110(x54751)+E(f777(f777(f85(x54751),f86(x54751,x54752)),f86(x54751,x54753)),f86(x54751,f777(f777(f85(x54751),x54752),x54753))) % 174.01/173.89 [5479]E(x54791,f117(x54792))+E(f777(f777(f127(x54792),f777(f159(x54792),x54791)),x54793),f777(f159(x54792),f777(f777(f127(x54792),x54791),x54793))) % 174.01/173.89 [5485]~E(x54852,f777(a116,f777(f777(f84(a851),x54851),x54853)))+P1(f777(f777(f235(a851),x54851),x54852)) % 174.01/173.89 [5486]~P121(x54861)+E(f777(f777(f85(x54861),f777(f83(x54861),x54862)),x54863),f777(f83(x54861),f777(f777(f85(x54861),x54862),x54863))) % 174.01/173.89 [5487]~P113(x54871)+E(f777(f777(f285(x54871),f777(f83(x54871),x54872)),x54873),f777(f83(x54871),f777(f777(f285(x54871),x54872),x54873))) % 174.01/173.89 [5488]~P110(x54881)+E(f777(f777(f244(x54881),f777(f79(x54881),x54882)),x54883),f777(f79(x54881),f777(f777(f244(x54881),x54882),x54883))) % 174.01/173.89 [5581]E(f495(x55811,x55812,x55813),f499(x55811,x55812,x55813))+E(f777(f777(f106(f858(x55813,a845)),x55812),x55811),f182(f858(x55813,a845))) % 174.01/173.89 [5595]~P66(x55952)+E(f777(f777(f10(x55951,x55952),f777(f20(x55952,x55951),f4(x55952))),x55953),f4(x55952)) % 174.01/173.89 [5596]~P70(x55962)+E(f777(f777(f13(x55961,x55962),f777(f20(x55962,x55961),f82(x55962))),x55963),f82(x55962)) % 174.01/173.89 [5598]~P2(x55981)+E(f777(f777(f84(x55981),f777(f104(x55981),x55982)),f777(f104(x55981),x55983)),f777(f104(x55981),f777(f777(f84(a851),x55982),x55983))) % 174.01/173.89 [5599]~P2(x55991)+E(f777(f777(f85(x55991),f777(f104(x55991),x55992)),f777(f104(x55991),x55993)),f777(f104(x55991),f777(f777(f85(a851),x55992),x55993))) % 174.01/173.89 [5600]~P133(x56001)+E(f777(f777(f84(x56001),f777(f107(x56001),x56002)),f777(f107(x56001),x56003)),f777(f107(x56001),f777(f777(f84(a3),x56002),x56003))) % 174.01/173.89 [5601]~P133(x56011)+E(f777(f777(f85(x56011),f777(f107(x56011),x56012)),f777(f107(x56011),x56013)),f777(f107(x56011),f777(f777(f85(a3),x56012),x56013))) % 174.01/173.89 [5602]~P133(x56021)+E(f777(f777(f5(x56021),f777(f107(x56021),x56022)),f777(f107(x56021),x56023)),f777(f107(x56021),f777(f777(f5(a3),x56022),x56023))) % 174.01/173.89 [5605]~P88(x56051)+E(f777(f777(f5(x56051),f777(f108(x56051),x56052)),f777(f108(x56051),x56053)),f777(f108(x56051),f777(f777(f5(a3),x56052),x56053))) % 174.01/173.89 [5606]~P88(x56061)+E(f777(f777(f84(x56061),f777(f108(x56061),x56062)),f777(f108(x56061),x56063)),f777(f108(x56061),f777(f777(f84(a3),x56062),x56063))) % 174.01/173.89 [5607]~P88(x56071)+E(f777(f777(f85(x56071),f777(f108(x56071),x56072)),f777(f108(x56071),x56073)),f777(f108(x56071),f777(f777(f85(a3),x56072),x56073))) % 174.01/173.89 [5654]~E(x56543,x56542)+P1(f777(f777(f234(f858(x56541,a845)),x56542),x56543)) % 174.01/173.89 [5660]~E(x56602,x56603)+P1(f777(f777(f234(f858(x56601,a845)),x56602),x56603)) % 174.01/173.89 [5665]~P69(x56651)+E(f777(f777(f84(x56651),f777(f83(x56651),x56652)),f777(f83(x56651),x56653)),f777(f83(x56651),f777(f777(f84(x56651),x56653),x56652))) % 174.01/173.89 [5666]~P6(x56661)+E(f777(f777(f84(x56661),f777(f83(x56661),x56662)),f777(f83(x56661),x56663)),f777(f83(x56661),f777(f777(f84(x56661),x56662),x56663))) % 174.01/173.89 [5667]~P68(x56671)+E(f777(f777(f181(x56671),f777(f83(x56671),x56672)),f777(f83(x56671),x56673)),f777(f83(x56671),f777(f777(f238(x56671),x56672),x56673))) % 174.01/173.89 [5668]~P68(x56681)+E(f777(f777(f238(x56681),f777(f83(x56681),x56682)),f777(f83(x56681),x56683)),f777(f83(x56681),f777(f777(f181(x56681),x56682),x56683))) % 174.01/173.89 [5669]~P90(x56691)+E(f777(f777(f106(x56691),f777(f83(x56691),x56692)),f777(f83(x56691),x56693)),f777(f83(x56691),f777(f777(f105(x56691),x56692),x56693))) % 174.01/173.89 [5670]~P90(x56701)+E(f777(f777(f105(x56701),f777(f83(x56701),x56702)),f777(f83(x56701),x56703)),f777(f83(x56701),f777(f777(f106(x56701),x56702),x56703))) % 174.01/173.89 [5671]~P110(x56711)+E(f777(f777(f85(x56711),f777(f79(x56711),x56712)),f777(f79(x56711),x56713)),f777(f79(x56711),f777(f777(f85(x56711),x56712),x56713))) % 174.01/173.89 [5672]~P62(x56721)+E(f777(f777(f285(x56721),f777(f79(x56721),x56722)),f777(f79(x56721),x56723)),f777(f79(x56721),f777(f777(f285(x56721),x56722),x56723))) % 174.01/173.89 [5673]~P67(x56731)+E(f777(f777(f84(x56731),f777(f157(x56731),x56732)),f777(f157(x56731),x56733)),f777(f157(x56731),f777(f777(f127(x56731),x56732),x56733))) % 174.01/173.89 [5674]E(x56741,f182(f858(x56742,a845)))+~E(f777(f777(f105(f858(x56742,a845)),x56743),x56741),f182(f858(x56742,a845))) % 174.01/173.89 [5675]E(x56751,f182(f858(x56752,a845)))+~E(f777(f777(f105(f858(x56752,a845)),x56751),x56753),f182(f858(x56752,a845))) % 174.01/173.89 [5676]~P141(x56761,x56763,x56762)+P1(f777(x56761,f777(f777(f45(a3),x56762),x56763))) % 174.01/173.89 [5738]~P1(f777(f65(x57381),x57383))+P1(f777(f65(x57381),f777(f777(f304(x57381),x57382),x57383))) % 174.01/173.89 [5739]~P1(f777(f129(x57391),x57393))+P1(f777(f129(x57391),f777(f777(f161(x57391),x57392),x57393))) % 174.01/173.89 [5740]~P1(f777(f129(x57401),x57403))+P1(f777(f129(x57401),f777(f777(f130(x57401),x57402),x57403))) % 174.01/173.89 [5771]~P100(x57711)+P1(f777(f777(f234(x57711),x57712),f777(f777(f181(x57711),x57713),x57712))) % 174.01/173.89 [5772]~P100(x57721)+P1(f777(f777(f234(x57721),x57722),f777(f777(f181(x57721),x57722),x57723))) % 174.01/173.89 [5773]~P92(x57731)+P1(f777(f777(f234(x57731),x57732),f777(f777(f105(x57731),x57733),x57732))) % 174.01/173.89 [5774]~P93(x57741)+P1(f777(f777(f234(x57741),x57742),f777(f777(f105(x57741),x57743),x57742))) % 174.01/173.89 [5775]~P92(x57751)+P1(f777(f777(f234(x57751),x57752),f777(f777(f105(x57751),x57752),x57753))) % 174.01/173.89 [5776]~P93(x57761)+P1(f777(f777(f234(x57761),x57762),f777(f777(f105(x57761),x57762),x57763))) % 174.01/173.89 [5777]~P85(x57771)+P1(f777(f777(f281(x57771),x57772),f777(f777(f85(x57771),x57773),x57772))) % 174.01/173.89 [5778]~P85(x57781)+P1(f777(f777(f281(x57781),x57782),f777(f777(f85(x57781),x57782),x57783))) % 174.01/173.89 [5791]~E(x57911,f4(a851))+E(f777(f777(f45(a851),f777(f777(f85(a851),x57911),x57912)),f777(f777(f85(a851),x57911),x57913)),f4(a851)) % 174.01/173.89 [5855]P1(f777(x58551,x58552))+P1(f777(f777(f189(f37(x58551,x58553)),x58552),x58552)) % 174.01/173.89 [5867]~P88(x58671)+E(f777(f777(f5(x58671),f777(f108(x58671),x58672)),f777(f108(x58671),x58673)),f777(f108(x58671),f777(f777(f84(a3),x58672),f777(f83(a3),x58673)))) % 174.01/173.89 [5923]E(x59231,f4(a851))+E(f777(f777(f45(a851),f777(f777(f85(a851),x59231),x59232)),f777(f777(f85(a851),x59231),x59233)),f777(f777(f45(a851),x59232),x59233)) % 174.01/173.89 [5992]P141(x59921,x59922,x59923)+~P1(f777(x59921,f777(f777(f45(a3),x59923),x59922))) % 174.01/173.89 [6069]E(x60691,f117(x60692))+E(f777(f777(f142(x60692),f777(f133(x60692),x60691)),f777(f777(f161(x60692),x60693),f777(f159(x60692),x60691))),f777(f777(f161(x60692),f777(a116,x60693)),x60691)) % 174.01/173.89 [6077]E(f777(f777(f5(f858(x60771,a845)),x60772),x60773),x60772)+~E(f777(f777(f106(f858(x60771,a845)),x60772),x60773),f182(f858(x60771,a845))) % 174.01/173.89 [6121]~P1(f777(f777(f235(a851),x61211),x61213))+P1(f777(f777(f235(a851),x61211),f777(f777(f84(a851),x61212),x61213))) % 174.01/173.89 [6123]~P1(f777(f777(f235(a851),x61231),x61232))+P1(f777(f777(f235(a851),x61231),f777(f777(f84(a851),x61232),x61233))) % 174.01/173.89 [6125]~P1(f777(f777(f234(a851),x61251),x61253))+P1(f777(f777(f234(a851),x61251),f777(f777(f84(a851),x61252),x61253))) % 174.01/173.89 [6127]~P1(f777(f777(f234(a851),x61271),x61272))+P1(f777(f777(f234(a851),x61271),f777(f777(f84(a851),x61272),x61273))) % 174.01/173.89 [6166]P1(f777(f65(x61661),x61662))+~P1(f777(f65(x61661),f777(f777(f304(x61661),x61663),x61662))) % 174.01/173.89 [6167]P1(f777(f129(x61671),x61672))+~P1(f777(f129(x61671),f777(f777(f142(x61671),x61673),x61672))) % 174.01/173.89 [6168]P1(f777(f129(x61681),x61682))+~P1(f777(f129(x61681),f777(f777(f127(x61681),x61683),x61682))) % 174.01/173.89 [6169]P1(f777(f129(x61691),x61692))+~P1(f777(f129(x61691),f777(f777(f127(x61691),x61692),x61693))) % 174.01/173.89 [6214]~E(f54(a3,x62142,x62141),f54(a3,x62143,x62141))+P1(f777(f777(f281(a3),x62141),f777(f777(f5(a3),x62142),x62143))) % 174.01/173.89 [6219]~P85(x62191)+E(f777(f777(f84(x62191),x62192),f777(f777(f85(x62191),x62193),x62192)),f777(f777(f85(x62191),f777(f777(f84(x62191),x62193),f82(x62191))),x62192)) % 174.01/173.89 [6268]~E(x62681,x62682)+~P1(f777(f777(f235(f858(x62683,a845)),x62681),x62682)) % 174.01/173.89 [6316]P1(f777(f777(f336(x63161),x63162),x63163))+P1(f777(f777(f336(x63161),x63162),f777(f83(f858(x63161,a845)),x63163))) % 174.01/173.89 [6323]E(f136(x63231,f777(f777(f130(x63231),x63232),x63233)),f136(x63231,x63233))+~P1(f777(f777(f235(a851),x63232),f777(f183(f852(x63231)),x63233))) % 174.01/173.89 [6324]E(f777(f777(f161(x63241),x63242),f118(x63241,x63243)),f777(f777(f161(x63241),x63242),x63243))+~P1(f777(f777(f235(a851),x63242),f777(f183(f852(x63241)),x63243))) % 174.01/173.89 [6383]E(f777(f777(f777(f175(f852(x63831),f852(x63831)),x63832),f143(x63831)),x63833),x63833)+~E(f54(a851,x63832,f777(f183(f852(x63831)),x63833)),f4(a851)) % 174.01/173.89 [6392]~P12(x63921,x63923,x63922)+E(f777(f777(f283(x63921,x63921,x63921),f777(f280(x63921,x63921),x63922)),x63922),x63922) % 174.01/173.89 [6435]~E(f777(f777(f105(f858(x64351,a845)),x64352),x64353),x64353)+P1(f777(f777(f234(f858(x64351,a845)),x64352),x64353)) % 174.01/173.89 [6440]~P53(x64401,x64401,x64403)+P53(x64401,x64401,f777(f777(f175(f857(x64401,x64401),a845),x64402),x64403)) % 174.01/173.89 [6442]~P1(f777(f777(f336(x64421),x64423),f777(f160(x64421),x64422)))+P1(f777(f777(f235(a851),f4(a851)),f777(f183(f852(x64421)),x64422))) % 174.01/173.89 [6472]~P79(x64721)+E(f777(f79(x64721),f777(f777(f84(x64721),f777(f79(x64721),x64722)),f777(f79(x64721),x64723))),f777(f777(f84(x64721),f777(f79(x64721),x64722)),f777(f79(x64721),x64723))) % 174.01/173.89 [6484]E(f777(f777(f45(a851),f777(f777(f85(a851),x64841),x64842)),f777(f777(f85(a851),x64841),x64843)),f777(f777(f45(a851),x64842),x64843))+~P1(f777(f777(f235(a851),f4(a851)),x64841)) % 174.01/173.89 [6511]E(f54(a3,x65111,x65112),f54(a3,x65113,x65112))+~P1(f777(f777(f281(a3),x65112),f777(f777(f5(a3),x65111),x65113))) % 174.01/173.89 [6625]~P1(f777(f65(x66251),x66253))+E(f777(f777(f68(x66251,f858(x66251,a845),f304(x66251)),x66252),x66253),f777(f777(f105(f858(x66251,a845)),x66253),x66252)) % 174.01/173.89 [6688]E(f777(f777(f105(f858(x66881,a845)),x66882),x66883),x66882)+~P1(f777(f777(f234(f858(x66881,a845)),x66883),x66882)) % 174.01/173.89 [6690]E(f777(f777(f105(f858(x66901,a845)),x66902),x66903),x66903)+~P1(f777(f777(f234(f858(x66901,a845)),x66902),x66903)) % 174.01/173.89 [6691]E(f777(f777(f106(f858(x66911,a845)),x66912),x66913),x66913)+~P1(f777(f777(f234(f858(x66911,a845)),x66913),x66912)) % 174.01/173.89 [6692]E(f777(f777(f106(f858(x66921,a845)),x66922),x66923),x66922)+~P1(f777(f777(f234(f858(x66921,a845)),x66922),x66923)) % 174.01/173.89 [6745]~P1(f777(f129(x67451),x67452))+E(f777(f777(f5(f858(x67451,a845)),f777(f160(x67451),x67452)),f777(f777(f304(x67451),x67453),f182(f858(x67451,a845)))),f777(f160(x67451),f153(x67451,x67453,x67452))) % 174.01/173.89 [6804]P36(x68041,x68042)+~P36(x68041,f777(f777(f175(f857(x68041,x68041),a845),x68043),x68042)) % 174.01/173.89 [6820]~E(x68201,f4(a851))+P1(f777(f777(f281(a851),f777(f777(f85(a851),x68201),x68202)),f777(f777(f85(a851),x68201),x68203))) % 174.01/173.89 [6874]P1(f777(f58(x68741,x68742),f777(a60,x68743)))+~P1(f777(f58(f777(f83(a3),x68741),f777(f83(a3),x68742)),x68743)) % 174.01/173.89 [6879]E(f777(f777(f5(f858(x68791,a845)),f777(f777(f304(x68791),x68792),x68793)),f777(f777(f304(x68791),x68792),f182(f858(x68791,a845)))),x68793)+P1(f777(f777(f336(x68791),x68792),x68793)) % 174.01/173.89 [6898]E(f777(f777(f106(f858(x68981,a845)),f777(f160(x68981),x68982)),f777(f160(x68981),x68983)),f182(f858(x68981,a845)))+~P1(f777(f129(x68981),f777(f777(f127(x68981),x68982),x68983))) % 174.01/173.89 [6915]~P1(f777(f777(f336(x69151),x69152),f777(f160(x69151),x69153)))+~P1(f777(f129(x69151),f777(f777(f142(x69151),x69152),x69153))) % 174.01/173.89 [6992]E(f777(f777(f106(f858(x69921,a845)),x69922),x69923),f182(f858(x69921,a845)))+P1(f777(f777(f336(x69921),f495(x69923,x69922,x69921)),x69922)) % 174.01/173.89 [6993]E(f777(f777(f106(f858(x69931,a845)),x69932),x69933),f182(f858(x69931,a845)))+P1(f777(f777(f336(x69931),f499(x69933,x69932,x69931)),x69933)) % 174.01/173.89 [6997]E(f118(x69971,f777(f777(f161(x69971),x69972),x69973)),f777(f777(f161(x69971),f777(f777(f5(a851),x69972),f82(a851))),x69973))+~P1(f777(f777(f234(a851),x69972),f777(f183(f852(x69971)),x69973))) % 174.01/173.89 [7079]P1(f777(f777(f235(a851),f4(a851)),x70791))+P1(f777(f777(f234(a851),f777(f777(f85(a851),x70792),x70791)),f777(f777(f85(a851),x70793),x70791))) % 174.01/173.89 [7080]P1(f777(f777(f235(a851),f4(a851)),x70801))+P1(f777(f777(f234(a851),f777(f777(f85(a851),x70801),x70802)),f777(f777(f85(a851),x70801),x70803))) % 174.01/173.89 [7083]~P1(f777(f777(f336(x70831),x70832),x70833))+~P1(f777(f777(f336(x70831),x70832),f777(f83(f858(x70831,a845)),x70833))) % 174.01/173.89 [7089]~P1(f777(f777(f235(f858(x70891,a845)),x70892),x70893))+P1(f777(f777(f234(f858(x70891,a845)),x70892),x70893)) % 174.01/173.89 [7194]~P1(f777(f777(f235(a851),x71942),x71943))+P1(f777(f777(f235(a851),f777(f777(f84(a851),x71941),x71942)),f777(f777(f84(a851),x71941),x71943))) % 174.01/173.89 [7195]~P1(f777(f777(f235(a851),x71951),x71953))+P1(f777(f777(f235(a851),f777(f777(f84(a851),x71951),x71952)),f777(f777(f84(a851),x71953),x71952))) % 174.01/173.89 [7196]~P1(f777(f777(f235(a3),x71961),x71963))+P1(f777(f777(f235(a3),f777(f777(f84(a3),x71961),x71962)),f777(f777(f84(a3),x71963),x71962))) % 174.01/173.89 [7199]~P1(f777(f777(f234(a851),x71992),x71993))+P1(f777(f777(f234(a851),f777(f777(f84(a851),x71991),x71992)),f777(f777(f84(a851),x71991),x71993))) % 174.01/173.89 [7200]~P1(f777(f777(f234(a851),x72001),x72003))+P1(f777(f777(f234(a851),f777(f777(f84(a851),x72001),x72002)),f777(f777(f84(a851),x72003),x72002))) % 174.01/173.89 [7202]~P1(f777(f777(f234(a851),x72022),x72023))+P1(f777(f777(f234(a851),f777(f777(f85(a851),x72021),x72022)),f777(f777(f85(a851),x72021),x72023))) % 174.01/173.89 [7204]~P1(f777(f777(f234(a851),x72041),x72043))+P1(f777(f777(f234(a851),f777(f777(f85(a851),x72041),x72042)),f777(f777(f85(a851),x72043),x72042))) % 174.01/173.89 [7205]~P1(f777(f777(f234(a851),x72051),x72053))+P1(f777(f777(f234(a851),f777(f777(f45(a851),x72051),x72052)),f777(f777(f45(a851),x72053),x72052))) % 174.01/173.89 [7206]~P1(f777(f777(f234(a851),x72063),x72062))+P1(f777(f777(f234(a851),f777(f777(f5(a851),x72061),x72062)),f777(f777(f5(a851),x72061),x72063))) % 174.01/173.89 [7207]~P1(f777(f777(f234(a851),x72071),x72073))+P1(f777(f777(f234(a851),f777(f777(f5(a851),x72071),x72072)),f777(f777(f5(a851),x72073),x72072))) % 174.01/173.89 [7208]~P1(f777(f777(f234(a3),x72082),x72083))+P1(f777(f777(f234(a3),f777(f777(f84(a3),x72081),x72082)),f777(f777(f84(a3),x72081),x72083))) % 174.01/173.89 [7211]~P1(f777(f777(f281(a851),x72112),x72113))+P1(f777(f777(f281(a851),f777(f777(f85(a851),x72111),x72112)),f777(f777(f85(a851),x72111),x72113))) % 174.01/173.89 [7299]E(x72991,x72992)+~P1(f777(f777(f336(x72993),x72991),f777(f777(f304(x72993),x72992),f182(f858(x72993,a845))))) % 174.01/173.89 [7301]~E(f777(f777(f106(f858(x73011,a845)),x73012),x73013),f182(f858(x73011,a845)))+P1(f777(f777(f234(f858(x73011,a845)),x73012),f777(f83(f858(x73011,a845)),x73013))) % 174.01/173.89 [7308]P1(f777(f777(f336(f858(x73081,a845)),x73082),f777(f303(x73081),x73083)))+~P1(f777(f777(f234(f858(x73081,a845)),x73082),x73083)) % 174.01/173.89 [7365]E(f777(f777(f142(x73651),f777(f777(f155(x73651),x73652),x73653)),f777(f777(f130(x73651),f777(a116,x73653)),x73652)),f777(f777(f130(x73651),x73653),x73652))+~P1(f777(f777(f235(a851),x73653),f777(f183(f852(x73651)),x73652))) % 174.01/173.89 [7395]P1(f777(f777(f336(f857(x73951,x73951)),x73952),f302(x73951,x73953)))+~P1(f777(f777(f336(f857(x73951,x73951)),x73952),x73953)) % 174.01/173.89 [7405]~P1(f777(f777(f336(f858(x74051,a845)),x74052),f777(f303(x74051),x74053)))+P1(f777(f777(f234(f858(x74051,a845)),x74052),x74053)) % 174.01/173.89 [7447]P1(f777(f777(f234(f858(x74471,a845)),x74472),f46(f858(x74471,a845),x74473)))+~P1(f777(f777(f336(f858(x74471,a845)),x74472),x74473)) % 174.01/173.89 [7475]~P133(x74751)+E(f777(f777(f85(x74751),f777(f777(f244(x74751),f777(f83(x74751),f82(x74751))),x74752)),f777(f777(f244(x74751),x74753),x74752)),f777(f777(f244(x74751),f777(f83(x74751),x74753)),x74752)) % 174.01/173.89 [7497]E(f777(f777(f155(x74971),x74972),f777(f777(f5(a851),f777(f183(f852(x74971)),x74972)),f777(a116,x74973))),f777(f777(f155(x74971),f777(f144(x74971),x74972)),x74973))+~P1(f777(f777(f235(a851),x74973),f777(f183(f852(x74971)),x74972))) % 174.01/173.89 [7514]~E(f777(f777(f106(f858(x75141,a845)),f652(x75143,x75142,x75141)),x75143),f182(f858(x75141,a845)))+E(f777(f777(f106(f858(x75141,a845)),f46(f858(x75141,a845),x75142)),x75143),f182(f858(x75141,a845))) % 174.01/173.89 [7578]~P1(f777(f777(f336(x75783),x75782),f777(f160(x75783),x75781)))+P1(f777(f777(f235(a851),f731(x75781,x75782,x75783)),f777(f183(f852(x75783)),x75781))) % 174.01/173.89 [7586]P1(f777(f777(f336(x75861),f777(f777(f155(x75861),x75862),x75863)),f777(f160(x75861),x75862)))+~P1(f777(f777(f235(a851),x75863),f777(f183(f852(x75861)),x75862))) % 174.01/173.89 [7695]P1(f777(f777(f234(f858(f852(x76951),a845)),f151(x76951,x76952)),f151(x76951,x76953)))+~P1(f777(f777(f234(f858(x76951,a845)),x76952),x76953)) % 174.01/173.89 [7724]E(f777(f777(f106(f858(x77241,a845)),f46(f858(x77241,a845),x77242)),x77243),f182(f858(x77241,a845)))+P1(f777(f777(f336(f858(x77241,a845)),f652(x77243,x77242,x77241)),x77242)) % 174.01/173.89 [7726]~P1(f777(f777(f336(f858(x77261,a845)),x77263),x77262))+P1(f777(f777(f234(f858(x77261,a845)),f47(f858(x77261,a845),x77262)),x77263)) % 174.01/173.89 [7728]E(f777(f777(f106(f858(x77281,a845)),x77282),x77283),f182(f858(x77281,a845)))+~P1(f777(f777(f234(f858(x77281,a845)),x77282),f777(f83(f858(x77281,a845)),x77283))) % 174.01/173.89 [7781]E(f777(f777(f5(a851),f777(f777(f84(a851),f777(f157(a851),x77811)),x77812)),f777(f777(f155(a851),x77811),x77813)),f777(f157(a851),f777(f777(f150(a851,x77811),x77813),x77812)))+~P1(f777(f777(f235(a851),x77813),f777(f183(f852(a851)),x77811))) % 174.01/173.89 [7831]P1(f777(f777(f235(a851),x78311),x78312))+~P1(f777(f777(f235(a851),f777(f777(f84(a851),x78313),x78311)),f777(f777(f84(a851),x78313),x78312))) % 174.01/173.89 [7832]P1(f777(f777(f235(a851),x78321),x78322))+~P1(f777(f777(f235(a851),f777(f777(f85(a851),x78323),x78321)),f777(f777(f85(a851),x78323),x78322))) % 174.01/173.89 [7833]P1(f777(f777(f235(a851),x78331),x78332))+~P1(f777(f777(f235(a851),f777(f777(f85(a851),x78331),x78333)),f777(f777(f85(a851),x78332),x78333))) % 174.01/173.89 [7836]P1(f777(f777(f234(a851),x78361),x78362))+~P1(f777(f777(f234(a851),f777(f777(f84(a851),x78363),x78361)),f777(f777(f84(a851),x78363),x78362))) % 174.01/173.89 [7865]P1(f777(f777(f235(a851),f4(a851)),x78651))+~P1(f777(f777(f235(a851),f777(f777(f85(a851),x78652),x78651)),f777(f777(f85(a851),x78653),x78651))) % 174.01/173.89 [7866]P1(f777(f777(f235(a851),f4(a851)),x78661))+~P1(f777(f777(f235(a851),f777(f777(f85(a851),x78661),x78662)),f777(f777(f85(a851),x78661),x78663))) % 174.01/173.89 [7939]E(f246(x79391,x79392,x79393),x79392)+~P1(f777(f777(f234(f858(x79391,a845)),x79393),f777(f777(f304(x79391),x79392),f182(f858(x79391,a845))))) % 174.01/173.89 [8018]E(f777(f777(f127(x80181),f777(f777(f161(x80181),x80182),x80183)),f777(f777(f142(x80181),f777(f777(f155(x80181),x80183),x80182)),f117(x80181))),f777(f777(f161(x80181),f777(a116,x80182)),x80183))+~P1(f777(f777(f235(a851),x80182),f777(f183(f852(x80181)),x80183))) % 174.01/173.89 [8087]P1(f777(f777(f234(f858(f858(x80871,a845),a845)),f247(x80871,x80872)),f247(x80871,x80873)))+~P1(f777(f777(f234(f858(x80871,a845)),x80872),x80873)) % 174.01/173.89 [8126]~P1(f777(f129(x81261),x81263))+P1(f777(f129(x81261),f777(f777(f777(f175(f852(x81261),f852(x81261)),x81262),f143(x81261)),x81263))) % 174.01/173.89 [8131]~P1(f777(f777(f235(a851),x81312),x81313))+P1(f777(f777(f235(a851),f777(f777(f85(a851),f777(a116,x81311)),x81312)),f777(f777(f85(a851),f777(a116,x81311)),x81313))) % 174.01/173.89 [8154]P1(f777(f777(f234(f858(f858(x81541,a845),a845)),f777(f303(x81541),x81542)),f777(f303(x81541),x81543)))+~P1(f777(f777(f234(f858(x81541,a845)),x81542),x81543)) % 174.01/173.89 [8311]~P1(f777(f777(f234(f858(x83111,a845)),x83113),x83112))+P1(f777(f777(f234(f858(x83111,a845)),f777(f83(f858(x83111,a845)),x83112)),f777(f83(f858(x83111,a845)),x83113))) % 174.01/173.89 [8350]E(f777(f305(a851,a851,f777(f777(f11(a851,a851,a851),f5(a851)),x83501)),f777(f296(a851,x83502),x83503)),f777(f296(a851,f777(f777(f5(a851),x83502),x83501)),f777(f777(f5(a851),x83503),x83501)))+~P1(f777(f777(f235(a851),x83501),x83503)) % 174.01/173.89 [8376]~P67(x83761)+E(f777(f777(f84(x83761),x83762),f777(f134(x83761,x83761,f84(x83761),f4(x83761)),x83763)),f777(f134(x83761,x83761,f84(x83761),x83762),x83763)) % 174.01/173.89 [8457]~P79(x84571)+P1(f777(f777(f234(x84571),f777(f79(x84571),f777(f777(f84(x84571),x84572),x84573))),f777(f777(f84(x84571),f777(f79(x84571),x84572)),f777(f79(x84571),x84573)))) % 174.01/173.89 [8458]~P79(x84581)+P1(f777(f777(f234(x84581),f777(f79(x84581),f777(f777(f5(x84581),x84582),x84583))),f777(f777(f84(x84581),f777(f79(x84581),x84582)),f777(f79(x84581),x84583)))) % 174.01/173.89 [8468]E(f777(f777(f84(a3),f777(f777(f85(a3),x84681),f54(a3,f777(f777(f45(a3),x84682),x84681),x84683))),f54(a3,x84682,x84681)),f54(a3,x84682,f777(f777(f85(a3),x84681),x84683)))+~P1(f777(f777(f235(a3),f4(a3)),x84683)) % 174.01/173.89 [8477]E(f777(f777(f127(x84771),f777(f777(f161(x84771),x84772),x84773)),f777(f777(f142(x84771),f777(f133(x84771),f777(f777(f130(x84771),x84772),x84773))),f117(x84771))),f777(f777(f161(x84771),f777(a116,x84772)),x84773))+~P1(f777(f777(f235(a851),x84772),f777(f183(f852(x84771)),x84773))) % 174.01/173.89 [8496]E(f777(f267(x84961,f777(f777(f145(x84961,f857(a103,x84961)),f777(f243(a103,x84961),f82(a103))),x84962)),f777(a7,x84963)),f777(f777(f155(x84961),x84962),x84963))+~P1(f777(f777(f235(a851),x84963),f777(f183(f852(x84961)),x84962))) % 174.01/173.89 [8553]P1(f777(f777(f336(f857(x85531,x85531)),x85532),f777(f777(f283(x85531,x85531,x85531),x85533),f302(x85531,x85533))))+~P1(f777(f777(f336(f857(x85531,x85531)),x85532),x85533)) % 174.01/173.89 [8570]P1(f777(f777(f234(a851),x85701),x85702))+~P1(f777(f777(f234(a851),f777(f777(f85(a851),f777(a116,x85703)),x85701)),f777(f777(f85(a851),f777(a116,x85703)),x85702))) % 174.01/173.89 [8581]P1(f777(f777(f234(f858(x85811,a845)),x85812),x85813))+~P1(f777(f777(f234(f858(x85811,a845)),f777(f83(f858(x85811,a845)),x85813)),f777(f83(f858(x85811,a845)),x85812))) % 174.01/173.89 [8599]P1(f777(f129(x85991),x85992))+~P1(f777(f129(x85991),f777(f777(f777(f175(f852(x85991),f852(x85991)),x85993),f143(x85991)),x85992))) % 174.01/173.89 [8665]E(f777(f279(x86651,x86651,f302(x86651,x86652)),x86653),x86653)+~P1(f777(f777(f234(f858(x86651,a845)),f777(f279(x86651,x86651,x86652),x86653)),x86653)) % 174.01/173.89 [8667]E(f777(f305(f857(x86671,x86672),x86672,f252(x86671,x86672)),f777(f160(f857(x86671,x86672)),x86673)),f173(x86671,x86672,f168(x86671,x86672,x86673)))+~P1(f777(f129(x86671),f777(f777(f145(f857(x86671,x86672),x86671),f242(x86671,x86672)),x86673))) % 174.01/173.89 [8706]~P100(x87061)+P18(x87061,f777(f128(x87061,f777(f777(f11(x87061,x87061,a845),a332),f777(x87062,x87063))),x87063)) % 174.01/173.89 [8711]~P1(f777(f777(f234(a851),x87111),x87112))+P1(f777(f777(f234(a851),x87111),f777(f134(a851,a851,f84(a851),x87112),x87113))) % 174.01/173.89 [8782]~P1(f777(f777(f336(f857(x87821,x87821)),x87822),f302(x87821,x87823)))+P1(f777(f777(f336(f857(x87821,x87821)),x87822),f777(f777(f175(f857(x87821,x87821),a845),f635(x87823,x87822,x87821)),x87823))) % 174.01/173.89 [8851]~P67(x88511)+E(f777(f777(f84(x88511),x88512),f777(f134(x88511,x88511,f777(f11(x88511,x88511,x88511),f84(x88511)),f4(x88511)),f777(f144(x88511),x88513))),f777(f134(x88511,x88511,f84(x88511),x88512),x88513)) % 174.01/173.89 [9110]P53(x91101,x91102,x91103)+P1(f777(f777(f336(f857(x91101,x91102)),f777(f777(f243(x91101,x91102),f648(x91103,x91102,x91101)),f642(x91103,x91102,x91101))),x91103)) % 174.01/173.89 [9111]P53(x91111,x91112,x91113)+P1(f777(f777(f336(f857(x91111,x91112)),f777(f777(f243(x91111,x91112),f648(x91113,x91112,x91111)),f641(x91113,x91112,x91111))),x91113)) % 174.01/173.89 [9166]~P1(f777(f777(f336(f857(x91661,x91661)),x91662),f777(f777(f283(x91661,x91661,x91661),x91663),f302(x91661,x91663))))+P1(f777(f777(f336(f857(x91661,x91661)),x91662),f777(f777(f175(f857(x91661,x91661),a845),f640(x91663,x91662,x91661)),x91663))) % 174.01/173.89 [9167]~P1(f777(x91671,f777(f777(f155(x91672),x91673),f777(f183(f852(x91672)),f164(x91672,x91671,x91673)))))+~P1(f777(f777(f235(a851),f777(f183(f852(x91672)),f164(x91672,x91671,x91673))),f777(f183(f852(x91672)),x91673))) % 174.01/173.89 [9243]~P1(f777(f777(f234(f858(x92431,a845)),x92432),x92433))+P1(f777(f777(f234(f858(x92431,a845)),f777(f777(f11(x92431,f858(x92431,a845),a845),f336(x92431)),x92432)),f777(f777(f11(x92431,f858(x92431,a845),a845),f336(x92431)),x92433))) % 174.01/173.89 [9299]~P1(f777(f777(f336(f857(f858(x92991,a845),f858(x92991,a845))),f777(f777(f243(f858(x92991,a845),f858(x92991,a845)),x92992),x92993)),f301(x92991)))+P1(f777(f777(f235(f858(x92991,a845)),x92992),x92993)) % 174.01/173.89 [9325]P54(x93251,x93252,x93253)+~P1(f777(f777(f336(f857(x93251,x93251)),f777(f777(f243(x93251,x93251),f629(x93253,x93252,x93251)),f628(x93253,x93252,x93251))),x93253)) % 174.01/173.89 [9326]P54(x93261,x93262,x93263)+~P1(f777(f777(f336(f857(x93261,x93261)),f777(f777(f243(x93261,x93261),f628(x93263,x93262,x93261)),f629(x93263,x93262,x93261))),x93263)) % 174.01/173.89 [9360]~P1(f777(f777(f336(f857(f852(x93601),f852(x93601))),f777(f777(f243(f852(x93601),f852(x93601)),x93602),x93602)),f139(x93601,x93603)))+P1(f777(f777(f336(f857(x93601,x93601)),f777(f777(f243(x93601,x93601),f756(x93602,x93603,x93601)),f756(x93602,x93603,x93601))),x93603)) % 174.01/173.89 [9405]P1(f777(f777(f234(f858(x94051,a845)),x94052),x94053))+~P1(f777(f777(f234(f858(x94051,a845)),f777(f777(f11(x94051,f858(x94051,a845),a845),f336(x94051)),x94052)),f777(f777(f11(x94051,f858(x94051,a845),a845),f336(x94051)),x94053))) % 174.01/173.89 [9491]E(f777(f777(f5(a851),f777(f777(f10(a851,a851),x94911),f777(f259(a851),x94912))),f777(f777(f10(a851,a851),x94913),f777(f259(a851),x94912))),f777(f777(f10(a851,a851),f777(f777(f22(a851,a851,a851),f777(f777(f12(a851,f858(a851,a851),a851),f5(a851)),x94911)),x94913)),f777(f259(a851),x94912)))+~P1(f777(f777(f234(a851),f777(x94913,f343(x94912,x94911,x94913))),f777(x94911,f343(x94912,x94911,x94913)))) % 174.01/173.89 [9773]E(f777(f258(f857(x97731,x97732)),f777(f253(x97731,x97732,a845),f777(f777(f11(x97731,f858(x97732,f855(x97732)),f858(x97732,a845)),f777(f777(f12(f858(f855(x97732),a845),f858(f858(x97732,f855(x97732)),f858(x97732,a845)),x97731),f12(f855(x97732),a845,x97732)),f777(f777(f12(f855(x97732),f858(f855(x97732),a845),x97731),a332),f168(x97731,x97732,x97733)))),f229(x97732)))),f777(f160(f857(x97731,x97732)),x97733))+~P1(f777(f129(x97731),f777(f777(f145(f857(x97731,x97732),x97731),f242(x97731,x97732)),x97733))) % 174.01/173.89 [5519]~P69(x55191)+E(f777(f777(f84(x55191),f777(f777(f5(x55191),x55192),x55193)),x55193),x55192) % 174.01/173.89 [5520]~P69(x55201)+E(f777(f777(f5(x55201),f777(f777(f84(x55201),x55202),x55203)),x55203),x55202) % 174.01/173.89 [5746]~P69(x57461)+E(f777(f777(f84(x57461),x57462),f777(f777(f84(x57461),f777(f83(x57461),x57462)),x57463)),x57463) % 174.01/173.89 [5829]~P75(x58291)+E(f777(f777(f85(x58291),f777(f777(f244(x58291),x58292),x58293)),x58292),f777(f777(f244(x58291),x58292),f777(a116,x58293))) % 174.01/173.89 [5830]~P85(x58301)+E(f777(f777(f85(x58301),f777(f777(f244(x58301),x58302),x58303)),x58302),f777(f777(f244(x58301),x58302),f777(a116,x58303))) % 174.01/173.89 [6045]~P110(x60451)+E(f777(f79(x60451),f777(f777(f244(x60451),f777(f83(x60451),x60452)),x60453)),f777(f79(x60451),f777(f777(f244(x60451),x60452),x60453))) % 174.01/173.89 [6097]~P75(x60971)+E(f777(f777(f85(x60971),f777(f777(f244(x60971),x60972),x60973)),x60972),f777(f777(f85(x60971),x60972),f777(f777(f244(x60971),x60972),x60973))) % 174.01/173.89 [6157]E(f777(f777(f5(a103),f777(f777(f84(a103),x61571),x61572)),x61573),f271(x61571,x61572,x61573))+~P1(f777(f777(f235(a103),x61572),x61573)) % 174.01/173.89 [6179]~E(f777(f777(f130(x61791),x61793),x61792),f117(x61791))+P1(f777(f777(f234(a851),f777(f183(f852(x61791)),x61792)),x61793)) % 174.01/173.89 [6321]E(f777(f777(f85(a851),f777(f108(a851),x63211)),f777(f777(f85(a851),f777(f108(a851),x63212)),x63213)),f4(a851))+~P1(f777(f777(f235(a3),x63211),a87)) % 174.01/173.89 [6337]~P60(x63371)+E(f777(f777(f244(x63371),f777(f777(f285(x63371),f82(x63371)),x63372)),x63373),f777(f777(f285(x63371),f82(x63371)),f777(f777(f244(x63371),x63372),x63373))) % 174.01/173.89 [6422]E(f777(f777(f5(a851),f777(f777(f84(a851),x64221),x64222)),x64223),f777(f777(f5(a851),x64221),f777(f777(f5(a851),x64223),x64222)))+~P1(f777(f777(f234(a851),x64222),x64223)) % 174.01/173.89 [6423]E(f777(f777(f5(a851),f777(f777(f84(a851),x64231),x64232)),x64233),f777(f777(f84(a851),x64231),f777(f777(f5(a851),x64232),x64233)))+~P1(f777(f777(f234(a851),x64233),x64232)) % 174.01/173.89 [6463]~P100(x64631)+P1(f777(f777(f234(x64631),f777(f777(f238(x64631),x64632),x64633)),x64633)) % 174.01/173.89 [6464]~P100(x64641)+P1(f777(f777(f234(x64641),f777(f777(f238(x64641),x64642),x64643)),x64642)) % 174.01/173.89 [6465]~P93(x64651)+P1(f777(f777(f234(x64651),f777(f777(f106(x64651),x64652),x64653)),x64653)) % 174.01/173.89 [6466]~P98(x64661)+P1(f777(f777(f234(x64661),f777(f777(f106(x64661),x64662),x64663)),x64663)) % 174.01/173.89 [6467]~P93(x64671)+P1(f777(f777(f234(x64671),f777(f777(f106(x64671),x64672),x64673)),x64672)) % 174.01/173.89 [6468]~P98(x64681)+P1(f777(f777(f234(x64681),f777(f777(f106(x64681),x64682),x64683)),x64682)) % 174.01/173.89 [6483]E(f777(f777(f45(a3),f777(f777(f45(a3),x64831),x64832)),x64833),f777(f777(f45(a3),x64831),f777(f777(f85(a3),x64832),x64833)))+~P1(f777(f777(f235(a3),f4(a3)),x64833)) % 174.01/173.89 [6536]~P85(x65361)+E(f777(f777(f84(x65361),f777(f777(f85(x65361),x65362),x65363)),x65363),f777(f777(f85(x65361),f777(f777(f84(x65361),x65362),f82(x65361))),x65363)) % 174.01/173.89 [6537]~P88(x65371)+E(f777(f777(f85(x65371),f777(f83(x65371),f777(f108(x65371),x65372))),x65373),f777(f777(f85(x65371),f777(f108(x65371),f777(f83(a3),x65372))),x65373)) % 174.01/173.89 [6610]~P67(x66101)+E(f777(f157(x66101),f777(f777(f145(x66102,x66101),f777(f20(x66101,x66102),f4(x66101))),x66103)),f4(x66101)) % 174.01/173.89 [6629]E(f777(f777(f84(a851),f777(f108(a851),x66291)),f777(f777(f84(a851),f777(f108(a851),x66292)),x66293)),f777(f777(f84(a851),f777(f108(a851),x66292)),x66293))+~P1(f777(a188,f777(f108(a3),x66291))) % 174.01/173.89 [6644]~P9(x66441)+E(f47(x66441,f777(f777(f304(x66441),x66442),f777(f777(f304(x66441),x66443),f182(f858(x66441,a845))))),f777(f777(f106(x66441),x66442),x66443)) % 174.01/173.89 [6645]~P9(x66451)+E(f46(x66451,f777(f777(f304(x66451),x66452),f777(f777(f304(x66451),x66453),f182(f858(x66451,a845))))),f777(f777(f105(x66451),x66452),x66453)) % 174.01/173.89 [6670]E(f777(f777(f161(x66701),x66702),x66703),x66703)+~P1(f777(f777(f234(a851),f777(f183(f852(x66701)),x66703)),x66702)) % 174.01/173.89 [6682]E(f777(f777(f130(x66821),x66822),x66823),f117(x66821))+~P1(f777(f777(f234(a851),f777(f183(f852(x66821)),x66823)),x66822)) % 174.01/173.89 [6694]E(f777(f777(f5(a851),f777(f777(f84(a851),x66941),x66942)),x66943),f777(f777(f84(a851),f777(f777(f5(a851),x66941),x66943)),x66942))+~P1(f777(f777(f234(a851),x66943),x66941)) % 174.01/173.89 [6708]~P1(f777(f777(f235(a851),x67081),x67083))+P1(f777(f777(f235(a851),f777(f777(f5(a851),x67081),x67082)),x67083)) % 174.01/173.89 [6736]~P100(x67361)+E(f153(x67361,x67362,f777(f777(f140(x67361,x67361,f9(x67361)),x67362),x67363)),x67363) % 174.01/173.89 [6834]E(f777(f777(f5(a851),f777(f777(f84(a851),x68341),x68342)),f777(a116,x68343)),f777(f777(f5(a851),x68341),f777(a116,f777(f777(f5(a851),x68343),x68342))))+~P1(f777(f777(f234(a851),x68342),x68343)) % 174.01/173.89 [6835]~P110(x68351)+P1(f777(f777(f234(x68351),f4(x68351)),f777(f777(f244(x68351),f777(f79(x68351),x68352)),x68353))) % 174.01/173.89 [6886]P28(x68861,x68862,x68863)+~P1(f777(f777(f234(f858(f850(x68861),a845)),x68863),x68862)) % 174.01/173.89 [6927]~P1(f777(f65(x69271),x69272))+P1(f777(f65(x69271),f777(f777(f5(f858(x69271,a845)),x69272),x69273))) % 174.01/173.89 [6928]~P1(f777(f65(x69281),x69283))+P1(f777(f65(x69281),f777(f777(f106(f858(x69281,a845)),x69282),x69283))) % 174.01/173.89 [6929]~P1(f777(f65(x69291),x69292))+P1(f777(f65(x69291),f777(f777(f106(f858(x69291,a845)),x69292),x69293))) % 174.01/173.89 [7068]~P36(x70681,x70683)+P36(x70681,f777(f777(f106(f858(f857(x70681,x70681),a845)),x70682),x70683)) % 174.01/173.89 [7069]~P36(x70691,x70692)+P36(x70691,f777(f777(f106(f858(f857(x70691,x70691),a845)),x70692),x70693)) % 174.01/173.89 [7189]~P93(x71891)+E(f17(x71891,f777(f160(x71891),f777(f777(f142(x71891),x71892),x71893))),f777(f134(x71891,x71891,f105(x71891),x71892),x71893)) % 174.01/173.89 [7190]~P100(x71901)+E(f18(x71901,f777(f160(x71901),f777(f777(f142(x71901),x71902),x71903))),f777(f134(x71901,x71901,f181(x71901),x71902),x71903)) % 174.01/173.89 [7191]~P100(x71911)+E(f19(x71911,f777(f160(x71911),f777(f777(f142(x71911),x71912),x71913))),f777(f134(x71911,x71911,f238(x71911),x71912),x71913)) % 174.01/173.89 [7192]~P93(x71921)+E(f14(x71921,f777(f160(x71921),f777(f777(f142(x71921),x71922),x71923))),f777(f134(x71921,x71921,f106(x71921),x71922),x71923)) % 174.01/173.89 [7193]~P1(f777(f777(f281(a3),x71931),x71932))+P1(f777(f777(f281(a3),x71931),f777(f777(f84(a3),x71932),f777(f777(f85(a3),x71931),x71933)))) % 174.01/173.89 [7263]~P1(f777(f65(x72631),x72632))+P1(f777(f777(f234(a851),f777(f44(x72631),x72632)),f777(f44(x72631),f777(f777(f304(x72631),x72633),x72632)))) % 174.01/173.89 [7270]E(f777(f777(f105(f858(a851,a845)),f777(f296(a851,x72701),x72702)),f777(f296(a851,x72702),f777(f777(f84(a851),x72702),x72703))),f777(f296(a851,x72701),f777(f777(f84(a851),x72702),x72703)))+~P1(f777(f777(f234(a851),x72701),x72702)) % 174.01/173.89 [7280]P1(f777(f777(f235(a851),x72801),x72802))+~P1(f777(f777(f235(a851),f777(f777(f84(a851),x72801),x72803)),x72802)) % 174.01/173.89 [7283]P1(f777(f777(f234(a851),x72831),x72832))+~P1(f777(f777(f234(a851),f777(f777(f84(a851),x72833),x72831)),x72832)) % 174.01/173.89 [7284]P1(f777(f777(f234(a851),x72841),x72842))+~P1(f777(f777(f234(a851),f777(f777(f84(a851),x72841),x72843)),x72842)) % 174.01/173.89 [7326]~P100(x73261)+E(f15(x73261,f181(x73261),f777(f160(x73261),f777(f777(f142(x73261),x73262),x73263))),f777(f134(x73261,x73261,f181(x73261),x73262),x73263)) % 174.01/173.89 [7327]~P100(x73271)+E(f16(x73271,f238(x73271),f777(f160(x73271),f777(f777(f142(x73271),x73272),x73273))),f777(f134(x73271,x73271,f238(x73271),x73272),x73273)) % 174.01/173.89 [7331]~E(x73312,f182(f858(f857(x73311,x73311),a845)))+P1(f777(f777(f234(f858(f857(x73311,x73311),a845)),x73312),x73313)) % 174.01/173.89 [7440]E(f777(f777(f105(f858(x74401,a845)),x74402),f777(f777(f5(f858(x74401,a845)),x74403),x74402)),x74403)+~P1(f777(f777(f234(f858(x74401,a845)),x74402),x74403)) % 174.01/173.89 [7443]~P1(f777(f777(f235(a851),x74431),f777(f777(f5(a851),x74433),x74432)))+P1(f777(f777(f235(a851),f777(f777(f84(a851),x74431),x74432)),x74433)) % 174.01/173.89 [7444]~P1(f777(f777(f234(a851),x74441),f777(f777(f84(a851),x74443),x74442)))+P1(f777(f777(f234(a851),f777(f777(f5(a851),x74441),x74442)),x74443)) % 174.01/173.89 [7504]E(x75041,f117(x75042))+E(f777(f133(x75042),f777(f777(f777(f175(f852(x75042),f852(x75042)),x75043),f143(x75042)),x75041)),f777(f777(f155(x75042),x75041),f54(a851,x75043,f777(f183(f852(x75042)),x75041)))) % 174.01/173.89 [7513]E(f777(f777(f304(x75131),x75132),f777(f777(f5(f858(x75131,a845)),x75133),f777(f777(f304(x75131),x75132),f182(f858(x75131,a845))))),x75133)+~P1(f777(f777(f336(x75131),x75132),x75133)) % 174.01/173.89 [7677]P1(f777(f777(f235(a851),x76771),f777(f777(f5(a851),x76772),x76773)))+~P1(f777(f777(f235(a851),f777(f777(f84(a851),x76771),x76773)),x76772)) % 174.01/173.89 [7678]P1(f777(f777(f234(a851),x76781),f777(f777(f84(a851),x76782),x76783)))+~P1(f777(f777(f234(a851),f777(f777(f5(a851),x76781),x76783)),x76782)) % 174.01/173.89 [7698]P1(f777(f65(x76981),x76982))+~P1(f777(f65(x76981),f777(f777(f105(f858(x76981,a845)),x76983),x76982))) % 174.01/173.89 [7699]P1(f777(f65(x76991),x76992))+~P1(f777(f65(x76991),f777(f777(f105(f858(x76991,a845)),x76992),x76993))) % 174.01/173.89 [7780]~P44(x77801,x77803)+P1(f777(f777(f336(f857(x77801,x77801)),f777(f777(f243(x77801,x77801),x77802),x77802)),x77803)) % 174.01/173.89 [7830]P1(f777(f777(f281(a3),x78301),x78302))+~P1(f777(f777(f281(a3),x78301),f777(f777(f84(a3),x78302),f777(f777(f85(a3),x78301),x78303)))) % 174.01/173.89 [7910]E(f777(f777(f155(a851),f132(a851,f777(f296(a851,x79101),x79102))),x79103),f777(f777(f84(a851),x79101),x79103))+~P1(f777(f777(f235(a851),f777(f777(f84(a851),x79101),x79103)),x79102)) % 174.01/173.89 [7980]~P1(f777(f777(f189(f777(a29,x79801)),x79802),x79803))+P1(f777(f777(f189(f777(f233(a846),f777(a32,x79801))),x79802),x79803)) % 174.01/173.89 [7984]E(f777(f777(f161(a851),x79841),f132(a851,f777(f296(a851,x79842),x79843))),f132(a851,f777(f296(a851,x79842),f777(f777(f84(a851),x79842),x79841))))+~P1(f777(f777(f234(a851),f777(f777(f84(a851),x79842),x79841)),x79843)) % 174.01/173.89 [8033]~P88(x80331)+E(f777(f777(f244(x80331),x80332),f777(f108(a851),f777(f777(f84(a3),x80333),x80333))),f777(f777(f90(x80331,x80331),f777(f777(f244(x80331),x80332),f777(f108(a851),x80333))),f777(f777(f22(x80331,x80331,x80331),f85(x80331)),f9(x80331)))) % 174.01/173.89 [8233]P1(f777(f777(f189(f777(a29,x82331)),x82332),x82333))+~P1(f777(f777(f189(f777(f233(a846),f777(a32,x82331))),x82332),x82333)) % 174.01/173.89 [8290]E(f777(f777(f127(x82901),f777(f777(f161(x82901),x82902),x82903)),f777(f777(f142(x82901),f777(f777(f155(x82901),x82903),x82902)),f777(f777(f130(x82901),f777(a116,x82902)),x82903))),x82903)+~P1(f777(f777(f235(a851),x82902),f777(f183(f852(x82901)),x82903))) % 174.01/173.89 [8297]P1(f777(f777(f234(f858(x82971,a845)),f323(x82971,x82972)),f323(x82971,x82973)))+~P1(f777(f777(f234(f858(x82971,f858(x82971,a845))),x82973),x82972)) % 174.01/173.89 [8298]~P54(x82981,x82982,x82983)+P54(x82981,x82982,f777(f777(f5(f858(f857(x82981,x82981),a845)),x82983),f302(x82981,f182(f858(f857(x82981,x82981),a845))))) % 174.01/173.89 [8320]P1(f777(f777(f234(f858(x83201,a845)),f324(x83201,x83202)),f324(x83201,x83203)))+~P1(f777(f777(f234(f858(f857(x83201,x83201),a845)),x83203),x83202)) % 174.01/173.89 [8327]~P118(x83271)+P1(f777(f777(f234(x83271),f4(x83271)),f777(f777(f84(x83271),f777(f777(f85(x83271),x83272),x83272)),f777(f777(f85(x83271),x83273),x83273)))) % 174.01/173.89 [8364]P1(f777(f777(f234(f858(x83641,a845)),f777(f278(x83641),x83642)),f777(f278(x83641),x83643)))+~P1(f777(f777(f234(f858(f857(x83641,x83641),a845)),x83642),x83643)) % 174.01/173.89 [8396]~P48(x83961,x83962)+~P1(f777(f777(f336(f857(x83961,x83961)),f777(f777(f243(x83961,x83961),x83963),x83963)),x83962)) % 174.01/173.89 [8398]~P36(x83981,x83982)+~P1(f777(f777(f336(f857(x83981,x83981)),f777(f777(f243(x83981,x83981),x83983),x83983)),x83982)) % 174.01/173.89 [8459]P1(f777(f777(f234(f858(x84591,a845)),f47(f858(x84591,a845),x84592)),f47(f858(x84591,a845),x84593)))+~P1(f777(f777(f234(f858(f858(x84591,a845),a845)),x84593),x84592)) % 174.01/173.89 [8460]P1(f777(f777(f234(f858(x84601,a845)),f46(f858(x84601,a845),x84602)),f46(f858(x84601,a845),x84603)))+~P1(f777(f777(f234(f858(f858(x84601,a845),a845)),x84602),x84603)) % 174.01/173.89 [8515]~P12(x85151,x85153,x85152)+P1(f777(f777(f234(f858(f857(x85151,x85151),a845)),x85152),f777(f777(f250(x85151,x85151),x85153),f777(f20(f858(x85151,a845),x85151),x85153)))) % 174.01/173.89 [8516]~P47(x85161,x85163,x85162)+P1(f777(f777(f234(f858(f857(x85161,x85161),a845)),x85162),f777(f777(f250(x85161,x85161),x85163),f777(f20(f858(x85161,a845),x85161),x85163)))) % 174.01/173.89 [8554]~P79(x85541)+P1(f777(f777(f234(x85541),f777(f777(f5(x85541),f777(f79(x85541),x85542)),f777(f79(x85541),x85543))),f777(f79(x85541),f777(f777(f5(x85541),x85543),x85542)))) % 174.01/173.89 [8555]~P79(x85551)+P1(f777(f777(f234(x85551),f777(f777(f5(x85551),f777(f79(x85551),x85552)),f777(f79(x85551),x85553))),f777(f79(x85551),f777(f777(f5(x85551),x85552),x85553)))) % 174.01/173.89 [8579]P1(f777(f777(f234(f858(f857(x85791,x85791),a845)),f302(x85791,x85792)),f302(x85791,x85793)))+~P1(f777(f777(f234(f858(f857(x85791,x85791),a845)),x85792),x85793)) % 174.01/173.89 [8725]P54(x87251,x87252,x87253)+~P54(x87251,x87252,f777(f777(f5(f858(f857(x87251,x87251),a845)),x87253),f302(x87251,f182(f858(f857(x87251,x87251),a845))))) % 174.01/173.89 [8744]P1(f777(f777(f234(f858(f857(f852(x87441),f852(x87441)),a845)),f149(x87441,x87442)),f149(x87441,x87443)))+~P1(f777(f777(f234(f858(f857(x87441,x87441),a845)),x87442),x87443)) % 174.01/173.89 [8745]P1(f777(f777(f234(f858(f857(f852(x87451),f852(x87451)),a845)),f148(x87451,x87452)),f148(x87451,x87453)))+~P1(f777(f777(f234(f858(f857(x87451,x87451),a845)),x87452),x87453)) % 174.01/173.89 [8762]~P47(x87621,x87623,x87622)+P1(f777(f777(f234(f858(f857(x87621,x87621),a845)),x87622),f777(f777(f283(x87621,x87621,x87621),f777(f280(x87621,x87621),x87622)),x87622))) % 174.01/173.89 [8803]~P1(f777(f129(x88031),x88032))+E(f777(f128(x88031,f777(f777(f11(x88031,f858(x88031,a845),a845),f336(x88031)),f777(f160(x88031),f162(x88031,x88032,x88033)))),x88032),f162(x88031,x88032,x88033)) % 174.01/173.89 [8849]E(x88491,x88492)+~P1(f777(f777(f336(f857(x88493,x88493)),f777(f777(f243(x88493,x88493),x88491),x88492)),f302(x88493,f182(f858(f857(x88493,x88493),a845))))) % 174.01/173.89 [8931]P1(f777(f777(f336(x89311),x89312),f324(x89311,x89313)))+P1(f777(f777(f336(f857(x89311,x89311)),f777(f777(f243(x89311,x89311),f528(x89313,x89312,x89311)),x89312)),x89313)) % 174.01/173.89 [8932]P1(f777(f777(f336(x89321),x89322),f324(x89321,x89323)))+P1(f777(f777(f336(f857(x89321,x89321)),f777(f777(f243(x89321,x89321),f621(x89323,x89322,x89321)),x89322)),x89323)) % 174.01/173.89 [8933]P1(f777(f777(f336(x89331),x89332),f324(x89331,x89333)))+P1(f777(f777(f336(f857(x89331,x89331)),f777(f777(f243(x89331,x89331),f623(x89333,x89332,x89331)),x89332)),x89333)) % 174.01/173.89 [9037]P1(f777(x90373,x90372))+E(f777(f258(x90371),f777(f777(f22(x90371,a845,a845),f777(f777(f12(a845,f858(a845,a845),x90371),a333),f777(a332,x90372))),x90373)),f182(f858(x90371,a845))) % 174.01/173.89 [9056]~P79(x90561)+P1(f777(f777(f234(x90561),f777(f79(x90561),f777(f777(f5(x90561),f777(f79(x90561),x90562)),f777(f79(x90561),x90563)))),f777(f79(x90561),f777(f777(f5(x90561),x90562),x90563)))) % 174.01/173.89 [9069]~P1(f777(x90693,x90692))+E(f777(f258(x90691),f777(f777(f22(x90691,a845,a845),f777(f777(f12(a845,f858(a845,a845),x90691),a333),f777(a332,x90692))),x90693)),f777(f777(f304(x90691),x90692),f182(f858(x90691,a845)))) % 174.01/173.89 [9075]~P1(f777(f777(f336(f858(x90751,a845)),x90753),f777(f303(x90751),x90752)))+P1(f777(f247(x90751,f777(f777(f11(x90751,f858(x90751,a845),a845),f336(x90751)),x90752)),x90753)) % 174.01/173.89 [9109]P36(x91091,x91092)+P1(f777(f777(f336(f857(x91091,x91091)),f777(f777(f243(x91091,x91091),f777(f591(x91092,x91091),f777(a116,x91093))),f777(f591(x91092,x91091),x91093))),x91092)) % 174.01/173.89 [9235]P1(f777(f777(f336(f858(x92351,a845)),x92352),f777(f303(x92351),x92353)))+~P1(f777(f247(x92351,f777(f777(f11(x92351,f858(x92351,a845),a845),f336(x92351)),x92353)),x92352)) % 174.01/173.89 [9295]P1(f777(f777(f336(x92951),f777(f267(x92951,x92952),x92953)),f777(f160(x92951),f777(f777(f145(f857(a103,x92951),x92951),f252(a103,x92951)),x92952))))+~P1(f777(f777(f235(a103),x92953),f777(f157(a103),f777(f777(f145(f857(a103,x92951),a103),f242(a103,x92951)),x92952)))) % 174.01/173.89 [9343]P1(f777(f777(f234(f858(f857(f852(x93431),f852(x93431)),a845)),f149(x93431,x93432)),f777(f777(f250(f852(x93431),f852(x93431)),f151(x93431,x93433)),f777(f20(f858(f852(x93431),a845),f852(x93431)),f151(x93431,x93433)))))+~P1(f777(f777(f234(f858(f857(x93431,x93431),a845)),x93432),f777(f777(f250(x93431,x93431),x93433),f777(f20(f858(x93431,a845),x93431),x93433)))) % 174.01/173.89 [9363]P1(f777(f777(f336(x93631),f777(f242(x93631,f857(a103,a103)),f777(f265(x93631,x93632),x93633))),f777(f160(x93631),f777(f777(f145(f857(a103,x93631),x93631),f252(a103,x93631)),x93632))))+~P1(f777(f777(f235(a103),f4(a103)),f777(f157(a103),f777(f777(f145(f857(a103,x93631),a103),f242(a103,x93631)),x93632)))) % 174.01/173.89 [9378]~P1(f777(f777(f234(f858(f857(x93781,x93781),a845)),x93782),f777(f777(f250(x93781,x93781),x93783),f777(f20(f858(x93781,a845),x93781),x93783))))+P1(f777(f777(f234(f858(f857(x93781,x93781),a845)),f777(f777(f283(x93781,x93781,x93781),x93782),f302(x93781,x93782))),f777(f777(f250(x93781,x93781),x93783),f777(f20(f858(x93781,a845),x93781),x93783)))) % 174.01/173.89 [9659]~P36(x96591,x96592)+~P1(f777(f777(f336(f857(x96591,x96591)),f777(f777(f243(x96591,x96591),f777(x96593,f777(a116,f592(x96592,x96591,x96593)))),f777(x96593,f592(x96592,x96591,x96593)))),x96592)) % 174.01/173.89 [9660]~P36(x96601,x96602)+~P1(f777(f777(f336(f857(x96601,x96601)),f777(f777(f243(x96601,x96601),f777(x96603,f777(a116,f637(x96603,x96602,x96601)))),f777(x96603,f637(x96603,x96602,x96601)))),x96602)) % 174.01/173.89 [9915]P1(f777(f777(f234(f858(f857(f858(x99151,a845),f858(x99151,a845)),a845)),f777(f777(f283(f858(x99151,a845),f858(x99151,a845),f858(x99151,a845)),f328(x99151,x99152)),f777(f777(f105(f858(f857(f858(x99151,a845),f858(x99151,a845)),a845)),f328(x99151,x99153)),f777(f777(f304(f857(f858(x99151,a845),f858(x99151,a845))),f777(f777(f243(f858(x99151,a845),f858(x99151,a845)),f182(f858(x99151,a845))),f182(f858(x99151,a845)))),f182(f858(f857(f858(x99151,a845),f858(x99151,a845)),a845)))))),f328(x99151,x99152)))+~P1(f777(f777(f234(f858(f857(x99151,x99151),a845)),f777(f777(f283(x99151,x99151,x99151),x99152),x99153)),x99152)) % 174.01/173.89 [9916]P1(f777(f777(f234(f858(f857(f858(x99161,a845),f858(x99161,a845)),a845)),f777(f777(f283(f858(x99161,a845),f858(x99161,a845),f858(x99161,a845)),f326(x99161,x99162)),f777(f777(f105(f858(f857(f858(x99161,a845),f858(x99161,a845)),a845)),f326(x99161,x99163)),f777(f777(f304(f857(f858(x99161,a845),f858(x99161,a845))),f777(f777(f243(f858(x99161,a845),f858(x99161,a845)),f182(f858(x99161,a845))),f182(f858(x99161,a845)))),f182(f858(f857(f858(x99161,a845),f858(x99161,a845)),a845)))))),f326(x99161,x99162)))+~P1(f777(f777(f234(f858(f857(x99161,x99161),a845)),f777(f777(f283(x99161,x99161,x99161),x99162),x99163)),x99162)) % 174.01/173.89 [7188]~P1(f777(f777(f234(a851),x71882),x71881))+E(f777(f777(f5(a851),f777(a116,f777(f777(f5(a851),x71881),x71882))),x71883),f777(f777(f5(a851),f777(a116,x71881)),f777(f777(f84(a851),x71882),x71883))) % 174.01/173.89 [7228]~P7(x72281)+E(f777(f777(f84(x72281),f54(x72281,x72282,x72283)),f777(f777(f85(x72281),f777(f777(f45(x72281),x72282),x72283)),x72283)),x72282) % 174.01/173.89 [7448]E(f777(f777(f85(a851),f777(f108(a851),x74481)),f777(f777(f85(a851),f777(f108(a851),x74482)),x74483)),f777(f777(f85(a851),f777(f108(a851),f777(f777(f85(a3),x74481),x74482))),x74483))+P1(f777(f777(f235(a3),x74481),a87)) % 174.01/173.89 [7921]~P1(f777(f777(f234(a851),x79213),x79212))+P1(f777(f777(f234(a851),x79211),f777(f777(f5(a851),f777(f777(f84(a851),x79212),x79211)),x79213))) % 174.01/173.89 [8116]~P1(f777(f777(f234(a851),x81161),x81162))+E(f777(f777(f127(a851),f132(a851,f777(f296(a851,x81161),x81162))),f132(a851,f777(f296(a851,x81162),f777(f777(f84(a851),x81162),x81163)))),f132(a851,f777(f296(a851,x81161),f777(f777(f84(a851),x81162),x81163)))) % 174.01/173.89 [8373]~P1(f777(f65(x83731),x83732))+E(f777(a116,f777(f44(x83731),f777(f777(f5(f858(x83731,a845)),x83732),f777(f777(f304(x83731),x83733),f182(f858(x83731,a845)))))),f777(f44(x83731),f777(f777(f304(x83731),x83733),x83732))) % 174.01/173.89 [8417]~P1(f777(f65(x84171),x84172))+E(f777(f777(f84(a851),f82(a851)),f777(f44(x84171),f777(f777(f5(f858(x84171,a845)),x84172),f777(f777(f304(x84171),x84173),f182(f858(x84171,a845)))))),f777(f44(x84171),f777(f777(f304(x84171),x84173),x84172))) % 174.01/173.89 [8588]E(f777(f777(f5(a851),f777(f44(x85881),x85882)),f777(f44(x85881),f777(f777(f106(f858(x85881,a845)),x85882),x85883))),f777(f44(x85881),f777(f777(f5(f858(x85881,a845)),x85882),x85883)))+~P1(f777(f65(x85881),f777(f777(f106(f858(x85881,a845)),x85882),x85883))) % 174.01/173.89 [8800]~P10(f777(x88002,f427(x88002,x88003,x88001)))+E(f777(f104(a3),f777(f777(f10(x88001,a851),f777(f777(f12(a3,a851,x88001),a109),x88002)),x88003)),f777(f777(f10(x88001,a3),x88002),x88003)) % 174.01/173.89 [8801]~P10(f777(x88012,f464(x88012,x88013,x88011)))+E(f777(f104(a3),f777(f777(f13(x88011,a851),f777(f777(f12(a3,a851,x88011),a109),x88012)),x88013)),f777(f777(f13(x88011,a3),x88012),x88013)) % 174.01/173.89 [8833]~P1(f777(f65(x88331),x88333))+P1(f777(f777(f234(a851),f777(f777(f5(a851),f777(f44(x88331),x88332)),f777(f44(x88331),x88333))),f777(f44(x88331),f777(f777(f5(f858(x88331,a845)),x88332),x88333)))) % 174.01/173.89 [8857]P1(f777(f777(f336(x88571),f427(x88572,x88573,x88571)),x88573))+E(f777(f104(a3),f777(f777(f10(x88571,a851),f777(f777(f12(a3,a851,x88571),a109),x88572)),x88573)),f777(f777(f10(x88571,a3),x88572),x88573)) % 174.01/173.89 [8858]P1(f777(f777(f336(x88581),f464(x88582,x88583,x88581)),x88583))+E(f777(f104(a3),f777(f777(f13(x88581,a851),f777(f777(f12(a3,a851,x88581),a109),x88582)),x88583)),f777(f777(f13(x88581,a3),x88582),x88583)) % 174.01/173.89 [8925]E(f89(x89251,f777(f777(f11(x89251,f858(x89251,a845),a845),f336(x89251)),f777(f777(f5(f858(x89251,a845)),x89252),f777(f777(f304(x89251),x89253),f182(f858(x89251,a845)))))),f246(x89251,x89253,x89252))+P1(f777(f777(f234(f858(x89251,a845)),x89252),f777(f777(f304(x89251),x89253),f182(f858(x89251,a845))))) % 174.01/173.89 [9236]E(f777(f777(f145(f852(x92361),x92361),f777(f777(f11(f852(x92361),a851,x92361),f155(x92361)),x92362)),f777(f128(f852(x92361),f777(f777(f12(a851,a845,f852(x92361)),f777(f235(a851),x92362)),f183(f852(x92361)))),x92363)),f777(f777(f155(f852(x92361)),f166(x92361,x92363)),x92362))+~P1(f777(f777(f235(a851),x92362),f777(f183(f852(f852(x92361))),f166(x92361,x92363)))) % 174.01/173.89 [9535]~P1(f777(f777(f336(f857(x95351,x95351)),x95352),f302(x95351,x95353)))+P1(f777(f777(f336(f857(x95351,x95351)),x95352),f777(f777(f48(a851,f858(f857(x95351,x95351),a845)),f241(f858(a851,a845))),f777(f777(f11(a851,f858(f857(x95351,x95351),a845),f858(f857(x95351,x95351),a845)),f175(f857(x95351,x95351),a845)),x95353)))) % 174.01/173.89 [9588]~P1(f777(f777(f234(f858(x95881,a845)),f777(f777(f48(a851,f858(x95881,a845)),f777(f296(a851,f4(a851)),f399(x95883,x95882,x95881))),x95882)),x95883))+P1(f777(f777(f234(f858(x95881,a845)),f777(f777(f48(a851,f858(x95881,a845)),f241(f858(a851,a845))),x95882)),x95883)) % 174.01/173.89 [9636]~P1(f777(f777(f235(a3),f4(a3)),x96363))+P1(f777(f777(f235(a3),x96361),f777(f777(f84(a3),x96362),f777(f777(f85(a3),f777(f777(f84(a3),f777(f79(a3),f777(f777(f5(a3),x96362),x96361))),f82(a3))),x96363)))) % 174.01/173.89 [9646]~P36(x96461,f777(f777(f105(f858(f857(x96461,x96461),a845)),x96462),x96463))+P36(x96461,f777(f777(f105(f858(f857(x96461,x96461),a845)),f777(f777(f105(f858(f857(x96461,x96461),a845)),f777(f777(f283(x96461,x96461,x96461),x96462),x96462)),f777(f777(f283(x96461,x96461,x96461),x96463),x96462))),x96463)) % 174.01/173.89 [9712]P36(x97121,f777(f777(f105(f858(f857(x97121,x97121),a845)),x97122),x97123))+~P36(x97121,f777(f777(f105(f858(f857(x97121,x97121),a845)),f777(f777(f105(f858(f857(x97121,x97121),a845)),f777(f777(f283(x97121,x97121,x97121),x97122),x97122)),f777(f777(f283(x97121,x97121,x97121),x97123),x97122))),x97123)) % 174.01/173.89 [9317]~P133(x93171)+E(f777(f107(x93171),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x93172),x93173)),f182(f858(f857(a851,a851),a845)))))),f777(f777(f5(x93171),f777(f104(x93171),x93172)),f777(f104(x93171),x93173))) % 174.01/173.89 [9396]P1(f777(x93963,x93962))+E(f777(f258(x93961),f777(f777(f22(x93961,a845,a845),f777(f777(f12(a845,f858(a845,a845),x93961),a333),f777(f777(f11(x93961,x93961,a845),a332),x93962))),x93963)),f182(f858(x93961,a845))) % 174.01/173.89 [9398]~P1(f777(x93983,x93982))+E(f777(f258(x93981),f777(f777(f22(x93981,a845,a845),f777(f777(f12(a845,f858(a845,a845),x93981),a333),f777(f777(f11(x93981,x93981,a845),a332),x93982))),x93983)),f777(f777(f304(x93981),x93982),f182(f858(x93981,a845)))) % 174.01/173.89 [9704]~P1(f777(f65(x97041),x97043))+E(f777(f777(f68(x97041,f858(x97041,a845),f777(f777(f12(f858(x97041,a845),f858(f858(x97041,a845),f858(x97041,a845)),x97041),f777(f11(f858(x97041,a845),f858(x97041,a845),f858(x97041,a845)),f5(f858(x97041,a845)))),f777(f777(f11(x97041,f858(x97041,a845),f858(x97041,a845)),f304(x97041)),f182(f858(x97041,a845))))),x97042),x97043),f777(f777(f5(f858(x97041,a845)),x97042),x97043)) % 174.01/173.89 [9737]~P1(f777(f777(f235(a3),f4(a3)),x97373))+P1(f777(f777(f235(a3),f777(f777(f5(a3),x97371),f777(f777(f85(a3),f777(f777(f84(a3),f777(f79(a3),f777(f777(f5(a3),x97371),x97372))),f82(a3))),x97373))),x97372)) % 174.01/173.89 [9983]~P1(f777(f777(f336(x99831),x99833),f324(x99831,x99832)))+P1(f777(f323(x99831,f777(f777(f11(x99831,f858(f857(x99831,x99831),a845),f858(x99831,a845)),f777(f777(f12(f858(x99831,f858(f858(f857(x99831,x99831),a845),a845)),f858(f858(f857(x99831,x99831),a845),f858(x99831,a845)),x99831),f11(x99831,f858(f857(x99831,x99831),a845),a845)),f777(f777(f12(f858(x99831,f857(x99831,x99831)),f858(x99831,f858(f858(f857(x99831,x99831),a845),a845)),x99831),f777(f12(f857(x99831,x99831),f858(f858(f857(x99831,x99831),a845),a845),x99831),f336(f857(x99831,x99831)))),f243(x99831,x99831)))),x99832)),x99833)) % 174.01/173.89 [9995]P1(f777(f777(f336(x99951),x99952),f324(x99951,x99953)))+~P1(f777(f323(x99951,f777(f777(f11(x99951,f858(f857(x99951,x99951),a845),f858(x99951,a845)),f777(f777(f12(f858(x99951,f858(f858(f857(x99951,x99951),a845),a845)),f858(f858(f857(x99951,x99951),a845),f858(x99951,a845)),x99951),f11(x99951,f858(f857(x99951,x99951),a845),a845)),f777(f777(f12(f858(x99951,f857(x99951,x99951)),f858(x99951,f858(f858(f857(x99951,x99951),a845),a845)),x99951),f777(f12(f857(x99951,x99951),f858(f858(f857(x99951,x99951),a845),a845),x99951),f336(f857(x99951,x99951)))),f243(x99951,x99951)))),x99953)),x99952)) % 174.01/173.89 [9586]~P1(f777(f65(x95861),f777(f258(x95861),x95863)))+P1(f777(f65(x95861),f777(f258(x95861),f777(f777(f22(x95861,a845,a845),f777(f777(f12(a845,f858(a845,a845),x95861),a333),x95862)),x95863)))) % 174.01/173.89 [9587]~P1(f777(f65(x95871),f777(f258(x95871),x95872)))+P1(f777(f65(x95871),f777(f258(x95871),f777(f777(f22(x95871,a845,a845),f777(f777(f12(a845,f858(a845,a845),x95871),a333),x95872)),x95873)))) % 174.01/173.89 [9671]P1(f777(f65(x96711),f777(f258(x96711),x96712)))+~P1(f777(f65(x96711),f777(f258(x96711),f777(f777(f22(x96711,a845,a845),f777(f777(f12(a845,f858(a845,a845),x96711),a334),x96713)),x96712)))) % 174.01/173.89 [9672]P1(f777(f65(x96721),f777(f258(x96721),x96722)))+~P1(f777(f65(x96721),f777(f258(x96721),f777(f777(f22(x96721,a845,a845),f777(f777(f12(a845,f858(a845,a845),x96721),a334),x96722)),x96723)))) % 174.01/173.89 [9968]~P1(f777(f65(x99681),x99682))+P1(f777(f65(f852(x99681)),f777(f258(f852(x99681)),f777(f777(f22(f852(x99681),a845,a845),f777(f777(f12(a845,f858(a845,a845),f852(x99681)),a333),f777(f777(f11(f852(x99681),f858(x99681,a845),a845),f777(f777(f12(f858(x99681,a845),f858(f858(x99681,a845),a845),f852(x99681)),f234(f858(x99681,a845))),f160(x99681))),x99682))),f777(f777(f11(f852(x99681),a851,a845),f777(f777(f12(a851,f858(a851,a845),f852(x99681)),a332),f183(f852(x99681)))),x99683))))) % 174.01/173.89 [9969]~P1(f777(f65(x99691),x99692))+P1(f777(f65(f852(x99691)),f777(f258(f852(x99691)),f777(f777(f22(f852(x99691),a845,a845),f777(f777(f12(a845,f858(a845,a845),f852(x99691)),a333),f777(f777(f11(f852(x99691),f858(x99691,a845),a845),f777(f777(f12(f858(x99691,a845),f858(f858(x99691,a845),a845),f852(x99691)),f234(f858(x99691,a845))),f160(x99691))),x99692))),f777(f777(f11(f852(x99691),a851,a845),f777(f777(f12(a851,f858(a851,a845),f852(x99691)),f234(a851)),f183(f852(x99691)))),x99693))))) % 174.01/173.89 [9685]~P85(x96851)+E(f777(f777(f244(x96851),x96852),f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x96853)),f777(f777(f85(x96851),f777(f777(f244(x96851),x96852),x96853)),f777(f777(f244(x96851),x96852),x96853))) % 174.01/173.89 [9716]~P75(x97161)+E(f777(f777(f244(x97161),f777(f777(f244(x97161),x97162),x97163)),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(f777(f244(x97161),x97162),f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x97163))) % 174.01/173.89 [9777]~P133(x97771)+E(f777(f777(f244(x97771),f777(f83(x97771),x97772)),f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x97773)),f777(f777(f244(x97771),x97772),f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x97773))) % 174.01/173.89 [9920]~P110(x99201)+P1(f777(f777(f234(x99201),f4(x99201)),f777(f777(f84(x99201),f777(f777(f244(x99201),x99202),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x99201),x99203),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))))) % 174.01/173.89 [9787]~P85(x97871)+E(f777(f777(f244(x97871),x97872),f777(a116,f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x97873))),f777(f777(f85(x97871),x97872),f777(f777(f85(x97871),f777(f777(f244(x97871),x97872),x97873)),f777(f777(f244(x97871),x97872),x97873)))) % 174.01/173.89 [9836]~P75(x98361)+E(f777(f777(f85(x98361),x98362),f777(f777(f244(x98361),f777(f777(f244(x98361),x98362),x98363)),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x98361),x98362),f777(a116,f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x98363)))) % 174.01/173.89 [9880]~P110(x98801)+P1(f777(f777(f234(x98801),f4(x98801)),f777(f777(f244(x98801),x98802),f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x98803)))) % 174.01/173.89 [9949]~P88(x99491)+E(f777(f777(f84(x99491),f777(f777(f84(x99491),f777(f777(f244(x99491),x99492),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x99491),x99493),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))),f777(f777(f85(x99491),f777(f777(f85(x99491),f777(f108(x99491),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x99492)),x99493)),f777(f777(f244(x99491),f777(f777(f84(x99491),x99492),x99493)),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))) % 174.01/173.89 [9950]~P88(x99501)+E(f777(f777(f5(x99501),f777(f777(f84(x99501),f777(f777(f244(x99501),x99502),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x99501),x99503),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))),f777(f777(f85(x99501),f777(f777(f85(x99501),f777(f108(x99501),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x99502)),x99503)),f777(f777(f244(x99501),f777(f777(f5(x99501),x99502),x99503)),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))) % 174.01/173.89 [4581]E(x45811,x45812)+~E(f37(x45813,x45811),f37(x45814,x45812)) % 174.01/173.89 [4582]E(x45821,x45822)+~E(f37(x45821,x45823),f37(x45822,x45824)) % 174.01/173.89 [4583]E(x45831,x45832)+~E(f38(x45833,x45831),f38(x45834,x45832)) % 174.01/173.89 [4584]E(x45841,x45842)+~E(f38(x45841,x45843),f38(x45842,x45844)) % 174.01/173.89 [4585]E(x45851,x45852)+~E(f30(x45853,x45851),f30(x45854,x45852)) % 174.01/173.89 [4586]E(x45861,x45862)+~E(f30(x45861,x45863),f30(x45862,x45864)) % 174.01/173.89 [5711]P39(f37(x57111,x57113),x57112,x57114,x57112)+P1(f777(x57111,x57112)) % 174.01/173.89 [6873]~P39(x68731,x68732,x68733,x68734)+P39(x68731,x68732,f777(a116,x68733),x68734) % 174.01/173.89 [7718]P29(x77181,x77182,x77183,x77184)+~E(f507(x77184,x77183,x77182,x77181),f521(x77184,x77183,x77182,x77181)) % 174.01/173.89 [8218]~P29(x82181,f855(x82182),x82184,f171(x82181,x82182,x82184))+P29(x82181,f855(x82182),f172(x82181,x82182,x82183,x82184),f171(x82181,x82182,x82184)) % 174.01/173.89 [8432]~P29(x84321,f855(x84322),f172(x84321,x84322,x84324,x84323),f171(x84321,x84322,x84323))+P29(x84321,f855(x84322),x84323,f171(x84321,x84322,x84323)) % 174.01/173.89 [4948]~P21(x49483,x49481,x49484)+E(f777(f777(x49481,x49482),x49482),x49482) % 174.01/173.89 [4951]E(x49511,x49512)+~E(f777(f306(x49513,x49514),x49511),f777(f306(x49513,x49514),x49512)) % 174.01/173.89 [4953]E(x49531,x49532)+~E(f777(f315(x49533,x49534),x49531),f777(f315(x49533,x49534),x49532)) % 174.01/173.89 [5236]~E(x52364,f182(f858(x52361,a845)))+E(f777(f305(x52361,x52362,x52363),x52364),f182(f858(x52362,a845))) % 174.01/173.89 [5501]~E(f777(f305(x55012,x55013,x55014),x55011),f182(f858(x55013,a845)))+E(x55011,f182(f858(x55012,a845))) % 174.01/173.89 [5792]~P100(x57922)+E(f777(f777(f140(x57921,x57922,x57923),x57924),f117(x57921)),f777(f777(f142(x57921),x57924),f117(x57921))) % 174.01/173.89 [5827]E(f777(x58271,x58272),f185(x58273))+P1(f777(f777(f336(x58274),x58272),f171(x58274,x58273,x58271))) % 174.01/173.89 [6151]~E(x61511,f182(f858(x61512,a845)))+~P1(f777(f66(x61512,x61513,x61511),x61514)) % 174.01/173.89 [6172]~P57(x61721,x61723,x61724,x61722)+P1(f777(f65(x61721),x61722)) % 174.01/173.89 [6173]~P57(x61731,x61733,x61732,x61734)+P1(f777(f65(x61731),x61732)) % 174.01/173.89 [6180]~P57(x61802,x61803,x61804,x61801)+~E(x61801,f182(f858(x61802,a845))) % 174.01/173.89 [6212]~P99(x62121)+E(f777(f777(f106(f858(x62121,a845)),f777(f296(x62121,x62122),x62123)),f297(x62121,x62123,x62124)),f182(f858(x62121,a845))) % 174.01/173.89 [6241]~P1(f777(f777(x62413,x62414),x62412))+P1(f777(f777(f336(x62411),x62412),f289(x62411,x62413,x62414))) % 174.01/173.89 [6242]~P1(f777(f777(x62423,x62424),x62422))+P1(f777(f777(f336(x62421),x62422),f288(x62421,x62423,x62424))) % 174.01/173.89 [6243]~P1(f777(f777(x62433,x62432),x62434))+P1(f777(f777(f336(x62431),x62432),f292(x62431,x62433,x62434))) % 174.01/173.89 [6244]~P1(f777(f777(x62443,x62442),x62444))+P1(f777(f777(f336(x62441),x62442),f290(x62441,x62443,x62444))) % 174.01/173.89 [6396]~P99(x63961)+E(f777(f777(f106(f858(x63961,a845)),f297(x63961,x63962,x63963)),f299(x63961,x63963,x63964)),f182(f858(x63961,a845))) % 174.01/173.89 [6397]~P99(x63971)+E(f777(f777(f106(f858(x63971,a845)),f297(x63971,x63972,x63973)),f300(x63971,x63973,x63974)),f182(f858(x63971,a845))) % 174.01/173.89 [6398]~P99(x63981)+E(f777(f777(f106(f858(x63981,a845)),f299(x63981,x63982,x63983)),f299(x63981,x63983,x63984)),f182(f858(x63981,a845))) % 174.01/173.89 [6399]~P99(x63991)+E(f777(f777(f106(f858(x63991,a845)),f299(x63991,x63992,x63993)),f300(x63991,x63993,x63994)),f182(f858(x63991,a845))) % 174.01/173.89 [6400]~P99(x64001)+E(f777(f777(f106(f858(x64001,a845)),f300(x64001,x64002,x64003)),f297(x64001,x64003,x64004)),f182(f858(x64001,a845))) % 174.01/173.89 [6438]P1(f777(f777(x64381,x64382),f598(x64382,x64381)))+~P1(f777(f248(x64383,x64384,x64381),x64382)) % 174.01/173.89 [6492]~E(f777(x64921,x64922),f185(x64923))+~P1(f777(f777(f336(x64924),x64922),f171(x64924,x64923,x64921))) % 174.01/173.89 [6574]~P2(x65741)+E(f184(x65741,x65742,f777(a116,x65743),x65744),f184(x65741,x65742,x65743,f777(x65742,x65744))) % 174.01/173.89 [6638]~P1(f777(f777(f336(x66384),x66383),f289(x66384,x66381,x66382)))+P1(f777(f777(x66381,x66382),x66383)) % 174.01/173.89 [6639]~P1(f777(f777(f336(x66394),x66393),f288(x66394,x66391,x66392)))+P1(f777(f777(x66391,x66392),x66393)) % 174.01/173.89 [6640]~P1(f777(f777(f336(x66404),x66402),f292(x66404,x66401,x66403)))+P1(f777(f777(x66401,x66402),x66403)) % 174.01/173.89 [6641]~P1(f777(f777(f336(x66414),x66412),f290(x66414,x66411,x66413)))+P1(f777(f777(x66411,x66412),x66413)) % 174.01/173.89 [6723]E(f777(f44(f859(x67231,x67232)),f316(x67231,x67232,x67233,x67234)),f4(a851))+P1(f777(f65(x67232),x67234)) % 174.01/173.89 [6724]E(f777(f44(f859(x67241,x67242)),f316(x67241,x67242,x67243,x67244)),f4(a851))+P1(f777(f65(x67241),x67243)) % 174.01/173.89 [6935]~P19(x69354,x69351,x69352)+E(f777(f77(x69351,x69351,x69351,f777(x69352,x69353)),f777(x69352,x69353)),f777(x69352,x69353)) % 174.01/173.89 [7173]E(f274(x71731,x71732,x71733,x71734),f777(f243(f858(a103,f858(a845,f855(f853(x71731)))),f857(a103,a103)),f50(x71731)))+~P1(f777(f777(f234(a103),x71733),f4(a103))) % 174.01/173.89 [7239]~P39(f777(a29,x72391),x72392,f777(a116,x72393),x72394)+P39(f777(f233(a846),f777(a32,x72391)),x72392,x72393,x72394) % 174.01/173.89 [7276]P39(f777(a29,x72761),x72762,f777(a116,x72763),x72764)+~P39(f777(f233(a846),f777(a32,x72761)),x72762,x72763,x72764) % 174.01/173.89 [7576]~P39(f777(a29,x75764),x75763,x75762,x75761)+E(f777(a116,f444(x75761,x75762,x75763,x75764)),x75762) % 174.01/173.89 [7846]~E(x78462,x78463)+P1(f777(f777(f336(f857(x78461,x78461)),f777(f777(f243(x78461,x78461),x78462),x78463)),f302(x78461,x78464))) % 174.01/173.89 [7872]~P29(x78721,x78722,x78723,f241(f858(x78721,a845)))+E(f777(f81(x78721,x78722,f241(f858(x78721,a845)),x78723),f777(x78723,x78724)),x78724) % 174.01/173.89 [7964]~P1(f777(f777(f336(f852(x79641)),f777(f777(f142(x79641),x79644),x79642)),f151(x79641,x79643)))+P1(f777(f777(f336(f852(x79641)),x79642),f151(x79641,x79643))) % 174.01/173.89 [7965]~P1(f777(f777(f336(f852(x79651)),f777(f777(f127(x79651),x79654),x79652)),f151(x79651,x79653)))+P1(f777(f777(f336(f852(x79651)),x79652),f151(x79651,x79653))) % 174.01/173.89 [7966]~P1(f777(f777(f336(f852(x79661)),f777(f777(f127(x79661),x79662),x79664)),f151(x79661,x79663)))+P1(f777(f777(f336(f852(x79661)),x79662),f151(x79661,x79663))) % 174.01/173.89 [8040]~P39(f777(a29,x80401),x80402,x80404,x80403)+P39(f777(f233(a846),f777(a32,x80401)),x80402,f444(x80403,x80404,x80402,x80401),x80403) % 174.01/173.89 [8077]P29(x80774,x80773,x80771,x80772)+E(f777(x80771,f507(x80772,x80771,x80773,x80774)),f777(x80771,f521(x80772,x80771,x80773,x80774))) % 174.01/173.89 [8086]E(f172(x80861,x80862,x80863,x80864),f172(x80861,x80862,x80864,x80863))+~E(f777(f777(f106(f858(x80861,a845)),f171(x80861,x80862,x80863)),f171(x80861,x80862,x80864)),f182(f858(x80861,a845))) % 174.01/173.89 [8183]~P29(x81832,x81831,x81834,x81833)+P29(x81831,x81832,f81(x81832,x81831,x81833,x81834),f777(f305(x81832,x81831,x81834),x81833)) % 174.01/173.89 [8318]P36(f857(x83182,x83184),f277(x83182,x83184,x83181,x83183))+P1(f777(x83181,f595(x83182,x83183,x83184,x83181))) % 174.01/173.89 [8439]E(x84391,x84392)+~P1(f777(f777(f336(f857(x84393,x84393)),f777(f777(f243(x84393,x84393),x84391),x84392)),f262(x84393,x84394))) % 174.01/173.89 [8473]~E(f777(x84731,f517(x84733,x84732,x84734,x84731)),f777(f176(x84734,x84732,x84733),f517(x84733,x84732,x84734,x84731)))+E(f777(x84731,f4(a851)),x84732) % 174.01/173.89 [8507]~P1(f777(f65(f859(x85073,x85071)),f316(x85073,x85071,x85074,x85072)))+P1(f777(f65(x85071),x85072)) % 174.01/173.89 [8508]~P1(f777(f65(f859(x85081,x85083)),f316(x85081,x85083,x85082,x85084)))+P1(f777(f65(x85081),x85082)) % 174.01/173.89 [8669]P36(f857(x86691,x86692),f277(x86691,x86692,x86693,x86694))+~P36(x86692,f777(x86694,f595(x86691,x86694,x86692,x86693))) % 174.01/173.89 [9170]E(f777(f777(f150(x91701,x91702),f739(x91703,x91704,x91702,x91701)),f740(x91703,x91704,x91702,x91701)),x91704)+~P1(f777(f777(f336(f857(f852(x91701),f852(x91701))),f777(f777(f243(f852(x91701),f852(x91701)),x91702),x91704)),f148(x91701,x91703))) % 174.01/173.89 [9174]~P1(f777(f777(f336(f857(f852(x91741),f852(x91741))),f777(f777(f243(f852(x91741),f852(x91741)),x91742),x91743)),f137(x91741,x91744)))+P1(f777(f777(f336(f857(f852(x91741),f852(x91741))),f777(f777(f243(f852(x91741),f852(x91741)),x91742),x91743)),f139(x91741,x91744))) % 174.01/173.89 [9271]P1(f777(f65(x92711),x92712))+~P1(f777(f777(f336(f857(f858(x92711,a845),f858(x92711,a845))),f777(f777(f243(f858(x92711,a845),f858(x92711,a845)),x92713),x92712)),f326(x92711,x92714))) % 174.01/173.89 [9272]P1(f777(f65(x92721),x92722))+~P1(f777(f777(f336(f857(f858(x92721,a845),f858(x92721,a845))),f777(f777(f243(f858(x92721,a845),f858(x92721,a845)),x92722),x92723)),f326(x92721,x92724))) % 174.01/173.89 [9275]~E(x92751,f182(f858(x92752,a845)))+~P1(f777(f777(f336(f857(f858(x92752,a845),f858(x92752,a845))),f777(f777(f243(f858(x92752,a845),f858(x92752,a845)),x92753),x92751)),f326(x92752,x92754))) % 174.01/173.89 [9891]P16(x98911,x98912,x98913,x98914)+~P1(f777(f777(f253(x98911,x98911,a845),f777(f777(f11(x98911,f858(x98911,x98912),f858(x98911,a845)),f777(f777(f12(f858(x98912,a845),f858(f858(x98911,x98912),f858(x98911,a845)),x98911),f12(x98912,a845,x98911)),f777(f777(f12(x98912,f858(x98912,a845),x98911),a332),x98914))),x98914)),f500(x98914,x98913,x98912,x98911))) % 174.01/173.89 [4851]~E(x48514,f117(x48511))+E(f777(f777(f145(x48511,x48512),x48513),x48514),f117(x48512)) % 174.01/173.89 [4852]~E(x48524,f185(x48521))+E(f777(f777(f198(x48521,x48522),x48523),x48524),f185(x48522)) % 174.01/173.89 [4853]~E(x48532,f117(x48531))+E(f777(f777(f150(x48531,x48532),x48533),x48534),f117(x48531)) % 174.01/173.89 [5093]E(x50931,f185(x50932))+~E(f777(f777(f198(x50932,x50933),x50934),x50931),f185(x50933)) % 174.01/173.89 [5094]E(x50941,f117(x50942))+~E(f777(f777(f145(x50942,x50943),x50944),x50941),f117(x50943)) % 174.01/173.89 [5095]E(x50951,f117(x50952))+~E(f777(f777(f150(x50952,x50951),x50953),x50954),f117(x50952)) % 174.01/173.89 [5125]E(x51251,x51252)+~E(f777(f777(f127(x51253),x51254),x51251),f777(f777(f127(x51253),x51254),x51252)) % 174.01/173.89 [5126]E(x51261,x51262)+~E(f777(f777(f127(x51263),x51261),x51264),f777(f777(f127(x51263),x51262),x51264)) % 174.01/173.89 [5272]P1(f777(x52723,x52722))+E(f153(x52721,x52722,f777(f128(x52721,x52723),x52724)),f777(f128(x52721,x52723),x52724)) % 174.01/173.89 [5283]E(x52831,x52832)+~E(f132(a851,f777(f296(a851,x52831),x52833)),f777(f777(f142(a851),x52832),x52834)) % 174.01/173.89 [5331]~P30(x53312,x53313)+P30(x53311,f777(f777(f78(x53312,x53311),x53313),x53314)) % 174.01/173.89 [5332]~P36(x53322,x53323)+P36(x53321,f777(f777(f282(x53322,x53321),x53323),x53324)) % 174.01/173.89 [5541]~E(x55411,f117(x55412))+~E(f777(f777(f127(x55412),x55413),f777(f777(f142(x55412),x55414),f117(x55412))),x55411) % 174.01/173.89 [5574]E(f136(x55741,x55742),x55743)+~E(f777(f777(f127(x55741),x55744),f777(f777(f142(x55741),x55743),f117(x55741))),x55742) % 174.01/173.89 [5575]E(f118(x55751,x55752),x55753)+~E(f777(f777(f127(x55751),x55753),f777(f777(f142(x55751),x55754),f117(x55751))),x55752) % 174.01/173.89 [5683]~E(f132(a851,f777(f296(a851,x56831),x56832)),f777(f777(f142(a851),x56833),x56834))+P1(f777(f777(f235(a851),x56831),x56832)) % 174.01/173.89 [5890]E(x58901,f777(f777(f127(x58902),f777(f144(x58902),x58903)),f777(f777(f142(x58902),x58904),f117(x58902))))+~E(f777(f144(x58902),x58901),f777(f777(f142(x58902),x58904),x58903)) % 174.01/173.89 [6073]~P99(x60731)+E(f777(f777(f106(f858(x60731,a845)),f777(f296(x60731,x60732),x60733)),f777(f296(x60731,x60733),x60734)),f182(f858(x60731,a845))) % 174.01/173.89 [6108]~P66(x61081)+E(f777(f157(x61081),f777(f777(f145(a3,x61081),x61082),f165(x61083,x61084))),f777(f777(f10(a3,x61081),x61082),f777(f160(a3),f165(x61083,x61084)))) % 174.01/173.89 [6109]~P66(x61091)+E(f777(f777(f10(a3,x61091),x61092),f777(f160(a3),f165(x61093,x61094))),f777(f157(x61091),f777(f777(f145(a3,x61091),x61092),f165(x61093,x61094)))) % 174.01/173.89 [6256]~E(x62562,f777(f777(f127(x62561),f777(f144(x62561),x62564)),f777(f777(f142(x62561),x62563),f117(x62561))))+E(f777(f144(x62561),x62562),f777(f777(f142(x62561),x62563),x62564)) % 174.01/173.89 [6272]~P23(x62722,x62723,x62724,x62721)+E(f777(x62721,f182(f858(x62722,a845))),f41(x62723)) % 174.01/173.89 [6302]~P99(x63021)+E(f777(f777(f106(f858(x63021,a845)),f300(x63021,x63022,x63023)),f777(f296(x63021,x63023),x63024)),f182(f858(x63021,a845))) % 174.01/173.89 [6389]~P39(x63891,x63892,x63894,x63893)+P1(f777(f777(f189(x63891),x63892),x63893)) % 174.01/173.89 [6523]E(x65231,f182(f858(x65232,a845)))+~E(f316(x65233,x65232,x65234,x65231),f182(f858(f859(x65233,x65232),a845))) % 174.01/173.89 [6524]E(x65241,f182(f858(x65242,a845)))+~E(f316(x65242,x65243,x65241,x65244),f182(f858(f859(x65242,x65243),a845))) % 174.01/173.89 [6604]~P1(f777(f249(x66043,x66044,x66041),x66042))+P1(f777(f777(x66041,f594(x66042,x66041)),x66042)) % 174.01/173.89 [6652]~P1(f777(f65(x66522),x66524))+P1(f777(f65(x66521),f777(f305(x66522,x66521,x66523),x66524))) % 174.01/173.89 [6894]~P29(x68942,x68941,x68943,x68944)+E(f777(f44(x68941),f777(f305(x68942,x68941,x68943),x68944)),f777(f44(x68942),x68944)) % 174.01/173.89 [6914]E(f777(f305(x69141,x69142,x69143),f777(f307(x69141,x69142,x69143),x69144)),x69144)+~E(f777(f305(x69141,x69142,x69143),f241(f858(x69141,a845))),f241(f858(x69142,a845))) % 174.01/173.89 [7340]~P29(x73401,x73402,x73403,f241(f858(x73401,a845)))+E(f777(f307(x73401,x73402,x73403),f777(f305(x73401,x73402,x73403),x73404)),x73404) % 174.01/173.89 [7680]P1(f777(x76801,x76802))+~P1(f777(f777(f336(x76803),x76802),f777(f160(x76803),f164(x76803,x76801,x76804)))) % 174.01/173.89 [7790]~P1(f777(f777(f336(f852(x77901)),f777(f777(f142(x77901),x77902),x77904)),f151(x77901,x77903)))+P1(f777(f777(f336(x77901),x77902),x77903)) % 174.01/173.89 [7917]~P1(f777(f777(f336(x79171),x79172),f777(f160(x79171),f153(x79171,x79174,x79173))))+P1(f777(f777(f336(x79171),x79172),f777(f160(x79171),x79173))) % 174.01/173.89 [7919]~P1(f777(f777(f336(x79191),x79192),f777(f160(x79191),f162(x79191,x79193,x79194))))+P1(f777(f777(f336(x79191),x79192),f777(f160(x79191),x79193))) % 174.01/173.89 [7920]~P1(f777(f777(f336(x79201),x79202),f777(f160(x79201),f164(x79201,x79204,x79203))))+P1(f777(f777(f336(x79201),x79202),f777(f160(x79201),x79203))) % 174.01/173.89 [8133]E(f777(f777(f155(x81331),f164(x81331,x81332,x81333)),x81334),f777(f777(f155(x81331),x81333),x81334))+~P1(f777(f777(f235(a851),x81334),f777(f183(f852(x81331)),f164(x81331,x81332,x81333)))) % 174.01/173.89 [8216]~P66(x82161)+E(f777(f777(f10(a851,x82161),f777(f777(f12(a851,x82161,a851),x82162),a116)),f777(f296(a851,x82163),x82164)),f777(f777(f10(a851,x82161),x82162),f777(f296(a851,f777(a116,x82163)),f777(a116,x82164)))) % 174.01/173.89 [8225]~P66(x82251)+E(f777(f777(f10(a851,x82251),f777(f777(f12(a851,x82251,a851),x82252),a116)),f297(a851,x82253,x82254)),f777(f777(f10(a851,x82251),x82252),f297(a851,f777(a116,x82253),f777(a116,x82254)))) % 174.01/173.89 [8357]~P29(x83571,x83573,x83574,f241(f858(x83571,a845)))+P29(x83571,f858(x83572,x83573),f777(f777(f12(x83573,f858(x83572,x83573),x83571),f20(x83573,x83572)),x83574),f241(f858(x83571,a845))) % 174.01/173.89 [8448]~P29(x84482,x84481,x84484,x84483)+E(f777(f305(x84481,x84482,f81(x84482,x84481,x84483,x84484)),f777(f305(x84482,x84481,x84484),x84483)),x84483) % 174.01/173.89 [8509]~P1(f777(f777(f336(f857(x85091,x85091)),f777(f777(f243(x85091,x85091),x85092),x85094)),f262(x85091,x85093)))+P1(f777(f777(f336(x85091),x85092),x85093)) % 174.01/173.89 [8584]E(f777(f777(f777(f76(x85841,f855(x85842)),f777(f20(f855(x85842),x85841),f185(x85842))),x85843),f777(f229(x85842),f531(x85843,x85844,x85842,x85841))),x85844)+~E(f171(x85841,x85842,x85844),f777(f777(f304(x85841),x85843),f182(f858(x85841,a845)))) % 174.01/173.89 [8702]~E(f777(f777(f10(x87021,a851),x87024),x87023),f777(a116,x87022))+P1(f777(f777(f336(x87021),f358(x87022,x87023,x87024,x87021)),x87023)) % 174.01/173.89 [8718]~E(f777(f777(f10(x87184,a851),x87181),x87183),f777(a116,x87182))+P1(f777(f777(f235(a851),f4(a851)),f777(x87181,f358(x87182,x87183,x87181,x87184)))) % 174.01/173.89 [8728]~P1(f777(f65(x87282),x87284))+P1(f777(f777(f234(a851),f777(f44(x87281),f777(f305(x87282,x87281,x87283),x87284))),f777(f44(x87282),x87284))) % 174.01/173.89 [8729]E(f777(f777(f243(x87291,x87292),f702(x87293,x87294,x87292,x87291)),f703(x87293,x87294,x87292,x87291)),x87294)+~P1(f777(f777(f336(f857(x87291,x87292)),x87294),f777(f280(x87292,x87291),x87293))) % 174.01/173.89 [8738]P29(x87381,x87382,x87383,x87384)+P1(f777(f777(f336(x87381),f507(x87384,x87383,x87382,x87381)),x87384)) % 174.01/173.89 [8739]P29(x87391,x87392,x87393,x87394)+P1(f777(f777(f336(x87391),f521(x87394,x87393,x87392,x87391)),x87394)) % 174.01/173.89 [8792]P16(x87921,x87922,x87923,x87924)+P1(f777(f777(f336(f857(x87921,x87921)),f500(x87924,x87923,x87922,x87921)),x87923)) % 174.01/173.89 [8839]P1(f777(x88391,x88392))+~P1(f777(x88391,f777(f777(f243(x88393,x88394),f831(x88394,x88393,x88391)),f832(x88394,x88393,x88391)))) % 174.01/173.89 [8852]E(f777(f183(f852(x88521)),x88522),f777(f183(f852(x88521)),x88523))+~P1(f777(f777(f336(f857(f852(x88521),f852(x88521))),f777(f777(f243(f852(x88521),f852(x88521)),x88522),x88523)),f137(x88521,x88524))) % 174.01/173.89 [8855]E(f777(f183(f852(x88551)),x88552),f777(f183(f852(x88551)),x88553))+~P1(f777(f777(f336(f857(f852(x88551),f852(x88551))),f777(f777(f243(f852(x88551),f852(x88551)),x88552),x88553)),f149(x88551,x88554))) % 174.01/173.89 [8856]E(f777(f183(f852(x88561)),x88562),f777(f183(f852(x88561)),x88563))+~P1(f777(f777(f336(f857(f852(x88561),f852(x88561))),f777(f777(f243(f852(x88561),f852(x88561)),x88562),x88563)),f148(x88561,x88564))) % 174.01/173.89 [8929]P1(f777(f777(f234(a851),f146(x89291,x89292,x89293)),f146(x89291,x89294,x89293)))+P1(f777(f777(f336(x89291),f759(x89294,x89292,x89293,x89291)),f777(f160(x89291),x89293))) % 174.01/173.89 [8930]E(f777(f183(f852(x89301)),x89302),f777(f183(f852(x89301)),x89303))+~P1(f777(f777(f336(f857(f852(x89301),f852(x89301))),f777(f777(f243(f852(x89301),f852(x89301)),x89302),x89303)),f302(f852(x89301),f148(x89301,x89304)))) % 174.01/173.89 [9042]P1(f777(f777(f281(a851),x90421),x90422))+P1(f777(f777(f234(f858(a851,a845)),f284(a851,f281(a851),x90421,x90422)),f284(a851,f281(a851),x90423,x90424))) % 174.01/173.89 [9150]~P29(x91501,x91502,x91503,x91504)+~P1(f777(f777(f235(a851),f777(f44(x91502),f777(f305(x91501,x91502,x91503),x91504))),f777(f44(x91501),x91504))) % 174.01/173.89 [9180]~P1(f777(f777(f336(f857(f852(x91801),f852(x91801))),f777(f777(f243(f852(x91801),f852(x91801)),x91802),x91803)),f148(x91801,x91804)))+P1(f777(f777(f336(f857(f852(x91801),f852(x91801))),f777(f777(f243(f852(x91801),f852(x91801)),x91802),x91803)),f149(x91801,f302(x91801,x91804)))) % 174.01/173.89 [9183]~P1(f777(f777(f336(f857(f852(x91831),f852(x91831))),f777(f777(f243(f852(x91831),f852(x91831)),x91832),x91833)),f149(x91831,x91834)))+P1(f777(f777(f336(f857(f852(x91831),f852(x91831))),f777(f777(f243(f852(x91831),f852(x91831)),x91832),x91833)),f302(f852(x91831),f148(x91831,x91834)))) % 174.01/173.89 [9198]P1(f777(f777(f336(f857(x91981,x91981)),f777(f777(f243(x91981,x91981),x91982),x91983)),f302(x91981,x91984)))+~P1(f777(f777(f336(f857(x91981,x91981)),f777(f777(f243(x91981,x91981),x91982),x91983)),f777(f777(f283(x91981,x91981,x91981),x91984),f302(x91981,x91984)))) % 174.01/173.89 [9267]P1(f777(f777(f281(a851),x92671),x92672))+~P1(f777(f777(f235(f858(a851,a845)),f284(a851,f281(a851),x92673,x92674)),f284(a851,f281(a851),x92671,x92672))) % 174.01/173.89 [9379]E(f777(f777(f127(x93791),f743(x93792,x93793,x93794,x93791)),f777(f777(f142(x93791),f744(x93792,x93793,x93794,x93791)),f746(x93792,x93793,x93794,x93791))),x93794)+~P1(f777(f777(f336(f857(f852(x93791),f852(x93791))),f777(f777(f243(f852(x93791),f852(x93791)),x93794),x93793)),f148(x93791,x93792))) % 174.01/173.89 [9380]E(f777(f777(f127(x93801),f743(x93802,x93803,x93804,x93801)),f777(f777(f142(x93801),f745(x93802,x93803,x93804,x93801)),f746(x93802,x93803,x93804,x93801))),x93803)+~P1(f777(f777(f336(f857(f852(x93801),f852(x93801))),f777(f777(f243(f852(x93801),f852(x93801)),x93804),x93803)),f148(x93801,x93802))) % 174.01/173.89 [9453]P1(f777(f777(f336(f857(x94531,x94531)),f777(f777(f243(x94531,x94531),x94532),f657(x94533,x94534,x94532,x94531))),f302(x94531,x94533)))+~P1(f777(f777(f336(f857(x94531,x94531)),f777(f777(f243(x94531,x94531),x94532),x94534)),f777(f777(f283(x94531,x94531,x94531),x94533),f302(x94531,x94533)))) % 174.01/173.89 [9518]P1(f777(f777(f234(a851),f146(x95181,x95182,x95183)),f146(x95181,x95184,x95183)))+~P1(f777(f777(f235(a851),f777(x95182,f759(x95184,x95182,x95183,x95181))),f777(x95184,f759(x95184,x95182,x95183,x95181)))) % 174.01/173.89 [9584]P1(f777(f777(f336(f857(x95841,x95841)),f777(f777(f243(x95841,x95841),f656(x95842,x95843,x95844,x95841)),x95843)),f302(x95841,x95842)))+~P1(f777(f777(f336(f857(x95841,x95841)),f777(f777(f243(x95841,x95841),x95844),x95843)),f777(f777(f283(x95841,x95841,x95841),x95842),f302(x95841,x95842)))) % 174.01/173.89 [5105]~E(x51052,x51053)+E(f153(x51051,x51052,f777(f777(f142(x51051),x51053),x51054)),x51054) % 174.01/173.89 [5228]P1(f777(x52282,x52283))+E(f164(x52281,x52282,f777(f777(f142(x52281),x52283),x52284)),f117(x52281)) % 174.01/173.89 [5295]~P84(x52952)+E(f777(f777(f83(f858(x52951,x52952)),x52953),x52954),f777(f83(x52952),f777(x52953,x52954))) % 174.01/173.89 [5307]~E(x53072,f4(a851))+E(f777(f777(f130(x53071),x53072),f777(f777(f142(x53071),x53073),x53074)),f777(f777(f142(x53071),x53073),x53074)) % 174.01/173.89 [5308]P1(f777(x53082,x53083))+E(f777(f128(x53081,x53082),f777(f777(f142(x53081),x53083),x53084)),f777(f128(x53081,x53082),x53084)) % 174.01/173.89 [5442]~E(x54422,x54424)+P1(f777(f777(f777(f304(x54421),x54422),x54423),x54424)) % 174.01/173.89 [5450]E(x54501,f117(x54502))+E(f136(x54503,f777(f777(f145(x54502,x54503),x54504),x54501)),f777(x54504,f136(x54502,x54501))) % 174.01/173.89 [5461]~E(x54611,f67(x54612,x54614))+E(f777(x54611,f777(f777(f304(x54612),x54613),f182(f858(x54612,a845)))),x54613) % 174.01/173.89 [5496]E(x54961,f117(x54962))+E(f777(f133(x54963),f777(f777(f145(x54962,x54963),x54964),x54961)),f777(x54964,f777(f133(x54962),x54961))) % 174.01/173.89 [5593]~P1(f777(x55933,x55934))+P1(f777(f777(f777(f304(x55931),x55932),x55933),x55934)) % 174.01/173.89 [5718]~P22(x57182,x57184,x57181)+E(f777(x57181,f777(f777(f304(x57182),x57183),f182(f858(x57182,a845)))),x57183) % 174.01/173.89 [5743]~E(x57432,x57433)+P1(f777(f777(f336(x57431),x57432),f777(f777(f304(x57431),x57433),x57434))) % 174.01/173.89 [5747]~P85(x57471)+E(f777(f777(f84(x57471),x57472),f777(f777(f84(x57471),x57473),x57474)),f777(f777(f84(x57471),x57473),f777(f777(f84(x57471),x57472),x57474))) % 174.01/173.89 [5748]~P85(x57481)+E(f777(f777(f85(x57481),x57482),f777(f777(f85(x57481),x57483),x57484)),f777(f777(f85(x57481),x57483),f777(f777(f85(x57481),x57482),x57484))) % 174.01/173.89 [5750]~P100(x57501)+E(f777(f777(f238(x57501),x57502),f777(f777(f238(x57501),x57503),x57504)),f777(f777(f238(x57501),x57503),f777(f777(f238(x57501),x57502),x57504))) % 174.01/173.89 [5752]~P100(x57521)+E(f777(f777(f181(x57521),x57522),f777(f777(f181(x57521),x57523),x57524)),f777(f777(f181(x57521),x57523),f777(f777(f181(x57521),x57522),x57524))) % 174.01/173.89 [5754]~P92(x57541)+E(f777(f777(f105(x57541),x57542),f777(f777(f105(x57541),x57543),x57544)),f777(f777(f105(x57541),x57543),f777(f777(f105(x57541),x57542),x57544))) % 174.01/173.89 [5755]~P93(x57551)+E(f777(f777(f105(x57551),x57552),f777(f777(f105(x57551),x57553),x57554)),f777(f777(f105(x57551),x57553),f777(f777(f105(x57551),x57552),x57554))) % 174.01/173.89 [5756]~P93(x57561)+E(f777(f777(f106(x57561),x57562),f777(f777(f106(x57561),x57563),x57564)),f777(f777(f106(x57561),x57563),f777(f777(f106(x57561),x57562),x57564))) % 174.01/173.89 [5758]~P98(x57581)+E(f777(f777(f106(x57581),x57582),f777(f777(f106(x57581),x57583),x57584)),f777(f777(f106(x57581),x57583),f777(f777(f106(x57581),x57582),x57584))) % 174.01/173.89 [5765]E(x57651,x57652)+E(f153(x57653,x57651,f777(f777(f142(x57653),x57652),x57654)),f777(f777(f142(x57653),x57652),f153(x57653,x57651,x57654))) % 174.01/173.89 [5780]~P1(f777(x57802,x57803))+E(f777(f128(x57801,x57802),f777(f777(f142(x57801),x57803),x57804)),f777(f777(f142(x57801),x57803),f777(f128(x57801,x57802),x57804))) % 174.01/173.89 [5911]~P1(f777(x59112,x59113))+E(f164(x59111,x59112,f777(f777(f142(x59111),x59113),x59114)),f777(f777(f142(x59111),x59113),f164(x59111,x59112,x59114))) % 174.01/173.89 [5963]P28(x59631,x59632,x59633)+~P28(x59631,x59632,f777(f777(f304(f850(x59631)),x59634),x59633)) % 174.01/173.89 [5976]E(x59761,f182(f858(x59762,a845)))+E(f777(f777(f48(x59762,f858(x59763,a845)),x59761),f777(f20(f858(x59763,a845),x59762),x59764)),x59764) % 174.01/173.89 [5977]E(x59771,f182(f858(x59772,a845)))+E(f777(f777(f49(x59772,f858(x59773,a845)),x59771),f777(f20(f858(x59773,a845),x59772),x59774)),x59774) % 174.01/173.89 [5986]~E(x59864,f182(f858(x59862,a845)))+E(f777(f777(f250(x59861,x59862),x59863),f777(f20(f858(x59862,a845),x59861),x59864)),f182(f858(f857(x59861,x59862),a845))) % 174.01/173.89 [5987]~E(x59873,f182(f858(x59871,a845)))+E(f777(f777(f250(x59871,x59872),x59873),f777(f20(f858(x59872,a845),x59871),x59874)),f182(f858(f857(x59871,x59872),a845))) % 174.01/173.89 [6038]E(x60381,f4(a851))+E(f777(f777(f130(x60382),x60381),f777(f777(f142(x60382),x60383),x60384)),f777(f777(f130(x60382),f777(f777(f5(a851),x60381),f82(a851))),x60384)) % 174.01/173.89 [6065]E(x60651,f182(f858(x60652,a845)))+E(f777(f305(x60652,x60653,f777(f20(x60653,x60652),x60654)),x60651),f777(f777(f304(x60653),x60654),f182(f858(x60653,a845)))) % 174.01/173.89 [6068]E(f777(f307(x60681,x60682,f777(f20(x60682,x60681),x60683)),x60684),f182(f858(x60681,a845)))+P1(f777(f777(f336(x60682),x60683),x60684)) % 174.01/173.89 [6135]~E(x61353,f182(f858(x61351,a845)))+E(f777(f777(f48(x61351,f858(x61352,a845)),x61353),f777(f20(f858(x61352,a845),x61351),x61354)),f182(f858(x61352,a845))) % 174.01/173.89 [6136]~E(x61363,f182(f858(x61361,a845)))+E(f777(f777(f49(x61361,f858(x61362,a845)),x61363),f777(f20(f858(x61362,a845),x61361),x61364)),f241(f858(x61362,a845))) % 174.01/173.89 [6138]~P7(x61381)+E(f54(x61381,f777(f777(f85(x61381),x61382),x61383),f777(f777(f85(x61381),x61382),x61384)),f777(f777(f85(x61381),x61382),f54(x61381,x61383,x61384))) % 174.01/173.89 [6312]E(f777(f307(x63121,x63122,f777(f20(x63122,x63121),x63123)),x63124),f241(f858(x63121,a845)))+~P1(f777(f777(f336(x63122),x63123),x63124)) % 174.01/173.89 [6335]~P1(f777(f777(f336(x63351),x63352),x63354))+P1(f777(f777(f336(x63351),x63352),f777(f777(f304(x63351),x63353),x63354))) % 174.01/173.89 [6348]~E(x63483,f777(f777(f5(a851),f777(f183(f852(x63481)),x63482)),f82(a851)))+E(f118(x63481,f777(f777(f150(x63481,x63482),x63483),x63484)),f118(x63481,x63482)) % 174.01/173.89 [6373]~P100(x63731)+E(f777(f777(f106(f858(x63731,a845)),f777(f295(x63731),x63732)),f297(x63731,x63733,x63734)),f297(x63731,x63733,f777(f777(f238(x63731),x63732),x63734))) % 174.01/173.89 [6374]~P100(x63741)+E(f777(f777(f106(f858(x63741,a845)),f777(f260(x63741),x63742)),f297(x63741,x63743,x63744)),f297(x63741,f777(f777(f181(x63741),x63742),x63743),x63744)) % 174.01/173.89 [6391]E(f777(f777(f106(f858(x63911,a845)),x63912),f777(f777(f304(x63911),x63913),x63914)),f777(f777(f106(f858(x63911,a845)),x63912),x63914))+P1(f777(f777(f336(x63911),x63913),x63912)) % 174.01/173.89 [6403]E(f153(x64031,x64032,f777(f777(f127(x64031),x64033),x64034)),f777(f777(f127(x64031),x64033),f153(x64031,x64032,x64034)))+P1(f777(f777(f336(x64031),x64032),f777(f160(x64031),x64033))) % 174.01/173.89 [6408]~P75(x64081)+E(f777(f777(f85(x64081),f777(f777(f244(x64081),x64082),x64083)),f777(f777(f244(x64081),x64082),x64084)),f777(f777(f244(x64081),x64082),f777(f777(f84(a851),x64083),x64084))) % 174.01/173.89 [6409]~P85(x64091)+E(f777(f777(f85(x64091),f777(f777(f244(x64091),x64092),x64093)),f777(f777(f244(x64091),x64092),x64094)),f777(f777(f244(x64091),x64092),f777(f777(f84(a851),x64093),x64094))) % 174.01/173.89 [6445]~P85(x64451)+E(f777(f777(f84(x64451),f777(f777(f85(x64451),x64452),x64453)),f777(f777(f85(x64451),x64452),x64454)),f777(f777(f85(x64451),x64452),f777(f777(f84(x64451),x64453),x64454))) % 174.01/173.89 [6446]~P100(x64461)+E(f777(f777(f181(x64461),f777(f777(f238(x64461),x64462),x64463)),f777(f777(f238(x64461),x64462),x64464)),f777(f777(f238(x64461),x64462),f777(f777(f181(x64461),x64463),x64464))) % 174.01/173.89 [6447]~P100(x64471)+E(f777(f777(f238(x64471),f777(f777(f181(x64471),x64472),x64473)),f777(f777(f181(x64471),x64472),x64474)),f777(f777(f181(x64471),x64472),f777(f777(f238(x64471),x64473),x64474))) % 174.01/173.89 [6448]~P97(x64481)+E(f777(f777(f106(x64481),f777(f777(f105(x64481),x64482),x64483)),f777(f777(f105(x64481),x64482),x64484)),f777(f777(f105(x64481),x64482),f777(f777(f106(x64481),x64483),x64484))) % 174.01/173.89 [6449]~P97(x64491)+E(f777(f777(f105(x64491),f777(f777(f106(x64491),x64492),x64493)),f777(f777(f106(x64491),x64492),x64494)),f777(f777(f106(x64491),x64492),f777(f777(f105(x64491),x64493),x64494))) % 174.01/173.89 [6486]~P7(x64861)+E(f54(x64861,f777(f777(f85(x64861),x64862),x64863),f777(f777(f85(x64861),x64864),x64863)),f777(f777(f85(x64861),f54(x64861,x64862,x64864)),x64863)) % 174.01/173.89 [6489]~E(f777(f183(f852(x64891)),x64893),f777(f183(f852(x64892)),x64894))+E(f777(f777(f145(f857(x64891,x64892),x64892),f252(x64891,x64892)),f777(f777(f169(x64891,x64892),x64893),x64894)),x64894) % 174.01/173.89 [6490]~E(f777(f183(f852(x64901)),x64903),f777(f183(f852(x64902)),x64904))+E(f777(f777(f145(f857(x64901,x64902),x64901),f242(x64901,x64902)),f777(f777(f169(x64901,x64902),x64903),x64904)),x64903) % 174.01/173.89 [6501]~P7(x65011)+E(f54(x65011,f777(f777(f85(x65011),x65012),f54(x65011,x65013,x65014)),x65014),f54(x65011,f777(f777(f85(x65011),x65012),x65013),x65014)) % 174.01/173.89 [6502]~P8(x65021)+E(f54(x65021,f777(f777(f5(x65021),x65022),f54(x65021,x65023,x65024)),x65024),f54(x65021,f777(f777(f5(x65021),x65022),x65023),x65024)) % 174.01/173.89 [6503]~P7(x65031)+E(f54(x65031,f777(f777(f84(x65031),x65032),f54(x65031,x65033,x65034)),x65034),f54(x65031,f777(f777(f84(x65031),x65032),x65033),x65034)) % 174.01/173.89 [6586]~P100(x65861)+E(f777(f777(f106(f858(x65861,a845)),f297(x65861,x65862,x65863)),f777(f295(x65861),x65864)),f297(x65861,x65862,f777(f777(f238(x65861),x65863),x65864))) % 174.01/173.89 [6587]~P100(x65871)+E(f777(f777(f106(f858(x65871,a845)),f297(x65871,x65872,x65873)),f777(f260(x65871),x65874)),f297(x65871,f777(f777(f181(x65871),x65872),x65874),x65873)) % 174.01/173.89 [6591]~E(f777(f183(f852(x65911)),x65913),f777(f183(f852(x65912)),x65914))+E(f777(f777(f169(x65911,x65912),f777(f144(x65911),x65913)),f777(f144(x65912),x65914)),f777(f144(f857(x65911,x65912)),f777(f777(f169(x65911,x65912),x65913),x65914))) % 174.01/173.89 [6600]E(x66001,f777(f777(f5(a851),f777(f183(f852(x66002)),x66003)),f82(a851)))+E(f118(x66002,f777(f777(f150(x66002,x66003),x66001),x66004)),f777(f777(f150(x66002,f118(x66002,x66003)),x66001),x66004)) % 174.01/173.89 [6617]~P1(f777(f129(x66172),x66174))+P1(f777(f129(f857(x66171,x66172)),f777(f777(f169(x66171,x66172),x66173),x66174))) % 174.01/173.89 [6618]~P1(f777(f129(x66181),x66183))+P1(f777(f129(f857(x66181,x66182)),f777(f777(f169(x66181,x66182),x66183),x66184))) % 174.01/173.89 [6716]E(x67161,f777(f777(f777(a191,x67162),x67163),f777(x67164,x67162)))+~P1(f777(f777(f189(f30(x67163,x67164)),x67162),x67161)) % 174.01/173.89 [6897]E(f777(f777(f45(a851),x68971),x68972),x68973)+~P1(f777(f57(x68971,x68972),f777(f777(f243(a851,a851),x68973),x68974))) % 174.01/173.89 [6923]E(f54(a851,x69231,x69232),x69233)+~P1(f777(f57(x69231,x69232),f777(f777(f243(a851,a851),x69234),x69233))) % 174.01/173.89 [6926]P1(f777(f129(x69261),x69262))+~P1(f777(f129(x69263),f777(f777(f145(x69261,x69263),x69264),x69262))) % 174.01/173.89 [6934]~P28(x69341,x69342,f777(f777(f304(f850(x69341)),x69343),x69344))+P28(x69341,x69342,f777(f777(f304(f850(x69341)),x69343),f182(f858(f850(x69341),a845)))) % 174.01/173.89 [7006]E(f153(x70061,x70062,f777(f777(f127(x70061),x70063),x70064)),f777(f777(f127(x70061),f153(x70061,x70062,x70063)),x70064))+~P1(f777(f777(f336(x70061),x70062),f777(f160(x70061),x70063))) % 174.01/173.89 [7102]~P8(x71021)+E(f54(x71021,f777(f777(f5(x71021),f54(x71021,x71022,x71023)),x71024),x71023),f54(x71021,f777(f777(f5(x71021),x71022),x71024),x71023)) % 174.01/173.89 [7103]~P7(x71031)+E(f54(x71031,f777(f777(f84(x71031),f54(x71031,x71032,x71033)),x71034),x71033),f54(x71031,f777(f777(f84(x71031),x71032),x71034),x71033)) % 174.01/173.89 [7104]~P7(x71041)+E(f54(x71041,f777(f777(f85(x71041),f54(x71041,x71042,x71043)),x71044),x71043),f54(x71041,f777(f777(f85(x71041),x71042),x71044),x71043)) % 174.01/173.89 [7310]~E(x73101,f777(f777(f142(x73102),x73103),x73104))+~P1(f777(f777(f234(a851),f777(f183(f852(x73102)),x73101)),f777(f183(f852(x73102)),x73104))) % 174.01/173.89 [7482]~E(f168(x74821,x74822,x74823),f168(x74821,x74822,x74824))+E(f777(f305(f857(x74821,x74822),x74821,f242(x74821,x74822)),f777(f160(f857(x74821,x74822)),x74823)),f777(f305(f857(x74821,x74822),x74821,f242(x74821,x74822)),f777(f160(f857(x74821,x74822)),x74824))) % 174.01/173.89 [7525]P29(x75251,x75252,x75253,f777(f160(x75251),x75254))+~P1(f777(f129(x75252),f777(f777(f145(x75251,x75252),x75253),x75254))) % 174.01/173.89 [7602]~P1(f777(f777(f234(f858(x76021,a845)),x76022),x76024))+P1(f777(f777(f234(f858(x76021,a845)),x76022),f777(f777(f304(x76021),x76023),x76024))) % 174.01/173.89 [7637]~P7(x76371)+E(f54(x76371,f777(f777(f84(x76371),f54(x76371,x76372,x76373)),f54(x76371,x76374,x76373)),x76373),f54(x76371,f777(f777(f84(x76371),x76372),x76374),x76373)) % 174.01/173.89 [7638]~P7(x76381)+E(f54(x76381,f777(f777(f85(x76381),f54(x76381,x76382,x76383)),f54(x76381,x76384,x76383)),x76383),f54(x76381,f777(f777(f85(x76381),x76382),x76384),x76383)) % 174.01/173.89 [7639]~P8(x76391)+E(f54(x76391,f777(f777(f5(x76391),f54(x76391,x76392,x76393)),f54(x76391,x76394,x76393)),x76393),f54(x76391,f777(f777(f5(x76391),x76392),x76394),x76393)) % 174.01/173.89 [7740]~E(f777(x77404,f653(x77404,x77403,x77401,x77402)),f241(f858(x77402,a845)))+E(f777(f777(f49(x77401,f858(x77402,a845)),x77403),x77404),f241(f858(x77402,a845))) % 174.01/173.89 [7741]~E(f777(x77414,f412(x77414,x77413,x77411,x77412)),f182(f858(x77412,a845)))+E(f777(f777(f48(x77411,f858(x77412,a845)),x77413),x77414),f182(f858(x77412,a845))) % 174.01/173.89 [7742]~E(f777(x77424,f413(x77424,x77423,x77422,x77421)),f182(f858(x77422,a845)))+E(f777(f777(f48(x77421,f858(x77422,a845)),x77423),x77424),f182(f858(x77422,a845))) % 174.01/173.89 [7743]~E(f777(x77434,f654(x77434,x77433,x77432,x77431)),f241(f858(x77432,a845)))+E(f777(f777(f49(x77431,f858(x77432,a845)),x77433),x77434),f241(f858(x77432,a845))) % 174.01/173.89 [8134]P1(f777(x81341,x81342))+~P1(f777(f777(f336(x81343),x81342),f777(f777(f106(f858(x81343,a845)),x81344),f777(f258(x81343),x81341)))) % 174.01/173.89 [8173]~P1(f777(f777(f234(f858(x81731,a845)),x81733),x81734))+P1(f777(f777(f234(f858(x81731,a845)),f777(f777(f304(x81731),x81732),x81733)),f777(f777(f304(x81731),x81732),x81734))) % 174.01/173.89 [8340]P1(f777(f777(f189(x83401),x83402),f437(x83403,x83402,x83404,x83401)))+~P1(f777(f777(f189(f38(x83401,x83404)),x83402),x83403)) % 174.01/173.89 [8341]P1(f777(f777(f189(x83411),x83412),f463(x83413,x83412,x83414,x83411)))+~P1(f777(f777(f189(f38(x83411,x83414)),x83412),x83413)) % 174.01/173.89 [8462]~P1(f777(f777(f235(a851),f777(x84624,x84622)),f777(x84624,x84623)))+P1(f777(f777(f336(f857(x84621,x84621)),f777(f777(f243(x84621,x84621),x84622),x84623)),f777(f777(f282(a851,x84621),a239),x84624))) % 174.01/173.89 [8609]P29(f852(x86091),f852(x86092),f777(f145(x86091,x86092),x86093),x86094)+~P29(x86091,x86092,x86093,f46(f858(x86091,a845),f777(f305(f852(x86091),f858(x86091,a845),f160(x86091)),x86094))) % 174.01/173.89 [8719]E(f777(f777(f49(x87191,f858(x87192,a845)),x87193),x87194),f241(f858(x87192,a845)))+P1(f777(f777(f336(x87191),f653(x87194,x87193,x87191,x87192)),x87193)) % 174.01/173.89 [8720]E(f777(f777(f48(x87201,f858(x87202,a845)),x87203),x87204),f182(f858(x87202,a845)))+P1(f777(f777(f336(x87201),f412(x87204,x87203,x87201,x87202)),x87203)) % 174.01/173.89 [8721]E(f777(f777(f48(x87211,f858(x87212,a845)),x87213),x87214),f182(f858(x87212,a845)))+P1(f777(f777(f336(x87211),f413(x87214,x87213,x87212,x87211)),x87213)) % 174.01/173.89 [8722]E(f777(f777(f49(x87221,f858(x87222,a845)),x87223),x87224),f241(f858(x87222,a845)))+P1(f777(f777(f336(x87221),f654(x87224,x87223,x87222,x87221)),x87223)) % 174.01/173.89 [8757]P1(f777(f777(f235(a851),f777(x87571,x87572)),f777(x87571,x87573)))+~P1(f777(f777(f336(f857(x87574,x87574)),f777(f777(f243(x87574,x87574),x87572),x87573)),f777(f777(f282(a851,x87574),a239),x87571))) % 174.01/173.89 [8806]P1(f777(f777(f189(x88061),f437(x88062,x88063,x88061,x88064)),x88062))+~P1(f777(f777(f189(f38(x88064,x88061)),x88063),x88062)) % 174.01/173.89 [8807]P1(f777(f777(f189(x88071),f463(x88072,x88073,x88071,x88074)),x88072))+~P1(f777(f777(f189(f38(x88074,x88071)),x88073),x88072)) % 174.01/173.89 [8918]P1(f777(f777(f336(x89181),f496(x89182,x89183,x89184,x89181)),x89183))+~P1(f777(f777(f336(f858(x89181,a845)),x89184),f777(f777(f63(x89181),x89183),x89182))) % 174.01/173.89 [8921]E(x89211,x89212)+~P1(f777(f777(f336(f857(x89213,x89213)),f777(f777(f243(x89213,x89213),x89211),x89212)),f777(f777(f175(f857(x89213,x89213),a845),f4(a851)),x89214))) % 174.01/173.89 [8993]E(f777(f279(x89931,x89931,x89932),f777(f777(f304(x89931),f496(x89932,x89933,x89934,x89931)),f182(f858(x89931,a845)))),x89934)+~P1(f777(f777(f336(f858(x89931,a845)),x89934),f777(f777(f63(x89931),x89933),x89932))) % 174.01/173.89 [9004]~P1(f777(f777(f336(f857(x90041,x90041)),f777(f777(f243(x90041,x90041),x90043),x90042)),f302(x90041,x90044)))+P1(f777(f777(f336(f857(x90041,x90041)),f777(f777(f243(x90041,x90041),x90042),x90043)),f302(x90041,f777(f280(x90041,x90041),x90044)))) % 174.01/173.89 [9017]~P7(x90171)+E(f777(f777(f84(x90171),f777(f777(f84(x90171),f777(f777(f85(x90171),x90172),f777(f777(f45(x90171),x90173),x90172))),f54(x90171,x90173,x90172))),x90174),f777(f777(f84(x90171),x90173),x90174)) % 174.01/173.89 [9024]~P1(f777(f777(f336(x90241),x90243),x90244))+P1(f777(f777(f336(f858(x90241,a845)),f777(f279(x90241,x90241,x90242),f777(f777(f304(x90241),x90243),f182(f858(x90241,a845))))),f777(f777(f63(x90241),x90244),x90242))) % 174.01/173.89 [9034]P1(f777(f777(f336(f857(x90341,x90341)),f777(f777(f243(x90341,x90341),x90342),x90343)),f302(x90341,x90344)))+~P1(f777(f777(f336(f857(x90341,x90341)),f777(f777(f243(x90341,x90341),x90343),x90342)),f302(x90341,f777(f280(x90341,x90341),x90344)))) % 174.01/173.89 [9117]E(f777(f777(f150(x91171,f777(f144(x91171),x91172)),f777(f777(f5(a851),f777(f777(f5(a851),f777(f183(f852(x91171)),x91172)),x91173)),f82(a851))),x91174),f777(f144(x91171),f777(f777(f150(x91171,x91172),x91173),x91174)))+~P1(f777(f777(f235(a851),x91173),f777(f183(f852(x91171)),x91172))) % 174.01/173.89 [9154]~P29(x91542,x91541,x91543,f241(f858(x91542,a845)))+P1(f777(f777(f234(f858(x91541,a845)),f777(f305(x91542,x91541,x91543),f777(f83(f858(x91542,a845)),x91544))),f777(f83(f858(x91541,a845)),f777(f305(x91542,x91541,x91543),x91544)))) % 174.01/173.89 [9162]~P9(x91621)+E(f777(f134(x91621,x91622,f777(f11(x91622,x91621,x91621),f777(f777(f12(x91621,f858(x91621,x91621),x91622),f105(x91621)),x91623)),f182(x91621)),x91624),f777(f777(f48(x91622,x91621),f777(f160(x91622),x91624)),x91623)) % 174.01/173.89 [9163]~P9(x91631)+E(f777(f134(x91631,x91632,f777(f11(x91632,x91631,x91631),f777(f777(f12(x91631,f858(x91631,x91631),x91632),f106(x91631)),x91633)),f241(x91631)),x91634),f777(f777(f49(x91632,x91631),f777(f160(x91632),x91634)),x91633)) % 174.01/173.89 [9229]~P1(f777(f777(f336(f857(f852(x92294),f852(x92294))),f777(f777(f243(f852(x92294),f852(x92294)),x92293),x92292)),f148(x92294,x92291)))+P1(f777(f777(f235(a851),f739(x92291,x92292,x92293,x92294)),f777(f183(f852(x92294)),x92293))) % 174.01/173.89 [9230]~P7(x92301)+E(f777(f777(f84(x92301),f777(f777(f84(x92301),f777(f777(f85(x92301),f777(f777(f45(x92301),x92302),x92303)),x92303)),f54(x92301,x92302,x92303))),x92304),f777(f777(f84(x92301),x92302),x92304)) % 174.01/173.89 [9259]~P1(f777(f777(f336(f857(f852(x92591),f852(x92591))),f777(f777(f243(f852(x92591),f852(x92591)),x92592),x92593)),f777(f280(f852(x92591),f852(x92591)),f148(x92591,x92594))))+P1(f777(f777(f336(f857(f852(x92591),f852(x92591))),f777(f777(f243(f852(x92591),f852(x92591)),x92592),x92593)),f148(x92591,f777(f280(x92591,x92591),x92594)))) % 174.01/173.89 [9260]P1(f777(f777(f336(f857(f852(x92601),f852(x92601))),f777(f777(f243(f852(x92601),f852(x92601)),x92602),x92603)),f777(f280(f852(x92601),f852(x92601)),f148(x92601,x92604))))+~P1(f777(f777(f336(f857(f852(x92601),f852(x92601))),f777(f777(f243(f852(x92601),f852(x92601)),x92602),x92603)),f148(x92601,f777(f280(x92601,x92601),x92604)))) % 174.01/173.89 [9297]~P1(f777(f777(f336(x92971),x92973),f777(f263(x92971,x92972),x92974)))+P1(f777(f777(f336(f857(x92971,x92972)),f777(f777(f243(x92971,x92972),x92973),f599(x92974,x92972,x92973,x92971))),x92974)) % 174.01/173.89 [9298]~P1(f777(f777(f336(x92981),x92983),f777(f263(x92981,x92982),x92984)))+P1(f777(f777(f336(f857(x92981,x92982)),f777(f777(f243(x92981,x92982),x92983),f600(x92984,x92982,x92983,x92981))),x92984)) % 174.01/173.89 [9424]~P1(f777(f65(f855(x94241)),f777(f305(x94242,f855(x94241),x94243),f241(f858(x94242,a845)))))+P1(f777(f65(f855(x94241)),f777(f305(x94242,f855(x94241),f172(x94242,x94241,x94243,f168(x94242,x94241,x94244))),f241(f858(x94242,a845))))) % 174.01/173.89 [9448]~P1(f777(f777(f336(f857(x94481,x94481)),f777(f777(f243(x94481,x94481),x94482),x94484)),f777(f777(f283(x94481,x94481,x94481),x94483),f302(x94481,x94483))))+P1(f777(f777(f336(f857(x94481,x94481)),f777(f777(f243(x94481,x94481),x94482),f656(x94483,x94484,x94482,x94481))),x94483)) % 174.01/173.89 [9606]~P1(f777(f777(f336(f857(x96062,x96061)),x96064),f777(f280(x96061,x96062),x96063)))+P1(f777(f777(f336(f857(x96061,x96062)),f777(f777(f243(x96061,x96062),f703(x96063,x96064,x96061,x96062)),f702(x96063,x96064,x96061,x96062))),x96063)) % 174.01/173.89 [9630]~P1(f777(f777(f336(f857(f852(x96301),f852(x96301))),f777(f777(f243(f852(x96301),f852(x96301)),x96304),x96303)),f148(x96301,x96302)))+P1(f777(f777(f336(f857(x96301,x96301)),f777(f777(f243(x96301,x96301),f744(x96302,x96303,x96304,x96301)),f745(x96302,x96303,x96304,x96301))),x96302)) % 174.01/173.89 [9706]~P1(f777(f777(f336(f857(f852(x97061),f852(x97061))),f777(f777(f243(f852(x97061),f852(x97061)),x97062),x97064)),f148(x97061,x97063)))+P1(f777(f777(f336(f857(x97061,x97061)),f777(f777(f243(x97061,x97061),f777(f777(f155(x97061),x97062),f739(x97063,x97064,x97062,x97061))),f740(x97063,x97064,x97062,x97061))),x97063)) % 174.01/173.89 [9727]~P1(f777(f65(x97272),x97274))+E(f777(f777(f777(f69(f858(x97271,a845),x97272,f105(f858(x97271,a845))),f777(f777(f11(x97272,f858(x97271,a845),f858(x97271,a845)),f777(f777(f12(x97271,f858(f858(x97271,a845),f858(x97271,a845)),x97272),f304(x97271)),x97273)),f182(f858(x97271,a845)))),f182(f858(x97271,a845))),x97274),f777(f305(x97272,x97271,x97273),x97274)) % 174.01/173.89 [9843]~P29(x98431,x98432,x98433,f241(f858(x98431,a845)))+P1(f777(f777(f234(f858(x98431,a845)),f777(f307(x98431,x98432,x98433),f777(f777(f304(x98432),x98434),f182(f858(x98432,a845))))),f777(f777(f304(x98431),f89(x98431,f777(f777(f11(x98431,x98432,a845),f777(f777(f12(x98432,f858(x98432,a845),x98431),a332),x98433)),x98434))),f182(f858(x98431,a845))))) % 174.01/173.89 [5505]~E(f777(f777(f127(x55051),x55052),x55054),x55053)+E(f777(f777(f161(x55051),f777(f183(f852(x55051)),x55052)),x55053),x55052) % 174.01/173.89 [5506]~E(f777(f777(f127(x55062),x55063),x55061),x55064)+E(x55061,f777(f777(f130(x55062),f777(f183(f852(x55062)),x55063)),x55064)) % 174.01/173.89 [5517]~E(x55174,f4(a851))+E(f777(f777(f155(x55171),f777(f777(f142(x55171),x55172),x55173)),x55174),x55172) % 174.01/173.89 [6049]~P85(x60491)+E(f777(f777(f244(x60491),f777(f777(f244(x60491),x60492),x60493)),x60494),f777(f777(f244(x60491),x60492),f777(f777(f85(a851),x60493),x60494))) % 174.01/173.89 [6050]~P75(x60501)+E(f777(f777(f244(x60501),f777(f777(f244(x60501),x60502),x60503)),x60504),f777(f777(f244(x60501),x60502),f777(f777(f85(a851),x60503),x60504))) % 174.01/173.89 [6066]E(x60661,f4(a851))+E(f777(f777(f155(x60662),f777(f777(f142(x60662),x60663),x60664)),x60661),f777(f777(f155(x60662),x60664),f777(f777(f5(a851),x60661),f82(a851)))) % 174.01/173.89 [6092]~P113(x60921)+E(f777(f777(f285(x60921),f777(f777(f85(x60921),x60922),x60923)),x60924),f777(f777(f85(x60921),x60922),f777(f777(f285(x60921),x60923),x60924))) % 174.01/173.89 [6093]~P5(x60931)+E(f777(f777(f84(x60931),f777(f777(f84(x60931),x60932),x60933)),x60934),f777(f777(f84(x60931),x60932),f777(f777(f84(x60931),x60933),x60934))) % 174.01/173.89 [6094]~P85(x60941)+E(f777(f777(f84(x60941),f777(f777(f84(x60941),x60942),x60943)),x60944),f777(f777(f84(x60941),x60942),f777(f777(f84(x60941),x60943),x60944))) % 174.01/173.89 [6095]~P85(x60951)+E(f777(f777(f85(x60951),f777(f777(f85(x60951),x60952),x60953)),x60954),f777(f777(f85(x60951),x60952),f777(f777(f85(x60951),x60953),x60954))) % 174.01/173.89 [6096]~P64(x60961)+E(f777(f777(f85(x60961),f777(f777(f85(x60961),x60962),x60963)),x60964),f777(f777(f85(x60961),x60962),f777(f777(f85(x60961),x60963),x60964))) % 174.01/173.89 [6099]~P100(x60991)+E(f777(f777(f238(x60991),f777(f777(f238(x60991),x60992),x60993)),x60994),f777(f777(f238(x60991),x60992),f777(f777(f238(x60991),x60993),x60994))) % 174.01/173.89 [6101]~P100(x61011)+E(f777(f777(f181(x61011),f777(f777(f181(x61011),x61012),x61013)),x61014),f777(f777(f181(x61011),x61012),f777(f777(f181(x61011),x61013),x61014))) % 174.01/173.89 [6103]~P92(x61031)+E(f777(f777(f105(x61031),f777(f777(f105(x61031),x61032),x61033)),x61034),f777(f777(f105(x61031),x61032),f777(f777(f105(x61031),x61033),x61034))) % 174.01/173.89 [6104]~P93(x61041)+E(f777(f777(f105(x61041),f777(f777(f105(x61041),x61042),x61043)),x61044),f777(f777(f105(x61041),x61042),f777(f777(f105(x61041),x61043),x61044))) % 174.01/173.89 [6105]~P93(x61051)+E(f777(f777(f106(x61051),f777(f777(f106(x61051),x61052),x61053)),x61054),f777(f777(f106(x61051),x61052),f777(f777(f106(x61051),x61053),x61054))) % 174.01/173.89 [6107]~P98(x61071)+E(f777(f777(f106(x61071),f777(f777(f106(x61071),x61072),x61073)),x61074),f777(f777(f106(x61071),x61072),f777(f777(f106(x61071),x61073),x61074))) % 174.01/173.89 [6118]~P7(x61181)+E(f54(x61181,f777(f777(f84(x61181),x61182),f777(f777(f85(x61181),x61183),x61184)),x61184),f54(x61181,x61182,x61184)) % 174.01/173.89 [6119]~P7(x61191)+E(f54(x61191,f777(f777(f84(x61191),x61192),f777(f777(f85(x61191),x61193),x61194)),x61193),f54(x61191,x61192,x61193)) % 174.01/173.89 [6257]E(f777(f777(f155(x62571),f777(f777(f161(x62571),x62572),x62573)),x62574),f777(f777(f155(x62571),x62573),x62574))+~P1(f777(f777(f235(a851),x62574),x62572)) % 174.01/173.89 [6443]~P85(x64431)+E(f777(f777(f84(x64431),f777(f777(f84(x64431),x64432),x64433)),x64434),f777(f777(f84(x64431),f777(f777(f84(x64431),x64432),x64434)),x64433)) % 174.01/173.89 [6444]~P85(x64441)+E(f777(f777(f85(x64441),f777(f777(f85(x64441),x64442),x64443)),x64444),f777(f777(f85(x64441),f777(f777(f85(x64441),x64442),x64444)),x64443)) % 174.01/173.89 [6506]~P2(x65062)+E(f777(f777(f10(x65061,x65062),f777(f20(x65062,x65061),x65063)),x65064),f777(f777(f85(x65062),f777(f104(x65062),f777(f44(x65061),x65064))),x65063)) % 174.01/173.89 [6685]E(f777(f777(f106(f858(x66851,a845)),f777(f777(f304(x66851),x66852),x66853)),x66854),f777(f777(f106(f858(x66851,a845)),x66853),x66854))+P1(f777(f777(f336(x66851),x66852),x66854)) % 174.01/173.89 [6760]~P74(x67601)+E(f777(f777(f238(x67601),f777(f777(f84(x67601),x67602),x67603)),f777(f777(f84(x67601),x67604),x67603)),f777(f777(f84(x67601),f777(f777(f238(x67601),x67602),x67604)),x67603)) % 174.01/173.89 [6761]~P74(x67611)+E(f777(f777(f181(x67611),f777(f777(f84(x67611),x67612),x67613)),f777(f777(f84(x67611),x67614),x67613)),f777(f777(f84(x67611),f777(f777(f181(x67611),x67612),x67614)),x67613)) % 174.01/173.89 [6763]~P109(x67631)+E(f777(f777(f84(x67631),f777(f777(f85(x67631),x67632),x67633)),f777(f777(f85(x67631),x67634),x67633)),f777(f777(f85(x67631),f777(f777(f84(x67631),x67632),x67634)),x67633)) % 174.01/173.89 [6764]~P77(x67641)+E(f777(f777(f238(x67641),f777(f777(f5(x67641),x67642),x67643)),f777(f777(f5(x67641),x67644),x67643)),f777(f777(f5(x67641),f777(f777(f238(x67641),x67642),x67644)),x67643)) % 174.01/173.89 [6765]~P77(x67651)+E(f777(f777(f181(x67651),f777(f777(f5(x67651),x67652),x67653)),f777(f777(f5(x67651),x67654),x67653)),f777(f777(f5(x67651),f777(f777(f181(x67651),x67652),x67654)),x67653)) % 174.01/173.89 [6766]~P85(x67661)+E(f777(f777(f85(x67661),f777(f777(f244(x67661),x67662),x67663)),f777(f777(f244(x67661),x67664),x67663)),f777(f777(f244(x67661),f777(f777(f85(x67661),x67662),x67664)),x67663)) % 174.01/173.89 [6767]~P70(x67671)+E(f777(f777(f85(x67671),f777(f777(f244(x67671),x67672),x67673)),f777(f777(f244(x67671),x67674),x67673)),f777(f777(f244(x67671),f777(f777(f85(x67671),x67672),x67674)),x67673)) % 174.01/173.89 [6768]~P60(x67681)+E(f777(f777(f285(x67681),f777(f777(f244(x67681),x67682),x67683)),f777(f777(f244(x67681),x67684),x67683)),f777(f777(f244(x67681),f777(f777(f285(x67681),x67682),x67684)),x67683)) % 174.01/173.89 [6769]~P113(x67691)+E(f777(f777(f84(x67691),f777(f777(f285(x67691),x67692),x67693)),f777(f777(f285(x67691),x67694),x67693)),f777(f777(f285(x67691),f777(f777(f84(x67691),x67692),x67694)),x67693)) % 174.01/173.89 [6770]~P113(x67701)+E(f777(f777(f5(x67701),f777(f777(f285(x67701),x67702),x67703)),f777(f777(f285(x67701),x67704),x67703)),f777(f777(f285(x67701),f777(f777(f5(x67701),x67702),x67704)),x67703)) % 174.01/173.89 [6771]~P100(x67711)+E(f777(f777(f181(x67711),f777(f777(f238(x67711),x67712),x67713)),f777(f777(f238(x67711),x67714),x67713)),f777(f777(f238(x67711),f777(f777(f181(x67711),x67712),x67714)),x67713)) % 174.01/173.89 [6772]~P100(x67721)+E(f777(f777(f238(x67721),f777(f777(f181(x67721),x67722),x67723)),f777(f777(f181(x67721),x67724),x67723)),f777(f777(f181(x67721),f777(f777(f238(x67721),x67722),x67724)),x67723)) % 174.01/173.89 [6773]~P97(x67731)+E(f777(f777(f106(x67731),f777(f777(f105(x67731),x67732),x67733)),f777(f777(f105(x67731),x67734),x67733)),f777(f777(f105(x67731),f777(f777(f106(x67731),x67732),x67734)),x67733)) % 174.01/173.89 [6774]~P97(x67741)+E(f777(f777(f105(x67741),f777(f777(f106(x67741),x67742),x67743)),f777(f777(f106(x67741),x67744),x67743)),f777(f777(f106(x67741),f777(f777(f105(x67741),x67742),x67744)),x67743)) % 174.01/173.89 [6775]~P85(x67751)+E(f777(f777(f84(x67751),f777(f777(f85(x67751),x67752),x67753)),f777(f777(f85(x67751),x67754),x67753)),f777(f777(f85(x67751),f777(f777(f84(x67751),x67752),x67754)),x67753)) % 174.01/173.89 [6810]E(f777(f777(f150(x68101,x68102),x68103),x68104),x68102)+~P1(f777(f777(f234(a851),f777(f183(f852(x68101)),x68102)),x68103)) % 174.01/173.89 [6837]~P1(f777(x68373,x68374))+P1(f777(f777(f777(f105(f858(x68371,a845)),x68372),x68373),x68374)) % 174.01/173.89 [6839]~P1(f777(x68392,x68394))+P1(f777(f777(f777(f105(f858(x68391,a845)),x68392),x68393),x68394)) % 174.01/173.89 [6861]E(f777(f777(f155(x68611),f777(f777(f127(x68611),x68612),x68613)),x68614),f777(f777(f155(x68611),x68612),x68614))+~P1(f777(f777(f235(a851),x68614),f777(f183(f852(x68611)),x68612))) % 174.01/173.89 [6871]E(f777(f777(f5(f858(x68711,a845)),f777(f777(f304(x68711),x68712),x68713)),x68714),f777(f777(f5(f858(x68711,a845)),x68713),x68714))+~P1(f777(f777(f336(x68711),x68712),x68714)) % 174.01/173.89 [6912]~E(f132(a851,f777(f296(a851,x69121),x69122)),f777(f777(f142(a851),x69124),x69123))+E(f132(a851,f777(f296(a851,f777(f777(f84(a851),x69121),f82(a851))),x69122)),x69123) % 174.01/173.89 [6981]E(x69811,f4(a851))+E(f777(f777(f142(x69812),x69813),f777(f777(f161(x69812),f777(f777(f5(a851),x69811),f82(a851))),x69814)),f777(f777(f161(x69812),x69811),f777(f777(f142(x69812),x69813),x69814))) % 174.01/173.89 [7085]E(f777(f777(f155(x70851),x70852),f777(f777(f5(a851),x70853),f777(f183(f852(x70851)),x70854))),f777(f777(f155(x70851),f777(f777(f127(x70851),x70854),x70852)),x70853))+P1(f777(f777(f235(a851),x70853),f777(f183(f852(x70851)),x70854))) % 174.01/173.89 [7113]E(f777(f777(f106(f858(x71131,a845)),x71132),f777(f777(f304(x71131),x71133),x71134)),f777(f777(f304(x71131),x71133),f777(f777(f106(f858(x71131,a845)),x71132),x71134)))+~P1(f777(f777(f336(x71131),x71133),x71132)) % 174.01/173.89 [7147]E(f777(f777(f155(x71471),f777(f777(f150(x71471,x71472),x71473),x71474)),x71473),x71474)+~P1(f777(f777(f235(a851),x71473),f777(f183(f852(x71471)),x71472))) % 174.01/173.89 [7168]E(x71681,f182(f858(x71682,a845)))+E(f777(f305(f857(x71683,x71682),x71683,f242(x71683,x71682)),f777(f777(f250(x71683,x71682),x71684),f777(f20(f858(x71682,a845),x71683),x71681))),x71684) % 174.01/173.89 [7169]E(x71691,f182(f858(x71692,a845)))+E(f777(f305(f857(x71692,x71693),x71693,f252(x71692,x71693)),f777(f777(f250(x71692,x71693),x71691),f777(f20(f858(x71693,a845),x71692),x71694))),x71694) % 174.01/173.89 [7253]E(f777(f777(f5(f858(x72531,a845)),f777(f777(f304(x72531),x72532),x72533)),x72534),f777(f777(f304(x72531),x72532),f777(f777(f5(f858(x72531,a845)),x72533),x72534)))+P1(f777(f777(f336(x72531),x72532),x72534)) % 174.01/173.89 [7294]~E(x72944,f182(f858(x72942,a845)))+E(f777(f305(f857(x72941,x72942),x72941,f242(x72941,x72942)),f777(f777(f250(x72941,x72942),x72943),f777(f20(f858(x72942,a845),x72941),x72944))),f182(f858(x72941,a845))) % 174.01/173.89 [7295]~E(x72953,f182(f858(x72951,a845)))+E(f777(f305(f857(x72951,x72952),x72952,f252(x72951,x72952)),f777(f777(f250(x72951,x72952),x72953),f777(f20(f858(x72952,a845),x72951),x72954))),f182(f858(x72952,a845))) % 174.01/173.89 [7354]~P1(f777(f777(f336(x73541),x73542),x73544))+P1(f777(f777(f336(x73541),x73542),f777(f777(f105(f858(x73541,a845)),x73543),x73544))) % 174.01/173.89 [7357]~P1(f777(f777(f336(x73571),x73572),x73573))+P1(f777(f777(f336(x73571),x73572),f777(f777(f105(f858(x73571,a845)),x73573),x73574))) % 174.01/173.89 [7379]E(f777(f777(f106(f858(x73791,a845)),f777(f777(f304(x73791),x73792),x73793)),x73794),f777(f777(f304(x73791),x73792),f777(f777(f106(f858(x73791,a845)),x73793),x73794)))+~P1(f777(f777(f336(x73791),x73792),x73794)) % 174.01/173.89 [7658]P1(f777(x76581,x76582))+~P1(f777(f777(f777(f106(f858(x76583,a845)),x76584),x76581),x76582)) % 174.01/173.89 [7659]P1(f777(x76591,x76592))+~P1(f777(f777(f777(f106(f858(x76593,a845)),x76591),x76594),x76592)) % 174.01/173.89 [7662]E(f777(f777(f10(x76621,a851),x76622),f777(f777(f5(f858(x76621,a845)),x76623),f777(f777(f304(x76621),x76624),f182(f858(x76621,a845))))),f777(f777(f10(x76621,a851),x76622),x76623))+P1(f777(f777(f336(x76621),x76624),x76623)) % 174.01/173.89 [7668]~P66(x76681)+E(f777(f157(x76681),f777(f777(f145(a851,x76681),x76682),f132(a851,f777(f296(a851,x76683),x76684)))),f777(f777(f10(a851,x76681),x76682),f777(f160(a851),f132(a851,f777(f296(a851,x76683),x76684))))) % 174.01/173.89 [7669]~P66(x76691)+E(f777(f777(f10(a851,x76691),x76692),f777(f160(a851),f132(a851,f777(f296(a851,x76693),x76694)))),f777(f157(x76691),f777(f777(f145(a851,x76691),x76692),f132(a851,f777(f296(a851,x76693),x76694))))) % 174.01/173.89 [7783]~E(x77833,x77834)+P1(f777(f66(x77831,x77832,f777(f777(f304(x77831),x77833),f182(f858(x77831,a845)))),x77834)) % 174.01/173.89 [7879]P1(f777(f777(f336(x78791),x78792),f777(f160(x78791),x78793)))+~P1(f777(f777(f336(x78791),x78792),f777(f160(x78791),f777(f777(f161(x78791),x78794),x78793)))) % 174.01/173.89 [7880]P1(f777(f777(f336(x78801),x78802),f777(f160(x78801),x78803)))+~P1(f777(f777(f336(x78801),x78802),f777(f160(x78801),f777(f777(f130(x78801),x78804),x78803)))) % 174.01/173.89 [7954]P1(f777(f777(f336(x79541),x79542),x79543))+~P1(f777(f777(f336(x79541),x79542),f777(f777(f5(f858(x79541,a845)),x79543),x79544))) % 174.01/173.89 [7956]P1(f777(f777(f336(x79561),x79562),x79563))+~P1(f777(f777(f336(x79561),x79562),f777(f777(f106(f858(x79561,a845)),x79564),x79563))) % 174.01/173.89 [7959]P1(f777(f777(f336(x79591),x79592),x79593))+~P1(f777(f777(f336(x79591),x79592),f777(f777(f106(f858(x79591,a845)),x79593),x79594))) % 174.01/173.89 [7976]E(f777(f777(f127(x79761),f777(f777(f161(x79761),x79762),x79763)),f777(f777(f142(x79761),x79764),f777(f777(f130(x79761),f777(a116,x79762)),x79763))),f777(f777(f150(x79761,x79763),x79762),x79764))+~P1(f777(f777(f235(a851),x79762),f777(f183(f852(x79761)),x79763))) % 174.01/173.89 [7999]P1(f777(f777(f336(x79991),x79992),x79993))+~P1(f777(f777(f234(f858(x79991,a845)),f777(f777(f304(x79991),x79992),x79994)),x79993)) % 174.01/173.89 [8029]~P1(f777(f777(f336(x80291),x80292),x80293))+~P1(f777(f777(f336(x80291),x80292),f777(f777(f5(f858(x80291,a845)),x80294),x80293))) % 174.01/173.89 [8062]~P1(f777(f777(f235(a851),x80624),f777(f183(f852(x80621)),x80623)))+P1(f777(f777(f336(x80621),x80622),f777(f160(x80621),f777(f777(f150(x80621,x80623),x80624),x80622)))) % 174.01/173.89 [8112]E(f777(f777(f155(x81121),f777(f777(f130(x81121),x81122),x81123)),x81124),f777(f777(f155(x81121),x81123),f777(f777(f84(a851),x81122),x81124)))+~P1(f777(f777(f234(a851),f777(f777(f84(a851),x81122),x81124)),f777(f183(f852(x81121)),x81123))) % 174.01/173.89 [8121]~P2(x81212)+E(f777(f777(f10(x81211,x81212),f777(f777(f12(a851,x81212,x81211),f104(x81212)),x81213)),x81214),f777(f104(x81212),f777(f777(f10(x81211,a851),x81213),x81214))) % 174.01/173.89 [8122]~P133(x81222)+E(f777(f777(f10(x81221,x81222),f777(f777(f12(a3,x81222,x81221),f107(x81222)),x81223)),x81224),f777(f107(x81222),f777(f777(f10(x81221,a3),x81223),x81224))) % 174.01/173.89 [8175]~P63(x81752)+E(f777(f777(f13(x81751,x81752),f777(f777(f12(x81752,x81752,x81751),f79(x81752)),x81753)),x81754),f777(f79(x81752),f777(f777(f13(x81751,x81752),x81753),x81754))) % 174.01/173.89 [8176]~P6(x81762)+E(f777(f777(f10(x81761,x81762),f777(f777(f12(x81762,x81762,x81761),f83(x81762)),x81763)),x81764),f777(f83(x81762),f777(f777(f10(x81761,x81762),x81763),x81764))) % 174.01/173.89 [8178]E(f777(f777(f10(x81781,a851),x81782),f777(f777(f5(f858(x81781,a845)),x81783),f777(f777(f304(x81781),x81784),f182(f858(x81781,a845))))),f777(f777(f5(a851),f777(f777(f10(x81781,a851),x81782),x81783)),f777(x81782,x81784)))+~P1(f777(f777(f336(x81781),x81784),x81783)) % 174.01/173.89 [8197]P1(f777(f777(f234(f858(x81971,a845)),x81972),x81973))+~P1(f777(f777(f234(f858(x81971,a845)),f777(f777(f304(x81971),x81974),x81972)),x81973)) % 174.01/173.89 [8405]P36(x84051,x84052)+~P36(x84051,f777(f777(f304(f857(x84051,x84051)),f777(f777(f243(x84051,x84051),x84053),x84054)),x84052)) % 174.01/173.89 [8406]P56(x84061,x84062)+~P56(x84061,f777(f777(f304(f857(x84061,x84061)),f777(f777(f243(x84061,x84061),x84063),x84064)),x84062)) % 174.01/173.89 [8414]~P100(x84141)+E(f777(f777(f140(x84141,x84141,f9(x84141)),x84142),f777(f777(f140(x84141,x84141,f9(x84141)),x84143),x84144)),f777(f777(f140(x84141,x84141,f9(x84141)),x84143),f777(f777(f140(x84141,x84141,f9(x84141)),x84142),x84144))) % 174.01/173.89 [8424]E(x84241,x84242)+~P1(f777(f66(x84243,x84244,f777(f777(f304(x84243),x84241),f182(f858(x84243,a845)))),x84242)) % 174.01/173.89 [8429]E(f777(f168(x84291,x84292,x84293),x84294),f185(x84292))+P1(f777(f777(f336(x84291),x84294),f777(f305(f857(x84291,x84292),x84291,f242(x84291,x84292)),f777(f160(f857(x84291,x84292)),x84293)))) % 174.01/173.89 [8435]E(f777(f777(f127(x84351),f777(f777(f161(x84351),x84352),x84353)),f777(f777(f161(x84351),x84354),f777(f777(f130(x84351),x84352),x84353))),f777(f777(f161(x84351),f777(f777(f84(a851),x84352),x84354)),x84353))+~P1(f777(f777(f234(a851),f777(f777(f84(a851),x84352),x84354)),f777(f183(f852(x84351)),x84353))) % 174.01/173.89 [8479]P1(f777(f65(x84791),x84792))+~E(x84792,f777(f305(a851,x84791,x84793),f777(f258(a851),f777(f777(f11(a851,a851,a845),f235(a851)),x84794)))) % 174.01/173.89 [8499]~P83(x84991)+E(f777(f134(x84991,x84991,f84(x84991),f777(f777(f84(x84991),x84992),x84993)),x84994),f777(f777(f84(x84991),x84992),f777(f134(x84991,x84991,f84(x84991),x84993),x84994))) % 174.01/173.89 [8531]P1(f777(f777(f234(f858(x85311,a845)),f777(f263(x85311,x85312),x85313)),f777(f263(x85311,x85312),x85314)))+~P1(f777(f777(f234(f858(f857(x85311,x85312),a845)),x85313),x85314)) % 174.01/173.89 [8542]~P1(f777(f777(f234(a851),x85422),x85424))+P1(f777(f777(f234(f858(x85421,a845)),f777(f160(x85421),f777(f777(f161(x85421),x85422),x85423))),f777(f160(x85421),f777(f777(f161(x85421),x85424),x85423)))) % 174.01/173.89 [8543]~P1(f777(f777(f234(a851),x85434),x85432))+P1(f777(f777(f234(f858(x85431,a845)),f777(f160(x85431),f777(f777(f130(x85431),x85432),x85433))),f777(f160(x85431),f777(f777(f130(x85431),x85434),x85433)))) % 174.01/173.89 [8586]~P1(f777(f65(x85861),f777(f777(f5(f858(x85861,a845)),x85862),x85864)))+P1(f777(f65(x85861),f777(f777(f5(f858(x85861,a845)),x85862),f777(f777(f304(x85861),x85863),x85864)))) % 174.01/173.89 [8620]P1(f777(f777(f336(f857(x86201,x86201)),x86202),f302(x86201,x86203)))+~P1(f777(f777(f336(f857(x86201,x86201)),x86202),f777(f777(f175(f857(x86201,x86201),a845),x86204),x86203))) % 174.01/173.89 [8695]~P1(f777(f65(x86951),f777(f777(f5(f858(x86951,a845)),x86952),f777(f777(f304(x86951),x86954),x86953))))+P1(f777(f65(x86951),f777(f777(f5(f858(x86951,a845)),x86952),x86953))) % 174.01/173.89 [8838]~E(f777(f168(x88381,x88382,x88383),x88384),f185(x88382))+~P1(f777(f777(f336(x88381),x88384),f777(f305(f857(x88381,x88382),x88381,f242(x88381,x88382)),f777(f160(f857(x88381,x88382)),x88383)))) % 174.01/173.89 [8875]~P100(x88751)+P1(f777(f777(f234(x88751),f777(f777(f181(x88751),x88752),f777(f777(f238(x88751),x88753),x88754))),f777(f777(f238(x88751),f777(f777(f181(x88751),x88752),x88753)),f777(f777(f181(x88751),x88752),x88754)))) % 174.01/173.89 [8876]~P93(x88761)+P1(f777(f777(f234(x88761),f777(f777(f105(x88761),x88762),f777(f777(f106(x88761),x88763),x88764))),f777(f777(f106(x88761),f777(f777(f105(x88761),x88762),x88763)),f777(f777(f105(x88761),x88762),x88764)))) % 174.01/173.89 [9020]E(x90201,x90202)+~P1(f777(f777(f336(f857(x90203,x90203)),f777(f777(f243(x90203,x90203),x90201),x90202)),f777(f160(f857(x90203,x90203)),f777(f777(f169(x90203,x90203),x90204),x90204)))) % 174.01/173.89 [9050]~P1(f777(f777(f336(f857(x90501,x90501)),f777(f777(f243(x90501,x90501),x90503),x90502)),f302(x90501,x90504)))+~P36(x90501,f777(f777(f304(f857(x90501,x90501)),f777(f777(f243(x90501,x90501),x90502),x90503)),x90504)) % 174.01/173.89 [9051]~P1(f777(f777(f336(f857(x90511,x90511)),f777(f777(f243(x90511,x90511),x90513),x90512)),f302(x90511,x90514)))+~P56(x90511,f777(f777(f304(f857(x90511,x90511)),f777(f777(f243(x90511,x90511),x90512),x90513)),x90514)) % 174.01/173.89 [9095]~P100(x90951)+P1(f777(f777(f234(x90951),f777(f777(f181(x90951),f777(f777(f238(x90951),x90952),x90953)),f777(f777(f238(x90951),x90952),x90954))),f777(f777(f238(x90951),x90952),f777(f777(f181(x90951),x90953),x90954)))) % 174.01/173.89 [9096]~P93(x90961)+P1(f777(f777(f234(x90961),f777(f777(f105(x90961),f777(f777(f106(x90961),x90962),x90963)),f777(f777(f106(x90961),x90962),x90964))),f777(f777(f106(x90961),x90962),f777(f777(f105(x90961),x90963),x90964)))) % 174.01/173.89 [9159]~E(f777(f305(x91592,x91591,x91593),f241(f858(x91592,a845))),f241(f858(x91591,a845)))+P1(f777(f777(f234(f858(x91591,a845)),f777(f83(f858(x91591,a845)),f777(f305(x91592,x91591,x91593),x91594))),f777(f305(x91592,x91591,x91593),f777(f83(f858(x91592,a845)),x91594)))) % 174.01/173.89 [9462]P1(f777(f777(f336(f857(x94621,x94621)),f777(f777(f243(x94621,x94621),x94622),x94623)),f777(f280(x94621,x94621),f777(f777(f283(x94621,x94621,x94621),x94624),f302(x94621,x94624)))))+~P1(f777(f777(f336(f857(x94621,x94621)),f777(f777(f243(x94621,x94621),x94622),x94623)),f777(f777(f283(x94621,x94621,x94621),f777(f280(x94621,x94621),x94624)),f302(x94621,f777(f280(x94621,x94621),x94624))))) % 174.01/173.89 [9463]~P1(f777(f777(f336(f857(x94631,x94631)),f777(f777(f243(x94631,x94631),x94632),x94633)),f777(f280(x94631,x94631),f777(f777(f283(x94631,x94631,x94631),x94634),f302(x94631,x94634)))))+P1(f777(f777(f336(f857(x94631,x94631)),f777(f777(f243(x94631,x94631),x94632),x94633)),f777(f777(f283(x94631,x94631,x94631),f777(f280(x94631,x94631),x94634)),f302(x94631,f777(f280(x94631,x94631),x94634))))) % 174.01/173.89 [9488]~P1(f777(f777(f336(x94882),x94884),f777(f261(x94881,x94882),x94883)))+P1(f777(f777(f336(f857(x94881,x94882)),f777(f777(f243(x94881,x94882),f596(x94883,x94881,x94884,x94882)),x94884)),x94883)) % 174.01/173.89 [9489]~P1(f777(f777(f336(x94892),x94894),f777(f261(x94891,x94892),x94893)))+P1(f777(f777(f336(f857(x94891,x94892)),f777(f777(f243(x94891,x94892),f597(x94893,x94891,x94894,x94892)),x94894)),x94893)) % 174.01/173.89 [9508]~P1(f777(f777(f336(x95081),x95084),f777(f777(f105(f858(x95081,a845)),x95082),x95083)))+P1(f777(f777(f777(f105(f858(x95081,a845)),f777(f777(f11(x95081,f858(x95081,a845),a845),f336(x95081)),x95082)),f777(f777(f11(x95081,f858(x95081,a845),a845),f336(x95081)),x95083)),x95084)) % 174.01/173.89 [9509]~P1(f777(f777(f336(x95091),x95094),f777(f777(f106(f858(x95091,a845)),x95092),x95093)))+P1(f777(f777(f777(f106(f858(x95091,a845)),f777(f777(f11(x95091,f858(x95091,a845),a845),f336(x95091)),x95092)),f777(f777(f11(x95091,f858(x95091,a845),a845),f336(x95091)),x95093)),x95094)) % 174.01/173.89 [9582]~P1(f777(f777(f336(f857(x95821,x95821)),f777(f777(f243(x95821,x95821),x95824),x95823)),f777(f777(f283(x95821,x95821,x95821),x95822),f302(x95821,x95822))))+P1(f777(f777(f336(f857(x95821,x95821)),f777(f777(f243(x95821,x95821),f657(x95822,x95823,x95824,x95821)),x95823)),x95822)) % 174.01/173.89 [9617]P1(f777(f777(f336(x96171),x96172),f777(f777(f105(f858(x96171,a845)),x96173),x96174)))+~P1(f777(f777(f777(f105(f858(x96171,a845)),f777(f777(f11(x96171,f858(x96171,a845),a845),f336(x96171)),x96173)),f777(f777(f11(x96171,f858(x96171,a845),a845),f336(x96171)),x96174)),x96172)) % 174.01/173.89 [9618]P1(f777(f777(f336(x96181),x96182),f777(f777(f106(f858(x96181,a845)),x96183),x96184)))+~P1(f777(f777(f777(f106(f858(x96181,a845)),f777(f777(f11(x96181,f858(x96181,a845),a845),f336(x96181)),x96183)),f777(f777(f11(x96181,f858(x96181,a845),a845),f336(x96181)),x96184)),x96182)) % 174.01/173.89 [9896]P34(x98961,f777(f777(f11(x98961,f858(f857(x98961,x98961),a845),f858(x98961,a845)),f777(f777(f12(f858(x98961,f858(f858(f857(x98961,x98961),a845),a845)),f858(f858(f857(x98961,x98961),a845),f858(x98961,a845)),x98961),f11(x98961,f858(f857(x98961,x98961),a845),a845)),f777(f777(f12(f858(x98961,f857(x98961,x98961)),f858(x98961,f858(f858(f857(x98961,x98961),a845),a845)),x98961),f777(f12(f857(x98961,x98961),f858(f858(f857(x98961,x98961),a845),a845),x98961),f336(f857(x98961,x98961)))),f243(x98961,x98961)))),x98962),x98963,x98964)+~P1(f777(f777(f336(f857(f852(x98961),f852(x98961))),f777(f777(f243(f852(x98961),f852(x98961)),x98963),x98964)),f149(x98961,x98962))) % 174.01/173.89 [9900]P57(x99001,f777(f777(f11(x99001,f858(f857(x99001,x99001),a845),f858(x99001,a845)),f777(f777(f12(f858(x99001,f858(f858(f857(x99001,x99001),a845),a845)),f858(f858(f857(x99001,x99001),a845),f858(x99001,a845)),x99001),f11(x99001,f858(f857(x99001,x99001),a845),a845)),f777(f777(f12(f858(x99001,f857(x99001,x99001)),f858(x99001,f858(f858(f857(x99001,x99001),a845),a845)),x99001),f777(f12(f857(x99001,x99001),f858(f858(f857(x99001,x99001),a845),a845),x99001),f336(f857(x99001,x99001)))),f243(x99001,x99001)))),x99002),x99003,x99004)+~P1(f777(f777(f336(f857(f858(x99001,a845),f858(x99001,a845))),f777(f777(f243(f858(x99001,a845),f858(x99001,a845)),x99003),x99004)),f326(x99001,x99002))) % 174.01/173.89 [9929]E(x99291,x99292)+~E(f777(f777(f11(x99293,f858(f857(x99293,x99294),a845),f858(x99294,a845)),f777(f777(f12(f858(x99294,f858(f858(f857(x99293,x99294),a845),a845)),f858(f858(f857(x99293,x99294),a845),f858(x99294,a845)),x99293),f11(x99294,f858(f857(x99293,x99294),a845),a845)),f777(f777(f12(f858(x99294,f857(x99293,x99294)),f858(x99294,f858(f858(f857(x99293,x99294),a845),a845)),x99293),f777(f12(f857(x99293,x99294),f858(f858(f857(x99293,x99294),a845),a845),x99294),f336(f857(x99293,x99294)))),f243(x99293,x99294)))),x99291),f777(f777(f11(x99293,f858(f857(x99293,x99294),a845),f858(x99294,a845)),f777(f777(f12(f858(x99294,f858(f858(f857(x99293,x99294),a845),a845)),f858(f858(f857(x99293,x99294),a845),f858(x99294,a845)),x99293),f11(x99294,f858(f857(x99293,x99294),a845),a845)),f777(f777(f12(f858(x99294,f857(x99293,x99294)),f858(x99294,f858(f858(f857(x99293,x99294),a845),a845)),x99293),f777(f12(f857(x99293,x99294),f858(f858(f857(x99293,x99294),a845),a845),x99294),f336(f857(x99293,x99294)))),f243(x99293,x99294)))),x99292)) % 174.01/173.89 [9932]~P34(x99321,f777(f777(f11(x99321,f858(f857(x99321,x99321),a845),f858(x99321,a845)),f777(f777(f12(f858(x99321,f858(f858(f857(x99321,x99321),a845),a845)),f858(f858(f857(x99321,x99321),a845),f858(x99321,a845)),x99321),f11(x99321,f858(f857(x99321,x99321),a845),a845)),f777(f777(f12(f858(x99321,f857(x99321,x99321)),f858(x99321,f858(f858(f857(x99321,x99321),a845),a845)),x99321),f777(f12(f857(x99321,x99321),f858(f858(f857(x99321,x99321),a845),a845),x99321),f336(f857(x99321,x99321)))),f243(x99321,x99321)))),x99324),x99322,x99323)+P1(f777(f777(f336(f857(f852(x99321),f852(x99321))),f777(f777(f243(f852(x99321),f852(x99321)),x99322),x99323)),f149(x99321,x99324))) % 174.01/173.89 [9933]~P57(x99331,f777(f777(f11(x99331,f858(f857(x99331,x99331),a845),f858(x99331,a845)),f777(f777(f12(f858(x99331,f858(f858(f857(x99331,x99331),a845),a845)),f858(f858(f857(x99331,x99331),a845),f858(x99331,a845)),x99331),f11(x99331,f858(f857(x99331,x99331),a845),a845)),f777(f777(f12(f858(x99331,f857(x99331,x99331)),f858(x99331,f858(f858(f857(x99331,x99331),a845),a845)),x99331),f777(f12(f857(x99331,x99331),f858(f858(f857(x99331,x99331),a845),a845),x99331),f336(f857(x99331,x99331)))),f243(x99331,x99331)))),x99334),x99332,x99333)+P1(f777(f777(f336(f857(f858(x99331,a845),f858(x99331,a845))),f777(f777(f243(f858(x99331,a845),f858(x99331,a845)),x99332),x99333)),f326(x99331,x99334))) % 174.01/173.89 [7427]~P88(x74271)+E(f777(f777(f84(x74271),f777(f108(x74271),x74272)),f777(f777(f84(x74271),f777(f108(x74271),x74273)),x74274)),f777(f777(f84(x74271),f777(f108(x74271),f777(f777(f84(a3),x74272),x74273))),x74274)) % 174.01/173.89 [7428]~P88(x74281)+E(f777(f777(f84(x74281),f777(f108(x74281),x74282)),f777(f777(f5(x74281),f777(f108(x74281),x74283)),x74284)),f777(f777(f5(x74281),f777(f108(x74281),f777(f777(f84(a3),x74282),x74283))),x74284)) % 174.01/173.89 [7429]~P88(x74291)+E(f777(f777(f85(x74291),f777(f108(x74291),x74292)),f777(f777(f85(x74291),f777(f108(x74291),x74293)),x74294)),f777(f777(f85(x74291),f777(f108(x74291),f777(f777(f85(a3),x74292),x74293))),x74294)) % 174.01/173.89 [7476]~P2(x74761)+E(f777(f157(x74761),f777(f777(f145(x74762,x74761),f777(f20(x74761,x74762),x74763)),x74764)),f777(f777(f85(x74761),f777(f104(x74761),f777(f183(f852(x74762)),x74764))),x74763)) % 174.01/173.89 [7712]E(f777(f267(x77121,f777(f777(f142(f857(a103,x77121)),x77122),x77123)),x77124),f777(f252(a103,x77121),x77122))+~P1(f777(f777(f235(a103),x77124),f777(f242(a103,x77121),x77122))) % 174.01/173.89 [7760]~P88(x77601)+E(f777(f777(f84(x77601),f777(f108(x77601),x77602)),f777(f777(f5(x77601),x77603),f777(f108(x77601),x77604))),f777(f777(f84(x77601),f777(f108(x77601),f777(f777(f84(a3),x77602),f777(f83(a3),x77604)))),x77603)) % 174.01/173.89 [7891]E(f777(f267(x78911,x78912),f777(f777(f5(a103),x78913),f777(f242(a103,x78911),x78914))),f777(f267(x78911,f777(f777(f142(f857(a103,x78911)),x78914),x78912)),x78913))+P1(f777(f777(f235(a103),x78913),f777(f242(a103,x78911),x78914))) % 174.01/173.89 [8322]~P1(f777(f777(f336(x83221),x83222),f777(f160(x83221),f118(x83221,x83224))))+P1(f777(f777(f336(x83221),x83222),f777(f160(x83221),f118(x83221,f777(f777(f127(x83221),x83223),x83224))))) % 174.01/173.89 [8323]~P1(f777(f777(f336(x83231),x83232),f777(f160(x83231),f118(x83231,x83233))))+P1(f777(f777(f336(x83231),x83232),f777(f160(x83231),f118(x83231,f777(f777(f127(x83231),x83233),x83234))))) % 174.01/173.89 [8346]E(f777(f777(f105(f858(x83461,a845)),f777(f777(f106(f858(x83461,a845)),x83462),x83463)),x83464),f777(f777(f106(f858(x83461,a845)),x83462),f777(f777(f105(f858(x83461,a845)),x83463),x83464)))+~P1(f777(f777(f234(f858(x83461,a845)),x83464),x83462)) % 174.01/173.89 [8633]~E(f777(f777(f105(f858(x86331,a845)),f777(f777(f106(f858(x86331,a845)),x86333),x86334)),x86332),f777(f777(f106(f858(x86331,a845)),x86333),f777(f777(f105(f858(x86331,a845)),x86334),x86332)))+P1(f777(f777(f234(f858(x86331,a845)),x86332),x86333)) % 174.01/173.89 [8882]~P1(f777(f777(f234(f858(x88821,a845)),x88822),f777(f777(f105(f858(x88821,a845)),x88823),x88824)))+P1(f777(f777(f234(f858(x88821,a845)),f777(f777(f5(f858(x88821,a845)),x88822),x88823)),x88824)) % 174.01/173.89 [9001]P1(f777(f777(f234(f858(x90011,a845)),x90012),f777(f777(f105(f858(x90011,a845)),x90013),x90014)))+~P1(f777(f777(f234(f858(x90011,a845)),f777(f777(f5(f858(x90011,a845)),x90012),x90013)),x90014)) % 174.01/173.89 [9077]~P79(x90771)+E(f777(f79(x90771),f777(f777(f10(x90772,x90771),f777(f777(f12(x90771,x90771,x90772),f79(x90771)),x90773)),x90774)),f777(f777(f10(x90772,x90771),f777(f777(f12(x90771,x90771,x90772),f79(x90771)),x90773)),x90774)) % 174.01/173.89 [9222]~P79(x92221)+P1(f777(f777(f234(x92221),f4(x92221)),f777(f777(f10(x92222,x92221),f777(f777(f12(x92221,x92221,x92222),f79(x92221)),x92223)),x92224))) % 174.01/173.89 [9225]~P6(x92251)+E(f777(f157(x92251),f777(f777(f145(x92252,x92251),f777(f77(x92251,x92251,x92252,f83(x92251)),x92253)),x92254)),f777(f83(x92251),f777(f157(x92251),f777(f777(f145(x92252,x92251),x92253),x92254)))) % 174.01/173.89 [9362]~P79(x93621)+P1(f777(f777(f234(x93621),f777(f79(x93621),f777(f777(f10(x93622,x93621),x93623),x93624))),f777(f777(f10(x93622,x93621),f777(f777(f12(x93621,x93621,x93622),f79(x93621)),x93623)),x93624))) % 174.01/173.89 [9390]~E(f777(f777(f84(a851),x93901),x93904),f777(f777(f84(a851),x93903),x93902))+P1(f777(f777(f336(f857(f857(a851,a851),f857(a851,a851))),f777(f777(f243(f857(a851,a851),f857(a851,a851)),f777(f777(f243(a851,a851),x93901),x93902)),f777(f777(f243(a851,a851),x93903),x93904))),a113)) % 174.01/173.89 [9391]~P1(f777(f777(f235(a851),x93911),x93913))+P1(f777(f777(f336(f857(f857(a851,a851),f857(a851,a851))),f777(f777(f243(f857(a851,a851),f857(a851,a851)),f777(f777(f243(a851,a851),x93911),x93912)),f777(f777(f243(a851,a851),x93913),x93914))),a42)) % 174.01/173.89 [9392]~P1(f777(f777(f235(a851),x93921),x93923))+P1(f777(f777(f336(f857(f857(a851,a851),f857(a851,a851))),f777(f777(f243(f857(a851,a851),f857(a851,a851)),f777(f777(f243(a851,a851),x93921),x93922)),f777(f777(f243(a851,a851),x93923),x93924))),a74)) % 174.01/173.89 [9531]E(f777(f777(f84(a851),x95311),x95312),f777(f777(f84(a851),x95313),x95314))+~P1(f777(f777(f336(f857(f857(a851,a851),f857(a851,a851))),f777(f777(f243(f857(a851,a851),f857(a851,a851)),f777(f777(f243(a851,a851),x95311),x95314)),f777(f777(f243(a851,a851),x95313),x95312))),a113)) % 174.01/173.89 [9575]~P1(f777(f777(f336(x95752),x95754),f777(f777(f48(x95751,f858(x95752,a845)),f241(f858(x95751,a845))),x95753)))+P1(f777(f777(f777(f48(x95751,f858(x95752,a845)),f241(f858(x95751,a845))),f777(f777(f12(f858(x95752,a845),f858(x95752,a845),x95751),f777(f11(x95752,f858(x95752,a845),a845),f336(x95752))),x95753)),x95754)) % 174.01/173.89 [9576]~P1(f777(f777(f336(x95762),x95764),f777(f777(f49(x95761,f858(x95762,a845)),f241(f858(x95761,a845))),x95763)))+P1(f777(f777(f777(f49(x95761,f858(x95762,a845)),f241(f858(x95761,a845))),f777(f777(f12(f858(x95762,a845),f858(x95762,a845),x95761),f777(f11(x95762,f858(x95762,a845),a845),f336(x95762))),x95763)),x95764)) % 174.01/173.89 [9642]~P1(f777(f58(x96421,x96422),f777(f777(f243(a3,a3),x96424),x96423)))+P1(f777(f58(f777(f83(a3),x96421),x96422),f777(f777(f243(a3,a3),f777(f777(f777(f100(a3),f777(f777(a332,x96423),f4(a3))),f777(f83(a3),x96424)),f777(f777(f5(a3),f777(f83(a3),x96424)),f82(a3)))),f777(f777(f777(f100(a3),f777(f777(a332,x96423),f4(a3))),f4(a3)),f777(f777(f5(a3),x96422),x96423))))) % 174.01/173.89 [9651]P1(f777(f777(f336(x96511),x96512),f777(f777(f48(x96513,f858(x96511,a845)),f241(f858(x96513,a845))),x96514)))+~P1(f777(f777(f777(f48(x96513,f858(x96511,a845)),f241(f858(x96513,a845))),f777(f777(f12(f858(x96511,a845),f858(x96511,a845),x96513),f777(f11(x96511,f858(x96511,a845),a845),f336(x96511))),x96514)),x96512)) % 174.01/173.89 [9652]P1(f777(f777(f336(x96521),x96522),f777(f777(f49(x96523,f858(x96521,a845)),f241(f858(x96523,a845))),x96524)))+~P1(f777(f777(f777(f49(x96523,f858(x96521,a845)),f241(f858(x96523,a845))),f777(f777(f12(f858(x96521,a845),f858(x96521,a845),x96523),f777(f11(x96521,f858(x96521,a845),a845),f336(x96521))),x96524)),x96522)) % 174.01/173.89 [9663]E(f777(f777(f48(a851,f858(x96631,a845)),f241(f858(a851,a845))),x96632),f777(f777(f48(a851,f858(x96631,a845)),f241(f858(a851,a845))),x96633))+~E(f777(f777(f48(a851,f858(x96631,a845)),f777(f296(a851,f4(a851)),f400(x96632,x96634,x96633,x96631))),x96633),f777(f777(f48(a851,f858(x96631,a845)),f777(f296(a851,f4(a851)),f777(f777(f84(a851),f400(x96632,x96634,x96633,x96631)),x96634))),x96632)) % 174.01/173.89 [9993]~P1(f777(f777(f234(f858(f857(x99931,x99932),a845)),x99933),x99934))+P1(f777(f777(f234(f858(x99931,f858(x99932,a845))),f777(f777(f11(x99931,f858(f857(x99931,x99932),a845),f858(x99932,a845)),f777(f777(f12(f858(x99932,f858(f858(f857(x99931,x99932),a845),a845)),f858(f858(f857(x99931,x99932),a845),f858(x99932,a845)),x99931),f11(x99932,f858(f857(x99931,x99932),a845),a845)),f777(f777(f12(f858(x99932,f857(x99931,x99932)),f858(x99932,f858(f858(f857(x99931,x99932),a845),a845)),x99931),f777(f12(f857(x99931,x99932),f858(f858(f857(x99931,x99932),a845),a845),x99932),f336(f857(x99931,x99932)))),f243(x99931,x99932)))),x99933)),f777(f777(f11(x99931,f858(f857(x99931,x99932),a845),f858(x99932,a845)),f777(f777(f12(f858(x99932,f858(f858(f857(x99931,x99932),a845),a845)),f858(f858(f857(x99931,x99932),a845),f858(x99932,a845)),x99931),f11(x99932,f858(f857(x99931,x99932),a845),a845)),f777(f777(f12(f858(x99932,f857(x99931,x99932)),f858(x99932,f858(f858(f857(x99931,x99932),a845),a845)),x99931),f777(f12(f857(x99931,x99932),f858(f858(f857(x99931,x99932),a845),a845),x99932),f336(f857(x99931,x99932)))),f243(x99931,x99932)))),x99934))) % 174.01/173.89 [10009]P1(f777(f777(f234(f858(f857(x100091,x100092),a845)),x100093),x100094))+~P1(f777(f777(f234(f858(x100091,f858(x100092,a845))),f777(f777(f11(x100091,f858(f857(x100091,x100092),a845),f858(x100092,a845)),f777(f777(f12(f858(x100092,f858(f858(f857(x100091,x100092),a845),a845)),f858(f858(f857(x100091,x100092),a845),f858(x100092,a845)),x100091),f11(x100092,f858(f857(x100091,x100092),a845),a845)),f777(f777(f12(f858(x100092,f857(x100091,x100092)),f858(x100092,f858(f858(f857(x100091,x100092),a845),a845)),x100091),f777(f12(f857(x100091,x100092),f858(f858(f857(x100091,x100092),a845),a845),x100092),f336(f857(x100091,x100092)))),f243(x100091,x100092)))),x100093)),f777(f777(f11(x100091,f858(f857(x100091,x100092),a845),f858(x100092,a845)),f777(f777(f12(f858(x100092,f858(f858(f857(x100091,x100092),a845),a845)),f858(f858(f857(x100091,x100092),a845),f858(x100092,a845)),x100091),f11(x100092,f858(f857(x100091,x100092),a845),a845)),f777(f777(f12(f858(x100092,f857(x100091,x100092)),f858(x100092,f858(f858(f857(x100091,x100092),a845),a845)),x100091),f777(f12(f857(x100091,x100092),f858(f858(f857(x100091,x100092),a845),a845),x100092),f336(f857(x100091,x100092)))),f243(x100091,x100092)))),x100094))) % 174.01/173.89 [9122]~P1(f777(f777(f336(f857(x91221,x91221)),x91222),f302(x91221,x91224)))+P1(f777(f777(f336(f857(x91221,x91221)),x91222),f302(x91221,f777(f777(f105(f858(f857(x91221,x91221),a845)),x91223),x91224)))) % 174.01/173.89 [9123]~P1(f777(f777(f336(f857(x91231,x91231)),x91232),f302(x91231,x91233)))+P1(f777(f777(f336(f857(x91231,x91231)),x91232),f302(x91231,f777(f777(f105(f858(f857(x91231,x91231),a845)),x91233),x91234)))) % 174.01/173.89 [9454]~E(f777(f160(x94541),x94544),f171(x94541,x94542,x94543))+E(f168(x94541,x94542,f777(f777(f145(x94541,f857(x94541,x94542)),f777(f777(f22(x94541,x94542,f857(x94541,x94542)),f243(x94541,x94542)),f777(f777(f12(f855(x94542),x94542,x94541),f233(x94542)),x94543))),x94544)),x94543) % 174.01/173.89 [9745]~P1(f777(f777(f235(a851),f777(f777(f84(a851),x97451),x97454)),f777(f777(f84(a851),x97453),x97452)))+P1(f777(f777(f235(a3),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x97451),x97452)),f182(f858(f857(a851,a851),a845)))))),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x97453),x97454)),f182(f858(f857(a851,a851),a845))))))) % 174.01/173.89 [9746]~P1(f777(f777(f234(a851),f777(f777(f84(a851),x97461),x97464)),f777(f777(f84(a851),x97463),x97462)))+P1(f777(f777(f234(a3),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x97461),x97462)),f182(f858(f857(a851,a851),a845)))))),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x97463),x97464)),f182(f858(f857(a851,a851),a845))))))) % 174.01/173.89 [9834]P1(f777(f777(f235(a851),f777(f777(f84(a851),x98341),x98342)),f777(f777(f84(a851),x98343),x98344)))+~P1(f777(f777(f235(a3),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x98341),x98344)),f182(f858(f857(a851,a851),a845)))))),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x98343),x98342)),f182(f858(f857(a851,a851),a845))))))) % 174.01/173.89 [9835]P1(f777(f777(f234(a851),f777(f777(f84(a851),x98351),x98352)),f777(f777(f84(a851),x98353),x98354)))+~P1(f777(f777(f234(a3),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x98351),x98354)),f182(f858(f857(a851,a851),a845)))))),f777(a93,f777(f279(f857(a851,a851),f857(a851,a851),a113),f777(f777(f304(f857(a851,a851)),f777(f777(f243(a851,a851),x98353),x98352)),f182(f858(f857(a851,a851),a845))))))) % 174.01/173.89 [9882]P1(f777(f777(f234(f858(x98821,a845)),f777(f777(f48(a851,f858(x98821,a845)),f241(f858(a851,a845))),x98822)),f777(f777(f48(a851,f858(x98821,a845)),f241(f858(a851,a845))),x98823)))+~P1(f777(f777(f234(f858(x98821,a845)),f777(f777(f48(a851,f858(x98821,a845)),f777(f296(a851,f4(a851)),f401(x98823,x98824,x98822,x98821))),x98822)),f777(f777(f48(a851,f858(x98821,a845)),f777(f296(a851,f4(a851)),f777(f777(f84(a851),f401(x98823,x98824,x98822,x98821)),x98824))),x98823))) % 174.01/173.89 [9935]P1(f777(f777(f234(a103),x99354),f4(a103)))+E(f777(f777(f255(f857(a103,a103),f857(x99351,f858(a854,a844)),f857(a103,a103),f857(f858(a103,f858(a845,f855(f853(x99351)))),f857(a103,a103))),f777(x99352,x99353)),f777(f777(f12(f858(f858(a103,f858(a845,f855(f853(x99351)))),f858(f857(a103,a103),f857(f858(a103,f858(a845,f855(f853(x99351)))),f857(a103,a103)))),f858(f857(a103,a103),f857(f858(a103,f858(a845,f855(f853(x99351)))),f857(a103,a103))),f857(x99351,f858(a854,a844))),f777(f255(f857(a103,a103),f858(a103,f858(a845,f855(f853(x99351)))),f857(a103,a103),f857(f858(a103,f858(a845,f855(f853(x99351)))),f857(a103,a103))),f274(x99351,x99352,f777(f777(f5(a103),x99354),f82(a103)),x99353))),f777(f777(f12(f858(f858(a103,f858(a845,f855(f853(x99351)))),f858(a103,f858(a845,f855(f853(x99351))))),f858(f858(a103,f858(a845,f855(f853(x99351)))),f858(f857(a103,a103),f857(f858(a103,f858(a845,f855(f853(x99351)))),f857(a103,a103)))),f857(x99351,f858(a854,a844))),f777(f12(f858(a103,f858(a845,f855(f853(x99351)))),f858(f857(a103,a103),f857(f858(a103,f858(a845,f855(f853(x99351)))),f857(a103,a103))),f858(a103,f858(a845,f855(f853(x99351))))),f243(f858(a103,f858(a845,f855(f853(x99351)))),f857(a103,a103)))),f777(f777(f12(f858(a103,f858(a845,f855(f853(x99351)))),f858(f858(a103,f858(a845,f855(f853(x99351)))),f858(a103,f858(a845,f855(f853(x99351))))),f857(x99351,f858(a854,a844))),f53(x99351)),f777(f777(f12(x99351,f858(a103,f858(a845,f855(f853(x99351)))),f857(x99351,f858(a854,a844))),f51(x99351)),f242(x99351,f858(a854,a844))))))),f274(x99351,x99352,x99354,x99353)) % 174.01/173.89 [9984]~P1(f777(f777(f336(x99842),x99844),f777(f261(x99841,x99842),x99843)))+P1(f777(f249(x99841,x99842,f777(f777(f11(x99841,f858(f857(x99841,x99842),a845),f858(x99842,a845)),f777(f777(f12(f858(x99842,f858(f858(f857(x99841,x99842),a845),a845)),f858(f858(f857(x99841,x99842),a845),f858(x99842,a845)),x99841),f11(x99842,f858(f857(x99841,x99842),a845),a845)),f777(f777(f12(f858(x99842,f857(x99841,x99842)),f858(x99842,f858(f858(f857(x99841,x99842),a845),a845)),x99841),f777(f12(f857(x99841,x99842),f858(f858(f857(x99841,x99842),a845),a845),x99842),f336(f857(x99841,x99842)))),f243(x99841,x99842)))),x99843)),x99844)) % 174.01/173.89 [9985]~P1(f777(f777(f336(x99851),x99854),f777(f263(x99851,x99852),x99853)))+P1(f777(f248(x99851,x99852,f777(f777(f11(x99851,f858(f857(x99851,x99852),a845),f858(x99852,a845)),f777(f777(f12(f858(x99852,f858(f858(f857(x99851,x99852),a845),a845)),f858(f858(f857(x99851,x99852),a845),f858(x99852,a845)),x99851),f11(x99852,f858(f857(x99851,x99852),a845),a845)),f777(f777(f12(f858(x99852,f857(x99851,x99852)),f858(x99852,f858(f858(f857(x99851,x99852),a845),a845)),x99851),f777(f12(f857(x99851,x99852),f858(f858(f857(x99851,x99852),a845),a845),x99852),f336(f857(x99851,x99852)))),f243(x99851,x99852)))),x99853)),x99854)) % 174.01/173.89 [9996]P1(f777(f777(f336(x99961),x99962),f777(f261(x99963,x99961),x99964)))+~P1(f777(f249(x99963,x99961,f777(f777(f11(x99963,f858(f857(x99963,x99961),a845),f858(x99961,a845)),f777(f777(f12(f858(x99961,f858(f858(f857(x99963,x99961),a845),a845)),f858(f858(f857(x99963,x99961),a845),f858(x99961,a845)),x99963),f11(x99961,f858(f857(x99963,x99961),a845),a845)),f777(f777(f12(f858(x99961,f857(x99963,x99961)),f858(x99961,f858(f858(f857(x99963,x99961),a845),a845)),x99963),f777(f12(f857(x99963,x99961),f858(f858(f857(x99963,x99961),a845),a845),x99961),f336(f857(x99963,x99961)))),f243(x99963,x99961)))),x99964)),x99962)) % 174.01/173.89 [9997]P1(f777(f777(f336(x99971),x99972),f777(f263(x99971,x99973),x99974)))+~P1(f777(f248(x99971,x99973,f777(f777(f11(x99971,f858(f857(x99971,x99973),a845),f858(x99973,a845)),f777(f777(f12(f858(x99973,f858(f858(f857(x99971,x99973),a845),a845)),f858(f858(f857(x99971,x99973),a845),f858(x99973,a845)),x99971),f11(x99973,f858(f857(x99971,x99973),a845),a845)),f777(f777(f12(f858(x99973,f857(x99971,x99973)),f858(x99973,f858(f858(f857(x99971,x99973),a845),a845)),x99971),f777(f12(f857(x99971,x99973),f858(f858(f857(x99971,x99973),a845),a845),x99973),f336(f857(x99971,x99973)))),f243(x99971,x99973)))),x99974)),x99972)) % 174.01/173.89 [9759]~P85(x97591)+E(f777(f777(f85(x97591),f777(f777(f84(x97591),f82(x97591)),f82(x97591))),f777(f777(f10(a851,x97591),f777(f777(f12(x97591,x97591,a851),f777(f84(x97591),x97592)),f777(f777(f11(a851,x97591,x97591),f777(f777(f12(x97591,f858(x97591,x97591),a851),f85(x97591)),f104(x97591))),x97593))),f777(f259(a851),x97594))),f777(f777(f85(x97591),f777(f104(x97591),x97594)),f777(f777(f84(x97591),x97592),f777(f777(f84(x97591),x97592),f777(f777(f85(x97591),f777(f104(x97591),f777(f777(f5(a851),x97594),f82(a851)))),x97593))))) % 174.01/173.89 [9903]P1(f777(x99031,f593(x99032,x99033,x99034,x99031)))+P36(x99032,f777(f258(f857(x99032,x99032)),f777(f253(x99032,x99032,a845),f777(f777(f12(f858(x99032,a845),f858(x99032,a845),x99032),f777(f22(x99032,a845,a845),f777(f777(f12(a845,f858(a845,a845),x99032),a333),x99031))),f777(f777(f11(x99032,f858(x99032,x99032),f858(x99032,a845)),f777(f777(f12(f858(x99032,a845),f858(f858(x99032,x99032),f858(x99032,a845)),x99032),f12(x99032,a845,x99032)),a332)),x99033))))) % 174.01/173.89 [9917]~P1(f777(f777(f235(a851),f777(x99174,f777(x99173,f593(x99171,x99173,x99174,x99172)))),f777(x99174,f593(x99171,x99173,x99174,x99172))))+P36(x99171,f777(f258(f857(x99171,x99171)),f777(f253(x99171,x99171,a845),f777(f777(f12(f858(x99171,a845),f858(x99171,a845),x99171),f777(f22(x99171,a845,a845),f777(f777(f12(a845,f858(a845,a845),x99171),a333),x99172))),f777(f777(f11(x99171,f858(x99171,x99171),f858(x99171,a845)),f777(f777(f12(f858(x99171,a845),f858(f858(x99171,x99171),f858(x99171,a845)),x99171),f12(x99171,a845,x99171)),a332)),x99173))))) % 174.01/173.89 [10021]~P1(f777(f777(f336(f857(x100211,x100211)),f777(f777(f243(x100211,x100211),x100213),x100214)),f777(f777(f105(f858(f857(x100211,x100211),a845)),x100212),f302(x100211,f182(f858(f857(x100211,x100211),a845))))))+P1(f777(f777(f777(f777(f105(f858(x100211,f858(x100211,a845))),f777(f777(f11(x100211,f858(f857(x100211,x100211),a845),f858(x100211,a845)),f777(f777(f12(f858(x100211,f858(f858(f857(x100211,x100211),a845),a845)),f858(f858(f857(x100211,x100211),a845),f858(x100211,a845)),x100211),f11(x100211,f858(f857(x100211,x100211),a845),a845)),f777(f777(f12(f858(x100211,f857(x100211,x100211)),f858(x100211,f858(f858(f857(x100211,x100211),a845),a845)),x100211),f777(f12(f857(x100211,x100211),f858(f858(f857(x100211,x100211),a845),a845),x100211),f336(f857(x100211,x100211)))),f243(x100211,x100211)))),x100212)),a332),x100213),x100214)) % 174.01/173.89 [10029]P1(f777(f777(f336(f857(x100291,x100291)),f777(f777(f243(x100291,x100291),x100292),x100293)),f777(f777(f105(f858(f857(x100291,x100291),a845)),x100294),f302(x100291,f182(f858(f857(x100291,x100291),a845))))))+~P1(f777(f777(f777(f777(f105(f858(x100291,f858(x100291,a845))),f777(f777(f11(x100291,f858(f857(x100291,x100291),a845),f858(x100291,a845)),f777(f777(f12(f858(x100291,f858(f858(f857(x100291,x100291),a845),a845)),f858(f858(f857(x100291,x100291),a845),f858(x100291,a845)),x100291),f11(x100291,f858(f857(x100291,x100291),a845),a845)),f777(f777(f12(f858(x100291,f857(x100291,x100291)),f858(x100291,f858(f858(f857(x100291,x100291),a845),a845)),x100291),f777(f12(f857(x100291,x100291),f858(f858(f857(x100291,x100291),a845),a845),x100291),f336(f857(x100291,x100291)))),f243(x100291,x100291)))),x100294)),a332),x100292),x100293)) % 174.01/173.89 [9981]E(f777(f777(f142(f852(x99811)),f777(f777(f142(x99811),x99812),f777(f134(f852(x99811),f852(x99811),f127(x99811),f117(x99811)),f777(f777(f145(f852(x99811),f852(x99811)),f147(f852(x99811),x99811,f117(x99811),f777(f777(f12(f852(x99811),f858(f852(x99811),f852(x99811)),x99811),f20(f852(x99811),f852(x99811))),f777(f777(f11(x99811,f852(x99811),f852(x99811)),f142(x99811)),f117(x99811))))),x99813)))),f166(x99811,f777(f777(f142(f852(x99811)),x99814),f777(f134(f852(f852(x99811)),f852(f852(x99811)),f127(f852(x99811)),f117(f852(x99811))),f777(f777(f145(f852(x99811),f852(f852(x99811))),f147(f852(f852(x99811)),x99811,f117(f852(x99811)),f777(f20(f858(f852(x99811),f852(f852(x99811))),x99811),f777(f777(f11(f852(x99811),f852(f852(x99811)),f852(f852(x99811))),f142(f852(x99811))),f117(f852(x99811)))))),x99813))))),f166(x99811,f777(f777(f142(f852(x99811)),f777(f777(f142(x99811),x99812),x99814)),x99813)))+~P1(f777(f323(f852(f852(x99811)),f167(x99811)),f777(f777(f142(f852(x99811)),f777(f777(f142(x99811),x99812),x99814)),x99813))) % 174.01/173.89 [10020]~P1(f777(f65(x100202),f777(f258(x100202),x100204)))+P1(f777(f65(x100201),f777(f258(x100201),f777(f777(f12(f858(x100202,a845),a845,x100201),f91(x100202)),f777(f777(f11(x100201,f858(x100202,a845),f858(x100202,a845)),f777(f777(f12(f858(x100202,f858(a845,a845)),f858(f858(x100202,a845),f858(x100202,a845)),x100201),f22(x100202,a845,a845)),f777(f777(f12(f858(x100202,a845),f858(x100202,f858(a845,a845)),x100201),f777(f12(a845,f858(a845,a845),x100202),a333)),f777(f777(f11(x100201,f858(x100202,x100201),f858(x100202,a845)),f777(f777(f12(f858(x100201,a845),f858(f858(x100202,x100201),f858(x100202,a845)),x100201),f12(x100201,a845,x100202)),a332)),x100203)))),x100204))))) % 174.01/173.89 [7182]E(x71821,x71822)+~E(f318(x71823,x71824,x71825,x71821),f318(x71823,x71824,x71825,x71822)) % 174.01/173.89 [7183]E(x71831,x71832)+~E(f319(x71833,x71834,x71835,x71831),f319(x71833,x71834,x71835,x71832)) % 174.01/173.89 [8995]~P39(f38(x89951,x89955),x89952,x89953,x89954)+P39(x89951,x89952,x89953,f373(x89954,x89953,x89952,x89955,x89951)) % 174.01/173.89 [8996]~P39(f38(x89961,x89965),x89962,x89963,x89964)+P39(x89961,x89962,x89963,f385(x89964,x89963,x89962,x89965,x89961)) % 174.01/173.89 [8997]~P39(f38(x89975,x89971),x89974,x89973,x89972)+P39(x89971,f373(x89972,x89973,x89974,x89971,x89975),x89973,x89972) % 174.01/173.89 [8998]~P39(f38(x89985,x89981),x89984,x89983,x89982)+P39(x89981,f385(x89982,x89983,x89984,x89981,x89985),x89983,x89982) % 174.01/173.89 [5529]E(f777(f777(f304(x55291),x55292),f171(x55291,x55293,x55294)),f171(x55291,x55293,x55294))+~E(f777(x55294,x55292),f777(f229(x55293),x55295)) % 174.01/173.89 [5943]P1(f777(f249(x59431,x59432,x59433),x59434))+~P1(f777(f777(x59433,x59435),x59434)) % 174.01/173.89 [5945]P1(f777(f248(x59451,x59452,x59453),x59454))+~P1(f777(f777(x59453,x59454),x59455)) % 174.01/173.89 [5948]~E(f777(x59484,x59482),f777(f229(x59483),x59485))+P1(f777(f777(f336(x59481),x59482),f171(x59481,x59483,x59484))) % 174.01/173.89 [5949]~E(f777(x59494,x59495),f777(f229(x59491),x59492))+P1(f777(f777(f336(x59491),x59492),f173(x59493,x59491,x59494))) % 174.01/173.89 [6433]~E(x64335,f4(a103))+E(f777(f195(x64331,x64332,x64333,x64334),x64335),f119(x64332)) % 174.01/173.89 [6434]~E(x64345,f4(a103))+E(f777(f193(x64341,x64342,x64343,x64344),x64345),f126(x64342)) % 174.01/173.89 [6530]~P39(f30(x65303,x65304),x65302,x65305,x65301)+E(x65301,f777(f777(f777(a191,x65302),x65303),f777(x65304,x65302))) % 174.01/173.89 [6575]~E(x65753,f4(a103))+E(f777(f270(x65751,x65752,x65753,x65754),x65755),f777(f243(x65751,x65752),x65755)) % 174.01/173.89 [6655]~E(f777(x66554,x66555),f185(x66552))+E(f777(f231(f855(x66551),x66552,f185(x66551),x66553),f777(x66554,x66555)),f185(x66551)) % 174.01/173.89 [7305]E(f777(x73051,x73052),f185(x73053))+~E(f777(f172(x73054,x73053,x73055,x73051),x73052),f185(x73053)) % 174.01/173.89 [7306]E(f777(x73061,x73062),f185(x73063))+~E(f777(f172(x73064,x73063,x73061,x73065),x73062),f185(x73063)) % 174.01/173.89 [7346]E(f777(f172(x73461,x73462,x73463,x73464),x73465),f777(x73463,x73465))+P1(f777(f777(f336(x73461),x73465),f171(x73461,x73462,x73464))) % 174.01/173.89 [7347]E(f777(f172(x73471,x73472,x73473,x73474),x73475),f777(x73474,x73475))+P1(f777(f777(f336(x73471),x73475),f171(x73471,x73472,x73473))) % 174.01/173.89 [7673]~P24(x76734,x76731,x76732,x76735)+E(f777(f77(x76731,x76731,x76731,f777(x76732,x76733)),f777(x76732,x76733)),f777(x76732,x76733)) % 174.01/173.89 [7716]E(f777(f172(x77161,x77162,x77163,x77164),x77165),f777(x77164,x77165))+~P1(f777(f777(f336(x77161),x77165),f171(x77161,x77162,x77164))) % 174.01/173.89 [8063]~P20(x80635,x80631,x80632)+E(f777(f77(x80631,x80631,x80631,f777(x80632,x80633)),f777(x80632,x80634)),f777(f77(x80631,x80631,x80631,f777(x80632,x80634)),f777(x80632,x80633))) % 174.01/173.89 [8385]P1(f777(f777(f336(f857(x83851,x83851)),f777(f777(f243(x83851,x83851),x83852),x83853)),f329(x83851,x83854,x83855)))+~P1(f777(f777(f235(a851),f777(x83854,x83852)),f777(x83854,x83853))) % 174.01/173.89 [8485]~P1(f777(f777(f336(x84854),x84853),f284(x84854,x84851,x84852,x84855)))+P1(f777(f777(x84851,x84852),x84853)) % 174.01/173.89 [8486]~P1(f777(f777(f336(x84864),x84863),f293(x84864,x84861,x84862,x84865)))+P1(f777(f777(x84861,x84862),x84863)) % 174.01/173.89 [8487]~P1(f777(f777(f336(x84874),x84872),f284(x84874,x84871,x84875,x84873)))+P1(f777(f777(x84871,x84872),x84873)) % 174.01/173.89 [8488]~P1(f777(f777(f336(x84884),x84882),f293(x84884,x84881,x84885,x84883)))+P1(f777(f777(x84881,x84882),x84883)) % 174.01/173.89 [8610]~P55(x86102,x86101,x86105,x86103,x86104)+E(f777(f305(x86101,x86102,x86103),x86104),f241(f858(x86102,a845))) % 174.01/173.89 [9381]P1(f777(f777(f336(f857(f852(x93811),f852(x93811))),f777(f777(f243(f852(x93811),f852(x93811)),f777(f777(f142(x93811),x93812),x93813)),f777(f777(f142(x93811),x93812),x93814))),f148(x93811,x93815)))+~P1(f777(f777(f336(f857(f852(x93811),f852(x93811))),f777(f777(f243(f852(x93811),f852(x93811)),x93813),x93814)),f148(x93811,x93815))) % 174.01/173.89 [9382]P1(f777(f777(f336(f857(f852(x93821),f852(x93821))),f777(f777(f243(f852(x93821),f852(x93821)),f777(f777(f127(x93821),x93822),x93823)),f777(f777(f127(x93821),x93822),x93824))),f139(x93821,x93825)))+~P1(f777(f777(f336(f857(f852(x93821),f852(x93821))),f777(f777(f243(f852(x93821),f852(x93821)),x93823),x93824)),f139(x93821,x93825))) % 174.01/173.89 [9433]~E(f777(x94333,f398(x94332,x94331,x94334,x94335,x94333)),f777(f176(x94335,x94334,x94331),f398(x94332,x94331,x94334,x94335,x94333)))+E(f777(f777(x94331,x94332),f777(x94333,x94332)),f777(x94333,f777(a116,x94332))) % 174.01/173.89 [9558]E(f777(f777(f142(x95581),f719(x95582,x95583,x95584,x95585,x95581)),f722(x95582,x95583,x95584,x95585,x95581)),x95585)+~P1(f777(f777(f336(f857(f852(x95581),f852(x95581))),f777(f777(f243(f852(x95581),f852(x95581)),x95585),f777(f777(f142(x95581),x95584),x95583))),f149(x95581,x95582))) % 174.01/173.89 [9585]E(f777(f777(f142(x95851),f720(x95852,x95853,x95854,x95855,x95851)),f721(x95852,x95853,x95854,x95855,x95851)),x95853)+~P1(f777(f777(f336(f857(f852(x95851),f852(x95851))),f777(f777(f243(f852(x95851),f852(x95851)),f777(f777(f142(x95851),x95855),x95854)),x95853)),f149(x95851,x95852))) % 174.01/173.89 [9717]~P1(f777(f777(f336(f857(f852(x97171),f852(x97171))),f777(f777(f243(f852(x97171),f852(x97171)),f777(f777(f142(x97171),x97175),x97172)),x97174)),f149(x97171,x97173)))+P1(f777(f777(f336(f857(f852(x97171),f852(x97171))),f777(f777(f243(f852(x97171),f852(x97171)),x97172),f721(x97173,x97174,x97172,x97175,x97171))),f149(x97171,x97173))) % 174.01/173.89 [9802]~P1(f777(f777(f336(f857(f852(x98021),f852(x98021))),f777(f777(f243(f852(x98021),f852(x98021)),x98025),f777(f777(f142(x98021),x98024),x98023))),f149(x98021,x98022)))+P1(f777(f777(f336(f857(f852(x98021),f852(x98021))),f777(f777(f243(f852(x98021),f852(x98021)),f722(x98022,x98023,x98024,x98025,x98021)),x98023)),f149(x98021,x98022))) % 174.01/173.89 [9975]P1(f777(f777(f336(f857(x99751,x99751)),f777(f777(f243(x99751,x99751),f777(x99752,f777(f777(f84(a851),x99753),x99754))),f777(x99752,x99753))),f302(x99751,x99755)))+~P1(f777(f777(f336(f857(x99751,x99751)),f777(f777(f243(x99751,x99751),f777(x99752,f777(a116,f639(x99754,x99753,x99755,x99752,x99751)))),f777(x99752,f639(x99754,x99753,x99755,x99752,x99751)))),f302(x99751,x99755))) % 174.01/173.89 [9999]E(x99991,f4(a103))+E(f777(f231(f857(f852(x99992),x99993),f857(x99992,x99993),f777(f777(f243(f852(x99992),x99993),f117(x99992)),x99994),f777(f253(x99992,x99993,f857(f852(x99992),x99993)),f777(f777(f11(x99992,f858(x99993,f857(f852(x99992),x99993)),f858(x99993,f857(f852(x99992),x99993))),f777(f777(f12(f858(f857(f852(x99992),x99993),f857(f852(x99992),x99993)),f858(f858(x99993,f857(f852(x99992),x99993)),f858(x99993,f857(f852(x99992),x99993))),x99992),f12(f857(f852(x99992),x99993),f857(f852(x99992),x99993),x99993)),f777(f777(f12(f858(f852(x99992),f858(x99993,f857(f852(x99992),x99993))),f858(f857(f852(x99992),x99993),f857(f852(x99992),x99993)),x99992),f253(f852(x99992),x99993,f857(f852(x99992),x99993))),f777(f777(f12(f858(f852(x99992),f852(x99992)),f858(f852(x99992),f858(x99993,f857(f852(x99992),x99993))),x99992),f777(f12(f852(x99992),f858(x99993,f857(f852(x99992),x99993)),f852(x99992)),f243(f852(x99992),x99993))),f142(x99992))))),f121(x99993,x99992,x99995,f777(f777(f5(a103),x99991),f82(a103)))))),f777(x99995,x99994)),f777(f121(x99993,x99992,x99995,x99991),x99994)) % 174.01/173.89 [5127]E(x51271,x51272)+~E(f777(f777(f142(x51273),x51274),x51271),f777(f777(f142(x51273),x51275),x51272)) % 174.01/173.89 [5128]E(x51281,x51282)+~E(f777(f777(f142(x51283),x51281),x51284),f777(f777(f142(x51283),x51282),x51285)) % 174.01/173.89 [5327]~E(f777(f777(f130(x53271),x53273),x53272),f777(f777(f142(x53271),x53274),x53275))+E(f777(f777(f155(x53271),x53272),x53273),x53274) % 174.01/173.89 [5460]~P19(x54604,x54605,x54601)+E(f777(f777(x54601,x54602),f777(f777(x54601,x54602),x54603)),f777(f777(x54601,x54602),x54603)) % 174.01/173.89 [6076]~P100(x60762)+~E(f777(f777(f140(x60761,x60762,x60763),x60764),x60765),f117(x60761)) % 174.01/173.89 [6475]E(x64751,x64752)+~E(f777(f777(f127(x64753),x64754),f777(f777(f142(x64753),x64751),f117(x64753))),f777(f777(f127(x64753),x64755),f777(f777(f142(x64753),x64752),f117(x64753)))) % 174.01/173.89 [6476]E(x64761,x64762)+~E(f777(f777(f127(x64763),x64761),f777(f777(f142(x64763),x64764),f117(x64763))),f777(f777(f127(x64763),x64762),f777(f777(f142(x64763),x64765),f117(x64763)))) % 174.01/173.89 [6738]E(f777(f174(x67381,x67382,x67383,x67384),x67385),f185(x67382))+P1(f777(f777(f336(x67381),x67385),x67384)) % 174.01/173.89 [6808]E(f777(f777(f304(x68081),f777(x68082,x68083)),f777(f305(x68084,x68081,x68082),x68085)),f777(f305(x68084,x68081,x68082),x68085))+~P1(f777(f777(f336(x68084),x68083),x68085)) % 174.01/173.89 [6817]~P1(f777(x68174,f777(x68173,x68175)))+P1(f777(f777(f307(x68171,x68172,x68173),x68174),x68175)) % 174.01/173.89 [6822]~E(x68224,f4(a103))+E(f777(f121(x68221,x68222,x68223,x68224),x68225),f777(f777(f243(f852(x68222),x68221),f117(x68222)),x68225)) % 174.01/173.89 [6916]~E(f777(f305(x69161,x69162,x69163),x69164),x69165)+E(f777(f305(f858(x69161,a845),f858(x69162,a845),f305(x69161,x69162,x69163)),f777(f303(x69161),x69164)),f777(f303(x69162),x69165)) % 174.01/173.89 [6947]E(f777(f174(x69471,x69472,x69473,x69474),x69475),f777(x69473,x69475))+~P1(f777(f777(f336(x69471),x69475),x69474)) % 174.01/173.89 [7262]P29(x72621,x72622,x72623,x72624)+~P29(x72621,x72622,x72623,f777(f777(f304(x72621),x72625),x72624)) % 174.01/173.89 [7333]P1(f777(x73331,x73332))+~P1(f777(f777(f96(x73333,x73334,x73331),x73335),x73332)) % 174.01/173.89 [7384]~P1(f777(f777(f336(x73844),x73843),x73845))+P1(f777(f777(f336(x73841),f777(x73842,x73843)),f777(f305(x73844,x73841,x73842),x73845))) % 174.01/173.89 [7436]P1(f777(x74361,f777(x74362,x74363)))+~P1(f777(f777(f307(x74364,x74365,x74362),x74361),x74363)) % 174.01/173.89 [7437]P1(f777(f777(x74371,x74372),x74373))+~P1(f777(f777(f96(x74374,x74371,x74375),x74372),x74373)) % 174.01/173.89 [7506]~P1(f777(f777(f336(x75063),f777(x75064,x75062)),x75065))+P1(f777(f777(f336(x75061),x75062),f777(f307(x75061,x75063,x75064),x75065))) % 174.01/173.89 [7905]~P1(f777(f777(f336(x79055),x79053),f777(f307(x79055,x79051,x79052),x79054)))+P1(f777(f777(f336(x79051),f777(x79052,x79053)),x79054)) % 174.01/173.89 [8123]~E(x81233,f777(f777(f777(f76(x81231,f855(x81232)),f777(f20(f855(x81232),x81231),f185(x81232))),x81234),f777(f229(x81232),x81235)))+E(f171(x81231,x81232,x81233),f777(f777(f304(x81231),x81234),f182(f858(x81231,a845)))) % 174.01/173.89 [8219]E(f777(x82191,f418(x82192,x82191,x82193,x82194)),x82194)+~P1(f777(f777(f336(x82195),x82194),f777(f305(x82193,x82195,x82191),x82192))) % 174.01/173.89 [8471]P1(f777(f777(f336(f859(x84711,x84712)),f777(f315(x84712,x84711),x84713)),f316(x84711,x84712,x84714,x84715)))+~P1(f777(f777(f336(x84712),x84713),x84715)) % 174.01/173.89 [8472]P1(f777(f777(f336(f859(x84721,x84722)),f777(f306(x84721,x84722),x84723)),f316(x84721,x84722,x84724,x84725)))+~P1(f777(f777(f336(x84721),x84723),x84724)) % 174.01/173.89 [8529]~E(x85292,f777(f777(f142(x85291),x85294),x85295))+P1(f777(f777(f336(f857(f852(x85291),f852(x85291))),f777(f777(f243(f852(x85291),f852(x85291)),f117(x85291)),x85292)),f139(x85291,x85293))) % 174.01/173.89 [8580]P1(f777(f777(f234(f858(x85801,a845)),f777(f777(f49(x85802,f858(x85801,a845)),x85803),x85804)),f777(x85804,x85805)))+~P1(f777(f777(f336(x85802),x85805),x85803)) % 174.01/173.89 [8626]~P55(x86261,x86262,x86263,x86265,x86264)+E(f777(f305(x86261,x86262,x86263),f241(f858(x86261,a845))),x86264) % 174.01/173.89 [8815]E(f777(f777(f777(f76(x88151,f855(x88152)),f174(x88151,x88152,x88153,x88154)),x88155),f185(x88152)),f174(x88151,x88152,x88153,x88154))+P1(f777(f777(f336(x88151),x88155),x88154)) % 174.01/173.89 [8818]E(f777(x88181,f704(x88182,x88183,x88181,x88184,x88185)),x88182)+~E(f777(f777(f198(x88185,x88184),x88181),x88183),f777(f229(x88184),x88182)) % 174.01/173.89 [8821]E(f777(f229(x88211),f704(x88212,x88213,x88214,x88215,x88211)),x88213)+~E(f777(f777(f198(x88211,x88215),x88214),x88213),f777(f229(x88215),x88212)) % 174.01/173.89 [8905]E(f777(f183(f852(x89051)),x89052),x89053)+~P1(f777(f777(f336(f857(f852(x89051),f852(x89051))),f777(f777(f243(f852(x89051),f852(x89051)),x89054),x89052)),f777(f135(x89051,x89055),x89053))) % 174.01/173.89 [8906]E(f777(f183(f852(x89061)),x89062),x89063)+~P1(f777(f777(f336(f857(f852(x89061),f852(x89061))),f777(f777(f243(f852(x89061),f852(x89061)),x89062),x89064)),f777(f135(x89061,x89065),x89063))) % 174.01/173.89 [8967]P1(f777(f777(f336(x89671),f418(x89672,x89673,x89671,x89674)),x89672))+~P1(f777(f777(f336(x89675),x89674),f777(f305(x89671,x89675,x89673),x89672))) % 174.01/173.89 [9120]E(f777(f305(x91201,x91202,x91203),f364(x91204,x91203,x91201,x91205,x91202)),x91205)+~P1(f777(f777(f234(f858(x91202,a845)),x91205),f777(f305(x91201,x91202,x91203),x91204))) % 174.01/173.89 [9353]E(f777(x93531,f538(x93532,x93531,x93533,x93534,x93535)),f777(f229(x93535),x93534))+~P1(f777(f777(f336(x93535),x93534),f173(x93533,x93535,f174(x93533,x93535,x93531,x93532)))) % 174.01/173.89 [9397]P1(f777(f777(f336(f857(f852(x93971),f852(x93971))),f777(f777(f243(f852(x93971),f852(x93971)),f777(f777(f142(x93971),x93972),x93973)),f777(f777(f142(x93971),x93972),x93974))),f302(f852(x93971),f148(x93971,x93975))))+~P1(f777(f777(f336(f857(f852(x93971),f852(x93971))),f777(f777(f243(f852(x93971),f852(x93971)),x93973),x93974)),f302(f852(x93971),f148(x93971,x93975)))) % 174.01/173.89 [9426]~E(f777(x94263,f705(x94265,x94264,x94263,x94262,x94261)),f777(x94265,f705(x94265,x94264,x94263,x94262,x94261)))+E(f777(f777(f145(x94261,x94262),x94263),x94264),f777(f777(f145(x94261,x94262),x94265),x94264)) % 174.01/173.89 [9504]E(f777(f777(f145(x95041,x95042),x95043),x95044),f777(f777(f145(x95041,x95042),x95045),x95044))+P1(f777(f777(f336(x95041),f705(x95043,x95044,x95045,x95042,x95041)),f777(f160(x95041),x95044))) % 174.01/173.89 [9532]~P1(f777(f777(f336(x95325),x95324),f777(f279(x95321,x95325,x95323),x95322)))+P1(f777(f777(f336(x95321),f490(x95322,x95323,x95321,x95324,x95325)),x95322)) % 174.01/173.89 [9533]~P1(f777(f777(f336(x95335),x95334),f777(f279(x95331,x95335,x95333),x95332)))+P1(f777(f777(f336(x95331),f536(x95332,x95333,x95331,x95334,x95335)),x95332)) % 174.01/173.89 [9556]~P1(f777(f777(f234(f858(x95565,a845)),x95564),f777(f305(x95561,x95565,x95563),x95562)))+P1(f777(f777(f234(f858(x95561,a845)),f364(x95562,x95563,x95561,x95564,x95565)),x95562)) % 174.01/173.89 [9600]~P1(f777(f777(f336(x96005),x96004),f173(x96001,x96005,f174(x96001,x96005,x96003,x96002))))+P1(f777(f777(f336(x96001),f538(x96002,x96003,x96001,x96004,x96005)),x96002)) % 174.01/173.89 [5341]~E(f777(x53413,x53414),x53415)+E(f777(f777(f777(f76(x53411,x53412),x53413),x53414),x53415),x53413) % 174.01/173.89 [5790]E(f777(x57901,x57902),x57903)+~E(f777(f777(f777(f76(x57904,x57905),x57901),x57902),x57903),x57901) % 174.01/173.89 [5879]E(x58791,x58792)+~E(f777(f252(x58793,x58794),f777(f777(f243(x58793,x58794),x58795),x58791)),x58792) % 174.01/173.89 [5880]E(x58801,x58802)+~E(f777(f242(x58803,x58804),f777(f777(f243(x58803,x58804),x58801),x58805)),x58802) % 174.01/173.89 [6563]E(f777(f305(x65631,x65632,f777(f20(x65632,x65631),x65633)),x65634),f777(f777(f304(x65632),x65633),f182(f858(x65632,a845))))+~P1(f777(f777(f336(x65631),x65635),x65634)) % 174.01/173.89 [6637]E(f777(f777(f105(f858(x66371,a845)),f777(f160(x66371),x66372)),f777(f160(x66371),x66373)),f777(f160(x66371),x66374))+~E(f158(x66371,x66375,x66374),f777(f777(f243(f852(x66371),f852(x66371)),x66372),x66373)) % 174.01/173.89 [6744]~P100(x67442)+E(f777(f183(f852(x67441)),f777(f777(f140(x67441,x67442,x67443),x67444),x67445)),f777(a116,f777(f183(f852(x67441)),x67445))) % 174.01/173.89 [6759]~P100(x67592)+E(f777(f160(x67591),f777(f777(f140(x67591,x67592,x67593),x67594),x67595)),f777(f777(f304(x67591),x67594),f777(f160(x67591),x67595))) % 174.01/173.89 [7037]~P85(x70371)+E(f777(f777(f84(x70371),f777(f777(f84(x70371),x70372),x70373)),f777(f777(f84(x70371),x70374),x70375)),f777(f777(f84(x70371),f777(f777(f84(x70371),x70372),x70374)),f777(f777(f84(x70371),x70373),x70375))) % 174.01/173.89 [7038]~P85(x70381)+E(f777(f777(f85(x70381),f777(f777(f85(x70381),x70382),x70383)),f777(f777(f85(x70381),x70384),x70385)),f777(f777(f85(x70381),f777(f777(f85(x70381),x70382),x70384)),f777(f777(f85(x70381),x70383),x70385))) % 174.01/173.89 [7039]~P60(x70391)+E(f777(f777(f285(x70391),f777(f777(f85(x70391),x70392),x70393)),f777(f777(f85(x70391),x70394),x70395)),f777(f777(f85(x70391),f777(f777(f285(x70391),x70392),x70394)),f777(f777(f285(x70391),x70393),x70395))) % 174.01/173.89 [7053]~P100(x70531)+E(f297(x70531,f777(f777(f181(x70531),x70532),x70533),f777(f777(f238(x70531),x70534),x70535)),f777(f777(f106(f858(x70531,a845)),f297(x70531,x70532,x70534)),f297(x70531,x70533,x70535))) % 174.01/173.89 [7054]~P100(x70541)+E(f299(x70541,f777(f777(f181(x70541),x70542),x70543),f777(f777(f238(x70541),x70544),x70545)),f777(f777(f106(f858(x70541,a845)),f299(x70541,x70542,x70544)),f299(x70541,x70543,x70545))) % 174.01/173.89 [7055]~P100(x70551)+E(f300(x70551,f777(f777(f181(x70551),x70552),x70553),f777(f777(f238(x70551),x70554),x70555)),f777(f777(f106(f858(x70551,a845)),f300(x70551,x70552,x70554)),f300(x70551,x70553,x70555))) % 174.01/173.89 [7056]~P100(x70561)+E(f777(f777(f106(f858(x70561,a845)),f777(f296(x70561,x70562),x70563)),f777(f296(x70561,x70564),x70565)),f777(f296(x70561,f777(f777(f181(x70561),x70562),x70564)),f777(f777(f238(x70561),x70563),x70565))) % 174.01/173.89 [7174]~P1(f777(x71741,f825(x71743,x71742,x71741)))+P1(f777(x71741,f777(f777(f243(x71742,x71743),x71744),x71745))) % 174.01/173.89 [7274]~E(f777(x72743,x72744),f185(x72742))+E(f173(x72741,x72742,f777(f777(f777(f76(x72741,f855(x72742)),x72743),x72744),f777(f229(x72742),x72745))),f777(f777(f304(x72742),x72745),f173(x72741,x72742,x72743))) % 174.01/173.89 [7297]~E(x72972,f777(x72974,x72975))+P1(f777(f777(f336(x72971),x72972),f777(f305(x72973,x72971,x72974),f241(f858(x72973,a845))))) % 174.01/173.89 [7358]~E(f777(x73583,x73584),f185(x73582))+E(f777(f777(f5(f858(x73581,a845)),f171(x73581,x73582,x73583)),f777(f777(f304(x73581),x73584),x73585)),f777(f777(f5(f858(x73581,a845)),f171(x73581,x73582,x73583)),x73585)) % 174.01/173.89 [7380]~P19(x73803,x73802,x73804)+P19(x73801,x73802,f777(f777(f12(x73803,f858(x73802,x73802),x73801),x73804),x73805)) % 174.01/173.89 [7381]~P20(x73813,x73812,x73814)+P20(x73811,x73812,f777(f777(f12(x73813,f858(x73812,x73812),x73811),x73814),x73815)) % 174.01/173.89 [7522]~P29(x75221,x75222,x75223,x75224)+P29(x75221,x75222,x75223,f777(f777(f5(f858(x75221,a845)),x75224),x75225)) % 174.01/173.89 [7682]~P1(f777(f777(x76823,x76824),x76825))+P1(f777(f777(f253(x76821,x76822,a845),x76823),f777(f777(f243(x76821,x76822),x76824),x76825))) % 174.01/173.89 [7816]P29(x78161,x78162,x78163,x78164)+~P29(x78161,x78162,x78163,f777(f777(f105(f858(x78161,a845)),x78165),x78164)) % 174.01/173.89 [7817]P29(x78171,x78172,x78173,x78174)+~P29(x78171,x78172,x78173,f777(f777(f105(f858(x78171,a845)),x78174),x78175)) % 174.01/173.89 [8022]~P31(x80221,f777(a116,x80222),f777(f777(f777(f95(x80221),x80223),f777(a29,x80224)),x80225))+P31(x80221,x80222,f777(f777(f777(f95(x80221),x80223),f777(f233(a846),f777(a32,x80224))),x80225)) % 174.01/173.89 [8150]P31(x81501,f777(a116,x81502),f777(f777(f777(f95(x81501),x81503),f777(a29,x81504)),x81505))+~P31(x81501,x81502,f777(f777(f777(f95(x81501),x81503),f777(f233(a846),f777(a32,x81504))),x81505)) % 174.01/173.89 [8179]~P19(x81792,x81791,x81793)+E(f777(f134(x81791,x81792,f777(f11(x81792,x81791,x81791),x81793),x81794),x81795),f777(f777(f68(x81792,x81791,x81793),x81794),f777(f160(x81792),x81795))) % 174.01/173.89 [8229]P1(f777(f777(x82291,x82292),x82293))+~P1(f777(f777(f253(x82294,x82295,a845),x82291),f777(f777(f243(x82294,x82295),x82292),x82293))) % 174.01/173.89 [8300]P39(x83004,f842(x83005,x83004,x83003,x83002),x83002,f347(x83005,x83004,x83003,x83002))+P31(x83001,x83002,f777(f777(f777(f95(x83001),x83003),x83004),x83005)) % 174.01/173.89 [8316]~E(f777(f168(x83161,x83162,x83165),x83163),f777(f229(x83162),x83164))+P1(f777(f777(f336(f857(x83161,x83162)),f777(f777(f243(x83161,x83162),x83163),x83164)),f777(f160(f857(x83161,x83162)),x83165))) % 174.01/173.89 [8679]P1(f777(f777(f234(f858(x86791,a845)),f777(f305(x86792,x86791,x86793),x86794)),f777(f305(x86792,x86791,x86793),x86795)))+~P1(f777(f777(f234(f858(x86792,a845)),x86794),x86795)) % 174.01/173.89 [8680]P1(f777(f777(f234(f858(x86801,a845)),f777(f307(x86801,x86802,x86803),x86804)),f777(f307(x86801,x86802,x86803),x86805)))+~P1(f777(f777(f234(f858(x86802,a845)),x86804),x86805)) % 174.01/173.89 [8751]E(x87511,f4(a103))+E(f777(f777(f255(x87512,x87513,x87512,f857(x87513,x87512)),f777(x87514,x87515)),f270(x87513,x87512,f777(f777(f5(a103),x87511),f82(a103)),x87514)),f777(f270(x87513,x87512,x87511,x87514),x87515)) % 174.01/173.89 [8837]P1(f777(f777(f251(x88371,x88372,a845,x88373),x88374),x88375))+~P1(f777(x88373,f777(f777(f243(x88371,x88372),x88374),x88375))) % 174.01/173.89 [9038]P31(x90381,x90382,f777(f777(f777(f95(x90381),x90383),x90384),x90385))+P1(f777(f777(x90383,f835(x90385,x90384,x90383,x90382)),f842(x90385,x90384,x90383,x90382))) % 174.01/173.89 [9099]~P1(f777(f777(f251(x90992,x90993,a845,x90991),x90994),x90995))+P1(f777(x90991,f777(f777(f243(x90992,x90993),x90994),x90995))) % 174.01/173.89 [9208]E(f777(f229(x92081),f716(x92082,x92083,x92084,x92081,x92085)),f777(f168(x92085,x92081,x92082),x92084))+~P1(f777(f777(f336(f857(x92085,x92081)),f777(f777(f243(x92085,x92081),x92084),x92083)),f777(f160(f857(x92085,x92081)),x92082))) % 174.01/173.89 [9251]P31(x92511,x92512,f777(f777(f777(f95(x92511),x92513),x92514),x92515))+~P1(f777(f777(x92515,f835(x92515,x92514,x92513,x92512)),f347(x92515,x92514,x92513,x92512))) % 174.01/173.89 [9318]~P28(x93181,x93182,f777(f777(f304(f850(x93181)),f777(f777(f777(f95(x93181),x93183),f777(f233(a846),f777(a32,x93184))),x93185)),f182(f858(f850(x93181),a845))))+P28(x93181,x93182,f777(f777(f304(f850(x93181)),f777(f777(f777(f95(x93181),x93183),f777(a29,x93184)),x93185)),f182(f858(f850(x93181),a845)))) % 174.01/173.89 [9345]~P1(f777(f65(x93453),f777(f305(x93452,x93453,x93455),f241(f858(x93452,a845)))))+P1(f777(f65(x93451),f777(f305(x93452,x93451,f777(f777(f12(x93453,x93451,x93452),x93454),x93455)),f241(f858(x93452,a845))))) % 174.01/173.89 [9367]P1(f777(f777(f234(f858(f858(x93671,a845),a845)),f777(f305(f858(x93672,a845),f858(x93671,a845),f305(x93672,x93671,x93673)),f777(f303(x93672),x93674))),f777(f303(x93671),x93675)))+~P1(f777(f777(f234(f858(x93671,a845)),f777(f305(x93672,x93671,x93673),x93674)),x93675)) % 174.01/173.89 [9377]~P1(f777(f65(f855(x93771)),f777(f305(x93772,f855(x93771),x93773),f241(f858(x93772,a845)))))+P1(f777(f65(f855(x93771)),f777(f305(x93772,f855(x93771),f777(f777(f777(f76(x93772,f855(x93771)),x93773),x93774),f777(f229(x93771),x93775))),f241(f858(x93772,a845))))) % 174.01/173.89 [9436]E(x94361,x94362)+~P1(f777(f70(x94363,x94364,x94365,x94361,f182(f858(x94363,a845))),x94362)) % 174.01/173.89 [9449]E(f777(f777(f243(x94491,x94492),f571(x94493,x94494,x94495,x94492,x94491)),f572(x94493,x94494,x94495,x94492,x94491)),x94495)+~P1(f777(f777(f336(f857(x94491,x94492)),x94495),f777(f777(f250(x94491,x94492),x94494),x94493))) % 174.01/173.89 [9537]P1(f777(f777(f336(x95371),f571(x95372,x95373,x95374,x95375,x95371)),x95373))+~P1(f777(f777(f336(f857(x95371,x95375)),x95374),f777(f777(f250(x95371,x95375),x95373),x95372))) % 174.01/173.89 [9633]P28(x96335,x96334,f777(f777(f304(f850(x96335)),f777(f777(f777(f95(x96335),x96331),x96333),x96332)),f182(f858(f850(x96335),a845))))+P1(f777(f777(x96331,f486(x96332,x96333,x96334,x96335,x96331)),f487(x96332,x96333,x96334,x96335,x96331))) % 174.01/173.89 [9675]P1(f777(f777(f336(x96751),f572(x96752,x96753,x96754,x96751,x96755)),f777(x96752,f571(x96752,x96753,x96754,x96751,x96755))))+~P1(f777(f777(f336(f857(x96755,x96751)),x96754),f777(f777(f250(x96755,x96751),x96753),x96752))) % 174.01/173.89 [9694]P1(f777(f777(f336(f857(x96941,x96941)),f777(f777(f243(x96941,x96941),x96942),f660(x96943,x96944,x96945,x96942,x96941))),x96943))+~P1(f777(f777(f336(f857(x96941,x96941)),f777(f777(f243(x96941,x96941),x96942),x96945)),f777(f777(f175(f857(x96941,x96941),a845),f777(a116,x96944)),x96943))) % 174.01/173.89 [9695]P1(f777(f777(f336(f857(x96951,x96951)),f777(f777(f243(x96951,x96951),x96952),f662(x96953,x96954,x96955,x96952,x96951))),x96953))+~P1(f777(f777(f336(f857(x96951,x96951)),f777(f777(f243(x96951,x96951),x96952),x96955)),f777(f777(f175(f857(x96951,x96951),a845),f777(a116,x96954)),x96953))) % 174.01/173.89 [9713]~P1(f777(f777(f336(f857(f852(x97131),f852(x97131))),f777(f777(f243(f852(x97131),f852(x97131)),f777(f777(f142(x97131),x97132),x97135)),x97134)),f149(x97131,x97133)))+P1(f777(f777(f336(f857(x97131,x97131)),f777(f777(f243(x97131,x97131),x97132),f720(x97133,x97134,x97135,x97132,x97131))),x97133)) % 174.01/173.89 [9715]~P28(x97151,x97152,f777(f777(f304(f850(x97151)),f777(f777(f777(f95(x97151),f96(x97151,x97153,x97154)),x97155),x97153)),f182(f858(f850(x97151),a845))))+P28(x97151,x97152,f777(f777(f304(f850(x97151)),f777(f777(f777(f95(x97151),x97153),f37(x97154,x97155)),f96(x97151,x97153,f777(f77(a845,a845,a848,a330),x97154)))),f182(f858(f850(x97151),a845)))) % 174.01/173.89 [10000]P28(x100001,x100002,f777(f777(f304(f850(x100001)),f777(f777(f777(f95(x100001),x100003),x100004),x100005)),f182(f858(f850(x100001),a845))))+~P28(x100001,x100002,f777(f777(f304(f850(x100001)),f777(f777(f777(f95(x100001),f777(f20(f858(a848,a845),x100001),f777(f777(f11(a848,a848,a845),a332),f487(x100005,x100004,x100002,x100001,x100003)))),x100004),f777(f20(f858(a848,a845),x100001),f777(x100005,f486(x100005,x100004,x100002,x100001,x100003))))),f182(f858(f850(x100001),a845)))) % 174.01/173.89 [6227]P1(f777(x62272,x62274))+E(f164(x62271,x62272,f777(f777(f127(x62271),x62273),f777(f777(f142(x62271),x62274),x62275))),f164(x62271,x62272,x62273)) % 174.01/173.89 [6277]~P71(x62772)+E(f777(f777(f777(f5(f858(x62771,x62772)),x62773),x62774),x62775),f777(f777(f5(x62772),f777(x62773,x62775)),f777(x62774,x62775))) % 174.01/173.89 [6279]~P93(x62792)+E(f777(f777(f777(f105(f858(x62791,x62792)),x62793),x62794),x62795),f777(f777(f105(x62792),f777(x62793,x62795)),f777(x62794,x62795))) % 174.01/173.89 [6281]~P93(x62812)+E(f777(f777(f777(f106(f858(x62811,x62812)),x62813),x62814),x62815),f777(f777(f106(x62812),f777(x62813,x62815)),f777(x62814,x62815))) % 174.01/173.89 [6303]E(x63031,x63032)+E(f777(f777(f155(x63033),f777(f777(f150(x63033,x63034),x63031),x63035)),x63032),f777(f777(f155(x63033),x63034),x63032)) % 174.01/173.89 [6580]~E(x65804,f182(f858(x65803,a845)))+E(f777(f777(f5(f858(x65801,a845)),x65802),f777(f777(f48(x65803,f858(x65801,a845)),x65804),x65805)),x65802) % 174.01/173.89 [6581]~E(x65814,f182(f858(x65813,a845)))+E(f777(f777(f105(f858(x65811,a845)),x65812),f777(f777(f48(x65813,f858(x65811,a845)),x65814),x65815)),x65812) % 174.01/173.89 [6582]~E(x65824,f182(f858(x65823,a845)))+E(f777(f777(f106(f858(x65821,a845)),x65822),f777(f777(f49(x65823,f858(x65821,a845)),x65824),x65825)),x65822) % 174.01/173.89 [6596]~E(x65964,f182(f858(x65963,a845)))+E(f777(f777(f304(x65961),x65962),f777(f777(f48(x65963,f858(x65961,a845)),x65964),x65965)),f777(f777(f304(x65961),x65962),f182(f858(x65961,a845)))) % 174.01/173.89 [7425]E(f777(f777(f155(x74251),f777(f777(f145(x74252,x74251),x74253),x74254)),x74255),f777(x74253,f777(f777(f155(x74252),x74254),x74255)))+~P1(f777(f777(f235(a851),x74255),f777(f183(f852(x74252)),x74254))) % 174.01/173.89 [7494]E(f777(f777(f105(f858(x74941,a845)),f777(x74942,x74943)),f777(f777(f48(x74944,f858(x74941,a845)),x74945),x74942)),f777(f777(f48(x74944,f858(x74941,a845)),x74945),x74942))+~P1(f777(f777(f336(x74944),x74943),x74945)) % 174.01/173.89 [7495]E(f777(f777(f106(f858(x74951,a845)),f777(x74952,x74953)),f777(f777(f49(x74954,f858(x74951,a845)),x74955),x74952)),f777(f777(f49(x74954,f858(x74951,a845)),x74955),x74952))+~P1(f777(f777(f336(x74954),x74953),x74955)) % 174.01/173.89 [8098]~E(x80983,f182(f858(x80981,a845)))+E(f777(f777(f48(x80981,f858(x80982,a845)),x80983),f777(f777(f12(f858(x80982,a845),f858(x80982,a845),x80981),f777(f304(x80982),x80984)),x80985)),f182(f858(x80982,a845))) % 174.01/173.89 [8104]~P1(f777(f777(f336(x81044),x81043),x81045))+P1(f777(f777(f234(f858(x81041,a845)),f777(x81042,x81043)),f777(f777(f48(x81044,f858(x81041,a845)),x81045),x81042))) % 174.01/173.89 [8228]~E(f777(x82284,x82282),x82285)+P1(f777(f777(f336(x82281),x82282),f777(f307(x82281,x82283,x82284),f777(f777(f304(x82283),x82285),f182(f858(x82283,a845)))))) % 174.01/173.89 [8274]~P53(x82741,x82742,f777(f280(x82742,x82741),x82743))+E(f777(f777(f106(f858(x82741,a845)),f777(f279(x82742,x82741,x82743),x82744)),f777(f279(x82742,x82741,x82743),x82745)),f777(f279(x82742,x82741,x82743),f777(f777(f106(f858(x82742,a845)),x82744),x82745))) % 174.01/173.89 [8299]E(x82991,f4(a103))+E(f120(x82992,x82993,f777(x82994,f777(f777(f5(a103),x82991),f82(a103))),f777(f777(f11(x82992,a103,f853(x82993)),x82995),x82991)),f777(f195(x82992,x82993,x82994,x82995),x82991)) % 174.01/173.89 [8395]E(x83951,f182(f858(x83952,a845)))+E(f777(f777(f48(x83952,f858(x83953,a845)),x83951),f777(f777(f12(f858(x83953,a845),f858(x83953,a845),x83952),f777(f304(x83953),x83954)),x83955)),f777(f777(f304(x83953),x83954),f777(f777(f48(x83952,f858(x83953,a845)),x83951),x83955))) % 174.01/173.89 [8449]~P29(x84492,x84491,x84493,f241(f858(x84492,a845)))+E(f777(f777(f5(f858(x84491,a845)),f777(f305(x84492,x84491,x84493),x84494)),f777(f305(x84492,x84491,x84493),x84495)),f777(f305(x84492,x84491,x84493),f777(f777(f5(f858(x84492,a845)),x84494),x84495))) % 174.01/173.89 [8450]~P29(x84502,x84501,x84503,f241(f858(x84502,a845)))+E(f777(f777(f106(f858(x84501,a845)),f777(f305(x84502,x84501,x84503),x84504)),f777(f305(x84502,x84501,x84503),x84505)),f777(f305(x84502,x84501,x84503),f777(f777(f106(f858(x84502,a845)),x84504),x84505))) % 174.01/173.89 [8517]~P1(f777(f777(f71(x85171,x85172,x85175),x85173),x85174))+P1(f777(f777(f336(f857(x85171,x85172)),f777(f777(f243(x85171,x85172),x85173),x85174)),x85175)) % 174.01/173.89 [8545]P1(f777(f777(f336(x85451),x85452),f777(f261(x85453,x85451),x85454)))+~P1(f777(f777(f336(f857(x85453,x85451)),f777(f777(f243(x85453,x85451),x85455),x85452)),x85454)) % 174.01/173.89 [8547]P1(f777(f777(f336(x85471),x85472),f777(f263(x85471,x85473),x85474)))+~P1(f777(f777(f336(f857(x85471,x85473)),f777(f777(f243(x85471,x85473),x85472),x85475)),x85474)) % 174.01/173.89 [8668]P1(f777(f777(f71(x86681,x86682,x86683),x86684),x86685))+~P1(f777(f777(f336(f857(x86681,x86682)),f777(f777(f243(x86681,x86682),x86684),x86685)),x86683)) % 174.01/173.89 [8701]E(f777(x87011,x87012),x87013)+~P1(f777(f777(f336(x87014),x87012),f777(f307(x87014,x87015,x87011),f777(f777(f304(x87015),x87013),f182(f858(x87015,a845)))))) % 174.01/173.89 [8902]P1(f777(f777(f336(f857(x89021,x89022)),f777(f777(f243(x89021,x89022),x89023),x89024)),f777(f280(x89022,x89021),x89025)))+~P1(f777(f777(f336(f857(x89022,x89021)),f777(f777(f243(x89022,x89021),x89024),x89023)),x89025)) % 174.01/173.89 [8920]~P1(f777(f777(x89201,x89205),x89204))+P1(f777(f777(x89201,f777(f252(x89202,x89203),f777(f777(f243(x89202,x89203),x89204),x89205))),f777(f242(x89202,x89203),f777(f777(f243(x89202,x89203),x89204),x89205)))) % 174.01/173.89 [8947]~P1(f777(f777(f336(f857(x89472,x89471)),f777(f777(f243(x89472,x89471),x89474),x89473)),f777(f280(x89471,x89472),x89475)))+P1(f777(f777(f336(f857(x89471,x89472)),f777(f777(f243(x89471,x89472),x89473),x89474)),x89475)) % 174.01/173.89 [8975]~P1(f777(f777(f336(f857(x89753,x89751)),f777(f777(f243(x89753,x89751),x89755),x89752)),x89754))+P1(f777(f777(f336(x89751),x89752),f777(f279(x89753,x89751,x89754),f777(f777(f304(x89753),x89755),f182(f858(x89753,a845)))))) % 174.01/173.89 [9022]P1(f777(f777(f336(f857(x90221,x90222)),f777(f777(f243(x90221,x90222),x90223),x90224)),x90225))+~P1(f777(f777(f336(x90222),x90224),f777(f279(x90221,x90222,x90225),f777(f777(f304(x90221),x90223),f182(f858(x90221,a845)))))) % 174.01/173.89 [9041]E(f777(f777(f777(f76(x90411,f855(x90412)),f174(x90411,x90412,x90413,x90414)),x90415),f185(x90412)),f174(x90411,x90412,x90413,f777(f777(f5(f858(x90411,a845)),x90414),f777(f777(f304(x90411),x90415),f182(f858(x90411,a845))))))+~P1(f777(f777(f336(x90411),x90415),x90414)) % 174.01/173.89 [9105]~P66(x91051)+E(f777(f777(f10(a851,x91051),x91052),f297(a851,f777(f777(f84(a851),x91053),x91054),f777(f777(f84(a851),x91055),x91054))),f777(f777(f10(a851,x91051),f777(f777(f12(a851,x91051,a851),x91052),f777(f777(f11(a851,a851,a851),f84(a851)),x91054))),f297(a851,x91053,x91055))) % 174.01/173.89 [9124]~P66(x91241)+E(f777(f777(f10(a851,x91241),x91242),f777(f296(a851,f777(f777(f84(a851),x91243),x91244)),f777(f777(f84(a851),x91245),x91244))),f777(f777(f10(a851,x91241),f777(f777(f12(a851,x91241,a851),x91242),f777(f777(f11(a851,a851,a851),f84(a851)),x91244))),f777(f296(a851,x91243),x91245))) % 174.01/173.89 [9333]P1(f777(f777(f336(f857(f852(x93331),f852(x93331))),f777(f777(f243(f852(x93331),f852(x93331)),f777(f777(f142(x93331),x93332),x93333)),f777(f777(f142(x93331),x93334),x93333))),f148(x93331,x93335)))+~P1(f777(f777(f336(f857(x93331,x93331)),f777(f777(f243(x93331,x93331),x93332),x93334)),x93335)) % 174.01/173.89 [9434]P28(x94341,x94342,f777(f777(f304(f850(x94341)),f777(f777(f777(f95(x94341),x94343),f777(a29,x94344)),x94345)),f182(f858(f850(x94341),a845))))+~P28(x94341,f777(f777(f304(f850(x94341)),f777(f777(f777(f95(x94341),x94343),f777(a29,x94344)),x94345)),x94342),f777(f777(f304(f850(x94341)),f777(f777(f777(f95(x94341),x94343),f777(f233(a846),f777(a32,x94344))),x94345)),f182(f858(f850(x94341),a845)))) % 174.01/173.89 [9445]E(f777(f777(f304(x94451),f542(x94452,x94453,x94454,x94455,x94451)),f547(x94452,x94453,x94454,x94455,x94451)),f777(f777(f304(x94451),x94454),x94453))+~P1(f777(f66(x94451,x94455,f777(f777(f304(x94451),x94454),x94453)),x94452)) % 174.01/173.89 [9446]E(f777(f777(f304(x94461),f548(x94462,x94463,x94464,x94465,x94461)),f553(x94462,x94463,x94464,x94465,x94461)),f777(f777(f304(x94461),x94464),x94463))+~P1(f777(f66(x94461,x94465,f777(f777(f304(x94461),x94464),x94463)),x94462)) % 174.01/173.89 [9523]P1(f777(f777(f336(x95231),f668(x95232,x95233,x95234,x95235,x95231)),x95234))+P1(f777(f777(f777(f49(x95231,f858(x95235,a845)),x95234),x95233),x95232)) % 174.01/173.89 [9528]P1(f777(f777(f336(x95281),f667(x95282,x95283,x95281,x95284,x95285)),x95283))+P1(f777(f777(f336(x95285),x95284),f777(f777(f49(x95281,f858(x95285,a845)),x95283),x95282))) % 174.01/173.89 [9536]P1(f777(f777(f336(x95361),f669(x95362,x95363,x95361,x95364,x95365)),x95363))+P1(f777(f777(f234(f858(x95365,a845)),x95364),f777(f777(f49(x95361,f858(x95365,a845)),x95363),x95362))) % 174.01/173.89 [9538]P1(f777(f777(x95381,f388(x95382,x95381,x95383,x95384,x95385)),x95382))+~P1(f777(f777(f777(f48(x95385,f858(x95384,a845)),x95383),x95381),x95382)) % 174.01/173.89 [9540]P1(f777(f777(f336(x95401),f388(x95402,x95403,x95404,x95405,x95401)),x95404))+~P1(f777(f777(f777(f48(x95401,f858(x95405,a845)),x95404),x95403),x95402)) % 174.01/173.89 [9550]P1(f777(f777(f336(x95501),f419(x95502,x95503,x95501,x95504,x95505)),x95503))+~P1(f777(f777(f336(x95505),x95504),f777(f777(f48(x95501,f858(x95505,a845)),x95503),x95502))) % 174.01/173.89 [9555]P1(f777(f777(f336(x95551),x95552),f777(x95553,f419(x95553,x95554,x95555,x95552,x95551))))+~P1(f777(f777(f336(x95551),x95552),f777(f777(f48(x95555,f858(x95551,a845)),x95554),x95553))) % 174.01/173.89 [9637]~P1(f777(f777(x96374,f668(x96375,x96374,x96373,x96372,x96371)),x96375))+P1(f777(f777(f777(f49(x96371,f858(x96372,a845)),x96373),x96374),x96375)) % 174.01/173.89 [9640]~P1(f777(f777(f336(x96401),x96402),f777(x96405,f667(x96405,x96404,x96403,x96402,x96401))))+P1(f777(f777(f336(x96401),x96402),f777(f777(f49(x96403,f858(x96401,a845)),x96404),x96405))) % 174.01/173.89 [9643]~P1(f777(f777(f234(f858(x96431,a845)),x96432),f777(x96435,f669(x96435,x96434,x96433,x96432,x96431))))+P1(f777(f777(f234(f858(x96431,a845)),x96432),f777(f777(f49(x96433,f858(x96431,a845)),x96434),x96435))) % 174.01/173.89 [9698]~P1(f777(f777(f336(x96981),f542(x96985,x96984,x96983,x96982,x96981)),f547(x96985,x96984,x96983,x96982,x96981)))+~P1(f777(f66(x96981,x96982,f777(f777(f304(x96981),x96983),x96984)),x96985)) % 174.01/173.89 [9699]~P1(f777(f777(f336(x96991),f548(x96995,x96994,x96993,x96992,x96991)),f553(x96995,x96994,x96993,x96992,x96991)))+~P1(f777(f66(x96991,x96992,f777(f777(f304(x96991),x96993),x96994)),x96995)) % 174.01/173.89 [9700]~P1(f777(f777(f336(f857(x97001,x97001)),f777(f777(f243(x97001,x97001),x97002),x97005)),f777(f777(f175(f857(x97001,x97001),a845),f777(a116,x97004)),x97003)))+P1(f777(f777(f336(f857(x97001,x97001)),f777(f777(f243(x97001,x97001),x97002),f661(x97003,x97004,x97005,x97002,x97001))),f777(f777(f175(f857(x97001,x97001),a845),x97004),x97003))) % 174.01/173.89 [9707]P1(f777(f70(x97071,x97071,x97072,f542(x97073,x97074,x97075,x97072,x97071),f547(x97073,x97074,x97075,x97072,x97071)),x97073))+~P1(f777(f66(x97071,x97072,f777(f777(f304(x97071),x97075),x97074)),x97073)) % 174.01/173.89 [9708]P1(f777(f70(x97081,x97081,x97082,f548(x97083,x97084,x97085,x97082,x97081),f553(x97083,x97084,x97085,x97082,x97081)),x97083))+~P1(f777(f66(x97081,x97082,f777(f777(f304(x97081),x97085),x97084)),x97083)) % 174.01/173.89 [9719]~P100(x97191)+P18(x97191,f777(f777(f145(x97192,x97191),x97193),f777(f128(x97192,f777(f777(f11(x97192,x97191,a845),f777(f777(f12(x97191,f858(x97191,a845),x97192),a332),x97193)),f777(x97194,x97195))),x97195))) % 174.01/173.89 [9774]~P1(f777(f777(f336(x97742),x97745),f777(f279(x97741,x97742,x97744),x97743)))+P1(f777(f777(f336(f857(x97741,x97742)),f777(f777(f243(x97741,x97742),f490(x97743,x97744,x97741,x97745,x97742)),x97745)),x97744)) % 174.01/173.89 [9775]~P1(f777(f777(f336(x97752),x97755),f777(f279(x97751,x97752,x97754),x97753)))+P1(f777(f777(f336(f857(x97751,x97752)),f777(f777(f243(x97751,x97752),f536(x97753,x97754,x97751,x97755,x97752)),x97755)),x97754)) % 174.01/173.89 [9795]~P1(f777(f777(f336(f857(x97951,x97951)),f777(f777(f243(x97951,x97951),x97955),x97954)),f777(f777(f175(f857(x97951,x97951),a845),f777(a116,x97953)),x97952)))+P1(f777(f777(f336(f857(x97951,x97951)),f777(f777(f243(x97951,x97951),f661(x97952,x97953,x97954,x97955,x97951)),x97954)),x97952)) % 174.01/173.89 [9798]~P1(f777(f777(f336(f857(x97981,x97981)),f777(f777(f243(x97981,x97981),x97985),x97984)),f777(f777(f175(f857(x97981,x97981),a845),f777(a116,x97983)),x97982)))+P1(f777(f777(f336(f857(x97981,x97981)),f777(f777(f243(x97981,x97981),f660(x97982,x97983,x97984,x97985,x97981)),x97984)),f777(f777(f175(f857(x97981,x97981),a845),x97983),x97982))) % 174.01/173.89 [9799]~P1(f777(f777(f336(f857(x97991,x97991)),f777(f777(f243(x97991,x97991),x97995),x97994)),f777(f777(f175(f857(x97991,x97991),a845),f777(a116,x97993)),x97992)))+P1(f777(f777(f336(f857(x97991,x97991)),f777(f777(f243(x97991,x97991),f662(x97992,x97993,x97994,x97995,x97991)),x97994)),f777(f777(f175(f857(x97991,x97991),a845),x97993),x97992))) % 174.01/173.89 [9800]~P1(f777(f777(f336(f857(f852(x98001),f852(x98001))),f777(f777(f243(f852(x98001),f852(x98001)),x98005),f777(f777(f142(x98001),x98004),x98003))),f149(x98001,x98002)))+P1(f777(f777(f336(f857(x98001,x98001)),f777(f777(f243(x98001,x98001),f719(x98002,x98003,x98004,x98005,x98001)),x98004)),x98002)) % 174.01/173.89 [6996]E(x69961,f185(x69962))+E(f171(x69963,x69962,f777(f777(f777(f76(x69963,f855(x69962)),x69964),x69965),x69961)),f777(f777(f304(x69963),x69965),f171(x69963,x69962,x69964))) % 174.01/173.89 [7515]~E(x75153,f182(f858(x75152,a845)))+E(f777(f777(f105(f858(x75151,a845)),f777(f777(f48(x75152,f858(x75151,a845)),x75153),x75154)),x75155),x75155) % 174.01/173.89 [7516]~E(x75163,f182(f858(x75162,a845)))+E(f777(f777(f106(f858(x75161,a845)),f777(f777(f49(x75162,f858(x75161,a845)),x75163),x75164)),x75165),x75165) % 174.01/173.89 [7878]~E(x78785,f185(x78782))+E(f171(x78781,x78782,f777(f777(f777(f76(x78781,f855(x78782)),x78783),x78784),x78785)),f777(f777(f5(f858(x78781,a845)),f171(x78781,x78782,x78783)),f777(f777(f304(x78781),x78784),f182(f858(x78781,a845))))) % 174.01/173.89 [7948]~E(x79483,f182(f858(x79482,a845)))+E(f777(f777(f5(f858(x79481,a845)),f777(f777(f49(x79482,f858(x79481,a845)),x79483),x79484)),x79485),f777(f777(f5(f858(x79481,a845)),f241(f858(x79481,a845))),x79485)) % 174.01/173.89 [8076]E(f777(f777(f150(x80761,f777(f777(f127(x80761),x80762),x80763)),x80764),x80765),f777(f777(f127(x80761),f777(f777(f150(x80761,x80762),x80764),x80765)),x80763))+~P1(f777(f777(f235(a851),x80764),f777(f183(f852(x80761)),x80762))) % 174.01/173.89 [8206]P1(f777(f777(f336(x82061),x82065),f777(f160(x82061),x82063)))+E(f777(f168(x82061,x82062,f777(f777(f169(x82061,x82062),x82063),f777(f777(f145(x82061,x82062),x82064),x82063))),x82065),f185(x82062)) % 174.01/173.89 [8314]~P1(f777(f777(f336(x83141),x83145),f777(f160(x83141),x83143)))+E(f777(f168(x83141,x83142,f777(f777(f169(x83141,x83142),x83143),f777(f777(f145(x83141,x83142),x83144),x83143))),x83145),f777(f229(x83142),f777(x83144,x83145))) % 174.01/173.89 [8345]E(f777(f777(f155(x83451),f777(f777(f145(a851,x83451),x83452),f132(a851,f777(f296(a851,x83453),x83454)))),x83455),f777(x83452,f777(f777(f84(a851),x83453),x83455)))+~P1(f777(f777(f235(a851),x83455),f777(f777(f5(a851),x83454),x83453))) % 174.01/173.89 [8358]E(x83581,f4(a103))+E(f123(x83582,x83583,f777(x83584,f777(f777(f5(a103),x83581),f82(a103))),f777(f777(f11(x83582,a103,f853(f855(x83583))),x83585),x83581)),f777(f193(x83582,x83583,x83584,x83585),x83581)) % 174.01/173.89 [8382]~E(x83823,f182(f858(x83821,a845)))+E(f777(f777(f48(x83821,f858(x83822,a845)),x83823),f777(f777(f12(f858(x83822,a845),f858(x83822,a845),x83821),f777(f105(f858(x83822,a845)),x83824)),x83825)),f182(f858(x83822,a845))) % 174.01/173.89 [8383]~E(x83833,f182(f858(x83831,a845)))+E(f777(f777(f49(x83831,f858(x83832,a845)),x83833),f777(f777(f12(f858(x83832,a845),f858(x83832,a845),x83831),f777(f5(f858(x83832,a845)),x83834)),x83835)),f241(f858(x83832,a845))) % 174.01/173.89 [8384]~E(x83843,f182(f858(x83841,a845)))+E(f777(f777(f49(x83841,f858(x83842,a845)),x83843),f777(f777(f12(f858(x83842,a845),f858(x83842,a845),x83841),f777(f106(f858(x83842,a845)),x83844)),x83845)),f241(f858(x83842,a845))) % 174.01/173.89 [8389]~P136(x83892)+E(f777(f777(f10(x83891,x83892),f777(f777(f12(x83892,x83892,x83891),f777(f85(x83892),x83893)),x83894)),x83895),f777(f777(f85(x83892),x83893),f777(f777(f10(x83891,x83892),x83894),x83895))) % 174.01/173.89 [8653]E(x86531,f182(f858(x86532,a845)))+E(f777(f777(f48(x86532,f858(x86533,a845)),x86531),f777(f777(f12(f858(x86533,a845),f858(x86533,a845),x86532),f777(f105(f858(x86533,a845)),x86534)),x86535)),f777(f777(f105(f858(x86533,a845)),x86534),f777(f777(f48(x86532,f858(x86533,a845)),x86531),x86535))) % 174.01/173.89 [8654]E(x86541,f182(f858(x86542,a845)))+E(f777(f777(f49(x86542,f858(x86543,a845)),x86541),f777(f777(f12(f858(x86543,a845),f858(x86543,a845),x86542),f777(f5(f858(x86543,a845)),x86544)),x86545)),f777(f777(f5(f858(x86543,a845)),x86544),f777(f777(f48(x86542,f858(x86543,a845)),x86541),x86545))) % 174.01/173.89 [8655]E(x86551,f182(f858(x86552,a845)))+E(f777(f777(f49(x86552,f858(x86553,a845)),x86551),f777(f777(f12(f858(x86553,a845),f858(x86553,a845),x86552),f777(f106(f858(x86553,a845)),x86554)),x86555)),f777(f777(f106(f858(x86553,a845)),x86554),f777(f777(f49(x86552,f858(x86553,a845)),x86551),x86555))) % 174.01/173.89 [9074]~P29(x90742,x90741,x90743,f777(f777(f105(f858(x90742,a845)),x90744),x90745))+E(f777(f777(f106(f858(x90741,a845)),f777(f305(x90742,x90741,x90743),f777(f777(f5(f858(x90742,a845)),x90744),x90745))),f777(f305(x90742,x90741,x90743),f777(f777(f5(f858(x90742,a845)),x90745),x90744))),f182(f858(x90741,a845))) % 174.01/173.89 [9329]~P1(f777(f777(f234(f858(x93293,a845)),f777(f279(x93291,x93293,x93294),x93292)),x93295))+P1(f777(f777(f234(f858(x93291,a845)),x93292),f777(f83(f858(x93291,a845)),f777(f279(x93293,x93291,f777(f280(x93291,x93293),x93294)),f777(f83(f858(x93293,a845)),x93295))))) % 174.01/173.89 [9352]~P29(x93521,x93522,x93523,f777(f777(f304(x93521),x93524),x93525))+~P1(f777(f777(f336(x93522),f777(x93523,x93524)),f777(f305(x93521,x93522,x93523),f777(f777(f5(f858(x93521,a845)),x93525),f777(f777(f304(x93521),x93524),f182(f858(x93521,a845))))))) % 174.01/173.89 [9401]P1(f777(f777(f234(f858(x94011,a845)),f777(f279(x94012,x94011,x94013),x94014)),x94015))+~P1(f777(f777(f234(f858(x94012,a845)),x94014),f777(f83(f858(x94012,a845)),f777(f279(x94011,x94012,f777(f280(x94012,x94011),x94013)),f777(f83(f858(x94011,a845)),x94015))))) % 174.01/173.89 [9474]~P79(x94741)+P1(f777(f777(f234(x94741),f777(f79(x94741),f777(f777(f5(x94741),f777(f777(f84(x94741),x94742),x94743)),f777(f777(f84(x94741),x94744),x94745)))),f777(f777(f84(x94741),f777(f79(x94741),f777(f777(f5(x94741),x94742),x94744))),f777(f79(x94741),f777(f777(f5(x94741),x94743),x94745))))) % 174.01/173.89 [9567]P1(f777(f777(f336(x95671),f394(x95672,x95673,x95674,x95671,x95675)),x95674))+P1(f777(f777(f234(f858(x95675,a845)),f777(f777(f48(x95671,f858(x95675,a845)),x95674),x95673)),x95672)) % 174.01/173.89 [9739]~P1(f777(f777(f234(f858(x97391,a845)),f777(x97394,f394(x97395,x97394,x97393,x97392,x97391))),x97395))+P1(f777(f777(f234(f858(x97391,a845)),f777(f777(f48(x97392,f858(x97391,a845)),x97393),x97394)),x97395)) % 174.01/173.89 [8498]E(f777(f777(f127(x84981),x84982),f777(f777(f150(x84981,x84983),f777(f777(f5(a851),x84984),f777(f183(f852(x84981)),x84982))),x84985)),f777(f777(f150(x84981,f777(f777(f127(x84981),x84982),x84983)),x84984),x84985))+P1(f777(f777(f235(a851),x84984),f777(f183(f852(x84981)),x84982))) % 174.01/173.89 [8523]~P135(x85231)+E(f777(f777(f84(x85231),f777(f777(f85(x85231),x85232),x85233)),f777(f777(f84(x85231),f777(f777(f85(x85231),x85234),x85233)),x85235)),f777(f777(f84(x85231),f777(f777(f85(x85231),f777(f777(f84(x85231),x85232),x85234)),x85233)),x85235)) % 174.01/173.89 [9031]~P136(x90311)+E(f777(f157(x90311),f777(f777(f145(x90312,x90311),f777(f777(f12(x90311,x90311,x90312),f777(f85(x90311),x90313)),x90314)),x90315)),f777(f777(f85(x90311),x90313),f777(f157(x90311),f777(f777(f145(x90312,x90311),x90314),x90315)))) % 174.01/173.89 [9408]~P136(x94082)+E(f777(f777(f10(x94081,x94082),f777(f777(f11(x94081,x94082,x94082),f777(f777(f12(x94082,f858(x94082,x94082),x94081),f85(x94082)),x94083)),x94084)),x94085),f777(f777(f85(x94082),f777(f777(f10(x94081,x94082),x94083),x94085)),x94084)) % 174.01/173.89 [9409]~P61(x94092)+E(f777(f777(f10(x94091,x94092),f777(f777(f11(x94091,x94092,x94092),f777(f777(f12(x94092,f858(x94092,x94092),x94091),f285(x94092)),x94093)),x94094)),x94095),f777(f777(f285(x94092),f777(f777(f10(x94091,x94092),x94093),x94095)),x94094)) % 174.01/173.89 [9416]~P66(x94162)+E(f777(f777(f10(x94161,x94162),f777(f777(f22(x94161,x94162,x94162),f777(f777(f12(x94162,f858(x94162,x94162),x94161),f84(x94162)),x94163)),x94164)),x94165),f777(f777(f84(x94162),f777(f777(f10(x94161,x94162),x94163),x94165)),f777(f777(f10(x94161,x94162),x94164),x94165))) % 174.01/173.89 [9417]~P6(x94172)+E(f777(f777(f10(x94171,x94172),f777(f777(f22(x94171,x94172,x94172),f777(f777(f12(x94172,f858(x94172,x94172),x94171),f5(x94172)),x94173)),x94174)),x94175),f777(f777(f5(x94172),f777(f777(f10(x94171,x94172),x94173),x94175)),f777(f777(f10(x94171,x94172),x94174),x94175))) % 174.01/173.89 [9418]~P70(x94182)+E(f777(f777(f13(x94181,x94182),f777(f777(f22(x94181,x94182,x94182),f777(f777(f12(x94182,f858(x94182,x94182),x94181),f85(x94182)),x94183)),x94184)),x94185),f777(f777(f85(x94182),f777(f777(f13(x94181,x94182),x94183),x94185)),f777(f777(f13(x94181,x94182),x94184),x94185))) % 174.01/173.89 [9457]~E(x94573,f182(f858(x94571,a845)))+E(f777(f777(f48(x94571,f858(x94572,a845)),x94573),f777(f777(f11(x94571,f858(x94572,a845),f858(x94572,a845)),f777(f777(f12(f858(x94572,a845),f858(f858(x94572,a845),f858(x94572,a845)),x94571),f105(f858(x94572,a845))),x94574)),x94575)),f182(f858(x94572,a845))) % 174.01/173.89 [9458]~E(x94583,f182(f858(x94581,a845)))+E(f777(f777(f49(x94581,f858(x94582,a845)),x94583),f777(f777(f11(x94581,f858(x94582,a845),f858(x94582,a845)),f777(f777(f12(f858(x94582,a845),f858(f858(x94582,a845),f858(x94582,a845)),x94581),f5(f858(x94582,a845))),x94584)),x94585)),f241(f858(x94582,a845))) % 174.01/173.89 [9459]~E(x94593,f182(f858(x94591,a845)))+E(f777(f777(f49(x94591,f858(x94592,a845)),x94593),f777(f777(f11(x94591,f858(x94592,a845),f858(x94592,a845)),f777(f777(f12(f858(x94592,a845),f858(f858(x94592,a845),f858(x94592,a845)),x94591),f106(f858(x94592,a845))),x94594)),x94595)),f241(f858(x94592,a845))) % 174.01/173.89 [9484]E(x94841,f182(f858(x94842,a845)))+E(f777(f777(f48(x94842,f858(x94843,a845)),x94841),f777(f777(f11(x94842,f858(x94843,a845),f858(x94843,a845)),f777(f777(f12(f858(x94843,a845),f858(f858(x94843,a845),f858(x94843,a845)),x94842),f105(f858(x94843,a845))),x94844)),x94845)),f777(f777(f105(f858(x94843,a845)),f777(f777(f48(x94842,f858(x94843,a845)),x94841),x94844)),x94845)) % 174.01/173.89 [9485]E(x94851,f182(f858(x94852,a845)))+E(f777(f777(f49(x94852,f858(x94853,a845)),x94851),f777(f777(f11(x94852,f858(x94853,a845),f858(x94853,a845)),f777(f777(f12(f858(x94853,a845),f858(f858(x94853,a845),f858(x94853,a845)),x94852),f5(f858(x94853,a845))),x94854)),x94855)),f777(f777(f5(f858(x94853,a845)),f777(f777(f49(x94852,f858(x94853,a845)),x94851),x94854)),x94855)) % 174.01/173.89 [9486]E(x94861,f182(f858(x94862,a845)))+E(f777(f777(f49(x94862,f858(x94863,a845)),x94861),f777(f777(f11(x94862,f858(x94863,a845),f858(x94863,a845)),f777(f777(f12(f858(x94863,a845),f858(f858(x94863,a845),f858(x94863,a845)),x94862),f106(f858(x94863,a845))),x94864)),x94865)),f777(f777(f106(f858(x94863,a845)),f777(f777(f49(x94862,f858(x94863,a845)),x94861),x94864)),x94865)) % 174.01/173.89 [9078]~P1(f777(f777(f234(a851),x90781),x90784))+E(f777(f777(f5(a851),f777(f777(f84(a851),f777(f777(f85(a851),x90781),x90782)),x90783)),f777(f777(f84(a851),f777(f777(f85(a851),x90784),x90782)),x90785)),f777(f777(f5(a851),x90783),f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x90784),x90781)),x90782)),x90785))) % 174.01/173.89 [9620]~P136(x96201)+E(f777(f157(x96201),f777(f777(f145(x96202,x96201),f777(f777(f11(x96202,x96201,x96201),f777(f777(f12(x96201,f858(x96201,x96201),x96202),f85(x96201)),x96203)),x96204)),x96205)),f777(f777(f85(x96201),f777(f157(x96201),f777(f777(f145(x96202,x96201),x96203),x96205))),x96204)) % 174.01/173.89 [9626]~P66(x96261)+E(f777(f157(x96261),f777(f777(f145(x96262,x96261),f777(f777(f22(x96262,x96261,x96261),f777(f777(f12(x96261,f858(x96261,x96261),x96262),f84(x96261)),x96263)),x96264)),x96265)),f777(f777(f84(x96261),f777(f157(x96261),f777(f777(f145(x96262,x96261),x96263),x96265))),f777(f157(x96261),f777(f777(f145(x96262,x96261),x96264),x96265)))) % 174.01/173.89 [9627]~P6(x96271)+E(f777(f157(x96271),f777(f777(f145(x96272,x96271),f777(f777(f22(x96272,x96271,x96271),f777(f777(f12(x96271,f858(x96271,x96271),x96272),f5(x96271)),x96273)),x96274)),x96275)),f777(f777(f5(x96271),f777(f157(x96271),f777(f777(f145(x96272,x96271),x96273),x96275))),f777(f157(x96271),f777(f777(f145(x96272,x96271),x96274),x96275)))) % 174.01/173.89 [9296]~P1(f777(f777(f234(a851),x92964),x92961))+E(f777(f777(f5(a851),f777(f777(f84(a851),f777(f777(f85(a851),x92961),x92962)),x92963)),f777(f777(f84(a851),f777(f777(f85(a851),x92964),x92962)),x92965)),f777(f777(f5(a851),f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x92961),x92964)),x92962)),x92963)),x92965)) % 174.01/173.89 [10024]P28(x100241,x100242,f777(f305(a847,f850(x100241),f777(f777(f22(a847,f858(x100241,f858(a848,a845)),f850(x100241)),f777(f777(f22(a847,a846,f858(f858(x100241,f858(a848,a845)),f850(x100241))),f777(f777(f12(f858(x100241,f858(a848,a845)),f858(a846,f858(f858(x100241,f858(a848,a845)),f850(x100241))),a847),f95(x100241)),x100243)),a29)),x100244)),x100245))+~P28(x100241,f777(f777(f105(f858(f850(x100241),a845)),x100242),f777(f305(a847,f850(x100241),f777(f777(f22(a847,f858(x100241,f858(a848,a845)),f850(x100241)),f777(f777(f22(a847,a846,f858(f858(x100241,f858(a848,a845)),f850(x100241))),f777(f777(f12(f858(x100241,f858(a848,a845)),f858(a846,f858(f858(x100241,f858(a848,a845)),f850(x100241))),a847),f95(x100241)),x100243)),a29)),x100244)),x100245)),f777(f305(a847,f850(x100241),f777(f777(f22(a847,f858(x100241,f858(a848,a845)),f850(x100241)),f777(f777(f22(a847,a846,f858(f858(x100241,f858(a848,a845)),f850(x100241))),f777(f777(f12(f858(x100241,f858(a848,a845)),f858(a846,f858(f858(x100241,f858(a848,a845)),f850(x100241))),a847),f95(x100241)),x100243)),f777(f777(f12(f855(a846),a846,a847),f233(a846)),a32))),x100244)),x100245)) % 174.01/173.89 [5154]E(x51541,x51542)+~E(f35(x51543,x51544,x51541),f35(x51545,x51546,x51542)) % 174.01/173.89 [5155]E(x51551,x51552)+~E(f35(x51553,x51551,x51554),f35(x51555,x51552,x51556)) % 174.01/173.89 [5156]E(x51561,x51562)+~E(f35(x51561,x51563,x51564),f35(x51562,x51565,x51566)) % 174.01/173.89 [5157]E(x51571,x51572)+~E(f34(x51573,x51574,x51571),f34(x51575,x51576,x51572)) % 174.01/173.89 [5158]E(x51581,x51582)+~E(f34(x51583,x51581,x51584),f34(x51585,x51582,x51586)) % 174.01/173.89 [5159]E(x51591,x51592)+~E(f34(x51591,x51593,x51594),f34(x51592,x51595,x51596)) % 174.01/173.89 [5160]E(x51601,x51602)+~E(f33(x51603,x51604,x51601),f33(x51605,x51606,x51602)) % 174.01/173.89 [5161]E(x51611,x51612)+~E(f33(x51613,x51611,x51614),f33(x51615,x51612,x51616)) % 174.01/173.89 [5162]E(x51621,x51622)+~E(f33(x51621,x51623,x51624),f33(x51622,x51625,x51626)) % 174.01/173.89 [7184]E(x71841,x71842)+~E(f217(x71843,x71844,x71845,x71841),f217(x71843,x71844,x71846,x71842)) % 174.01/173.89 [7185]E(x71851,x71852)+~E(f217(x71853,x71854,x71851,x71855),f217(x71853,x71854,x71852,x71856)) % 174.01/173.89 [6627]E(f777(f172(x66271,x66272,x66273,x66274),x66275),f777(f229(x66272),x66276))+~E(f777(x66274,x66275),f777(f229(x66272),x66276)) % 174.01/173.89 [6779]E(f777(f231(f855(x67791),x67792,f185(x67791),x67793),f777(x67794,x67795)),f777(x67793,x67796))+~E(f777(x67794,x67795),f777(f229(x67792),x67796)) % 174.01/173.89 [8325]~P23(x83255,x83251,x83252,x83256)+E(f777(f77(x83251,x83251,x83251,f777(x83252,x83253)),f777(x83252,x83254)),f777(f77(x83251,x83251,x83251,f777(x83252,x83254)),f777(x83252,x83253))) % 174.01/173.89 [8558]~P55(x85584,x85585,x85582,x85581,x85586)+E(f777(x85581,f777(x85582,x85583)),x85583) % 174.01/173.89 [8699]P29(x86991,x86992,x86993,x86994)+~P29(x86991,x86995,f777(f77(x86992,x86995,x86991,x86996),x86993),x86994) % 174.01/173.89 [8776]~P29(x87764,x87762,f777(f77(x87761,x87762,x87764,x87763),x87765),x87766)+P29(x87761,x87762,x87763,f777(f305(x87764,x87761,x87765),x87766)) % 174.01/173.89 [9419]P1(f777(f65(x94191),x94192))+~P1(f777(f70(x94191,x94193,x94194,x94195,x94192),x94196)) % 174.01/173.89 [9429]~P1(f777(f777(f336(x94294),x94293),f294(x94294,x94295,x94291,x94292,x94296)))+P1(f777(f777(x94291,x94292),x94293)) % 174.01/173.89 [9430]~P1(f777(f777(f336(x94304),x94303),f291(x94304,x94301,x94305,x94302,x94306)))+P1(f777(f777(x94301,x94302),x94303)) % 174.01/173.89 [9431]~P1(f777(f777(f336(x94314),x94312),f294(x94314,x94311,x94315,x94316,x94313)))+P1(f777(f777(x94311,x94312),x94313)) % 174.01/173.89 [9432]~P1(f777(f777(f336(x94324),x94322),f291(x94324,x94325,x94321,x94326,x94323)))+P1(f777(f777(x94321,x94322),x94323)) % 174.01/173.89 [5644]E(x56441,x56442)+~E(f777(f777(f243(x56443,x56444),x56445),x56441),f777(f777(f243(x56443,x56444),x56446),x56442)) % 174.01/173.89 [5646]E(x56461,x56462)+~E(f777(f777(f243(x56463,x56464),x56461),x56465),f777(f777(f243(x56463,x56464),x56462),x56466)) % 174.01/173.90 [5785]~P20(x57855,x57856,x57851)+E(f777(f777(x57851,x57852),f777(f777(x57851,x57853),x57854)),f777(f777(x57851,x57853),f777(f777(x57851,x57852),x57854))) % 174.01/173.90 [7255]~P34(x72554,x72551,f777(f777(f142(x72554),x72552),x72555),f777(f777(f142(x72554),x72553),x72556))+P1(f777(f777(x72551,x72552),x72553)) % 174.01/173.90 [7634]P34(x76341,x76342,x76343,x76344)+~P34(x76341,x76342,f777(f777(f142(x76341),x76345),x76343),f777(f777(f142(x76341),x76346),x76344)) % 174.01/173.90 [8644]~P55(x86445,x86441,x86442,x86446,x86444)+P1(f777(f777(f336(x86441),f777(x86442,x86443)),x86444)) % 174.01/173.90 [8798]E(f777(f80(x87981,x87982,x87983,x87984,x87985),x87986),f777(x87983,x87986))+P1(f777(f777(f336(x87981),x87986),x87985)) % 174.01/173.90 [8816]~E(x88163,f777(f777(f142(x88161),x88165),x88166))+P1(f777(f777(f336(f857(f852(x88161),f852(x88161))),f777(f777(f243(f852(x88161),f852(x88161)),x88162),f777(f777(f127(x88161),x88162),x88163))),f139(x88161,x88164))) % 174.01/173.90 [8820]E(f777(f80(x88201,x88202,x88203,x88204,x88205),x88206),f777(x88204,x88206))+~P1(f777(f777(f336(x88201),x88206),x88205)) % 174.01/173.90 [9496]~P27(x94964,x94962,x94965,x94963,x94966,x94961)+E(f777(x94961,f182(f858(x94962,a845))),x94963) % 174.01/173.90 [9701]~E(f777(x97014,f777(f242(x97011,x97013),x97015)),f777(x97016,f777(f242(x97011,x97013),x97015)))+E(f777(f254(x97011,x97012,x97013,x97013,x97014,f41(x97013)),x97015),f777(f254(x97011,x97012,x97013,x97013,x97016,f41(x97013)),x97015)) % 174.01/173.90 [9702]~E(f777(x97024,f777(f252(x97021,x97022),x97025)),f777(x97026,f777(f252(x97021,x97022),x97025)))+E(f777(f254(x97021,x97021,x97022,x97023,f41(x97021),x97024),x97025),f777(f254(x97021,x97021,x97022,x97023,f41(x97021),x97026),x97025)) % 174.01/173.90 [9762]~E(f777(f254(x97622,x97626,x97623,x97623,x97621,f41(x97623)),x97624),f777(f254(x97622,x97626,x97623,x97623,x97625,f41(x97623)),x97624))+E(f777(x97621,f777(f242(x97622,x97623),x97624)),f777(x97625,f777(f242(x97622,x97623),x97624))) % 174.01/173.90 [9763]~E(f777(f254(x97632,x97632,x97633,x97636,f41(x97632),x97631),x97634),f777(f254(x97632,x97632,x97633,x97636,f41(x97632),x97635),x97634))+E(f777(x97631,f777(f252(x97632,x97633),x97634)),f777(x97635,f777(f252(x97632,x97633),x97634))) % 174.01/173.90 [8733]P1(f777(f777(f336(x87331),x87332),x87333))+~P1(f777(f777(f336(f857(x87331,x87334)),f777(f777(f243(x87331,x87334),x87332),x87335)),f777(f777(f250(x87331,x87334),x87333),x87336))) % 174.01/173.90 [8748]P1(f777(f777(f336(x87481),x87482),f777(x87483,x87484)))+~P1(f777(f777(f336(f857(x87485,x87481)),f777(f777(f243(x87485,x87481),x87484),x87482)),f777(f777(f250(x87485,x87481),x87486),x87483))) % 174.01/173.90 [9054]P1(f777(f777(f336(x90541),x90544),f171(x90541,x90542,x90546)))+E(f172(x90541,x90542,f777(f777(f777(f76(x90541,f855(x90542)),x90543),x90544),f777(f229(x90542),x90545)),x90546),f777(f777(f777(f76(x90541,f855(x90542)),f172(x90541,x90542,x90543,x90546)),x90544),f777(f229(x90542),x90545))) % 174.01/173.90 [9145]P1(f777(f777(f336(f857(x91451,x91451)),f777(f777(f243(x91451,x91451),f777(x91452,x91453)),f777(x91452,x91454))),x91455))+~P1(f777(f777(f336(f857(x91456,x91456)),f777(f777(f243(x91456,x91456),x91453),x91454)),f777(f777(f282(x91451,x91456),x91455),x91452))) % 174.01/173.90 [9157]~P1(f777(f777(f336(f857(x91574,x91574)),f777(f777(f243(x91574,x91574),f777(x91576,x91572)),f777(x91576,x91573))),x91575))+P1(f777(f777(f336(f857(x91571,x91571)),f777(f777(f243(x91571,x91571),x91572),x91573)),f777(f777(f282(x91574,x91571),x91575),x91576))) % 174.01/173.90 [9765]E(f777(f777(f243(x97651,x97652),f707(x97653,x97654,x97655,x97656,x97652,x97651)),f710(x97653,x97654,x97655,x97656,x97652,x97651)),x97656)+~P1(f777(f777(f336(f857(x97651,x97652)),x97656),f777(f777(f283(x97651,x97655,x97652),x97654),x97653))) % 174.01/173.90 [9973]~P1(f777(f777(f336(f857(x99731,x99736)),x99735),f777(f777(f283(x99731,x99732,x99736),x99734),x99733)))+P1(f777(f777(f336(f857(x99731,x99732)),f777(f777(f243(x99731,x99732),f707(x99733,x99734,x99732,x99735,x99736,x99731)),f711(x99733,x99734,x99732,x99735,x99736,x99731))),x99734)) % 174.01/173.90 [9974]~P1(f777(f777(f336(f857(x99746,x99742)),x99745),f777(f777(f283(x99746,x99741,x99742),x99744),x99743)))+P1(f777(f777(f336(f857(x99741,x99742)),f777(f777(f243(x99741,x99742),f711(x99743,x99744,x99741,x99745,x99742,x99746)),f710(x99743,x99744,x99741,x99745,x99742,x99746))),x99743)) % 174.01/173.90 [6063]~E(x60636,x60634)+E(f777(f777(f777(f777(f76(x60631,x60632),x60633),x60634),x60635),x60636),x60635) % 174.01/173.90 [6112]E(x61121,x61122)+E(f777(f777(f777(f777(f76(x61123,x61124),x61125),x61122),x61126),x61121),f777(x61125,x61121)) % 174.01/173.90 [7700]~P9(x77002)+E(f777(f777(f48(x77001,x77002),x77003),f777(f777(f11(x77001,x77004,x77002),x77005),x77006)),f777(f777(f777(f48(x77001,f858(x77004,x77002)),x77003),x77005),x77006)) % 174.01/173.90 [7701]~P9(x77012)+E(f777(f777(f49(x77011,x77012),x77013),f777(f777(f11(x77011,x77014,x77012),x77015),x77016)),f777(f777(f777(f49(x77011,f858(x77014,x77012)),x77013),x77015),x77016)) % 174.01/173.90 [8480]E(f777(f777(f48(x84801,f858(x84802,a845)),x84803),f777(f777(f12(f858(x84802,a845),f858(x84802,a845),x84801),f777(f304(x84802),x84804)),x84805)),f777(f777(f304(x84802),x84804),f777(f777(f48(x84801,f858(x84802,a845)),x84803),x84805)))+~P1(f777(f777(f336(x84801),x84806),x84803)) % 174.01/173.90 [8860]~P9(x88602)+E(f777(f777(f48(x88601,x88602),x88603),f777(f777(f12(f858(x88604,x88602),x88602,x88601),f777(f48(x88604,x88602),x88605)),f777(f11(x88604,x88601,x88602),x88606))),f777(f777(f48(x88604,x88602),x88605),f777(f777(f12(f858(x88601,x88602),x88602,x88604),f777(f48(x88601,x88602),x88603)),x88606))) % 174.01/173.90 [8861]~P9(x88612)+E(f777(f777(f49(x88611,x88612),x88613),f777(f777(f12(f858(x88614,x88612),x88612,x88611),f777(f49(x88614,x88612),x88615)),f777(f11(x88614,x88611,x88612),x88616))),f777(f777(f49(x88614,x88612),x88615),f777(f777(f12(f858(x88611,x88612),x88612,x88614),f777(f49(x88611,x88612),x88613)),x88616))) % 174.01/173.90 [9062]P1(f777(f777(f336(x90621),x90622),f777(f160(x90621),x90623)))+~P1(f777(f777(f336(f857(x90624,x90621)),f777(f777(f243(x90624,x90621),x90625),x90622)),f777(f160(f857(x90624,x90621)),f777(f777(f169(x90624,x90621),x90626),x90623)))) % 174.01/173.90 [9063]P1(f777(f777(f336(x90631),x90632),f777(f160(x90631),x90633)))+~P1(f777(f777(f336(f857(x90631,x90634)),f777(f777(f243(x90631,x90634),x90632),x90635)),f777(f160(f857(x90631,x90634)),f777(f777(f169(x90631,x90634),x90633),x90636)))) % 174.01/173.90 [9155]P1(f777(f777(f234(f858(x91551,a845)),f777(f279(x91552,x91551,x91553),x91554)),x91555))+~P1(f777(f777(f234(f858(f857(x91552,x91551),a845)),x91553),f777(f777(f250(x91552,x91551),x91556),f777(f20(f858(x91551,a845),x91552),x91555)))) % 174.01/173.90 [9332]P1(f777(f777(f336(f857(f852(x93321),f852(x93321))),f777(f777(f243(f852(x93321),f852(x93321)),f777(f777(f142(x93321),x93322),x93323)),f777(f777(f142(x93321),x93324),x93325))),f139(x93321,x93326)))+~P1(f777(f777(f336(f857(x93321,x93321)),f777(f777(f243(x93321,x93321),x93322),x93324)),x93326)) % 174.01/173.90 [9761]E(f777(f777(f243(x97611,x97612),f614(x97613,x97614,x97615,x97612,x97611,x97616)),f617(x97613,x97614,x97615,x97612,x97611,x97616)),x97616)+P1(f777(f777(f336(x97615),x97614),f777(f777(f253(x97611,x97612,f858(x97615,a845)),x97613),x97616))) % 174.01/173.90 [9766]E(f777(f777(f243(x97661,x97662),f615(x97663,x97664,x97662,x97661,x97665,x97666)),f616(x97663,x97664,x97662,x97661,x97665,x97666)),x97663)+~P1(f777(f777(f336(x97666),x97665),f777(f777(f253(x97661,x97662,f858(x97666,a845)),x97664),x97663))) % 174.01/173.90 [9928]P1(f777(f777(f336(x99281),x99282),f777(f777(x99283,f615(x99284,x99283,x99285,x99286,x99282,x99281)),f616(x99284,x99283,x99285,x99286,x99282,x99281))))+~P1(f777(f777(f336(x99281),x99282),f777(f777(f253(x99286,x99285,f858(x99281,a845)),x99283),x99284))) % 174.01/173.90 [9952]~P1(f777(f777(f336(x99521),x99522),f777(f777(x99525,f614(x99525,x99522,x99521,x99524,x99523,x99526)),f617(x99525,x99522,x99521,x99524,x99523,x99526))))+P1(f777(f777(f336(x99521),x99522),f777(f777(f253(x99523,x99524,f858(x99521,a845)),x99525),x99526))) % 174.01/173.90 [7825]P1(f777(f777(f336(x78251),x78254),x78256))+E(f174(x78251,x78252,f777(f777(f777(f76(x78251,f855(x78252)),x78253),x78254),x78255),x78256),f174(x78251,x78252,x78253,x78256)) % 174.01/173.90 [7900]P1(f777(f777(f336(x79001),x79004),x79006))+E(f777(f305(x79001,x79002,f777(f777(f777(f76(x79001,x79002),x79003),x79004),x79005)),x79006),f777(f305(x79001,x79002,x79003),x79006)) % 174.01/173.90 [7928]P1(f777(f777(f336(x79281),x79284),f777(f160(x79281),x79286)))+E(f777(f777(f145(x79281,x79282),f777(f777(f777(f76(x79281,x79282),x79283),x79284),x79285)),x79286),f777(f777(f145(x79281,x79282),x79283),x79286)) % 174.01/173.90 [8375]E(x83751,x83752)+E(f777(f777(f150(x83753,f777(f777(f150(x83753,x83754),x83751),x83755)),x83752),x83756),f777(f777(f150(x83753,f777(f777(f150(x83753,x83754),x83752),x83756)),x83751),x83755)) % 174.01/173.90 [8866]~P1(f777(f777(f336(x88663),x88666),x88665))+E(f777(f777(f304(x88661),x88662),f777(f305(x88663,x88661,x88664),f777(f777(f5(f858(x88663,a845)),x88665),f777(f777(f304(x88663),x88666),f182(f858(x88663,a845)))))),f777(f305(x88663,x88661,f777(f777(f777(f76(x88663,x88661),x88664),x88666),x88662)),x88665)) % 174.01/173.90 [8694]~E(x86943,x86946)+E(f777(f168(x86941,x86942,f777(f777(f142(f857(x86941,x86942)),f777(f777(f243(x86941,x86942),x86943),x86944)),x86945)),x86946),f777(f229(x86942),x86944)) % 174.01/173.90 [8735]E(x87351,x87352)+E(f777(f168(x87353,x87354,f777(f777(f142(f857(x87353,x87354)),f777(f777(f243(x87353,x87354),x87351),x87355)),x87356)),x87352),f777(f168(x87353,x87354,x87356),x87352)) % 174.01/173.90 [8941]~P1(f777(f777(x89414,x89415),x89416))+P1(f777(f777(f777(f777(f105(f858(x89411,f858(x89412,a845))),x89413),x89414),x89415),x89416)) % 174.01/173.90 [8943]~P1(f777(f777(x89433,x89435),x89436))+P1(f777(f777(f777(f777(f105(f858(x89431,f858(x89432,a845))),x89433),x89434),x89435),x89436)) % 174.01/173.90 [8959]P1(f777(f777(f336(x89591),x89596),f777(f160(x89591),x89594)))+E(f777(f172(x89591,x89592,x89593,f168(x89591,x89592,f777(f144(f857(x89591,x89592)),f777(f777(f169(x89591,x89592),x89594),x89595)))),x89596),f777(x89593,x89596)) % 174.01/173.90 [9108]~E(f777(f183(f852(x91081)),x91084),f777(f183(f852(x91082)),x91085))+E(f172(x91081,x91082,x91083,f168(x91081,x91082,f777(f144(f857(x91081,x91082)),f777(f777(f169(x91081,x91082),x91084),f777(f777(f127(x91082),x91085),x91086))))),f172(x91081,x91082,x91083,f168(x91081,x91082,f777(f144(f857(x91081,x91082)),f777(f777(f169(x91081,x91082),x91084),x91085))))) % 174.01/173.90 [9195]P1(f777(f777(x91951,x91952),x91953))+~P1(f777(f777(f777(f777(f106(f858(x91954,f858(x91955,a845))),x91956),x91951),x91952),x91953)) % 174.01/173.90 [9196]P1(f777(f777(x91961,x91962),x91963))+~P1(f777(f777(f777(f777(f106(f858(x91964,f858(x91965,a845))),x91961),x91966),x91962),x91963)) % 174.01/173.90 [9609]~P66(x96092)+E(f777(f777(f10(x96091,x96092),f777(f777(f11(x96091,f858(x96093,a845),x96092),f777(f777(f12(f858(x96093,x96092),f858(f858(x96093,a845),x96092),x96091),f10(x96093,x96092)),x96094)),x96095)),x96096),f777(f777(f10(f857(x96091,x96093),x96092),f777(f253(x96091,x96093,x96092),x96094)),f777(f777(f250(x96091,x96093),x96096),f777(f20(f858(x96093,a845),x96091),x96095)))) % 174.01/173.90 [9610]~P70(x96102)+E(f777(f777(f13(x96101,x96102),f777(f777(f11(x96101,f858(x96103,a845),x96102),f777(f777(f12(f858(x96103,x96102),f858(f858(x96103,a845),x96102),x96101),f13(x96103,x96102)),x96104)),x96105)),x96106),f777(f777(f13(f857(x96101,x96103),x96102),f777(f253(x96101,x96103,x96102),x96104)),f777(f777(f250(x96101,x96103),x96106),f777(f20(f858(x96103,a845),x96101),x96105)))) % 174.01/173.90 [9728]~P66(x97282)+E(f777(f777(f10(x97281,x97282),f777(f777(f11(x97281,f858(x97283,a845),x97282),f777(f777(f12(f858(x97283,x97282),f858(f858(x97283,a845),x97282),x97281),f10(x97283,x97282)),f777(f11(x97283,x97281,x97282),x97284))),x97285)),x97286),f777(f777(f10(x97283,x97282),f777(f777(f11(x97283,f858(x97281,a845),x97282),f777(f777(f12(f858(x97281,x97282),f858(f858(x97281,a845),x97282),x97283),f10(x97281,x97282)),x97284)),x97286)),x97285)) % 174.01/173.90 [9197]~E(f777(f183(f852(x91971)),x91974),f777(f183(f852(x91972)),x91976))+E(f172(x91971,x91972,x91973,f168(x91971,x91972,f777(f144(f857(x91971,x91972)),f777(f777(f169(x91971,x91972),f777(f777(f127(x91971),x91974),x91975)),x91976)))),f172(x91971,x91972,x91973,f168(x91971,x91972,f777(f144(f857(x91971,x91972)),f777(f777(f169(x91971,x91972),x91974),x91976))))) % 174.01/173.90 [9461]~P1(f777(f777(f336(x94611),x94615),x94614))+E(f777(f777(f777(f76(x94611,f855(x94612)),f174(x94611,x94612,x94613,f777(f777(f5(f858(x94611,a845)),x94614),f777(f777(f304(x94611),x94615),f182(f858(x94611,a845)))))),x94615),x94616),f174(x94611,x94612,f777(f777(f777(f76(x94611,f855(x94612)),x94613),x94615),x94616),x94614)) % 174.01/173.90 [9668]E(f172(x96681,x96682,x96683,f168(x96681,x96682,f777(f144(f857(x96681,x96682)),f777(f777(f169(x96681,x96682),f777(f777(f127(x96681),x96684),f777(f777(f142(x96681),x96685),f117(x96681)))),x96686)))),f777(f777(f777(f76(x96681,f855(x96682)),f172(x96681,x96682,x96683,f168(x96681,x96682,f777(f144(f857(x96681,x96682)),f777(f777(f169(x96681,x96682),x96684),x96686))))),x96685),f777(f229(x96682),f777(f777(f155(x96682),x96686),f777(f183(f852(x96681)),x96684)))))+~P1(f777(f777(f235(a851),f777(f183(f852(x96681)),x96684)),f777(f183(f852(x96682)),x96686))) % 174.01/173.90 [10027]~P1(f777(f777(f336(f857(x100271,x100272)),f777(f777(f243(x100271,x100272),x100275),x100276)),f777(f777(f105(f858(f857(x100271,x100272),a845)),x100273),x100274)))+P1(f777(f777(f777(f777(f105(f858(x100271,f858(x100272,a845))),f777(f777(f11(x100271,f858(f857(x100271,x100272),a845),f858(x100272,a845)),f777(f777(f12(f858(x100272,f858(f858(f857(x100271,x100272),a845),a845)),f858(f858(f857(x100271,x100272),a845),f858(x100272,a845)),x100271),f11(x100272,f858(f857(x100271,x100272),a845),a845)),f777(f777(f12(f858(x100272,f857(x100271,x100272)),f858(x100272,f858(f858(f857(x100271,x100272),a845),a845)),x100271),f777(f12(f857(x100271,x100272),f858(f858(f857(x100271,x100272),a845),a845),x100272),f336(f857(x100271,x100272)))),f243(x100271,x100272)))),x100273)),f777(f777(f11(x100271,f858(f857(x100271,x100272),a845),f858(x100272,a845)),f777(f777(f12(f858(x100272,f858(f858(f857(x100271,x100272),a845),a845)),f858(f858(f857(x100271,x100272),a845),f858(x100272,a845)),x100271),f11(x100272,f858(f857(x100271,x100272),a845),a845)),f777(f777(f12(f858(x100272,f857(x100271,x100272)),f858(x100272,f858(f858(f857(x100271,x100272),a845),a845)),x100271),f777(f12(f857(x100271,x100272),f858(f858(f857(x100271,x100272),a845),a845),x100272),f336(f857(x100271,x100272)))),f243(x100271,x100272)))),x100274)),x100275),x100276)) % 174.01/173.90 [10028]~P1(f777(f777(f336(f857(x100281,x100282)),f777(f777(f243(x100281,x100282),x100285),x100286)),f777(f777(f106(f858(f857(x100281,x100282),a845)),x100283),x100284)))+P1(f777(f777(f777(f777(f106(f858(x100281,f858(x100282,a845))),f777(f777(f11(x100281,f858(f857(x100281,x100282),a845),f858(x100282,a845)),f777(f777(f12(f858(x100282,f858(f858(f857(x100281,x100282),a845),a845)),f858(f858(f857(x100281,x100282),a845),f858(x100282,a845)),x100281),f11(x100282,f858(f857(x100281,x100282),a845),a845)),f777(f777(f12(f858(x100282,f857(x100281,x100282)),f858(x100282,f858(f858(f857(x100281,x100282),a845),a845)),x100281),f777(f12(f857(x100281,x100282),f858(f858(f857(x100281,x100282),a845),a845),x100282),f336(f857(x100281,x100282)))),f243(x100281,x100282)))),x100283)),f777(f777(f11(x100281,f858(f857(x100281,x100282),a845),f858(x100282,a845)),f777(f777(f12(f858(x100282,f858(f858(f857(x100281,x100282),a845),a845)),f858(f858(f857(x100281,x100282),a845),f858(x100282,a845)),x100281),f11(x100282,f858(f857(x100281,x100282),a845),a845)),f777(f777(f12(f858(x100282,f857(x100281,x100282)),f858(x100282,f858(f858(f857(x100281,x100282),a845),a845)),x100281),f777(f12(f857(x100281,x100282),f858(f858(f857(x100281,x100282),a845),a845),x100282),f336(f857(x100281,x100282)))),f243(x100281,x100282)))),x100284)),x100285),x100286)) % 174.01/173.90 [10032]P1(f777(f777(f336(f857(x100321,x100322)),f777(f777(f243(x100321,x100322),x100323),x100324)),f777(f777(f105(f858(f857(x100321,x100322),a845)),x100325),x100326)))+~P1(f777(f777(f777(f777(f105(f858(x100321,f858(x100322,a845))),f777(f777(f11(x100321,f858(f857(x100321,x100322),a845),f858(x100322,a845)),f777(f777(f12(f858(x100322,f858(f858(f857(x100321,x100322),a845),a845)),f858(f858(f857(x100321,x100322),a845),f858(x100322,a845)),x100321),f11(x100322,f858(f857(x100321,x100322),a845),a845)),f777(f777(f12(f858(x100322,f857(x100321,x100322)),f858(x100322,f858(f858(f857(x100321,x100322),a845),a845)),x100321),f777(f12(f857(x100321,x100322),f858(f858(f857(x100321,x100322),a845),a845),x100322),f336(f857(x100321,x100322)))),f243(x100321,x100322)))),x100325)),f777(f777(f11(x100321,f858(f857(x100321,x100322),a845),f858(x100322,a845)),f777(f777(f12(f858(x100322,f858(f858(f857(x100321,x100322),a845),a845)),f858(f858(f857(x100321,x100322),a845),f858(x100322,a845)),x100321),f11(x100322,f858(f857(x100321,x100322),a845),a845)),f777(f777(f12(f858(x100322,f857(x100321,x100322)),f858(x100322,f858(f858(f857(x100321,x100322),a845),a845)),x100321),f777(f12(f857(x100321,x100322),f858(f858(f857(x100321,x100322),a845),a845),x100322),f336(f857(x100321,x100322)))),f243(x100321,x100322)))),x100326)),x100323),x100324)) % 174.01/173.90 [10033]P1(f777(f777(f336(f857(x100331,x100332)),f777(f777(f243(x100331,x100332),x100333),x100334)),f777(f777(f106(f858(f857(x100331,x100332),a845)),x100335),x100336)))+~P1(f777(f777(f777(f777(f106(f858(x100331,f858(x100332,a845))),f777(f777(f11(x100331,f858(f857(x100331,x100332),a845),f858(x100332,a845)),f777(f777(f12(f858(x100332,f858(f858(f857(x100331,x100332),a845),a845)),f858(f858(f857(x100331,x100332),a845),f858(x100332,a845)),x100331),f11(x100332,f858(f857(x100331,x100332),a845),a845)),f777(f777(f12(f858(x100332,f857(x100331,x100332)),f858(x100332,f858(f858(f857(x100331,x100332),a845),a845)),x100331),f777(f12(f857(x100331,x100332),f858(f858(f857(x100331,x100332),a845),a845),x100332),f336(f857(x100331,x100332)))),f243(x100331,x100332)))),x100335)),f777(f777(f11(x100331,f858(f857(x100331,x100332),a845),f858(x100332,a845)),f777(f777(f12(f858(x100332,f858(f858(f857(x100331,x100332),a845),a845)),f858(f858(f857(x100331,x100332),a845),f858(x100332,a845)),x100331),f11(x100332,f858(f857(x100331,x100332),a845),a845)),f777(f777(f12(f858(x100332,f857(x100331,x100332)),f858(x100332,f858(f858(f857(x100331,x100332),a845),a845)),x100331),f777(f12(f857(x100331,x100332),f858(f858(f857(x100331,x100332),a845),a845),x100332),f336(f857(x100331,x100332)))),f243(x100331,x100332)))),x100336)),x100333),x100334)) % 174.01/173.90 [10022]~P1(f777(f777(f336(f857(x100222,x100223)),f777(f777(f243(x100222,x100223),x100225),x100226)),f777(f777(f48(x100221,f858(f857(x100222,x100223),a845)),f241(f858(x100221,a845))),x100224)))+P1(f777(f777(f777(f777(f48(x100221,f858(x100222,f858(x100223,a845))),f241(f858(x100221,a845))),f777(f777(f12(f858(f857(x100222,x100223),a845),f858(x100222,f858(x100223,a845)),x100221),f777(f11(x100222,f858(f857(x100222,x100223),a845),f858(x100223,a845)),f777(f777(f12(f858(x100223,f858(f858(f857(x100222,x100223),a845),a845)),f858(f858(f857(x100222,x100223),a845),f858(x100223,a845)),x100222),f11(x100223,f858(f857(x100222,x100223),a845),a845)),f777(f777(f12(f858(x100223,f857(x100222,x100223)),f858(x100223,f858(f858(f857(x100222,x100223),a845),a845)),x100222),f777(f12(f857(x100222,x100223),f858(f858(f857(x100222,x100223),a845),a845),x100223),f336(f857(x100222,x100223)))),f243(x100222,x100223))))),x100224)),x100225),x100226)) % 174.01/173.90 [10023]~P1(f777(f777(f336(f857(x100232,x100233)),f777(f777(f243(x100232,x100233),x100235),x100236)),f777(f777(f49(x100231,f858(f857(x100232,x100233),a845)),f241(f858(x100231,a845))),x100234)))+P1(f777(f777(f777(f777(f49(x100231,f858(x100232,f858(x100233,a845))),f241(f858(x100231,a845))),f777(f777(f12(f858(f857(x100232,x100233),a845),f858(x100232,f858(x100233,a845)),x100231),f777(f11(x100232,f858(f857(x100232,x100233),a845),f858(x100233,a845)),f777(f777(f12(f858(x100233,f858(f858(f857(x100232,x100233),a845),a845)),f858(f858(f857(x100232,x100233),a845),f858(x100233,a845)),x100232),f11(x100233,f858(f857(x100232,x100233),a845),a845)),f777(f777(f12(f858(x100233,f857(x100232,x100233)),f858(x100233,f858(f858(f857(x100232,x100233),a845),a845)),x100232),f777(f12(f857(x100232,x100233),f858(f858(f857(x100232,x100233),a845),a845),x100233),f336(f857(x100232,x100233)))),f243(x100232,x100233))))),x100234)),x100235),x100236)) % 174.01/173.90 [10030]P1(f777(f777(f336(f857(x100301,x100302)),f777(f777(f243(x100301,x100302),x100303),x100304)),f777(f777(f48(x100305,f858(f857(x100301,x100302),a845)),f241(f858(x100305,a845))),x100306)))+~P1(f777(f777(f777(f777(f48(x100305,f858(x100301,f858(x100302,a845))),f241(f858(x100305,a845))),f777(f777(f12(f858(f857(x100301,x100302),a845),f858(x100301,f858(x100302,a845)),x100305),f777(f11(x100301,f858(f857(x100301,x100302),a845),f858(x100302,a845)),f777(f777(f12(f858(x100302,f858(f858(f857(x100301,x100302),a845),a845)),f858(f858(f857(x100301,x100302),a845),f858(x100302,a845)),x100301),f11(x100302,f858(f857(x100301,x100302),a845),a845)),f777(f777(f12(f858(x100302,f857(x100301,x100302)),f858(x100302,f858(f858(f857(x100301,x100302),a845),a845)),x100301),f777(f12(f857(x100301,x100302),f858(f858(f857(x100301,x100302),a845),a845),x100302),f336(f857(x100301,x100302)))),f243(x100301,x100302))))),x100306)),x100303),x100304)) % 174.01/173.90 [10031]P1(f777(f777(f336(f857(x100311,x100312)),f777(f777(f243(x100311,x100312),x100313),x100314)),f777(f777(f49(x100315,f858(f857(x100311,x100312),a845)),f241(f858(x100315,a845))),x100316)))+~P1(f777(f777(f777(f777(f49(x100315,f858(x100311,f858(x100312,a845))),f241(f858(x100315,a845))),f777(f777(f12(f858(f857(x100311,x100312),a845),f858(x100311,f858(x100312,a845)),x100315),f777(f11(x100311,f858(f857(x100311,x100312),a845),f858(x100312,a845)),f777(f777(f12(f858(x100312,f858(f858(f857(x100311,x100312),a845),a845)),f858(f858(f857(x100311,x100312),a845),f858(x100312,a845)),x100311),f11(x100312,f858(f857(x100311,x100312),a845),a845)),f777(f777(f12(f858(x100312,f857(x100311,x100312)),f858(x100312,f858(f858(f857(x100311,x100312),a845),a845)),x100311),f777(f12(f857(x100311,x100312),f858(f858(f857(x100311,x100312),a845),a845),x100312),f336(f857(x100311,x100312)))),f243(x100311,x100312))))),x100316)),x100313),x100314)) % 174.01/173.90 [9130]E(x91301,x91302)+~E(f321(x91303,x91304,x91305,x91306,x91301),f321(x91303,x91304,x91305,x91307,x91302)) % 174.01/173.90 [9131]E(x91311,x91312)+~E(f321(x91313,x91314,x91315,x91311,x91316),f321(x91313,x91314,x91315,x91312,x91317)) % 174.01/173.90 [7373]E(f777(x73731,f777(x73732,x73733)),f777(x73734,x73733))+~E(f777(f77(x73735,x73736,x73737,x73731),x73732),x73734) % 174.01/173.90 [9495]~P26(x94953,x94954,x94951,x94955,x94956,x94957)+E(f777(f777(x94951,x94952),x94952),x94952) % 174.01/173.90 [9821]~P51(x98215,x98216,x98217,x98211,x98214,x98212,x98213)+P1(f777(f777(x98211,x98212),f590(x98213,x98212,x98214,x98211))) % 174.01/173.90 [9846]~E(f777(f231(f855(x98467),x98461,f185(x98467),x98465),f777(x98464,x98463)),f777(f229(x98467),x98462))+E(f777(f229(x98461),f714(x98462,x98463,x98464,x98465,x98466,x98467,x98461)),f777(x98464,x98463)) % 174.01/173.90 [9847]~E(f777(f231(f855(x98476),x98477,f185(x98476),x98471),f777(x98474,x98473)),f777(f229(x98476),x98472))+E(f777(x98471,f714(x98472,x98473,x98474,x98471,x98475,x98476,x98477)),f777(f229(x98476),x98472)) % 174.01/173.90 [5881]~E(f777(f777(f145(x58811,x58815),x58816),x58812),f777(f777(f145(x58813,x58815),x58817),x58814))+E(f777(f183(f852(x58811)),x58812),f777(f183(f852(x58813)),x58814)) % 174.01/173.90 [7449]E(x74491,x74492)+~E(f777(f777(f777(f76(x74493,f855(x74494)),x74495),x74496),f777(f229(x74494),x74491)),f777(f777(f777(f76(x74493,f855(x74494)),x74497),x74496),f777(f229(x74494),x74492))) % 174.01/173.90 [8410]E(f777(x84101,f777(x84102,x84103)),f777(x84104,x84103))+~E(f777(f77(x84105,x84106,x84107,x84101),x84102),f777(f77(x84106,x84106,x84107,f41(x84106)),x84104)) % 174.01/173.90 [9826]~P51(x98265,x98266,x98267,x98264,x98261,x98263,x98262)+P1(f777(f777(x98261,f590(x98262,x98263,x98261,x98264)),x98262)) % 174.01/173.90 [5928]E(x59281,x59282)+~E(f777(f777(f777(f95(x59283),x59284),x59285),x59281),f777(f777(f777(f95(x59283),x59286),x59287),x59282)) % 174.01/173.90 [5929]E(x59291,x59292)+~E(f777(f777(f777(f95(x59293),x59294),x59291),x59295),f777(f777(f777(f95(x59293),x59296),x59292),x59297)) % 174.01/173.90 [5930]E(x59301,x59302)+~E(f777(f777(f777(f95(x59303),x59301),x59304),x59305),f777(f777(f777(f95(x59303),x59302),x59306),x59307)) % 174.01/173.90 [8823]~P24(x88236,x88231,x88233,x88237)+E(f777(f77(x88231,x88231,x88232,f777(x88233,x88234)),f777(f77(x88231,x88231,x88232,f777(x88233,x88234)),x88235)),f777(f77(x88231,x88231,x88232,f777(x88233,x88234)),x88235)) % 174.01/173.90 [8822]~P1(f777(f777(f336(x88221),x88222),f777(f777(x88225,x88226),x88227)))+P1(f777(f777(f336(x88221),x88222),f777(f777(f253(x88223,x88224,f858(x88221,a845)),x88225),f777(f777(f243(x88223,x88224),x88226),x88227)))) % 174.01/173.90 [9089]P1(f777(f777(f777(x90891,x90892),x90893),x90894))+~P1(f777(f777(f777(f253(x90895,x90896,f858(x90897,a845)),x90891),f777(f777(f243(x90895,x90896),x90892),x90893)),x90894)) % 174.01/173.90 [9209]P1(f777(f777(f336(x92091),f777(f777(x92092,x92093),x92094)),f777(f305(f857(x92095,x92096),x92091,f777(f253(x92095,x92096,x92091),x92092)),x92097)))+~P1(f777(f777(f336(f857(x92095,x92096)),f777(f777(f243(x92095,x92096),x92093),x92094)),x92097)) % 174.01/173.90 [9534]P1(f777(f777(f336(f857(f852(x95341),f852(x95341))),f777(f777(f243(f852(x95341),f852(x95341)),f777(f777(f127(x95341),x95342),f777(f777(f142(x95341),x95343),x95344))),f777(f777(f127(x95341),x95342),f777(f777(f142(x95341),x95345),x95346)))),f139(x95341,x95347)))+~P1(f777(f777(f336(f857(x95341,x95341)),f777(f777(f243(x95341,x95341),x95343),x95345)),x95347)) % 174.01/173.90 [9951]P51(x99511,x99512,x99513,f777(f777(f11(x99511,f858(f857(x99511,x99512),a845),f858(x99512,a845)),f777(f777(f12(f858(x99512,f858(f858(f857(x99511,x99512),a845),a845)),f858(f858(f857(x99511,x99512),a845),f858(x99512,a845)),x99511),f11(x99512,f858(f857(x99511,x99512),a845),a845)),f777(f777(f12(f858(x99512,f857(x99511,x99512)),f858(x99512,f858(f858(f857(x99511,x99512),a845),a845)),x99511),f777(f12(f857(x99511,x99512),f858(f858(f857(x99511,x99512),a845),a845),x99512),f336(f857(x99511,x99512)))),f243(x99511,x99512)))),x99514),f777(f777(f11(x99512,f858(f857(x99512,x99513),a845),f858(x99513,a845)),f777(f777(f12(f858(x99513,f858(f858(f857(x99512,x99513),a845),a845)),f858(f858(f857(x99512,x99513),a845),f858(x99513,a845)),x99512),f11(x99513,f858(f857(x99512,x99513),a845),a845)),f777(f777(f12(f858(x99513,f857(x99512,x99513)),f858(x99513,f858(f858(f857(x99512,x99513),a845),a845)),x99512),f777(f12(f857(x99512,x99513),f858(f858(f857(x99512,x99513),a845),a845),x99513),f336(f857(x99512,x99513)))),f243(x99512,x99513)))),x99515),x99516,x99517)+~P1(f777(f777(f336(f857(x99511,x99513)),f777(f777(f243(x99511,x99513),x99516),x99517)),f777(f777(f283(x99511,x99512,x99513),x99514),x99515))) % 174.01/173.90 [9980]~P51(x99801,x99805,x99802,f777(f777(f11(x99801,f858(f857(x99801,x99805),a845),f858(x99805,a845)),f777(f777(f12(f858(x99805,f858(f858(f857(x99801,x99805),a845),a845)),f858(f858(f857(x99801,x99805),a845),f858(x99805,a845)),x99801),f11(x99805,f858(f857(x99801,x99805),a845),a845)),f777(f777(f12(f858(x99805,f857(x99801,x99805)),f858(x99805,f858(f858(f857(x99801,x99805),a845),a845)),x99801),f777(f12(f857(x99801,x99805),f858(f858(f857(x99801,x99805),a845),a845),x99805),f336(f857(x99801,x99805)))),f243(x99801,x99805)))),x99806),f777(f777(f11(x99805,f858(f857(x99805,x99802),a845),f858(x99802,a845)),f777(f777(f12(f858(x99802,f858(f858(f857(x99805,x99802),a845),a845)),f858(f858(f857(x99805,x99802),a845),f858(x99802,a845)),x99805),f11(x99802,f858(f857(x99805,x99802),a845),a845)),f777(f777(f12(f858(x99802,f857(x99805,x99802)),f858(x99802,f858(f858(f857(x99805,x99802),a845),a845)),x99805),f777(f12(f857(x99805,x99802),f858(f858(f857(x99805,x99802),a845),a845),x99802),f336(f857(x99805,x99802)))),f243(x99805,x99802)))),x99807),x99803,x99804)+P1(f777(f777(f336(f857(x99801,x99802)),f777(f777(f243(x99801,x99802),x99803),x99804)),f777(f777(f283(x99801,x99805,x99802),x99806),x99807))) % 174.01/173.90 [9598]P1(f777(f777(f336(x95981),x95984),f777(f160(x95981),x95986)))+E(f172(x95981,x95982,f777(f777(f777(f76(x95981,f855(x95982)),x95983),x95984),f777(f229(x95982),x95985)),f168(x95981,x95982,f777(f144(f857(x95981,x95982)),f777(f777(f169(x95981,x95982),x95986),x95987)))),f777(f777(f777(f76(x95981,f855(x95982)),f172(x95981,x95982,x95983,f168(x95981,x95982,f777(f144(f857(x95981,x95982)),f777(f777(f169(x95981,x95982),x95986),x95987))))),x95984),f777(f229(x95982),x95985))) % 174.01/173.90 [9084]E(x90841,x90842)+E(f777(f777(f777(f76(x90843,x90844),f777(f777(f777(f76(x90843,x90844),x90845),x90841),x90846)),x90842),x90847),f777(f777(f777(f76(x90843,x90844),f777(f777(f777(f76(x90843,x90844),x90845),x90842),x90847)),x90841),x90846)) % 174.01/173.90 [9336]E(f172(x93361,x93362,f777(f777(f777(f76(x93361,f855(x93362)),x93363),x93364),f777(f229(x93362),x93365)),f168(x93361,x93362,f777(f144(f857(x93361,x93362)),f777(f777(f169(x93361,x93362),x93366),x93367)))),f172(x93361,x93362,x93363,f168(x93361,x93362,f777(f144(f857(x93361,x93362)),f777(f777(f169(x93361,x93362),x93366),x93367)))))+~P1(f777(f777(f336(x93361),x93364),f777(f160(x93361),f777(f777(f161(x93361),f777(f183(f852(x93362)),x93367)),x93366)))) % 174.01/173.90 [9616]E(f172(x96161,x96162,f777(f777(f777(f76(x96161,f855(x96162)),x96163),x96164),f777(f229(x96162),x96165)),f168(x96161,x96162,f777(f144(f857(x96161,x96162)),f777(f777(f169(x96161,x96162),x96166),x96167)))),f777(f777(f777(f76(x96161,f855(x96162)),f172(x96161,x96162,x96163,f168(x96161,x96162,f777(f144(f857(x96161,x96162)),f777(f777(f169(x96161,x96162),x96166),x96167))))),x96164),f777(f229(x96162),x96165)))+P1(f777(f777(f336(x96161),x96164),f777(f160(x96161),f777(f777(f161(x96161),f777(f183(f852(x96162)),x96167)),x96166)))) % 174.01/173.90 [9962]P1(f777(f777(f336(x99621),f670(x99622,x99623,x99624,x99625,x99626,x99627,x99621)),x99625))+P1(f777(f777(f777(f777(f49(x99621,f858(x99627,f858(x99626,a845))),x99625),x99624),x99623),x99622)) % 174.01/173.90 [9963]P1(f777(f777(f336(x99631),f432(x99632,x99633,x99634,x99635,x99636,x99637,x99631)),x99635))+~P1(f777(f777(f777(f777(f48(x99631,f858(x99637,f858(x99636,a845))),x99635),x99634),x99633),x99632)) % 174.01/173.90 [9990]P1(f777(f777(f777(x99901,f432(x99902,x99903,x99901,x99904,x99905,x99906,x99907)),x99903),x99902))+~P1(f777(f777(f777(f777(f48(x99907,f858(x99906,f858(x99905,a845))),x99904),x99901),x99903),x99902)) % 174.01/173.90 [10007]~P1(f777(f777(f777(x100075,f670(x100077,x100076,x100075,x100074,x100073,x100072,x100071)),x100076),x100077))+P1(f777(f777(f777(f777(f49(x100071,f858(x100072,f858(x100073,a845))),x100074),x100075),x100076),x100077)) % 174.01/173.90 [9972]~P136(x99722)+E(f777(f777(f10(x99721,x99722),f777(f777(f11(x99721,f858(x99723,a845),x99722),f777(f777(f12(f858(x99723,x99722),f858(f858(x99723,a845),x99722),x99721),f10(x99723,x99722)),f777(f777(f11(x99721,f858(x99723,x99722),f858(x99723,x99722)),f777(f777(f12(f858(x99722,x99722),f858(f858(x99723,x99722),f858(x99723,x99722)),x99721),f12(x99722,x99722,x99723)),f777(f777(f12(x99722,f858(x99722,x99722),x99721),f85(x99722)),x99724))),x99725))),x99726)),x99727),f777(f777(f85(x99722),f777(f777(f10(x99721,x99722),x99724),x99727)),f777(f777(f10(x99723,x99722),x99725),x99726))) % 174.01/173.90 [9121]~P23(x91217,x91211,x91213,x91218)+E(f777(f77(x91211,x91211,x91212,f777(x91213,x91214)),f777(f77(x91211,x91211,x91212,f777(x91213,x91215)),x91216)),f777(f77(x91211,x91211,x91212,f777(x91213,x91215)),f777(f77(x91211,x91211,x91212,f777(x91213,x91214)),x91216))) % 174.01/173.90 [10025]E(f777(f777(f243(x100251,x100252),f777(x100253,f575(x100254,x100255,x100253,x100256,x100257,x100258,x100252,x100251))),f777(x100255,f576(x100254,x100255,x100253,x100256,x100257,x100258,x100252,x100251))),x100258)+~P1(f777(f777(f336(f857(x100251,x100252)),x100258),f777(f305(f857(x100257,x100256),f857(x100251,x100252),f254(x100257,x100251,x100256,x100252,x100253,x100255)),x100254))) % 174.01/173.90 [10037]~P1(f777(f777(f336(f857(x100378,x100377)),x100376),f777(f305(f857(x100371,x100372),f857(x100378,x100377),f254(x100371,x100378,x100372,x100377,x100375,x100374)),x100373)))+P1(f777(f777(f336(f857(x100371,x100372)),f777(f777(f243(x100371,x100372),f575(x100373,x100374,x100375,x100372,x100371,x100376,x100377,x100378)),f576(x100373,x100374,x100375,x100372,x100371,x100376,x100377,x100378))),x100373)) % 174.01/173.90 [9524]P1(f777(f777(f336(f857(f857(x95241,x95242),f857(x95241,x95242))),f777(f777(f243(f857(x95241,x95242),f857(x95241,x95242)),f777(f777(f243(x95241,x95242),x95243),x95244)),f777(f777(f243(x95241,x95242),x95245),x95246))),f327(x95241,x95242,x95247,x95248)))+~P1(f777(f777(f336(f857(x95241,x95241)),f777(f777(f243(x95241,x95241),x95243),x95245)),x95247)) % 174.01/173.90 [8416]E(f777(x84161,f777(x84162,x84163)),f777(x84164,f777(x84165,x84163)))+~E(f777(f77(x84166,x84167,x84168,x84161),x84162),f777(f77(x84169,x84167,x84168,x84164),x84165)) % 174.01/173.90 [9897]P1(f777(f777(f336(f857(x98971,x98972)),f777(f777(f243(x98971,x98972),f777(x98973,x98974)),f777(x98975,x98976))),f777(f305(f857(x98977,x98978),f857(x98971,x98972),f254(x98977,x98971,x98978,x98972,x98973,x98975)),x98979)))+~P1(f777(f777(f336(f857(x98977,x98978)),f777(f777(f243(x98977,x98978),x98974),x98976)),x98979)) % 174.01/173.90 [8675]~E(f777(x86754,f777(x86755,x86756)),f777(x86759,f777(x867510,x867511)))+E(f777(f777(f77(x86751,x86752,x86753,x86754),x86755),x86756),f777(f777(f77(x86757,x86752,x86758,x86759),x867510),x867511)) % 174.01/173.90 [4495]~P100(x44951)+~P92(x44951)+E(f181(x44951),f105(x44951)) % 174.01/173.90 [4496]~P100(x44961)+~P98(x44961)+E(f238(x44961),f106(x44961)) % 174.01/173.90 [4730]~P110(x47301)+~P88(x47301)+E(f777(f79(x47301),f777(f108(x47301),a101)),f82(x47301)) % 174.01/173.90 [5006]E(x50061,f4(a3))+E(f86(a3,x50061),f777(f83(a3),f82(a3)))+P1(f777(f777(f235(a3),f4(a3)),x50061)) % 174.01/173.90 [5212]E(x52121,f4(a3))+E(f86(a3,x52121),f82(a3))+~P1(f777(f777(f235(a3),f4(a3)),x52121)) % 174.01/173.90 [7260]~P38(x72601)+P1(f777(f65(a3),x72601))+~P1(f777(f65(a851),f777(f305(a3,a851,a109),x72601))) % 174.01/173.90 [8522]~P13(a5000)+~P1(f777(f777(f336(f857(a847,a846)),x85221),f777(f160(f857(a847,a846)),a31)))+P1(f777(f777(f253(a847,a846,a845),f777(f20(f858(a846,a845),a847),a28)),x85221)) % 174.01/173.90 [9494]E(x94941,f182(f858(f857(a851,a851),a845)))+~P1(f777(f65(f857(a851,a851)),x94941))+P1(f777(f777(f336(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),f182(f858(f857(a851,a851),a845))),x94941)),a43)) % 174.01/173.90 [9641]E(x96411,f4(a851))+E(x96411,f777(a116,f4(a851)))+~P1(f777(f777(f235(a851),x96411),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))) % 174.01/173.90 [9923]E(x99231,f4(a103))+E(f777(f777(f84(a3),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(a25,f777(f777(f45(a103),x99231),f777(f108(a103),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))))),f82(a3)),f777(a25,x99231))+E(f54(a103,x99231,f777(f108(a103),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f4(a103)) % 174.01/173.90 [9770]E(x97701,f4(a103))+~E(f54(a103,x97701,f777(f108(a103),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f4(a103))+E(f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(a25,f777(f777(f45(a103),x97701),f777(f108(a103),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))),f777(a25,x97701)) % 174.01/173.90 [4566]~P56(x45661,x45662)+P42(x45661,x45662)+~P43(a845) % 174.01/173.90 [4506]~P2(x45061)+P33(x45061,x45062)+~E(x45062,f4(x45061)) % 174.01/173.90 [4515]~P110(x45151)+~E(x45152,f4(x45151))+E(f86(x45151,x45152),f4(x45151)) % 174.01/173.90 [4516]~P82(x45161)+~E(x45162,f4(x45161))+E(f86(x45161,x45162),f4(x45161)) % 174.01/173.90 [4522]~P2(x45222)+~P33(x45222,x45221)+E(x45221,f4(x45222)) % 174.01/173.90 [4556]~P110(x45562)+~E(f86(x45562,x45561),f4(x45562))+E(x45561,f4(x45562)) % 174.01/173.90 [4574]~P10(x45742)+~P10(x45741)+P10(f190(x45741,x45742)) % 174.01/173.90 [4575]~P59(x45752)+~P59(x45751)+P59(f859(x45751,x45752)) % 174.01/173.90 [4576]~P59(x45762)+~P59(x45761)+P59(f858(x45761,x45762)) % 174.01/173.90 [4577]~P59(x45772)+~P59(x45771)+P59(f857(x45771,x45772)) % 174.01/173.90 [4578]~P139(x45782)+~P139(x45781)+P139(f857(x45781,x45782)) % 174.01/173.90 [4933]~P10(x49332)+~P10(x49331)+P10(f54(a3,x49331,x49332)) % 174.01/173.90 [4524]~P68(x45241)+~E(x45242,f4(x45241))+E(f777(f83(x45241),x45242),x45242) % 174.01/173.90 [4528]~P87(x45281)+~E(x45282,f4(a3))+E(f777(f107(x45281),x45282),f4(x45281)) % 174.01/173.90 [4529]~P133(x45291)+~E(x45292,f4(a3))+E(f777(f107(x45291),x45292),f4(x45291)) % 174.01/173.90 [4553]~P69(x45531)+~E(f4(x45531),x45532)+E(f777(f83(x45531),x45532),f4(x45531)) % 174.01/173.90 [4554]~P69(x45541)+~E(x45542,f4(x45541))+E(f777(f83(x45541),x45542),f4(x45541)) % 174.01/173.90 [4555]~P79(x45551)+~E(x45552,f4(x45551))+E(f777(f79(x45551),x45552),f4(x45551)) % 174.01/173.90 [4580]~P68(x45802)+E(x45801,f4(x45802))+~E(f777(f83(x45802),x45801),x45801) % 174.01/173.90 [4588]E(x45881,f777(a109,x45882))+~E(x45881,f4(a851))+~E(x45882,f777(f104(a3),x45881)) % 174.01/173.90 [4589]E(f777(a109,x45891),x45892)+~E(x45892,f4(a851))+~E(x45891,f777(f104(a3),x45892)) % 174.01/173.90 [4593]~P87(x45932)+E(x45931,f4(a3))+~E(f777(f107(x45932),x45931),f4(x45932)) % 174.01/173.90 [4598]~P69(x45982)+E(x45981,f4(x45982))+~E(f777(f83(x45982),x45981),f4(x45982)) % 174.01/173.90 [4599]~P79(x45992)+E(x45991,f4(x45992))+~E(f777(f79(x45992),x45991),f4(x45992)) % 174.01/173.90 [4600]~P69(x46001)+E(f4(x46001),x46002)+~E(f777(f83(x46001),x46002),f4(x46001)) % 174.01/173.90 [4734]~P13(a5000)+~E(f777(a32,x47342),f777(f229(a846),x47341))+P1(f777(a28,x47341)) % 174.01/173.90 [4773]~P100(x47731)+~P18(x47731,x47732)+P18(x47731,f777(f159(x47731),x47732)) % 174.01/173.90 [4799]~P1(x47992)+~P1(x47991)+P1(f777(f777(a333,x47991),x47992)) % 174.01/173.90 [4833]~E(f82(a851),f4(a851))+E(f777(f44(x48331),x48332),f4(a851))+~P1(f777(f65(x48331),x48332)) % 174.01/173.90 [4864]~P105(x48641)+~P136(x48641)+E(f777(f777(f244(x48641),f4(x48641)),f777(a116,x48642)),f4(x48641)) % 174.01/173.90 [4904]~P100(x49041)+P18(x49041,f132(x49041,x49042))+~P1(f777(f65(x49041),x49042)) % 174.01/173.90 [4924]~P100(x49241)+E(f777(f160(x49241),f132(x49241,x49242)),x49242)+~P1(f777(f65(x49241),x49242)) % 174.01/173.90 [4958]P1(x49581)+P1(x49582)+~P1(f777(f777(a334,x49582),x49581)) % 174.01/173.90 [4971]E(x49711,f182(f858(x49712,a845)))+~E(f777(f44(x49712),x49711),f4(a851))+~P1(f777(f65(x49712),x49711)) % 174.01/173.90 [4976]P1(x49761)+~P1(x49762)+~P1(f777(f777(a337,x49762),x49761)) % 174.01/173.90 [5025]~P65(x50251)+E(f777(f79(x50251),x50252),x50252)+P1(f777(f777(f235(x50251),x50252),f4(x50251))) % 174.01/173.90 [5123]~P1(f777(a28,x51232))+~P1(f777(a28,x51231))+P1(f777(a28,f38(x51231,x51232))) % 174.01/173.90 [5130]E(x51301,f117(x51302))+P1(f777(f129(x51302),f118(x51302,x51301)))+~P1(f777(f129(x51302),x51301)) % 174.01/173.90 [5135]~P100(x51351)+~P1(f777(f65(x51351),x51352))+P1(f777(f129(x51351),f132(x51351,x51352))) % 174.01/173.90 [5141]~P133(x51411)+E(f777(f104(x51411),f777(a109,x51412)),f777(f107(x51411),x51412))+P1(f777(f777(f235(a3),x51412),f4(a3))) % 174.01/173.90 [5169]P11(x51692,x51691)+E(f777(x51691,f506(x51691)),f777(x51691,f522(x51691)))+P1(f777(f777(x51691,f506(x51691)),f522(x51691))) % 174.01/173.90 [5182]E(f777(f104(a3),f618(x51821,x51822)),x51821)+P1(f777(x51822,f777(a109,x51821)))+~P1(f777(x51822,f4(a851))) % 174.01/173.90 [5222]~P110(x52221)+~E(f86(x52221,x52222),f777(f83(x52221),f82(x52221)))+P1(f777(f777(f235(x52221),x52222),f4(x52221))) % 174.01/173.90 [5297]~E(x52972,f4(a3))+E(f212(x52971,x52972),f777(f777(f243(a3,a3),f4(a3)),f82(a3)))+P1(f777(f777(f235(a3),x52972),f4(a3))) % 174.01/173.90 [5298]~E(x52981,f4(a3))+E(f212(x52981,x52982),f777(f777(f243(a3,a3),f4(a3)),f82(a3)))+P1(f777(f777(f235(a3),x52982),f4(a3))) % 174.01/173.90 [5350]E(f777(f104(a3),f618(x53501,x53502)),x53501)+P1(f777(x53502,f777(a109,x53501)))+P1(f777(f777(f235(a3),x53501),f4(a3))) % 174.01/173.90 [5416]~P110(x54161)+E(f86(x54161,x54162),f777(f83(x54161),f82(x54161)))+~P1(f777(f777(f235(x54161),x54162),f4(x54161))) % 174.01/173.90 [5417]~P79(x54171)+E(f777(f79(x54171),x54172),f777(f83(x54171),x54172))+~P1(f777(f777(f235(x54171),x54172),f4(x54171))) % 174.01/173.90 [5418]~P79(x54181)+E(f777(f79(x54181),x54182),f777(f83(x54181),x54182))+~P1(f777(f777(f234(x54181),x54182),f4(x54181))) % 174.01/173.90 [5419]~P65(x54191)+E(f777(f79(x54191),x54192),f777(f83(x54191),x54192))+~P1(f777(f777(f235(x54191),x54192),f4(x54191))) % 174.01/173.90 [5511]~P1(f777(x55111,f618(x55112,x55111)))+P1(f777(x55111,f777(a109,x55112)))+~P1(f777(x55111,f4(a851))) % 174.01/173.90 [5518]E(x55181,f4(a851))+E(f777(a116,f561(x55182,x55181)),x55181)+~P1(f777(f777(f235(a851),x55181),f777(a116,x55182))) % 174.01/173.90 [5521]P11(x55211,x55212)+~E(f777(x55212,f506(x55212)),f777(x55212,f522(x55212)))+~P1(f777(f777(x55212,f506(x55212)),f522(x55212))) % 174.01/173.90 [5540]~P100(x55401)+P18(x55401,x55402)+P1(f777(f777(f234(a851),f763(x55402,x55401)),f764(x55402,x55401))) % 174.01/173.90 [5626]~P79(x56261)+~E(x56262,f4(x56261))+P1(f777(f777(f234(x56261),f777(f79(x56261),x56262)),f4(x56261))) % 174.01/173.90 [5715]~P1(f777(x57151,f618(x57152,x57151)))+P1(f777(x57151,f777(a109,x57152)))+P1(f777(f777(f235(a3),x57152),f4(a3))) % 174.01/173.90 [5741]~P1(f777(x57411,f777(a109,x57412)))+P1(f777(x57411,f4(a851)))+~P1(f777(f777(f235(a3),x57412),f4(a3))) % 174.01/173.90 [6085]~P110(x60851)+~P1(f777(f777(f235(x60851),x60852),f4(x60851)))+P1(f777(f777(f235(x60851),f86(x60851,x60852)),f4(x60851))) % 174.01/173.90 [6202]~P110(x62021)+P1(f777(f777(f235(x62021),f777(f107(x62021),x62022)),f4(x62021)))+~P1(f777(f777(f235(a3),x62022),f4(a3))) % 174.01/173.90 [6203]~P110(x62031)+P1(f777(f777(f234(x62031),f777(f107(x62031),x62032)),f4(x62031)))+~P1(f777(f777(f234(a3),x62032),f4(a3))) % 174.01/173.90 [6208]~P79(x62082)+E(x62081,f4(x62082))+~P1(f777(f777(f234(x62082),f777(f79(x62082),x62081)),f4(x62082))) % 174.01/173.90 [6293]~P133(x62931)+~P1(f777(f777(f336(x62931),x62932),f114(x62931)))+P1(f777(f777(f336(x62931),f777(f83(x62931),x62932)),f114(x62931))) % 174.01/173.90 [6325]~P110(x63251)+~P1(f777(f777(f235(x63251),f86(x63251,x63252)),f4(x63251)))+P1(f777(f777(f235(x63251),x63252),f4(x63251))) % 174.01/173.90 [6406]~P99(x64061)+P50(a851,x64061,f281(a851),x64062)+P1(f777(f777(f281(a851),f379(x64062,x64061)),f395(x64062,x64061))) % 174.01/173.90 [6504]~P110(x65042)+~P1(f777(f777(f235(x65042),f777(f107(x65042),x65041)),f4(x65042)))+P1(f777(f777(f235(a3),x65041),f4(a3))) % 174.01/173.90 [6505]~P110(x65052)+~P1(f777(f777(f234(x65052),f777(f107(x65052),x65051)),f4(x65052)))+P1(f777(f777(f234(a3),x65051),f4(a3))) % 174.01/173.90 [7030]~P68(x70301)+~P1(f777(f777(f235(x70301),x70302),f4(x70301)))+P1(f777(f777(f235(x70301),f777(f777(f84(x70301),x70302),x70302)),f4(x70301))) % 174.01/173.90 [7031]~P110(x70311)+~P1(f777(f777(f235(x70311),x70312),f4(x70311)))+P1(f777(f777(f235(x70311),f777(f777(f84(x70311),x70312),x70312)),f4(x70311))) % 174.01/173.90 [7032]~P68(x70321)+~P1(f777(f777(f234(x70321),x70322),f4(x70321)))+P1(f777(f777(f234(x70321),f777(f777(f84(x70321),x70322),x70322)),f4(x70321))) % 174.01/173.90 [7627]~P68(x76271)+~P1(f777(f777(f235(x76271),f777(f777(f84(x76271),x76272),x76272)),f4(x76271)))+P1(f777(f777(f235(x76271),x76272),f4(x76271))) % 174.01/173.90 [7628]~P110(x76281)+~P1(f777(f777(f235(x76281),f777(f777(f84(x76281),x76282),x76282)),f4(x76281)))+P1(f777(f777(f235(x76281),x76282),f4(x76281))) % 174.01/173.90 [7629]~P68(x76291)+~P1(f777(f777(f234(x76291),f777(f777(f84(x76291),x76292),x76292)),f4(x76291)))+P1(f777(f777(f234(x76291),x76292),f4(x76291))) % 174.01/173.90 [4637]~E(x46372,f4(a851))+~E(x46371,f4(a851))+E(f777(f777(f84(a851),x46371),x46372),f4(a851)) % 174.01/173.90 [4638]~E(x46382,f82(a851))+~E(x46381,f82(a851))+E(f777(f777(f85(a851),x46381),x46382),f82(a851)) % 174.01/173.90 [4639]~E(x46392,f82(a3))+~E(x46391,f82(a3))+E(f777(f777(f85(a3),x46391),x46392),f82(a3)) % 174.01/173.90 [4689]~P7(x46892)+E(x46891,f4(x46892))+E(f777(f777(f45(x46892),x46891),x46891),f82(x46892)) % 174.01/173.90 [4690]~P113(x46902)+E(x46901,f4(x46902))+E(f777(f777(f285(x46902),x46901),x46901),f82(x46902)) % 174.01/173.90 [4691]~P114(x46912)+E(x46911,f4(x46912))+E(f777(f777(f285(x46912),x46911),x46911),f82(x46912)) % 174.01/173.90 [4706]~P68(x47061)+~E(x47062,f4(x47061))+E(f777(f777(f84(x47061),x47062),x47062),f4(x47061)) % 174.01/173.90 [4709]~P120(x47091)+~E(x47092,f82(x47091))+E(f777(f777(f85(x47091),x47092),x47092),f82(x47091)) % 174.01/173.90 [4710]~P114(x47101)+~E(x47102,f4(x47101))+E(f777(f777(f285(x47101),x47102),x47102),f4(x47101)) % 174.01/173.90 [4754]~E(x47542,f4(a851))+~E(x47541,f4(a851))+E(f777(f83(a3),f777(f104(a3),x47541)),f777(f104(a3),x47542)) % 174.01/173.90 [4772]E(x47721,f82(a851))+E(x47722,f4(a851))+~E(f777(f777(f85(a851),x47722),x47721),x47722) % 174.01/173.90 [4780]E(x47801,f4(a851))+E(x47802,f4(a851))+~E(f777(f777(f85(a851),x47802),x47801),f4(a851)) % 174.01/173.90 [4808]~E(x48082,f4(a851))+~E(x48081,f777(a116,f4(a851)))+E(f777(f777(f84(a851),x48081),x48082),f777(a116,f4(a851))) % 174.01/173.90 [4809]~E(x48091,f4(a851))+~E(x48092,f777(a116,f4(a851)))+E(f777(f777(f84(a851),x48091),x48092),f777(a116,f4(a851))) % 174.01/173.90 [4814]E(x48141,f82(a3))+E(x48142,f777(f108(a3),a101))+~E(f777(f777(f85(a3),x48141),x48142),f82(a3)) % 174.01/173.90 [4815]E(x48151,f82(a3))+E(x48152,f777(f108(a3),a101))+~E(f777(f777(f85(a3),x48152),x48151),f82(a3)) % 174.01/173.90 [4816]E(x48161,f82(a3))+E(x48161,f777(f108(a3),a101))+~E(f777(f777(f85(a3),x48162),x48161),f82(a3)) % 174.01/173.90 [4818]E(x48181,f82(a3))+E(x48181,f777(f108(a3),a101))+~E(f777(f777(f85(a3),x48181),x48182),f82(a3)) % 174.01/173.90 [4837]~P68(x48372)+E(x48371,f4(x48372))+~E(f777(f777(f84(x48372),x48371),x48371),f4(x48372)) % 174.01/173.90 [4843]~E(x48431,f777(f108(a3),a101))+~E(x48432,f777(f108(a3),a101))+E(f777(f777(f85(a3),x48431),x48432),f82(a3)) % 174.01/173.90 [4855]E(x48551,f4(a851))+E(x48552,f4(a851))+~E(f777(f777(f84(a851),x48552),x48551),f777(a116,f4(a851))) % 174.01/173.90 [4863]~P88(x48631)+~P60(x48631)+E(f777(f777(f285(x48631),x48632),f777(f108(x48631),a87)),f4(x48631)) % 174.01/173.90 [4870]~P120(x48701)+~E(x48702,f777(f83(x48701),f82(x48701)))+E(f777(f777(f85(x48701),x48702),x48702),f82(x48701)) % 174.01/173.90 [4875]~P10(x48752)+~P10(x48751)+P10(f777(f777(f84(a3),x48751),x48752)) % 174.01/173.90 [4876]~P10(x48762)+~P10(x48761)+P10(f777(f777(f85(a3),x48761),x48762)) % 174.01/173.90 [4877]~P10(x48772)+~P10(x48771)+P10(f777(f777(f45(a3),x48771),x48772)) % 174.01/173.90 [4879]~E(x48792,f4(a3))+E(x48791,f4(a3))+E(f55(x48791,x48792),f777(f777(f243(a3,a3),f4(a3)),x48791)) % 174.01/173.90 [4902]~E(x49022,f777(a116,f4(a851)))+~E(x49021,f777(a116,f4(a851)))+E(f777(f777(f85(a851),x49021),x49022),f777(a116,f4(a851))) % 174.01/173.90 [4915]E(x49151,f4(a851))+E(x49152,f777(a116,f4(a851)))+~E(f777(f777(f244(a851),x49152),x49151),f777(a116,f4(a851))) % 174.01/173.90 [4916]E(x49161,f4(a851))+E(x49161,f777(a116,f4(a851)))+~E(f777(f777(f84(a851),x49162),x49161),f777(a116,f4(a851))) % 174.01/173.90 [4917]E(x49171,f4(a851))+E(x49171,f777(a116,f4(a851)))+~E(f777(f777(f84(a851),x49171),x49172),f777(a116,f4(a851))) % 174.01/173.90 [4925]~P88(x49251)+~P60(x49251)+E(f777(f777(f285(x49251),x49252),f777(f108(x49251),a101)),f777(f83(x49251),x49252)) % 174.01/173.90 [4946]E(x49461,f777(a109,x49462))+~E(x49461,f4(a851))+P1(f777(f777(f234(a3),f4(a3)),x49462)) % 174.01/173.90 [4947]E(f777(a109,x49471),x49472)+~E(x49472,f4(a851))+P1(f777(f777(f234(a3),f4(a3)),x49471)) % 174.01/173.90 [4967]E(x49671,f777(a116,f4(a851)))+E(x49672,f777(a116,f4(a851)))+~E(f777(f777(f84(a851),x49671),x49672),f777(a116,f4(a851))) % 174.01/173.90 [4978]~E(x49781,f777(a109,x49782))+E(x49781,f4(a851))+P1(f777(f777(f234(a3),f4(a3)),x49782)) % 174.01/173.90 [4979]~E(f777(a109,x49792),x49791)+E(x49791,f4(a851))+P1(f777(f777(f234(a3),f4(a3)),x49792)) % 174.01/173.90 [5002]~P93(x50021)+E(f777(f67(x50021,f105(x50021)),x50022),f17(x50021,x50022))+~P1(f777(f65(x50021),x50022)) % 174.01/173.90 [5003]~P100(x50031)+E(f777(f67(x50031,f181(x50031)),x50032),f18(x50031,x50032))+~P1(f777(f65(x50031),x50032)) % 174.01/173.90 [5004]~P100(x50041)+E(f777(f67(x50041,f238(x50041)),x50042),f19(x50041,x50042))+~P1(f777(f65(x50041),x50042)) % 174.01/173.90 [5005]~P93(x50051)+E(f777(f67(x50051,f106(x50051)),x50052),f14(x50051,x50052))+~P1(f777(f65(x50051),x50052)) % 174.01/173.90 [5089]E(x50891,x50892)+~E(f777(f777(f5(a851),x50892),x50891),f4(a851))+~E(f777(f777(f5(a851),x50891),x50892),f4(a851)) % 174.01/173.90 [5100]P10(x51001)+~P38(x51002)+~P1(f777(f777(f336(a3),x51001),x51002)) % 174.01/173.90 [5131]~P110(x51311)+~E(f86(x51311,x51312),f82(x51311))+P1(f777(f777(f235(x51311),f4(x51311)),x51312)) % 174.01/173.90 [5142]~P88(x51421)+E(f777(f104(x51421),f777(f108(a851),x51422)),f777(f108(x51421),x51422))+P1(f777(a188,f777(f108(a3),x51422))) % 174.01/173.90 [5147]~P42(x51471,x51472)+P43(a845)+P1(f777(f65(f857(x51471,x51471)),x51472)) % 174.01/173.90 [5214]~P100(x52141)+E(f777(f67(x52141,f181(x52141)),x52142),f15(x52141,f181(x52141),x52142))+~P1(f777(f65(x52141),x52142)) % 174.01/173.90 [5215]~P100(x52151)+E(f777(f67(x52151,f238(x52151)),x52152),f16(x52151,f238(x52151),x52152))+~P1(f777(f65(x52151),x52152)) % 174.01/173.90 [5230]E(x52301,x52302)+P1(f777(f777(f235(a851),x52302),x52301))+P1(f777(f777(f235(a851),x52301),x52302)) % 174.01/173.90 [5231]E(x52311,x52312)+P1(f777(f777(f235(a3),x52312),x52311))+P1(f777(f777(f235(a3),x52311),x52312)) % 174.01/173.90 [5284]~P88(x52841)+E(f777(f104(x52841),f777(f108(a851),x52842)),f4(x52841))+~P1(f777(a188,f777(f108(a3),x52842))) % 174.01/173.90 [5287]~E(x52872,f777(a109,x52871))+E(x52871,f777(f104(a3),x52872))+~P1(f777(f777(f234(a3),f4(a3)),x52871)) % 174.01/173.90 [5288]~E(f777(a109,x52881),x52882)+E(x52881,f777(f104(a3),x52882))+~P1(f777(f777(f234(a3),f4(a3)),x52881)) % 174.01/173.90 [5289]~E(x52891,f777(a109,x52892))+E(f777(f104(a3),x52891),x52892)+~P1(f777(f777(f234(a3),f4(a3)),x52892)) % 174.01/173.90 [5299]E(x52991,f777(a109,x52992))+~E(x52992,f777(f104(a3),x52991))+~P1(f777(f777(f234(a3),f4(a3)),x52992)) % 174.01/173.90 [5300]E(f777(a109,x53001),x53002)+~E(x53001,f777(f104(a3),x53002))+~P1(f777(f777(f234(a3),f4(a3)),x53001)) % 174.01/173.90 [5330]~P85(x53302)+E(x53301,f4(x53302))+~P1(f777(f777(f281(x53302),f4(x53302)),x53301)) % 174.01/173.90 [5339]~P79(x53392)+E(x53391,f4(x53392))+P1(f777(f777(f235(x53392),f4(x53392)),f777(f79(x53392),x53391))) % 174.01/173.90 [5407]~P110(x54071)+E(f86(x54071,x54072),f82(x54071))+~P1(f777(f777(f235(x54071),f4(x54071)),x54072)) % 174.01/173.90 [5413]~P88(x54131)+E(f777(f104(x54131),f777(f108(a851),x54132)),f4(x54131))+P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x54132))) % 174.01/173.90 [5420]~P79(x54201)+E(f777(f79(x54201),x54202),x54202)+~P1(f777(f777(f235(x54201),f4(x54201)),x54202)) % 174.01/173.90 [5421]~P79(x54211)+E(f777(f79(x54211),x54212),x54212)+~P1(f777(f777(f234(x54211),f4(x54211)),x54212)) % 174.01/173.90 [5428]E(x54281,f4(a851))+~E(f132(a851,f777(f296(a851,x54282),x54281)),f117(a851))+P1(f777(f777(f234(a851),x54281),x54282)) % 174.01/173.90 [5438]~P66(x54381)+E(f777(f777(f10(x54381,x54381),f9(x54381)),f777(f160(x54381),x54382)),f777(f157(x54381),x54382))+~P1(f777(f129(x54381),x54382)) % 174.01/173.90 [5441]~P133(x54411)+E(f777(f104(x54411),f777(a109,x54412)),f777(f107(x54411),x54412))+~P1(f777(f777(f234(a3),f4(a3)),x54412)) % 174.01/173.90 [5464]E(x54641,x54642)+P1(f777(f777(f235(a851),x54641),x54642))+~P1(f777(f777(f234(a851),x54641),x54642)) % 174.01/173.90 [5465]E(x54651,x54652)+P1(f777(f777(f235(a3),x54651),x54652))+~P1(f777(f777(f234(a3),x54651),x54652)) % 174.01/173.90 [5468]E(x54681,f82(a3))+~E(f777(f777(f85(a3),x54682),x54681),f82(a3))+~P1(f777(f777(f235(a3),f4(a3)),x54682)) % 174.01/173.90 [5469]E(x54691,f82(a3))+~E(f777(f777(f85(a3),x54691),x54692),f82(a3))+~P1(f777(f777(f235(a3),f4(a3)),x54691)) % 174.01/173.90 [5508]~P38(x55082)+P1(f777(f777(f234(a3),f4(a3)),x55081))+~P1(f777(f777(f336(a3),x55081),x55082)) % 174.01/173.90 [5526]~P56(x55261,x55262)+P36(x55261,x55262)+~P1(f777(f65(f857(x55261,x55261)),x55262)) % 174.01/173.90 [5528]~P56(x55281,x55282)+P42(x55281,x55282)+~P1(f777(f65(f857(x55281,x55281)),x55282)) % 174.01/173.90 [5568]E(x55681,f182(f858(x55682,a845)))+~P1(f777(f65(x55682),x55681))+P1(f777(f777(f235(a851),f4(a851)),f777(f44(x55682),x55681))) % 174.01/173.90 [5594]~P1(f777(x55941,x55942))+P1(f777(x55941,f4(a851)))+P1(f777(f777(f235(a851),f793(x55942,x55941)),x55942)) % 174.01/173.90 [5619]E(x56191,f4(a851))+~E(f777(f157(a851),x56192),f4(a851))+~P1(f777(f777(f336(a851),x56191),f777(f160(a851),x56192))) % 174.01/173.90 [5681]~E(x56812,f4(a851))+P1(f777(f777(f234(a3),f4(a3)),x56811))+P1(f777(f777(f281(a851),f777(a109,x56811)),x56812)) % 174.01/173.90 [5684]E(x56841,x56842)+~P1(f777(f777(f234(a851),x56842),x56841))+~P1(f777(f777(f234(a851),x56841),x56842)) % 174.01/173.90 [5685]E(x56851,x56852)+~P1(f777(f777(f234(a3),x56852),x56851))+~P1(f777(f777(f234(a3),x56851),x56852)) % 174.01/173.90 [5694]E(x56941,x56942)+~P1(f777(f777(f281(a851),x56942),x56941))+~P1(f777(f777(f281(a851),x56941),x56942)) % 174.01/173.90 [5695]E(f777(f44(x56951),x56952),f4(a851))+~P1(f777(f65(x56951),x56952))+P1(f777(f777(f336(x56951),f620(x56952,x56951)),x56952)) % 174.01/173.90 [5701]E(f59(x57011,x57012),f55(x57011,x57012))+P1(f777(f777(f234(a3),f4(a3)),x57011))+~P1(f777(f777(f235(a3),f4(a3)),x57012)) % 174.01/173.90 [5730]~P1(f777(x57301,f779(x57301)))+P1(f777(x57301,f777(a109,x57302)))+~P1(f777(f777(f234(a3),f4(a3)),x57302)) % 174.01/173.90 [5732]P1(f777(f777(f235(a851),x57321),f403(x57322)))+~P1(f777(f65(a851),x57322))+~P1(f777(f777(f336(a851),x57321),x57322)) % 174.01/173.90 [5733]P1(f777(f777(f234(a851),x57331),f378(x57332)))+~P1(f777(f65(a851),x57332))+~P1(f777(f777(f336(a851),x57331),x57332)) % 174.01/173.90 [5762]E(x57621,x57622)+~P1(f777(f777(f235(a851),x57621),f777(a116,x57622)))+P1(f777(f777(f235(a851),x57621),x57622)) % 174.01/173.90 [5800]E(x58001,f777(a116,x58002))+~P1(f777(f777(f234(a851),x58001),f777(a116,x58002)))+P1(f777(f777(f234(a851),x58001),x58002)) % 174.01/173.90 [5810]P1(f777(x58101,f780(x58101)))+~P1(f777(x58101,f777(a109,x58102)))+~P1(f777(f777(f234(a3),f4(a3)),x58102)) % 174.01/173.90 [5812]E(f777(f79(a3),x58121),f777(f79(a3),x58122))+~P1(f777(f777(f281(a3),x58122),x58121))+~P1(f777(f777(f281(a3),x58121),x58122)) % 174.01/173.90 [5824]~P1(f777(x58241,x58242))+~P1(f777(f777(f234(a3),f4(a3)),x58242))+P1(f777(x58241,f777(f104(a3),f725(x58241)))) % 174.01/173.90 [5836]~P79(x58362)+~E(x58361,f4(x58362))+~P1(f777(f777(f235(x58362),f4(x58362)),f777(f79(x58362),x58361))) % 174.01/173.90 [5861]~P56(x58611,x58612)+P36(x58611,f777(f280(x58611,x58611),x58612))+~P1(f777(f65(f857(x58611,x58611)),x58612)) % 174.01/173.90 [5869]~P88(x58691)+E(f777(f104(x58691),f777(f108(a851),x58692)),f777(f108(x58691),x58692))+~P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x58692))) % 174.01/173.90 [5873]E(f777(a116,x58731),x58732)+~P1(f777(f777(f235(a851),x58731),x58732))+P1(f777(f777(f235(a851),f777(a116,x58731)),x58732)) % 174.01/173.90 [5886]E(f777(f777(f45(a3),x58861),x58862),f4(a3))+~P1(f777(f777(f234(a3),x58861),f4(a3)))+~P1(f777(f777(f235(a3),x58862),x58861)) % 174.01/173.90 [5899]E(f54(a3,x58991,x58992),x58991)+~P1(f777(f777(f234(a3),x58991),f4(a3)))+~P1(f777(f777(f235(a3),x58992),x58991)) % 174.01/173.90 [5912]E(f56(x59121,x59122),f55(x59121,x59122))+~P1(f777(f777(f234(a3),f4(a3)),x59121))+~P1(f777(f777(f234(a3),f4(a3)),x59122)) % 174.01/173.90 [5920]E(f777(f777(f45(a3),x59201),x59202),f4(a3))+~P1(f777(f777(f234(a3),f4(a3)),x59201))+~P1(f777(f777(f235(a3),x59201),x59202)) % 174.01/173.90 [5934]E(f54(a851,f777(f108(a851),x59341),f777(f108(a851),x59342)),f777(f108(a851),x59341))+P1(f777(a188,f777(f108(a3),x59341)))+~P1(f777(a188,f777(f108(a3),x59342))) % 174.01/173.90 [5936]E(f54(a3,x59361,x59362),x59361)+~P1(f777(f777(f234(a3),f4(a3)),x59361))+~P1(f777(f777(f235(a3),x59361),x59362)) % 174.01/173.90 [5938]E(x59381,x59382)+~P1(f777(f777(f235(a851),x59381),f777(a116,x59382)))+~P1(f777(f777(f234(a851),x59382),x59381)) % 174.01/173.90 [5954]~P110(x59541)+~P1(f777(f777(f235(x59541),x59542),f4(x59541)))+P1(f777(f777(f235(x59541),x59542),f777(f83(x59541),x59542))) % 174.01/173.90 [5955]~P68(x59551)+~P1(f777(f777(f234(x59551),x59552),f4(x59551)))+P1(f777(f777(f234(x59551),x59552),f777(f83(x59551),x59552))) % 174.01/173.90 [5964]~P9(x59641)+E(f777(f777(f68(x59641,x59641,f106(x59641)),f241(x59641)),x59642),f47(x59641,x59642))+~P1(f777(f65(x59641),x59642)) % 174.01/173.90 [5965]~P9(x59651)+E(f777(f777(f68(x59651,x59651,f105(x59651)),f182(x59651)),x59652),f46(x59651,x59652))+~P1(f777(f65(x59651),x59652)) % 174.01/173.90 [5979]~P117(x59791)+~P1(f777(f777(f235(a851),f4(a851)),x59792))+P1(f777(f777(f235(x59791),f4(x59791)),f777(f104(x59791),x59792))) % 174.01/173.90 [5980]~P110(x59801)+~P1(f777(f777(f235(a3),f4(a3)),x59802))+P1(f777(f777(f235(x59801),f4(x59801)),f777(f107(x59801),x59802))) % 174.01/173.90 [5981]~P110(x59811)+~P1(f777(f777(f234(a3),f4(a3)),x59812))+P1(f777(f777(f234(x59811),f4(x59811)),f777(f107(x59811),x59812))) % 174.01/173.90 [5984]~P10(x59842)+~P10(x59841)+E(f777(f305(a851,a3,f104(a3)),f297(a851,f777(a109,x59841),f777(a109,x59842))),f297(a3,x59841,x59842)) % 174.01/173.90 [5990]P1(f777(x59901,x59902))+~P1(f777(f777(f234(a3),f4(a3)),x59902))+~P1(f777(x59901,f777(f104(a3),f749(x59901)))) % 174.01/173.90 [6017]E(f777(f777(f84(a851),f777(f108(a851),x60171)),f777(f108(a851),x60172)),f777(f108(a851),x60171))+P1(f777(f777(f235(a3),x60171),a87))+~P1(f777(f777(f235(a3),x60172),a87)) % 174.01/173.90 [6021]~P110(x60211)+P1(f777(f777(f235(x60211),f4(x60211)),f86(x60211,x60212)))+~P1(f777(f777(f235(x60211),f4(x60211)),x60212)) % 174.01/173.90 [6035]~P77(x60351)+~P1(f777(f777(f235(x60351),x60352),f4(x60351)))+P1(f777(f777(f235(x60351),f4(x60351)),f777(f83(x60351),x60352))) % 174.01/173.90 [6036]~P77(x60361)+~P1(f777(f777(f234(x60361),x60362),f4(x60361)))+P1(f777(f777(f234(x60361),f4(x60361)),f777(f83(x60361),x60362))) % 174.01/173.90 [6039]E(x60391,f4(a851))+P1(f777(f777(f234(a3),f4(a3)),x60392))+~P1(f777(f777(f281(a851),f777(a109,x60392)),x60391)) % 174.01/173.90 [6040]E(x60401,f241(f858(x60402,a845)))+~E(f777(f44(x60402),x60401),f777(f44(x60402),f241(f858(x60402,a845))))+~P1(f777(f65(x60402),f241(f858(x60402,a845)))) % 174.01/173.90 [6071]~P1(f777(f777(f235(a851),f4(a851)),x60712))+~P1(f777(f777(f281(a851),x60711),x60712))+P1(f777(f777(f234(a851),x60711),x60712)) % 174.01/173.90 [6072]~P1(f777(f777(f235(a3),f4(a3)),x60722))+~P1(f777(f777(f281(a3),x60721),x60722))+P1(f777(f777(f234(a3),x60721),x60722)) % 174.01/173.90 [6078]~P110(x60781)+P1(f777(f777(f235(x60781),x60782),f4(x60781)))+~P1(f777(f777(f235(x60781),x60782),f777(f83(x60781),x60782))) % 174.01/173.90 [6079]~P68(x60791)+P1(f777(f777(f234(x60791),x60792),f4(x60791)))+~P1(f777(f777(f234(x60791),x60792),f777(f83(x60791),x60792))) % 174.01/173.90 [6087]~P88(x60871)+P1(f777(f777(f336(x60871),f777(f108(x60871),x60872)),f178(x60871)))+~P1(f777(f777(f234(a3),a87),x60872)) % 174.01/173.90 [6117]E(x61171,f4(a851))+~P1(f777(f777(f235(a851),x61171),f777(a116,x61172)))+P1(f777(f777(f235(a851),f561(x61172,x61171)),x61172)) % 174.01/173.90 [6141]~P110(x61411)+~P1(f777(f777(f235(x61411),f4(x61411)),f86(x61411,x61412)))+P1(f777(f777(f235(x61411),f4(x61411)),x61412)) % 174.01/173.90 [6143]~E(f777(f108(a851),x61432),f777(f108(a851),x61431))+P1(f777(f777(f234(a3),f777(f108(a3),x61431)),f4(a3)))+~P1(f777(a188,f777(f108(a3),x61432))) % 174.01/173.90 [6171]E(f777(f242(a3,a3),f59(x61711,x61712)),f777(f777(f45(a3),x61711),x61712))+~P1(f777(f777(f235(a3),x61711),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x61712)) % 174.01/173.90 [6205]E(f777(f252(a3,a3),f59(x62051,x62052)),f54(a3,x62051,x62052))+~P1(f777(f777(f235(a3),x62051),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x62052)) % 174.01/173.90 [6207]E(x62071,f4(a3))+~P1(f777(f777(f281(a3),x62072),x62071))+P1(f777(f777(f234(a3),f777(f79(a3),x62072)),f777(f79(a3),x62071))) % 174.01/173.90 [6209]~P117(x62092)+~P1(f777(f777(f235(x62092),f4(x62092)),f777(f104(x62092),x62091)))+P1(f777(f777(f235(a851),f4(a851)),x62091)) % 174.01/173.90 [6210]~P110(x62102)+~P1(f777(f777(f235(x62102),f4(x62102)),f777(f107(x62102),x62101)))+P1(f777(f777(f235(a3),f4(a3)),x62101)) % 174.01/173.90 [6211]~P110(x62112)+~P1(f777(f777(f234(x62112),f4(x62112)),f777(f107(x62112),x62111)))+P1(f777(f777(f234(a3),f4(a3)),x62111)) % 174.01/173.90 [6215]~E(x62152,f4(a851))+P1(f777(f777(f281(a851),f777(a109,x62151)),x62152))+~P1(f777(f777(f281(a3),x62151),f777(f104(a3),x62152))) % 174.01/173.90 [6216]E(f777(f242(a3,a3),f56(x62161,x62162)),f777(f777(f45(a3),x62161),x62162))+~P1(f777(f777(f235(a3),f4(a3)),x62161))+~P1(f777(f777(f234(a3),f4(a3)),x62162)) % 174.01/173.90 [6230]E(f777(f252(a3,a3),f56(x62301,x62302)),f54(a3,x62301,x62302))+~P1(f777(f777(f235(a3),f4(a3)),x62301))+~P1(f777(f777(f234(a3),f4(a3)),x62302)) % 174.01/173.90 [6248]~P77(x62481)+P1(f777(f777(f235(x62481),x62482),f4(x62481)))+~P1(f777(f777(f235(x62481),f4(x62481)),f777(f83(x62481),x62482))) % 174.01/173.90 [6249]~P77(x62491)+P1(f777(f777(f234(x62491),x62492),f4(x62491)))+~P1(f777(f777(f234(x62491),f4(x62491)),f777(f83(x62491),x62492))) % 174.01/173.90 [6275]P1(f777(f58(x62751,x62752),f59(x62751,x62752)))+~P1(f777(f777(f235(a3),x62751),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x62752)) % 174.01/173.90 [6291]~P1(f777(f777(f235(a851),f4(a851)),x62911))+~P1(f777(f777(f281(a851),x62912),x62911))+~P1(f777(f777(f235(a851),x62911),x62912)) % 174.01/173.90 [6292]~P1(f777(f777(f235(a3),f4(a3)),x62921))+~P1(f777(f777(f281(a3),x62922),x62921))+~P1(f777(f777(f235(a3),x62921),x62922)) % 174.01/173.90 [6304]P1(f777(f58(x63041,x63042),f56(x63041,x63042)))+~P1(f777(f777(f235(a3),f4(a3)),x63042))+~P1(f777(f777(f234(a3),f4(a3)),x63041)) % 174.01/173.90 [6346]~P77(x63461)+P1(f777(f777(f235(x63461),f777(f83(x63461),x63462)),f4(x63461)))+~P1(f777(f777(f235(x63461),f4(x63461)),x63462)) % 174.01/173.90 [6347]~P77(x63471)+P1(f777(f777(f234(x63471),f777(f83(x63471),x63472)),f4(x63471)))+~P1(f777(f777(f234(x63471),f4(x63471)),x63472)) % 174.01/173.90 [6369]E(f777(f777(f5(a851),f777(a109,x63691)),f777(a109,x63692)),f777(a109,f190(x63691,x63692)))+~P1(f777(f777(f234(a3),f4(a3)),x63692))+~P1(f777(f777(f234(a3),f4(a3)),x63691)) % 174.01/173.90 [6387]P1(f777(f777(f234(a3),f4(a3)),f190(x63871,x63872)))+~P1(f777(f777(f234(a3),f4(a3)),x63872))+~P1(f777(f777(f234(a3),f4(a3)),x63871)) % 174.01/173.90 [6426]~P1(f777(x64261,x64262))+P1(f777(x64261,f4(a851)))+P1(f777(x64261,f777(f777(f84(a851),f793(x64262,x64261)),f82(a851)))) % 174.01/173.90 [6512]E(f777(f108(a851),x65121),f777(f108(a851),x65122))+~P1(f777(f777(f234(a3),f777(f108(a3),x65122)),f4(a3)))+~P1(f777(a188,f777(f108(a3),x65121))) % 174.01/173.90 [6525]~E(x65251,f4(a851))+~E(f738(x65252,x65251),f4(a851))+E(f777(f134(a851,a851,f84(a851),x65251),x65252),f4(a851)) % 174.01/173.90 [6551]~P1(f777(f65(x65511),f672(x65512,x65511)))+~P1(f777(f65(f858(x65511,a845)),x65512))+P1(f777(f65(x65511),f46(f858(x65511,a845),x65512))) % 174.01/173.90 [6557]E(x65571,x65572)+P1(f777(f777(f235(a3),x65571),x65572))+~P1(f777(f777(f235(a3),x65571),f777(f777(f84(a3),x65572),f82(a3)))) % 174.01/173.90 [6559]P1(f777(f777(f235(a851),f777(a109,x65591)),f777(a109,x65592)))+~P1(f777(f777(f235(a3),f4(a3)),x65592))+~P1(f777(f777(f235(a3),x65591),x65592)) % 174.01/173.90 [6560]P1(f777(f777(f235(a851),f777(a109,x65601)),f777(a109,x65602)))+~P1(f777(f777(f234(a3),f4(a3)),x65601))+~P1(f777(f777(f235(a3),x65601),x65602)) % 174.01/173.90 [6561]P1(f777(f777(f234(a851),f777(a109,x65611)),f777(a109,x65612)))+~P1(f777(f777(f235(a3),f4(a3)),x65611))+~P1(f777(f777(f234(a3),x65611),x65612)) % 174.01/173.90 [6562]P1(f777(f777(f234(a851),f777(a109,x65621)),f777(a109,x65622)))+~P1(f777(f777(f234(a3),f4(a3)),x65622))+~P1(f777(f777(f234(a3),x65621),x65622)) % 174.01/173.90 [6573]E(f54(a851,f777(a109,x65731),f777(a109,x65732)),f777(a109,f54(a3,x65731,x65732)))+~P1(f777(f777(f234(a3),f4(a3)),x65732))+~P1(f777(f777(f234(a3),f4(a3)),x65731)) % 174.01/173.90 [6594]~P77(x65941)+~P1(f777(f777(f235(x65941),f777(f83(x65941),x65942)),f4(x65941)))+P1(f777(f777(f235(x65941),f4(x65941)),x65942)) % 174.01/173.90 [6595]~P77(x65951)+~P1(f777(f777(f234(x65951),f777(f83(x65951),x65952)),f4(x65951)))+P1(f777(f777(f234(x65951),f4(x65951)),x65952)) % 174.01/173.90 [6612]~P1(f777(f777(f235(a3),a87),x66122))+~P1(f777(f777(f235(a3),x66121),x66122))+P1(f777(f777(f235(a851),f777(f108(a851),x66121)),f777(f108(a851),x66122))) % 174.01/173.90 [6709]~P1(f777(f777(f234(a3),f4(a3)),x67091))+P1(f777(f777(f235(a851),f777(a109,x67091)),x67092))+~P1(f777(f777(f235(a3),x67091),f777(f104(a3),x67092))) % 174.01/173.90 [6710]~P1(f777(f777(f234(a3),f4(a3)),x67101))+P1(f777(f777(f281(a851),f777(a109,x67101)),x67102))+~P1(f777(f777(f281(a3),x67101),f777(f104(a3),x67102))) % 174.01/173.90 [6726]E(x67261,f4(a3))+E(f54(a3,x67262,x67261),f4(a3))+E(f777(f777(f5(a3),f777(f83(a3),f777(f777(f45(a3),x67262),x67261))),f82(a3)),f777(f777(f45(a3),x67262),f777(f83(a3),x67261))) % 174.01/173.90 [6742]~P1(f777(f777(f234(a3),f4(a3)),x67421))+~P1(f777(f777(f235(a851),f777(a109,x67421)),x67422))+P1(f777(f777(f235(a3),x67421),f777(f104(a3),x67422))) % 174.01/173.90 [6743]~P1(f777(f777(f234(a3),f4(a3)),x67431))+~P1(f777(f777(f281(a851),f777(a109,x67431)),x67432))+P1(f777(f777(f281(a3),x67431),f777(f104(a3),x67432))) % 174.01/173.90 [6783]~P1(f777(f777(f234(a851),f777(a109,x67831)),f777(a109,x67832)))+~P1(f777(f777(f235(a3),f4(a3)),x67831))+P1(f777(f777(f234(a3),x67831),x67832)) % 174.01/173.90 [6784]~P1(f777(f777(f234(a851),f777(a109,x67841)),f777(a109,x67842)))+~P1(f777(f777(f234(a3),f4(a3)),x67842))+P1(f777(f777(f234(a3),x67841),x67842)) % 174.01/173.90 [6815]P1(f777(f777(f234(a3),x68151),x68152))+~P1(f777(f777(f234(a851),f777(f108(a851),x68151)),f777(f108(a851),x68152)))+P1(f777(f777(f234(a3),x68151),a87)) % 174.01/173.90 [6842]P1(f777(f777(f234(a3),f4(a3)),f54(a3,x68421,x68422)))+~P1(f777(f777(f234(a3),f4(a3)),x68422))+~P1(f777(f777(f234(a3),f4(a3)),x68421)) % 174.01/173.90 [6941]P1(f777(f777(f235(a3),a87),x69411))+~P1(f777(f777(f235(a3),x69412),x69411))+~P1(f777(f777(f235(a851),f777(f108(a851),x69412)),f777(f108(a851),x69411))) % 174.01/173.90 [6989]E(f777(f777(f243(a3,a3),f777(f777(f45(a3),x69891),x69892)),f54(a3,x69891,x69892)),f59(x69891,x69892))+~P1(f777(f777(f235(a3),x69891),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x69892)) % 174.01/173.90 [7010]E(f777(f777(f243(a3,a3),f777(f777(f45(a3),x70101),x70102)),f54(a3,x70101,x70102)),f56(x70101,x70102))+~P1(f777(f777(f234(a3),f4(a3)),x70102))+~P1(f777(f777(f234(a3),f4(a3)),x70101)) % 174.01/173.90 [7065]~P91(x70652)+E(x70651,f117(x70652))+E(f777(f134(x70652,x70652,f85(x70652),f777(f133(x70652),x70651)),f777(f159(x70652),x70651)),f777(f67(x70652,f85(x70652)),f777(f160(x70652),x70651))) % 174.01/173.90 [7179]~E(x71791,f4(a851))+E(f777(f134(a851,a851,f84(a851),x71791),x71792),f4(a851))+P1(f777(f777(f336(a851),f738(x71792,x71791)),f777(f160(a851),x71792))) % 174.01/173.90 [7233]~P1(f777(f777(f235(a3),x72332),f4(a3)))+P1(f777(f777(f235(a3),f777(f777(f45(a3),x72331),x72332)),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x72331)) % 174.01/173.90 [7235]~P1(f777(f777(f235(a3),x72351),f4(a3)))+P1(f777(f777(f235(a3),f777(f777(f45(a3),x72351),x72352)),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x72352)) % 174.01/173.90 [7236]~P1(f777(f777(f235(a3),x72362),f4(a3)))+P1(f777(f777(f234(a3),f777(f777(f45(a3),x72361),x72362)),f4(a3)))+~P1(f777(f777(f234(a3),f4(a3)),x72361)) % 174.01/173.90 [7237]~P1(f777(f777(f234(a3),x72371),f4(a3)))+P1(f777(f777(f234(a3),f777(f777(f45(a3),x72371),x72372)),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x72372)) % 174.01/173.90 [7246]P1(f777(f777(f336(f858(x72461,a845)),f672(x72462,x72461)),x72462))+~P1(f777(f65(f858(x72461,a845)),x72462))+P1(f777(f65(x72461),f46(f858(x72461,a845),x72462))) % 174.01/173.90 [7351]P29(x73511,x73511,x73512,f241(f858(x73511,a845)))+~E(f777(f305(x73511,x73511,x73512),f241(f858(x73511,a845))),f241(f858(x73511,a845)))+~P1(f777(f65(x73511),f241(f858(x73511,a845)))) % 174.01/173.90 [7480]~P29(x74801,x74801,x74802,f241(f858(x74801,a845)))+E(f777(f305(x74801,x74801,x74802),f241(f858(x74801,a845))),f241(f858(x74801,a845)))+~P1(f777(f65(x74801),f241(f858(x74801,a845)))) % 174.01/173.90 [7621]E(f777(f777(f45(a3),x76211),x76212),f777(f108(a3),a101))+~P1(f777(f777(f234(a3),f777(f777(f84(a3),x76211),x76212)),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x76211)) % 174.01/173.90 [7679]~P1(f777(f777(f235(a3),x76792),f4(a3)))+~P1(f777(f777(f235(a3),f777(f777(f45(a3),x76791),x76792)),f4(a3)))+P1(f777(f777(f235(a3),f4(a3)),x76791)) % 174.01/173.90 [7684]E(f777(f777(f84(a3),x76841),x76842),f54(a3,x76841,x76842))+~P1(f777(f777(f234(a3),f777(f777(f84(a3),x76841),x76842)),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x76841)) % 174.01/173.90 [7686]P1(f777(f777(f235(a3),x76861),f4(a3)))+~P1(f777(f777(f235(a3),f777(f777(f45(a3),x76861),x76862)),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x76862)) % 174.01/173.90 [7938]~P99(x79381)+P50(a851,x79381,f281(a851),x79382)+~P1(f777(f777(f234(x79381),f777(x79382,f379(x79382,x79381))),f777(x79382,f395(x79382,x79381)))) % 174.01/173.90 [8380]~P100(x83801)+P18(x83801,x83802)+~P1(f777(f777(f234(x83801),f777(f777(f155(x83801),x83802),f763(x83802,x83801))),f777(f777(f155(x83801),x83802),f764(x83802,x83801)))) % 174.01/173.90 [5562]E(x55621,f4(a3))+~E(f54(a3,x55622,x55621),f4(a3))+E(f777(f777(f45(a3),x55622),f777(f83(a3),x55621)),f777(f83(a3),f777(f777(f45(a3),x55622),x55621))) % 174.01/173.90 [5579]~P38(x55792)+~P38(x55791)+P38(f777(f777(f105(f858(a3,a845)),x55791),x55792)) % 174.01/173.90 [5580]~P38(x55802)+~P38(x55801)+P38(f777(f777(f106(f858(a3,a845)),x55801),x55802)) % 174.01/173.90 [5597]~P88(x55971)+~P60(x55971)+E(f777(f83(x55971),f777(f777(f285(x55971),f82(x55971)),x55972)),f777(f777(f285(x55971),f777(f108(x55971),a101)),x55972)) % 174.01/173.90 [5722]E(x57221,f4(a3))+~E(f54(a3,x57222,x57221),f4(a3))+E(f777(f777(f45(a3),f777(f83(a3),x57222)),x57221),f777(f83(a3),f777(f777(f45(a3),x57222),x57221))) % 174.01/173.90 [5856]~P100(x58561)+P18(x58561,x58562)+P1(f777(f777(f235(a851),f764(x58562,x58561)),f777(f183(f852(x58561)),x58562))) % 174.01/173.90 [6013]~P88(x60131)+~E(f777(f108(x60131),x60132),f4(x60131))+P33(x60131,f777(f108(x60131),f777(f777(f84(a3),x60132),f777(f83(a3),a87)))) % 174.01/173.90 [6014]~P88(x60141)+~E(f777(f108(x60141),x60142),f4(x60141))+P33(x60141,f777(f108(x60141),f777(f777(f84(a3),a87),f777(f83(a3),x60142)))) % 174.01/173.90 [6016]E(f777(a60,f56(f777(f83(a3),x60161),f777(f83(a3),x60162))),f55(x60161,x60162))+P1(f777(f777(f235(a3),f4(a3)),x60162))+P1(f777(f777(f234(a3),f4(a3)),x60161)) % 174.01/173.90 [6149]~E(x61492,f4(a851))+~E(x61491,f4(a851))+P1(f777(f777(f234(a3),f777(f104(a3),x61491)),f777(f83(a3),f777(f104(a3),x61492)))) % 174.01/173.90 [6175]E(f777(f777(f84(a851),f777(f108(a851),x61751)),f777(f108(a851),x61752)),f777(f108(a851),f777(f777(f84(a3),x61751),x61752)))+P1(f777(f777(f235(a3),x61751),a87))+P1(f777(f777(f235(a3),x61752),a87)) % 174.01/173.90 [6313]~P68(x63131)+~P1(f777(f777(f235(x63131),f4(x63131)),x63132))+P1(f777(f777(f235(x63131),f777(f83(x63131),x63132)),x63132)) % 174.01/173.90 [6314]~P68(x63141)+~P1(f777(f777(f234(x63141),f4(x63141)),x63142))+P1(f777(f777(f234(x63141),f777(f83(x63141),x63142)),x63142)) % 174.01/173.90 [6497]E(f777(f777(f5(a851),f777(a109,x64971)),f777(a109,x64972)),f777(a109,f777(f777(f5(a3),x64971),x64972)))+~P1(f777(f777(f234(a3),f4(a3)),x64972))+~P1(f777(f777(f234(a3),x64972),x64971)) % 174.01/173.90 [6534]E(f777(a109,f54(a3,f777(f108(a3),x65341),f777(f108(a3),x65342))),f54(a851,f777(f108(a851),x65341),f777(f108(a851),x65342)))+P1(f777(a188,f777(f108(a3),x65341)))+P1(f777(a188,f777(f108(a3),x65342))) % 174.01/173.90 [6552]~P68(x65521)+P1(f777(f777(f235(x65521),f4(x65521)),x65522))+~P1(f777(f777(f235(x65521),f777(f83(x65521),x65522)),x65522)) % 174.01/173.90 [6553]~P68(x65531)+P1(f777(f777(f234(x65531),f4(x65531)),x65532))+~P1(f777(f777(f234(x65531),f777(f83(x65531),x65532)),x65532)) % 174.01/173.90 [6564]~P68(x65641)+~P1(f777(f777(f235(x65641),f4(x65641)),x65642))+P1(f777(f777(f235(x65641),f4(x65641)),f777(f777(f84(x65641),x65642),x65642))) % 174.01/173.90 [6566]~P68(x65661)+~P1(f777(f777(f234(x65661),f4(x65661)),x65662))+P1(f777(f777(f234(x65661),f4(x65661)),f777(f777(f84(x65661),x65662),x65662))) % 174.01/173.90 [6577]E(f777(f777(f84(a851),f777(a109,x65771)),f777(a109,x65772)),f777(a109,f777(f777(f84(a3),x65771),x65772)))+~P1(f777(f777(f234(a3),f4(a3)),x65772))+~P1(f777(f777(f234(a3),f4(a3)),x65771)) % 174.01/173.90 [6590]E(x65901,f4(a851))+P1(f777(f777(f235(a851),f4(a851)),x65902))+~P1(f777(f777(f235(a851),f4(a851)),f777(f777(f244(a851),x65902),x65901))) % 174.01/173.90 [6623]~P88(x66231)+E(f777(f108(x66231),x66232),f4(x66231))+~P33(x66231,f777(f108(x66231),f777(f777(f84(a3),a87),f777(f83(a3),x66232)))) % 174.01/173.90 [6624]~P88(x66241)+E(f777(f108(x66241),x66242),f4(x66241))+~P33(x66241,f777(f108(x66241),f777(f777(f84(a3),x66242),f777(f83(a3),a87)))) % 174.01/173.90 [6686]~P1(f777(f65(x66861),x66862))+~P1(f777(f65(x66861),f241(f858(x66861,a845))))+P1(f777(f65(x66861),f777(f83(f858(x66861,a845)),x66862))) % 174.01/173.90 [6711]~P1(f777(f777(f235(a3),f4(a3)),x67112))+~P1(f777(f777(f234(a3),x67112),x67111))+P1(f777(f777(f235(a3),f4(a3)),f777(f777(f45(a3),x67111),x67112))) % 174.01/173.90 [6712]~P1(f777(f777(f235(a3),x67122),f4(a3)))+~P1(f777(f777(f234(a3),x67121),f4(a3)))+P1(f777(f777(f234(a3),f4(a3)),f777(f777(f45(a3),x67121),x67122))) % 174.01/173.90 [6754]~P1(f777(f777(f235(a851),f4(a851)),x67542))+~P1(f777(f777(f235(a851),f4(a851)),x67541))+P1(f777(f777(f235(a851),f4(a851)),f777(f777(f85(a851),x67541),x67542))) % 174.01/173.90 [6755]~P1(f777(f777(f234(a3),f4(a3)),x67552))+~P1(f777(f777(f234(a3),f4(a3)),x67551))+P1(f777(f777(f234(a3),f4(a3)),f777(f777(f84(a3),x67551),x67552))) % 174.01/173.90 [6756]~P1(f777(f777(f234(a3),f4(a3)),x67562))+~P1(f777(f777(f234(a3),f4(a3)),x67561))+P1(f777(f777(f234(a3),f4(a3)),f777(f777(f85(a3),x67561),x67562))) % 174.01/173.90 [6757]~P1(f777(f777(f235(a3),f4(a3)),x67572))+~P1(f777(f777(f234(a3),f4(a3)),x67571))+P1(f777(f777(f234(a3),f4(a3)),f777(f777(f45(a3),x67571),x67572))) % 174.01/173.90 [6758]~P1(f777(f777(f234(a3),f4(a3)),x67582))+~P1(f777(f777(f234(a3),f4(a3)),x67581))+P1(f777(f777(f234(a3),f4(a3)),f777(f777(f45(a3),x67581),x67582))) % 174.01/173.90 [6827]E(x68271,f4(a3))+E(f54(a3,x68272,x68271),f4(a3))+E(f777(f777(f5(a3),f777(f83(a3),f777(f777(f45(a3),x68272),x68271))),f82(a3)),f777(f777(f45(a3),f777(f83(a3),x68272)),x68271)) % 174.01/173.90 [6887]P1(f777(f777(f235(a851),f4(a851)),x68871))+P1(f777(f777(f235(a851),f4(a851)),x68872))+~P1(f777(f777(f235(a851),f4(a851)),f777(f777(f84(a851),x68872),x68871))) % 174.01/173.90 [6888]~P68(x68881)+P1(f777(f777(f235(x68881),f4(x68881)),x68882))+~P1(f777(f777(f235(x68881),f4(x68881)),f777(f777(f84(x68881),x68882),x68882))) % 174.01/173.90 [6889]~P68(x68891)+P1(f777(f777(f234(x68891),f4(x68891)),x68892))+~P1(f777(f777(f234(x68891),f4(x68891)),f777(f777(f84(x68891),x68892),x68892))) % 174.01/173.90 [6942]~P1(f777(f65(x69421),x69422))+P1(f777(f65(x69421),f241(f858(x69421,a845))))+~P1(f777(f65(x69421),f777(f83(f858(x69421,a845)),x69422))) % 174.01/173.90 [7002]P1(f777(f777(f234(a3),x70021),f4(a3)))+~P1(f777(f777(f235(a3),x70022),f4(a3)))+~P1(f777(f777(f234(a3),f4(a3)),f777(f777(f45(a3),x70021),x70022))) % 174.01/173.90 [7008]~P1(f777(f777(f235(a3),f4(a3)),x70081))+P1(f777(f777(f234(a3),x70081),x70082))+~P1(f777(f777(f235(a3),f4(a3)),f777(f777(f45(a3),x70082),x70081))) % 174.01/173.90 [7009]~P1(f777(f777(f234(a3),f4(a3)),x70092))+P1(f777(f777(f234(a3),x70091),x70092))+~P1(f777(f777(f235(a3),f4(a3)),f777(f777(f45(a3),x70092),x70091))) % 174.01/173.90 [7041]P1(f777(f777(f235(a3),f4(a3)),x70411))+~P1(f777(f777(f234(a3),f4(a3)),x70412))+~P1(f777(f777(f235(a3),f4(a3)),f777(f777(f45(a3),x70412),x70411))) % 174.01/173.90 [7042]P1(f777(f777(f234(a3),f4(a3)),x70421))+~P1(f777(f777(f235(a3),f4(a3)),x70422))+~P1(f777(f777(f234(a3),f4(a3)),f777(f777(f45(a3),x70421),x70422))) % 174.01/173.90 [7511]~P1(f777(f65(x75112),f241(f858(x75112,a845))))+~P1(f777(f65(x75111),f241(f858(x75111,a845))))+P1(f777(f65(f859(x75111,x75112)),f241(f858(f859(x75111,x75112),a845)))) % 174.01/173.90 [7512]~P1(f777(f65(x75122),f241(f858(x75122,a845))))+~P1(f777(f65(x75121),f241(f858(x75121,a845))))+P1(f777(f65(f857(x75121,x75122)),f241(f858(f857(x75121,x75122),a845)))) % 174.01/173.90 [7584]~P1(f777(f777(f235(a851),f777(a116,f4(a851))),x75841))+~P1(f777(f777(f235(a851),f777(a116,f4(a851))),x75842))+P1(f777(f777(f235(a851),x75841),f777(f777(f85(a851),x75842),x75841))) % 174.01/173.90 [7585]~P1(f777(f777(f235(a851),f777(a116,f4(a851))),x75851))+~P1(f777(f777(f235(a851),f777(a116,f4(a851))),x75852))+P1(f777(f777(f235(a851),x75851),f777(f777(f85(a851),x75851),x75852))) % 174.01/173.90 [7620]E(f777(f44(x76201),f241(f858(x76201,a845))),f777(a116,f4(a851)))+P1(f777(f65(x76202),f241(f858(x76202,a845))))+~P1(f777(f65(f858(x76202,x76201)),f241(f858(f858(x76202,x76201),a845)))) % 174.01/173.90 [7745]~P1(f777(f777(f235(a851),f777(a116,f4(a851))),x77452))+~P1(f777(f777(f235(a851),f777(a116,f4(a851))),x77451))+P1(f777(f777(f235(a851),f777(a116,f4(a851))),f777(f777(f85(a851),x77451),x77452))) % 174.01/173.90 [7746]~P1(f777(f777(f234(a851),f777(a116,f4(a851))),x77461))+~P1(f777(f777(f234(a851),f777(a116,f4(a851))),x77462))+P1(f777(f777(f234(a851),f777(a116,f4(a851))),f777(f777(f85(a851),x77461),x77462))) % 174.01/173.90 [8427]E(x84271,f117(x84272))+~P1(f777(f129(x84272),x84271))+E(f164(x84272,f777(f777(f12(a845,a845,x84272),a330),f777(f777(f11(x84272,x84272,a845),a332),f136(x84272,x84271))),x84271),f118(x84272,x84271)) % 174.01/173.90 [8525]~P38(x85252)+~P38(x85251)+E(f777(f305(a851,a3,f104(a3)),f777(f777(f105(f858(a851,a845)),f777(f305(a3,a851,a109),x85251)),f777(f305(a3,a851,a109),x85252))),f777(f777(f105(f858(a3,a845)),x85251),x85252)) % 174.01/173.90 [8526]~P38(x85262)+~P38(x85261)+E(f777(f305(a851,a3,f104(a3)),f777(f777(f106(f858(a851,a845)),f777(f305(a3,a851,a109),x85261)),f777(f305(a3,a851,a109),x85262))),f777(f777(f106(f858(a3,a845)),x85261),x85262)) % 174.01/173.90 [9115]~P88(x91151)+~E(f777(f108(x91151),x91152),f82(x91151))+P33(x91151,f777(f108(x91151),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f83(a3),x91152)))) % 174.01/173.90 [9330]~P88(x93301)+E(f777(f108(x93301),x93302),f82(x93301))+~P33(x93301,f777(f108(x93301),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f83(a3),x93302)))) % 174.01/173.90 [9744]~P99(x97442)+P52(a851,x97442,f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x97441)+P1(f777(f777(f281(a851),f371(x97441,x97442)),f372(x97441,x97442))) % 174.01/173.90 [9747]~P99(x97471)+P52(a851,x97471,f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x97472)+~P1(f777(f777(f281(a851),f372(x97472,x97471)),f371(x97472,x97471))) % 174.01/173.90 [9748]~P99(x97481)+P52(a851,x97481,f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x97482)+~P1(f777(f777(f235(x97481),f777(x97482,f371(x97482,x97481))),f777(x97482,f372(x97482,x97481)))) % 174.01/173.90 [9837]~P99(x98371)+P50(a851,x98371,f281(a851),x98372)+~P52(a851,x98371,f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x98372) % 174.01/173.90 [10035]E(x100351,f4(a3))+E(x100352,f4(a3))+E(f777(f254(a3,a3,a3,a3,f41(a3),f777(f85(a3),f86(a3,x100352))),f777(f777(f777(f100(f857(a3,a3)),f777(f777(a332,f86(a3,x100351)),f86(a3,x100352))),f62(x100351,x100352)),f777(f777(f253(a3,a3,f857(a3,a3)),f777(f777(f22(a3,f858(a3,f857(a3,a3)),f858(a3,f857(a3,a3))),f777(f777(f12(f858(a3,f858(f857(a3,a3),f857(a3,a3))),f858(f858(a3,f857(a3,a3)),f858(a3,f857(a3,a3))),a3),f22(a3,f857(a3,a3),f857(a3,a3))),f777(f777(f12(f857(a3,a3),f858(a3,f858(f857(a3,a3),f857(a3,a3))),a3),f777(f11(a3,f857(a3,a3),f858(f857(a3,a3),f857(a3,a3))),f777(f777(f12(a845,f858(f857(a3,a3),f858(f857(a3,a3),f857(a3,a3))),a3),f100(f857(a3,a3))),f777(f777(f11(a3,a3,a845),a332),f4(a3))))),f777(f777(f11(a3,a3,f857(a3,a3)),f777(f777(f12(a3,f858(a3,f857(a3,a3)),a3),f243(a3,a3)),f83(a3))),f4(a3))))),f777(f777(f11(a3,f858(a3,a3),f858(a3,f857(a3,a3))),f777(f777(f12(f858(a3,f857(a3,a3)),f858(f858(a3,a3),f858(a3,f857(a3,a3))),a3),f12(a3,f857(a3,a3),a3)),f777(f777(f12(a3,f858(a3,f857(a3,a3)),a3),f243(a3,a3)),f777(f777(f11(a3,a3,a3),f777(f777(f12(a3,f858(a3,a3),a3),f5(a3)),f83(a3))),f82(a3))))),f777(f5(a3),f777(f79(a3),x100352))))),f62(x100351,x100352)))),f55(x100351,x100352)) % 174.01/173.90 [10036]E(x100361,f4(a3))+E(x100362,f4(a3))+E(f777(f254(a3,a3,a3,a3,f41(a3),f777(f85(a3),f86(a3,x100362))),f777(f777(f777(f100(f857(a3,a3)),f777(f777(a334,f777(f777(a333,f777(f777(f235(a3),f4(a3)),x100362)),f777(f777(f234(a3),f4(a3)),x100361))),f777(f777(a333,f777(f777(f235(a3),x100362),f4(a3))),f777(f777(f235(a3),x100361),f4(a3))))),f62(x100361,x100362)),f777(f777(f253(a3,a3,f857(a3,a3)),f777(f777(f22(a3,f858(a3,f857(a3,a3)),f858(a3,f857(a3,a3))),f777(f777(f12(f858(a3,f858(f857(a3,a3),f857(a3,a3))),f858(f858(a3,f857(a3,a3)),f858(a3,f857(a3,a3))),a3),f22(a3,f857(a3,a3),f857(a3,a3))),f777(f777(f12(f857(a3,a3),f858(a3,f858(f857(a3,a3),f857(a3,a3))),a3),f777(f11(a3,f857(a3,a3),f858(f857(a3,a3),f857(a3,a3))),f777(f777(f12(a845,f858(f857(a3,a3),f858(f857(a3,a3),f857(a3,a3))),a3),f100(f857(a3,a3))),f777(f777(f11(a3,a3,a845),a332),f4(a3))))),f777(f777(f11(a3,a3,f857(a3,a3)),f777(f777(f12(a3,f858(a3,f857(a3,a3)),a3),f243(a3,a3)),f83(a3))),f4(a3))))),f777(f777(f11(a3,f858(a3,a3),f858(a3,f857(a3,a3))),f777(f777(f12(f858(a3,f857(a3,a3)),f858(f858(a3,a3),f858(a3,f857(a3,a3))),a3),f12(a3,f857(a3,a3),a3)),f777(f777(f12(a3,f858(a3,f857(a3,a3)),a3),f243(a3,a3)),f777(f777(f11(a3,a3,a3),f777(f777(f12(a3,f858(a3,a3),a3),f5(a3)),f83(a3))),f82(a3))))),f777(f5(a3),f777(f79(a3),x100362))))),f62(x100361,x100362)))),f55(x100361,x100362)) % 174.01/173.90 [5587]~P110(x55871)+~P88(x55871)+E(f777(f79(x55871),f777(f777(f244(x55871),f777(f108(x55871),a101)),x55872)),f82(x55871)) % 174.01/173.90 [6088]~P133(x60881)+~P1(f777(f777(f235(a3),x60882),f4(a3)))+E(f777(f83(x60881),f777(f104(x60881),f777(a109,f777(f83(a3),x60882)))),f777(f107(x60881),x60882)) % 174.01/173.90 [6297]P1(f777(f777(f234(a103),x62971),f82(a103)))+E(f777(f777(f84(a103),f82(a103)),f269(x62971,f777(f777(f45(a103),x62972),x62971))),f269(x62971,x62972))+P1(f777(f777(f235(a103),x62972),x62971)) % 174.01/173.90 [6370]E(x63701,f4(a3))+~E(f777(f79(a3),x63702),f82(a3))+P1(f777(f777(f281(a3),f777(f777(f85(a3),x63701),x63702)),x63701)) % 174.01/173.90 [6796]~E(x67962,f82(a851))+~P1(f777(f777(f235(a851),f4(a851)),x67961))+P1(f777(f777(f281(a851),f777(f777(f85(a851),x67961),x67962)),x67961)) % 174.01/173.90 [6797]~E(x67971,f82(a851))+~P1(f777(f777(f235(a851),f4(a851)),x67972))+P1(f777(f777(f281(a851),f777(f777(f85(a851),x67971),x67972)),x67972)) % 174.01/173.90 [6930]~P87(x69301)+~P1(f777(f777(f336(x69301),x69302),f114(x69301)))+~E(f777(f777(f84(x69301),f777(f777(f84(x69301),f82(x69301)),x69302)),x69302),f4(x69301)) % 174.01/173.90 [7043]~P1(f777(f777(f235(a3),x70431),f4(a3)))+~P1(f777(f777(f234(a3),x70432),f4(a3)))+E(f777(f242(a3,a3),f777(a60,f56(f777(f83(a3),x70431),f777(f83(a3),x70432)))),f777(f777(f45(a3),x70431),x70432)) % 174.01/173.90 [7059]~P1(f777(f777(f235(a3),x70591),f4(a3)))+~P1(f777(f777(f234(a3),x70592),f4(a3)))+E(f777(f252(a3,a3),f777(a60,f56(f777(f83(a3),x70591),f777(f83(a3),x70592)))),f54(a3,x70591,x70592)) % 174.01/173.90 [7067]~P1(f777(f777(f235(a3),x70672),f4(a3)))+E(f777(f242(a3,a3),f777(a60,f59(f777(f83(a3),x70671),f777(f83(a3),x70672)))),f777(f777(f45(a3),x70671),x70672))+~P1(f777(f777(f235(a3),f4(a3)),x70671)) % 174.01/173.90 [7071]E(x70711,f4(a3))+E(f777(f79(a3),x70712),f82(a3))+~P1(f777(f777(f281(a3),f777(f777(f85(a3),x70711),x70712)),x70711)) % 174.01/173.90 [7086]~P1(f777(f777(f235(a3),x70862),f4(a3)))+E(f777(f252(a3,a3),f777(a60,f59(f777(f83(a3),x70861),f777(f83(a3),x70862)))),f54(a3,x70861,x70862))+~P1(f777(f777(f235(a3),f4(a3)),x70861)) % 174.01/173.90 [7137]E(f777(f777(f45(a3),f777(f777(f244(a3),x71371),x71372)),x71371),f777(f777(f244(a3),x71371),f777(f777(f5(a851),x71372),f777(a116,f4(a851)))))+~P1(f777(f777(f235(a851),f4(a851)),x71372))+~P1(f777(f777(f235(a3),f4(a3)),x71371)) % 174.01/173.90 [7242]~P1(f777(f777(f235(a851),f4(a851)),x72421))+~P1(f777(f777(f235(a851),f82(a851)),x72422))+P1(f777(f777(f235(a851),f777(f777(f45(a851),x72421),x72422)),x72421)) % 174.01/173.90 [7243]~P1(f777(f777(f235(a851),f4(a851)),x72431))+~P1(f777(f777(f235(a851),f4(a851)),x72432))+P1(f777(f777(f235(a851),f777(f777(f5(a851),x72431),x72432)),x72431)) % 174.01/173.90 [7244]~P1(f777(f777(f235(a3),f4(a3)),x72441))+~P1(f777(f777(f235(a3),f82(a3)),x72442))+P1(f777(f777(f235(a3),f777(f777(f45(a3),x72441),x72442)),x72441)) % 174.01/173.90 [7403]E(x74031,f4(a851))+~E(x74032,f4(a3))+~P1(f777(f777(f235(a3),f4(a3)),f777(f777(f244(a3),f777(f79(a3),x74032)),x74031))) % 174.01/173.90 [7441]E(x74411,f82(a851))+~P1(f777(f777(f235(a851),f4(a851)),x74412))+~P1(f777(f777(f281(a851),f777(f777(f85(a851),x74412),x74411)),x74412)) % 174.01/173.90 [7442]E(x74421,f82(a851))+~P1(f777(f777(f235(a851),f4(a851)),x74422))+~P1(f777(f777(f281(a851),f777(f777(f85(a851),x74421),x74422)),x74422)) % 174.01/173.90 [7828]~E(x78282,f117(f852(x78281)))+E(f777(f183(f852(f852(x78281))),f166(x78281,x78282)),f4(a851))+~P18(a851,f777(f144(a851),f777(f777(f145(f852(x78281),a851),f183(f852(x78281))),x78282))) % 174.01/173.90 [8078]P1(f777(x80781,x80782))+~P1(f777(x80781,f777(a111,f577(x80781,x80782))))+~P1(f777(f777(f336(f858(f857(a851,a851),a845)),x80782),a102)) % 174.01/173.90 [8092]E(x80921,f117(f852(x80922)))+E(f777(f183(f852(x80922)),f777(f777(f155(f852(x80922)),x80921),f4(a851))),f777(f183(f852(f852(x80922))),f166(x80922,x80921)))+~P18(a851,f777(f144(a851),f777(f777(f145(f852(x80922),a851),f183(f852(x80922))),x80921))) % 174.01/173.90 [8764]~P1(f777(f65(x87641),f777(f258(x87641),x87642)))+~P1(f777(f65(x87641),f241(f858(x87641,a845))))+P1(f777(f65(x87641),f777(f258(x87641),f777(f777(f12(a845,a845,x87641),a330),x87642)))) % 174.01/173.90 [8817]E(f777(f777(f243(a851,a851),f777(a116,f777(f777(f45(a851),f777(f777(f5(a851),x88171),x88172)),x88172))),f54(a851,f777(f777(f5(a851),x88171),x88172),x88172)),f89(f857(a851,a851),f57(x88171,x88172)))+~P1(f777(f777(f235(a851),f4(a851)),x88172))+~P1(f777(f777(f234(a851),x88172),x88171)) % 174.01/173.90 [9082]~P1(f777(f65(x90821),f777(f258(x90821),x90822)))+P1(f777(f65(x90821),f241(f858(x90821,a845))))+~P1(f777(f65(x90821),f777(f258(x90821),f777(f777(f12(a845,a845,x90821),a330),x90822)))) % 174.01/173.90 [9741]P30(x97411,x97412)+~P36(x97411,f777(f242(f858(f857(x97411,x97411),a845),f858(f857(x97411,x97411),a845)),x97412))+~P1(f777(f777(f234(f858(f857(x97411,x97411),a845)),f777(f777(f283(x97411,x97411,x97411),f777(f242(f858(f857(x97411,x97411),a845),f858(f857(x97411,x97411),a845)),x97412)),f777(f252(f858(f857(x97411,x97411),a845),f858(f857(x97411,x97411),a845)),x97412))),f777(f242(f858(f857(x97411,x97411),a845),f858(f857(x97411,x97411),a845)),x97412))) % 174.01/173.90 [9841]~E(f294(a851,f281(a851),f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x98412,x98411),f182(f858(a851,a845)))+~P1(f777(f777(f281(a851),x98412),x98411))+P1(f777(f777(f281(a851),x98411),x98412)) % 174.01/173.90 [9842]~E(f291(a851,f281(a851),f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x98422,x98421),f182(f858(a851,a845)))+~P1(f777(f777(f281(a851),x98422),x98421))+P1(f777(f777(f281(a851),x98421),x98422)) % 174.01/173.90 [7161]~P1(f777(f777(f235(a851),f4(a851)),x71612))+P1(f777(f777(f235(a851),x71611),x71612))+E(f777(a116,f777(f777(f45(a851),f777(f777(f5(a851),x71611),x71612)),x71612)),f777(f777(f45(a851),x71611),x71612)) % 174.01/173.90 [7318]~P1(f777(f777(f235(a851),f4(a851)),x73182))+~P1(f777(f777(f234(a851),x73182),x73181))+E(f777(a116,f777(f777(f45(a851),f777(f777(f5(a851),x73181),x73182)),x73182)),f777(f777(f45(a851),x73181),x73182)) % 174.01/173.90 [8291]~P88(x82911)+~P87(x82911)+~P33(x82911,f777(f108(x82911),f777(f777(f5(a3),f777(f777(f84(a3),x82912),x82912)),a101))) % 174.01/173.90 [8992]E(x89921,f4(a851))+E(f777(f777(f253(a851,a851,f857(a851,a851)),f777(f777(f12(a851,f858(a851,f857(a851,a851)),a851),f243(a851,a851)),a116)),f89(f857(a851,a851),f57(f777(f777(f5(a851),x89922),x89921),x89921))),f89(f857(a851,a851),f57(x89922,x89921)))+P1(f777(f777(f235(a851),x89922),x89921)) % 174.01/173.90 [9389]P1(f777(x93892,f700(x93892,x93891)))+P1(f777(x93891,f700(x93892,x93891)))+E(f777(f258(a3),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f234(a3),f4(a3)))),x93891)),f777(f258(a3),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f234(a3),f4(a3)))),x93892))) % 174.01/173.90 [9393]~P1(f777(x93932,f700(x93932,x93931)))+~P1(f777(x93931,f700(x93932,x93931)))+E(f777(f258(a3),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f234(a3),f4(a3)))),x93931)),f777(f258(a3),f777(f777(f22(a3,a845,a845),f777(f777(f12(a845,f858(a845,a845),a3),a333),f777(f234(a3),f4(a3)))),x93932))) % 174.01/173.90 [9924]~P1(f777(f777(f281(a851),x99242),x99241))+P1(f777(f777(f281(a851),x99241),x99242))+P1(f777(f777(f336(a851),x99241),f289(a851,f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x99242))) % 174.01/173.90 [9925]~P1(f777(f777(f281(a851),x99252),x99251))+P1(f777(f777(f281(a851),x99251),x99252))+P1(f777(f777(f336(a851),x99252),f292(a851,f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x99251))) % 174.01/173.90 [7541]~P88(x75411)+~P61(x75411)+E(f777(f777(f285(x75411),x75412),f777(f108(x75411),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))),x75412) % 174.01/173.90 [9114]~P88(x91141)+~E(f777(f108(x91141),x91142),f82(x91141))+P33(x91141,f777(f108(x91141),f777(f777(f84(a3),x91142),f777(f83(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))) % 174.01/173.90 [9269]~P120(x92691)+~E(x92692,f4(x92691))+E(f777(f777(f244(x92691),x92692),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f4(x92691)) % 174.01/173.90 [9270]~P120(x92701)+~E(x92702,f82(x92701))+E(f777(f777(f244(x92701),x92702),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f82(x92701)) % 174.01/173.90 [9283]~P120(x92831)+~E(x92832,f777(f83(x92831),f82(x92831)))+E(f777(f777(f244(x92831),x92832),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f82(x92831)) % 174.01/173.90 [9331]~P88(x93311)+E(f777(f108(x93311),x93312),f82(x93311))+~P33(x93311,f777(f108(x93311),f777(f777(f84(a3),x93312),f777(f83(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))) % 174.01/173.90 [9682]~P110(x96822)+E(x96821,f4(x96822))+P1(f777(f777(f235(x96822),f4(x96822)),f777(f777(f244(x96822),x96821),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))) % 174.01/173.90 [9740]~P110(x97402)+~E(x97401,f4(x97402))+~P1(f777(f777(f235(x97402),f4(x97402)),f777(f777(f244(x97402),x97401),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))) % 174.01/173.90 [9779]P1(f777(f777(f234(a3),x97791),f4(a3)))+P1(f777(f777(f235(a3),x97792),x97791))+E(f777(f52(x97791),f56(x97792,f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x97791))),f56(x97792,x97791)) % 174.01/173.90 [9780]~P1(f777(f777(f235(a3),f4(a3)),x97801))+P1(f777(f777(f235(a3),x97802),x97801))+E(f777(f52(x97801),f56(x97802,f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x97801))),f56(x97802,x97801)) % 174.01/173.90 [9781]P1(f777(f777(f234(a3),x97811),f4(a3)))+P1(f777(f777(f234(a3),f4(a3)),f777(f777(f84(a3),x97812),x97811)))+E(f777(f52(x97811),f59(x97812,f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x97811))),f59(x97812,x97811)) % 174.01/173.90 [9782]~P1(f777(f777(f235(a3),f4(a3)),x97821))+P1(f777(f777(f234(a3),f4(a3)),f777(f777(f84(a3),x97822),x97821)))+E(f777(f52(x97821),f59(x97822,f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x97821))),f59(x97822,x97821)) % 174.01/173.90 [9783]~P2(x97831)+~P1(f777(f777(f234(a3),f4(a3)),x97832))+E(f777(f104(x97831),f777(a109,f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x97832))),f777(f777(f84(x97831),f777(f104(x97831),f777(a109,x97832))),f777(f104(x97831),f777(a109,x97832)))) % 174.01/173.90 [4934]~P140(x49341,x49343,x49342)+~E(x49343,f4(a3))+P1(f777(x49341,x49342)) % 174.01/173.90 [5062]~P100(x50621)+~P18(x50621,x50623)+P18(x50621,f153(x50621,x50622,x50623)) % 174.01/173.90 [5063]~P100(x50631)+~P18(x50631,x50633)+P18(x50631,f164(x50631,x50632,x50633)) % 174.01/173.90 [4647]~P69(x46472)+~E(x46473,f777(f83(x46472),x46471))+E(x46471,f777(f83(x46472),x46473)) % 174.01/173.90 [4649]~P69(x46491)+~E(f777(f83(x46491),x46493),x46492)+E(f777(f83(x46491),x46492),x46493) % 174.01/173.90 [4720]~P86(x47203)+E(x47201,x47202)+~E(f777(f104(x47203),x47201),f777(f104(x47203),x47202)) % 174.01/173.90 [4721]~P87(x47213)+E(x47211,x47212)+~E(f777(f107(x47213),x47211),f777(f107(x47213),x47212)) % 174.01/173.90 [4722]~P69(x47223)+E(x47221,x47222)+~E(f777(f83(x47223),x47221),f777(f83(x47223),x47222)) % 174.01/173.90 [4723]~P90(x47233)+E(x47231,x47232)+~E(f777(f83(x47233),x47231),f777(f83(x47233),x47232)) % 174.01/173.90 [4724]~P100(x47243)+E(x47241,x47242)+~E(f777(f259(x47243),x47241),f777(f259(x47243),x47242)) % 174.01/173.90 [4725]~P100(x47253)+E(x47251,x47252)+~E(f777(f298(x47253),x47251),f777(f298(x47253),x47252)) % 174.01/173.90 [4726]~P100(x47263)+E(x47261,x47262)+~E(f777(f295(x47263),x47261),f777(f295(x47263),x47262)) % 174.01/173.90 [4727]~P100(x47273)+E(x47271,x47272)+~E(f777(f260(x47273),x47271),f777(f260(x47273),x47272)) % 174.01/173.90 [4957]~P141(x49571,x49572,x49573)+~E(x49572,f4(a3))+P1(f777(x49571,f4(a3))) % 174.01/173.90 [4997]~E(x49971,f4(a851))+E(f376(x49971,x49972,x49973),f182(f858(x49973,a845)))+~E(f777(f44(x49973),x49972),f777(a116,x49971)) % 174.01/173.90 [5146]~E(x51462,f4(a851))+E(f777(f242(a851,a851),x51461),f4(a851))+~P1(f777(f57(x51463,x51462),x51461)) % 174.01/173.90 [5192]P1(f777(x51921,x51922))+~E(x51923,f777(f104(a3),x51922))+~P1(f777(x51921,f777(a109,x51923))) % 174.01/173.90 [5649]~E(x56493,f4(a851))+~P1(f777(x56491,x56492))+P1(f777(x56491,f54(a851,x56492,x56493))) % 174.01/173.90 [5796]~P1(f777(a28,x57963))+~P1(f777(a28,x57962))+P1(f777(a28,f35(x57961,x57962,x57963))) % 174.01/173.90 [6070]~E(x60703,f4(a851))+P1(f777(x60701,x60702))+~P1(f777(x60701,f54(a851,x60702,x60703))) % 174.01/173.90 [6780]E(x67801,f4(a851))+~P1(f777(x67802,f805(x67801,x67803,x67802)))+P1(f777(x67802,f54(a851,x67803,x67801))) % 174.01/173.90 [6893]~P9(x68931)+~P1(f777(f777(f234(x68931),x68932),f674(x68933,x68932,x68931)))+P1(f777(f777(f234(x68931),x68932),f47(x68931,x68933))) % 174.01/173.90 [6895]~P1(f777(x68951,x68952))+~P1(f777(x68951,f805(x68953,x68952,x68951)))+P1(f777(x68951,f54(a851,x68952,x68953))) % 174.01/173.90 [6995]E(x69951,f117(x69952))+E(f777(f777(f142(x69952),f750(x69953,x69951,x69952)),f757(x69953,x69951,x69952)),x69951)+~P1(f777(f777(f336(f852(x69952)),x69951),f151(x69952,x69953))) % 174.01/173.90 [7029]~P133(x70291)+~P1(f777(f777(f336(x70291),x70292),f114(x70291)))+P1(f777(f777(f336(x70291),f777(f777(f244(x70291),x70292),x70293)),f114(x70291))) % 174.01/173.90 [7370]P36(x73701,x73702)+~P1(f777(f777(f336(x73701),x73703),f684(x73702,x73701)))+P1(f777(f777(f336(x73701),f699(x73702,x73701,x73703)),f684(x73702,x73701))) % 174.01/173.90 [7646]E(x76461,f117(x76462))+~P1(f777(f777(f336(f852(x76462)),x76461),f151(x76462,x76463)))+P1(f777(f777(f336(f852(x76462)),f757(x76463,x76461,x76462)),f151(x76462,x76463))) % 174.01/173.90 [7696]E(x76961,f4(a851))+E(f777(f777(f84(a851),f777(f777(f85(a851),x76961),f807(x76961,x76962,x76963))),f805(x76961,x76962,x76963)),x76962)+P1(f777(x76963,f54(a851,x76962,x76961))) % 174.01/173.90 [7739]~P1(f777(x77393,x77392))+E(f777(f777(f84(a851),f777(f777(f85(a851),x77391),f807(x77391,x77392,x77393))),f805(x77391,x77392,x77393)),x77392)+P1(f777(x77393,f54(a851,x77392,x77391))) % 174.01/173.90 [7883]P1(f777(f777(f235(a3),x78831),f795(x78832,x78833,x78831)))+P1(f777(f777(x78833,f777(f777(f45(a3),x78832),x78831)),f54(a3,x78832,x78831)))+~P1(f777(f777(f235(a3),x78831),f4(a3))) % 174.01/173.90 [8149]P1(f777(f777(x81492,f777(f777(f45(a3),x81491),x81493)),f54(a3,x81491,x81493)))+~P1(f777(f777(f235(a3),x81493),f4(a3)))+P1(f777(f777(f234(a3),f795(x81491,x81492,x81493)),f4(a3))) % 174.01/173.90 [8328]E(f777(f777(f84(a3),f777(f777(f85(a3),x83281),f798(x83282,x83283,x83281))),f795(x83282,x83283,x83281)),x83282)+P1(f777(f777(x83283,f777(f777(f45(a3),x83282),x83281)),f54(a3,x83282,x83281)))+~P1(f777(f777(f235(a3),x83281),f4(a3))) % 174.01/173.90 [8563]~P1(f777(f777(x85631,f798(x85632,x85631,x85633)),f795(x85632,x85631,x85633)))+P1(f777(f777(x85631,f777(f777(f45(a3),x85632),x85633)),f54(a3,x85632,x85633)))+~P1(f777(f777(f235(a3),x85633),f4(a3))) % 174.01/173.90 [8774]~P100(x87741)+~P18(x87741,x87743)+P18(x87741,f141(x87741,x87741,f9(x87741),x87742,x87743)) % 174.01/173.90 [9219]~P119(x92192)+E(x92191,f4(x92192))+~P1(f777(f777(f234(x92192),f777(f777(f84(x92192),f777(f777(f85(x92192),x92193),x92193)),f777(f777(f85(x92192),x92191),x92191))),f4(x92192))) % 174.01/173.90 [9220]~P119(x92202)+E(x92201,f4(x92202))+~P1(f777(f777(f234(x92202),f777(f777(f84(x92202),f777(f777(f85(x92202),x92201),x92201)),f777(f777(f85(x92202),x92203),x92203))),f4(x92202))) % 174.01/173.90 [9978]~P110(x99781)+~P1(f777(f777(f235(x99781),x99782),f4(x99781)))+P1(f777(f777(f235(x99781),f777(f777(f244(x99781),x99782),f777(a116,f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x99783)))),f4(x99781))) % 174.01/173.90 [9988]~P110(x99882)+E(x99881,f4(x99882))+~P1(f777(f777(f234(x99882),f777(f777(f84(x99882),f777(f777(f244(x99882),x99883),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x99882),x99881),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))),f4(x99882))) % 174.01/173.90 [9989]~P110(x99892)+E(x99891,f4(x99892))+~P1(f777(f777(f234(x99892),f777(f777(f84(x99892),f777(f777(f244(x99892),x99891),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x99892),x99893),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))),f4(x99892))) % 174.01/173.90 [4678]~E(x46782,x46783)+~P69(x46781)+E(f777(f777(f5(x46781),x46782),x46783),f4(x46781)) % 174.01/173.90 [4679]~E(x46792,x46793)+~P6(x46791)+E(f777(f777(f5(x46791),x46792),x46793),f4(x46791)) % 174.01/173.90 [4692]~P137(x46921)+~E(x46923,f4(x46921))+E(f777(f777(f84(x46921),x46922),x46923),x46922) % 174.01/173.90 [4707]~P134(x47071)+~E(x47073,f4(x47071))+E(f777(f777(f85(x47071),x47072),x47073),f4(x47071)) % 174.01/173.90 [4708]~P134(x47081)+~E(x47082,f4(x47081))+E(f777(f777(f85(x47081),x47082),x47083),f4(x47081)) % 174.01/173.90 [4729]~E(x47293,f117(x47291))+~E(x47292,f117(x47291))+E(f777(f777(f127(x47291),x47292),x47293),f117(x47291)) % 174.01/173.90 [4812]~P137(x48122)+E(x48121,f4(x48122))+~E(f777(f777(f84(x48122),x48123),x48121),x48123) % 174.01/173.90 [4813]~P69(x48131)+~E(x48132,f777(f83(x48131),x48133))+E(f777(f777(f84(x48131),x48132),x48133),f4(x48131)) % 174.01/173.90 [4820]E(x48201,f117(x48202))+E(x48203,f4(a851))+~E(f777(f777(f161(x48202),x48203),x48201),f117(x48202)) % 174.01/173.90 [4828]~P69(x48283)+E(x48281,x48282)+~E(f777(f777(f5(x48283),x48281),x48282),f4(x48283)) % 174.01/173.90 [4829]~P6(x48293)+E(x48291,x48292)+~E(f777(f777(f5(x48293),x48291),x48292),f4(x48293)) % 174.01/173.90 [4838]~P120(x48382)+E(x48381,f4(x48382))+~E(f777(f777(f244(x48382),x48381),x48383),f4(x48382)) % 174.01/173.90 [4839]~P94(x48392)+E(x48391,f241(x48392))+~E(f777(f777(f106(x48392),x48393),x48391),f241(x48392)) % 174.01/173.90 [4840]~P94(x48402)+E(x48401,f241(x48402))+~E(f777(f777(f106(x48402),x48401),x48403),f241(x48402)) % 174.01/173.90 [4841]~P95(x48412)+E(x48411,f182(x48412))+~E(f777(f777(f105(x48412),x48413),x48411),f182(x48412)) % 174.01/173.90 [4842]~P95(x48422)+E(x48421,f182(x48422))+~E(f777(f777(f105(x48422),x48421),x48423),f182(x48422)) % 174.01/173.90 [4907]~P69(x49072)+E(x49071,f777(f83(x49072),x49073))+~E(f777(f777(f84(x49072),x49071),x49073),f4(x49072)) % 174.01/173.90 [4908]~P69(x49081)+E(f777(f83(x49081),x49082),x49083)+~E(f777(f777(f84(x49081),x49082),x49083),f4(x49081)) % 174.01/173.90 [4911]~E(x49112,x49113)+~P99(x49111)+P1(f777(f777(f234(x49111),x49112),x49113)) % 174.01/173.90 [4912]~E(x49122,x49123)+~P103(x49121)+P1(f777(f777(f234(x49121),x49122),x49123)) % 174.01/173.90 [5011]~P111(x50111)+~E(x50112,f777(f83(x50111),x50113))+E(f777(f777(f85(x50111),x50112),x50112),f777(f777(f85(x50111),x50113),x50113)) % 174.01/173.90 [5019]~P100(x50191)+~P18(x50191,x50193)+P18(x50191,f777(f777(f161(x50191),x50192),x50193)) % 174.01/173.90 [5020]~P100(x50201)+~P18(x50201,x50203)+P18(x50201,f777(f777(f130(x50201),x50202),x50203)) % 174.01/173.90 [5060]E(x50601,x50602)+E(x50603,f4(a851))+~E(f777(f777(f85(a851),x50603),x50601),f777(f777(f85(a851),x50603),x50602)) % 174.01/173.90 [5061]E(x50611,x50612)+E(x50613,f4(a851))+~E(f777(f777(f85(a851),x50611),x50613),f777(f777(f85(a851),x50612),x50613)) % 174.01/173.90 [5138]~E(x51382,x51383)+~P99(x51381)+E(f297(x51381,x51382,x51383),f777(f777(f304(x51381),x51382),f182(f858(x51381,a845)))) % 174.01/173.90 [5180]~P110(x51801)+~E(f777(f79(x51801),x51802),f777(f79(x51801),x51803))+P1(f777(f777(f281(x51801),x51802),x51803)) % 174.01/173.90 [5189]~E(x51891,x51892)+~P99(x51893)+~P1(f777(f777(f235(x51893),x51891),x51892)) % 174.01/173.90 [5190]~E(x51901,x51902)+~P100(x51903)+~P1(f777(f777(f235(x51903),x51901),x51902)) % 174.01/173.90 [5197]~P99(x51971)+E(f777(f296(x51971,x51972),x51973),f182(f858(x51971,a845)))+P1(f777(f777(f235(x51971),x51972),x51973)) % 174.01/173.90 [5244]~P99(x52441)+E(f297(x52441,x52442,x52443),f182(f858(x52441,a845)))+P1(f777(f777(f234(x52441),x52442),x52443)) % 174.01/173.90 [5245]~P99(x52451)+E(f299(x52451,x52452,x52453),f182(f858(x52451,a845)))+P1(f777(f777(f235(x52451),x52452),x52453)) % 174.01/173.90 [5246]~P99(x52461)+E(f182(f858(x52461,a845)),f297(x52461,x52462,x52463))+P1(f777(f777(f234(x52461),x52462),x52463)) % 174.01/173.90 [5247]~P99(x52471)+E(f182(f858(x52471,a845)),f299(x52471,x52472,x52473))+P1(f777(f777(f235(x52471),x52472),x52473)) % 174.01/173.90 [5255]~P100(x52551)+~E(f777(f777(f238(x52551),x52552),x52553),x52552)+P1(f777(f777(f234(x52551),x52552),x52553)) % 174.01/173.90 [5256]~P100(x52561)+~E(f777(f777(f181(x52561),x52562),x52563),x52563)+P1(f777(f777(f234(x52561),x52562),x52563)) % 174.01/173.90 [5257]~P92(x52571)+~E(f777(f777(f105(x52571),x52572),x52573),x52573)+P1(f777(f777(f234(x52571),x52572),x52573)) % 174.01/173.90 [5258]~P98(x52581)+~E(f777(f777(f106(x52581),x52582),x52583),x52582)+P1(f777(f777(f234(x52581),x52582),x52583)) % 174.01/173.90 [5275]~P100(x52751)+P18(x52751,x52752)+~P18(x52751,f777(f777(f142(x52751),x52753),x52752)) % 174.01/173.90 [5276]~P100(x52761)+P18(x52761,x52762)+~P18(x52761,f777(f777(f127(x52761),x52763),x52762)) % 174.01/173.90 [5277]~P100(x52771)+P18(x52771,x52772)+~P18(x52771,f777(f777(f127(x52771),x52772),x52773)) % 174.01/173.90 [5282]~P7(x52821)+~E(f54(x52821,x52823,x52822),f4(x52821))+P1(f777(f777(f281(x52821),x52822),x52823)) % 174.01/173.90 [5346]~P100(x53461)+P1(f777(f777(f234(x53461),x53463),x53462))+P1(f777(f777(f235(x53461),x53462),x53463)) % 174.01/173.90 [5348]~P100(x53481)+P1(f777(f777(f234(x53481),x53483),x53482))+P1(f777(f777(f234(x53481),x53482),x53483)) % 174.01/173.90 [5387]~P100(x53871)+E(f777(f777(f238(x53871),x53872),x53873),x53873)+~P1(f777(f777(f234(x53871),x53873),x53872)) % 174.01/173.90 [5389]~P100(x53891)+E(f777(f777(f238(x53891),x53892),x53893),x53892)+~P1(f777(f777(f234(x53891),x53892),x53893)) % 174.01/173.90 [5390]~P100(x53901)+E(f777(f777(f181(x53901),x53902),x53903),x53902)+~P1(f777(f777(f234(x53901),x53903),x53902)) % 174.01/173.90 [5392]~P100(x53921)+E(f777(f777(f181(x53921),x53922),x53923),x53923)+~P1(f777(f777(f234(x53921),x53922),x53923)) % 174.01/173.90 [5393]~P92(x53931)+E(f777(f777(f105(x53931),x53932),x53933),x53932)+~P1(f777(f777(f234(x53931),x53933),x53932)) % 174.01/173.90 [5395]~P92(x53951)+E(f777(f777(f105(x53951),x53952),x53953),x53953)+~P1(f777(f777(f234(x53951),x53952),x53953)) % 174.01/173.90 [5396]~P98(x53961)+E(f777(f777(f106(x53961),x53962),x53963),x53963)+~P1(f777(f777(f234(x53961),x53963),x53962)) % 174.01/173.90 [5398]~P98(x53981)+E(f777(f777(f106(x53981),x53982),x53983),x53982)+~P1(f777(f777(f234(x53981),x53982),x53983)) % 174.01/173.90 [5405]~P113(x54052)+E(x54051,f4(x54052))+E(f777(f777(f285(x54052),f777(f83(x54052),x54053)),f777(f83(x54052),x54051)),f777(f777(f285(x54052),x54053),x54051)) % 174.01/173.90 [5412]~P7(x54121)+E(f54(x54121,x54122,x54123),f4(x54121))+~P1(f777(f777(f281(x54121),x54123),x54122)) % 174.01/173.90 [5452]~P99(x54521)+E(f777(f296(x54521,x54522),x54523),f182(f858(x54521,a845)))+~P1(f777(f777(f234(x54521),x54523),x54522)) % 174.01/173.90 [5481]~P99(x54811)+E(f297(x54811,x54812,x54813),f182(f858(x54811,a845)))+~P1(f777(f777(f235(x54811),x54813),x54812)) % 174.01/173.90 [5482]~P99(x54821)+E(f299(x54821,x54822,x54823),f182(f858(x54821,a845)))+~P1(f777(f777(f234(x54821),x54823),x54822)) % 174.01/173.90 [5483]~P99(x54831)+E(f300(x54831,x54832,x54833),f182(f858(x54831,a845)))+~P1(f777(f777(f234(x54831),x54833),x54832)) % 174.01/173.90 [5532]~E(f777(f777(f5(a851),x55321),x55323),x55322)+E(x55321,f777(f777(f84(a851),x55322),x55323))+~P1(f777(f777(f234(a851),x55323),x55321)) % 174.01/173.90 [5533]~E(x55331,f777(f777(f84(a851),x55333),x55332))+E(f777(f777(f5(a851),x55331),x55332),x55333)+~P1(f777(f777(f234(a851),x55332),x55331)) % 174.01/173.90 [5576]~P1(f777(x55761,x55763))+P1(f777(x55761,f800(x55761,x55762)))+~P1(f777(f777(f234(a851),x55763),x55762)) % 174.01/173.90 [5577]~P1(f777(x55771,x55773))+P1(f777(x55771,f341(x55771,x55772)))+~P1(f777(f777(f235(a851),x55773),x55772)) % 174.01/173.90 [5585]~P99(x55851)+~E(f777(f296(x55851,x55852),x55853),f182(f858(x55851,a845)))+~P1(f777(f777(f235(x55851),x55852),x55853)) % 174.01/173.90 [5589]~P99(x55891)+~P1(f777(f777(f235(x55891),x55892),x55893))+P1(f777(f777(f234(x55891),x55892),x55893)) % 174.01/173.90 [5591]~P103(x55911)+~P1(f777(f777(f235(x55911),x55912),x55913))+P1(f777(f777(f234(x55911),x55912),x55913)) % 174.01/173.90 [5704]~P99(x57041)+~E(f297(x57041,x57042,x57043),f182(f858(x57041,a845)))+~P1(f777(f777(f234(x57041),x57042),x57043)) % 174.01/173.90 [5705]~P99(x57051)+~E(f299(x57051,x57052,x57053),f182(f858(x57051,a845)))+~P1(f777(f777(f235(x57051),x57052),x57053)) % 174.01/173.90 [5706]~P99(x57061)+~E(f182(f858(x57061,a845)),f297(x57061,x57062,x57063))+~P1(f777(f777(f234(x57061),x57062),x57063)) % 174.01/173.90 [5707]~P99(x57071)+~E(f182(f858(x57071,a845)),f299(x57071,x57072,x57073))+~P1(f777(f777(f235(x57071),x57072),x57073)) % 174.01/173.90 [5720]P1(f777(x57201,x57202))+~P1(f777(x57201,f801(x57201,x57203)))+~P1(f777(f777(f234(a851),x57202),x57203)) % 174.01/173.90 [5721]P1(f777(x57211,x57212))+~P1(f777(x57211,f344(x57211,x57213)))+~P1(f777(f777(f235(a851),x57212),x57213)) % 174.01/173.90 [5729]~E(x57291,f777(a116,x57293))+P1(f777(f777(f235(a851),x57291),f777(a116,x57292)))+~P1(f777(f777(f235(a851),x57293),x57292)) % 174.01/173.90 [5745]E(x57451,x57452)+~E(f777(f777(f85(a851),x57453),x57451),f777(f777(f85(a851),x57453),x57452))+~P1(f777(f777(f235(a851),f4(a851)),x57453)) % 174.01/173.90 [5806]E(f777(x58061,f406(x58061,x58062,x58063)),f82(a851))+~E(f777(f777(f10(x58063,a851),x58061),x58062),f82(a851))+~P1(f777(f65(x58063),x58062)) % 174.01/173.90 [5816]~P9(x58161)+P1(f777(f777(f234(x58161),x58162),f46(x58161,x58163)))+~P1(f777(f777(f336(x58161),x58162),x58163)) % 174.01/173.90 [5840]~P99(x58401)+~P1(f777(f777(f235(x58401),x58403),x58402))+~P1(f777(f777(f235(x58401),x58402),x58403)) % 174.01/173.90 [5844]~P103(x58441)+~P1(f777(f777(f235(x58441),x58443),x58442))+~P1(f777(f777(f235(x58441),x58442),x58443)) % 174.01/173.90 [5845]~P103(x58451)+~P1(f777(f777(f234(x58451),x58453),x58452))+~P1(f777(f777(f235(x58451),x58452),x58453)) % 174.01/173.90 [5846]~P100(x58461)+~P1(f777(f777(f235(x58461),x58463),x58462))+~P1(f777(f777(f235(x58461),x58462),x58463)) % 174.01/173.90 [5849]~P100(x58491)+~P1(f777(f777(f234(x58491),x58493),x58492))+~P1(f777(f777(f235(x58491),x58492),x58493)) % 174.01/173.90 [5868]~E(x58682,x58683)+~E(x58681,x58682)+E(f284(a851,f281(a851),x58681,x58682),f777(f777(f304(a851),x58683),f182(f858(a851,a845)))) % 174.01/173.90 [5876]~E(f777(x58762,f407(x58762,x58763,x58761)),f4(a851))+E(f777(f777(f10(x58761,a851),x58762),x58763),f4(a851))+~P1(f777(f65(x58761),x58763)) % 174.01/173.90 [5877]~E(f777(x58772,f452(x58772,x58773,x58771)),f82(a851))+E(f777(f777(f13(x58771,a851),x58772),x58773),f82(a851))+~P1(f777(f65(x58771),x58773)) % 174.01/173.90 [5891]~P102(x58911)+~P1(f777(f777(f235(x58911),x58913),x58912))+P1(f777(f777(f336(x58911),x58912),f777(f298(x58911),x58913))) % 174.01/173.90 [5892]~P102(x58921)+~P1(f777(f777(f234(x58921),x58923),x58922))+P1(f777(f777(f336(x58921),x58922),f777(f260(x58921),x58923))) % 174.01/173.90 [5893]~P102(x58931)+~P1(f777(f777(f235(x58931),x58932),x58933))+P1(f777(f777(f336(x58931),x58932),f777(f259(x58931),x58933))) % 174.01/173.90 [5894]~P102(x58941)+~P1(f777(f777(f234(x58941),x58942),x58943))+P1(f777(f777(f336(x58941),x58942),f777(f295(x58941),x58943))) % 174.01/173.90 [5895]~P104(x58951)+~P1(f777(f777(f281(x58951),x58952),x58953))+P1(f777(f777(f281(x58951),x58952),f777(f83(x58951),x58953))) % 174.01/173.90 [5896]~P110(x58961)+~P1(f777(f777(f281(x58961),x58962),x58963))+P1(f777(f777(f281(x58961),x58962),f777(f79(x58961),x58963))) % 174.01/173.90 [5907]E(f777(x59071,f408(x59071,x59072,x59073)),f777(a116,f4(a851)))+~E(f777(f777(f10(x59073,a851),x59071),x59072),f777(a116,f4(a851)))+~P1(f777(f65(x59073),x59072)) % 174.01/173.90 [5991]~P9(x59911)+~P1(f777(f777(f336(x59911),x59913),x59912))+P1(f777(f777(f234(x59911),f47(x59911,x59912)),x59913)) % 174.01/173.90 [6009]~P1(f777(f777(f234(a851),x60091),x60093))+P1(f777(f777(f234(a851),x60091),x60092))+~P1(f777(f777(f234(a851),x60093),x60092)) % 174.01/173.90 [6010]~P1(f777(f777(f234(a3),x60101),x60103))+P1(f777(f777(f234(a3),x60101),x60102))+~P1(f777(f777(f234(a3),x60103),x60102)) % 174.01/173.90 [6011]~P1(f777(f777(f281(a851),x60111),x60113))+P1(f777(f777(f281(a851),x60111),x60112))+~P1(f777(f777(f281(a851),x60113),x60112)) % 174.01/173.90 [6029]~P102(x60291)+~P1(f777(f777(f336(x60291),x60293),f777(f298(x60291),x60292)))+P1(f777(f777(f235(x60291),x60292),x60293)) % 174.01/173.90 [6030]~P102(x60301)+~P1(f777(f777(f336(x60301),x60302),f777(f259(x60301),x60303)))+P1(f777(f777(f235(x60301),x60302),x60303)) % 174.01/173.90 [6031]~P102(x60311)+~P1(f777(f777(f336(x60311),x60313),f777(f260(x60311),x60312)))+P1(f777(f777(f234(x60311),x60312),x60313)) % 174.01/173.90 [6032]~P102(x60321)+~P1(f777(f777(f336(x60321),x60322),f777(f295(x60321),x60323)))+P1(f777(f777(f234(x60321),x60322),x60323)) % 174.01/173.90 [6033]~P110(x60331)+~P1(f777(f777(f281(x60331),x60332),f777(f79(x60331),x60333)))+P1(f777(f777(f281(x60331),x60332),x60333)) % 174.01/173.90 [6034]~P104(x60341)+~P1(f777(f777(f281(x60341),x60342),f777(f83(x60341),x60343)))+P1(f777(f777(f281(x60341),x60342),x60343)) % 174.01/173.90 [6258]~P62(x62581)+P1(f777(f777(f235(x62581),f4(x62581)),f803(x62583,x62582,x62581)))+P1(f777(f777(f234(x62581),x62582),x62583)) % 174.01/173.90 [6259]~P63(x62591)+P1(f777(f777(f235(x62591),f4(x62591)),f810(x62593,x62592,x62591)))+P1(f777(f777(f234(x62591),x62592),x62593)) % 174.01/173.90 [6330]~P77(x63301)+~P1(f777(f777(f235(x63301),x63303),f777(f83(x63301),x63302)))+P1(f777(f777(f235(x63301),x63302),f777(f83(x63301),x63303))) % 174.01/173.90 [6332]~P77(x63321)+~P1(f777(f777(f234(x63321),x63323),f777(f83(x63321),x63322)))+P1(f777(f777(f234(x63321),x63322),f777(f83(x63321),x63323))) % 174.01/173.90 [6343]~P1(f777(f777(f235(a851),x63431),x63433))+~P1(f777(f777(f235(a851),x63433),x63432))+P1(f777(f777(f235(a851),f777(a116,x63431)),x63432)) % 174.01/173.90 [6376]~P110(x63761)+P1(f777(f777(f235(x63761),f777(f107(x63761),x63762)),f777(f107(x63761),x63763)))+~P1(f777(f777(f235(a3),x63762),x63763)) % 174.01/173.90 [6377]~P117(x63771)+P1(f777(f777(f235(x63771),f777(f104(x63771),x63772)),f777(f104(x63771),x63773)))+~P1(f777(f777(f235(a851),x63772),x63773)) % 174.01/173.90 [6378]~P117(x63781)+P1(f777(f777(f234(x63781),f777(f104(x63781),x63782)),f777(f104(x63781),x63783)))+~P1(f777(f777(f234(a851),x63782),x63783)) % 174.01/173.90 [6379]~P110(x63791)+P1(f777(f777(f234(x63791),f777(f107(x63791),x63792)),f777(f107(x63791),x63793)))+~P1(f777(f777(f234(a3),x63792),x63793)) % 174.01/173.90 [6385]~P100(x63851)+E(f777(f777(f105(f858(x63851,a845)),f777(f259(x63851),x63852)),f777(f296(x63851,x63852),x63853)),f777(f259(x63851),x63853))+~P1(f777(f777(f234(x63851),x63852),x63853)) % 174.01/173.90 [6416]~P77(x64161)+~P1(f777(f777(f235(x64161),x64163),x64162))+P1(f777(f777(f235(x64161),f777(f83(x64161),x64162)),f777(f83(x64161),x64163))) % 174.01/173.90 [6418]~P77(x64181)+~P1(f777(f777(f234(x64181),x64183),x64182))+P1(f777(f777(f234(x64181),f777(f83(x64181),x64182)),f777(f83(x64181),x64183))) % 174.01/173.90 [6420]~P90(x64201)+~P1(f777(f777(f234(x64201),x64203),x64202))+P1(f777(f777(f234(x64201),f777(f83(x64201),x64202)),f777(f83(x64201),x64203))) % 174.01/173.90 [6455]~P100(x64551)+E(f777(f777(f105(f858(x64551,a845)),f777(f259(x64551),x64552)),f297(x64551,x64552,x64553)),f777(f295(x64551),x64553))+~P1(f777(f777(f234(x64551),x64552),x64553)) % 174.01/173.90 [6456]~P100(x64561)+E(f777(f777(f105(f858(x64561,a845)),f777(f295(x64561),x64562)),f299(x64561,x64562,x64563)),f777(f295(x64561),x64563))+~P1(f777(f777(f234(x64561),x64562),x64563)) % 174.01/173.90 [6457]~P100(x64571)+E(f777(f777(f105(f858(x64571,a845)),f777(f295(x64571),x64572)),f300(x64571,x64572,x64573)),f777(f259(x64571),x64573))+~P1(f777(f777(f235(x64571),x64572),x64573)) % 174.01/173.90 [6495]~P100(x64951)+E(f777(f777(f105(f858(x64951,a845)),f777(f296(x64951,x64952),x64953)),f777(f260(x64951),x64953)),f777(f260(x64951),x64952))+~P1(f777(f777(f234(x64951),x64952),x64953)) % 174.01/173.90 [6658]~P100(x66581)+E(f777(f777(f105(f858(x66581,a845)),f297(x66581,x66582,x66583)),f777(f298(x66581),x66583)),f777(f260(x66581),x66582))+~P1(f777(f777(f234(x66581),x66582),x66583)) % 174.01/173.90 [6659]~P100(x66591)+E(f777(f777(f105(f858(x66591,a845)),f299(x66591,x66592,x66593)),f777(f298(x66591),x66593)),f777(f298(x66591),x66592))+~P1(f777(f777(f234(x66591),x66592),x66593)) % 174.01/173.90 [6660]~P100(x66601)+E(f777(f777(f105(f858(x66601,a845)),f300(x66601,x66602,x66603)),f777(f260(x66601),x66603)),f777(f298(x66601),x66602))+~P1(f777(f777(f235(x66601),x66602),x66603)) % 174.01/173.90 [6677]P1(f777(x66771,x66772))+~P1(f777(f777(f234(a851),x66772),x66773))+P1(f777(f777(f336(a851),f801(x66771,x66773)),f297(a851,f4(a851),x66773))) % 174.01/173.90 [6687]P1(f777(f777(f281(a3),x66871),f54(a3,x66872,x66873)))+~P1(f777(f777(f281(a3),x66871),x66872))+~P1(f777(f777(f281(a3),x66871),x66873)) % 174.01/173.90 [6713]E(x67131,x67132)+~E(f777(f777(f155(x67133),x67131),f732(x67133,x67132,x67131)),f777(f777(f155(x67133),x67132),f732(x67133,x67132,x67131)))+~E(f777(f183(f852(x67133)),x67131),f777(f183(f852(x67133)),x67132)) % 174.01/173.90 [6719]~E(x67193,f777(f777(f45(a851),x67191),x67192))+~P1(f777(f777(f235(a851),f4(a851)),x67192))+P1(f777(f777(f235(a851),x67191),f777(f777(f85(a851),x67192),f777(a116,x67193)))) % 174.01/173.90 [6734]~P1(f777(x67341,x67343))+~P1(f777(f777(f234(a851),x67343),x67342))+P1(f777(f777(f336(a851),f800(x67341,x67342)),f297(a851,f4(a851),x67342))) % 174.01/173.90 [6777]~P1(f777(x67771,x67773))+P1(f777(x67771,f342(x67771,x67772)))+~P1(f777(f777(f336(a851),x67773),f297(a851,f4(a851),x67772))) % 174.01/173.90 [6800]~P117(x68003)+~P1(f777(f777(f235(x68003),f777(f104(x68003),x68001)),f777(f104(x68003),x68002)))+P1(f777(f777(f235(a851),x68001),x68002)) % 174.01/173.90 [6801]~P110(x68013)+~P1(f777(f777(f235(x68013),f777(f107(x68013),x68011)),f777(f107(x68013),x68012)))+P1(f777(f777(f235(a3),x68011),x68012)) % 174.01/173.90 [6802]~P117(x68023)+~P1(f777(f777(f234(x68023),f777(f104(x68023),x68021)),f777(f104(x68023),x68022)))+P1(f777(f777(f234(a851),x68021),x68022)) % 174.01/173.90 [6803]~P110(x68033)+~P1(f777(f777(f234(x68033),f777(f107(x68033),x68031)),f777(f107(x68033),x68032)))+P1(f777(f777(f234(a3),x68031),x68032)) % 174.01/173.90 [6819]~P117(x68191)+~P1(f777(f777(f235(x68191),f82(x68191)),x68192))+P1(f777(f777(f235(x68191),f82(x68191)),f777(f777(f244(x68191),x68192),f777(a116,x68193)))) % 174.01/173.90 [6823]~P77(x68231)+~P1(f777(f777(f235(x68231),f777(f83(x68231),x68233)),f777(f83(x68231),x68232)))+P1(f777(f777(f235(x68231),x68232),x68233)) % 174.01/173.90 [6824]~P77(x68241)+~P1(f777(f777(f234(x68241),f777(f83(x68241),x68243)),f777(f83(x68241),x68242)))+P1(f777(f777(f234(x68241),x68242),x68243)) % 174.01/173.90 [6825]~P90(x68251)+~P1(f777(f777(f234(x68251),f777(f83(x68251),x68253)),f777(f83(x68251),x68252)))+P1(f777(f777(f234(x68251),x68252),x68253)) % 174.01/173.90 [6851]P1(f777(x68511,x68512))+~P1(f777(x68511,f840(x68511,x68513)))+~P1(f777(f777(f336(a851),x68512),f297(a851,f4(a851),x68513))) % 174.01/173.90 [6872]~P62(x68721)+P1(f777(f777(f235(x68721),f803(x68723,x68722,x68721)),f82(x68721)))+P1(f777(f777(f234(x68721),x68722),x68723)) % 174.01/173.90 [6891]~E(f54(a851,x68913,x68912),f54(a851,x68911,x68912))+E(f777(f777(f84(a851),x68911),f777(f777(f85(a851),x68912),f812(x68911,x68912,x68913))),x68913)+~P1(f777(f777(f234(a851),x68911),x68913)) % 174.01/173.90 [6909]E(f777(x69091,f608(x69091,x69092,x69093)),f185(x69092))+~P1(f777(f65(x69093),f171(x69093,x69092,x69091)))+P1(f777(f65(x69093),f241(f858(x69093,a845)))) % 174.01/173.90 [6950]E(f777(f777(f10(x69501,a851),x69502),x69503),f4(a851))+~P1(f777(f65(x69501),x69503))+P1(f777(f777(f336(x69501),f407(x69502,x69503,x69501)),x69503)) % 174.01/173.90 [6951]E(f777(f777(f13(x69511,a851),x69512),x69513),f82(a851))+~P1(f777(f65(x69511),x69513))+P1(f777(f777(f336(x69511),f452(x69512,x69513,x69511)),x69513)) % 174.01/173.90 [6973]~P100(x69731)+~P1(f777(f777(f235(x69731),x69732),x69733))+P1(f777(f777(f235(f858(x69731,a845)),f777(f259(x69731),x69732)),f777(f259(x69731),x69733))) % 174.01/173.90 [6974]~P100(x69741)+~P1(f777(f777(f234(x69741),x69742),x69743))+P1(f777(f777(f234(f858(x69741,a845)),f777(f259(x69741),x69742)),f777(f259(x69741),x69743))) % 174.01/173.90 [6975]~P100(x69751)+~P1(f777(f777(f234(x69751),x69753),x69752))+P1(f777(f777(f234(f858(x69751,a845)),f777(f298(x69751),x69752)),f777(f298(x69751),x69753))) % 174.01/173.90 [6976]~P99(x69761)+~P1(f777(f777(f234(x69761),x69762),x69763))+P1(f777(f777(f234(f858(x69761,a845)),f777(f295(x69761),x69762)),f777(f295(x69761),x69763))) % 174.01/173.90 [6977]~P99(x69771)+~P1(f777(f777(f234(x69771),x69773),x69772))+P1(f777(f777(f234(f858(x69771,a845)),f777(f260(x69771),x69772)),f777(f260(x69771),x69773))) % 174.01/173.90 [6982]~P9(x69821)+P1(f777(f777(f234(x69821),x69822),f47(x69821,x69823)))+P1(f777(f777(f336(x69821),f674(x69823,x69822,x69821)),x69823)) % 174.01/173.90 [6987]~P77(x69871)+P1(f777(f777(f235(x69871),f777(f777(f5(x69871),x69872),x69873)),f4(x69871)))+~P1(f777(f777(f235(x69871),x69872),x69873)) % 174.01/173.90 [6988]~P77(x69881)+P1(f777(f777(f234(x69881),f777(f777(f5(x69881),x69882),x69883)),f4(x69881)))+~P1(f777(f777(f234(x69881),x69882),x69883)) % 174.01/173.90 [7026]~P1(f777(f777(f281(a3),x70261),f54(a3,x70262,x70263)))+~P1(f777(f777(f281(a3),x70261),x70263))+P1(f777(f777(f281(a3),x70261),x70262)) % 174.01/173.90 [7033]P1(f777(x70331,x70332))+P1(f777(f777(f234(a851),f840(x70331,x70333)),x70333))+~P1(f777(f777(f336(a851),x70332),f297(a851,f4(a851),x70333))) % 174.01/173.90 [7075]~E(f777(f777(f10(x70751,a851),x70752),x70753),f82(a851))+~P1(f777(f65(x70751),x70753))+P1(f777(f777(f336(x70751),f406(x70752,x70753,x70751)),x70753)) % 174.01/173.90 [7076]~P1(f777(x70761,x70763))+P1(f777(f777(f234(a851),f342(x70761,x70762)),x70762))+~P1(f777(f777(f336(a851),x70763),f297(a851,f4(a851),x70762))) % 174.01/173.90 [7114]~P9(x71141)+P1(f777(f777(f336(x71141),f675(x71143,x71142,x71141)),x71142))+P1(f777(f777(f234(x71141),f46(x71141,x71142)),x71143)) % 174.01/173.90 [7144]~E(f777(f777(f10(x71441,a851),x71442),x71443),f777(a116,f4(a851)))+~P1(f777(f65(x71441),x71443))+P1(f777(f777(f336(x71441),f408(x71442,x71443,x71441)),x71443)) % 174.01/173.90 [7155]E(x71551,f4(a851))+P1(f777(x71552,f54(a851,x71553,x71551)))+P1(f777(f777(f235(a851),f805(x71551,x71553,x71552)),x71551)) % 174.01/173.90 [7279]~P1(f777(x72791,x72792))+P1(f777(x72791,f54(a851,x72792,x72793)))+P1(f777(f777(f235(a851),f805(x72793,x72792,x72791)),x72793)) % 174.01/173.90 [7406]E(x74061,f117(x74062))+~P1(f777(f777(f336(f852(x74062)),x74061),f151(x74062,x74063)))+P1(f777(f777(f336(x74062),f750(x74063,x74061,x74062)),x74063)) % 174.01/173.90 [7426]~P100(x74261)+E(f777(f777(f105(f858(x74261,a845)),f777(f777(f304(x74261),x74262),f182(f858(x74261,a845)))),f300(x74261,x74262,x74263)),f777(f296(x74261,x74262),x74263))+~P1(f777(f777(f235(x74261),x74262),x74263)) % 174.01/173.90 [7451]~P100(x74511)+E(f777(f777(f105(f858(x74511,a845)),f777(f777(f304(x74511),x74512),f182(f858(x74511,a845)))),f299(x74511,x74512,x74513)),f297(x74511,x74512,x74513))+~P1(f777(f777(f234(x74511),x74512),x74513)) % 174.01/173.90 [7563]~P100(x75631)+P1(f777(f777(f235(x75631),x75632),x75633))+~P1(f777(f777(f235(f858(x75631,a845)),f777(f259(x75631),x75632)),f777(f259(x75631),x75633))) % 174.01/173.90 [7564]~P99(x75641)+P1(f777(f777(f234(x75641),x75642),x75643))+~P1(f777(f777(f234(f858(x75641,a845)),f777(f260(x75641),x75643)),f777(f260(x75641),x75642))) % 174.01/173.90 [7565]~P100(x75651)+P1(f777(f777(f234(x75651),x75652),x75653))+~P1(f777(f777(f234(f858(x75651,a845)),f777(f298(x75651),x75653)),f777(f298(x75651),x75652))) % 174.01/173.90 [7566]~P99(x75661)+P1(f777(f777(f234(x75661),x75662),x75663))+~P1(f777(f777(f234(f858(x75661,a845)),f777(f295(x75661),x75662)),f777(f295(x75661),x75663))) % 174.01/173.90 [7567]~P100(x75671)+P1(f777(f777(f234(x75671),x75672),x75673))+~P1(f777(f777(f234(f858(x75671,a845)),f777(f259(x75671),x75672)),f777(f259(x75671),x75673))) % 174.01/173.90 [7591]~P77(x75911)+~P1(f777(f777(f235(x75911),f777(f777(f5(x75911),x75912),x75913)),f4(x75911)))+P1(f777(f777(f235(x75911),x75912),x75913)) % 174.01/173.90 [7592]~P77(x75921)+~P1(f777(f777(f234(x75921),f777(f777(f5(x75921),x75922),x75923)),f4(x75921)))+P1(f777(f777(f234(x75921),x75922),x75923)) % 174.01/173.90 [7752]E(x77521,f4(a851))+~E(f777(f134(a851,a851,f84(a851),x77522),x77523),f4(a851))+~P1(f777(f777(f336(a851),x77521),f777(f160(a851),x77523))) % 174.01/173.90 [7756]~P9(x77561)+~P1(f777(f777(f234(x77561),f675(x77563,x77562,x77561)),x77563))+P1(f777(f777(f234(x77561),f46(x77561,x77562)),x77563)) % 174.01/173.90 [7907]P1(f777(f777(f234(a3),f4(a3)),f796(x79071,x79072,x79073)))+P1(f777(f777(x79072,f777(f777(f45(a3),x79071),x79073)),f54(a3,x79071,x79073)))+~P1(f777(f777(f235(a3),f4(a3)),x79073)) % 174.01/173.90 [8000]E(x80001,x80002)+~E(f777(f183(f852(x80003)),x80001),f777(f183(f852(x80003)),x80002))+~P1(f777(f777(f253(x80003,x80003,a845),a332),f715(x80003,x80001,x80002))) % 174.01/173.90 [8066]~P36(x80662,x80663)+E(x80661,f182(f858(x80662,a845)))+~P1(f777(f777(f234(f858(x80662,a845)),x80661),f777(f279(x80662,x80662,x80663),x80661))) % 174.01/173.90 [8094]~P63(x80941)+~P1(f777(f777(f234(x80941),x80942),f777(f777(f84(x80941),x80943),f810(x80943,x80942,x80941))))+P1(f777(f777(f234(x80941),x80942),x80943)) % 174.01/173.90 [8130]P47(x81301,x81302,x81303)+P1(f777(f777(f336(x81301),f508(x81303,x81302,x81301)),x81302))+P1(f777(f777(f336(f857(x81301,x81301)),f509(x81303,x81302,x81301)),x81303)) % 174.01/173.90 [8153]P1(f777(f777(x81532,f777(f777(f45(a3),x81531),x81533)),f54(a3,x81531,x81533)))+~P1(f777(f777(f235(a3),f4(a3)),x81533))+P1(f777(f777(f235(a3),f796(x81531,x81532,x81533)),x81533)) % 174.01/173.90 [8177]E(f777(f305(a851,a851,f777(f777(f11(a851,a851,a851),f5(a851)),x81771)),f777(f296(a851,x81772),x81773)),f182(f858(a851,a845)))+P1(f777(f777(f235(a851),x81771),x81773))+P1(f777(f777(f235(a851),x81772),x81773)) % 174.01/173.90 [8279]E(f777(f305(a851,a851,f777(f777(f11(a851,a851,a851),f5(a851)),x82791)),f777(f296(a851,x82792),x82793)),f777(f777(f304(a851),f4(a851)),f182(f858(a851,a845))))+P1(f777(f777(f235(a851),x82791),x82793))+~P1(f777(f777(f235(a851),x82792),x82793)) % 174.01/173.90 [8294]~P100(x82941)+E(f141(x82941,x82941,f9(x82941),x82942,x82943),x82943)+~P1(f777(f777(f336(x82941),x82942),f777(f160(x82941),x82943))) % 174.01/173.90 [8309]P29(x83091,x83091,x83092,x83093)+~P1(f777(f65(x83091),x83093))+~P1(f777(f777(f234(f858(x83091,a845)),x83093),f777(f305(x83091,x83091,x83092),x83093))) % 174.01/173.90 [8336]E(f777(f777(f84(a3),f777(f777(f85(a3),x83361),f797(x83362,x83363,x83361))),f796(x83362,x83363,x83361)),x83362)+P1(f777(f777(x83363,f777(f777(f45(a3),x83362),x83361)),f54(a3,x83362,x83361)))+~P1(f777(f777(f235(a3),f4(a3)),x83361)) % 174.01/173.90 [8568]~P1(f777(f777(x85681,f797(x85682,x85681,x85683)),f796(x85682,x85681,x85683)))+P1(f777(f777(x85681,f777(f777(f45(a3),x85682),x85683)),f54(a3,x85682,x85683)))+~P1(f777(f777(f235(a3),f4(a3)),x85683)) % 174.01/173.90 [9358]~P1(f777(f65(x93581),x93582))+~P1(f777(f777(f336(x93581),x93583),x93582))+P1(f777(f777(f235(a851),f777(f44(x93581),f777(f777(f5(f858(x93581,a845)),x93582),f777(f777(f304(x93581),x93583),f182(f858(x93581,a845)))))),f777(f44(x93581),x93582))) % 174.01/173.90 [9934]P47(x99341,x99342,x99343)+~P1(f777(f777(f253(x99341,x99341,a845),f777(f777(f11(x99341,f858(x99341,a845),f858(x99341,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x99341,a845),f858(x99341,a845)),x99341),f12(a845,a845,x99341)),f777(f777(f12(a845,f858(a845,a845),x99341),a333),f777(f777(f11(x99341,f858(x99341,a845),a845),f336(x99341)),x99342)))),f777(f777(f11(x99341,f858(x99341,a845),a845),f336(x99341)),x99342))),f509(x99343,x99342,x99341)))+P1(f777(f777(f336(x99341),f508(x99343,x99342,x99341)),x99342)) % 174.01/173.90 [5366]~P113(x53662)+E(x53661,f4(x53662))+E(f777(f777(f285(x53662),x53663),f777(f83(x53662),x53661)),f777(f83(x53662),f777(f777(f285(x53662),x53663),x53661))) % 174.01/173.90 [5497]~E(x54973,f182(f858(x54971,a845)))+~E(x54972,f182(f858(x54971,a845)))+E(f777(f777(f105(f858(x54971,a845)),x54972),x54973),f182(f858(x54971,a845))) % 174.01/173.90 [5551]~E(x55513,f4(a851))+~P1(f777(x55511,f4(a851)))+P1(f777(x55511,f777(f777(f45(a851),x55512),x55513))) % 174.01/173.90 [5699]~P63(x56992)+E(x56991,f4(x56992))+E(f777(f777(f285(x56992),f777(f79(x56992),x56993)),f777(f79(x56992),x56991)),f777(f79(x56992),f777(f777(f285(x56992),x56993),x56991))) % 174.01/173.90 [5794]~P85(x57941)+~E(x57942,f82(x57941))+P1(f777(f777(f281(x57941),x57942),f777(f777(f244(x57941),x57942),x57943))) % 174.01/173.90 [5811]~P7(x58111)+E(f777(f777(f85(x58111),x58112),f777(f777(f45(x58111),x58113),x58112)),x58113)+~P1(f777(f777(f281(x58111),x58112),x58113)) % 174.01/173.90 [5865]~P1(f777(f65(x58651),x58653))+E(f777(f44(x58651),f777(f777(f304(x58651),x58652),x58653)),f777(a116,f777(f44(x58651),x58653)))+P1(f777(f777(f336(x58651),x58652),x58653)) % 174.01/173.90 [5941]~E(x59412,f4(a851))+P1(f777(x59411,f4(a851)))+~P1(f777(x59411,f777(f777(f45(a851),x59413),x59412))) % 174.01/173.90 [5959]~P1(f777(f65(x59591),x59593))+E(f777(f44(x59591),f777(f777(f304(x59591),x59592),x59593)),f777(f44(x59591),x59593))+~P1(f777(f777(f336(x59591),x59592),x59593)) % 174.01/173.90 [5993]~P1(f777(f65(x59931),x59933))+E(f777(f44(x59931),f777(f777(f304(x59931),x59932),x59933)),f777(f777(f84(a851),f82(a851)),f777(f44(x59931),x59933)))+P1(f777(f777(f336(x59931),x59932),x59933)) % 174.01/173.90 [6000]~P8(x60001)+E(f777(f777(f45(x60001),x60002),f777(f83(x60001),x60003)),f777(f83(x60001),f777(f777(f45(x60001),x60002),x60003)))+~P1(f777(f777(f281(x60001),x60003),x60002)) % 174.01/173.90 [6115]E(f777(f777(f84(a851),x61151),f802(x61151,x61152,x61153)),x61152)+~P1(f777(x61153,f4(a851)))+P1(f777(x61153,f777(f777(f5(a851),x61152),x61151))) % 174.01/173.90 [6116]E(f777(f777(f84(a851),x61161),f809(x61161,x61162,x61163)),x61162)+~P1(f777(x61163,f4(a851)))+P1(f777(x61163,f777(f777(f5(a851),x61162),x61161))) % 174.01/173.90 [6140]~P8(x61401)+E(f777(f777(f45(x61401),f777(f83(x61401),x61402)),x61403),f777(f83(x61401),f777(f777(f45(x61401),x61402),x61403)))+~P1(f777(f777(f281(x61401),x61403),x61402)) % 174.01/173.90 [6163]~P9(x61631)+~P1(f777(f65(x61631),x61633))+E(f777(f777(f68(x61631,x61631,f105(x61631)),x61632),x61633),f777(f777(f105(x61631),x61632),f46(x61631,x61633))) % 174.01/173.90 [6164]~P9(x61641)+~P1(f777(f65(x61641),x61643))+E(f777(f777(f68(x61641,x61641,f106(x61641)),x61642),x61643),f777(f777(f106(x61641),x61642),f47(x61641,x61643))) % 174.01/173.90 [6170]~P88(x61701)+~E(f777(f108(x61701),x61702),f777(f108(x61701),x61703))+P33(x61701,f777(f108(x61701),f777(f777(f84(a3),x61702),f777(f83(a3),x61703)))) % 174.01/173.90 [6177]~P133(x61771)+E(f777(f777(f5(x61771),f777(f104(x61771),x61772)),f777(f104(x61771),x61773)),f777(f104(x61771),f777(f777(f5(a851),x61772),x61773)))+~P1(f777(f777(f234(a851),x61773),x61772)) % 174.01/173.90 [6183]~P104(x61831)+~P1(f777(f777(f281(x61831),x61832),x61833))+P1(f777(f777(f281(x61831),f777(f83(x61831),x61832)),x61833)) % 174.01/173.90 [6184]~P110(x61841)+~P1(f777(f777(f281(x61841),x61842),x61843))+P1(f777(f777(f281(x61841),f777(f79(x61841),x61842)),x61843)) % 174.01/173.90 [6269]E(f777(f777(f84(a851),x62691),f802(x62691,x62692,x62693)),x62692)+P1(f777(f777(f235(a851),x62692),x62691))+P1(f777(x62693,f777(f777(f5(a851),x62692),x62691))) % 174.01/173.90 [6270]E(f777(f777(f84(a851),x62701),f809(x62701,x62702,x62703)),x62702)+P1(f777(f777(f235(a851),x62702),x62701))+P1(f777(x62703,f777(f777(f5(a851),x62702),x62701))) % 174.01/173.90 [6288]~P110(x62881)+E(f777(f777(f85(x62881),f777(f79(x62881),x62882)),x62883),f777(f79(x62881),f777(f777(f85(x62881),x62882),x62883)))+~P1(f777(f777(f234(x62881),f4(x62881)),x62883)) % 174.01/173.90 [6289]~P62(x62891)+E(f777(f777(f285(x62891),f777(f79(x62891),x62892)),x62893),f777(f79(x62891),f777(f777(f285(x62891),x62892),x62893)))+~P1(f777(f777(f235(x62891),f4(x62891)),x62893)) % 174.01/173.90 [6298]~P93(x62981)+~P1(f777(f65(x62981),x62983))+E(f777(f777(f68(x62981,x62981,f105(x62981)),x62982),x62983),f17(x62981,f777(f777(f304(x62981),x62982),x62983))) % 174.01/173.90 [6299]~P100(x62991)+~P1(f777(f65(x62991),x62993))+E(f777(f777(f68(x62991,x62991,f181(x62991)),x62992),x62993),f18(x62991,f777(f777(f304(x62991),x62992),x62993))) % 174.01/173.90 [6300]~P100(x63001)+~P1(f777(f65(x63001),x63003))+E(f777(f777(f68(x63001,x63001,f238(x63001)),x63002),x63003),f19(x63001,f777(f777(f304(x63001),x63002),x63003))) % 174.01/173.90 [6301]~P93(x63011)+~P1(f777(f65(x63011),x63013))+E(f777(f777(f68(x63011,x63011,f106(x63011)),x63012),x63013),f14(x63011,f777(f777(f304(x63011),x63012),x63013))) % 174.01/173.90 [6345]E(x63451,f117(x63452))+~E(f166(x63452,x63453),f117(f852(x63452)))+~P1(f777(f777(f336(f852(x63452)),x63451),f777(f160(f852(x63452)),x63453))) % 174.01/173.90 [6364]~P85(x63641)+~P1(f777(f777(f235(a851),f4(a851)),x63643))+P1(f777(f777(f281(x63641),x63642),f777(f777(f244(x63641),x63642),x63643))) % 174.01/173.90 [6395]~P1(f777(f129(x63951),x63953))+P1(f777(f777(f336(x63951),x63952),f777(f160(x63951),x63953)))+P1(f777(f129(x63951),f777(f777(f142(x63951),x63952),x63953))) % 174.01/173.90 [6407]~P91(x64071)+~P1(f777(f65(x64071),x64073))+E(f777(f67(x64071,f85(x64071)),f777(f777(f304(x64071),x64072),x64073)),f777(f777(f68(x64071,x64071,f85(x64071)),x64072),x64073)) % 174.01/173.90 [6428]~P100(x64281)+~P1(f777(f65(x64281),x64283))+E(f15(x64281,f181(x64281),f777(f777(f304(x64281),x64282),x64283)),f777(f777(f68(x64281,x64281,f181(x64281)),x64282),x64283)) % 174.01/173.90 [6429]~P100(x64291)+~P1(f777(f65(x64291),x64293))+E(f16(x64291,f238(x64291),f777(f777(f304(x64291),x64292),x64293)),f777(f777(f68(x64291,x64291,f238(x64291)),x64292),x64293)) % 174.01/173.90 [6431]P1(f777(x64311,f4(a851)))+~P1(f777(f777(f235(a851),x64312),x64313))+~P1(f777(x64311,f777(f777(f5(a851),x64312),x64313))) % 174.01/173.90 [6450]~P110(x64501)+P1(f777(f777(f235(x64501),x64502),x64503))+~P1(f777(f777(f235(x64501),f777(f79(x64501),x64502)),x64503)) % 174.01/173.90 [6452]~P79(x64521)+P1(f777(f777(f234(x64521),x64522),x64523))+~P1(f777(f777(f234(x64521),f777(f79(x64521),x64522)),x64523)) % 174.01/173.90 [6453]~P110(x64531)+P1(f777(f777(f281(x64531),x64532),x64533))+~P1(f777(f777(f281(x64531),f777(f79(x64531),x64532)),x64533)) % 174.01/173.90 [6454]~P104(x64541)+P1(f777(f777(f281(x64541),x64542),x64543))+~P1(f777(f777(f281(x64541),f777(f83(x64541),x64542)),x64543)) % 174.01/173.90 [6473]E(x64731,f117(x64732))+E(f777(f133(x64732),f777(f777(f130(x64732),x64733),x64731)),f777(f777(f155(x64732),x64731),x64733))+~P1(f777(f777(f235(a851),x64733),f777(f183(f852(x64732)),x64731))) % 174.01/173.90 [6527]~P1(f777(x65271,x65273))+P1(f777(x65271,f345(x65271,x65272)))+~P1(f777(f777(f336(a851),x65273),f777(f296(a851,f4(a851)),x65272))) % 174.01/173.90 [6550]P1(f777(x65501,x65502))+~P1(f777(f777(f235(a851),x65502),x65503))+P1(f777(f777(f336(a851),f344(x65501,x65503)),f777(f296(a851,f4(a851)),x65503))) % 174.01/173.90 [6565]~P117(x65651)+~P1(f777(f777(f235(x65651),f4(x65651)),x65652))+P1(f777(f777(f235(x65651),f4(x65651)),f777(f777(f244(x65651),x65652),x65653))) % 174.01/173.90 [6567]~P117(x65671)+~P1(f777(f777(f234(x65671),f4(x65671)),x65672))+P1(f777(f777(f234(x65671),f4(x65671)),f777(f777(f244(x65671),x65672),x65673))) % 174.01/173.90 [6568]~P117(x65681)+~P1(f777(f777(f234(x65681),f82(x65681)),x65682))+P1(f777(f777(f234(x65681),f82(x65681)),f777(f777(f244(x65681),x65682),x65683))) % 174.01/173.90 [6593]~P1(f777(x65931,x65933))+~P1(f777(f777(f235(a851),x65933),x65932))+P1(f777(f777(f336(a851),f341(x65931,x65932)),f777(f296(a851,f4(a851)),x65932))) % 174.01/173.90 [6598]P1(f777(f65(x65981),x65982))+~P1(f777(f65(x65981),x65983))+~P1(f777(f777(f234(f858(x65981,a845)),x65982),x65983)) % 174.01/173.90 [6607]~P1(f777(f777(f281(a851),x66071),x66072))+~P1(f777(f777(f281(a851),x66071),x66073))+P1(f777(f777(f281(a851),x66071),f777(f777(f5(a851),x66072),x66073))) % 174.01/173.90 [6608]P1(f777(x66081,x66082))+~P1(f777(x66081,f346(x66081,x66083)))+~P1(f777(f777(f336(a851),x66082),f777(f296(a851,f4(a851)),x66083))) % 174.01/173.90 [6621]E(x66211,f4(a851))+P1(f777(x66212,f794(x66211,x66213,x66212)))+~P1(f777(x66212,f777(f777(f45(a851),x66213),x66211))) % 174.01/173.90 [6630]~P119(x66302)+E(x66301,f4(x66302))+~E(f777(f777(f84(x66302),f777(f777(f85(x66302),x66303),x66303)),f777(f777(f85(x66302),x66301),x66301)),f4(x66302)) % 174.01/173.90 [6631]~P119(x66312)+E(x66311,f4(x66312))+~E(f777(f777(f84(x66312),f777(f777(f85(x66312),x66311),x66311)),f777(f777(f85(x66312),x66313),x66313)),f4(x66312)) % 174.01/173.90 [6678]E(x66781,f4(a851))+~P1(f777(x66782,f804(x66781,x66783,x66782)))+P1(f777(x66782,f777(f777(f45(a851),x66783),x66781))) % 174.01/173.90 [6683]~P100(x66831)+~P18(x66831,x66833)+P18(x66831,f777(f777(f140(x66831,x66831,f9(x66831)),x66832),x66833)) % 174.01/173.90 [6727]P1(f777(x67271,f794(x67272,x67273,x67271)))+P1(f777(x67271,f4(a851)))+~P1(f777(x67271,f777(f777(f45(a851),x67273),x67272))) % 174.01/173.90 [6733]~P88(x67331)+E(f777(f108(x67331),x67332),f777(f108(x67331),x67333))+~P33(x67331,f777(f108(x67331),f777(f777(f84(a3),x67332),f777(f83(a3),x67333)))) % 174.01/173.90 [6806]E(x68061,f4(a3))+E(x68062,f4(a3))+~P1(f777(f58(x68062,x68062),f777(f777(f243(a3,a3),x68063),x68061))) % 174.01/173.90 [6807]E(x68071,f82(a3))+E(x68072,f4(a3))+~P1(f777(f58(x68072,x68072),f777(f777(f243(a3,a3),x68071),x68073))) % 174.01/173.90 [6821]P1(f777(x68211,x68212))+P1(f777(f777(f235(a851),f346(x68211,x68213)),x68213))+~P1(f777(f777(f336(a851),x68212),f777(f296(a851,f4(a851)),x68213))) % 174.01/173.90 [6846]~P1(f777(x68461,f804(x68463,x68462,x68461)))+~P1(f777(x68461,f4(a851)))+P1(f777(x68461,f777(f777(f45(a851),x68462),x68463))) % 174.01/173.90 [6847]~P1(f777(x68471,f802(x68473,x68472,x68471)))+~P1(f777(x68471,f4(a851)))+P1(f777(x68471,f777(f777(f5(a851),x68472),x68473))) % 174.01/173.90 [6848]~P1(f777(x68481,f809(x68483,x68482,x68481)))+~P1(f777(x68481,f4(a851)))+P1(f777(x68481,f777(f777(f5(a851),x68482),x68483))) % 174.01/173.90 [6868]~P1(f777(x68681,x68683))+P1(f777(f777(f235(a851),f345(x68681,x68682)),x68682))+~P1(f777(f777(f336(a851),x68683),f777(f296(a851,f4(a851)),x68682))) % 174.01/173.90 [6869]E(f777(f777(f5(a851),f777(f777(f5(a851),x68691),x68692)),f777(f777(f5(a851),x68693),x68692)),f777(f777(f5(a851),x68691),x68693))+~P1(f777(f777(f234(a851),x68692),x68691))+~P1(f777(f777(f234(a851),x68692),x68693)) % 174.01/173.90 [6903]~P77(x69031)+~P1(f777(f777(f235(x69031),f777(f83(x69031),x69033)),x69032))+P1(f777(f777(f235(x69031),f777(f83(x69031),x69032)),x69033)) % 174.01/173.90 [6904]~P110(x69041)+~P1(f777(f777(f235(x69041),f777(f79(x69041),x69042)),x69043))+P1(f777(f777(f235(x69041),f777(f83(x69041),x69042)),x69043)) % 174.01/173.90 [6906]~P77(x69061)+~P1(f777(f777(f234(x69061),f777(f83(x69061),x69063)),x69062))+P1(f777(f777(f234(x69061),f777(f83(x69061),x69062)),x69063)) % 174.01/173.90 [6908]~P79(x69081)+~P1(f777(f777(f234(x69081),f777(f79(x69081),x69082)),x69083))+P1(f777(f777(f234(x69081),f777(f83(x69081),x69082)),x69083)) % 174.01/173.90 [6911]~P1(f777(f777(f281(a3),x69111),x69113))+P1(f777(f777(f281(a3),x69111),x69112))+~P1(f777(f777(f281(a3),x69111),f777(f777(f5(a3),x69112),x69113))) % 174.01/173.90 [6944]~P1(f777(x69443,f802(x69442,x69441,x69443)))+P1(f777(f777(f235(a851),x69441),x69442))+P1(f777(x69443,f777(f777(f5(a851),x69441),x69442))) % 174.01/173.90 [6945]~P1(f777(x69453,f809(x69452,x69451,x69453)))+P1(f777(f777(f235(a851),x69451),x69452))+P1(f777(x69453,f777(f777(f5(a851),x69451),x69452))) % 174.01/173.90 [6991]~E(f686(x69913,x69912,x69911),f681(x69913,x69912,x69911))+E(f777(f777(f106(f858(x69911,a845)),x69912),f46(f858(x69911,a845),x69913)),f182(f858(x69911,a845)))+P1(f777(f777(f336(f858(x69911,a845)),x69912),x69913)) % 174.01/173.90 [7000]~P1(f777(f65(x70001),x70003))+P1(f777(f65(x70001),f47(f858(x70001,a845),x70002)))+~P1(f777(f777(f336(f858(x70001,a845)),x70003),x70002)) % 174.01/173.90 [7061]~P100(x70611)+E(f777(f777(f105(f858(x70611,a845)),f777(f296(x70611,x70612),x70613)),f777(f777(f304(x70611),x70613),f182(f858(x70611,a845)))),f297(x70611,x70612,x70613))+~P1(f777(f777(f234(x70611),x70612),x70613)) % 174.01/173.90 [7064]E(x70641,f4(a851))+P1(f777(f777(f235(a851),f806(x70641,x70643,x70642)),x70641))+P1(f777(x70642,f777(f777(f45(a851),x70643),x70641))) % 174.01/173.90 [7099]E(x70991,x70992)+~P1(f777(f777(f234(f858(x70993,a845)),x70991),x70992))+P1(f777(f777(f235(f858(x70993,a845)),x70991),x70992)) % 174.01/173.90 [7111]E(x71111,x71112)+~E(f777(f183(f852(x71113)),x71111),f777(f183(f852(x71113)),x71112))+P1(f777(f777(f235(a851),f732(x71113,x71111,x71112)),f777(f183(f852(x71113)),x71112))) % 174.01/173.90 [7156]P12(x71561,x71562,x71563)+~E(f777(f263(x71561,x71561),x71563),x71562)+~E(f777(f777(f283(x71561,x71561,x71561),f777(f280(x71561,x71561),x71563)),x71563),x71563) % 174.01/173.90 [7238]E(x72381,f4(a3))+~P1(f777(f777(f281(a3),x72382),x72383))+P1(f777(f777(f281(a3),f777(f777(f85(a3),x72381),x72382)),f777(f777(f85(a3),x72381),x72383))) % 174.01/173.90 [7241]~P1(f777(x72411,f4(a851)))+P1(f777(f777(f235(a851),f806(x72413,x72412,x72411)),x72413))+P1(f777(x72411,f777(f777(f45(a851),x72412),x72413))) % 174.01/173.90 [7254]~P100(x72541)+E(f777(f777(f105(f858(x72541,a845)),f300(x72541,x72542,x72543)),f777(f777(f304(x72541),x72543),f182(f858(x72541,a845)))),f299(x72541,x72542,x72543))+~P1(f777(f777(f235(x72541),x72542),x72543)) % 174.01/173.90 [7359]~P1(f777(f65(x73591),x73593))+P1(f777(f777(f235(a851),f777(f44(x73591),x73592)),f777(f44(x73591),x73593)))+~P1(f777(f777(f235(f858(x73591,a845)),x73592),x73593)) % 174.01/173.90 [7360]~P1(f777(f65(x73601),x73603))+P1(f777(f777(f234(a851),f777(f44(x73601),x73602)),f777(f44(x73601),x73603)))+~P1(f777(f777(f234(f858(x73601,a845)),x73602),x73603)) % 174.01/173.90 [7401]~P1(f777(x74013,x74012))+P1(f777(f777(f189(x74011),x74012),f417(x74012,x74011,x74013)))+~P1(f777(f777(f189(f37(x74013,x74011)),x74012),x74012)) % 174.01/173.90 [7499]E(x74991,x74992)+~P1(f777(f777(f234(f858(x74993,a845)),x74992),x74991))+~P1(f777(f777(f234(f858(x74993,a845)),x74991),x74992)) % 174.01/173.90 [7502]~P100(x75021)+P18(x75021,x75022)+~P18(x75021,f777(f777(f140(x75021,x75021,f9(x75021)),x75023),x75022)) % 174.01/173.90 [7571]~P1(f777(f777(f235(a851),x75713),x75712))+~P1(f777(f777(f235(a851),x75713),x75711))+P1(f777(f777(f235(a851),f777(f777(f5(a851),x75711),x75712)),f777(f777(f5(a851),x75711),x75713))) % 174.01/173.90 [7572]~P1(f777(f777(f235(a851),x75721),x75723))+~P1(f777(f777(f234(a851),x75722),x75721))+P1(f777(f777(f235(a851),f777(f777(f5(a851),x75721),x75722)),f777(f777(f5(a851),x75723),x75722))) % 174.01/173.90 [7589]~P1(f777(f777(f235(a3),x75892),f4(a3)))+~P1(f777(f777(f234(a3),x75893),x75891))+P1(f777(f777(f234(a3),f777(f777(f45(a3),x75891),x75892)),f777(f777(f45(a3),x75893),x75892))) % 174.01/173.90 [7609]~P1(f777(f777(f235(a851),f4(a851)),x76092))+~P1(f777(f777(f235(a851),x76091),x76093))+P1(f777(f777(f235(a851),f777(f777(f85(a851),x76091),x76092)),f777(f777(f85(a851),x76093),x76092))) % 174.01/173.90 [7610]~P1(f777(f777(f235(a851),f4(a851)),x76101))+~P1(f777(f777(f235(a851),x76102),x76103))+P1(f777(f777(f235(a851),f777(f777(f85(a851),x76101),x76102)),f777(f777(f85(a851),x76101),x76103))) % 174.01/173.90 [7611]~P1(f777(f777(f235(a3),f4(a3)),x76111))+~P1(f777(f777(f235(a3),x76112),x76113))+P1(f777(f777(f235(a3),f777(f777(f85(a3),x76111),x76112)),f777(f777(f85(a3),x76111),x76113))) % 174.01/173.90 [7613]~P1(f777(f777(f235(a851),f4(a851)),x76133))+~P1(f777(f777(f234(a851),x76133),x76132))+P1(f777(f777(f234(a851),f777(f777(f45(a851),x76131),x76132)),f777(f777(f45(a851),x76131),x76133))) % 174.01/173.90 [7614]~P1(f777(f777(f235(a3),f4(a3)),x76142))+~P1(f777(f777(f234(a3),x76141),x76143))+P1(f777(f777(f234(a3),f777(f777(f45(a3),x76141),x76142)),f777(f777(f45(a3),x76143),x76142))) % 174.01/173.90 [7663]E(x76631,f4(a851))+E(f777(f777(f84(a851),f777(f777(f85(a851),x76631),f804(x76631,x76632,x76633))),f806(x76631,x76632,x76633)),x76632)+P1(f777(x76633,f777(f777(f45(a851),x76632),x76631))) % 174.01/173.90 [7721]E(f777(f777(f84(a851),f777(f777(f85(a851),x77211),f804(x77211,x77212,x77213))),f806(x77211,x77212,x77213)),x77212)+~P1(f777(x77213,f4(a851)))+P1(f777(x77213,f777(f777(f45(a851),x77212),x77211))) % 174.01/173.90 [7737]~P1(f777(f65(x77371),x77373))+P1(f777(f777(f336(x77371),f462(x77372,x77373,x77371)),x77373))+P1(f777(f777(f235(a851),f4(a851)),f777(f777(f13(x77371,a851),x77372),x77373))) % 174.01/173.90 [7738]~P1(f777(f65(x77381),x77383))+P1(f777(f777(f336(x77381),f574(x77382,x77383,x77381)),x77383))+P1(f777(f777(f235(a851),f4(a851)),f777(f777(f13(x77381,a851),x77382),x77383))) % 174.01/173.90 [7843]E(x78431,f4(a851))+P1(f777(f777(f281(a851),x78432),x78433))+~P1(f777(f777(f281(a851),f777(f777(f85(a851),x78431),x78432)),f777(f777(f85(a851),x78431),x78433))) % 174.01/173.90 [7845]E(x78451,f4(a3))+P1(f777(f777(f281(a3),x78452),x78453))+~P1(f777(f777(f281(a3),f777(f777(f85(a3),x78451),x78452)),f777(f777(f85(a3),x78451),x78453))) % 174.01/173.90 [8031]E(x80311,f182(f858(x80312,a845)))+E(x80311,f777(f777(f304(x80312),x80313),f182(f858(x80312,a845))))+~P1(f777(f777(f234(f858(x80312,a845)),x80311),f777(f777(f304(x80312),x80313),f182(f858(x80312,a845))))) % 174.01/173.90 [8068]~P1(f777(f777(f235(a851),f4(a851)),x80683))+P1(f777(f777(f235(a851),x80681),x80682))+~P1(f777(f777(f235(a851),f777(f777(f244(a851),x80683),x80681)),f777(f777(f244(a851),x80683),x80682))) % 174.01/173.90 [8070]~P1(f777(f777(f235(a851),f4(a851)),x80703))+P1(f777(f777(f234(a851),x80701),x80702))+~P1(f777(f777(f234(a851),f777(f777(f85(a851),x80703),x80701)),f777(f777(f85(a851),x80703),x80702))) % 174.01/173.90 [8071]~P1(f777(f777(f235(a851),f82(a851)),x80713))+P1(f777(f777(f234(a851),x80711),x80712))+~P1(f777(f777(f281(a851),f777(f777(f244(a851),x80713),x80711)),f777(f777(f244(a851),x80713),x80712))) % 174.01/173.90 [8072]~P1(f777(f777(f235(a851),f4(a851)),x80723))+P1(f777(f777(f234(a851),x80721),x80722))+~P1(f777(f777(f234(a851),f777(f777(f85(a851),x80721),x80723)),f777(f777(f85(a851),x80722),x80723))) % 174.01/173.90 [8074]~P1(f777(f777(f235(a851),f4(a851)),x80743))+P1(f777(f777(f281(a851),x80741),x80742))+~P1(f777(f777(f281(a851),f777(f777(f85(a851),x80743),x80741)),f777(f777(f85(a851),x80743),x80742))) % 174.01/173.90 [8102]~P1(f777(x81021,x81023))+P1(f777(f777(f189(f37(x81021,x81022)),f417(x81023,x81022,x81021)),x81023))+~P1(f777(f777(f189(f37(x81021,x81022)),x81023),x81023)) % 174.01/173.90 [8110]~E(f777(f777(f106(f858(x81101,a845)),f681(x81103,x81102,x81101)),f686(x81103,x81102,x81101)),f182(f858(x81101,a845)))+E(f777(f777(f106(f858(x81101,a845)),x81102),f46(f858(x81101,a845),x81103)),f182(f858(x81101,a845)))+P1(f777(f777(f336(f858(x81101,a845)),x81102),x81103)) % 174.01/173.90 [8125]E(x81251,f117(x81252))+~E(f777(f134(f852(x81252),f852(x81252),f127(x81252),f117(x81252)),x81253),f117(x81252))+~P1(f777(f777(f336(f852(x81252)),x81251),f777(f160(f852(x81252)),x81253))) % 174.01/173.90 [8182]E(x81821,f182(f858(f858(x81822,a845),a845)))+P1(f777(f777(f336(f858(x81822,a845)),f688(x81823,x81821,x81822)),x81821))+P1(f777(f777(f234(f858(x81822,a845)),f47(f858(x81822,a845),x81821)),x81823)) % 174.01/173.90 [8188]~P66(x81881)+~P70(x81881)+E(f777(f777(f10(a3,x81881),f777(f777(f12(a851,x81881,a3),x81882),a109)),f777(f305(a851,a3,f104(a3)),x81883)),f777(f777(f10(a851,x81881),x81882),x81883)) % 174.01/173.90 [8189]~P66(x81891)+~P70(x81891)+E(f777(f777(f13(a3,x81891),f777(f777(f12(a851,x81891,a3),x81892),a109)),f777(f305(a851,a3,f104(a3)),x81893)),f777(f777(f13(a851,x81891),x81892),x81893)) % 174.01/173.90 [8226]~P1(f777(f65(x82261),x82263))+~P1(f777(f777(f235(a851),f4(a851)),f777(x82262,f462(x82262,x82263,x82261))))+P1(f777(f777(f235(a851),f4(a851)),f777(f777(f13(x82261,a851),x82262),x82263))) % 174.01/173.90 [8227]~P1(f777(f65(x82271),x82273))+~P1(f777(f777(f235(a851),f4(a851)),f777(x82272,f574(x82272,x82273,x82271))))+P1(f777(f777(f235(a851),f4(a851)),f777(f777(f13(x82271,a851),x82272),x82273))) % 174.01/173.90 [8262]~P61(x82622)+E(x82621,f82(x82622))+E(f777(f777(f285(x82622),f777(f777(f5(x82622),f777(f777(f244(x82622),x82621),x82623)),f82(x82622))),f777(f777(f5(x82622),x82621),f82(x82622))),f777(f777(f10(a851,x82622),f777(f244(x82622),x82621)),f777(f296(a851,f4(a851)),x82623))) % 174.01/173.90 [8321]E(x83211,f4(a851))+~P1(f777(x83213,f777(f777(f45(a851),x83212),x83211)))+P1(f777(f777(f235(a851),x83212),f777(f777(f85(a851),x83211),f777(a116,f794(x83211,x83212,x83213))))) % 174.01/173.90 [8342]P1(f777(x83421,f4(a851)))+~P1(f777(x83421,f777(f777(f45(a851),x83422),x83423)))+P1(f777(f777(f235(a851),x83422),f777(f777(f85(a851),x83423),f777(a116,f794(x83423,x83422,x83421))))) % 174.01/173.90 [8381]E(x83811,f4(a851))+~P1(f777(x83813,f777(f777(f45(a851),x83812),x83811)))+P1(f777(f777(f234(a851),f777(f777(f85(a851),x83811),f794(x83811,x83812,x83813))),x83812)) % 174.01/173.90 [8418]P1(f777(x84181,f4(a851)))+~P1(f777(x84181,f777(f777(f45(a851),x84183),x84182)))+P1(f777(f777(f234(a851),f777(f777(f85(a851),x84182),f794(x84182,x84183,x84181))),x84183)) % 174.01/173.90 [8421]~P100(x84211)+E(f777(f777(f140(x84211,x84211,f9(x84211)),x84212),x84213),f141(x84211,x84211,f9(x84211),x84212,x84213))+P1(f777(f777(f336(x84211),x84212),f777(f160(x84211),x84213))) % 174.01/173.90 [8461]~E(f777(x84613,f611(x84612,x84613,x84611)),f777(x84613,f613(x84612,x84613,x84611)))+~P58(x84611,f777(x84613,f612(x84612,x84613,x84611)))+P58(x84611,f777(f777(f48(x84612,f858(x84611,f858(x84611,a845))),f241(f858(x84612,a845))),x84613)) % 174.01/173.90 [8469]E(x84691,f182(f858(f858(x84692,a845),a845)))+~P1(f777(f777(f234(f858(x84692,a845)),f688(x84693,x84691,x84692)),x84693))+P1(f777(f777(f234(f858(x84692,a845)),f47(f858(x84692,a845),x84691)),x84693)) % 174.01/173.90 [8528]~P63(x85281)+~P1(f777(f777(f235(x85281),x85282),x85283))+P1(f777(f777(f235(x85281),x85282),f777(f777(f285(x85281),f777(f777(f84(x85281),x85282),x85283)),f777(f777(f84(x85281),f82(x85281)),f82(x85281))))) % 174.01/173.90 [8571]~P1(f777(f777(x85711,f826(x85711,x85713,x85712)),f827(x85711,x85713,x85712)))+P1(f777(f777(x85711,x85712),x85713))+~P1(f777(f323(f857(a3,a3),a61),f777(f777(f243(a3,a3),x85712),x85713))) % 174.01/173.90 [8572]~P1(f777(f777(x85721,f828(x85721,x85723,x85722)),f829(x85721,x85723,x85722)))+P1(f777(f777(x85721,x85722),x85723))+~P1(f777(f323(f857(a3,a3),a64),f777(f777(f243(a3,a3),x85722),x85723))) % 174.01/173.90 [8573]~P1(f777(f777(x85731,f830(x85731,x85733,x85732)),f833(x85731,x85733,x85732)))+P1(f777(f777(x85731,x85732),x85733))+~P1(f777(f323(f857(a3,a3),a218),f777(f777(f243(a3,a3),x85732),x85733))) % 174.01/173.90 [8574]~P1(f777(f777(x85741,f834(x85741,x85743,x85742)),f836(x85741,x85743,x85742)))+P1(f777(f777(x85741,x85742),x85743))+~P1(f777(f323(f857(a851,a851),a216),f777(f777(f243(a851,a851),x85742),x85743))) % 174.01/173.90 [8575]~P1(f777(f777(x85751,f396(x85751,x85753,x85752)),f397(x85751,x85753,x85752)))+P1(f777(f777(x85751,x85752),x85753))+~P1(f777(f323(f857(a3,a3),a170),f777(f777(f243(a3,a3),x85752),x85753))) % 174.01/173.90 [8809]P1(f777(f777(x88091,x88092),x88093))+P1(f777(f323(f857(a851,a851),a216),f777(f777(f243(a851,a851),f834(x88091,x88093,x88092)),f836(x88091,x88093,x88092))))+~P1(f777(f323(f857(a851,a851),a216),f777(f777(f243(a851,a851),x88092),x88093))) % 174.01/173.90 [8810]P1(f777(f777(x88101,x88102),x88103))+P1(f777(f323(f857(a3,a3),a61),f777(f777(f243(a3,a3),f826(x88101,x88103,x88102)),f827(x88101,x88103,x88102))))+~P1(f777(f323(f857(a3,a3),a61),f777(f777(f243(a3,a3),x88102),x88103))) % 174.01/173.90 [8811]P1(f777(f777(x88111,x88112),x88113))+P1(f777(f323(f857(a3,a3),a64),f777(f777(f243(a3,a3),f828(x88111,x88113,x88112)),f829(x88111,x88113,x88112))))+~P1(f777(f323(f857(a3,a3),a64),f777(f777(f243(a3,a3),x88112),x88113))) % 174.01/173.90 [8812]P1(f777(f777(x88121,x88122),x88123))+P1(f777(f323(f857(a3,a3),a218),f777(f777(f243(a3,a3),f830(x88121,x88123,x88122)),f833(x88121,x88123,x88122))))+~P1(f777(f323(f857(a3,a3),a218),f777(f777(f243(a3,a3),x88122),x88123))) % 174.01/173.90 [8813]P1(f777(f777(x88131,x88132),x88133))+P1(f777(f323(f857(a3,a3),a170),f777(f777(f243(a3,a3),f396(x88131,x88133,x88132)),f397(x88131,x88133,x88132))))+~P1(f777(f323(f857(a3,a3),a170),f777(f777(f243(a3,a3),x88132),x88133))) % 174.01/173.90 [9125]~P1(f777(f65(x91251),x91253))+P1(f777(f777(f336(f857(f858(x91251,a845),f858(x91251,a845))),f777(f777(f243(f858(x91251,a845),f858(x91251,a845)),x91252),x91253)),f301(x91251)))+~P1(f777(f777(f235(f858(x91251,a845)),x91252),x91253)) % 174.01/173.90 [9178]~P58(x91781,f777(x91783,f612(x91782,x91783,x91781)))+P58(x91781,f777(f777(f48(x91782,f858(x91781,f858(x91781,a845))),f241(f858(x91782,a845))),x91783))+~E(f777(f777(f106(f858(x91781,a845)),f248(x91781,x91781,f777(x91783,f611(x91782,x91783,x91781)))),f249(x91781,x91781,f777(x91783,f613(x91782,x91783,x91781)))),f182(f858(x91781,a845))) % 174.01/173.90 [9371]P47(x93711,x93712,x93713)+P1(f777(f777(f336(f857(x93711,x93711)),f509(x93713,x93712,x93711)),x93713))+~P1(f777(f777(f336(f857(x93711,x93711)),f777(f777(f243(x93711,x93711),f508(x93713,x93712,x93711)),f508(x93713,x93712,x93711))),x93713)) % 174.01/173.90 [9936]P47(x99361,x99362,x99363)+~P1(f777(f777(f253(x99361,x99361,a845),f777(f777(f11(x99361,f858(x99361,a845),f858(x99361,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x99361,a845),f858(x99361,a845)),x99361),f12(a845,a845,x99361)),f777(f777(f12(a845,f858(a845,a845),x99361),a333),f777(f777(f11(x99361,f858(x99361,a845),a845),f336(x99361)),x99362)))),f777(f777(f11(x99361,f858(x99361,a845),a845),f336(x99361)),x99362))),f509(x99363,x99362,x99361)))+~P1(f777(f777(f336(f857(x99361,x99361)),f777(f777(f243(x99361,x99361),f508(x99363,x99362,x99361)),f508(x99363,x99362,x99361))),x99363)) % 174.01/173.90 [5534]~P7(x55342)+E(x55341,f4(x55342))+E(f777(f777(f45(x55342),f777(f777(f85(x55342),x55343),x55341)),x55341),x55343) % 174.01/173.90 [5535]~P7(x55352)+E(x55351,f4(x55352))+E(f777(f777(f45(x55352),f777(f777(f85(x55352),x55351),x55353)),x55351),x55353) % 174.01/173.90 [6178]~P7(x61781)+E(f777(f777(f85(x61781),f777(f777(f45(x61781),x61782),x61783)),x61783),x61782)+~P1(f777(f777(f281(x61781),x61783),x61782)) % 174.01/173.90 [6344]~P66(x63441)+~E(f777(x63442,f4(a851)),f4(x63441))+E(f777(f777(f10(a851,x63441),x63442),f777(f296(a851,f777(a116,f4(a851))),x63443)),f777(f777(f10(a851,x63441),x63442),f777(f296(a851,f4(a851)),x63443))) % 174.01/173.90 [6487]~P7(x64872)+E(x64871,f4(x64872))+E(f777(f777(f45(x64872),f777(f777(f84(x64872),x64873),x64871)),x64871),f777(f777(f84(x64872),f777(f777(f45(x64872),x64873),x64871)),f82(x64872))) % 174.01/173.90 [6488]~P7(x64882)+E(x64881,f4(x64882))+E(f777(f777(f45(x64882),f777(f777(f84(x64882),x64881),x64883)),x64881),f777(f777(f84(x64882),f777(f777(f45(x64882),x64883),x64881)),f82(x64882))) % 174.01/173.90 [6717]~P1(f777(x67173,f4(a3)))+P1(f777(f777(f234(a851),x67171),x67172))+P1(f777(x67173,f777(f104(a3),f777(f777(f5(a851),x67172),x67171)))) % 174.01/173.90 [6828]P1(f777(f777(f234(a851),x68282),x68281))+P1(f777(f777(f235(a851),x68281),x68282))+P1(f777(x68283,f777(f104(a3),f777(f777(f5(a851),x68281),x68282)))) % 174.01/173.90 [6901]E(f777(f777(f84(a851),f777(f108(a851),x69011)),f777(f777(f84(a851),f777(f108(a851),x69012)),x69013)),f777(f777(f84(a851),f777(f108(a851),x69011)),x69013))+P1(f777(a188,f777(f108(a3),x69011)))+~P1(f777(a188,f777(f108(a3),x69012))) % 174.01/173.90 [6979]~E(x69792,f777(f777(f45(a851),x69793),x69791))+~P1(f777(f777(f235(a851),f4(a851)),x69791))+P1(f777(f777(f234(a851),f777(f777(f85(a851),x69791),x69792)),x69793)) % 174.01/173.90 [7097]~P1(f777(f65(x70971),x70973))+~P1(f777(f65(x70971),x70972))+P1(f777(f65(x70971),f777(f777(f105(f858(x70971,a845)),x70972),x70973))) % 174.01/173.90 [7412]~P100(x74121)+~P1(f777(f65(x74121),x74122))+E(f132(x74121,f777(f777(f5(f858(x74121,a845)),x74122),f777(f777(f304(x74121),x74123),f182(f858(x74121,a845))))),f153(x74121,x74123,f132(x74121,x74122))) % 174.01/173.90 [7478]P1(f777(x74781,f4(a3)))+~P1(f777(f777(f235(a851),x74782),x74783))+~P1(f777(x74781,f777(f104(a3),f777(f777(f5(a851),x74782),x74783)))) % 174.01/173.90 [7496]~P1(f777(f65(x74961),x74962))+E(f777(f44(x74961),f777(f777(f5(f858(x74961,a845)),x74962),f777(f777(f304(x74961),x74963),f182(f858(x74961,a845))))),f777(f44(x74961),x74962))+P1(f777(f777(f336(x74961),x74963),x74962)) % 174.01/173.90 [7630]~P117(x76301)+~P1(f777(f777(f235(x76301),f82(x76301)),x76302))+P1(f777(f777(f235(x76301),f82(x76301)),f777(f777(f85(x76301),x76302),f777(f777(f244(x76301),x76302),x76303)))) % 174.01/173.90 [7674]~P1(f777(f65(x76741),x76743))+E(f777(f777(f5(a851),f777(f44(x76741),x76742)),f777(f44(x76741),x76743)),f777(f44(x76741),f777(f777(f5(f858(x76741,a845)),x76742),x76743)))+~P1(f777(f777(f234(f858(x76741,a845)),x76743),x76742)) % 174.01/173.90 [7729]~P1(f777(f777(f234(a851),x77292),x77293))+~P1(f777(f777(f234(a851),x77291),f777(f777(f5(a851),x77293),x77292)))+P1(f777(f777(f234(a851),f777(f777(f84(a851),x77291),x77292)),x77293)) % 174.01/173.90 [7786]P1(f777(f65(x77861),x77862))+~P1(f777(f65(x77861),x77863))+~P1(f777(f65(x77861),f777(f777(f5(f858(x77861,a845)),x77862),x77863))) % 174.01/173.90 [7793]~P1(f777(f65(x77931),x77932))+E(f777(f44(x77931),f777(f777(f5(f858(x77931,a845)),x77932),f777(f777(f304(x77931),x77933),f182(f858(x77931,a845))))),f777(f777(f5(a851),f777(f44(x77931),x77932)),f82(a851)))+~P1(f777(f777(f336(x77931),x77933),x77932)) % 174.01/173.90 [7868]P58(x78681,x78682)+~P58(x78681,x78683)+~P1(f777(f777(f234(f858(x78681,f858(x78681,a845))),x78682),x78683)) % 174.01/173.90 [7906]~P1(f777(f777(f234(a851),x79063),x79062))+P1(f777(f777(f234(a851),x79061),f777(f777(f5(a851),x79062),x79063)))+~P1(f777(f777(f234(a851),f777(f777(f84(a851),x79061),x79063)),x79062)) % 174.01/173.90 [7926]P36(x79261,x79262)+~P36(x79261,x79263)+~P1(f777(f777(f234(f858(f857(x79261,x79261),a845)),x79262),x79263)) % 174.01/173.90 [7927]P56(x79271,x79272)+~P56(x79271,x79273)+~P1(f777(f777(f234(f858(f857(x79271,x79271),a845)),x79272),x79273)) % 174.01/173.90 [8160]~P117(x81601)+~P1(f777(f777(f235(x81601),f82(x81601)),x81602))+P1(f777(f777(f235(x81601),f777(f777(f244(x81601),x81602),x81603)),f777(f777(f85(x81601),x81602),f777(f777(f244(x81601),x81602),x81603)))) % 174.01/173.90 [8246]~P1(f777(x82461,f4(a3)))+~P1(f777(x82461,f777(f777(f5(a3),f777(f104(a3),x82462)),f777(f104(a3),x82463))))+P1(f777(x82461,f777(f104(a3),f777(f777(f5(a851),x82462),x82463)))) % 174.01/173.90 [8259]~P1(f777(f777(f234(a851),x82593),x82592))+P1(f777(x82591,f777(f777(f5(a3),f777(f104(a3),x82592)),f777(f104(a3),x82593))))+~P1(f777(x82591,f777(f104(a3),f777(f777(f5(a851),x82592),x82593)))) % 174.01/173.90 [8276]P1(f777(f777(f235(a851),x82761),x82762))+~P1(f777(x82763,f777(f777(f5(a3),f777(f104(a3),x82761)),f777(f104(a3),x82762))))+P1(f777(x82763,f777(f104(a3),f777(f777(f5(a851),x82761),x82762)))) % 174.01/173.90 [8333]~P119(x83332)+E(x83331,f4(x83332))+P1(f777(f777(f235(x83332),f4(x83332)),f777(f777(f84(x83332),f777(f777(f85(x83332),x83333),x83333)),f777(f777(f85(x83332),x83331),x83331)))) % 174.01/173.90 [8334]~P119(x83342)+E(x83341,f4(x83342))+P1(f777(f777(f235(x83342),f4(x83342)),f777(f777(f84(x83342),f777(f777(f85(x83342),x83341),x83341)),f777(f777(f85(x83342),x83343),x83343)))) % 174.01/173.90 [8440]~P1(f777(f777(f235(a851),f4(a851)),x84401))+~P1(f777(f777(f235(a3),x84402),x84403))+P1(f777(f777(f235(a3),f777(f777(f85(a3),f777(f104(a3),x84401)),x84402)),f777(f777(f85(a3),f777(f104(a3),x84401)),x84403))) % 174.01/173.90 [8500]E(f777(f777(f106(f858(x85001,a845)),x85002),f46(f858(x85001,a845),x85003)),f182(f858(x85001,a845)))+P1(f777(f777(f336(f858(x85001,a845)),x85002),x85003))+P1(f777(f777(f336(f858(x85001,a845)),f681(x85003,x85002,x85001)),f777(f777(f304(f858(x85001,a845)),x85002),x85003))) % 174.01/173.90 [8501]E(f777(f777(f106(f858(x85011,a845)),x85012),f46(f858(x85011,a845),x85013)),f182(f858(x85011,a845)))+P1(f777(f777(f336(f858(x85011,a845)),x85012),x85013))+P1(f777(f777(f336(f858(x85011,a845)),f686(x85013,x85012,x85011)),f777(f777(f304(f858(x85011,a845)),x85012),x85013))) % 174.01/173.90 [8527]E(x85271,x85272)+~E(f777(f183(f852(x85273)),x85271),f777(f183(f852(x85273)),x85272))+P1(f777(f777(f336(f857(x85273,x85273)),f715(x85273,x85271,x85272)),f777(f160(f857(x85273,x85273)),f777(f777(f169(x85273,x85273),x85272),x85271)))) % 174.01/173.90 [8737]E(f302(x87371,x87372),f302(x87371,x87373))+~P1(f777(f777(f234(f858(f857(x87371,x87371),a845)),x87373),f302(x87371,x87372)))+~P1(f777(f777(f234(f858(f857(x87371,x87371),a845)),x87372),x87373)) % 174.01/173.90 [8790]~P47(x87901,f241(f858(x87901,a845)),x87903)+P1(f777(f777(f234(f858(f857(f852(x87901),f852(x87901)),a845)),f148(x87901,x87902)),f149(x87901,x87903)))+~P1(f777(f777(f234(f858(f857(x87901,x87901),a845)),x87902),x87903)) % 174.01/173.90 [8969]P36(x89691,x89692)+~P1(f777(f777(f336(x89691),x89693),f684(x89692,x89691)))+P1(f777(f777(f336(f857(x89691,x89691)),f777(f777(f243(x89691,x89691),f699(x89692,x89691,x89693)),x89693)),x89692)) % 174.01/173.90 [9008]~P1(f777(f65(x90081),x90082))+P1(f777(f65(f858(x90081,a845)),f777(f777(f63(x90081),x90082),x90083)))+~P1(f777(f777(f234(f858(f857(x90081,x90081),a845)),x90083),f777(f777(f250(x90081,x90081),x90082),f777(f20(f858(x90081,a845),x90081),x90082)))) % 174.01/173.90 [9039]P47(x90391,x90392,x90393)+P1(f777(f777(f336(x90391),f552(x90393,x90392,x90391)),x90392))+~P1(f777(f777(f234(f858(f857(x90391,x90391),a845)),x90393),f777(f777(f250(x90391,x90391),x90392),f777(f20(f858(x90391,a845),x90391),x90392)))) % 174.01/173.90 [9040]P47(x90401,x90402,x90403)+P1(f777(f777(f336(x90401),f557(x90402,x90403,x90401)),x90402))+~P1(f777(f777(f234(f858(f857(x90401,x90401),a845)),x90403),f777(f777(f250(x90401,x90401),x90402),f777(f20(f858(x90401,a845),x90401),x90402)))) % 174.01/173.90 [9073]~P63(x90731)+~P1(f777(f777(f235(x90731),x90732),x90733))+P1(f777(f777(f235(x90731),f777(f777(f285(x90731),f777(f777(f84(x90731),x90732),x90733)),f777(f777(f84(x90731),f82(x90731)),f82(x90731)))),x90733)) % 174.01/173.90 [9100]~P62(x91001)+P1(f777(f777(f234(x91001),x91002),x91003))+~P1(f777(f777(f234(x91001),f777(f777(f85(x91001),f803(x91003,x91002,x91001)),x91002)),x91003)) % 174.01/173.90 [9210]E(f777(f183(f852(f852(x92101))),f777(f128(f852(x92101),f777(f777(f12(a851,a845,f852(x92101)),f777(f235(a851),x92102)),f183(f852(x92101)))),f166(x92101,x92103))),f777(f183(f852(x92101)),f777(f777(f155(f852(x92101)),x92103),x92102)))+~P18(a851,f777(f144(a851),f777(f777(f145(f852(x92101),a851),f183(f852(x92101))),x92103)))+~P1(f777(f777(f235(a851),x92102),f777(f183(f852(f852(x92101))),x92103))) % 174.01/173.90 [9321]~P36(x93211,x93212)+P30(x93211,f777(f777(f243(f858(f857(x93211,x93211),a845),f858(f857(x93211,x93211),a845)),x93212),x93213))+~P1(f777(f777(f234(f858(f857(x93211,x93211),a845)),f777(f777(f283(x93211,x93211,x93211),x93212),x93213)),x93212)) % 174.01/173.90 [9328]E(f777(f777(f145(f852(x93281),x93281),f777(f777(f11(f852(x93281),a851,x93281),f155(x93281)),x93282)),f777(f128(f852(x93281),f777(f777(f12(a851,a845,f852(x93281)),f777(f235(a851),x93282)),f183(f852(x93281)))),f166(x93281,x93283))),f777(f777(f155(f852(x93281)),x93283),x93282))+~P18(a851,f777(f144(a851),f777(f777(f145(f852(x93281),a851),f183(f852(x93281))),x93283)))+~P1(f777(f777(f235(a851),x93282),f777(f183(f852(f852(x93281))),x93283))) % 174.01/173.90 [9455]P47(x94551,x94552,x94553)+~P1(f777(f777(f336(f857(x94551,x94551)),f777(f777(f243(x94551,x94551),f552(x94553,x94552,x94551)),f552(x94553,x94552,x94551))),x94553))+~P1(f777(f777(f234(f858(f857(x94551,x94551),a845)),x94553),f777(f777(f250(x94551,x94551),x94552),f777(f20(f858(x94551,a845),x94551),x94552)))) % 174.01/173.90 [9456]P47(x94561,x94562,x94563)+~P1(f777(f777(f336(f857(x94561,x94561)),f777(f777(f243(x94561,x94561),f557(x94562,x94563,x94561)),f557(x94562,x94563,x94561))),x94563))+~P1(f777(f777(f234(f858(f857(x94561,x94561),a845)),x94563),f777(f777(f250(x94561,x94561),x94562),f777(f20(f858(x94561,a845),x94561),x94562)))) % 174.01/173.90 [9615]~P133(x96151)+~P116(x96151)+E(f777(f777(f285(x96151),f777(f107(x96151),f777(f777(f77(f857(a3,a3),a3,x96152,f242(a3,a3)),f209(x96152)),x96153))),f777(f107(x96151),f777(f777(f77(f857(a3,a3),a3,x96152,f252(a3,a3)),f209(x96152)),x96153))),f219(x96152,x96151,x96153)) % 174.01/173.90 [9811]~E(x98113,f4(a851))+~E(f777(f183(f852(x98111)),f777(f777(f155(f852(x98111)),x98112),f769(x98113,x98111,x98112))),x98113)+E(f777(f777(f145(a851,f852(x98111)),f777(f777(f11(a851,f852(a851),f852(x98111)),f777(f777(f12(f858(a851,x98111),f858(f852(a851),f852(x98111)),a851),f145(a851,x98111)),f777(f11(a851,a851,x98111),f777(f777(f12(f852(x98111),f858(a851,x98111),a851),f155(x98111)),f777(f155(f852(x98111)),x98112))))),f132(a851,f777(f296(a851,f4(a851)),f777(f183(f852(f852(x98111))),x98112))))),f132(a851,f777(f296(a851,f4(a851)),x98113))),f166(x98111,x98112)) % 174.01/173.90 [9812]E(x98121,f117(f852(x98122)))+~E(f777(f183(f852(x98122)),f777(f777(f155(f852(x98122)),x98121),f769(x98123,x98122,x98121))),x98123)+E(f777(f777(f145(a851,f852(x98122)),f777(f777(f11(a851,f852(a851),f852(x98122)),f777(f777(f12(f858(a851,x98122),f858(f852(a851),f852(x98122)),a851),f145(a851,x98122)),f777(f11(a851,a851,x98122),f777(f777(f12(f852(x98122),f858(a851,x98122),a851),f155(x98122)),f777(f155(f852(x98122)),x98121))))),f132(a851,f777(f296(a851,f4(a851)),f777(f183(f852(f852(x98122))),x98121))))),f132(a851,f777(f296(a851,f4(a851)),x98123))),f166(x98122,x98121)) % 174.01/173.90 [9813]~E(x98133,f4(a851))+E(f777(f777(f145(a851,f852(x98131)),f777(f777(f11(a851,f852(a851),f852(x98131)),f777(f777(f12(f858(a851,x98131),f858(f852(a851),f852(x98131)),a851),f145(a851,x98131)),f777(f11(a851,a851,x98131),f777(f777(f12(f852(x98131),f858(a851,x98131),a851),f155(x98131)),f777(f155(f852(x98131)),x98132))))),f132(a851,f777(f296(a851,f4(a851)),f777(f183(f852(f852(x98131))),x98132))))),f132(a851,f777(f296(a851,f4(a851)),x98133))),f166(x98131,x98132))+P1(f777(f777(f235(a851),f769(x98133,x98131,x98132)),f777(f183(f852(f852(x98131))),x98132))) % 174.01/173.90 [9814]E(x98141,f117(f852(x98142)))+E(f777(f777(f145(a851,f852(x98142)),f777(f777(f11(a851,f852(a851),f852(x98142)),f777(f777(f12(f858(a851,x98142),f858(f852(a851),f852(x98142)),a851),f145(a851,x98142)),f777(f11(a851,a851,x98142),f777(f777(f12(f852(x98142),f858(a851,x98142),a851),f155(x98142)),f777(f155(f852(x98142)),x98141))))),f132(a851,f777(f296(a851,f4(a851)),f777(f183(f852(f852(x98142))),x98141))))),f132(a851,f777(f296(a851,f4(a851)),x98143))),f166(x98142,x98141))+P1(f777(f777(f235(a851),f769(x98143,x98142,x98141)),f777(f183(f852(f852(x98142))),x98141))) % 174.01/173.90 [7671]E(f777(f777(f84(a851),f777(f108(a851),x76711)),f777(f777(f84(a851),f777(f108(a851),x76712)),x76713)),f777(f777(f84(a851),f777(f108(a851),f777(f777(f84(a3),x76711),x76712))),x76713))+P1(f777(a188,f777(f108(a3),x76711)))+P1(f777(a188,f777(f108(a3),x76712))) % 174.01/173.90 [8431]~P1(f777(f65(x84311),x84312))+~P1(f777(f777(f336(x84311),x84313),x84312))+E(f777(a116,f777(f44(x84311),f777(f777(f5(f858(x84311,a845)),x84312),f777(f777(f304(x84311),x84313),f182(f858(x84311,a845)))))),f777(f44(x84311),x84312)) % 174.01/173.90 [8451]~P1(f777(f65(x84511),x84512))+~P1(f777(f777(f336(x84511),x84513),x84512))+E(f777(f777(f84(a851),f82(a851)),f777(f44(x84511),f777(f777(f5(f858(x84511,a845)),x84512),f777(f777(f304(x84511),x84513),f182(f858(x84511,a845)))))),f777(f44(x84511),x84512)) % 174.01/173.90 [8535]~P100(x85351)+~P1(f777(f65(x85351),x85353))+E(f777(f777(f140(x85351,x85351,f9(x85351)),x85352),f132(x85351,f777(f777(f5(f858(x85351,a845)),x85353),f777(f777(f304(x85351),x85352),f182(f858(x85351,a845)))))),f132(x85351,f777(f777(f304(x85351),x85352),x85353))) % 174.01/173.90 [8673]~P1(f777(f65(x86731),x86733))+~P1(f777(f65(x86731),x86732))+E(f777(f777(f84(a851),f777(f44(x86731),f777(f777(f105(f858(x86731,a845)),x86732),x86733))),f777(f44(x86731),f777(f777(f106(f858(x86731,a845)),x86732),x86733))),f777(f777(f84(a851),f777(f44(x86731),x86732)),f777(f44(x86731),x86733))) % 174.01/173.90 [9760]~P29(x97601,f858(f858(x97601,a845),a845),f777(f777(f11(x97601,f858(f857(x97601,x97601),a845),f858(f858(x97601,a845),a845)),f777(f777(f12(f858(x97601,a845),f858(f858(f857(x97601,x97601),a845),f858(f858(x97601,a845),a845)),x97601),f63(x97601)),f777(f777(f11(x97601,f858(x97601,a845),f858(x97601,a845)),f304(x97601)),f182(f858(x97601,a845))))),x97603),x97602)+~P1(f777(f65(x97601),x97602))+E(f777(f44(f858(x97601,a845)),f777(f777(f63(x97601),x97602),x97603)),f777(f44(x97601),x97602)) % 174.01/173.90 [7943]~P88(x79431)+P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x79433)))+E(f777(f777(f244(x79431),x79432),f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),x79433),x79433)),a101))),f82(x79431)) % 174.01/173.90 [9304]~P88(x93041)+~P1(f777(f777(f234(a3),f4(a3)),f777(f108(a3),x93043)))+E(f777(f777(f244(x93041),x93042),f777(f108(a851),f777(f777(f5(a3),f777(f777(f84(a3),x93043),x93043)),a101))),f777(f777(f90(x93041,x93041),f777(f777(f244(x93041),x93042),f777(f108(a851),x93043))),f777(f777(f22(x93041,x93041,x93041),f777(f777(f12(x93041,f858(x93041,x93041),x93041),f85(x93041)),f777(f85(x93041),x93042))),f9(x93041)))) % 174.01/173.90 [9725]P1(f777(f777(f234(f858(f857(x97251,x97251),a845)),f302(x97251,x97252)),x97253))+~P1(f777(f777(f234(f858(f857(x97251,x97251),a845)),f302(x97251,f182(f858(f857(x97251,x97251),a845)))),x97253))+~P1(f777(f777(f234(f858(f857(x97251,x97251),a845)),f777(f777(f283(x97251,x97251,x97251),f777(f777(f106(f858(f857(x97251,x97251),a845)),f302(x97251,x97252)),x97253)),x97252)),x97253)) % 174.01/173.90 [9591]~P1(f777(f65(x95911),f777(f258(x95911),x95913)))+~P1(f777(f65(x95911),f777(f258(x95911),x95912)))+P1(f777(f65(x95911),f777(f258(x95911),f777(f777(f22(x95911,a845,a845),f777(f777(f12(a845,f858(a845,a845),x95911),a334),x95912)),x95913)))) % 174.01/173.90 [9879]P1(f777(f777(f234(f858(f857(x98791,x98791),a845)),f777(f777(f283(x98791,x98791,x98791),x98792),f302(x98791,x98792))),x98793))+~P1(f777(f777(f234(f858(f857(x98791,x98791),a845)),x98792),x98793))+~P1(f777(f777(f234(f858(f857(x98791,x98791),a845)),f777(f777(f283(x98791,x98791,x98791),f777(f777(f106(f858(f857(x98791,x98791),a845)),f777(f777(f283(x98791,x98791,x98791),x98792),f302(x98791,x98792))),x98793)),x98792)),x98793)) % 174.01/173.90 [9827]~P110(x98272)+E(x98271,f4(x98272))+~E(f777(f777(f84(x98272),f777(f777(f244(x98272),x98273),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x98272),x98271),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f4(x98272)) % 174.01/173.90 [9828]~P110(x98282)+E(x98281,f4(x98282))+~E(f777(f777(f84(x98282),f777(f777(f244(x98282),x98281),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x98282),x98283),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f4(x98282)) % 174.01/173.90 [9921]~P110(x99212)+E(x99211,f4(x99212))+P1(f777(f777(f235(x99212),f4(x99212)),f777(f777(f84(x99212),f777(f777(f244(x99212),x99213),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x99212),x99211),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))))) % 174.01/173.90 [9922]~P110(x99222)+E(x99221,f4(x99222))+P1(f777(f777(f235(x99222),f4(x99222)),f777(f777(f84(x99222),f777(f777(f244(x99222),x99221),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x99222),x99223),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))))) % 174.01/173.90 [9970]~P110(x99701)+P1(f777(f777(f234(x99701),f4(x99701)),x99702))+~P1(f777(f777(f234(x99701),f4(x99701)),f777(f777(f244(x99701),x99702),f777(a116,f777(f777(f85(a851),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),x99703))))) % 174.01/173.90 [5379]~P28(x53791,x53794,x53793)+P28(x53791,x53792,x53793)+~P28(x53791,x53792,x53794) % 174.01/173.90 [4848]~E(x48482,f94(x48483,x48481))+P1(f777(x48481,x48482))+~P1(f777(x48481,x48484)) % 174.01/173.90 [6622]~P36(x66222,x66224)+~P36(x66221,x66223)+P36(f857(x66221,x66222),f327(x66221,x66222,x66223,x66224)) % 174.01/173.90 [8014]~P39(f37(x80144,x80141),x80142,x80143,x80142)+P39(x80141,x80142,x80143,f799(x80143,x80142,x80141,x80144))+~P1(f777(x80144,x80142)) % 174.01/173.90 [8041]~P39(f37(x80411,x80412),x80414,x80413,x80414)+P39(f37(x80411,x80412),f799(x80413,x80414,x80412,x80411),x80413,x80414)+~P1(f777(x80411,x80414)) % 174.01/173.90 [5031]~P11(x50314,x50311)+~E(f777(x50311,x50312),f777(x50311,x50313))+P1(f777(f777(x50311,x50312),x50313)) % 174.01/173.90 [5195]~P11(x51954,x51951)+E(f777(x51951,x51952),f777(x51951,x51953))+~P1(f777(f777(x51951,x51952),x51953)) % 174.01/173.90 [5285]~P22(x52853,x52854,x52851)+E(f777(x52851,x52852),f777(f67(x52853,x52854),x52852))+~P1(f777(f65(x52853),x52852)) % 174.01/173.90 [5286]~P14(x52863,x52864,x52861)+E(f777(x52861,x52862),f777(f67(x52863,x52864),x52862))+~P1(f777(f65(x52863),x52862)) % 174.01/173.90 [5414]~P11(x54144,x54141)+~P1(f777(f777(x54141,x54143),x54142))+P1(f777(f777(x54141,x54142),x54143)) % 174.01/173.90 [5478]E(x54781,x54782)+~E(f777(f242(x54783,x54784),x54781),f777(f242(x54783,x54784),x54782))+~E(f777(f252(x54783,x54784),x54781),f777(f252(x54783,x54784),x54782)) % 174.01/173.90 [5504]E(x55041,x55042)+~P1(f777(f57(x55043,x55044),x55042))+~P1(f777(f57(x55043,x55044),x55041)) % 174.01/173.90 [5698]~P66(x56982)+E(f227(x56981,x56982,x56983,x56984),f4(x56982))+P1(f777(f65(x56981),x56984)) % 174.01/173.90 [5835]~P1(f777(f323(x58351,x58352),x58354))+P1(f777(f323(x58351,x58352),x58353))+~P1(f777(f777(x58352,x58353),x58354)) % 174.01/173.90 [8085]~P1(f777(f65(x80852),x80854))+~P1(f777(f65(x80851),x80853))+P1(f777(f65(f859(x80851,x80852)),f316(x80851,x80852,x80853,x80854))) % 174.01/173.90 [8088]P1(f777(f777(f336(f852(x80881)),f777(f777(f127(x80881),x80882),x80883)),f151(x80881,x80884)))+~P1(f777(f777(f336(f852(x80881)),x80883),f151(x80881,x80884)))+~P1(f777(f777(f336(f852(x80881)),x80882),f151(x80881,x80884))) % 174.01/173.90 [8663]~P1(f777(f777(f336(f857(x86631,x86631)),f777(f777(f243(x86631,x86631),x86632),x86634)),f302(x86631,x86633)))+P1(f777(f777(f336(x86631),x86632),f324(x86631,x86633)))+~P1(f777(f777(f336(x86631),x86634),f324(x86631,x86633))) % 174.01/173.90 [5014]~P66(x50142)+E(f777(f777(f10(x50141,x50142),x50143),x50144),f4(x50142))+P1(f777(f65(x50141),x50144)) % 174.01/173.90 [5017]~P70(x50172)+E(f777(f777(f13(x50171,x50172),x50173),x50174),f82(x50172))+P1(f777(f65(x50171),x50174)) % 174.01/173.90 [5164]~P3(x51643)+E(x51641,x51642)+~E(f777(f777(f84(x51643),x51644),x51641),f777(f777(f84(x51643),x51644),x51642)) % 174.01/173.90 [5165]~P4(x51653)+E(x51651,x51652)+~E(f777(f777(f84(x51653),x51654),x51651),f777(f777(f84(x51653),x51654),x51652)) % 174.01/173.90 [5167]~P3(x51673)+E(x51671,x51672)+~E(f777(f777(f84(x51673),x51671),x51674),f777(f777(f84(x51673),x51672),x51674)) % 174.01/173.90 [5254]~P112(x52541)+~E(x52543,f777(f777(f85(x52541),x52542),x52544))+P1(f777(f777(f281(x52541),x52542),x52543)) % 174.01/173.90 [5280]~P9(x52803)+E(x52801,f182(f858(x52802,a845)))+E(f777(f777(f48(x52802,x52803),x52801),f777(f20(x52803,x52802),x52804)),x52804) % 174.01/173.90 [5281]~P9(x52813)+E(x52811,f182(f858(x52812,a845)))+E(f777(f777(f49(x52812,x52813),x52811),f777(f20(x52813,x52812),x52814)),x52814) % 174.01/173.90 [5492]~P99(x54923)+E(x54921,x54922)+~E(f297(x54923,x54924,x54921),f777(f777(f304(x54923),x54922),f182(f858(x54923,a845)))) % 174.01/173.90 [5493]~P99(x54933)+E(x54931,x54932)+~E(f297(x54933,x54931,x54932),f777(f777(f304(x54933),x54934),f182(f858(x54933,a845)))) % 174.01/173.90 [5797]P1(f777(x57971,x57972))+~P1(f777(f247(x57973,x57971),x57974))+~P1(f777(f777(f336(x57973),x57972),x57974)) % 174.01/173.90 [5826]E(x58261,x58262)+~P1(f777(f777(f189(x58263),x58264),x58262))+~P1(f777(f777(f189(x58263),x58264),x58261)) % 174.01/173.90 [5908]~P66(x59081)+E(f777(f777(f10(a851,x59081),x59082),f777(f296(a851,x59083),f777(a116,x59084))),f4(x59081))+~P1(f777(f777(f235(a851),x59084),x59083)) % 174.01/173.90 [5913]~P8(x59131)+~E(f54(x59131,x59132,x59133),f54(x59131,x59134,x59133))+E(f54(x59131,f777(f83(x59131),x59132),x59133),f54(x59131,f777(f83(x59131),x59134),x59133)) % 174.01/173.90 [5982]P1(f777(x59821,x59822))+~E(f777(f128(x59823,x59821),x59824),x59824)+~P1(f777(f777(f336(x59823),x59822),f777(f160(x59823),x59824))) % 174.01/173.90 [6001]~E(f777(f777(f84(a851),x60013),x60012),f777(f777(f84(a851),x60011),x60014))+~P1(f777(f777(f235(a851),x60013),x60014))+P1(f777(f777(f235(a851),x60011),x60012)) % 174.01/173.90 [6008]~P7(x60081)+E(f54(x60081,f54(x60081,x60082,x60083),x60084),f54(x60081,x60082,x60084))+~P1(f777(f777(f281(x60081),x60084),x60083)) % 174.01/173.90 [6046]~E(f777(f128(x60461,x60462),x60463),f117(x60461))+~P1(f777(x60462,x60464))+~P1(f777(f777(f336(x60461),x60464),f777(f160(x60461),x60463))) % 174.01/173.90 [6047]~E(f164(x60473,x60471,x60474),x60474)+P1(f777(x60471,x60472))+~P1(f777(f777(f336(x60473),x60472),f777(f160(x60473),x60474))) % 174.01/173.90 [6082]~E(x60824,f182(f858(x60822,a845)))+~E(x60823,f182(f858(x60821,a845)))+E(f316(x60821,x60822,x60823,x60824),f182(f858(f859(x60821,x60822),a845))) % 174.01/173.90 [6516]~P66(x65161)+E(f777(f777(f10(a851,x65161),x65162),f297(a851,x65163,f777(a116,x65164))),f4(x65161))+~P1(f777(f777(f235(a851),f777(a116,x65164)),x65163)) % 174.01/173.90 [6665]~P100(x66651)+E(f777(f777(f5(f858(x66651,a845)),f777(f296(x66651,x66652),x66653)),f777(f296(x66651,x66652),x66654)),f777(f296(x66651,x66654),x66653))+~P1(f777(f777(f234(x66651),x66652),x66654)) % 174.01/173.90 [7027]~P1(f777(f777(f336(f852(x70271)),x70274),f151(x70271,x70273)))+P1(f777(f777(f336(x70271),x70272),x70273))+~P1(f777(f777(f336(x70271),x70272),f777(f160(x70271),x70274))) % 174.01/173.90 [7034]~P36(x70341,x70342)+P1(f777(f777(f336(x70341),f696(x70342,x70341,x70343)),x70343))+~P1(f777(f777(f336(x70341),x70344),x70343)) % 174.01/173.90 [7091]~P66(x70911)+E(f777(f777(f777(f69(x70911,x70912,f84(x70911)),x70913),f4(x70911)),x70914),f777(f777(f10(x70912,x70911),x70913),x70914))+~P1(f777(f65(x70912),x70914)) % 174.01/173.90 [7093]~P70(x70931)+E(f777(f777(f777(f69(x70931,x70932,f85(x70931)),x70933),f82(x70931)),x70934),f777(f777(f13(x70932,x70931),x70933),x70934))+~P1(f777(f65(x70932),x70934)) % 174.01/173.90 [7120]P29(x71201,x71202,x71203,x71204)+~E(f777(f44(x71202),f777(f305(x71201,x71202,x71203),x71204)),f777(f44(x71201),x71204))+~P1(f777(f65(x71201),x71204)) % 174.01/173.90 [7324]~P66(x73241)+E(f777(f777(f84(x73241),f777(x73242,x73243)),f777(f777(f10(a851,x73241),x73242),f299(a851,x73243,x73244))),f777(f777(f10(a851,x73241),x73242),f297(a851,x73243,x73244)))+~P1(f777(f777(f234(a851),x73243),x73244)) % 174.01/173.90 [7334]~P66(x73341)+~P29(x73342,x73341,x73343,x73344)+E(f777(f777(f10(x73341,x73341),f41(x73341)),f777(f305(x73342,x73341,x73343),x73344)),f777(f777(f10(x73342,x73341),x73343),x73344)) % 174.01/173.90 [7335]~P70(x73351)+~P29(x73352,x73351,x73353,x73354)+E(f777(f777(f13(x73351,x73351),f41(x73351)),f777(f305(x73352,x73351,x73353),x73354)),f777(f777(f13(x73352,x73351),x73353),x73354)) % 174.01/173.90 [7394]E(f777(f44(f859(x73941,x73942)),f316(x73941,x73942,x73943,x73944)),f777(f777(f84(a851),f777(f44(x73941),x73943)),f777(f44(x73942),x73944)))+~P1(f777(f65(x73942),x73944))+~P1(f777(f65(x73941),x73943)) % 174.01/173.90 [7479]E(x74791,x74792)+P1(f777(f777(f336(x74793),x74791),f777(f160(x74793),f153(x74793,x74792,x74794))))+~P1(f777(f777(f336(x74793),x74791),f777(f160(x74793),x74794))) % 174.01/173.90 [7705]~P66(x77051)+E(f777(f777(f84(x77051),f777(f777(f10(a851,x77051),x77052),f777(f296(a851,x77053),x77054))),f777(x77052,x77054)),f777(f777(f10(a851,x77051),x77052),f777(f296(a851,x77053),f777(a116,x77054))))+P1(f777(f777(f235(a851),x77054),x77053)) % 174.01/173.90 [7762]~P29(x77621,x77622,x77623,f241(f858(x77621,a845)))+~P1(f777(f65(x77622),x77624))+P1(f777(f65(x77621),f777(f307(x77621,x77622,x77623),x77624))) % 174.01/173.90 [7876]P1(f777(f777(f336(f852(x78761)),f777(f777(f142(x78761),x78762),x78763)),f151(x78761,x78764)))+~P1(f777(f777(f336(f852(x78761)),x78763),f151(x78761,x78764)))+~P1(f777(f777(f336(x78761),x78762),x78764)) % 174.01/173.90 [7967]~E(f777(f305(x79673,x79671,x79674),f241(f858(x79673,a845))),f241(f858(x79671,a845)))+P1(f777(f65(x79671),x79672))+~P1(f777(f65(x79673),f777(f307(x79673,x79671,x79674),x79672))) % 174.01/173.90 [8057]~P29(x80571,x80573,x80574,x80572)+P1(f777(f65(x80571),x80572))+~P1(f777(f65(x80573),f777(f305(x80571,x80573,x80574),x80572))) % 174.01/173.90 [8080]~E(x80802,x80803)+P1(f777(f777(f336(f857(x80801,x80801)),f777(f777(f243(x80801,x80801),x80802),x80803)),f262(x80801,x80804)))+~P1(f777(f777(f336(x80801),x80802),x80804)) % 174.01/173.90 [8111]~P66(x81111)+E(f777(f777(f84(x81111),f777(f777(f10(a851,x81111),x81112),f297(a851,x81113,x81114))),f777(x81112,f777(a116,x81114))),f777(f777(f10(a851,x81111),x81112),f297(a851,x81113,f777(a116,x81114))))+P1(f777(f777(f235(a851),f777(a116,x81114)),x81113)) % 174.01/173.90 [8174]P1(f777(x81741,x81742))+~P1(f777(x81741,f777(f777(f155(x81743),x81744),f727(x81741,x81744,x81743))))+~P1(f777(f777(f336(x81743),x81742),f777(f160(x81743),x81744))) % 174.01/173.90 [8308]~P1(f777(f777(f336(x83081),x83082),f324(x83081,x83084)))+P1(f777(f777(f336(f852(x83081)),f777(f777(f142(x83081),x83082),x83083)),f324(f852(x83081),f148(x83081,x83084))))+~P1(f777(f777(f336(f852(x83081)),x83083),f324(f852(x83081),f148(x83081,x83084)))) % 174.01/173.90 [8324]~P29(x83242,x83243,x83244,f689(x83244,x83243,x83242,x83241))+P29(x83242,x83243,x83244,f47(f858(x83242,a845),x83241))+E(x83241,f182(f858(f858(x83242,a845),a845))) % 174.01/173.90 [8585]E(x85851,x85852)+~P1(f777(f777(f336(f857(x85853,x85853)),f777(f777(f243(x85853,x85853),x85851),x85852)),f302(x85853,x85854)))+P1(f777(f777(f336(x85853),x85851),f777(f263(x85853,x85853),x85854))) % 174.01/173.90 [8832]P29(x88322,x88323,x88324,f47(f858(x88322,a845),x88321))+E(x88321,f182(f858(f858(x88322,a845),a845)))+P1(f777(f777(f336(f858(x88322,a845)),f689(x88324,x88323,x88322,x88321)),x88321)) % 174.01/173.90 [8960]P1(f777(f65(x89601),x89602))+~P1(f777(f65(x89604),f777(f305(x89601,x89604,x89603),x89602)))+P1(f777(f777(f336(x89601),f601(x89603,x89604,x89602,x89601)),x89602)) % 174.01/173.90 [9052]~P9(x90522)+E(f777(f777(f68(x90521,x90522,f777(f777(f12(x90522,f858(x90522,x90522),x90521),f105(x90522)),x90523)),f182(x90522)),x90524),f777(f777(f48(x90521,x90522),x90524),x90523))+~P1(f777(f65(x90521),x90524)) % 174.01/173.90 [9053]~P9(x90532)+E(f777(f777(f68(x90531,x90532,f777(f777(f12(x90532,f858(x90532,x90532),x90531),f106(x90532)),x90533)),f241(x90532)),x90534),f777(f777(f49(x90531,x90532),x90534),x90533))+~P1(f777(f65(x90531),x90534)) % 174.01/173.90 [9079]~P1(f777(f777(f281(a851),x90793),x90794))+P1(f777(f777(f281(a851),x90791),x90792))+P1(f777(f777(f235(f858(a851,a845)),f284(a851,f281(a851),x90791,x90792)),f284(a851,f281(a851),x90793,x90794))) % 174.01/173.90 [9090]~P1(f777(f777(f281(a851),x90902),x90904))+~P1(f777(f777(f281(a851),x90903),x90901))+P1(f777(f777(f234(f858(a851,a845)),f284(a851,f281(a851),x90901,x90902)),f284(a851,f281(a851),x90903,x90904))) % 174.01/173.90 [9148]E(x91481,x91482)+~P1(f777(f777(f336(f857(x91483,x91483)),f777(f777(f243(x91483,x91483),x91481),x91482)),f302(x91483,x91484)))+P1(f777(f777(f336(f857(x91483,x91483)),f777(f777(f243(x91483,x91483),x91481),x91482)),f777(f777(f283(x91483,x91483,x91483),x91484),f302(x91483,x91484)))) % 174.01/173.90 [9179]~E(f777(f183(f852(x91791)),x91792),f777(f183(f852(x91791)),x91793))+~P1(f777(f777(f336(f857(f852(x91791),f852(x91791))),f777(f777(f243(f852(x91791),f852(x91791)),x91792),x91793)),f139(x91791,x91794)))+P1(f777(f777(f336(f857(f852(x91791),f852(x91791))),f777(f777(f243(f852(x91791),f852(x91791)),x91792),x91793)),f137(x91791,x91794))) % 174.01/173.90 [9291]P1(f777(f777(f281(a851),x92911),x92912))+~P1(f777(f777(f281(a851),x92913),x92911))+~P1(f777(f777(f235(f858(a851,a845)),f284(a851,f281(a851),x92913,x92911)),f284(a851,f281(a851),x92914,x92912))) % 174.01/173.90 [9292]P1(f777(f777(f281(a851),x92921),x92922))+~P1(f777(f777(f281(a851),x92923),x92921))+~P1(f777(f777(f234(f858(a851,a845)),f284(a851,f281(a851),x92923,x92921)),f284(a851,f281(a851),x92924,x92922))) % 174.01/173.90 [9293]P1(f777(f777(f281(a851),x92931),x92932))+~P1(f777(f777(f281(a851),x92932),x92933))+~P1(f777(f777(f235(f858(a851,a845)),f284(a851,f281(a851),x92932,x92933)),f284(a851,f281(a851),x92931,x92934))) % 174.01/173.90 [9294]P1(f777(f777(f281(a851),x92941),x92942))+~P1(f777(f777(f281(a851),x92942),x92943))+~P1(f777(f777(f234(f858(a851,a845)),f284(a851,f281(a851),x92942,x92943)),f284(a851,f281(a851),x92941,x92944))) % 174.01/173.90 [9594]~P6(x95941)+E(f777(f777(f10(a851,x95941),f777(f777(f22(a851,x95941,x95941),f777(f777(f12(x95941,f858(x95941,x95941),a851),f5(x95941)),x95942)),f777(f777(f12(a851,x95941,a851),x95942),f777(f777(f11(a851,a851,a851),f84(a851)),f82(a851))))),f297(a851,x95943,x95944)),f4(x95941))+P1(f777(f777(f234(a851),x95943),x95944)) % 174.01/173.90 [9825]~P36(x98252,x98254)+~P29(x98252,x98251,x98253,f241(f858(x98252,a845)))+P36(x98251,f777(f305(f857(x98252,x98252),f857(x98251,x98251),f254(x98252,x98251,x98252,x98251,x98253,x98253)),x98254)) % 174.01/173.90 [9998]~E(f777(f183(f852(x99981)),x99983),f777(f183(f852(x99981)),x99982))+P1(f777(f777(f336(f857(f852(x99981),f852(x99981))),f777(f777(f243(f852(x99981),f852(x99981)),x99982),x99983)),f149(x99981,x99984)))+~P1(f777(f777(f253(x99981,x99981,a845),f777(f777(f11(x99981,f858(f857(x99981,x99981),a845),f858(x99981,a845)),f777(f777(f12(f858(x99981,f858(f858(f857(x99981,x99981),a845),a845)),f858(f858(f857(x99981,x99981),a845),f858(x99981,a845)),x99981),f11(x99981,f858(f857(x99981,x99981),a845),a845)),f777(f777(f12(f858(x99981,f857(x99981,x99981)),f858(x99981,f858(f858(f857(x99981,x99981),a845),a845)),x99981),f777(f12(f857(x99981,x99981),f858(f858(f857(x99981,x99981),a845),a845),x99981),f336(f857(x99981,x99981)))),f243(x99981,x99981)))),x99984)),f718(x99984,x99983,x99982,x99981))) % 174.01/173.90 [5872]~E(x58724,x58722)+P1(f777(x58721,x58722))+P1(f777(f777(f189(f37(x58721,x58723)),x58722),x58724)) % 174.01/173.90 [5966]~P7(x59661)+~E(x59662,f4(x59661))+E(f777(f777(f45(x59661),f777(f777(f85(x59661),x59662),x59663)),f777(f777(f85(x59661),x59662),x59664)),f4(x59661)) % 174.01/173.90 [6005]E(x60051,f117(x60052))+E(x60053,f777(f777(f5(a851),f777(f183(f852(x60052)),x60051)),f82(a851)))+E(f136(x60052,f777(f777(f150(x60052,x60051),x60053),x60054)),f136(x60052,x60051)) % 174.01/173.90 [6037]E(x60371,x60372)+P1(f777(x60373,x60372))+~P1(f777(f777(f777(f304(x60374),x60371),x60373),x60372)) % 174.01/173.90 [6051]~P66(x60511)+~P1(f777(f129(x60512),x60514))+E(f777(f157(x60511),f777(f777(f145(x60512,x60511),x60513),x60514)),f777(f777(f10(x60512,x60511),x60513),f777(f160(x60512),x60514))) % 174.01/173.90 [6075]~P70(x60752)+~P1(f777(f65(x60751),x60754))+E(f777(f777(f13(x60751,x60752),f777(f20(x60752,x60751),x60753)),x60754),f777(f777(f244(x60752),x60753),f777(f44(x60751),x60754))) % 174.01/173.90 [6129]~P7(x61292)+E(x61291,f4(x61292))+E(f777(f777(f45(x61292),f777(f777(f85(x61292),x61293),x61291)),f777(f777(f85(x61292),x61294),x61291)),f777(f777(f45(x61292),x61293),x61294)) % 174.01/173.90 [6131]~P60(x61312)+E(x61311,f4(x61312))+E(f777(f777(f285(x61312),f777(f777(f85(x61312),x61313),x61311)),f777(f777(f85(x61312),x61314),x61311)),f777(f777(f285(x61312),x61313),x61314)) % 174.01/173.90 [6132]~P60(x61322)+E(x61321,f4(x61322))+E(f777(f777(f285(x61322),f777(f777(f85(x61322),x61321),x61323)),f777(f777(f85(x61322),x61321),x61324)),f777(f777(f285(x61322),x61323),x61324)) % 174.01/173.90 [6133]~P7(x61332)+E(x61331,f4(x61332))+E(f777(f777(f45(x61332),f777(f777(f85(x61332),x61331),x61333)),f777(f777(f85(x61332),x61331),x61334)),f777(f777(f45(x61332),x61333),x61334)) % 174.01/173.90 [6199]P1(f777(x61991,x61992))+~E(x61993,f777(f777(f84(a851),x61994),x61992))+~P1(f777(x61991,f777(f777(f5(a851),x61993),x61994))) % 174.01/173.90 [6282]P32(x62821,x62822,x62823)+P31(x62821,f671(x62823,x62822,x62821),x62824)+~P1(f777(f777(f336(f850(x62821)),x62824),x62822)) % 174.01/173.90 [6328]E(x63281,f117(x63282))+~E(x63283,f777(f777(f5(a851),f777(f183(f852(x63282)),x63281)),f82(a851)))+E(f136(x63282,f777(f777(f150(x63282,x63281),x63283),x63284)),x63284) % 174.01/173.90 [6351]~P100(x63511)+~P1(f777(f777(f235(x63511),x63512),x63514))+P1(f777(f777(f235(x63511),x63512),f777(f777(f181(x63511),x63513),x63514))) % 174.01/173.90 [6353]~P100(x63531)+~P1(f777(f777(f235(x63531),x63532),x63533))+P1(f777(f777(f235(x63531),x63532),f777(f777(f181(x63531),x63533),x63534))) % 174.01/173.90 [6354]~P92(x63541)+~P1(f777(f777(f235(x63541),x63542),x63544))+P1(f777(f777(f235(x63541),x63542),f777(f777(f105(x63541),x63543),x63544))) % 174.01/173.90 [6355]~P92(x63551)+~P1(f777(f777(f235(x63551),x63552),x63553))+P1(f777(f777(f235(x63551),x63552),f777(f777(f105(x63551),x63553),x63554))) % 174.01/173.90 [6357]~P100(x63571)+~P1(f777(f777(f234(x63571),x63572),x63574))+P1(f777(f777(f234(x63571),x63572),f777(f777(f181(x63571),x63573),x63574))) % 174.01/173.90 [6359]~P100(x63591)+~P1(f777(f777(f234(x63591),x63592),x63593))+P1(f777(f777(f234(x63591),x63592),f777(f777(f181(x63591),x63593),x63594))) % 174.01/173.90 [6360]~P92(x63601)+~P1(f777(f777(f234(x63601),x63602),x63604))+P1(f777(f777(f234(x63601),x63602),f777(f777(f105(x63601),x63603),x63604))) % 174.01/173.90 [6361]~P92(x63611)+~P1(f777(f777(f234(x63611),x63612),x63613))+P1(f777(f777(f234(x63611),x63612),f777(f777(f105(x63611),x63613),x63614))) % 174.01/173.90 [6362]~P85(x63621)+~P1(f777(f777(f281(x63621),x63622),x63624))+P1(f777(f777(f281(x63621),x63622),f777(f777(f85(x63621),x63623),x63624))) % 174.01/173.90 [6363]~P85(x63631)+~P1(f777(f777(f281(x63631),x63632),x63633))+P1(f777(f777(f281(x63631),x63632),f777(f777(f85(x63631),x63633),x63634))) % 174.01/173.90 [6458]~E(f777(f777(f155(x64581),x64582),x64583),x64584)+E(f777(f777(f150(x64581,x64582),x64583),x64584),x64582)+~P1(f777(f777(f235(a851),x64583),f777(f183(f852(x64581)),x64582))) % 174.01/173.90 [6478]E(x64781,x64782)+P1(f777(x64783,x64781))+~P1(f777(f777(f189(f37(x64783,x64784)),x64781),x64782)) % 174.01/173.90 [6499]P1(f777(x64991,x64992))+~P1(f777(x64993,x64992))+~P1(f777(f777(f234(f858(x64994,a845)),x64993),x64991)) % 174.01/173.90 [6535]~E(f777(f777(f150(x65351,x65352),x65353),x65354),x65352)+E(f777(f777(f155(x65351),x65352),x65353),x65354)+~P1(f777(f777(f235(a851),x65353),f777(f183(f852(x65351)),x65352))) % 174.01/173.90 [6653]P31(x66531,x66532,x66533)+~P31(x66531,f777(a116,x66532),f824(x66532,x66534,x66531))+~P1(f777(f777(f336(f850(x66531)),x66533),x66534)) % 174.01/173.90 [6662]E(x66621,f182(f858(x66622,a845)))+E(x66623,f182(f858(x66624,a845)))+~E(f777(f777(f250(x66624,x66622),x66623),f777(f20(f858(x66622,a845),x66624),x66621)),f182(f858(f857(x66624,x66622),a845))) % 174.01/173.90 [6680]E(x66801,x66802)+P1(f777(f777(f336(x66803),x66801),x66804))+~P1(f777(f777(f336(x66803),x66801),f777(f777(f304(x66803),x66802),x66804))) % 174.01/173.90 [6697]~P100(x66971)+P1(f777(f777(f235(x66971),x66972),x66973))+~P1(f777(f777(f235(x66971),x66972),f777(f777(f238(x66971),x66974),x66973))) % 174.01/173.90 [6698]~P100(x66981)+P1(f777(f777(f235(x66981),x66982),x66983))+~P1(f777(f777(f235(x66981),x66982),f777(f777(f238(x66981),x66983),x66984))) % 174.01/173.90 [6700]~P100(x67001)+P1(f777(f777(f234(x67001),x67002),x67003))+~P1(f777(f777(f234(x67001),x67002),f777(f777(f238(x67001),x67004),x67003))) % 174.01/173.90 [6702]~P100(x67021)+P1(f777(f777(f234(x67021),x67022),x67023))+~P1(f777(f777(f234(x67021),x67022),f777(f777(f238(x67021),x67023),x67024))) % 174.01/173.90 [6704]~P98(x67041)+P1(f777(f777(f234(x67041),x67042),x67043))+~P1(f777(f777(f234(x67041),x67042),f777(f777(f106(x67041),x67044),x67043))) % 174.01/173.90 [6706]~P98(x67061)+P1(f777(f777(f234(x67061),x67062),x67063))+~P1(f777(f777(f234(x67061),x67062),f777(f777(f106(x67061),x67063),x67064))) % 174.01/173.90 [6728]~E(f777(f777(f155(x67281),x67283),x67284),x67282)+P1(f777(f777(f336(x67281),x67282),f777(f160(x67281),x67283)))+~P1(f777(f777(f235(a851),x67284),f777(f183(f852(x67281)),x67283))) % 174.01/173.90 [6740]~P100(x67401)+~P18(x67401,f777(f777(f142(x67401),x67402),f777(f777(f142(x67401),x67403),x67404)))+P1(f777(f777(f234(x67401),x67402),x67403)) % 174.01/173.90 [6910]E(x69101,f4(a3))+E(f777(f777(f45(a3),x69102),x69101),x69103)+~P1(f777(f58(x69102,x69101),f777(f777(f243(a3,a3),x69103),x69104))) % 174.01/173.90 [6933]E(f54(a3,x69332,x69331),x69333)+E(x69331,f4(a3))+~P1(f777(f58(x69332,x69331),f777(f777(f243(a3,a3),x69334),x69333))) % 174.01/173.90 [7048]P1(f777(f777(f336(x70481),x70482),x70483))+~P1(f777(f777(f336(x70481),x70482),x70484))+~P1(f777(f777(f235(f858(x70481,a845)),x70484),x70483)) % 174.01/173.90 [7052]P1(f777(f777(f336(x70521),x70522),x70523))+~P1(f777(f777(f336(x70521),x70522),x70524))+~P1(f777(f777(f234(f858(x70521,a845)),x70524),x70523)) % 174.01/173.90 [7062]~P111(x70621)+~E(x70623,f4(x70621))+P1(f777(f777(f281(x70621),f777(f777(f85(x70621),x70622),x70623)),f777(f777(f85(x70621),x70624),x70623))) % 174.01/173.90 [7063]~P111(x70631)+~E(x70632,f4(x70631))+P1(f777(f777(f281(x70631),f777(f777(f85(x70631),x70632),x70633)),f777(f777(f85(x70631),x70632),x70634))) % 174.01/173.90 [7288]~P102(x72882)+~P1(f777(f777(f235(f858(x72881,x72882)),x72883),x72884))+P1(f777(f777(f234(f858(x72881,x72882)),x72883),x72884)) % 174.01/173.90 [7383]~P28(x73831,x73832,x73834)+P28(x73831,x73832,f777(f777(f304(f850(x73831)),x73833),x73834))+~P28(x73831,x73832,f777(f777(f304(f850(x73831)),x73833),f182(f858(f850(x73831),a845)))) % 174.01/173.90 [7422]~P1(f777(f777(f336(x74221),x74222),x74224))+P1(f777(f777(f336(x74221),x74222),f46(f858(x74221,a845),x74223)))+~P1(f777(f777(f336(f858(x74221,a845)),x74224),x74223)) % 174.01/173.90 [7424]~P85(x74241)+~P1(f777(f777(f234(a851),x74243),x74244))+P1(f777(f777(f281(x74241),f777(f777(f244(x74241),x74242),x74243)),f777(f777(f244(x74241),x74242),x74244))) % 174.01/173.90 [7435]P31(x74351,x74352,x74353)+P1(f777(f777(f336(f850(x74351)),f824(x74352,x74354,x74351)),x74354))+~P1(f777(f777(f336(f850(x74351)),x74353),x74354)) % 174.01/173.90 [7454]~P74(x74541)+~P1(f777(f777(f235(x74541),x74543),x74544))+P1(f777(f777(f235(x74541),f777(f777(f84(x74541),x74542),x74543)),f777(f777(f84(x74541),x74542),x74544))) % 174.01/173.90 [7455]~P80(x74551)+~P1(f777(f777(f235(x74551),x74553),x74554))+P1(f777(f777(f235(x74551),f777(f777(f84(x74551),x74552),x74553)),f777(f777(f84(x74551),x74552),x74554))) % 174.01/173.90 [7456]~P74(x74561)+~P1(f777(f777(f235(x74561),x74562),x74564))+P1(f777(f777(f235(x74561),f777(f777(f84(x74561),x74562),x74563)),f777(f777(f84(x74561),x74564),x74563))) % 174.01/173.90 [7457]~P80(x74571)+~P1(f777(f777(f235(x74571),x74572),x74574))+P1(f777(f777(f235(x74571),f777(f777(f84(x74571),x74572),x74573)),f777(f777(f84(x74571),x74574),x74573))) % 174.01/173.90 [7458]~P74(x74581)+~P1(f777(f777(f234(x74581),x74583),x74584))+P1(f777(f777(f234(x74581),f777(f777(f84(x74581),x74582),x74583)),f777(f777(f84(x74581),x74582),x74584))) % 174.01/173.90 [7459]~P78(x74591)+~P1(f777(f777(f234(x74591),x74593),x74594))+P1(f777(f777(f234(x74591),f777(f777(f84(x74591),x74592),x74593)),f777(f777(f84(x74591),x74592),x74594))) % 174.01/173.90 [7460]~P74(x74601)+~P1(f777(f777(f234(x74601),x74602),x74604))+P1(f777(f777(f234(x74601),f777(f777(f84(x74601),x74602),x74603)),f777(f777(f84(x74601),x74604),x74603))) % 174.01/173.90 [7461]~P78(x74611)+~P1(f777(f777(f234(x74611),x74612),x74614))+P1(f777(f777(f234(x74611),f777(f777(f84(x74611),x74612),x74613)),f777(f777(f84(x74611),x74614),x74613))) % 174.01/173.90 [7462]~P111(x74621)+~P1(f777(f777(f281(x74621),x74623),x74624))+P1(f777(f777(f281(x74621),f777(f777(f85(x74621),x74622),x74623)),f777(f777(f85(x74621),x74622),x74624))) % 174.01/173.90 [7463]~P111(x74631)+~P1(f777(f777(f281(x74631),x74632),x74634))+P1(f777(f777(f281(x74631),f777(f777(f85(x74631),x74632),x74633)),f777(f777(f85(x74631),x74634),x74633))) % 174.01/173.90 [7464]~P85(x74641)+~P1(f777(f777(f281(x74641),x74642),x74644))+P1(f777(f777(f281(x74641),f777(f777(f244(x74641),x74642),x74643)),f777(f777(f244(x74641),x74644),x74643))) % 174.01/173.90 [7473]~P135(x74731)+~P89(x74731)+E(f777(f777(f84(x74731),f777(f777(f85(x74731),x74732),f777(f108(x74731),x74733))),f777(f777(f85(x74731),x74734),f777(f108(x74731),x74733))),f777(f777(f85(x74731),f777(f777(f84(x74731),x74732),x74734)),f777(f108(x74731),x74733))) % 174.01/173.90 [7474]~P121(x74741)+~P89(x74741)+E(f777(f777(f5(x74741),f777(f777(f85(x74741),x74742),f777(f108(x74741),x74743))),f777(f777(f85(x74741),x74744),f777(f108(x74741),x74743))),f777(f777(f85(x74741),f777(f777(f5(x74741),x74742),x74744)),f777(f108(x74741),x74743))) % 174.01/173.90 [7510]~P66(x75101)+E(f777(f777(f84(x75101),f777(x75102,x75103)),f777(f777(f10(a851,x75101),x75102),f297(a851,f777(a116,x75103),x75104))),f777(f777(f10(a851,x75101),x75102),f297(a851,x75103,x75104)))+~P1(f777(f777(f234(a851),x75103),x75104)) % 174.01/173.90 [7521]~P29(x75212,x75211,x75213,f777(f160(x75212),x75214))+~P1(f777(f129(x75212),x75214))+P1(f777(f129(x75211),f777(f777(f145(x75212,x75211),x75213),x75214))) % 174.01/173.90 [7570]~P1(f777(f777(f235(a851),x75702),x75704))+~P1(f777(f777(f235(a851),x75701),x75703))+P1(f777(f777(f235(a851),f777(f777(f84(a851),x75701),x75702)),f777(f777(f84(a851),x75703),x75704))) % 174.01/173.90 [7573]~P1(f777(f777(f235(a3),x75731),x75733))+~P1(f777(f777(f234(a3),x75732),x75734))+P1(f777(f777(f235(a3),f777(f777(f84(a3),x75731),x75732)),f777(f777(f84(a3),x75733),x75734))) % 174.01/173.90 [7574]~P1(f777(f777(f234(a851),x75742),x75744))+~P1(f777(f777(f234(a851),x75741),x75743))+P1(f777(f777(f234(a851),f777(f777(f84(a851),x75741),x75742)),f777(f777(f84(a851),x75743),x75744))) % 174.01/173.90 [7575]~P1(f777(f777(f234(a851),x75752),x75754))+~P1(f777(f777(f234(a851),x75751),x75753))+P1(f777(f777(f234(a851),f777(f777(f85(a851),x75751),x75752)),f777(f777(f85(a851),x75753),x75754))) % 174.01/173.90 [7625]P1(f777(f777(f336(x76251),x76252),x76253))+~P1(f777(f777(f336(x76251),x76252),f47(f858(x76251,a845),x76254)))+~P1(f777(f777(f336(f858(x76251,a845)),x76253),x76254)) % 174.01/173.90 [7641]~P1(f777(x76411,f726(x76411,x76413,x76412)))+P1(f777(x76411,f777(f777(f155(x76412),x76413),x76414)))+~P1(f777(f777(f235(a851),x76414),f777(f183(f852(x76412)),x76413))) % 174.01/173.90 [7645]P1(f777(x76451,x76452))+~P1(f777(f777(f336(x76454),x76452),f777(f160(x76454),x76453)))+P1(f777(f777(f235(a851),f727(x76451,x76453,x76454)),f777(f183(f852(x76454)),x76453))) % 174.01/173.90 [7664]~P1(f777(f777(f189(x76642),x76643),x76644))+~P1(f777(f777(f189(f37(x76641,x76642)),x76644),x76643))+P1(f777(f777(f189(f37(x76641,x76642)),x76643),x76643)) % 174.01/173.90 [7692]~P102(x76921)+~P1(f777(f777(f234(f858(x76922,x76921)),x76924),x76923))+~P1(f777(f777(f235(f858(x76922,x76921)),x76923),x76924)) % 174.01/173.90 [7735]~P1(f777(x77354,x77352))+~P1(f777(f777(f336(x77351),x77352),x77353))+P1(f777(f777(f336(x77351),x77352),f777(f777(f106(f858(x77351,a845)),x77353),f777(f258(x77351),x77354)))) % 174.01/173.90 [7884]~P1(f777(f777(f336(x78841),x78843),x78844))+~P1(f777(f777(f235(f858(x78841,a845)),x78842),x78844))+P1(f777(f777(f235(f858(x78841,a845)),x78842),f777(f777(f304(x78841),x78843),x78844))) % 174.01/173.90 [7886]E(f777(f777(f106(f858(x78861,a845)),x78862),x78863),f182(f858(x78861,a845)))+~E(f777(f777(f106(f858(x78861,a845)),f46(f858(x78861,a845),x78864)),x78863),f182(f858(x78861,a845)))+~P1(f777(f777(f336(f858(x78861,a845)),x78862),x78864)) % 174.01/173.90 [7963]P1(f777(f777(f336(x79631),x79632),x79633))+~P1(f777(f777(f234(f858(x79631,a845)),x79633),f777(f777(f304(x79631),x79632),x79634)))+P1(f777(f777(f234(f858(x79631,a845)),x79633),x79634)) % 174.01/173.90 [7983]P1(f777(f777(f336(x79832),f726(x79831,x79833,x79832)),f777(f160(x79832),x79833)))+P1(f777(x79831,f777(f777(f155(x79832),x79833),x79834)))+~P1(f777(f777(f235(a851),x79834),f777(f183(f852(x79832)),x79833))) % 174.01/173.90 [7991]~P1(f777(f777(f235(f858(x79911,a845)),x79912),x79914))+P1(f777(f777(f235(f858(x79911,a845)),x79912),x79913))+~P1(f777(f777(f235(f858(x79911,a845)),x79914),x79913)) % 174.01/173.90 [7992]~P1(f777(f777(f234(f858(x79921,a845)),x79922),x79924))+P1(f777(f777(f235(f858(x79921,a845)),x79922),x79923))+~P1(f777(f777(f235(f858(x79921,a845)),x79924),x79923)) % 174.01/173.90 [7993]~P1(f777(f777(f234(f858(x79931,a845)),x79934),x79933))+~P1(f777(f777(f235(f858(x79931,a845)),x79932),x79934))+P1(f777(f777(f235(f858(x79931,a845)),x79932),x79933)) % 174.01/173.90 [7994]~P1(f777(f777(f234(f858(x79941,a845)),x79942),x79944))+P1(f777(f777(f234(f858(x79941,a845)),x79942),x79943))+~P1(f777(f777(f234(f858(x79941,a845)),x79944),x79943)) % 174.01/173.90 [8030]~P1(f777(f777(f336(x80301),x80304),x80303))+~P1(f777(f777(f235(f858(x80301,a845)),x80302),f777(f777(f304(x80301),x80304),x80303)))+P1(f777(f777(f235(f858(x80301,a845)),x80302),x80303)) % 174.01/173.90 [8043]~P74(x80431)+P1(f777(f777(f235(x80431),x80432),x80433))+~P1(f777(f777(f235(x80431),f777(f777(f84(x80431),x80434),x80432)),f777(f777(f84(x80431),x80434),x80433))) % 174.01/173.90 [8045]~P74(x80451)+P1(f777(f777(f235(x80451),x80452),x80453))+~P1(f777(f777(f235(x80451),f777(f777(f84(x80451),x80452),x80454)),f777(f777(f84(x80451),x80453),x80454))) % 174.01/173.90 [8047]~P74(x80471)+P1(f777(f777(f234(x80471),x80472),x80473))+~P1(f777(f777(f234(x80471),f777(f777(f84(x80471),x80474),x80472)),f777(f777(f84(x80471),x80474),x80473))) % 174.01/173.90 [8049]~P74(x80491)+P1(f777(f777(f234(x80491),x80492),x80493))+~P1(f777(f777(f234(x80491),f777(f777(f84(x80491),x80492),x80494)),f777(f777(f84(x80491),x80493),x80494))) % 174.01/173.90 [8213]P1(f777(x82131,x82132))+~P1(f777(f777(f336(x82133),x82132),f777(f160(x82133),x82134)))+P1(f777(f777(f235(a851),f777(f183(f852(x82133)),f777(f128(x82133,x82131),x82134))),f777(f183(f852(x82133)),x82134))) % 174.01/173.90 [8343]E(x83431,x83432)+P1(f777(f777(f189(x83433),x83431),f424(x83432,x83431,x83433,x83434)))+~P1(f777(f777(f189(f37(x83434,x83433)),x83431),x83432)) % 174.01/173.90 [8344]E(x83441,x83442)+P1(f777(f777(f189(x83443),x83441),f530(x83442,x83441,x83443,x83444)))+~P1(f777(f777(f189(f37(x83444,x83443)),x83441),x83442)) % 174.01/173.90 [8371]~P1(f777(x83714,x83712))+P1(f777(f777(f189(x83711),x83712),f424(x83713,x83712,x83711,x83714)))+~P1(f777(f777(f189(f37(x83714,x83711)),x83712),x83713)) % 174.01/173.90 [8372]~P1(f777(x83724,x83722))+P1(f777(f777(f189(x83721),x83722),f530(x83723,x83722,x83721,x83724)))+~P1(f777(f777(f189(f37(x83724,x83721)),x83722),x83723)) % 174.01/173.90 [8696]~P29(x86964,x86963,x86961,f241(f858(x86964,a845)))+E(f777(x86961,f525(x86962,x86961,x86963,x86964)),x86962)+~P1(f777(f777(f336(x86963),x86962),f777(f305(x86964,x86963,x86961),f241(f858(x86964,a845))))) % 174.01/173.90 [8834]~P1(f777(f65(x88341),x88344))+P1(f777(f777(f336(x88341),f563(x88342,x88343,x88344,x88341)),x88344))+P1(f777(f65(f857(x88341,x88343)),f777(f777(f250(x88341,x88343),x88344),x88342))) % 174.01/173.90 [8878]E(x88781,x88782)+P1(f777(f777(f189(f37(x88783,x88784)),f424(x88781,x88782,x88784,x88783)),x88781))+~P1(f777(f777(f189(f37(x88783,x88784)),x88782),x88781)) % 174.01/173.90 [8879]E(x88791,x88792)+P1(f777(f777(f189(f37(x88793,x88794)),f530(x88791,x88792,x88794,x88793)),x88791))+~P1(f777(f777(f189(f37(x88793,x88794)),x88792),x88791)) % 174.01/173.90 [8899]~P1(f777(x88991,x88994))+P1(f777(f777(f189(f37(x88991,x88992)),f424(x88993,x88994,x88992,x88991)),x88993))+~P1(f777(f777(f189(f37(x88991,x88992)),x88994),x88993)) % 174.01/173.90 [8900]~P1(f777(x89001,x89004))+P1(f777(f777(f189(f37(x89001,x89002)),f530(x89003,x89004,x89002,x89001)),x89003))+~P1(f777(f777(f189(f37(x89001,x89002)),x89004),x89003)) % 174.01/173.90 [9139]~P1(f777(f65(x91391),x91393))+~P1(f777(f65(x91392),f777(x91394,f563(x91394,x91392,x91393,x91391))))+P1(f777(f65(f857(x91391,x91392)),f777(f777(f250(x91391,x91392),x91393),x91394))) % 174.01/173.90 [9153]~E(f777(f183(f852(x91534)),x91532),f777(f183(f852(x91534)),x91533))+P1(f777(f777(f336(f857(f852(x91534),f852(x91534))),f777(f777(f243(f852(x91534),f852(x91534)),x91533),x91532)),f149(x91534,x91531)))+P1(f777(f777(f235(a851),f734(x91531,x91532,x91533,x91534)),f777(f183(f852(x91534)),x91533))) % 174.01/173.90 [9266]E(f777(f777(f161(x92661),f741(x92662,x92663,x92664,x92661)),x92663),f777(f777(f161(x92661),f741(x92662,x92663,x92664,x92661)),x92664))+~P1(f777(f777(f336(f857(f852(x92661),f852(x92661))),f777(f777(f243(f852(x92661),f852(x92661)),x92664),x92663)),f139(x92661,x92662)))+P1(f777(f777(f235(a851),f777(f183(f852(x92661)),x92664)),f777(f183(f852(x92661)),x92663))) % 174.01/173.90 [9324]~P1(f777(f777(f235(a851),f4(a851)),x93243))+~P1(f777(f777(f235(a851),x93244),x93241))+P1(f777(f777(f235(a851),f777(f777(f84(a851),f777(f777(f85(a851),x93241),f54(a851,x93242,x93243))),x93244)),f777(f777(f85(a851),x93241),x93243))) % 174.01/173.90 [9506]~P102(x95062)+~P1(f777(f777(f234(x95062),f777(x95063,f706(x95064,x95063,x95061,x95062))),f777(x95064,f706(x95064,x95063,x95061,x95062))))+P1(f777(f777(f234(f858(x95061,x95062)),x95063),x95064)) % 174.01/173.90 [9597]~P6(x95971)+E(f777(f777(f10(a851,x95971),f777(f777(f22(a851,x95971,x95971),f777(f777(f12(x95971,f858(x95971,x95971),a851),f5(x95971)),x95972)),f777(f777(f12(a851,x95971,a851),x95972),f777(f777(f11(a851,a851,a851),f84(a851)),f82(a851))))),f297(a851,x95973,x95974)),f777(f777(f5(x95971),f777(x95972,x95973)),f777(x95972,f777(f777(f84(a851),x95974),f82(a851)))))+~P1(f777(f777(f234(a851),x95973),x95974)) % 174.01/173.90 [6642]~P7(x66421)+E(f777(f777(f45(x66421),f777(f777(f85(x66421),x66422),x66423)),x66424),f777(f777(f85(x66421),x66422),f777(f777(f45(x66421),x66423),x66424)))+~P1(f777(f777(f281(x66421),x66424),x66423)) % 174.01/173.90 [6732]E(f777(f777(f127(x67321),x67322),x67323),x67324)+~E(x67323,f777(f777(f130(x67321),f777(f183(f852(x67321)),x67322)),x67324))+~E(f777(f777(f161(x67321),f777(f183(f852(x67321)),x67322)),x67324),x67322) % 174.01/173.90 [6793]~P61(x67932)+E(x67931,f4(x67932))+E(f777(f777(f285(x67932),f777(f777(f244(x67932),x67933),x67934)),f777(f777(f244(x67932),x67931),x67934)),f777(f777(f244(x67932),f777(f777(f285(x67932),x67933),x67931)),x67934)) % 174.01/173.90 [6943]~P7(x69431)+E(f777(f777(f45(x69431),f777(f777(f85(x69431),x69432),x69433)),x69434),f777(f777(f85(x69431),f777(f777(f45(x69431),x69432),x69434)),x69433))+~P1(f777(f777(f281(x69431),x69434),x69432)) % 174.01/173.90 [6953]~P100(x69531)+~P1(f777(f777(f235(x69531),x69533),x69534))+P1(f777(f777(f235(x69531),f777(f777(f238(x69531),x69532),x69533)),x69534)) % 174.01/173.90 [6955]~P100(x69551)+~P1(f777(f777(f235(x69551),x69552),x69554))+P1(f777(f777(f235(x69551),f777(f777(f238(x69551),x69552),x69553)),x69554)) % 174.01/173.90 [6956]~P98(x69561)+~P1(f777(f777(f235(x69561),x69563),x69564))+P1(f777(f777(f235(x69561),f777(f777(f106(x69561),x69562),x69563)),x69564)) % 174.01/173.90 [6957]~P98(x69571)+~P1(f777(f777(f235(x69571),x69572),x69574))+P1(f777(f777(f235(x69571),f777(f777(f106(x69571),x69572),x69573)),x69574)) % 174.01/173.90 [6959]~P100(x69591)+~P1(f777(f777(f234(x69591),x69593),x69594))+P1(f777(f777(f234(x69591),f777(f777(f238(x69591),x69592),x69593)),x69594)) % 174.01/173.90 [6961]~P100(x69611)+~P1(f777(f777(f234(x69611),x69612),x69614))+P1(f777(f777(f234(x69611),f777(f777(f238(x69611),x69612),x69613)),x69614)) % 174.01/173.90 [6962]~P98(x69621)+~P1(f777(f777(f234(x69621),x69623),x69624))+P1(f777(f777(f234(x69621),f777(f777(f106(x69621),x69622),x69623)),x69624)) % 174.01/173.90 [6963]~P98(x69631)+~P1(f777(f777(f234(x69631),x69632),x69634))+P1(f777(f777(f234(x69631),f777(f777(f106(x69631),x69632),x69633)),x69634)) % 174.01/173.90 [6980]~P1(f777(x69803,x69804))+~P1(f777(x69802,x69804))+P1(f777(f777(f777(f106(f858(x69801,a845)),x69802),x69803),x69804)) % 174.01/173.90 [7012]~E(f777(f183(f852(x70121)),x70123),f777(f183(f852(x70122)),x70124))+~P1(f777(f129(x70121),x70123))+E(f171(x70121,x70122,f168(x70121,x70122,f777(f777(f169(x70121,x70122),x70123),x70124))),f777(f160(x70121),x70123)) % 174.01/173.90 [7106]P28(x71061,x71062,x71063)+~P28(x71061,x71064,x71063)+~P1(f777(f777(f234(f858(f850(x71061),a845)),x71064),x71062)) % 174.01/173.90 [7107]P28(x71071,x71072,x71073)+~P28(x71071,x71072,x71074)+~P1(f777(f777(f234(f858(f850(x71071),a845)),x71073),x71074)) % 174.01/173.90 [7245]~P7(x72451)+E(f777(f777(f45(x72451),f777(f777(f244(x72451),x72452),x72453)),f777(f777(f244(x72451),x72454),x72453)),f777(f777(f244(x72451),f777(f777(f45(x72451),x72452),x72454)),x72453))+~P1(f777(f777(f281(x72451),x72454),x72452)) % 174.01/173.90 [7500]~P66(x75001)+E(f777(f777(f84(x75001),f777(x75002,x75003)),f777(f777(f10(a851,x75001),x75002),f777(f296(a851,f777(a116,x75003)),x75004))),f777(f777(f10(a851,x75001),x75002),f777(f296(a851,x75003),x75004)))+~P1(f777(f777(f235(a851),x75003),x75004)) % 174.01/173.90 [7528]~P100(x75281)+P1(f777(f777(f235(x75281),x75282),x75283))+~P1(f777(f777(f235(x75281),f777(f777(f181(x75281),x75284),x75282)),x75283)) % 174.01/173.90 [7529]~P100(x75291)+P1(f777(f777(f235(x75291),x75292),x75293))+~P1(f777(f777(f235(x75291),f777(f777(f181(x75291),x75292),x75294)),x75293)) % 174.01/173.90 [7531]~P100(x75311)+P1(f777(f777(f234(x75311),x75312),x75313))+~P1(f777(f777(f234(x75311),f777(f777(f181(x75311),x75314),x75312)),x75313)) % 174.01/173.90 [7533]~P100(x75331)+P1(f777(f777(f234(x75331),x75332),x75333))+~P1(f777(f777(f234(x75331),f777(f777(f181(x75331),x75332),x75334)),x75333)) % 174.01/173.90 [7535]~P92(x75351)+P1(f777(f777(f234(x75351),x75352),x75353))+~P1(f777(f777(f234(x75351),f777(f777(f105(x75351),x75354),x75352)),x75353)) % 174.01/173.90 [7537]~P92(x75371)+P1(f777(f777(f234(x75371),x75372),x75373))+~P1(f777(f777(f234(x75371),f777(f777(f105(x75371),x75372),x75374)),x75373)) % 174.01/173.90 [7538]~P85(x75381)+P1(f777(f777(f281(x75381),x75382),x75383))+~P1(f777(f777(f281(x75381),f777(f777(f85(x75381),x75384),x75382)),x75383)) % 174.01/173.90 [7539]~P85(x75391)+P1(f777(f777(f281(x75391),x75392),x75393))+~P1(f777(f777(f281(x75391),f777(f777(f85(x75391),x75392),x75394)),x75393)) % 174.01/173.90 [7617]~P1(f777(f777(f336(x76171),x76172),x76174))+P1(f777(f777(f336(x76171),x76172),x76173))+P1(f777(f777(f336(x76171),x76172),f777(f777(f5(f858(x76171,a845)),x76174),x76173))) % 174.01/173.90 [7697]P1(f777(x76971,x76972))+P1(f777(x76973,x76972))+~P1(f777(f777(f777(f105(f858(x76974,a845)),x76973),x76971),x76972)) % 174.01/173.90 [7707]~P1(f777(f777(f336(x77071),x77072),x77074))+~P1(f777(f777(f336(x77071),x77072),x77073))+P1(f777(f777(f336(x77071),x77072),f777(f777(f106(f858(x77071,a845)),x77073),x77074))) % 174.01/173.90 [7763]~P100(x77631)+~P1(f777(f65(x77631),x77634))+E(f777(f777(f68(x77631,x77631,f238(x77631)),x77632),f777(f777(f304(x77631),x77633),x77634)),f777(f777(f238(x77631),x77633),f777(f777(f68(x77631,x77631,f238(x77631)),x77632),x77634))) % 174.01/173.90 [7764]~P100(x77641)+~P1(f777(f65(x77641),x77644))+E(f777(f777(f68(x77641,x77641,f181(x77641)),x77642),f777(f777(f304(x77641),x77643),x77644)),f777(f777(f181(x77641),x77643),f777(f777(f68(x77641,x77641,f181(x77641)),x77642),x77644))) % 174.01/173.90 [7765]~P92(x77651)+~P1(f777(f65(x77651),x77654))+E(f777(f777(f68(x77651,x77651,f105(x77651)),x77652),f777(f777(f304(x77651),x77653),x77654)),f777(f777(f105(x77651),x77653),f777(f777(f68(x77651,x77651,f105(x77651)),x77652),x77654))) % 174.01/173.90 [7766]~P98(x77661)+~P1(f777(f65(x77661),x77664))+E(f777(f777(f68(x77661,x77661,f106(x77661)),x77662),f777(f777(f304(x77661),x77663),x77664)),f777(f777(f106(x77661),x77663),f777(f777(f68(x77661,x77661,f106(x77661)),x77662),x77664))) % 174.01/173.90 [7768]~P135(x77681)+~P89(x77681)+E(f777(f777(f84(x77681),f777(f777(f85(x77681),f777(f108(x77681),x77682)),x77683)),f777(f777(f85(x77681),f777(f108(x77681),x77682)),x77684)),f777(f777(f85(x77681),f777(f108(x77681),x77682)),f777(f777(f84(x77681),x77683),x77684))) % 174.01/173.90 [7769]~P121(x77691)+~P89(x77691)+E(f777(f777(f5(x77691),f777(f777(f85(x77691),f777(f108(x77691),x77692)),x77693)),f777(f777(f85(x77691),f777(f108(x77691),x77692)),x77694)),f777(f777(f85(x77691),f777(f108(x77691),x77692)),f777(f777(f5(x77691),x77693),x77694))) % 174.01/173.90 [7882]E(x78821,x78822)+P1(f777(f777(f336(x78823),x78821),f777(f160(x78823),x78824)))+~P1(f777(f777(f336(x78823),x78821),f777(f160(x78823),f777(f777(f142(x78823),x78822),x78824)))) % 174.01/173.90 [8053]P53(x80531,x80532,x80533)+~P53(x80531,x80532,x80534)+~P1(f777(f777(f234(f858(f857(x80531,x80532),a845)),x80533),x80534)) % 174.01/173.90 [8096]P1(f777(f777(f336(x80961),x80962),x80963))+P1(f777(f777(f336(x80961),x80962),x80964))+~P1(f777(f777(f336(x80961),x80962),f777(f777(f105(f858(x80961,a845)),x80964),x80963))) % 174.01/173.90 [8107]~P47(x81071,x81074,x81073)+~P1(f777(f777(f336(x81071),x81072),x81074))+P1(f777(f777(f336(f857(x81071,x81071)),f777(f777(f243(x81071,x81071),x81072),x81072)),x81073)) % 174.01/173.90 [8119]~P1(f777(f65(x81192),x81194))+~P1(f777(f65(x81191),x81193))+P1(f777(f65(f857(x81191,x81192)),f777(f777(f250(x81191,x81192),x81193),f777(f20(f858(x81192,a845),x81191),x81194)))) % 174.01/173.90 [8120]~P1(f777(f777(f336(x81201),x81202),x81204))+~P1(f777(f777(f234(f858(x81201,a845)),x81203),x81204))+P1(f777(f777(f234(f858(x81201,a845)),f777(f777(f304(x81201),x81202),x81203)),x81204)) % 174.01/173.90 [8128]~P2(x81282)+~P70(x81282)+E(f777(f777(f13(x81281,x81282),f777(f777(f12(a851,x81282,x81281),f104(x81282)),x81283)),x81284),f777(f104(x81282),f777(f777(f13(x81281,a851),x81283),x81284))) % 174.01/173.90 [8129]~P70(x81292)+~P133(x81292)+E(f777(f777(f13(x81291,x81292),f777(f777(f12(a3,x81292,x81291),f107(x81292)),x81293)),x81294),f777(f107(x81292),f777(f777(f13(x81291,a3),x81293),x81294))) % 174.01/173.90 [8155]E(f777(f777(f5(f858(x81551,a845)),x81552),f777(f777(f5(f858(x81551,a845)),x81553),x81554)),x81554)+~P1(f777(f777(f234(f858(x81551,a845)),x81552),x81553))+~P1(f777(f777(f234(f858(x81551,a845)),x81554),x81552)) % 174.01/173.90 [8247]~P1(f777(f65(x82471),x82474))+E(f777(f777(f5(a851),f777(f777(f10(x82471,a851),x82472),x82473)),f777(f777(f10(x82471,a851),x82472),x82474)),f777(f777(f10(x82471,a851),x82472),f777(f777(f5(f858(x82471,a845)),x82473),x82474)))+~P1(f777(f777(f234(f858(x82471,a845)),x82474),x82473)) % 174.01/173.90 [8404]~P12(x84041,x84044,x84043)+~P1(f777(f777(f336(x84041),x84042),x84044))+P1(f777(f777(f336(x84041),x84042),f777(f279(x84041,x84041,x84043),f777(f777(f304(x84041),x84042),f182(f858(x84041,a845)))))) % 174.01/173.90 [8467]~P1(f777(f777(f234(f858(x84671,a845)),x84672),x84673))+~P1(f777(f777(f234(f858(x84671,a845)),x84672),x84674))+P1(f777(f777(f234(f858(x84671,a845)),x84672),f777(f777(f106(f858(x84671,a845)),x84673),x84674))) % 174.01/173.90 [8559]E(x85591,f182(f858(x85592,a845)))+P1(f777(f65(x85593),x85594))+~P1(f777(f65(f857(x85593,x85592)),f777(f777(f250(x85593,x85592),x85594),f777(f20(f858(x85592,a845),x85593),x85591)))) % 174.01/173.90 [8560]E(x85601,f182(f858(x85602,a845)))+P1(f777(f65(x85603),x85604))+~P1(f777(f65(f857(x85602,x85603)),f777(f777(f250(x85602,x85603),x85601),f777(f20(f858(x85603,a845),x85602),x85604)))) % 174.01/173.90 [8618]P1(f777(f777(f336(x86181),x86182),f324(x86181,x86183)))+~P1(f777(f777(f336(x86181),x86184),f324(x86181,x86183)))+~P1(f777(f777(f336(f857(x86181,x86181)),f777(f777(f243(x86181,x86181),x86182),x86184)),x86183)) % 174.01/173.90 [8670]~P36(x86701,x86704)+P1(f777(f777(f336(f857(x86701,x86701)),f777(f777(f243(x86701,x86701),x86703),x86702)),f302(x86701,x86704)))+P36(x86701,f777(f777(f304(f857(x86701,x86701)),f777(f777(f243(x86701,x86701),x86702),x86703)),x86704)) % 174.01/173.90 [8671]~P56(x86711,x86714)+P1(f777(f777(f336(f857(x86711,x86711)),f777(f777(f243(x86711,x86711),x86713),x86712)),f302(x86711,x86714)))+P56(x86711,f777(f777(f304(f857(x86711,x86711)),f777(f777(f243(x86711,x86711),x86712),x86713)),x86714)) % 174.01/173.90 [8742]~E(x87422,x87423)+~P1(f777(f777(f336(x87421),x87422),f777(f160(x87421),x87424)))+P1(f777(f777(f336(f857(x87421,x87421)),f777(f777(f243(x87421,x87421),x87422),x87423)),f777(f160(f857(x87421,x87421)),f777(f777(f169(x87421,x87421),x87424),x87424)))) % 174.01/173.90 [8814]~E(x88143,x88144)+P1(f777(f777(f253(x88141,x88141,a845),a332),x88142))+~P1(f777(f777(f336(f857(x88141,x88141)),x88142),f777(f160(f857(x88141,x88141)),f777(f777(f169(x88141,x88141),x88143),x88144)))) % 174.01/173.90 [8850]P1(f777(f777(f336(f857(f852(x88501),f852(x88501))),f777(f777(f243(f852(x88501),f852(x88501)),x88502),x88503)),f139(x88501,x88504)))+~E(f777(f777(f161(x88501),f777(f183(f852(x88501)),x88502)),x88503),x88502)+~P1(f777(f777(f235(a851),f777(f183(f852(x88501)),x88502)),f777(f183(f852(x88501)),x88503))) % 174.01/173.90 [8944]~P1(f777(f65(x89441),x89444))+P1(f777(f777(f336(x89441),f414(x89442,x89443,x89444,x89441)),x89444))+P1(f777(f65(x89443),f777(f777(f48(x89441,f858(x89443,a845)),x89444),x89442))) % 174.01/173.90 [8945]~P1(f777(f65(x89451),x89454))+P1(f777(f777(f336(x89451),f610(x89452,x89453,x89454,x89451)),x89454))+P1(f777(f65(x89453),f777(f777(f48(x89451,f858(x89453,a845)),x89454),x89452))) % 174.01/173.90 [9025]P1(f777(f777(f336(f857(x90251,x90251)),x90252),f777(f777(f283(x90251,x90251,x90251),x90253),f302(x90251,x90253))))+~P1(f777(f777(f235(a851),f4(a851)),x90254))+~P1(f777(f777(f336(f857(x90251,x90251)),x90252),f777(f777(f175(f857(x90251,x90251),a845),x90254),x90253))) % 174.01/173.90 [9033]~P36(x90331,x90332)+~P1(f777(f777(f336(f857(x90331,x90331)),f777(f777(f243(x90331,x90331),x90334),x90333)),x90332))+~P1(f777(f777(f336(f857(x90331,x90331)),f777(f777(f243(x90331,x90331),x90333),x90334)),x90332)) % 174.01/173.90 [9149]~P1(f777(f65(x91491),x91494))+E(f777(f777(f10(x91491,a851),f777(f777(f12(f858(x91492,a845),a851,x91491),f44(x91492)),x91493)),x91494),f777(f44(f857(x91491,x91492)),f777(f777(f250(x91491,x91492),x91494),x91493)))+P1(f777(f777(f336(x91491),f564(x91493,x91492,x91494,x91491)),x91494)) % 174.01/173.90 [9151]~P1(f777(f129(x91511),x91512))+P1(f777(f129(x91511),f777(f777(f150(x91511,x91512),x91513),x91514)))+P1(f777(f777(f336(x91511),x91514),f777(f777(f5(f858(x91511,a845)),f777(f160(x91511),x91512)),f777(f777(f304(x91511),f777(f777(f155(x91511),x91512),x91513)),f182(f858(x91511,a845)))))) % 174.01/173.90 [9160]~P1(f777(f65(x91602),x91603))+~P1(f777(f65(x91601),f777(x91604,f414(x91604,x91601,x91603,x91602))))+P1(f777(f65(x91601),f777(f777(f48(x91602,f858(x91601,a845)),x91603),x91604))) % 174.01/173.90 [9161]~P1(f777(f65(x91612),x91613))+~P1(f777(f65(x91611),f777(x91614,f610(x91614,x91611,x91613,x91612))))+P1(f777(f65(x91611),f777(f777(f48(x91612,f858(x91611,a845)),x91613),x91614))) % 174.01/173.90 [9226]~P1(f777(f777(f336(f857(x92261,x92261)),x92262),f777(f777(f283(x92261,x92261,x92261),x92264),f302(x92261,x92264))))+P1(f777(f777(f336(f857(x92261,x92261)),x92262),f777(f777(f283(x92261,x92261,x92261),x92263),f302(x92261,x92263))))+~P1(f777(f777(f234(f858(f857(x92261,x92261),a845)),x92264),x92263)) % 174.01/173.90 [9234]E(f777(f777(f161(x92341),f741(x92344,x92343,x92342,x92341)),x92343),f777(f777(f161(x92341),f741(x92344,x92343,x92342,x92341)),x92342))+~P1(f777(f777(f336(f857(f852(x92341),f852(x92341))),f777(f777(f243(f852(x92341),f852(x92341)),x92342),x92343)),f139(x92341,x92344)))+E(f777(f777(f161(x92341),f777(f183(f852(x92341)),x92342)),x92343),x92342) % 174.01/173.90 [9250]~P1(f777(f65(x92501),x92504))+E(f777(f777(f10(x92501,a851),f777(f777(f12(f858(x92502,a845),a851,x92501),f44(x92502)),x92503)),x92504),f777(f44(f857(x92501,x92502)),f777(f777(f250(x92501,x92502),x92504),x92503)))+~P1(f777(f65(x92502),f777(x92503,f564(x92503,x92502,x92504,x92501)))) % 174.01/173.90 [9255]~E(f777(f183(f852(x92551)),x92553),f777(f183(f852(x92551)),x92552))+P1(f777(f777(f336(f857(f852(x92551),f852(x92551))),f777(f777(f243(f852(x92551),f852(x92551)),x92552),x92553)),f149(x92551,x92554)))+P1(f777(f777(f336(f857(x92551,x92551)),f718(x92554,x92553,x92552,x92551)),f777(f160(f857(x92551,x92551)),f777(f777(f169(x92551,x92551),x92552),x92553)))) % 174.01/173.90 [9337]~P1(f777(f777(f336(f857(f852(x93371),f852(x93371))),f777(f777(f243(f852(x93371),f852(x93371)),x93372),x93373)),f139(x93371,x93374)))+E(f777(f777(f161(x93371),f777(f183(f852(x93371)),x93372)),x93373),x93372)+P1(f777(f777(f235(a851),f741(x93374,x93373,x93372,x93371)),f777(f777(f238(a851),f777(f183(f852(x93371)),x93372)),f777(f183(f852(x93371)),x93373)))) % 174.01/173.90 [9356]~P1(f777(f777(f336(f857(f852(x93561),f852(x93561))),f777(f777(f243(f852(x93561),f852(x93561)),x93562),x93563)),f139(x93561,x93564)))+P1(f777(f777(f235(a851),f777(f183(f852(x93561)),x93562)),f777(f183(f852(x93561)),x93563)))+P1(f777(f777(f235(a851),f741(x93564,x93563,x93562,x93561)),f777(f777(f238(a851),f777(f183(f852(x93561)),x93562)),f777(f183(f852(x93561)),x93563)))) % 174.01/173.90 [9632]~P1(f777(f777(f777(x96321,f709(x96321,x96324,x96323,x96322)),f712(x96321,x96324,x96323,x96322)),f713(x96321,x96324,x96323,x96322)))+P1(f777(f777(f777(x96321,x96322),x96323),x96324))+~P1(f777(f323(f857(f858(a3,f855(f852(a844))),f857(a3,a3)),a313),f777(f777(f243(f858(a3,f855(f852(a844))),f857(a3,a3)),x96322),f777(f777(f243(a3,a3),x96323),x96324)))) % 174.01/173.90 [9693]P1(f777(f777(f777(x96931,x96932),x96933),x96934))+P1(f777(f323(f857(f858(a3,f855(f852(a844))),f857(a3,a3)),a313),f777(f777(f243(f858(a3,f855(f852(a844))),f857(a3,a3)),f709(x96931,x96934,x96933,x96932)),f777(f777(f243(a3,a3),f712(x96931,x96934,x96933,x96932)),f713(x96931,x96934,x96933,x96932)))))+~P1(f777(f323(f857(f858(a3,f855(f852(a844))),f857(a3,a3)),a313),f777(f777(f243(f858(a3,f855(f852(a844))),f857(a3,a3)),x96932),f777(f777(f243(a3,a3),x96933),x96934)))) % 174.01/173.90 [9731]~P1(f777(f777(f336(f857(f852(x97311),f852(x97311))),f777(f777(f243(f852(x97311),f852(x97311)),x97312),x97313)),f139(x97311,x97314)))+E(f777(f777(f161(x97311),f777(f183(f852(x97311)),x97312)),x97313),x97312)+P1(f777(f777(f336(f857(x97311,x97311)),f777(f777(f243(x97311,x97311),f777(f777(f155(x97311),x97312),f741(x97314,x97313,x97312,x97311))),f777(f777(f155(x97311),x97313),f741(x97314,x97313,x97312,x97311)))),x97314)) % 174.01/173.90 [9734]~P1(f777(f777(f336(f857(f852(x97341),f852(x97341))),f777(f777(f243(f852(x97341),f852(x97341)),x97342),x97343)),f139(x97341,x97344)))+P1(f777(f777(f235(a851),f777(f183(f852(x97341)),x97342)),f777(f183(f852(x97341)),x97343)))+P1(f777(f777(f336(f857(x97341,x97341)),f777(f777(f243(x97341,x97341),f777(f777(f155(x97341),x97342),f741(x97344,x97343,x97342,x97341))),f777(f777(f155(x97341),x97343),f741(x97344,x97343,x97342,x97341)))),x97344)) % 174.01/173.90 [9804]~E(f777(f183(f852(x98041)),x98042),f777(f183(f852(x98041)),x98043))+P1(f777(f777(f336(f857(f852(x98041),f852(x98041))),f777(f777(f243(f852(x98041),f852(x98041)),x98042),x98043)),f149(x98041,x98044)))+~P1(f777(f777(f336(f857(x98041,x98041)),f777(f777(f243(x98041,x98041),f777(f777(f155(x98041),x98042),f734(x98044,x98043,x98042,x98041))),f777(f777(f155(x98041),x98043),f734(x98044,x98043,x98042,x98041)))),x98044)) % 174.01/173.90 [9944]~P66(x99441)+~P1(f777(f65(x99442),x99444))+E(f777(f157(x99441),f777(f777(f145(x99442,x99441),x99443),f94(f852(x99442),f777(f777(f22(f852(x99442),a845,a845),f777(f777(f12(a845,f858(a845,a845),f852(x99442)),a333),f777(f777(f11(f852(x99442),f858(x99442,a845),a845),f777(f777(f12(f858(x99442,a845),f858(f858(x99442,a845),a845),f852(x99442)),a332),f160(x99442))),x99444))),f129(x99442))))),f227(x99442,x99441,x99443,x99444)) % 174.01/173.90 [7336]~P60(x73362)+E(x73361,f4(x73362))+E(f777(f777(f285(x73362),f777(f777(f84(x73362),x73363),f777(f777(f85(x73362),x73364),x73361))),x73361),f777(f777(f84(x73362),x73364),f777(f777(f285(x73362),x73363),x73361))) % 174.01/173.90 [7337]~P7(x73372)+E(x73371,f4(x73372))+E(f777(f777(f45(x73372),f777(f777(f84(x73372),x73373),f777(f777(f85(x73372),x73374),x73371))),x73371),f777(f777(f84(x73372),x73374),f777(f777(f45(x73372),x73373),x73371))) % 174.01/173.90 [7338]~P7(x73382)+E(x73381,f4(x73382))+E(f777(f777(f45(x73382),f777(f777(f84(x73382),x73383),f777(f777(f85(x73382),x73381),x73384))),x73381),f777(f777(f84(x73382),x73384),f777(f777(f45(x73382),x73383),x73381))) % 174.01/173.90 [7579]~P60(x75792)+E(x75791,f4(x75792))+E(f777(f777(f285(x75792),f777(f777(f84(x75792),x75793),f777(f777(f85(x75792),x75794),x75791))),x75791),f777(f777(f84(x75792),f777(f777(f285(x75792),x75793),x75791)),x75794)) % 174.01/173.90 [7580]~P61(x75802)+E(x75801,f4(x75802))+E(f777(f777(f285(x75802),f777(f777(f84(x75802),x75803),f777(f777(f85(x75802),x75801),x75804))),x75801),f777(f777(f84(x75802),f777(f777(f285(x75802),x75803),x75801)),x75804)) % 174.01/173.90 [7581]~P61(x75812)+E(x75811,f4(x75812))+E(f777(f777(f285(x75812),f777(f777(f5(x75812),x75813),f777(f777(f85(x75812),x75811),x75814))),x75811),f777(f777(f5(x75812),f777(f777(f285(x75812),x75813),x75811)),x75814)) % 174.01/173.90 [8632]~E(f777(f777(f283(x86321,x86321,x86321),x86322),x86324),f182(f858(f857(x86321,x86321),a845)))+~E(f777(f777(f283(x86321,x86321,x86321),x86322),x86323),f182(f858(f857(x86321,x86321),a845)))+E(f777(f777(f283(x86321,x86321,x86321),x86322),f777(f777(f105(f858(f857(x86321,x86321),a845)),x86323),x86324)),f182(f858(f857(x86321,x86321),a845))) % 174.01/173.90 [8743]~P1(f777(f777(f234(f858(x87431,a845)),x87433),x87434))+~P1(f777(f777(f234(f858(x87431,a845)),x87432),x87434))+P1(f777(f777(f234(f858(x87431,a845)),f777(f777(f105(f858(x87431,a845)),x87432),x87433)),x87434)) % 174.01/173.90 [9083]~P1(f777(f65(x90831),x90834))+~P1(f777(f65(x90831),x90833))+E(f777(f777(f5(a851),f777(f777(f84(a851),f777(f777(f10(x90831,a851),x90832),x90833)),f777(f777(f10(x90831,a851),x90832),x90834))),f777(f777(f10(x90831,a851),x90832),f777(f777(f106(f858(x90831,a845)),x90833),x90834))),f777(f777(f10(x90831,a851),x90832),f777(f777(f105(f858(x90831,a845)),x90833),x90834))) % 174.01/173.90 [9158]~P1(f777(f777(f336(x91581),x91583),x91582))+~P1(f777(f777(f234(f858(x91581,a845)),x91582),f777(f777(f304(x91581),x91583),x91584)))+P1(f777(f777(f234(f858(x91581,a845)),f777(f777(f5(f858(x91581,a845)),x91582),f777(f777(f304(x91581),x91583),f182(f858(x91581,a845))))),x91584)) % 174.01/173.90 [9309]~P1(f777(f777(f336(x93091),x93093),x93092))+P1(f777(f777(f234(f858(x93091,a845)),x93092),f777(f777(f304(x93091),x93093),x93094)))+~P1(f777(f777(f234(f858(x93091,a845)),f777(f777(f5(f858(x93091,a845)),x93092),f777(f777(f304(x93091),x93093),f182(f858(x93091,a845))))),x93094)) % 174.01/173.90 [9394]~P1(f777(f777(f235(a851),x93942),x93944))+~P1(f777(f777(f234(a851),x93941),x93943))+P1(f777(f777(f336(f857(f857(a851,a851),f857(a851,a851))),f777(f777(f243(f857(a851,a851),f857(a851,a851)),f777(f777(f243(a851,a851),x93941),x93942)),f777(f777(f243(a851,a851),x93943),x93944))),a42)) % 174.01/173.90 [9395]~P1(f777(f777(f234(a851),x93952),x93954))+~P1(f777(f777(f234(a851),x93951),x93953))+P1(f777(f777(f336(f857(f857(a851,a851),f857(a851,a851))),f777(f777(f243(f857(a851,a851),f857(a851,a851)),f777(f777(f243(a851,a851),x93951),x93952)),f777(f777(f243(a851,a851),x93953),x93954))),a74)) % 174.01/173.90 [9769]~P29(x97691,f858(f858(x97691,a845),a845),f777(f777(f11(x97691,f858(f857(x97691,x97691),a845),f858(f858(x97691,a845),a845)),f777(f777(f12(f858(x97691,a845),f858(f858(f857(x97691,x97691),a845),f858(f858(x97691,a845),a845)),x97691),f63(x97691)),f777(f777(f11(x97691,f858(x97691,a845),f858(x97691,a845)),f304(x97691)),f182(f858(x97691,a845))))),x97693),x97692)+~P1(f777(f777(f336(x97691),x97694),x97692))+E(f777(f777(f5(f858(f858(x97691,a845),a845)),f777(f777(f63(x97691),x97692),x97693)),f777(f777(f63(x97691),f777(f777(f304(x97691),x97694),f182(f858(x97691,a845)))),x97693)),f777(f777(f63(x97691),f777(f777(f5(f858(x97691,a845)),x97692),f777(f777(f304(x97691),x97694),f182(f858(x97691,a845))))),x97693)) % 174.01/173.90 [9908]~P47(x99081,x99082,x99084)+~P1(f777(f777(f336(f857(x99081,x99081)),x99083),x99084))+P1(f777(f777(f253(x99081,x99081,a845),f777(f777(f11(x99081,f858(x99081,a845),f858(x99081,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x99081,a845),f858(x99081,a845)),x99081),f12(a845,a845,x99081)),f777(f777(f12(a845,f858(a845,a845),x99081),a333),f777(f777(f11(x99081,f858(x99081,a845),a845),f336(x99081)),x99082)))),f777(f777(f11(x99081,f858(x99081,a845),a845),f336(x99081)),x99082))),x99083)) % 174.01/173.90 [9918]P1(f777(f65(x99181),x99182))+~P1(f777(f65(x99183),f777(f305(x99181,x99183,x99184),x99182)))+~P1(f777(f65(x99181),f777(f258(x99181),f777(f777(f22(x99181,a845,a845),f777(f777(f12(a845,f858(a845,a845),x99181),a333),f777(f777(f11(x99181,f858(x99181,a845),a845),f336(x99181)),x99182))),f777(f777(f11(x99181,x99183,a845),f777(f777(f12(x99183,f858(x99183,a845),x99181),a332),x99184)),f777(x99184,f601(x99184,x99183,x99182,x99181))))))) % 174.01/173.90 [8036]~P61(x80362)+E(x80361,f4(x80362))+E(f777(f777(f285(x80362),f777(f777(f84(x80362),f777(f777(f85(x80362),x80361),x80363)),x80364)),x80361),f777(f777(f84(x80362),x80363),f777(f777(f285(x80362),x80364),x80361))) % 174.01/173.90 [8037]~P61(x80372)+E(x80371,f4(x80372))+E(f777(f777(f285(x80372),f777(f777(f5(x80372),f777(f777(f85(x80372),x80371),x80373)),x80374)),x80371),f777(f777(f5(x80372),x80373),f777(f777(f285(x80372),x80374),x80371))) % 174.01/173.90 [8877]~E(f777(f777(f283(x88771,x88771,x88771),x88773),x88774),f182(f858(f857(x88771,x88771),a845)))+~E(f777(f777(f283(x88771,x88771,x88771),x88772),x88774),f182(f858(f857(x88771,x88771),a845)))+E(f777(f777(f283(x88771,x88771,x88771),f777(f777(f105(f858(f857(x88771,x88771),a845)),x88772),x88773)),x88774),f182(f858(f857(x88771,x88771),a845))) % 174.01/173.90 [9852]~P139(x98521)+~P139(x98522)+E(f777(f777(f312(x98521),f777(f777(f11(x98521,a103,f855(f852(a844))),f777(f777(f12(f858(x98522,f855(f852(a844))),f858(a103,f855(f852(a844))),x98521),f312(x98522)),f777(f777(f12(f858(x98522,f857(x98521,x98522)),f858(x98522,f855(f852(a844))),x98521),f777(f12(f857(x98521,x98522),f855(f852(a844)),x98522),x98523)),f243(x98521,x98522)))),x98524)),x98524),f777(f777(f312(f857(x98521,x98522)),x98523),x98524)) % 174.01/173.90 [9844]P1(f777(x98441,f587(x98442,x98443,x98441,x98444)))+~P1(f777(f65(x98444),f777(f258(x98444),x98441)))+P1(f777(f65(x98443),f777(f258(x98443),f777(f777(f12(f858(x98444,a845),a845,x98443),f91(x98444)),f777(f777(f12(f858(x98444,a845),f858(x98444,a845),x98443),f777(f22(x98444,a845,a845),f777(f777(f12(a845,f858(a845,a845),x98444),a333),x98441))),x98442))))) % 174.01/173.90 [9865]~P1(f777(f65(x98652),f777(f258(x98652),x98653)))+~P1(f777(f65(x98651),f777(f258(x98651),f777(f777(f11(x98651,x98652,a845),x98654),f587(x98654,x98651,x98653,x98652)))))+P1(f777(f65(x98651),f777(f258(x98651),f777(f777(f12(f858(x98652,a845),a845,x98651),f91(x98652)),f777(f777(f12(f858(x98652,a845),f858(x98652,a845),x98651),f777(f22(x98652,a845,a845),f777(f777(f12(a845,f858(a845,a845),x98652),a333),x98653))),x98654))))) % 174.01/173.90 [5719]~E(x57195,x57192)+P39(f37(x57191,x57193),x57192,x57194,x57195)+P1(f777(x57191,x57192)) % 174.01/173.90 [6287]E(x62871,x62872)+~P39(f37(x62873,x62874),x62871,x62875,x62872)+P1(f777(x62873,x62871)) % 174.01/173.90 [7842]~P39(x78422,x78423,x78424,x78425)+~P39(f37(x78421,x78422),x78425,x78424,x78423)+P39(f37(x78421,x78422),x78423,x78424,x78423) % 174.01/173.90 [8999]E(x89991,x89992)+~P39(f37(x89995,x89993),x89991,x89994,x89992)+P39(x89993,x89991,x89994,f814(x89992,x89994,x89991,x89993,x89995)) % 174.01/173.90 [9000]E(x90001,x90002)+~P39(f37(x90005,x90003),x90001,x90004,x90002)+P39(x90003,x90001,x90004,f361(x90002,x90004,x90001,x90003,x90005)) % 174.01/173.90 [9002]E(x90021,x90022)+P39(f37(x90023,x90024),f814(x90021,x90025,x90022,x90024,x90023),x90025,x90021)+~P39(f37(x90023,x90024),x90022,x90025,x90021) % 174.01/173.90 [9003]E(x90031,x90032)+P39(f37(x90033,x90034),f361(x90031,x90035,x90032,x90034,x90033),x90035,x90031)+~P39(f37(x90033,x90034),x90032,x90035,x90031) % 174.01/173.90 [9005]~P39(f37(x90055,x90051),x90052,x90053,x90054)+P39(x90051,x90052,x90053,f814(x90054,x90053,x90052,x90051,x90055))+~P1(f777(x90055,x90052)) % 174.01/173.90 [9006]~P39(f37(x90065,x90061),x90062,x90063,x90064)+P39(x90061,x90062,x90063,f361(x90064,x90063,x90062,x90061,x90065))+~P1(f777(x90065,x90062)) % 174.01/173.90 [9010]~P39(f37(x90101,x90102),x90105,x90104,x90103)+P39(f37(x90101,x90102),f814(x90103,x90104,x90105,x90102,x90101),x90104,x90103)+~P1(f777(x90101,x90105)) % 174.01/173.90 [9011]~P39(f37(x90111,x90112),x90115,x90114,x90113)+P39(f37(x90111,x90112),f361(x90113,x90114,x90115,x90112,x90111),x90114,x90113)+~P1(f777(x90111,x90115)) % 174.01/173.90 [6437]E(x64371,x64372)+~E(f777(x64373,x64371),f777(x64373,x64372))+~P29(x64374,x64375,x64373,f241(f858(x64374,a845))) % 174.01/173.90 [6602]~E(f777(x66023,x66025),f185(x66022))+~E(f777(x66024,x66025),f185(x66022))+E(f777(f172(x66021,x66022,x66023,x66024),x66025),f185(x66022)) % 174.01/173.90 [7377]E(x73771,x73772)+~P29(x73773,x73774,x73775,f241(f858(x73773,a845)))+~E(f777(f305(x73773,x73774,x73775),x73771),f777(f305(x73773,x73774,x73775),x73772)) % 174.01/173.90 [7635]P29(x76352,x76353,f524(x76354,x76353,x76352,x76351),x76351)+~E(f777(f305(x76353,x76352,x76355),x76354),x76351)+E(x76351,f182(f858(x76352,a845))) % 174.01/173.90 [8166]~P1(f777(f777(x81663,x81662),x81665))+~P1(f777(f777(x81663,x81664),x81662))+P1(f777(f777(f336(x81661),x81662),f284(x81661,x81663,x81664,x81665))) % 174.01/173.90 [8167]~P1(f777(f777(x81673,x81672),x81675))+~P1(f777(f777(x81673,x81674),x81672))+P1(f777(f777(f336(x81671),x81672),f293(x81671,x81673,x81674,x81675))) % 174.01/173.90 [8705]~P29(x87051,x87053,x87055,f241(f858(x87051,a845)))+~P29(x87053,x87052,x87054,f241(f858(x87053,a845)))+P29(x87051,x87052,f777(f77(x87053,x87052,x87051,x87054),x87055),f241(f858(x87051,a845))) % 174.01/173.90 [9204]P1(f777(f777(f336(f857(x92041,x92041)),f777(f777(f243(x92041,x92041),x92042),x92043)),f302(x92041,x92044)))+~P1(f777(f777(f336(f857(x92041,x92041)),f777(f777(f243(x92041,x92041),x92042),x92045)),f302(x92041,x92044)))+~P1(f777(f777(f336(f857(x92041,x92041)),f777(f777(f243(x92041,x92041),x92045),x92043)),f302(x92041,x92044))) % 174.01/173.90 [9241]~P100(x92412)+~P1(f777(f129(x92411),x92415))+P1(f777(f129(x92411),f141(x92411,x92412,x92413,x92414,x92415))) % 174.01/173.90 [5249]~E(x52492,f117(x52491))+E(f777(f777(f127(x52491),x52492),x52493),f777(f777(f142(x52491),x52494),x52495))+~E(x52493,f777(f777(f142(x52491),x52494),x52495)) % 174.01/173.90 [5250]~E(x52502,f117(x52501))+E(f777(f777(f127(x52501),x52502),x52503),f777(f777(f142(x52501),x52504),x52505))+~E(f777(f777(f142(x52501),x52504),x52505),x52503) % 174.01/173.90 [6393]~E(f777(f183(f852(x63931)),x63935),f777(f183(f852(x63932)),x63934))+E(f777(f777(f145(f857(x63931,x63932),x63932),f252(x63931,x63932)),x63933),x63934)+~E(f777(f777(f169(x63931,x63932),x63935),x63934),x63933) % 174.01/173.90 [6394]~E(f777(f183(f852(x63941)),x63944),f777(f183(f852(x63942)),x63945))+E(f777(f777(f145(f857(x63941,x63942),x63941),f242(x63941,x63942)),x63943),x63944)+~E(f777(f777(f169(x63941,x63942),x63944),x63945),x63943) % 174.01/173.90 [6892]~P100(x68921)+~P18(x68921,f777(f777(f145(x68922,x68921),x68923),x68925))+P18(x68921,f777(f777(f145(x68922,x68921),x68923),f777(f128(x68922,x68924),x68925))) % 174.01/173.90 [6938]~P1(f777(x69383,x69385))+~P1(f777(f777(x69382,x69384),x69385))+P1(f777(f777(f96(x69381,x69382,x69383),x69384),x69385)) % 174.01/173.90 [7035]~P100(x70351)+P18(x70351,f777(f777(f145(x70352,x70351),x70353),f153(x70352,x70354,x70355)))+~P18(x70351,f777(f777(f145(x70352,x70351),x70353),x70355)) % 174.01/173.90 [7058]~P53(x70583,x70582,x70585)+~P53(x70581,x70583,x70584)+P53(x70581,x70582,f777(f777(f283(x70581,x70583,x70582),x70584),x70585)) % 174.01/173.90 [7149]E(x71491,x71492)+~P29(x71493,x71494,x71495,f241(f858(x71493,a845)))+~E(f777(f777(f145(x71493,x71494),x71495),x71491),f777(f777(f145(x71493,x71494),x71495),x71492)) % 174.01/173.90 [7232]P39(x72321,x72322,x72323,x72324)+~P39(x72321,x72322,x72325,x72324)+~P1(f777(f777(f234(a851),x72325),x72323)) % 174.01/173.90 [7322]~P1(f777(f777(f235(a851),x73221),f777(x73223,x73225)))+P1(f777(f777(f235(a851),x73221),f146(x73222,x73223,x73224)))+~P1(f777(f777(f336(x73222),x73225),f777(f160(x73222),x73224))) % 174.01/173.90 [7323]~P1(f777(f777(f234(a851),x73231),f777(x73233,x73235)))+P1(f777(f777(f234(a851),x73231),f146(x73232,x73233,x73234)))+~P1(f777(f777(f336(x73232),x73235),f777(f160(x73232),x73234))) % 174.01/173.90 [7734]~P99(x77341)+P1(f777(f777(f234(f858(x77341,a845)),f297(x77341,x77342,x77343)),f297(x77341,x77344,x77345)))+P1(f777(f777(f234(x77341),x77342),x77343)) % 174.01/173.90 [7761]~P9(x77611)+P1(f777(f777(f234(x77611),f777(f777(f49(x77612,x77611),x77613),x77614)),f777(x77614,x77615)))+~P1(f777(f777(f336(x77612),x77615),x77613)) % 174.01/173.90 [7829]~P29(x78291,x78292,x78294,x78293)+E(f777(f81(x78291,x78292,x78293,x78294),f777(x78294,x78295)),x78295)+~P1(f777(f777(f336(x78291),x78295),x78293)) % 174.01/173.90 [8025]~P1(f777(x80251,x80255))+P1(f777(x80251,f380(x80251,x80252,x80253,x80254)))+~P1(f777(f777(f336(x80254),x80255),x80253)) % 174.01/173.90 [8026]~P1(f777(x80261,x80265))+P1(f777(x80261,f380(x80261,x80262,x80263,x80264)))+~P1(f777(f777(f336(x80264),x80265),x80262)) % 174.01/173.90 [8117]P1(f777(f65(x81171),x81172))+~P1(f777(f65(x81173),x81174))+~P1(f777(f777(f234(f858(x81171,a845)),x81172),f777(f305(x81173,x81171,x81175),x81174))) % 174.01/173.90 [8278]E(x82781,x82782)+~P29(x82783,x82784,x82785,f777(f777(f105(f858(x82783,a845)),f777(f160(x82783),x82781)),f777(f160(x82783),x82782)))+~E(f777(f777(f145(x82783,x82784),x82785),x82781),f777(f777(f145(x82783,x82784),x82785),x82782)) % 174.01/173.90 [8335]~P99(x83351)+~P1(f777(f777(f235(f858(x83351,a845)),f297(x83351,x83354,x83355)),f297(x83351,x83352,x83353)))+P1(f777(f777(f234(x83351),x83352),x83353)) % 174.01/173.90 [8403]~P29(x84031,x84034,x84035,f241(f858(x84031,a845)))+~P1(f777(f777(f336(x84034),f777(x84035,x84032)),f777(f305(x84031,x84034,x84035),x84033)))+P1(f777(f777(f336(x84031),x84032),x84033)) % 174.01/173.90 [8483]P1(f777(x84831,x84832))+~P1(f777(x84831,f384(x84831,x84833,x84834,x84835)))+~P1(f777(f777(f336(x84835),x84832),x84834)) % 174.01/173.90 [8484]P1(f777(x84841,x84842))+~P1(f777(x84841,f384(x84841,x84843,x84844,x84845)))+~P1(f777(f777(f336(x84845),x84842),x84843)) % 174.01/173.90 [8740]~P29(x87402,x87403,x87401,x87404)+E(f777(x87401,f777(f81(x87402,x87403,x87404,x87401),x87405)),x87405)+~P1(f777(f777(f336(x87403),x87405),f777(f305(x87402,x87403,x87401),x87404))) % 174.01/173.90 [8824]E(x88241,f117(x88242))+E(f777(f777(f142(x88242),x88243),f733(x88244,x88243,x88245,x88241,x88242)),x88241)+~E(f777(f777(f127(x88242),x88241),x88245),f777(f777(f142(x88242),x88243),x88244)) % 174.01/173.90 [8825]E(x88251,f117(x88252))+E(f777(f777(f142(x88252),x88253),f735(x88254,x88251,x88255,x88253,x88252)),x88251)+~E(f777(f777(f127(x88252),x88251),x88254),f777(f777(f142(x88252),x88253),x88255)) % 174.01/173.90 [8840]E(f777(f777(f142(x88402),x88403),f733(x88404,x88403,x88401,x88405,x88402)),x88405)+~E(f777(f777(f127(x88402),x88405),x88401),f777(f777(f142(x88402),x88403),x88404))+E(x88401,f777(f777(f142(x88402),x88403),x88404)) % 174.01/173.90 [8841]E(f777(f777(f142(x88411),x88412),f735(x88414,x88415,x88413,x88412,x88411)),x88415)+~E(f777(f777(f127(x88411),x88415),x88414),f777(f777(f142(x88411),x88412),x88413))+E(f777(f777(f142(x88411),x88412),x88413),x88414) % 174.01/173.90 [8917]~E(f777(f305(x89173,x89172,x89174),f241(f858(x89173,a845))),f241(f858(x89172,a845)))+~E(f777(f305(x89171,x89173,x89175),f241(f858(x89171,a845))),f241(f858(x89173,a845)))+E(f777(f305(x89171,x89172,f777(f77(x89173,x89172,x89171,x89174),x89175)),f241(f858(x89171,a845))),f241(f858(x89172,a845))) % 174.01/173.90 [9247]E(x92471,f117(x92472))+~E(f777(f777(f127(x92472),x92471),x92473),f777(f777(f142(x92472),x92475),x92474))+E(f777(f777(f127(x92472),f735(x92473,x92471,x92474,x92475,x92472)),x92473),x92474) % 174.01/173.90 [9248]E(x92481,f117(x92482))+~E(f777(f777(f127(x92482),x92481),x92485),f777(f777(f142(x92482),x92484),x92483))+E(f777(f777(f127(x92482),f733(x92483,x92484,x92485,x92481,x92482)),x92485),x92483) % 174.01/173.90 [9256]E(f777(f777(f127(x92562),f733(x92564,x92563,x92561,x92565,x92562)),x92561),x92564)+~E(f777(f777(f127(x92562),x92565),x92561),f777(f777(f142(x92562),x92563),x92564))+E(x92561,f777(f777(f142(x92562),x92563),x92564)) % 174.01/173.90 [9257]~E(f777(f777(f127(x92571),x92575),x92574),f777(f777(f142(x92571),x92572),x92573))+E(f777(f777(f127(x92571),f735(x92574,x92575,x92573,x92572,x92571)),x92574),x92573)+E(f777(f777(f142(x92571),x92572),x92573),x92574) % 174.01/173.90 [9258]E(f777(f777(f127(x92581),x92585),f737(x92583,x92582,x92584,x92585,x92581)),x92582)+E(f777(f777(f127(x92581),x92582),f736(x92583,x92582,x92584,x92585,x92581)),x92585)+~E(f777(f777(f127(x92581),x92585),x92584),f777(f777(f127(x92581),x92582),x92583)) % 174.01/173.90 [9289]~P100(x92891)+P18(x92891,f777(f777(f145(x92892,x92891),x92893),f141(x92892,x92891,x92893,x92894,x92895)))+~P18(x92891,f777(f777(f145(x92892,x92891),x92893),x92895)) % 174.01/173.90 [9305]~P57(x93055,x93051,x93054,x93053)+P1(f777(f777(x93051,x93052),f540(x93053,x93054,x93051,x93055,x93052)))+~P1(f777(f777(f336(x93055),x93052),x93054)) % 174.01/173.90 [9403]~P1(f777(f777(f336(f857(x94031,x94031)),f777(f777(f243(x94031,x94031),x94035),x94033)),f302(x94031,x94034)))+P1(f777(f777(f336(f857(x94031,x94031)),f777(f777(f243(x94031,x94031),x94032),x94033)),f777(f777(f283(x94031,x94031,x94031),x94034),f302(x94031,x94034))))+~P1(f777(f777(f336(f857(x94031,x94031)),f777(f777(f243(x94031,x94031),x94032),x94035)),f777(f777(f283(x94031,x94031,x94031),x94034),f302(x94031,x94034)))) % 174.01/173.90 [9404]~P1(f777(f777(f336(f857(x94041,x94041)),f777(f777(f243(x94041,x94041),x94042),x94045)),f302(x94041,x94044)))+P1(f777(f777(f336(f857(x94041,x94041)),f777(f777(f243(x94041,x94041),x94042),x94043)),f777(f777(f283(x94041,x94041,x94041),x94044),f302(x94041,x94044))))+~P1(f777(f777(f336(f857(x94041,x94041)),f777(f777(f243(x94041,x94041),x94045),x94043)),f777(f777(f283(x94041,x94041,x94041),x94044),f302(x94041,x94044)))) % 174.01/173.90 [9406]P1(f777(f777(f336(f857(f852(x94061),f852(x94061))),f777(f777(f243(f852(x94061),f852(x94061)),x94062),x94063)),f149(x94061,f302(x94061,x94064))))+~P1(f777(f777(f336(f857(f852(x94061),f852(x94061))),f777(f777(f243(f852(x94061),f852(x94061)),x94062),x94065)),f149(x94061,f302(x94061,x94064))))+~P1(f777(f777(f336(f857(f852(x94061),f852(x94061))),f777(f777(f243(f852(x94061),f852(x94061)),x94065),x94063)),f149(x94061,f302(x94061,x94064)))) % 174.01/173.90 [9410]E(f777(f777(f127(x94101),x94102),f736(x94103,x94102,x94104,x94105,x94101)),x94105)+E(f777(f777(f127(x94101),f737(x94103,x94102,x94104,x94105,x94101)),x94103),x94104)+~E(f777(f777(f127(x94101),x94102),x94103),f777(f777(f127(x94101),x94105),x94104)) % 174.01/173.90 [9411]E(f777(f777(f127(x94111),x94112),f737(x94113,x94114,x94115,x94112,x94111)),x94114)+E(f777(f777(f127(x94111),f736(x94113,x94114,x94115,x94112,x94111)),x94115),x94113)+~E(f777(f777(f127(x94111),x94112),x94115),f777(f777(f127(x94111),x94114),x94113)) % 174.01/173.90 [9468]P1(f777(f777(f336(f857(x94681,x94681)),f777(f777(f243(x94681,x94681),x94682),x94683)),f777(f777(f283(x94681,x94681,x94681),x94684),f302(x94681,x94684))))+~P1(f777(f777(f336(f857(x94681,x94681)),f777(f777(f243(x94681,x94681),x94682),x94685)),f777(f777(f283(x94681,x94681,x94681),x94684),f302(x94681,x94684))))+~P1(f777(f777(f336(f857(x94681,x94681)),f777(f777(f243(x94681,x94681),x94685),x94683)),f777(f777(f283(x94681,x94681,x94681),x94684),f302(x94681,x94684)))) % 174.01/173.90 [9501]E(f777(f777(f127(x95011),f736(x95012,x95013,x95014,x95015,x95011)),x95014),x95012)+~E(f777(f777(f127(x95011),x95013),x95012),f777(f777(f127(x95011),x95015),x95014))+E(f777(f777(f127(x95011),f737(x95012,x95013,x95014,x95015,x95011)),x95012),x95014) % 174.01/173.90 [9516]~P57(x95161,x95164,x95163,x95162)+~P1(f777(f777(f336(x95161),x95165),x95163))+P1(f777(f777(f336(x95161),f540(x95162,x95163,x95164,x95161,x95165)),x95162)) % 174.01/173.90 [9624]~P1(f777(f777(f336(f857(f858(x96241,a845),f858(x96241,a845))),f777(f777(f243(f858(x96241,a845),f858(x96241,a845)),x96244),x96243)),f326(x96241,x96242)))+~P1(f777(f777(f336(x96241),x96245),x96244))+P1(f777(f777(f336(x96241),f626(x96242,x96243,x96244,x96241,x96245)),x96243)) % 174.01/173.90 [6469]~P21(x64692,x64695,x64691)+~P1(f777(f65(x64692),x64694))+E(f777(x64691,f777(f777(f304(x64692),x64693),x64694)),f777(f777(f68(x64692,x64692,x64695),x64693),x64694)) % 174.01/173.90 [6470]~E(x64703,x64704)+~E(x64702,x64705)+E(f777(f777(f304(x64701),x64702),f777(f777(f304(x64701),x64703),f182(f858(x64701,a845)))),f777(f777(f304(x64701),x64704),f777(f777(f304(x64701),x64705),f182(f858(x64701,a845))))) % 174.01/173.90 [6482]P1(f777(x64822,x64825))+E(f164(x64821,x64822,f777(f777(f127(x64821),x64823),x64824)),f164(x64821,x64822,x64823))+~P1(f777(f777(f336(x64821),x64825),f777(f160(x64821),x64823))) % 174.01/173.90 [6519]E(f777(x65191,x65192),f241(f858(x65193,a845)))+~E(f777(f777(f49(x65194,f858(x65193,a845)),x65195),x65191),f241(f858(x65193,a845)))+~P1(f777(f777(f336(x65194),x65192),x65195)) % 174.01/173.90 [6520]E(f777(x65201,x65202),f182(f858(x65203,a845)))+~E(f777(f777(f48(x65204,f858(x65203,a845)),x65205),x65201),f182(f858(x65203,a845)))+~P1(f777(f777(f336(x65204),x65202),x65205)) % 174.01/173.90 [6841]~P1(f777(f777(f189(x68411),x68413),x68415))+~P1(f777(f777(f189(x68412),x68415),x68414))+P1(f777(f777(f189(f38(x68411,x68412)),x68413),x68414)) % 174.01/173.90 [7045]~E(x70452,x70454)+~P137(x70451)+E(f777(f777(f84(x70451),f777(f777(f85(x70451),x70452),x70453)),f777(f777(f85(x70451),x70454),x70455)),f777(f777(f84(x70451),f777(f777(f85(x70451),x70452),x70455)),f777(f777(f85(x70451),x70454),x70453))) % 174.01/173.90 [7105]~P9(x71051)+~P1(f777(f777(f336(x71054),x71053),x71055))+P1(f777(f777(f234(x71051),f777(x71052,x71053)),f777(f777(f48(x71054,x71051),x71055),x71052))) % 174.01/173.90 [7154]~P102(x71541)+P1(f777(f777(f234(x71541),f777(x71542,x71543)),f777(x71544,x71543)))+~P1(f777(f777(f234(f858(x71545,x71541)),x71542),x71544)) % 174.01/173.90 [7290]E(x72901,x72902)+E(x72903,x72901)+~E(f777(f777(f304(x72904),x72901),f777(f777(f304(x72904),x72905),f182(f858(x72904,a845)))),f777(f777(f304(x72904),x72902),f777(f777(f304(x72904),x72903),f182(f858(x72904,a845))))) % 174.01/173.90 [7291]E(x72911,x72912)+E(x72913,x72911)+~E(f777(f777(f304(x72914),x72913),f777(f777(f304(x72914),x72912),f182(f858(x72914,a845)))),f777(f777(f304(x72914),x72915),f777(f777(f304(x72914),x72911),f182(f858(x72914,a845))))) % 174.01/173.90 [7292]E(x72921,x72922)+E(x72921,x72923)+~E(f777(f777(f304(x72924),x72923),f777(f777(f304(x72924),x72922),f182(f858(x72924,a845)))),f777(f777(f304(x72924),x72925),f777(f777(f304(x72924),x72921),f182(f858(x72924,a845))))) % 174.01/173.90 [7293]E(x72931,x72932)+E(x72931,x72933)+~E(f777(f777(f304(x72934),x72931),f777(f777(f304(x72934),x72935),f182(f858(x72934,a845)))),f777(f777(f304(x72934),x72932),f777(f777(f304(x72934),x72933),f182(f858(x72934,a845))))) % 174.01/173.90 [7839]P29(x78391,x78392,x78393,x78394)+~P29(x78391,x78392,x78393,x78395)+~P1(f777(f777(f234(f858(x78391,a845)),x78394),x78395)) % 174.01/173.90 [7942]P1(f777(x79421,x79422))+~P1(f777(f777(f189(x79424),x79422),x79425))+P1(f777(f777(f189(f35(x79421,x79423,x79424)),x79422),x79425)) % 174.01/173.90 [7970]~P1(f777(x79701,x79704))+~P1(f777(f777(f189(x79702),x79704),x79705))+P1(f777(f777(f189(f35(x79701,x79702,x79703)),x79704),x79705)) % 174.01/173.90 [8015]E(x80151,x80152)+~E(f777(f305(x80153,x80154,x80155),x80151),f777(f305(x80153,x80154,x80155),x80152))+~P29(x80153,x80154,x80155,f777(f777(f105(f858(x80153,a845)),x80151),x80152)) % 174.01/173.90 [8115]~P29(x81151,x81152,x81153,x81155)+~P29(x81151,x81152,x81153,x81154)+P29(x81151,x81152,x81153,f777(f777(f106(f858(x81151,a845)),x81154),x81155)) % 174.01/173.90 [8220]~P66(x82201)+E(f777(f777(f84(x82201),f777(x82202,x82203)),f777(f157(x82201),f777(f777(f145(x82204,x82201),x82202),f153(x82204,x82203,x82205)))),f777(f157(x82201),f777(f777(f145(x82204,x82201),x82202),x82205)))+~P1(f777(f777(f336(x82204),x82203),f777(f160(x82204),x82205))) % 174.01/173.90 [8307]~P100(x83071)+~P18(x83071,f777(f777(f145(x83072,x83071),x83073),x83075))+P18(x83071,f777(f777(f145(x83072,x83071),x83073),f777(f777(f140(x83072,x83071,x83073),x83074),x83075))) % 174.01/173.90 [8388]P1(f777(x83881,x83882))+P1(f777(f777(f189(x83883),x83882),x83884))+~P1(f777(f777(f189(f35(x83881,x83885,x83883)),x83882),x83884)) % 174.01/173.90 [8399]~P9(x83991)+P1(f777(f777(f234(x83991),f777(f777(f48(x83992,x83991),x83993),x83994)),f777(f777(f48(x83992,x83991),x83995),x83994)))+~P1(f777(f777(f234(f858(x83992,a845)),x83993),x83995)) % 174.01/173.90 [8400]~P9(x84001)+P1(f777(f777(f234(x84001),f777(f777(f49(x84002,x84001),x84003),x84004)),f777(f777(f49(x84002,x84001),x84005),x84004)))+~P1(f777(f777(f234(f858(x84002,a845)),x84005),x84003)) % 174.01/173.90 [8409]~P1(f777(x84094,x84092))+P1(f777(f777(f189(x84091),x84092),x84093))+~P1(f777(f777(f189(f35(x84094,x84091,x84095)),x84092),x84093)) % 174.01/173.90 [8433]~P100(x84333)+P1(f777(f129(x84331),x84332))+~P1(f777(f129(x84331),f777(f777(f140(x84331,x84333,x84334),x84335),x84332))) % 174.01/173.90 [8443]P1(f777(f777(f189(x84431),x84432),x84433))+P1(f777(f777(f189(x84434),x84432),x84433))+~P1(f777(f777(f189(f35(x84435,x84431,x84434)),x84432),x84433)) % 174.01/173.90 [8567]~P100(x85671)+~P1(f777(f777(f336(x85672),x85673),f777(f160(x85672),x85674)))+~P1(f777(f129(x85672),f777(f777(f140(x85672,x85671,x85675),x85673),x85674))) % 174.01/173.90 [8642]~P100(x86421)+P18(x86421,f777(f777(f145(x86422,x86421),x86423),x86424))+~P18(x86421,f777(f777(f145(x86422,x86421),x86423),f777(f777(f140(x86422,x86421,x86423),x86425),x86424))) % 174.01/173.90 [8727]~P100(x87272)+E(f777(f777(f140(x87271,x87272,x87273),x87274),x87275),f141(x87271,x87272,x87273,x87274,x87275))+P1(f777(f777(f336(x87272),f777(x87273,x87274)),f777(f305(x87271,x87272,x87273),f777(f160(x87271),x87275)))) % 174.01/173.90 [8794]~P100(x87942)+E(f141(x87941,x87942,x87943,x87944,x87945),x87945)+~P1(f777(f777(f336(x87942),f777(x87943,x87944)),f777(f305(x87941,x87942,x87943),f777(f160(x87941),x87945)))) % 174.01/173.90 [8808]~P29(x88082,x88081,x88083,x88085)+P1(f777(f777(f235(f858(x88081,a845)),f777(f305(x88082,x88081,x88083),x88084)),f777(f305(x88082,x88081,x88083),x88085)))+~P1(f777(f777(f235(f858(x88082,a845)),x88084),x88085)) % 174.01/173.90 [8955]~P29(x89551,x89552,x89553,f241(f858(x89551,a845)))+~P1(f777(f777(f234(f858(x89552,a845)),x89554),f777(f305(x89551,x89552,x89553),x89555)))+P1(f777(f777(f234(f858(x89551,a845)),f777(f307(x89551,x89552,x89553),x89554)),x89555)) % 174.01/173.90 [8974]~E(f777(f305(x89743,x89741,x89744),f241(f858(x89743,a845))),f241(f858(x89741,a845)))+P1(f777(f777(f234(f858(x89741,a845)),x89742),f777(f305(x89743,x89741,x89744),x89745)))+~P1(f777(f777(f234(f858(x89743,a845)),f777(f307(x89743,x89741,x89744),x89742)),x89745)) % 174.01/173.90 [9012]~E(f777(f229(x90122),x90124),f777(f168(x90121,x90122,x90125),x90123))+~P1(f777(f129(x90121),f777(f777(f145(f857(x90121,x90122),x90121),f242(x90121,x90122)),x90125)))+P1(f777(f777(f336(f857(x90121,x90122)),f777(f777(f243(x90121,x90122),x90123),x90124)),f777(f160(f857(x90121,x90122)),x90125))) % 174.01/173.90 [9076]~P29(x90761,x90764,x90765,f241(f858(x90761,a845)))+~P1(f777(f777(f234(f858(x90764,a845)),f777(f305(x90761,x90764,x90765),x90762)),f777(f305(x90761,x90764,x90765),x90763)))+P1(f777(f777(f234(f858(x90761,a845)),x90762),x90763)) % 174.01/173.90 [9142]E(f777(f229(x91421),x91422),f777(f168(x91423,x91421,x91424),x91425))+~P1(f777(f129(x91423),f777(f777(f145(f857(x91423,x91421),x91423),f242(x91423,x91421)),x91424)))+~P1(f777(f777(f336(f857(x91423,x91421)),f777(f777(f243(x91423,x91421),x91425),x91422)),f777(f160(f857(x91423,x91421)),x91424))) % 174.01/173.90 [9144]E(f777(f168(x91441,x91442,x91443),x91444),f777(f229(x91442),x91445))+~P1(f777(f129(x91441),f777(f777(f145(f857(x91441,x91442),x91441),f242(x91441,x91442)),x91443)))+~P1(f777(f777(f336(f857(x91441,x91442)),f777(f777(f243(x91441,x91442),x91444),x91445)),f777(f160(f857(x91441,x91442)),x91443))) % 174.01/173.90 [9351]~P20(x93511,x93512,x93513)+~P1(f777(f65(x93511),x93515))+P1(f777(f70(x93511,x93512,x93513,x93514,x93515),f777(f777(f68(x93511,x93512,x93513),x93514),x93515))) % 174.01/173.90 [9425]P1(f777(x94251,f701(x94252,x94251,x94253,x94254,x94255)))+~P1(f777(f777(f234(f858(x94255,a845)),x94254),x94253))+P1(f777(f777(f234(f858(x94255,a845)),f777(f777(f106(f858(x94255,a845)),x94254),f777(f258(x94255),x94251))),f777(f777(f106(f858(x94255,a845)),x94253),f777(f258(x94255),x94252)))) % 174.01/173.90 [9514]~P9(x95145)+P1(f777(f777(f336(x95141),f666(x95142,x95143,x95141,x95144,x95145)),x95143))+P1(f777(f777(f234(x95145),x95144),f777(f777(f49(x95141,x95145),x95143),x95142))) % 174.01/173.90 [9526]~P1(f777(x95265,f701(x95265,x95263,x95264,x95262,x95261)))+~P1(f777(f777(f234(f858(x95261,a845)),x95262),x95264))+P1(f777(f777(f234(f858(x95261,a845)),f777(f777(f106(f858(x95261,a845)),x95262),f777(f258(x95261),x95263))),f777(f777(f106(f858(x95261,a845)),x95264),f777(f258(x95261),x95265)))) % 174.01/173.90 [9589]P1(f777(f777(f336(x95891),f701(x95892,x95893,x95894,x95895,x95891)),x95895))+~P1(f777(f777(f234(f858(x95891,a845)),x95895),x95894))+P1(f777(f777(f234(f858(x95891,a845)),f777(f777(f106(f858(x95891,a845)),x95895),f777(f258(x95891),x95893))),f777(f777(f106(f858(x95891,a845)),x95894),f777(f258(x95891),x95892)))) % 174.01/173.90 [9635]~P9(x96351)+~P1(f777(f777(f234(x96351),x96352),f777(x96355,f666(x96355,x96354,x96353,x96352,x96351))))+P1(f777(f777(f234(x96351),x96352),f777(f777(f49(x96353,x96351),x96354),x96355))) % 174.01/173.90 [9665]~P70(x96651)+~P1(f777(f65(x96652),x96655))+E(f777(f777(f777(f69(x96651,x96652,f85(x96651)),f777(f777(f22(x96652,x96651,x96651),f777(f777(f12(x96651,f858(x96651,x96651),x96652),f85(x96651)),x96653)),x96654)),f82(x96651)),x96655),f777(f777(f85(x96651),f777(f777(f777(f69(x96651,x96652,f85(x96651)),x96653),f82(x96651)),x96655)),f777(f777(f777(f69(x96651,x96652,f85(x96651)),x96654),f82(x96651)),x96655))) % 174.01/173.90 [9714]~P1(f777(f777(f336(f857(f858(x97141,a845),f858(x97141,a845))),f777(f777(f243(f858(x97141,a845),f858(x97141,a845)),x97145),x97144)),f326(x97141,x97143)))+~P1(f777(f777(f336(x97141),x97142),x97145))+P1(f777(f777(f336(f857(x97141,x97141)),f777(f777(f243(x97141,x97141),x97142),f626(x97143,x97144,x97145,x97141,x97142))),x97143)) % 174.01/173.90 [9862]~P1(f777(f777(f336(f857(f852(x98621),f852(x98621))),f777(f777(f243(f852(x98621),f852(x98621)),f777(f777(f127(x98621),x98625),x98622)),f777(f777(f127(x98621),x98625),x98623))),f139(x98621,x98624)))+P1(f777(f777(f336(f857(f852(x98621),f852(x98621))),f777(f777(f243(f852(x98621),f852(x98621)),x98622),x98623)),f139(x98621,x98624)))+P1(f777(f777(f336(f857(x98621,x98621)),f777(f777(f243(x98621,x98621),f742(x98624,x98623,x98622,x98625,x98621)),f742(x98624,x98623,x98622,x98625,x98621))),x98624)) % 174.01/173.90 [7157]~E(x71573,x71575)+E(f777(f777(f155(x71571),f777(f777(f150(x71571,x71572),x71573),x71574)),x71575),x71574)+~P1(f777(f777(f235(a851),x71573),f777(f183(f852(x71571)),x71572))) % 174.01/173.90 [7166]~E(f777(f183(f852(x71661)),x71663),f777(f183(f852(x71662)),x71664))+E(f777(f168(x71661,x71662,f777(f777(f169(x71661,x71662),x71663),x71664)),x71665),f185(x71662))+P1(f777(f777(f336(x71661),x71665),f777(f160(x71661),x71663))) % 174.01/173.90 [7286]~E(f777(f777(f127(x72861),x72862),x72864),f777(f777(f127(x72861),x72863),x72865))+E(f777(f777(f161(x72861),f777(f183(f852(x72861)),x72862)),x72863),x72862)+P1(f777(f777(f234(a851),f777(f183(f852(x72861)),x72863)),f777(f183(f852(x72861)),x72862))) % 174.01/173.90 [7800]~E(f777(f777(f127(x78001),x78002),x78004),f777(f777(f127(x78001),x78003),x78005))+E(f777(f777(f161(x78001),f777(f183(f852(x78001)),x78002)),x78003),x78002)+~P1(f777(f777(f234(a851),f777(f183(f852(x78001)),x78002)),f777(f183(f852(x78001)),x78003))) % 174.01/173.90 [7824]~P1(f777(f65(x78241),f777(x78244,x78245)))+~P1(f777(f777(f336(x78242),x78245),x78243))+P1(f777(f65(x78241),f777(f777(f49(x78242,f858(x78241,a845)),x78243),x78244))) % 174.01/173.90 [7936]~E(f777(f183(f852(x79361)),x79362),f777(f183(f852(x79363)),x79364))+~E(f777(f168(x79361,x79363,f777(f777(f169(x79361,x79363),x79362),x79364)),x79365),f185(x79363))+~P1(f777(f777(f336(x79361),x79365),f777(f160(x79361),x79362))) % 174.01/173.90 [8002]~P47(x80021,x80023,x80025)+~P47(x80021,x80022,x80024)+P47(x80021,f777(f777(f105(f858(x80021,a845)),x80022),x80023),f777(f777(f105(f858(f857(x80021,x80021),a845)),x80024),x80025)) % 174.01/173.90 [8003]~P47(x80031,x80033,x80035)+~P47(x80031,x80032,x80034)+P47(x80031,f777(f777(f106(f858(x80031,a845)),x80032),x80033),f777(f777(f106(f858(f857(x80031,x80031),a845)),x80034),x80035)) % 174.01/173.90 [8351]E(f777(f777(f243(x83511,x83512),f777(f777(f155(x83511),x83513),x83514)),f777(f777(f155(x83512),x83515),x83514)),f777(f777(f155(f857(x83511,x83512)),f777(f777(f169(x83511,x83512),x83513),x83515)),x83514))+~P1(f777(f777(f235(a851),x83514),f777(f183(f852(x83511)),x83513)))+~P1(f777(f777(f235(a851),x83514),f777(f183(f852(x83512)),x83515))) % 174.01/173.90 [8511]~P47(x85111,x85113,x85114)+P1(f777(f777(f336(x85111),x85112),x85113))+~P1(f777(f777(f336(f857(x85111,x85111)),f777(f777(f243(x85111,x85111),x85115),x85112)),x85114)) % 174.01/173.90 [8512]~P47(x85121,x85123,x85124)+P1(f777(f777(f336(x85121),x85122),x85123))+~P1(f777(f777(f336(f857(x85121,x85121)),f777(f777(f243(x85121,x85121),x85122),x85125)),x85124)) % 174.01/173.90 [8513]~P12(x85131,x85133,x85134)+P1(f777(f777(f336(x85131),x85132),x85133))+~P1(f777(f777(f336(f857(x85131,x85131)),f777(f777(f243(x85131,x85131),x85135),x85132)),x85134)) % 174.01/173.90 [8514]~P12(x85141,x85143,x85144)+P1(f777(f777(f336(x85141),x85142),x85143))+~P1(f777(f777(f336(f857(x85141,x85141)),f777(f777(f243(x85141,x85141),x85142),x85145)),x85144)) % 174.01/173.90 [8750]~P12(x87501,x87505,x87502)+E(f777(f279(x87501,x87501,x87502),f777(f777(f304(x87501),x87503),f182(f858(x87501,a845)))),f777(f279(x87501,x87501,x87502),f777(f777(f304(x87501),x87504),f182(f858(x87501,a845)))))+~P1(f777(f777(f336(f857(x87501,x87501)),f777(f777(f243(x87501,x87501),x87503),x87504)),x87502)) % 174.01/173.90 [8914]P1(f777(x89141,x89142))+~P1(f777(f777(f336(x89143),x89142),x89145))+P1(f777(f777(f336(x89143),f384(x89141,x89144,x89145,x89143)),f777(f777(f105(f858(x89143,a845)),x89145),x89144))) % 174.01/173.90 [8915]P1(f777(x89151,x89152))+~P1(f777(f777(f336(x89153),x89152),x89154))+P1(f777(f777(f336(x89153),f384(x89151,x89154,x89155,x89153)),f777(f777(f105(f858(x89153,a845)),x89155),x89154))) % 174.01/173.90 [8923]~P1(f777(x89232,x89235))+~P1(f777(f777(f336(x89231),x89235),x89234))+P1(f777(f777(f336(x89231),f380(x89232,x89233,x89234,x89231)),f777(f777(f105(f858(x89231,a845)),x89234),x89233))) % 174.01/173.90 [8924]~P1(f777(x89242,x89245))+~P1(f777(f777(f336(x89241),x89245),x89243))+P1(f777(f777(f336(x89241),f380(x89242,x89243,x89244,x89241)),f777(f777(f105(f858(x89241,a845)),x89244),x89243))) % 174.01/173.90 [8937]~P1(f777(f777(f234(f858(x89371,a845)),x89375),x89373))+~P1(f777(f777(f234(f858(x89371,a845)),x89372),x89374))+P1(f777(f777(f234(f858(x89371,a845)),f777(f777(f5(f858(x89371,a845)),x89372),x89373)),f777(f777(f5(f858(x89371,a845)),x89374),x89375))) % 174.01/173.90 [8938]~P1(f777(f777(f234(f858(x89381,a845)),x89383),x89385))+~P1(f777(f777(f234(f858(x89381,a845)),x89382),x89384))+P1(f777(f777(f234(f858(x89381,a845)),f777(f777(f105(f858(x89381,a845)),x89382),x89383)),f777(f777(f105(f858(x89381,a845)),x89384),x89385))) % 174.01/173.90 [8939]~P1(f777(f777(f234(f858(x89391,a845)),x89393),x89395))+~P1(f777(f777(f234(f858(x89391,a845)),x89392),x89394))+P1(f777(f777(f234(f858(x89391,a845)),f777(f777(f106(f858(x89391,a845)),x89392),x89393)),f777(f777(f106(f858(x89391,a845)),x89394),x89395))) % 174.01/173.90 [9028]P1(f777(f777(f336(f857(x90281,x90281)),f777(f777(f243(x90281,x90281),x90282),x90283)),f329(x90281,x90284,x90285)))+~P1(f777(f777(f234(a851),f777(x90284,x90282)),f777(x90284,x90283)))+~P1(f777(f777(f336(f857(x90281,x90281)),f777(f777(f243(x90281,x90281),x90282),x90283)),x90285)) % 174.01/173.90 [9035]~E(f777(f183(f852(x90351)),x90353),f777(f183(f852(x90352)),x90354))+E(f777(f168(x90351,x90352,f777(f777(f169(x90351,x90352),x90353),x90354)),x90355),f777(f229(x90352),f717(x90355,x90354,x90352,x90353,x90351)))+~P1(f777(f777(f336(x90351),x90355),f777(f160(x90351),x90353))) % 174.01/173.90 [9184]P1(f777(f777(f336(f857(x91841,x91841)),f777(f777(f243(x91841,x91841),x91842),x91843)),f302(x91841,x91844)))+~P1(f777(f777(f336(f857(x91841,x91841)),f777(f777(f243(x91841,x91841),x91842),x91845)),f302(x91841,x91844)))+~P1(f777(f777(f336(f857(x91841,x91841)),f777(f777(f243(x91841,x91841),x91845),x91843)),x91844)) % 174.01/173.90 [9185]P1(f777(f777(f336(f857(x91851,x91851)),f777(f777(f243(x91851,x91851),x91852),x91853)),f302(x91851,x91854)))+~P1(f777(f777(f336(f857(x91851,x91851)),f777(f777(f243(x91851,x91851),x91855),x91853)),f302(x91851,x91854)))+~P1(f777(f777(f336(f857(x91851,x91851)),f777(f777(f243(x91851,x91851),x91852),x91855)),x91854)) % 174.01/173.90 [9279]E(x92791,x92792)+E(f777(a116,f644(x92793,x92794,x92791,x92792,x92795)),x92794)+~P1(f777(f777(f336(f857(x92795,x92795)),f777(f777(f243(x92795,x92795),x92792),x92791)),f777(f777(f175(f857(x92795,x92795),a845),x92794),x92793))) % 174.01/173.90 [9280]E(x92801,x92802)+E(f777(a116,f646(x92803,x92804,x92801,x92802,x92805)),x92804)+~P1(f777(f777(f336(f857(x92805,x92805)),f777(f777(f243(x92805,x92805),x92802),x92801)),f777(f777(f175(f857(x92805,x92805),a845),x92804),x92803))) % 174.01/173.90 [9281]E(x92811,f4(a851))+E(f777(a116,f644(x92812,x92811,x92813,x92814,x92815)),x92811)+~P1(f777(f777(f336(f857(x92815,x92815)),f777(f777(f243(x92815,x92815),x92814),x92813)),f777(f777(f175(f857(x92815,x92815),a845),x92811),x92812))) % 174.01/173.90 [9282]E(x92821,f4(a851))+E(f777(a116,f646(x92822,x92821,x92823,x92824,x92825)),x92821)+~P1(f777(f777(f336(f857(x92825,x92825)),f777(f777(f243(x92825,x92825),x92824),x92823)),f777(f777(f175(f857(x92825,x92825),a845),x92821),x92822))) % 174.01/173.90 [9301]P1(f777(f777(f336(f857(x93011,x93011)),f777(f777(f243(x93011,x93011),x93012),x93013)),f777(f777(f283(x93011,x93011,x93011),x93014),f302(x93011,x93014))))+~P1(f777(f777(f336(f857(x93011,x93011)),f777(f777(f243(x93011,x93011),x93012),x93015)),x93014))+~P1(f777(f777(f336(f857(x93011,x93011)),f777(f777(f243(x93011,x93011),x93015),x93013)),x93014)) % 174.01/173.90 [9310]~P1(f777(f777(f336(f857(x93101,x93101)),f777(f777(f243(x93101,x93101),x93102),x93105)),f302(x93101,x93104)))+P1(f777(f777(f336(f857(x93101,x93101)),f777(f777(f243(x93101,x93101),x93102),x93103)),f777(f777(f283(x93101,x93101,x93101),x93104),f302(x93101,x93104))))+~P1(f777(f777(f336(f857(x93101,x93101)),f777(f777(f243(x93101,x93101),x93105),x93103)),x93104)) % 174.01/173.90 [9347]~P12(x93471,x93475,x93472)+~P1(f777(f777(f336(f857(x93471,x93471)),f777(f777(f243(x93471,x93471),x93473),x93474)),x93472))+P1(f777(f777(f234(f858(x93471,a845)),f777(f279(x93471,x93471,x93472),f777(f777(f304(x93471),x93473),f182(f858(x93471,a845))))),f777(f279(x93471,x93471,x93472),f777(f777(f304(x93471),x93474),f182(f858(x93471,a845)))))) % 174.01/173.90 [9399]P1(f777(f777(f336(f857(x93991,x93991)),f777(f777(f243(x93991,x93991),x93992),x93993)),f777(f777(f283(x93991,x93991,x93991),x93994),f302(x93991,x93994))))+~P1(f777(f777(f336(f857(x93991,x93991)),f777(f777(f243(x93991,x93991),x93992),x93995)),f777(f777(f283(x93991,x93991,x93991),x93994),f302(x93991,x93994))))+~P1(f777(f777(f336(f857(x93991,x93991)),f777(f777(f243(x93991,x93991),x93995),x93993)),x93994)) % 174.01/173.90 [9400]P1(f777(f777(f336(f857(x94001,x94001)),f777(f777(f243(x94001,x94001),x94002),x94003)),f777(f777(f283(x94001,x94001,x94001),x94004),f302(x94001,x94004))))+~P1(f777(f777(f336(f857(x94001,x94001)),f777(f777(f243(x94001,x94001),x94005),x94003)),f777(f777(f283(x94001,x94001,x94001),x94004),f302(x94001,x94004))))+~P1(f777(f777(f336(f857(x94001,x94001)),f777(f777(f243(x94001,x94001),x94002),x94005)),x94004)) % 174.01/173.90 [9447]~P1(f777(f70(x94471,x94471,x94474,x94472,x94473),x94475))+P1(f777(f777(f336(x94471),x94472),x94473))+P1(f777(f66(x94471,x94474,f777(f777(f304(x94471),x94472),x94473)),x94475)) % 174.01/173.90 [9490]~E(f777(f305(x94903,x94902,x94905),x94904),x94901)+E(x94901,f182(f858(x94902,a845)))+P1(f777(f777(f234(f858(x94903,a845)),f777(f305(x94902,x94903,f524(x94904,x94903,x94902,x94901)),x94901)),x94904)) % 174.01/173.90 [9529]~P9(x95295)+P1(f777(f777(f336(x95291),f393(x95292,x95293,x95294,x95291,x95295)),x95294))+P1(f777(f777(f234(x95295),f777(f777(f48(x95291,x95295),x95294),x95293)),x95292)) % 174.01/173.90 [9691]E(x96911,x96912)+P1(f777(f777(f336(f857(x96913,x96913)),f777(f777(f243(x96913,x96913),x96911),f645(x96914,x96915,x96912,x96911,x96913))),x96914))+~P1(f777(f777(f336(f857(x96913,x96913)),f777(f777(f243(x96913,x96913),x96911),x96912)),f777(f777(f175(f857(x96913,x96913),a845),x96915),x96914))) % 174.01/173.90 [9692]E(x96921,f4(a851))+P1(f777(f777(f336(f857(x96922,x96922)),f777(f777(f243(x96922,x96922),x96923),f645(x96924,x96921,x96925,x96923,x96922))),x96924))+~P1(f777(f777(f336(f857(x96922,x96922)),f777(f777(f243(x96922,x96922),x96923),x96925)),f777(f777(f175(f857(x96922,x96922),a845),x96921),x96924))) % 174.01/173.90 [9736]~P9(x97361)+~P1(f777(f777(f234(x97361),f777(x97364,f393(x97365,x97364,x97363,x97362,x97361))),x97365))+P1(f777(f777(f234(x97361),f777(f777(f48(x97362,x97361),x97363),x97364)),x97365)) % 174.01/173.90 [9791]E(x97911,x97912)+P1(f777(f777(f336(f857(x97913,x97913)),f777(f777(f243(x97913,x97913),f647(x97914,x97915,x97911,x97912,x97913)),x97911)),x97914))+~P1(f777(f777(f336(f857(x97913,x97913)),f777(f777(f243(x97913,x97913),x97912),x97911)),f777(f777(f175(f857(x97913,x97913),a845),x97915),x97914))) % 174.01/173.90 [9792]E(x97921,f4(a851))+P1(f777(f777(f336(f857(x97922,x97922)),f777(f777(f243(x97922,x97922),f647(x97923,x97921,x97924,x97925,x97922)),x97924)),x97923))+~P1(f777(f777(f336(f857(x97922,x97922)),f777(f777(f243(x97922,x97922),x97925),x97924)),f777(f777(f175(f857(x97922,x97922),a845),x97921),x97923))) % 174.01/173.90 [9796]E(x97961,x97962)+P1(f777(f777(f336(f857(x97963,x97963)),f777(f777(f243(x97963,x97963),x97961),f647(x97964,x97965,x97962,x97961,x97963))),f777(f777(f175(f857(x97963,x97963),a845),f646(x97964,x97965,x97962,x97961,x97963)),x97964)))+~P1(f777(f777(f336(f857(x97963,x97963)),f777(f777(f243(x97963,x97963),x97961),x97962)),f777(f777(f175(f857(x97963,x97963),a845),x97965),x97964))) % 174.01/173.90 [9797]E(x97971,f4(a851))+P1(f777(f777(f336(f857(x97972,x97972)),f777(f777(f243(x97972,x97972),x97973),f647(x97974,x97971,x97975,x97973,x97972))),f777(f777(f175(f857(x97972,x97972),a845),f646(x97974,x97971,x97975,x97973,x97972)),x97974)))+~P1(f777(f777(f336(f857(x97972,x97972)),f777(f777(f243(x97972,x97972),x97973),x97975)),f777(f777(f175(f857(x97972,x97972),a845),x97971),x97974))) % 174.01/173.90 [9853]E(x98531,x98532)+P1(f777(f777(f336(f857(x98533,x98533)),f777(f777(f243(x98533,x98533),f645(x98534,x98535,x98531,x98532,x98533)),x98531)),f777(f777(f175(f857(x98533,x98533),a845),f644(x98534,x98535,x98531,x98532,x98533)),x98534)))+~P1(f777(f777(f336(f857(x98533,x98533)),f777(f777(f243(x98533,x98533),x98532),x98531)),f777(f777(f175(f857(x98533,x98533),a845),x98535),x98534))) % 174.01/173.90 [9854]E(x98541,f4(a851))+P1(f777(f777(f336(f857(x98542,x98542)),f777(f777(f243(x98542,x98542),f645(x98543,x98541,x98544,x98545,x98542)),x98544)),f777(f777(f175(f857(x98542,x98542),a845),f644(x98543,x98541,x98544,x98545,x98542)),x98543)))+~P1(f777(f777(f336(f857(x98542,x98542)),f777(f777(f243(x98542,x98542),x98545),x98544)),f777(f777(f175(f857(x98542,x98542),a845),x98541),x98543))) % 174.01/173.90 [9887]~P66(x98872)+~P1(f777(f65(x98871),x98875))+E(f777(f777(f10(x98871,x98872),f777(f777(f11(x98871,x98872,x98872),f777(f777(f22(x98871,x98872,f858(x98872,x98872)),f777(f777(f12(a845,f858(x98872,f858(x98872,x98872)),x98871),f100(x98872)),f777(f777(f11(x98871,f858(x98871,a845),a845),f336(x98871)),x98873))),x98874)),f4(x98872))),x98875),f777(f777(f10(x98871,x98872),x98874),f777(f777(f106(f858(x98871,a845)),x98875),x98873))) % 174.01/173.90 [8565]~P66(x85651)+~P1(f777(f65(x85654),x85655))+E(f777(f777(f84(x85651),f777(x85652,x85653)),f777(f777(f10(x85654,x85651),x85652),f777(f777(f5(f858(x85654,a845)),x85655),f777(f777(f304(x85654),x85653),f182(f858(x85654,a845)))))),f777(f777(f10(x85654,x85651),x85652),f777(f777(f304(x85654),x85653),x85655))) % 174.01/173.90 [8566]~P70(x85661)+~P1(f777(f65(x85664),x85665))+E(f777(f777(f85(x85661),f777(x85662,x85663)),f777(f777(f13(x85664,x85661),x85662),f777(f777(f5(f858(x85664,a845)),x85665),f777(f777(f304(x85664),x85663),f182(f858(x85664,a845)))))),f777(f777(f13(x85664,x85661),x85662),f777(f777(f304(x85664),x85663),x85665))) % 174.01/173.90 [8846]~P100(x88462)+~P18(x88462,f777(f144(x88462),f777(f777(f145(x88461,x88462),x88464),x88465)))+E(f777(f128(x88461,f777(f777(f12(x88462,a845,x88461),f777(f235(x88462),x88463)),x88464)),x88465),f164(x88461,f777(f777(f12(x88462,a845,x88461),f777(f235(x88462),x88463)),x88464),x88465)) % 174.01/173.90 [8867]~P66(x88671)+E(f777(f777(f84(x88671),f777(f777(f10(a851,x88671),x88672),f297(a851,x88673,x88674))),f777(f777(f10(a851,x88671),x88672),f297(a851,f777(f777(f84(a851),x88674),f82(a851)),f777(f777(f84(a851),x88674),x88675)))),f777(f777(f10(a851,x88671),x88672),f297(a851,x88673,f777(f777(f84(a851),x88674),x88675))))+~P1(f777(f777(f234(a851),x88673),f777(f777(f84(a851),x88674),f82(a851)))) % 174.01/173.90 [8868]~P1(f777(f777(f336(x88681),x88684),x88685))+~P1(f777(f777(f234(f858(x88681,a845)),f777(f160(x88681),x88682)),x88685))+P1(f777(f777(f234(f858(x88681,a845)),f777(f160(x88681),f777(f777(f150(x88681,x88682),x88683),x88684))),x88685)) % 174.01/173.90 [9085]~P9(x90852)+~P1(f777(f65(x90851),x90855))+E(f777(f777(f68(x90851,x90852,f777(f777(f12(x90852,f858(x90852,x90852),x90851),f105(x90852)),x90853)),x90854),x90855),f777(f777(f105(x90852),x90854),f777(f777(f48(x90851,x90852),x90855),x90853))) % 174.01/173.90 [9086]~P9(x90862)+~P1(f777(f65(x90861),x90865))+E(f777(f777(f68(x90861,x90862,f777(f777(f12(x90862,f858(x90862,x90862),x90861),f106(x90862)),x90863)),x90864),x90865),f777(f777(f106(x90862),x90864),f777(f777(f49(x90861,x90862),x90865),x90863))) % 174.01/173.90 [9171]~P29(x91711,x91712,x91713,x91715)+P29(x91711,x91712,x91713,f777(f777(f304(x91711),x91714),x91715))+P1(f777(f777(f336(x91712),f777(x91713,x91714)),f777(f305(x91711,x91712,x91713),f777(f777(f5(f858(x91711,a845)),x91715),f777(f777(f304(x91711),x91714),f182(f858(x91711,a845))))))) % 174.01/173.90 [9373]~P1(f777(f777(f336(f857(f852(x93731),f852(x93731))),f777(f777(f243(f852(x93731),f852(x93731)),x93732),x93734)),f149(x93731,x93735)))+~P1(f777(f777(f235(a851),x93733),f777(f183(f852(x93731)),x93732)))+P1(f777(f777(f336(f857(x93731,x93731)),f777(f777(f243(x93731,x93731),f777(f777(f155(x93731),x93732),x93733)),f777(f777(f155(x93731),x93734),x93733))),x93735)) % 174.01/173.90 [9599]E(x95991,f4(a3))+~P1(f777(f58(x95993,x95991),f777(f777(f243(a3,a3),x95994),x95995)))+P1(f777(f58(f777(f777(f85(a3),x95992),x95993),x95991),f777(f777(f243(a3,a3),f777(f777(f84(a3),f777(f777(f85(a3),x95992),x95994)),f777(f777(f45(a3),f777(f777(f85(a3),x95992),x95995)),x95991))),f54(a3,f777(f777(f85(a3),x95992),x95995),x95991)))) % 174.01/173.90 [9604]~P1(f777(f777(f235(a851),f4(a851)),x96043))+~P1(f777(f57(x96042,x96043),f777(f777(f243(a851,a851),x96044),x96045)))+P1(f777(f57(f777(f777(f85(a851),x96041),x96042),x96043),f777(f777(f243(a851,a851),f777(f777(f84(a851),f777(f777(f85(a851),x96041),x96044)),f777(f777(f45(a851),f777(f777(f85(a851),x96041),x96045)),x96043))),f54(a851,f777(f777(f85(a851),x96041),x96045),x96043)))) % 174.01/173.90 [9909]~P66(x99092)+~P1(f777(f65(x99091),x99094))+E(f777(f777(f10(x99091,x99092),x99093),f777(f258(x99091),f777(f777(f22(x99091,a845,a845),f777(f777(f12(a845,f858(a845,a845),x99091),a333),f777(f777(f11(x99091,f858(x99091,a845),a845),f336(x99091)),x99094))),f777(f777(f11(x99091,f858(x99091,a845),a845),f336(x99091)),x99095)))),f777(f777(f10(x99091,x99092),f777(f777(f11(x99091,x99092,x99092),f777(f777(f22(x99091,x99092,f858(x99092,x99092)),f777(f777(f12(a845,f858(x99092,f858(x99092,x99092)),x99091),f100(x99092)),f777(f777(f11(x99091,f858(x99091,a845),a845),f336(x99091)),x99095))),x99093)),f4(x99092))),x99094)) % 174.01/173.90 [8203]~E(f777(f777(f127(x82031),x82032),x82035),f777(f777(f127(x82031),x82033),x82034))+E(f777(f777(f127(x82031),f777(f777(f130(x82031),f777(f183(f852(x82031)),x82032)),x82033)),x82034),x82035)+P1(f777(f777(f234(a851),f777(f183(f852(x82031)),x82033)),f777(f183(f852(x82031)),x82032))) % 174.01/173.90 [8402]~E(f777(f777(f127(x84022),x84023),x84021),f777(f777(f127(x84022),x84024),x84025))+E(x84021,f777(f777(f127(x84022),f777(f777(f130(x84022),f777(f183(f852(x84022)),x84023)),x84024)),x84025))+~P1(f777(f777(f234(a851),f777(f183(f852(x84022)),x84023)),f777(f183(f852(x84022)),x84024))) % 174.01/173.90 [8494]~E(f777(f777(f84(a851),f777(f777(f85(a851),x84943),x84944)),x84941),f777(f777(f84(a851),f777(f777(f85(a851),x84942),x84944)),x84945))+~P1(f777(f777(f234(a851),x84943),x84942))+E(x84941,f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x84942),x84943)),x84944)),x84945)) % 174.01/173.90 [8495]~E(f777(f777(f84(a851),f777(f777(f85(a851),x84951),x84953)),x84954),f777(f777(f84(a851),f777(f777(f85(a851),x84952),x84953)),x84955))+~P1(f777(f777(f234(a851),x84952),x84951))+E(f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x84951),x84952)),x84953)),x84954),x84955) % 174.01/173.90 [8635]E(f777(f777(f84(a851),f777(f777(f85(a851),x86351),x86352)),x86353),f777(f777(f84(a851),f777(f777(f85(a851),x86354),x86352)),x86355))+~P1(f777(f777(f234(a851),x86354),x86351))+~E(x86355,f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x86351),x86354)),x86352)),x86353)) % 174.01/173.90 [8636]E(f777(f777(f84(a851),f777(f777(f85(a851),x86361),x86362)),x86363),f777(f777(f84(a851),f777(f777(f85(a851),x86364),x86362)),x86365))+~P1(f777(f777(f234(a851),x86364),x86361))+~E(f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x86361),x86364)),x86362)),x86363),x86365) % 174.01/173.90 [8970]~P1(f777(f777(f281(a3),x89701),x89704))+~P1(f777(f777(f281(a3),x89701),f777(f777(f84(a3),x89702),x89705)))+P1(f777(f777(f281(a3),x89701),f777(f777(f84(a3),f777(f777(f84(a3),x89702),f777(f777(f85(a3),x89703),x89704))),x89705))) % 174.01/173.90 [9172]~P1(f777(f777(f281(a3),x91721),x91724))+P1(f777(f777(f281(a3),x91721),f777(f777(f84(a3),x91722),x91723)))+~P1(f777(f777(f281(a3),x91721),f777(f777(f84(a3),f777(f777(f84(a3),x91722),f777(f777(f85(a3),x91725),x91724))),x91723))) % 174.01/173.90 [9423]~P60(x94232)+~P1(f777(f65(x94231),x94235))+E(f777(f777(f13(x94231,x94232),f777(f777(f22(x94231,x94232,x94232),f777(f777(f12(x94232,f858(x94232,x94232),x94231),f285(x94232)),x94233)),x94234)),x94235),f777(f777(f285(x94232),f777(f777(f13(x94231,x94232),x94233),x94235)),f777(f777(f13(x94231,x94232),x94234),x94235))) % 174.01/173.90 [9543]~E(f649(x95435,x95434,x95433,x95432,x95431),f650(x95435,x95434,x95433,x95432,x95431))+P1(f777(f777(f336(f857(x95431,x95431)),f777(f777(f243(x95431,x95431),x95432),x95433)),f302(x95431,x95434)))+~P1(f777(f777(f336(f857(x95431,x95431)),f777(f777(f243(x95431,x95431),x95432),x95433)),f302(x95431,f777(f777(f105(f858(f857(x95431,x95431),a845)),x95434),x95435)))) % 174.01/173.90 [9544]~E(f658(x95445,x95444,x95443,x95442,x95441),f659(x95445,x95444,x95443,x95442,x95441))+P1(f777(f777(f336(f857(x95441,x95441)),f777(f777(f243(x95441,x95441),x95442),x95443)),f302(x95441,x95444)))+~P1(f777(f777(f336(f857(x95441,x95441)),f777(f777(f243(x95441,x95441),x95442),x95443)),f302(x95441,f777(f777(f105(f858(f857(x95441,x95441),a845)),x95444),x95445)))) % 174.01/173.90 [9724]P1(f777(f777(f336(f857(x97241,x97241)),f777(f777(f243(x97241,x97241),x97242),f659(x97245,x97244,x97243,x97242,x97241))),f302(x97241,x97244)))+P1(f777(f777(f336(f857(x97241,x97241)),f777(f777(f243(x97241,x97241),x97242),x97243)),f302(x97241,x97244)))+~P1(f777(f777(f336(f857(x97241,x97241)),f777(f777(f243(x97241,x97241),x97242),x97243)),f302(x97241,f777(f777(f105(f858(f857(x97241,x97241),a845)),x97244),x97245)))) % 174.01/173.90 [9818]P1(f777(f777(f336(f857(x98181,x98181)),f777(f777(f243(x98181,x98181),f650(x98185,x98184,x98183,x98182,x98181)),x98183)),f302(x98181,x98184)))+P1(f777(f777(f336(f857(x98181,x98181)),f777(f777(f243(x98181,x98181),x98182),x98183)),f302(x98181,x98184)))+~P1(f777(f777(f336(f857(x98181,x98181)),f777(f777(f243(x98181,x98181),x98182),x98183)),f302(x98181,f777(f777(f105(f858(f857(x98181,x98181),a845)),x98184),x98185)))) % 174.01/173.90 [9860]P1(f777(f777(f336(f857(x98601,x98601)),f777(f777(f243(x98601,x98601),x98602),x98603)),f302(x98601,x98604)))+P1(f777(f777(f336(f857(x98601,x98601)),f777(f777(f243(x98601,x98601),f649(x98605,x98604,x98603,x98602,x98601)),f650(x98605,x98604,x98603,x98602,x98601))),x98605))+~P1(f777(f777(f336(f857(x98601,x98601)),f777(f777(f243(x98601,x98601),x98602),x98603)),f302(x98601,f777(f777(f105(f858(f857(x98601,x98601),a845)),x98604),x98605)))) % 174.01/173.90 [9861]P1(f777(f777(f336(f857(x98611,x98611)),f777(f777(f243(x98611,x98611),x98612),x98613)),f302(x98611,x98614)))+P1(f777(f777(f336(f857(x98611,x98611)),f777(f777(f243(x98611,x98611),f659(x98615,x98614,x98613,x98612,x98611)),f658(x98615,x98614,x98613,x98612,x98611))),x98615))+~P1(f777(f777(f336(f857(x98611,x98611)),f777(f777(f243(x98611,x98611),x98612),x98613)),f302(x98611,f777(f777(f105(f858(f857(x98611,x98611),a845)),x98614),x98615)))) % 174.01/173.90 [9986]~P1(f777(f777(f336(f857(f852(x99861),f852(x99861))),f777(f777(f243(f852(x99861),f852(x99861)),x99864),x99865)),f149(x99861,x99862)))+~P1(f777(f777(f336(f857(x99861,x99861)),x99863),f777(f160(f857(x99861,x99861)),f777(f777(f169(x99861,x99861),x99864),x99865))))+P1(f777(f777(f253(x99861,x99861,a845),f777(f777(f11(x99861,f858(f857(x99861,x99861),a845),f858(x99861,a845)),f777(f777(f12(f858(x99861,f858(f858(f857(x99861,x99861),a845),a845)),f858(f858(f857(x99861,x99861),a845),f858(x99861,a845)),x99861),f11(x99861,f858(f857(x99861,x99861),a845),a845)),f777(f777(f12(f858(x99861,f857(x99861,x99861)),f858(x99861,f858(f858(f857(x99861,x99861),a845),a845)),x99861),f777(f12(f857(x99861,x99861),f858(f858(f857(x99861,x99861),a845),a845),x99861),f336(f857(x99861,x99861)))),f243(x99861,x99861)))),x99862)),x99863)) % 174.01/173.90 [9451]~P1(f777(f777(f234(a851),x94513),x94512))+~P1(f777(f777(f235(a851),f777(f777(f84(a851),f777(f777(f85(a851),x94513),x94514)),x94511)),f777(f777(f84(a851),f777(f777(f85(a851),x94512),x94514)),x94515)))+P1(f777(f777(f235(a851),x94511),f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x94512),x94513)),x94514)),x94515))) % 174.01/173.90 [9452]~P1(f777(f777(f234(a851),x94523),x94522))+~P1(f777(f777(f234(a851),f777(f777(f84(a851),f777(f777(f85(a851),x94523),x94524)),x94521)),f777(f777(f84(a851),f777(f777(f85(a851),x94522),x94524)),x94525)))+P1(f777(f777(f234(a851),x94521),f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x94522),x94523)),x94524)),x94525))) % 174.01/173.90 [9472]~P1(f777(f777(f234(a851),x94721),x94724))+P1(f777(f777(f235(a851),f777(f777(f84(a851),f777(f777(f85(a851),x94721),x94722)),x94723)),f777(f777(f84(a851),f777(f777(f85(a851),x94724),x94722)),x94725)))+~P1(f777(f777(f235(a851),x94723),f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x94724),x94721)),x94722)),x94725))) % 174.01/173.90 [9473]~P1(f777(f777(f234(a851),x94731),x94734))+P1(f777(f777(f234(a851),f777(f777(f84(a851),f777(f777(f85(a851),x94731),x94732)),x94733)),f777(f777(f84(a851),f777(f777(f85(a851),x94734),x94732)),x94735)))+~P1(f777(f777(f234(a851),x94733),f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x94734),x94731)),x94732)),x94735))) % 174.01/173.90 [9579]~P1(f777(f777(f234(a851),x95792),x95791))+~P1(f777(f777(f235(a851),f777(f777(f84(a851),f777(f777(f85(a851),x95791),x95793)),x95794)),f777(f777(f84(a851),f777(f777(f85(a851),x95792),x95793)),x95795)))+P1(f777(f777(f235(a851),f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x95791),x95792)),x95793)),x95794)),x95795)) % 174.01/173.90 [9580]~P1(f777(f777(f234(a851),x95802),x95801))+~P1(f777(f777(f234(a851),f777(f777(f84(a851),f777(f777(f85(a851),x95801),x95803)),x95804)),f777(f777(f84(a851),f777(f777(f85(a851),x95802),x95803)),x95805)))+P1(f777(f777(f234(a851),f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x95801),x95802)),x95803)),x95804)),x95805)) % 174.01/173.90 [9621]~P1(f777(f777(f234(a851),x96214),x96211))+P1(f777(f777(f235(a851),f777(f777(f84(a851),f777(f777(f85(a851),x96211),x96212)),x96213)),f777(f777(f84(a851),f777(f777(f85(a851),x96214),x96212)),x96215)))+~P1(f777(f777(f235(a851),f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x96211),x96214)),x96212)),x96213)),x96215)) % 174.01/173.90 [9622]~P1(f777(f777(f234(a851),x96224),x96221))+P1(f777(f777(f234(a851),f777(f777(f84(a851),f777(f777(f85(a851),x96221),x96222)),x96223)),f777(f777(f84(a851),f777(f777(f85(a851),x96224),x96222)),x96225)))+~P1(f777(f777(f234(a851),f777(f777(f84(a851),f777(f777(f85(a851),f777(f777(f5(a851),x96221),x96224)),x96222)),x96223)),x96225)) % 174.01/173.90 [9845]~P16(x98451,x98452,x98455,x98453)+~P1(f777(f777(f336(f857(x98451,x98451)),x98454),x98455))+P1(f777(f777(f253(x98451,x98451,a845),f777(f777(f11(x98451,f858(x98451,x98452),f858(x98451,a845)),f777(f777(f12(f858(x98452,a845),f858(f858(x98451,x98452),f858(x98451,a845)),x98451),f12(x98452,a845,x98451)),f777(f777(f12(x98452,f858(x98452,a845),x98451),a332),x98453))),x98453)),x98454)) % 174.01/173.90 [7172]~P39(x71724,x71722,x71725,x71726)+P39(f35(x71721,x71723,x71724),x71722,x71725,x71726)+P1(f777(x71721,x71722)) % 174.01/173.90 [7252]~P39(x72522,x72524,x72525,x72526)+P39(f35(x72521,x72522,x72523),x72524,x72525,x72526)+~P1(f777(x72521,x72524)) % 174.01/173.90 [7343]P39(x73433,x73432,x73434,x73435)+~P39(f35(x73431,x73436,x73433),x73432,x73434,x73435)+P1(f777(x73431,x73432)) % 174.01/173.90 [7376]P39(x73761,x73762,x73763,x73764)+~P39(f35(x73765,x73761,x73766),x73762,x73763,x73764)+~P1(f777(x73765,x73762)) % 174.01/173.90 [7748]~P39(x77481,x77483,x77484,x77486)+~P39(x77482,x77486,x77484,x77485)+P39(f38(x77481,x77482),x77483,x77484,x77485) % 174.01/173.90 [7751]P39(x77511,x77512,x77513,x77514)+P39(x77515,x77512,x77513,x77514)+~P39(f35(x77516,x77511,x77515),x77512,x77513,x77514) % 174.01/173.90 [6722]~E(f777(x67224,x67225),f185(x67222))+E(f777(f172(x67221,x67222,x67223,x67224),x67225),f777(f229(x67222),x67226))+~E(f777(x67223,x67225),f777(f229(x67222),x67226)) % 174.01/173.90 [6829]~E(f777(x68293,x68296),f185(x68291))+E(f777(f231(f855(x68291),x68292,f185(x68291),x68293),f777(x68294,x68295)),f185(x68291))+~E(f777(x68294,x68295),f777(f229(x68292),x68296)) % 174.01/173.90 [7434]E(f777(x74341,x74342),f185(x74343))+~E(f777(f172(x74345,x74343,x74346,x74341),x74342),f777(f229(x74343),x74344))+E(f777(x74341,x74342),f777(f229(x74343),x74344)) % 174.01/173.90 [7472]~E(f777(f172(x74726,x74723,x74725,x74721),x74722),f777(f229(x74723),x74724))+E(f777(x74721,x74722),f777(f229(x74723),x74724))+E(f777(x74725,x74722),f777(f229(x74723),x74724)) % 174.01/173.90 [8363]~P23(x83636,x83631,x83632,x83634)+E(f777(f77(x83631,x83631,x83631,f777(x83632,x83633)),f777(x83634,x83635)),f777(f77(x83631,x83631,x83631,f777(x83634,x83635)),f777(x83632,x83633)))+~P1(f777(f65(x83636),x83635)) % 174.01/173.90 [8760]~P29(x87601,x87603,x87605,x87606)+~P29(x87603,x87602,x87604,f777(f305(x87601,x87603,x87605),x87606))+P29(x87601,x87602,f777(f77(x87603,x87602,x87601,x87604),x87605),x87606) % 174.01/173.90 [9264]~P1(f777(f777(x92643,x92642),x92646))+~P1(f777(f777(x92644,x92645),x92642))+P1(f777(f777(f336(x92641),x92642),f294(x92641,x92643,x92644,x92645,x92646))) % 174.01/173.90 [9265]~P1(f777(f777(x92654,x92652),x92656))+~P1(f777(f777(x92653,x92655),x92652))+P1(f777(f777(f336(x92651),x92652),f291(x92651,x92653,x92654,x92655,x92656))) % 174.01/173.90 [9374]E(x93741,x93742)+E(x93743,x93744)+~P1(f777(f777(f336(f857(f852(x93745),f852(x93745))),f777(f777(f243(f852(x93745),f852(x93745)),f777(f777(f142(x93745),x93743),x93741)),f777(f777(f142(x93745),x93744),x93742))),f148(x93745,x93746))) % 174.01/173.90 [9383]~E(x93832,x93834)+P1(f777(f777(f336(f857(f852(x93831),f852(x93831))),f777(f777(f243(f852(x93831),f852(x93831)),f777(f777(f142(x93831),x93832),x93833)),f777(f777(f142(x93831),x93834),x93835))),f137(x93831,x93836)))+~P1(f777(f777(f336(f857(f852(x93831),f852(x93831))),f777(f777(f243(f852(x93831),f852(x93831)),x93833),x93835)),f137(x93831,x93836))) % 174.01/173.90 [9384]~E(x93842,x93844)+P1(f777(f777(f336(f857(f852(x93841),f852(x93841))),f777(f777(f243(f852(x93841),f852(x93841)),f777(f777(f142(x93841),x93842),x93843)),f777(f777(f142(x93841),x93844),x93845))),f139(x93841,x93846)))+~P1(f777(f777(f336(f857(f852(x93841),f852(x93841))),f777(f777(f243(f852(x93841),f852(x93841)),x93843),x93845)),f139(x93841,x93846))) % 174.01/173.90 [9385]~E(x93852,x93854)+P1(f777(f777(f336(f857(f852(x93851),f852(x93851))),f777(f777(f243(f852(x93851),f852(x93851)),f777(f777(f142(x93851),x93852),x93853)),f777(f777(f142(x93851),x93854),x93855))),f148(x93851,x93856)))+~P1(f777(f777(f336(f857(f852(x93851),f852(x93851))),f777(f777(f243(f852(x93851),f852(x93851)),x93853),x93855)),f148(x93851,x93856))) % 174.01/173.90 [9386]~E(x93862,x93864)+P1(f777(f777(f336(f857(f852(x93861),f852(x93861))),f777(f777(f243(f852(x93861),f852(x93861)),f777(f777(f127(x93861),x93862),x93863)),f777(f777(f127(x93861),x93864),x93865))),f148(x93861,x93866)))+~P1(f777(f777(f336(f857(f852(x93861),f852(x93861))),f777(f777(f243(f852(x93861),f852(x93861)),x93863),x93865)),f148(x93861,x93866))) % 174.01/173.90 [9387]~E(x93873,x93875)+P1(f777(f777(f336(f857(f852(x93871),f852(x93871))),f777(f777(f243(f852(x93871),f852(x93871)),f777(f777(f127(x93871),x93872),x93873)),f777(f777(f127(x93871),x93874),x93875))),f148(x93871,x93876)))+~P1(f777(f777(f336(f857(f852(x93871),f852(x93871))),f777(f777(f243(f852(x93871),f852(x93871)),x93872),x93874)),f148(x93871,x93876))) % 174.01/173.90 [9440]E(x94401,x94402)+P1(f777(f777(f336(f857(f852(x94403),f852(x94403))),f777(f777(f243(f852(x94403),f852(x94403)),x94401),x94402)),f148(x94403,x94404)))+~P1(f777(f777(f336(f857(f852(x94403),f852(x94403))),f777(f777(f243(f852(x94403),f852(x94403)),f777(f777(f142(x94403),x94405),x94401)),f777(f777(f142(x94403),x94406),x94402))),f148(x94403,x94404))) % 174.01/173.90 [9581]~E(x95813,x95815)+P1(f777(f777(f336(f857(f852(x95811),f852(x95811))),f777(f777(f243(f852(x95811),f852(x95811)),f777(f777(f127(x95811),x95812),f777(f777(f142(x95811),x95813),f117(x95811)))),f777(f777(f127(x95811),x95814),f777(f777(f142(x95811),x95815),f117(x95811))))),f148(x95811,x95816)))+~P1(f777(f777(f336(f857(f852(x95811),f852(x95811))),f777(f777(f243(f852(x95811),f852(x95811)),x95812),x95814)),f148(x95811,x95816))) % 174.01/173.90 [9592]E(f777(x95921,x95922),f185(x95923))+~E(f777(f231(f855(x95926),x95923,f185(x95926),x95924),f777(x95921,x95922)),f185(x95926))+E(f777(x95924,f708(x95922,x95921,x95924,x95925,x95926,x95923)),f185(x95926)) % 174.01/173.90 [9593]E(f777(x95931,x95932),f185(x95933))+~E(f777(f231(f855(x95936),x95933,f185(x95936),x95934),f777(x95931,x95932)),f185(x95936))+E(f777(f229(x95933),f708(x95932,x95931,x95934,x95935,x95936,x95933)),f777(x95931,x95932)) % 174.01/173.90 [9625]E(x96251,x96252)+E(x96253,x96254)+~P1(f777(f777(f336(f857(f852(x96255),f852(x96255))),f777(f777(f243(f852(x96255),f852(x96255)),f777(f777(f127(x96255),x96253),f777(f777(f142(x96255),x96251),f117(x96255)))),f777(f777(f127(x96255),x96254),f777(f777(f142(x96255),x96252),f117(x96255))))),f148(x96255,x96256))) % 174.01/173.90 [9647]E(x96471,x96472)+~P1(f777(f777(f336(f857(f852(x96473),f852(x96473))),f777(f777(f243(f852(x96473),f852(x96473)),f777(f777(f127(x96473),x96471),f777(f777(f142(x96473),x96475),f117(x96473)))),f777(f777(f127(x96473),x96472),f777(f777(f142(x96473),x96476),f117(x96473))))),f148(x96473,x96474)))+P1(f777(f777(f336(f857(f852(x96473),f852(x96473))),f777(f777(f243(f852(x96473),f852(x96473)),x96471),x96472)),f148(x96473,x96474))) % 174.01/173.90 [9676]~P1(f777(f777(f336(f857(f858(x96761,a845),f858(x96761,a845))),f777(f777(f243(f858(x96761,a845),f858(x96761,a845)),x96762),x96764)),f326(x96761,x96766)))+~P1(f777(f777(f336(f857(f858(x96761,a845),f858(x96761,a845))),f777(f777(f243(f858(x96761,a845),f858(x96761,a845)),x96763),x96765)),f326(x96761,x96766)))+P1(f777(f777(f336(f857(f858(x96761,a845),f858(x96761,a845))),f777(f777(f243(f858(x96761,a845),f858(x96761,a845)),f777(f777(f105(f858(x96761,a845)),x96762),x96763)),f777(f777(f105(f858(x96761,a845)),x96764),x96765))),f326(x96761,x96766))) % 174.01/173.90 [5139]~E(f777(x51393,x51396),x51395)+~E(x51394,f777(f229(x51391),x51396))+E(f777(f777(f198(x51391,x51392),x51393),x51394),f777(f229(x51392),x51395)) % 174.01/173.90 [5542]~E(f777(f777(f127(x55421),x55426),x55423),x55425)+E(f777(f777(f127(x55421),x55422),x55423),f777(f777(f142(x55421),x55424),x55425))+~E(x55422,f777(f777(f142(x55421),x55424),x55426)) % 174.01/173.90 [5543]~E(f777(f777(f127(x55431),x55436),x55433),x55435)+E(f777(f777(f127(x55431),x55432),x55433),f777(f777(f127(x55431),x55434),x55435))+~E(x55432,f777(f777(f127(x55431),x55434),x55436)) % 174.01/173.90 [5545]E(f777(f777(f127(x55451),x55452),x55453),f777(f777(f142(x55451),x55454),x55455))+~E(f777(f777(f142(x55451),x55454),x55456),x55452)+~E(x55455,f777(f777(f127(x55451),x55456),x55453)) % 174.01/173.90 [5547]~E(f777(f777(f127(x55471),x55472),x55476),x55474)+E(f777(f777(f127(x55471),x55472),x55473),f777(f777(f127(x55471),x55474),x55475))+~E(x55473,f777(f777(f127(x55471),x55476),x55475)) % 174.01/173.90 [6715]E(f777(x67151,x67152),f777(x67153,x67152))+~E(f777(f777(f145(x67154,x67155),x67151),x67156),f777(f777(f145(x67154,x67155),x67153),x67156))+~P1(f777(f777(f336(x67154),x67152),f777(f160(x67154),x67156))) % 174.01/173.90 [7108]~P23(x71084,x71085,x71086,x71081)+E(f777(f777(x71081,x71082),x71083),f777(f777(f68(x71084,x71085,x71086),x71083),x71082))+~P1(f777(f65(x71084),x71082)) % 174.01/173.90 [7177]~E(x71772,f777(x71774,x71776))+~P1(f777(f777(f336(x71773),x71776),x71775))+P1(f777(f777(f336(x71771),x71772),f777(f305(x71773,x71771,x71774),x71775))) % 174.01/173.90 [7178]~E(f777(x71784,x71782),x71786)+~P1(f777(f777(f336(x71783),x71786),x71785))+P1(f777(f777(f336(x71781),x71782),f777(f307(x71781,x71783,x71784),x71785))) % 174.01/173.90 [7654]~P34(x76541,x76542,x76544,x76546)+P34(x76541,x76542,f777(f777(f142(x76541),x76543),x76544),f777(f777(f142(x76541),x76545),x76546))+~P1(f777(f777(x76542,x76543),x76545)) % 174.01/173.90 [8643]~P55(x86434,x86435,x86431,x86432,x86436)+E(f777(x86431,f777(x86432,x86433)),x86433)+~P1(f777(f777(f336(x86435),x86433),x86436)) % 174.01/173.90 [9376]E(x93761,x93762)+E(f777(f183(f852(x93763)),x93764),f777(f183(f852(x93763)),x93765))+~P1(f777(f777(f336(f857(f852(x93763),f852(x93763))),f777(f777(f243(f852(x93763),f852(x93763)),f777(f777(f142(x93763),x93761),x93764)),f777(f777(f142(x93763),x93762),x93765))),f137(x93763,x93766))) % 174.01/173.90 [9437]~P20(x94371,x94372,x94373)+E(f777(f777(f68(x94371,x94372,x94373),x94374),x94375),x94376)+~P1(f777(f70(x94371,x94372,x94373,x94374,x94375),x94376)) % 174.01/173.90 [9443]E(f777(f183(f852(x94431)),x94432),f777(f183(f852(x94431)),x94433))+P1(f777(f777(f336(f857(f852(x94431),f852(x94431))),f777(f777(f243(f852(x94431),f852(x94431)),x94432),x94433)),f137(x94431,x94434)))+~P1(f777(f777(f336(f857(f852(x94431),f852(x94431))),f777(f777(f243(f852(x94431),f852(x94431)),f777(f777(f142(x94431),x94435),x94432)),f777(f777(f142(x94431),x94436),x94433))),f137(x94431,x94434))) % 174.01/173.90 [9464]~P1(f777(f777(f336(f857(x94641,x94641)),f777(f777(f243(x94641,x94641),x94642),x94644)),f302(x94641,x94646)))+P1(f777(f777(f336(f857(f852(x94641),f852(x94641))),f777(f777(f243(f852(x94641),f852(x94641)),f777(f777(f142(x94641),x94642),x94643)),f777(f777(f142(x94641),x94644),x94645))),f302(f852(x94641),f148(x94641,x94646))))+~P1(f777(f777(f336(f857(f852(x94641),f852(x94641))),f777(f777(f243(f852(x94641),f852(x94641)),x94643),x94645)),f302(f852(x94641),f148(x94641,x94646)))) % 174.01/173.90 [9937]~P66(x99372)+E(f777(f777(f10(x99371,x99372),f777(f777(f12(f858(x99373,a845),x99372,x99371),f777(f10(x99373,x99372),x99374)),f777(f777(f12(f858(x99373,a845),f858(x99373,a845),x99371),f258(x99373)),f777(f777(f12(f858(x99373,a845),f858(x99373,a845),x99371),f777(f22(x99373,a845,a845),f777(f777(f12(a845,f858(a845,a845),x99373),a333),f777(f777(f11(x99373,f858(x99373,a845),a845),f336(x99373)),x99375)))),f777(f11(x99373,x99371,a845),f777(f777(f12(x99371,f858(x99371,a845),x99373),a332),x99376)))))),f777(f305(x99373,x99371,x99376),x99375)),f777(f777(f10(x99373,x99372),x99374),x99375))+~P1(f777(f65(x99373),x99375)) % 174.01/173.90 [6776]~P100(x67763)+P1(f777(x67762,x67765))+E(f777(f128(x67761,x67762),f777(f777(f140(x67761,x67763,x67764),x67765),x67766)),f777(f128(x67761,x67762),x67766)) % 174.01/173.90 [6778]P1(f777(x67781,x67782))+~E(f158(x67783,x67781,x67784),f777(f777(f243(f852(x67783),f852(x67783)),x67785),x67786))+~P1(f777(f777(f336(x67783),x67782),f777(f160(x67783),x67785))) % 174.01/173.90 [6826]~P1(f777(x68262,x68266))+~E(f158(x68261,x68262,x68263),f777(f777(f243(f852(x68261),f852(x68261)),x68264),x68265))+~P1(f777(f777(f336(x68261),x68266),f777(f160(x68261),x68265))) % 174.01/173.90 [7517]~P19(x75171,x75172,x75173)+~P1(f777(f65(x75171),x75176))+E(f777(f777(f68(x75171,x75172,x75173),x75174),f777(f777(f304(x75171),x75175),x75176)),f777(f777(f68(x75171,x75172,x75173),f777(f777(x75173,x75175),x75174)),x75176)) % 174.01/173.90 [7569]~P100(x75692)+~P1(f777(f777(f234(x75692),f777(x75693,x75694)),f777(x75693,x75695)))+E(f777(f777(f140(x75691,x75692,x75693),x75694),f777(f777(f142(x75691),x75695),x75696)),f777(f777(f142(x75691),x75694),f777(f777(f142(x75691),x75695),x75696))) % 174.01/173.90 [7685]E(x76851,x76852)+~E(f777(f777(f250(x76853,x76854),x76851),f777(f20(f858(x76854,a845),x76853),x76855)),f777(f777(f250(x76853,x76854),x76852),f777(f20(f858(x76854,a845),x76853),x76855)))+~P1(f777(f777(f336(x76854),x76856),x76855)) % 174.01/173.90 [7753]~P19(x77531,x77532,x77533)+~P1(f777(f65(x77531),x77536))+E(f777(f777(f68(x77531,x77532,x77533),x77534),f777(f777(f304(x77531),x77535),x77536)),f777(f777(x77533,x77535),f777(f777(f68(x77531,x77532,x77533),x77534),x77536))) % 174.01/173.90 [7869]~P20(x78691,x78692,x78693)+~P1(f777(f65(x78691),x78696))+E(f777(f777(f68(x78691,x78692,x78693),f777(f777(x78693,x78694),x78695)),x78696),f777(f777(x78693,x78694),f777(f777(f68(x78691,x78692,x78693),x78695),x78696))) % 174.01/173.90 [7937]~P24(x79372,x79375,x79376,x79371)+~P1(f777(f65(x79372),x79374))+E(f777(x79371,f777(f777(f304(x79372),x79373),x79374)),f777(f77(x79375,x79375,x79375,f777(x79371,x79374)),f777(x79376,x79373))) % 174.01/173.90 [7975]~P100(x79752)+P1(f777(f777(f234(x79752),f777(x79753,x79754)),f777(x79753,x79755)))+E(f777(f777(f140(x79751,x79752,x79753),x79754),f777(f777(f142(x79751),x79755),x79756)),f777(f777(f142(x79751),x79755),f777(f777(f140(x79751,x79752,x79753),x79754),x79756))) % 174.01/173.90 [8108]~E(f777(f183(f852(x81081)),x81085),f777(f183(f852(x81082)),x81086))+~E(f777(f183(f852(x81081)),x81083),f777(f183(f852(x81082)),x81084))+E(f777(f777(f127(f857(x81081,x81082)),f777(f777(f169(x81081,x81082),x81083),x81084)),f777(f777(f169(x81081,x81082),x81085),x81086)),f777(f777(f169(x81081,x81082),f777(f777(f127(x81081),x81083),x81085)),f777(f777(f127(x81082),x81084),x81086))) % 174.01/173.90 [8217]~E(x82172,f777(f305(x82173,x82171,x82174),x82176))+P1(f777(f777(f234(f858(x82171,a845)),x82172),f777(f305(x82173,x82171,x82174),x82175)))+~P1(f777(f777(f234(f858(x82173,a845)),x82176),x82175)) % 174.01/173.90 [8319]~P100(x83195)+E(f777(x83191,x83192),f777(x83191,x83193))+E(f777(f777(f140(x83194,x83195,x83191),x83192),f777(f777(f140(x83194,x83195,x83191),x83193),x83196)),f777(f777(f140(x83194,x83195,x83191),x83193),f777(f777(f140(x83194,x83195,x83191),x83192),x83196))) % 174.01/173.90 [8356]~P29(x83563,x83561,x83564,x83565)+P29(x83563,x83561,f777(f777(f777(f76(x83563,x83561),x83564),x83566),x83562),x83565)+P1(f777(f777(f336(x83561),x83562),f777(f305(x83563,x83561,x83564),x83565))) % 174.01/173.90 [8503]~P1(f777(f777(f336(x85032),x85034),f777(x85036,x85033)))+~P1(f777(f777(f336(x85031),x85033),x85035))+P1(f777(f777(f336(f857(x85031,x85032)),f777(f777(f243(x85031,x85032),x85033),x85034)),f777(f777(f250(x85031,x85032),x85035),x85036))) % 174.01/173.90 [8912]~P66(x89122)+~P29(x89124,x89121,x89125,x89126)+E(f777(f777(f10(x89121,x89122),x89123),f777(f305(x89124,x89121,x89125),x89126)),f777(f777(f10(x89124,x89122),f777(f77(x89121,x89122,x89124,x89123),x89125)),x89126)) % 174.01/173.90 [8913]~P70(x89132)+~P29(x89134,x89131,x89135,x89136)+E(f777(f777(f13(x89131,x89132),x89133),f777(f305(x89134,x89131,x89135),x89136)),f777(f777(f13(x89134,x89132),f777(f77(x89131,x89132,x89134,x89133),x89135)),x89136)) % 174.01/173.90 [9152]~P23(x91523,x91521,x91526,x91522)+~P1(f777(f65(x91523),x91524))+E(f777(f77(x91521,x91521,x91521,f777(x91522,f777(f777(f5(f858(x91523,a845)),x91524),f777(f777(f304(x91523),x91525),f182(f858(x91523,a845)))))),f777(x91526,x91525)),f777(x91522,f777(f777(f304(x91523),x91525),x91524))) % 174.01/173.90 [9705]~E(f777(f305(x97052,x97054,x97056),f241(f858(x97052,a845))),f241(f858(x97054,a845)))+~E(f777(f305(x97051,x97053,x97055),f241(f858(x97051,a845))),f241(f858(x97053,a845)))+E(f777(f305(f857(x97051,x97052),f857(x97053,x97054),f254(x97051,x97053,x97052,x97054,x97055,x97056)),f241(f858(f857(x97051,x97052),a845))),f241(f858(f857(x97053,x97054),a845))) % 174.01/173.90 [9767]~P29(x97673,x97674,x97675,f777(x97676,f692(x97676,x97675,x97674,x97673,x97672,x97671)))+P29(x97673,x97674,x97675,f777(f777(f49(x97672,f858(x97673,a845)),x97671),x97676))+E(x97671,f182(f858(x97672,a845))) % 174.01/173.90 [9824]P29(x98246,x98245,x98244,f777(f777(f49(x98242,f858(x98246,a845)),x98241),x98243))+E(x98241,f182(f858(x98242,a845)))+P1(f777(f777(f336(x98242),f692(x98243,x98244,x98245,x98246,x98242,x98241)),x98241)) % 174.01/173.90 [9831]P1(f777(f777(f336(x98311),f622(x98312,x98313,x98314,x98315,x98316,x98311)),x98316))+P1(f777(f777(f234(f858(f857(x98311,x98314),a845)),f777(f777(f250(x98311,x98314),x98316),x98313)),f777(f777(f250(x98311,x98314),x98315),x98312)))+~P1(f777(f777(f234(f858(x98311,a845)),x98316),x98315)) % 174.01/173.90 [9874]P28(x98746,x98745,f777(f777(f304(f850(x98746)),f777(f777(f777(f95(x98746),x98744),x98743),x98742)),f182(f858(f850(x98746),a845))))+~P28(x98746,x98745,f777(f777(f304(f850(x98746)),f777(f777(f777(f95(x98746),x98744),x98743),x98741)),f182(f858(f850(x98746),a845))))+P1(f777(f777(x98741,f543(x98742,x98741,x98743,x98744,x98745,x98746)),f544(x98742,x98741,x98743,x98744,x98745,x98746))) % 174.01/173.90 [9875]P28(x98756,x98755,f777(f777(f304(f850(x98756)),f777(f777(f777(f95(x98756),x98751),x98753),x98752)),f182(f858(f850(x98756),a845))))+~P28(x98756,x98755,f777(f777(f304(f850(x98756)),f777(f777(f777(f95(x98756),x98754),x98753),x98752)),f182(f858(f850(x98756),a845))))+P1(f777(f777(x98751,f545(x98751,x98752,x98753,x98754,x98755,x98756)),f546(x98751,x98752,x98753,x98754,x98755,x98756))) % 174.01/173.90 [9912]~P28(x99121,x99122,f777(f777(f304(f850(x99121)),f777(f777(f777(f95(x99121),x99123),x99124),x99126)),f182(f858(f850(x99121),a845))))+P28(x99121,x99122,f777(f777(f304(f850(x99121)),f777(f777(f777(f95(x99121),x99123),x99124),x99125)),f182(f858(f850(x99121),a845))))+~P1(f777(f777(x99125,f543(x99125,x99126,x99124,x99123,x99122,x99121)),f544(x99125,x99126,x99124,x99123,x99122,x99121))) % 174.01/173.90 [9913]~P28(x99131,x99132,f777(f777(f304(f850(x99131)),f777(f777(f777(f95(x99131),x99136),x99134),x99135)),f182(f858(f850(x99131),a845))))+P28(x99131,x99132,f777(f777(f304(f850(x99131)),f777(f777(f777(f95(x99131),x99133),x99134),x99135)),f182(f858(f850(x99131),a845))))+~P1(f777(f777(x99136,f545(x99133,x99135,x99134,x99136,x99132,x99131)),f546(x99133,x99135,x99134,x99136,x99132,x99131))) % 174.01/173.90 [9954]~P1(f777(f777(f234(f858(x99542,a845)),f777(x99544,f622(x99546,x99544,x99542,x99545,x99543,x99541))),f777(x99546,f622(x99546,x99544,x99542,x99545,x99543,x99541))))+~P1(f777(f777(f234(f858(x99541,a845)),x99543),x99545))+P1(f777(f777(f234(f858(f857(x99541,x99542),a845)),f777(f777(f250(x99541,x99542),x99543),x99544)),f777(f777(f250(x99541,x99542),x99545),x99546))) % 174.01/173.90 [7702]~P1(f777(x77021,x77025))+~P1(f777(x77026,x77024))+P1(f777(x77021,f777(f252(x77022,x77023),f777(f777(f243(x77022,x77023),x77024),x77025)))) % 174.01/173.90 [7703]~P1(f777(x77031,x77034))+~P1(f777(x77036,x77035))+P1(f777(x77031,f777(f242(x77032,x77033),f777(f777(f243(x77032,x77033),x77034),x77035)))) % 174.01/173.90 [7758]~P1(f777(f777(x77584,x77586),x77585))+~P1(f777(f777(f336(x77581),x77586),x77583))+P1(f777(f777(f777(f48(x77581,f858(x77582,a845)),x77583),x77584),x77585)) % 174.01/173.90 [7791]~E(f777(f183(f852(x77911)),x77913),f777(f183(f852(x77914)),x77915))+~E(f777(f168(x77911,x77914,f777(f777(f169(x77911,x77914),x77913),x77915)),x77912),f777(f229(x77914),x77916))+P1(f777(f777(f336(x77911),x77912),f777(f160(x77911),x77913))) % 174.01/173.90 [8061]~P1(f777(f777(f336(x80611),x80612),f777(x80615,x80616)))+~P1(f777(f777(f336(x80613),x80616),x80614))+P1(f777(f777(f336(x80611),x80612),f777(f777(f48(x80613,f858(x80611,a845)),x80614),x80615))) % 174.01/173.90 [8101]P1(f777(f777(x81011,x81012),x81013))+~P1(f777(f777(x81014,x81012),x81013))+~P1(f777(f777(f234(f858(x81015,f858(x81016,a845))),x81014),x81011)) % 174.01/173.90 [8241]P1(f777(f777(x82411,x82412),x82413))+~P1(f777(f777(f336(x82414),x82412),x82415))+~P1(f777(f777(f777(f49(x82414,f858(x82416,a845)),x82415),x82411),x82413)) % 174.01/173.90 [8379]P1(f777(f777(f336(x83791),x83792),f777(x83793,x83794)))+~P1(f777(f777(f336(x83795),x83794),x83796))+~P1(f777(f777(f336(x83791),x83792),f777(f777(f49(x83795,f858(x83791,a845)),x83796),x83793))) % 174.01/173.90 [8625]~P16(x86254,x86255,x86256,x86251)+E(f777(x86251,x86252),f777(x86251,x86253))+~P1(f777(f777(f336(f857(x86254,x86254)),f777(f777(f243(x86254,x86254),x86252),x86253)),x86256)) % 174.01/173.90 [8656]P1(f777(f777(f234(f858(x86561,a845)),x86562),f777(x86563,x86564)))+~P1(f777(f777(f336(x86565),x86564),x86566))+~P1(f777(f777(f234(f858(x86561,a845)),x86562),f777(f777(f49(x86565,f858(x86561,a845)),x86566),x86563))) % 174.01/173.90 [8681]~P53(x86813,x86814,f777(f280(x86814,x86813),x86815))+E(x86811,f182(f858(x86812,a845)))+E(f777(f777(f49(x86812,f858(x86813,a845)),x86811),f777(f777(f12(f858(x86814,a845),f858(x86813,a845),x86812),f279(x86814,x86813,x86815)),x86816)),f777(f279(x86814,x86813,x86815),f777(f777(f49(x86812,f858(x86814,a845)),x86811),x86816))) % 174.01/173.90 [8753]P1(f777(f777(f336(x87531),x87532),f777(f279(x87533,x87531,x87534),x87535)))+~P1(f777(f777(f336(x87533),x87536),x87535))+~P1(f777(f777(f336(f857(x87533,x87531)),f777(f777(f243(x87533,x87531),x87536),x87532)),x87534)) % 174.01/173.90 [9030]P1(f777(f777(f234(f858(x90301,a845)),f777(f279(x90302,x90301,x90303),x90304)),f777(f279(x90302,x90301,x90305),x90306)))+~P1(f777(f777(f234(f858(x90302,a845)),x90304),x90306))+~P1(f777(f777(f234(f858(f857(x90302,x90301),a845)),x90303),x90305)) % 174.01/173.90 [9186]~P1(f777(f777(f336(x91862),x91866),x91864))+~P1(f777(f777(f234(f858(x91861,a845)),x91863),x91865))+P1(f777(f777(f234(f858(f857(x91861,x91862),a845)),f777(f777(f250(x91861,x91862),x91863),f777(f20(f858(x91862,a845),x91861),x91864))),f777(f777(f250(x91861,x91862),x91865),f777(f20(f858(x91862,a845),x91861),x91864)))) % 174.01/173.90 [9334]~E(x93343,x93345)+P1(f777(f777(f336(f857(f852(x93341),f852(x93341))),f777(f777(f243(f852(x93341),f852(x93341)),f777(f777(f142(x93341),x93342),x93343)),f777(f777(f142(x93341),x93344),x93345))),f148(x93341,x93346)))+~P1(f777(f777(f336(f857(x93341,x93341)),f777(f777(f243(x93341,x93341),x93342),x93344)),x93346)) % 174.01/173.90 [9340]~E(f777(f183(f852(x93401)),x93403),f777(f183(f852(x93401)),x93405))+P1(f777(f777(f336(f857(f852(x93401),f852(x93401))),f777(f777(f243(f852(x93401),f852(x93401)),f777(f777(f142(x93401),x93402),x93403)),f777(f777(f142(x93401),x93404),x93405))),f137(x93401,x93406)))+~P1(f777(f777(f336(f857(x93401,x93401)),f777(f777(f243(x93401,x93401),x93402),x93404)),x93406)) % 174.01/173.90 [9368]P1(f777(f777(f336(f857(x93681,x93681)),f777(f777(f243(x93681,x93681),x93682),x93683)),f777(f777(f175(f857(x93681,x93681),a845),f777(a116,x93684)),x93685)))+~P1(f777(f777(f336(f857(x93681,x93681)),f777(f777(f243(x93681,x93681),x93686),x93683)),x93685))+~P1(f777(f777(f336(f857(x93681,x93681)),f777(f777(f243(x93681,x93681),x93682),x93686)),f777(f777(f175(f857(x93681,x93681),a845),x93684),x93685))) % 174.01/173.90 [9369]P1(f777(f777(f336(f857(x93691,x93691)),f777(f777(f243(x93691,x93691),x93692),x93693)),f777(f777(f175(f857(x93691,x93691),a845),f777(a116,x93694)),x93695)))+~P1(f777(f777(f336(f857(x93691,x93691)),f777(f777(f243(x93691,x93691),x93692),x93696)),x93695))+~P1(f777(f777(f336(f857(x93691,x93691)),f777(f777(f243(x93691,x93691),x93696),x93693)),f777(f777(f175(f857(x93691,x93691),a845),x93694),x93695))) % 174.01/173.90 [9372]~P1(f777(f777(f336(x93724),x93725),x93726))+P1(f777(f777(f234(f858(x93721,a845)),x93722),x93723))+~P1(f777(f777(f234(f858(f857(x93721,x93724),a845)),f777(f777(f250(x93721,x93724),x93722),f777(f20(f858(x93724,a845),x93721),x93726))),f777(f777(f250(x93721,x93724),x93723),f777(f20(f858(x93724,a845),x93721),x93726)))) % 174.01/173.90 [9412]E(x94121,x94122)+~P1(f777(f777(f336(f857(f852(x94123),f852(x94123))),f777(f777(f243(f852(x94123),f852(x94123)),f777(f777(f142(x94123),x94121),x94125)),f777(f777(f142(x94123),x94122),x94126))),f137(x94123,x94124)))+P1(f777(f777(f336(f857(x94123,x94123)),f777(f777(f243(x94123,x94123),x94121),x94122)),x94124)) % 174.01/173.90 [9413]E(x94131,x94132)+~P1(f777(f777(f336(f857(f852(x94133),f852(x94133))),f777(f777(f243(f852(x94133),f852(x94133)),f777(f777(f142(x94133),x94131),x94135)),f777(f777(f142(x94133),x94132),x94136))),f139(x94133,x94134)))+P1(f777(f777(f336(f857(x94133,x94133)),f777(f777(f243(x94133,x94133),x94131),x94132)),x94134)) % 174.01/173.90 [9414]E(x94141,x94142)+~P1(f777(f777(f336(f857(f852(x94143),f852(x94143))),f777(f777(f243(f852(x94143),f852(x94143)),f777(f777(f142(x94143),x94141),x94145)),f777(f777(f142(x94143),x94142),x94146))),f148(x94143,x94144)))+P1(f777(f777(f336(f857(x94143,x94143)),f777(f777(f243(x94143,x94143),x94141),x94142)),x94144)) % 174.01/173.90 [9450]P1(f777(f777(f336(f857(f852(x94501),f852(x94501))),f777(f777(f243(f852(x94501),f852(x94501)),f777(f777(f142(x94501),x94502),x94503)),f777(f777(f142(x94501),x94504),x94505))),f149(x94501,x94506)))+~P1(f777(f777(f336(f857(f852(x94501),f852(x94501))),f777(f777(f243(f852(x94501),f852(x94501)),x94503),x94505)),f149(x94501,x94506)))+~P1(f777(f777(f336(f857(x94501,x94501)),f777(f777(f243(x94501,x94501),x94502),x94504)),x94506)) % 174.01/173.90 [9470]P1(f777(x94701,x94702))+~P1(f777(x94701,f390(x94701,x94703,x94704,x94705,x94706)))+~P1(f777(f777(f336(x94706),x94702),f777(f777(f48(x94705,f858(x94706,a845)),x94704),x94703))) % 174.01/173.90 [9475]~P1(f777(f777(f336(f857(f852(x94751),f852(x94751))),f777(f777(f243(f852(x94751),f852(x94751)),f777(f777(f142(x94751),x94752),x94755)),f777(f777(f142(x94751),x94753),x94756))),f137(x94751,x94754)))+P1(f777(f777(f336(f857(f852(x94751),f852(x94751))),f777(f777(f243(f852(x94751),f852(x94751)),x94755),x94756)),f137(x94751,x94754)))+P1(f777(f777(f336(f857(x94751,x94751)),f777(f777(f243(x94751,x94751),x94752),x94753)),x94754)) % 174.01/173.90 [9476]~P1(f777(f777(f336(f857(f852(x94761),f852(x94761))),f777(f777(f243(f852(x94761),f852(x94761)),f777(f777(f142(x94761),x94762),x94765)),f777(f777(f142(x94761),x94763),x94766))),f139(x94761,x94764)))+P1(f777(f777(f336(f857(f852(x94761),f852(x94761))),f777(f777(f243(f852(x94761),f852(x94761)),x94765),x94766)),f139(x94761,x94764)))+P1(f777(f777(f336(f857(x94761,x94761)),f777(f777(f243(x94761,x94761),x94762),x94763)),x94764)) % 174.01/173.90 [9477]~P1(f777(f777(f336(f857(f852(x94771),f852(x94771))),f777(f777(f243(f852(x94771),f852(x94771)),f777(f777(f142(x94771),x94772),x94775)),f777(f777(f142(x94771),x94773),x94776))),f148(x94771,x94774)))+P1(f777(f777(f336(f857(f852(x94771),f852(x94771))),f777(f777(f243(f852(x94771),f852(x94771)),x94775),x94776)),f148(x94771,x94774)))+P1(f777(f777(f336(f857(x94771,x94771)),f777(f777(f243(x94771,x94771),x94772),x94773)),x94774)) % 174.01/173.90 [9553]P1(f777(x95531,x95532))+P1(f777(f777(f336(x95533),f391(x95531,x95534,x95535,x95533,x95536)),x95535))+~P1(f777(f777(f336(x95536),x95532),f777(f777(f48(x95533,f858(x95536,a845)),x95535),x95534))) % 174.01/173.90 [9559]~E(x95592,x95594)+P1(f777(f777(f336(f857(f852(x95591),f852(x95591))),f777(f777(f243(f852(x95591),f852(x95591)),f777(f777(f127(x95591),x95592),f777(f777(f142(x95591),x95593),f117(x95591)))),f777(f777(f127(x95591),x95594),f777(f777(f142(x95591),x95595),f117(x95591))))),f148(x95591,x95596)))+~P1(f777(f777(f336(f857(x95591,x95591)),f777(f777(f243(x95591,x95591),x95593),x95595)),x95596)) % 174.01/173.90 [9639]E(x96391,x96392)+~P1(f777(f777(f336(f857(f852(x96393),f852(x96393))),f777(f777(f243(f852(x96393),f852(x96393)),f777(f777(f127(x96393),x96395),f777(f777(f142(x96393),x96391),f117(x96393)))),f777(f777(f127(x96393),x96396),f777(f777(f142(x96393),x96392),f117(x96393))))),f148(x96393,x96394)))+P1(f777(f777(f336(f857(x96393,x96393)),f777(f777(f243(x96393,x96393),x96391),x96392)),x96394)) % 174.01/173.90 [9664]~P1(f777(f777(f336(f857(f852(x96641),f852(x96641))),f777(f777(f243(f852(x96641),f852(x96641)),f777(f777(f127(x96641),x96645),f777(f777(f142(x96641),x96642),f117(x96641)))),f777(f777(f127(x96641),x96646),f777(f777(f142(x96641),x96643),f117(x96641))))),f148(x96641,x96644)))+P1(f777(f777(f336(f857(f852(x96641),f852(x96641))),f777(f777(f243(f852(x96641),f852(x96641)),x96645),x96646)),f148(x96641,x96644)))+P1(f777(f777(f336(f857(x96641,x96641)),f777(f777(f243(x96641,x96641),x96642),x96643)),x96644)) % 174.01/173.90 [9677]P1(f777(x96771,x96772))+P1(f777(f777(f336(x96773),f390(x96771,x96774,x96775,x96776,x96773)),f777(x96774,f391(x96771,x96774,x96775,x96776,x96773))))+~P1(f777(f777(f336(x96773),x96772),f777(f777(f48(x96776,f858(x96773,a845)),x96775),x96774))) % 174.01/173.90 [8766]~P20(x87663,x87664,x87661)+~P1(f777(f65(x87663),x87666))+E(f777(f777(x87661,x87662),f777(f777(f68(x87663,x87664,x87661),x87665),f777(f777(f5(f858(x87663,a845)),x87666),f777(f777(f304(x87663),x87662),f182(f858(x87663,a845)))))),f777(f777(f68(x87663,x87664,x87661),x87665),f777(f777(f304(x87663),x87662),x87666))) % 174.01/173.90 [8863]~E(f777(f168(x88631,x88632,x88634),x88635),f777(f229(x88632),x88636))+~P1(f777(f777(x88633,x88635),x88636))+E(f777(f168(x88631,x88632,f777(f128(f857(x88631,x88632),f777(f253(x88631,x88632,a845),x88633)),x88634)),x88635),f777(f229(x88632),x88636)) % 174.01/173.90 [9036]~P1(f777(f777(f336(x90365),x90363),x90366))+P1(f777(f777(f234(f858(x90361,a845)),f777(x90362,x90363)),x90364))+~P1(f777(f777(f234(f858(x90361,a845)),f777(f777(f48(x90365,f858(x90361,a845)),x90366),x90362)),x90364)) % 174.01/173.90 [9614]~P12(x96141,x96145,x96144)+P1(f777(f777(f336(f857(x96141,x96141)),f777(f777(f243(x96141,x96141),x96142),x96143)),x96144))+~P1(f777(f777(f336(x96141),x96146),f777(f777(f106(f858(x96141,a845)),f777(f279(x96141,x96141,x96144),f777(f777(f304(x96141),x96142),f182(f858(x96141,a845))))),f777(f279(x96141,x96141,x96144),f777(f777(f304(x96141),x96143),f182(f858(x96141,a845))))))) % 174.01/173.90 [8536]~P121(x85362)+~E(f777(f777(f84(x85362),f777(f777(f85(x85362),x85364),x85365)),x85361),f777(f777(f84(x85362),f777(f777(f85(x85362),x85363),x85365)),x85366))+E(x85361,f777(f777(f84(x85362),f777(f777(f85(x85362),f777(f777(f5(x85362),x85363),x85364)),x85365)),x85366)) % 174.01/173.90 [8537]~P121(x85371)+~E(f777(f777(f84(x85371),f777(f777(f85(x85371),x85372),x85374)),x85375),f777(f777(f84(x85371),f777(f777(f85(x85371),x85373),x85374)),x85376))+E(f777(f777(f84(x85371),f777(f777(f85(x85371),f777(f777(f5(x85371),x85372),x85373)),x85374)),x85375),x85376) % 174.01/173.90 [8684]~P121(x86841)+E(f777(f777(f84(x86841),f777(f777(f85(x86841),x86842),x86843)),x86844),f777(f777(f84(x86841),f777(f777(f85(x86841),x86845),x86843)),x86846))+~E(x86846,f777(f777(f84(x86841),f777(f777(f85(x86841),f777(f777(f5(x86841),x86842),x86845)),x86843)),x86844)) % 174.01/173.90 [8685]~P121(x86851)+E(f777(f777(f84(x86851),f777(f777(f85(x86851),x86852),x86853)),x86854),f777(f777(f84(x86851),f777(f777(f85(x86851),x86855),x86853)),x86856))+~E(f777(f777(f84(x86851),f777(f777(f85(x86851),f777(f777(f5(x86851),x86852),x86855)),x86853)),x86854),x86856) % 174.01/173.90 [8976]~P1(f777(f777(x89764,x89765),x89766))+~P1(f777(f777(x89763,x89765),x89766))+P1(f777(f777(f777(f777(f106(f858(x89761,f858(x89762,a845))),x89763),x89764),x89765),x89766)) % 174.01/173.90 [9205]P1(f777(f777(x92051,x92052),x92053))+P1(f777(f777(x92054,x92052),x92053))+~P1(f777(f777(f777(f777(f105(f858(x92055,f858(x92056,a845))),x92054),x92051),x92052),x92053)) % 174.01/173.90 [9364]~E(f777(f183(f852(x93641)),x93645),f777(f183(f852(x93642)),x93646))+E(f172(x93641,x93642,f174(x93641,x93642,x93643,f777(f777(f5(f858(x93641,a845)),x93644),f777(f160(x93641),x93645))),f168(x93641,x93642,f777(f144(f857(x93641,x93642)),f777(f777(f169(x93641,x93642),x93645),x93646)))),f174(x93641,x93642,f172(x93641,x93642,x93643,f168(x93641,x93642,f777(f144(f857(x93641,x93642)),f777(f777(f169(x93641,x93642),x93645),x93646)))),x93644))+~P1(f777(f777(f234(f858(x93641,a845)),f777(f160(x93641),x93645)),x93644)) % 174.01/173.90 [9492]~P129(x94921)+~P1(f777(f777(f235(x94921),f777(f777(f84(x94921),f777(f777(f85(x94921),x94924),x94925)),x94922)),f777(f777(f84(x94921),f777(f777(f85(x94921),x94923),x94925)),x94926)))+P1(f777(f777(f235(x94921),x94922),f777(f777(f84(x94921),f777(f777(f85(x94921),f777(f777(f5(x94921),x94923),x94924)),x94925)),x94926))) % 174.01/173.90 [9493]~P129(x94931)+~P1(f777(f777(f234(x94931),f777(f777(f84(x94931),f777(f777(f85(x94931),x94934),x94935)),x94932)),f777(f777(f84(x94931),f777(f777(f85(x94931),x94933),x94935)),x94936)))+P1(f777(f777(f234(x94931),x94932),f777(f777(f84(x94931),f777(f777(f85(x94931),f777(f777(f5(x94931),x94933),x94934)),x94935)),x94936))) % 174.01/173.90 [9510]~P129(x95101)+P1(f777(f777(f235(x95101),f777(f777(f84(x95101),f777(f777(f85(x95101),x95102),x95103)),x95104)),f777(f777(f84(x95101),f777(f777(f85(x95101),x95105),x95103)),x95106)))+~P1(f777(f777(f235(x95101),x95104),f777(f777(f84(x95101),f777(f777(f85(x95101),f777(f777(f5(x95101),x95105),x95102)),x95103)),x95106))) % 174.01/173.90 [9511]~P129(x95111)+P1(f777(f777(f234(x95111),f777(f777(f84(x95111),f777(f777(f85(x95111),x95112),x95113)),x95114)),f777(f777(f84(x95111),f777(f777(f85(x95111),x95115),x95113)),x95116)))+~P1(f777(f777(f234(x95111),x95114),f777(f777(f84(x95111),f777(f777(f85(x95111),f777(f777(f5(x95111),x95115),x95112)),x95113)),x95116))) % 174.01/173.90 [9607]~P129(x96071)+~P1(f777(f777(f235(x96071),f777(f777(f84(x96071),f777(f777(f85(x96071),x96072),x96074)),x96075)),f777(f777(f84(x96071),f777(f777(f85(x96071),x96073),x96074)),x96076)))+P1(f777(f777(f235(x96071),f777(f777(f84(x96071),f777(f777(f85(x96071),f777(f777(f5(x96071),x96072),x96073)),x96074)),x96075)),x96076)) % 174.01/173.90 [9608]~P129(x96081)+~P1(f777(f777(f234(x96081),f777(f777(f84(x96081),f777(f777(f85(x96081),x96082),x96084)),x96085)),f777(f777(f84(x96081),f777(f777(f85(x96081),x96083),x96084)),x96086)))+P1(f777(f777(f234(x96081),f777(f777(f84(x96081),f777(f777(f85(x96081),f777(f777(f5(x96081),x96082),x96083)),x96084)),x96085)),x96086)) % 174.01/173.90 [9649]~P129(x96491)+P1(f777(f777(f235(x96491),f777(f777(f84(x96491),f777(f777(f85(x96491),x96492),x96493)),x96494)),f777(f777(f84(x96491),f777(f777(f85(x96491),x96495),x96493)),x96496)))+~P1(f777(f777(f235(x96491),f777(f777(f84(x96491),f777(f777(f85(x96491),f777(f777(f5(x96491),x96492),x96495)),x96493)),x96494)),x96496)) % 174.01/173.90 [9650]~P129(x96501)+P1(f777(f777(f234(x96501),f777(f777(f84(x96501),f777(f777(f85(x96501),x96502),x96503)),x96504)),f777(f777(f84(x96501),f777(f777(f85(x96501),x96505),x96503)),x96506)))+~P1(f777(f777(f234(x96501),f777(f777(f84(x96501),f777(f777(f85(x96501),f777(f777(f5(x96501),x96502),x96505)),x96503)),x96504)),x96506)) % 174.01/173.90 [9819]~P66(x98192)+~P1(f777(f65(x98191),x98196))+E(f777(f777(f10(x98191,x98192),f777(f777(f22(x98191,x98192,x98192),f777(f777(f22(x98191,x98192,f858(x98192,x98192)),f777(f777(f12(a845,f858(x98192,f858(x98192,x98192)),x98191),f100(x98192)),x98193)),x98194)),x98195)),x98196),f777(f777(f84(x98192),f777(f777(f10(x98191,x98192),x98194),f777(f777(f106(f858(x98191,a845)),x98196),f777(f258(x98191),x98193)))),f777(f777(f10(x98191,x98192),x98195),f777(f777(f106(f858(x98191,a845)),x98196),f777(f83(f858(x98191,a845)),f777(f258(x98191),x98193)))))) % 174.01/173.90 [9883]P1(f777(f777(f336(x98832),x98834),x98836))+P1(f777(f777(f336(x98832),x98835),x98836))+E(f777(f307(x98831,x98832,f777(f777(f11(x98831,x98832,x98832),f777(f777(f11(x98831,x98832,f858(x98832,x98832)),f777(f777(f12(a845,f858(x98832,f858(x98832,x98832)),x98831),f100(x98832)),f777(f777(f11(x98831,f858(x98831,a845),a845),f336(x98831)),x98833))),x98834)),x98835)),x98836),f182(f858(x98831,a845))) % 174.01/173.90 [9884]P1(f777(f777(f336(x98842),x98845),x98846))+~P1(f777(f777(f336(x98842),x98844),x98846))+E(f777(f307(x98841,x98842,f777(f777(f11(x98841,x98842,x98842),f777(f777(f11(x98841,x98842,f858(x98842,x98842)),f777(f777(f12(a845,f858(x98842,f858(x98842,x98842)),x98841),f100(x98842)),f777(f777(f11(x98841,f858(x98841,a845),a845),f336(x98841)),x98843))),x98844)),x98845)),x98846),x98843) % 174.01/173.90 [9885]P1(f777(f777(f336(x98852),x98854),x98856))+~P1(f777(f777(f336(x98852),x98855),x98856))+E(f777(f307(x98851,x98852,f777(f777(f11(x98851,x98852,x98852),f777(f777(f11(x98851,x98852,f858(x98852,x98852)),f777(f777(f12(a845,f858(x98852,f858(x98852,x98852)),x98851),f100(x98852)),f777(f777(f11(x98851,f858(x98851,a845),a845),f336(x98851)),x98853))),x98854)),x98855)),x98856),f777(f83(f858(x98851,a845)),x98853)) % 174.01/173.90 [9886]~P1(f777(f777(f336(x98862),x98864),x98866))+~P1(f777(f777(f336(x98862),x98865),x98866))+E(f777(f307(x98861,x98862,f777(f777(f11(x98861,x98862,x98862),f777(f777(f11(x98861,x98862,f858(x98862,x98862)),f777(f777(f12(a845,f858(x98862,f858(x98862,x98862)),x98861),f100(x98862)),f777(f777(f11(x98861,f858(x98861,a845),a845),f336(x98861)),x98863))),x98864)),x98865)),x98866),f241(f858(x98861,a845))) % 174.01/173.90 [10018]P28(x100181,x100182,f777(f777(f304(f850(x100181)),f777(f777(f777(f95(x100181),f777(x100183,x100184)),f777(a29,x100184)),f777(x100185,x100184))),f182(f858(f850(x100181),a845))))+~P1(f777(f777(f336(a847),x100184),x100186))+~P28(x100181,f777(f777(f105(f858(f850(x100181),a845)),x100182),f777(f305(a847,f850(x100181),f777(f777(f22(a847,f858(x100181,f858(a848,a845)),f850(x100181)),f777(f777(f22(a847,a846,f858(f858(x100181,f858(a848,a845)),f850(x100181))),f777(f777(f12(f858(x100181,f858(a848,a845)),f858(a846,f858(f858(x100181,f858(a848,a845)),f850(x100181))),a847),f95(x100181)),x100183)),a29)),x100185)),x100186)),f777(f305(a847,f850(x100181),f777(f777(f22(a847,f858(x100181,f858(a848,a845)),f850(x100181)),f777(f777(f22(a847,a846,f858(f858(x100181,f858(a848,a845)),f850(x100181))),f777(f777(f12(f858(x100181,f858(a848,a845)),f858(a846,f858(f858(x100181,f858(a848,a845)),f850(x100181))),a847),f95(x100181)),x100183)),f777(f777(f12(f855(a846),a846,a847),f233(a846)),a32))),x100185)),x100186)) % 174.01/173.90 [8561]E(x85611,x85612)+~P55(x85614,x85615,x85613,x85616,x85617)+~E(f777(x85613,x85611),f777(x85613,x85612)) % 174.01/173.90 [6936]E(f777(f231(f855(x69361),x69362,f185(x69361),x69363),f777(x69364,x69365)),f777(f229(x69361),x69366))+~E(f777(x69364,x69365),f777(f229(x69362),x69367))+~E(f777(x69363,x69367),f777(f229(x69361),x69366)) % 174.01/173.90 [8583]~P15(x85836,x85835,x85837,x85834,x85831)+E(f777(f777(x85831,x85832),x85833),x85834)+P1(f777(f65(x85835),x85833)) % 174.01/173.90 [9359]P41(x93591,x93592,x93593,x93594,x93595,f777(f777(x93593,x93596),x93597))+~E(f777(f777(x93593,x93596),x93597),x93594)+~E(x93595,f182(f858(x93591,a845))) % 174.01/173.90 [9530]~P1(f777(x95306,x95303))+~P1(f777(f777(f336(f857(x95302,x95302)),f777(f777(f243(x95302,x95302),x95304),x95305)),f777(x95307,x95303)))+P1(f777(f777(f336(f857(f857(x95301,x95302),f857(x95301,x95302))),f777(f777(f243(f857(x95301,x95302),f857(x95301,x95302)),f777(f777(f243(x95301,x95302),x95303),x95304)),f777(f777(f243(x95301,x95302),x95303),x95305))),f277(x95301,x95302,x95306,x95307))) % 174.01/173.90 [9703]~P29(x97033,x97031,x97034,f241(f858(x97033,a845)))+E(f777(f168(x97031,x97032,f777(f777(f145(f857(x97033,x97032),f857(x97031,x97032)),f777(f253(x97033,x97032,f857(x97031,x97032)),f777(f777(f12(x97031,f858(x97032,f857(x97031,x97032)),x97033),f243(x97031,x97032)),x97034))),x97035)),f777(x97034,x97036)),f777(f229(x97032),x97037))+~E(f777(f168(x97033,x97032,x97035),x97036),f777(f229(x97032),x97037)) % 174.01/173.90 [9939]~P41(x99392,x99397,x99393,x99396,x99391,f777(f777(x99393,x99395),x99394))+E(f777(f777(x99393,f455(x99394,x99395,x99391,x99396,x99393,x99397,x99392)),f456(x99394,x99395,x99391,x99396,x99393,x99397,x99392)),f777(f777(x99393,x99395),x99394))+E(x99391,f182(f858(x99392,a845))) % 174.01/173.90 [9940]~P41(x99407,x99406,x99401,x99404,x99405,f777(f777(x99401,x99402),x99403))+E(f777(f777(x99401,f455(x99403,x99402,x99405,x99404,x99401,x99406,x99407)),f456(x99403,x99402,x99405,x99404,x99401,x99406,x99407)),f777(f777(x99401,x99402),x99403))+E(f777(f777(x99401,x99402),x99403),x99404) % 174.01/173.90 [9595]~P1(f777(f70(x95951,x95954,x95955,x95956,x95953),x95957))+P1(f777(f70(x95951,x95954,x95955,x95956,f777(f777(f304(x95951),x95952),x95953)),f777(f777(x95955,x95952),x95957)))+P1(f777(f777(f336(x95951),x95952),x95953)) % 174.01/173.90 [9964]~P41(x99642,x99647,x99646,x99645,x99641,f777(f777(x99646,x99644),x99643))+E(x99641,f182(f858(x99642,a845)))+P1(f777(f777(f336(x99642),f455(x99643,x99644,x99641,x99645,x99646,x99647,x99642)),x99641)) % 174.01/173.90 [9965]~P41(x99655,x99657,x99651,x99654,x99656,f777(f777(x99651,x99652),x99653))+E(f777(f777(x99651,x99652),x99653),x99654)+P1(f777(f777(f336(x99655),f455(x99653,x99652,x99656,x99654,x99651,x99657,x99655)),x99656)) % 174.01/173.90 [6714]~E(x67145,x67147)+~E(x67146,x67144)+E(f777(f777(f777(f777(f76(x67141,f855(x67142)),x67143),x67144),f777(f229(x67142),x67145)),x67146),f777(f229(x67142),x67147)) % 174.01/173.90 [6850]E(x68501,x68502)+~E(f777(x68505,x68501),f777(f229(x68504),x68507))+E(f777(f777(f777(f777(f76(x68503,f855(x68504)),x68505),x68502),f777(f229(x68504),x68506)),x68501),f777(f229(x68504),x68507)) % 174.01/173.90 [7595]E(x75951,x75952)+~E(x75953,x75954)+~E(f777(f777(f777(f777(f76(x75955,f855(x75956)),x75957),x75954),f777(f229(x75956),x75951)),x75953),f777(f229(x75956),x75952)) % 174.01/173.90 [7660]E(x76601,x76602)+E(f777(x76603,x76604),f777(f229(x76605),x76601))+~E(f777(f777(f777(f777(f76(x76606,f855(x76605)),x76603),x76607),f777(f229(x76605),x76602)),x76604),f777(f229(x76605),x76601)) % 174.01/173.90 [7661]E(x76611,x76612)+E(f777(x76613,x76611),f777(f229(x76614),x76615))+~E(f777(f777(f777(f777(f76(x76616,f855(x76614)),x76613),x76612),f777(f229(x76614),x76617)),x76611),f777(f229(x76614),x76615)) % 174.01/173.90 [8787]~P25(x87874,x87875,x87876,x87877,x87871)+~P1(f777(f65(x87875),x87873))+E(f777(f777(x87871,x87872),x87873),f777(f777(f777(f69(x87874,x87875,x87876),x87872),x87877),x87873)) % 174.01/173.90 [8788]~P15(x87884,x87885,x87886,x87887,x87881)+~P1(f777(f65(x87885),x87883))+E(f777(f777(x87881,x87882),x87883),f777(f777(f777(f69(x87884,x87885,x87886),x87882),x87887),x87883)) % 174.01/173.90 [9327]~P28(x93271,x93272,f777(f777(f304(f850(x93271)),f777(f777(f777(f95(x93271),x93273),x93274),x93277)),f182(f858(f850(x93271),a845))))+P28(x93271,x93272,f777(f777(f304(f850(x93271)),f777(f777(f777(f95(x93271),x93273),f38(x93274,x93275)),x93276)),f182(f858(f850(x93271),a845))))+~P28(x93271,x93272,f777(f777(f304(f850(x93271)),f777(f777(f777(f95(x93271),x93277),x93275),x93276)),f182(f858(f850(x93271),a845)))) % 174.01/173.90 [9505]~P27(x95053,x95054,x95055,x95057,x95056,x95051)+~P1(f777(f65(x95054),x95052))+E(f777(x95051,x95052),f777(f777(f777(f69(x95053,x95054,x95055),x95056),x95057),x95052)) % 174.01/173.90 [9644]P41(x96441,x96442,x96443,x96444,x96445,f777(f777(x96443,x96446),x96447))+~P41(x96441,x96442,x96443,x96444,f777(f777(f5(f858(x96441,a845)),x96445),f777(f777(f304(x96441),x96446),f182(f858(x96441,a845)))),x96447)+~P1(f777(f777(f336(x96441),x96446),x96445)) % 174.01/173.90 [9914]~P28(x99141,x99142,f777(f777(f304(f850(x99141)),f777(f777(f777(f95(x99141),f96(x99141,x99143,x99144)),x99145),x99147)),f182(f858(f850(x99141),a845))))+P28(x99141,x99142,f777(f777(f304(f850(x99141)),f777(f777(f777(f95(x99141),x99143),f35(x99144,x99145,x99146)),x99147)),f182(f858(f850(x99141),a845))))+~P28(x99141,x99142,f777(f777(f304(f850(x99141)),f777(f777(f777(f95(x99141),f96(x99141,x99143,f777(f77(a845,a845,a848,a330),x99144))),x99146),x99147)),f182(f858(f850(x99141),a845)))) % 174.01/173.90 [9982]P1(f777(f777(x99827,f837(x99824,x99825,x99821,x99826,x99823,x99822,x99827)),f838(x99824,x99825,x99821,x99826,x99823,x99822,x99827)))+~P1(f777(f777(x99827,f777(f252(x99822,x99823),x99826)),f777(f242(x99822,x99823),x99826)))+P1(f777(x99821,f777(f777(f253(x99822,x99823,x99824),x99825),x99826))) % 174.01/173.90 [9991]~P41(x99912,x99913,x99914,x99915,x99911,f777(f777(x99914,x99917),x99916))+P41(x99912,x99913,x99914,x99915,f777(f777(f5(f858(x99912,a845)),x99911),f777(f777(f304(x99912),f455(x99916,x99917,x99911,x99915,x99914,x99913,x99912)),f182(f858(x99912,a845)))),f456(x99916,x99917,x99911,x99915,x99914,x99913,x99912))+E(x99911,f182(f858(x99912,a845))) % 174.01/173.90 [9992]~P41(x99925,x99926,x99921,x99924,x99927,f777(f777(x99921,x99922),x99923))+P41(x99925,x99926,x99921,x99924,f777(f777(f5(f858(x99925,a845)),x99927),f777(f777(f304(x99925),f455(x99923,x99922,x99927,x99924,x99921,x99926,x99925)),f182(f858(x99925,a845)))),f456(x99923,x99922,x99927,x99924,x99921,x99926,x99925))+E(f777(f777(x99921,x99922),x99923),x99924) % 174.01/173.90 [10012]~P1(f777(x100121,f777(f777(x100125,f838(x100124,x100125,x100121,x100126,x100123,x100122,x100127)),f837(x100124,x100125,x100121,x100126,x100123,x100122,x100127))))+~P1(f777(f777(x100127,f777(f252(x100122,x100123),x100126)),f777(f242(x100122,x100123),x100126)))+P1(f777(x100121,f777(f777(f253(x100122,x100123,x100124),x100125),x100126))) % 174.01/173.90 [9348]P1(f777(f777(f234(f858(f857(x93481,x93482),a845)),f777(f777(f283(x93481,x93483,x93482),x93484),x93485)),f777(f777(f283(x93481,x93483,x93482),x93486),x93487)))+~P1(f777(f777(f234(f858(f857(x93483,x93482),a845)),x93485),x93487))+~P1(f777(f777(f234(f858(f857(x93481,x93483),a845)),x93484),x93486)) % 174.01/173.90 [9655]~P1(f777(f777(f336(x96551),x96556),x96555))+P1(f777(f70(x96551,x96552,x96553,x96554,x96555),f777(f777(x96553,x96556),x96557)))+~P1(f777(f70(x96551,x96552,x96553,x96554,f777(f777(f5(f858(x96551,a845)),x96555),f777(f777(f304(x96551),x96556),f182(f858(x96551,a845))))),x96557)) % 174.01/173.90 [9254]E(f172(x92541,x92542,x92543,f168(x92541,x92542,f777(f144(f857(x92541,x92542)),f777(f777(f169(x92541,x92542),x92544),f777(f777(f150(x92542,x92545),x92546),x92547))))),f172(x92541,x92542,x92543,f168(x92541,x92542,f777(f144(f857(x92541,x92542)),f777(f777(f169(x92541,x92542),x92544),x92545)))))+~P1(f777(f777(f235(a851),x92546),f777(f183(f852(x92542)),x92545)))+~P1(f777(f777(f234(a851),f777(f183(f852(x92541)),x92544)),x92546)) % 174.01/173.90 [10042]~P136(x100421)+~P29(f857(x100422,x100423),x100421,f777(f253(x100422,x100423,x100421),f777(f777(f11(x100422,f858(x100423,x100421),f858(x100423,x100421)),f777(f777(f12(f858(x100421,x100421),f858(f858(x100423,x100421),f858(x100423,x100421)),x100422),f12(x100421,x100421,x100423)),f777(f777(f12(x100421,f858(x100421,x100421),x100422),f85(x100421)),x100424))),x100425)),f777(f777(f250(x100422,x100423),x100426),f777(f20(f858(x100423,a845),x100422),x100427)))+E(f777(f777(f10(x100421,x100421),f41(x100421)),f777(f258(x100421),f777(f777(f12(f858(x100422,a845),a845,x100421),f91(x100422)),f777(f777(f12(f858(x100422,f858(x100423,a845)),f858(x100422,a845),x100421),f777(f12(f858(x100423,a845),a845,x100422),f91(x100423))),f777(f777(f11(x100421,f858(x100422,f858(x100423,a845)),f858(x100422,f858(x100423,a845))),f777(f777(f12(f858(x100422,f858(f858(x100423,a845),f858(x100423,a845))),f858(f858(x100422,f858(x100423,a845)),f858(x100422,f858(x100423,a845))),x100421),f22(x100422,f858(x100423,a845),f858(x100423,a845))),f777(f777(f12(f858(x100422,f858(x100423,f858(a845,a845))),f858(x100422,f858(f858(x100423,a845),f858(x100423,a845))),x100421),f777(f12(f858(x100423,f858(a845,a845)),f858(f858(x100423,a845),f858(x100423,a845)),x100422),f22(x100423,a845,a845))),f777(f777(f12(f858(x100422,f858(x100423,a845)),f858(x100422,f858(x100423,f858(a845,a845))),x100421),f777(f12(f858(x100423,a845),f858(x100423,f858(a845,a845)),x100422),f777(f12(a845,f858(a845,a845),x100423),a333))),f777(f777(f11(x100421,f858(x100422,f858(x100423,x100421)),f858(x100422,f858(x100423,a845))),f777(f777(f12(f858(f858(x100423,x100421),f858(x100423,a845)),f858(f858(x100422,f858(x100423,x100421)),f858(x100422,f858(x100423,a845))),x100421),f12(f858(x100423,x100421),f858(x100423,a845),x100422)),f777(f777(f12(f858(x100421,a845),f858(f858(x100423,x100421),f858(x100423,a845)),x100421),f12(x100421,a845,x100423)),a332))),f777(f777(f11(x100422,f858(x100423,x100421),f858(x100423,x100421)),f777(f777(f12(f858(x100421,x100421),f858(f858(x100423,x100421),f858(x100423,x100421)),x100422),f12(x100421,x100421,x100423)),f777(f777(f12(x100421,f858(x100421,x100421),x100422),f85(x100421)),x100424))),x100425)))))),f777(f777(f11(x100422,f858(x100423,a845),f858(x100423,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x100423,a845),f858(x100423,a845)),x100422),f12(a845,a845,x100423)),f777(f777(f12(a845,f858(a845,a845),x100422),a333),f777(f777(f11(x100422,f858(x100422,a845),a845),f336(x100422)),x100426)))),f777(f777(f11(x100423,f858(x100423,a845),a845),f336(x100423)),x100427))))))),f777(f777(f85(x100421),f777(f777(f10(x100422,x100421),x100424),x100426)),f777(f777(f10(x100423,x100421),x100425),x100427))) % 174.01/173.90 [9733]P51(x97331,x97332,x97333,x97334,x97335,x97336,x97337)+~P1(f777(f777(x97334,x97336),x97338))+~P1(f777(f777(x97335,x97338),x97337)) % 174.01/173.90 [9134]~P23(x91348,x91341,x91343,x91345)+~P1(f777(f65(x91348),x91346))+E(f777(f77(x91341,x91341,x91342,f777(x91343,x91344)),f777(f77(x91341,x91341,x91342,f777(x91345,x91346)),x91347)),f777(f77(x91341,x91341,x91342,f777(x91345,x91346)),f777(f77(x91341,x91341,x91342,f777(x91343,x91344)),x91347))) % 174.01/173.90 [9497]~P26(x94977,x94972,x94975,x94978,x94976,x94971)+~P1(f777(f65(x94972),x94974))+E(f777(x94971,f777(f777(f304(x94972),x94973),x94974)),f777(f777(x94975,f777(x94976,x94973)),f777(x94971,x94974))) % 174.01/173.90 [9605]~P29(x96052,x96054,x96056,x96058)+~P29(x96051,x96053,x96055,x96057)+P29(f857(x96051,x96052),f857(x96053,x96054),f254(x96051,x96053,x96052,x96054,x96055,x96056),f777(f777(f250(x96051,x96052),x96057),f777(f20(f858(x96052,a845),x96051),x96058))) % 174.01/173.90 [9290]P1(f777(f777(f336(f857(x92901,x92902)),f777(f777(f243(x92901,x92902),x92903),x92904)),f777(f777(f283(x92901,x92905,x92902),x92906),x92907)))+~P1(f777(f777(f336(f857(x92901,x92905)),f777(f777(f243(x92901,x92905),x92903),x92908)),x92906))+~P1(f777(f777(f336(f857(x92905,x92902)),f777(f777(f243(x92905,x92902),x92908),x92904)),x92907)) % 174.01/173.90 [9480]~P1(f777(f777(f234(f858(f857(x94803,x94802),a845)),x94805),f777(f777(f250(x94803,x94802),x94808),f777(f20(f858(x94802,a845),x94803),x94807))))+~P1(f777(f777(f234(f858(f857(x94801,x94803),a845)),x94804),f777(f777(f250(x94801,x94803),x94806),f777(f20(f858(x94803,a845),x94801),x94808))))+P1(f777(f777(f234(f858(f857(x94801,x94802),a845)),f777(f777(f283(x94801,x94803,x94802),x94804),x94805)),f777(f777(f250(x94801,x94802),x94806),f777(f20(f858(x94802,a845),x94801),x94807)))) % 174.01/173.90 [9525]~E(x95253,x95255)+P1(f777(f777(f336(f857(f857(x95251,x95252),f857(x95251,x95252))),f777(f777(f243(f857(x95251,x95252),f857(x95251,x95252)),f777(f777(f243(x95251,x95252),x95253),x95254)),f777(f777(f243(x95251,x95252),x95255),x95256))),f327(x95251,x95252,x95257,x95258)))+~P1(f777(f777(f336(f857(x95252,x95252)),f777(f777(f243(x95252,x95252),x95254),x95256)),x95258)) % 174.01/173.90 [9623]E(x96231,x96232)+~P1(f777(f777(f336(f857(f857(x96233,x96235),f857(x96233,x96235))),f777(f777(f243(f857(x96233,x96235),f857(x96233,x96235)),f777(f777(f243(x96233,x96235),x96231),x96236)),f777(f777(f243(x96233,x96235),x96232),x96237))),f327(x96233,x96235,x96234,x96238)))+P1(f777(f777(f336(f857(x96233,x96233)),f777(f777(f243(x96233,x96233),x96231),x96232)),x96234)) % 174.01/173.90 [9638]~P1(f777(f777(f336(f857(f857(x96381,x96385),f857(x96381,x96385))),f777(f777(f243(f857(x96381,x96385),f857(x96381,x96385)),f777(f777(f243(x96381,x96385),x96382),x96386)),f777(f777(f243(x96381,x96385),x96383),x96387))),f327(x96381,x96385,x96384,x96388)))+P1(f777(f777(f336(f857(x96381,x96381)),f777(f777(f243(x96381,x96381),x96382),x96383)),x96384))+P1(f777(f777(f336(f857(x96385,x96385)),f777(f777(f243(x96385,x96385),x96386),x96387)),x96388)) % 174.01/173.90 [9554]~P27(x95547,x95545,x95541,x95548,x95542,x95544)+~P1(f777(f65(x95545),x95546))+E(f777(f777(x95541,f777(x95542,x95543)),f777(x95544,f777(f777(f5(f858(x95545,a845)),x95546),f777(f777(f304(x95545),x95543),f182(f858(x95545,a845)))))),f777(x95544,f777(f777(f304(x95545),x95543),x95546))) % 174.01/173.90 [9093]~P1(f777(f777(f777(x90935,x90938),x90936),x90937))+~P1(f777(f777(f336(x90931),x90938),x90934))+P1(f777(f777(f777(f777(f48(x90931,f858(x90932,f858(x90933,a845))),x90934),x90935),x90936),x90937)) % 174.01/173.90 [9278]P1(f777(f777(f777(x92781,x92782),x92783),x92784))+~P1(f777(f777(f336(x92785),x92782),x92786))+~P1(f777(f777(f777(f777(f49(x92785,f858(x92787,f858(x92788,a845))),x92786),x92781),x92783),x92784)) % 174.01/173.90 [9471]~P25(x94713,x94712,x94714,x94718,x94711)+~P1(f777(f65(x94712),x94717))+E(f777(f777(x94711,f777(f777(f22(x94712,x94713,x94713),f777(f777(f12(x94713,f858(x94713,x94713),x94712),x94714),x94715)),x94716)),x94717),f777(f777(x94714,f777(f777(x94711,x94715),x94717)),f777(f777(x94711,x94716),x94717))) % 174.01/173.90 [9711]~E(f777(f305(x97112,x97114,x97116),x97118),x971110)+~E(f777(f305(x97111,x97113,x97115),x97117),x97119)+E(f777(f305(f857(x97111,x97112),f857(x97113,x97114),f254(x97111,x97113,x97112,x97114,x97115,x97116)),f777(f777(f250(x97111,x97112),x97117),f777(f20(f858(x97112,a845),x97111),x97118))),f777(f777(f250(x97113,x97114),x97119),f777(f20(f858(x97114,a845),x97113),x971110))) % 174.01/173.90 [4965]~P142(x49651,a863)+P142(x49651,a865)+~P31(a843,a864,a761)+~E(f37(a2,a861),a862) % 174.01/173.90 [5021]~P142(x50211,a865)+P142(x50211,a866)+~E(f37(a1,a862),f37(a2,a861))+~P31(a843,a864,a776) % 174.01/173.90 [5090]~P31(a843,a864,a761)+~P142(x50901,a863)+~E(f37(a2,a861),a862)+~P1(f777(a2,a865)) % 174.01/173.90 [5149]~P31(a843,a864,a776)+~P142(x51491,a865)+~E(f37(a1,a862),f37(a2,a861))+~P1(f777(a2,a866)) % 174.01/173.90 [5151]~P142(x51511,a863)+P142(x51511,a865)+~E(f37(a2,a861),a862)+P1(f777(f777(f336(f850(a843)),a761),a860)) % 174.01/173.90 [5223]~P142(x52231,a865)+P142(x52231,a866)+~E(f37(a1,a862),f37(a2,a861))+P1(f777(f777(f336(f850(a843)),a776),a860)) % 174.01/173.90 [5260]~P142(x52601,a863)+~E(f37(a2,a861),a862)+~P1(f777(a2,a865))+P1(f777(f777(f336(f850(a843)),a761),a860)) % 174.01/173.90 [5324]~P142(x53241,a865)+~E(f37(a1,a862),f37(a2,a861))+~P1(f777(a2,a866))+P1(f777(f777(f336(f850(a843)),a776),a860)) % 174.01/173.90 [4735]~P100(x47352)+~P18(x47352,x47351)+P18(x47352,f118(x47352,x47351))+E(x47351,f117(x47352)) % 174.01/173.90 [4969]~P9(x49692)+E(f14(x49692,x49691),f47(x49692,x49691))+E(x49691,f182(f858(x49692,a845)))+~P1(f777(f65(x49692),x49691)) % 174.01/173.90 [4970]~P9(x49702)+E(f17(x49702,x49701),f46(x49702,x49701))+E(x49701,f182(f858(x49702,a845)))+~P1(f777(f65(x49702),x49701)) % 174.01/173.90 [5917]~P93(x59172)+E(x59171,f182(f858(x59172,a845)))+P1(f777(f777(f234(x59172),f14(x59172,x59171)),f17(x59172,x59171)))+~P1(f777(f65(x59172),x59171)) % 174.01/173.90 [5931]~P38(x59312)+~P38(x59311)+E(x59311,x59312)+~E(f777(f305(a3,a851,a109),x59311),f777(f305(a3,a851,a109),x59312)) % 174.01/173.90 [8956]~P110(x89561)+~P1(f777(f777(f336(x89561),x89562),f114(x89561)))+P1(f777(f777(f235(x89561),f777(f777(f84(x89561),f777(f777(f84(x89561),f82(x89561)),x89562)),x89562)),f4(x89561)))+~P1(f777(f777(f235(x89561),x89562),f4(x89561))) % 174.01/173.90 [9175]~P110(x91751)+~P1(f777(f777(f336(x91751),x91752),f114(x91751)))+~P1(f777(f777(f235(x91751),f777(f777(f84(x91751),f777(f777(f84(x91751),f82(x91751)),x91752)),x91752)),f4(x91751)))+P1(f777(f777(f235(x91751),x91752),f4(x91751))) % 174.01/173.90 [4788]~P105(x47882)+~P136(x47882)+E(x47881,f4(a851))+E(f777(f777(f244(x47882),f4(x47882)),x47881),f4(x47882)) % 174.01/173.90 [4792]~P105(x47921)+~P136(x47921)+~E(x47922,f4(a851))+E(f777(f777(f244(x47921),f4(x47921)),x47922),f82(x47921)) % 174.01/173.90 [4955]~P120(x49552)+E(x49551,f82(x49552))+E(x49551,f777(f83(x49552),f82(x49552)))+~E(f777(f777(f85(x49552),x49551),x49551),f82(x49552)) % 174.01/173.90 [5204]~P82(x52042)+E(x52041,f4(x52042))+E(f86(x52042,x52041),f777(f83(x52042),f82(x52042)))+P1(f777(f777(f235(x52042),f4(x52042)),x52041)) % 174.01/173.90 [5439]~P82(x54392)+E(f86(x54392,x54391),f82(x54392))+E(x54391,f4(x54392))+~P1(f777(f777(f235(x54392),f4(x54392)),x54391)) % 174.01/173.90 [5448]E(x54481,x54482)+~E(f777(f108(a851),x54481),f777(f108(a851),x54482))+P1(f777(a188,f777(f108(a3),x54482)))+P1(f777(a188,f777(f108(a3),x54481))) % 174.01/173.90 [5495]~P87(x54951)+~E(x54952,f4(x54951))+E(f777(f777(f84(x54951),x54952),x54952),f4(x54951))+~P1(f777(f777(f336(x54951),x54952),f114(x54951))) % 174.01/173.90 [5531]E(x55311,f4(a3))+~E(f777(f777(f45(a3),x55312),x55311),f4(a3))+P1(f777(f777(f235(a3),x55311),x55312))+P1(f777(f777(f235(a3),x55312),x55311)) % 174.01/173.90 [5560]E(x55601,f4(a3))+~E(f777(f777(f45(a3),x55602),x55601),f4(a3))+P1(f777(f777(f234(a3),x55602),f4(a3)))+P1(f777(f777(f235(a3),x55602),x55601)) % 174.01/173.90 [5592]E(x55921,f4(a3))+~E(f777(f777(f45(a3),x55922),x55921),f4(a3))+P1(f777(f777(f234(a3),f4(a3)),x55922))+P1(f777(f777(f235(a3),x55921),x55922)) % 174.01/173.90 [5629]~P87(x56292)+E(x56291,f4(x56292))+~E(f777(f777(f84(x56292),x56291),x56291),f4(x56292))+~P1(f777(f777(f336(x56292),x56291),f114(x56292))) % 174.01/173.90 [5696]E(f777(f108(a851),x56961),f777(f108(a851),x56962))+~E(f777(f108(a3),x56962),f4(a3))+P1(f777(a188,f777(f108(a3),x56962)))+~P1(f777(a188,f777(f108(a3),x56961))) % 174.01/173.90 [5725]~E(f777(f108(a851),x57252),f777(f108(a851),x57251))+E(f777(f108(a3),x57251),f4(a3))+P1(f777(a188,f777(f108(a3),x57251)))+~P1(f777(a188,f777(f108(a3),x57252))) % 174.01/173.90 [5734]~P100(x57342)+E(x57341,f182(f858(x57342,a845)))+~P1(f777(f65(x57342),x57341))+P1(f777(f777(f336(x57342),f18(x57342,x57341)),x57341)) % 174.01/173.90 [5735]~P100(x57352)+E(x57351,f182(f858(x57352,a845)))+~P1(f777(f65(x57352),x57351))+P1(f777(f777(f336(x57352),f19(x57352,x57351)),x57351)) % 174.01/173.90 [5897]~P110(x58971)+~P88(x58971)+P1(f777(f777(f235(x58971),f4(x58971)),f777(f108(x58971),x58972)))+~P1(f777(f777(f235(a3),a87),x58972)) % 174.01/173.90 [5898]~P110(x58981)+~P88(x58981)+P1(f777(f777(f234(x58981),f4(x58981)),f777(f108(x58981),x58982)))+~P1(f777(f777(f234(a3),a87),x58982)) % 174.01/173.90 [5916]~P110(x59161)+~P88(x59161)+E(f777(f79(x59161),f777(f108(x59161),x59162)),f777(f108(x59161),x59162))+P1(f777(f777(f235(x59161),f777(f108(x59161),x59162)),f4(x59161))) % 174.01/173.90 [5958]E(x59581,x59582)+~E(f777(a109,x59581),f777(a109,x59582))+~P1(f777(f777(f234(a3),f4(a3)),x59582))+~P1(f777(f777(f234(a3),f4(a3)),x59581)) % 174.01/173.90 [6155]~P88(x61552)+~P110(x61552)+~P1(f777(f777(f235(x61552),f4(x61552)),f777(f108(x61552),x61551)))+P1(f777(f777(f235(a3),a87),x61551)) % 174.01/173.90 [6156]~P88(x61562)+~P110(x61562)+~P1(f777(f777(f234(x61562),f4(x61562)),f777(f108(x61562),x61561)))+P1(f777(f777(f234(a3),a87),x61561)) % 174.01/173.90 [6161]~P110(x61611)+~P88(x61611)+P1(f777(f777(f235(x61611),f777(f108(x61611),x61612)),f4(x61611)))+~P1(f777(f777(f235(a3),x61612),a87)) % 174.01/173.90 [6162]~P110(x61621)+~P88(x61621)+P1(f777(f777(f234(x61621),f777(f108(x61621),x61622)),f4(x61621)))+~P1(f777(f777(f234(a3),x61622),a87)) % 174.01/173.90 [6493]~P88(x64932)+~P110(x64932)+~P1(f777(f777(f235(x64932),f777(f108(x64932),x64931)),f4(x64932)))+P1(f777(f777(f235(a3),x64931),a87)) % 174.01/173.90 [6494]~P88(x64942)+~P110(x64942)+~P1(f777(f777(f234(x64942),f777(f108(x64942),x64941)),f4(x64942)))+P1(f777(f777(f234(a3),x64941),a87)) % 174.01/173.90 [6585]~P110(x65851)+~P88(x65851)+E(f777(f79(x65851),f777(f108(x65851),x65852)),f777(f83(x65851),f777(f108(x65851),x65852)))+~P1(f777(f777(f235(x65851),f777(f108(x65851),x65852)),f4(x65851))) % 174.01/173.90 [6603]E(f777(f108(a851),x66031),f777(f108(a851),x66032))+~E(f777(f108(a3),x66032),f4(a3))+~P1(f777(f777(f234(a3),f777(f108(a3),x66031)),f4(a3)))+~P1(f777(a188,f777(f108(a3),x66031))) % 174.01/173.90 [7016]P1(f777(f777(f281(a851),f777(a109,x70161)),f777(a109,x70162)))+~P1(f777(f777(f234(a3),f4(a3)),x70162))+~P1(f777(f777(f234(a3),f4(a3)),x70161))+~P1(f777(f777(f281(a3),x70161),x70162)) % 174.01/173.90 [7259]~P1(f777(f777(f281(a851),f777(a109,x72591)),f777(a109,x72592)))+~P1(f777(f777(f234(a3),f4(a3)),x72592))+~P1(f777(f777(f234(a3),f4(a3)),x72591))+P1(f777(f777(f281(a3),x72591),x72592)) % 174.01/173.90 [7523]~P100(x75232)+E(x75231,f182(f858(x75232,a845)))+~P1(f777(f65(x75232),x75231))+P1(f777(f777(f234(x75232),f16(x75232,f238(x75232),x75231)),f15(x75232,f181(x75232),x75231))) % 174.01/173.90 [7848]~P10(x78481)+~P38(x78482)+P1(f777(f777(f336(a3),x78481),x78482))+~P1(f777(f777(f336(a851),f777(a109,x78481)),f777(f305(a3,a851,a109),x78482))) % 174.01/173.90 [5731]~P133(x57312)+E(x57311,f4(a3))+E(f777(f83(x57312),f777(f107(x57312),f777(f83(a3),x57311))),f777(f107(x57312),x57311))+~P1(f777(f777(f235(a3),x57311),f4(a3))) % 174.01/173.90 [5807]~P87(x58071)+~P88(x58071)+~P33(x58071,f777(f108(x58071),x58072))+P33(x58071,f777(f108(x58071),f777(f777(f84(a3),x58072),x58072))) % 174.01/173.90 [6145]~P68(x61452)+E(x61451,f182(f858(x61452,a845)))+E(f19(x61452,f777(f305(x61452,x61452,f83(x61452)),x61451)),f777(f83(x61452),f18(x61452,x61451)))+~P1(f777(f65(x61452),x61451)) % 174.01/173.90 [6146]~P68(x61462)+E(x61461,f182(f858(x61462,a845)))+E(f18(x61462,f777(f305(x61462,x61462,f83(x61462)),x61461)),f777(f83(x61462),f19(x61462,x61461)))+~P1(f777(f65(x61462),x61461)) % 174.01/173.90 [6176]~P87(x61761)+~P88(x61761)+P33(x61761,f777(f108(x61761),x61762))+~P33(x61761,f777(f108(x61761),f777(f777(f84(a3),x61762),x61762))) % 174.01/173.90 [6271]E(x62711,f4(a3))+E(f777(a60,f59(f777(f83(a3),x62711),f777(f83(a3),x62712))),f55(x62711,x62712))+P1(f777(f777(f234(a3),f4(a3)),x62712))+~P1(f777(f777(f234(a3),f4(a3)),x62711)) % 174.01/173.90 [8605]~P38(x86052)+~P38(x86051)+P1(f777(f777(f235(f858(a851,a845)),f777(f305(a3,a851,a109),x86051)),f777(f305(a3,a851,a109),x86052)))+~P1(f777(f777(f235(f858(a3,a845)),x86051),x86052)) % 174.01/173.90 [8880]~P38(x88802)+~P38(x88801)+~P1(f777(f777(f235(f858(a851,a845)),f777(f305(a3,a851,a109),x88801)),f777(f305(a3,a851,a109),x88802)))+P1(f777(f777(f235(f858(a3,a845)),x88801),x88802)) % 174.01/173.90 [8881]~P38(x88812)+~P38(x88811)+~P1(f777(f777(f234(f858(a851,a845)),f777(f305(a3,a851,a109),x88811)),f777(f305(a3,a851,a109),x88812)))+P1(f777(f777(f234(f858(a3,a845)),x88811),x88812)) % 174.01/173.90 [9319]E(x93191,f4(a3))+E(x93192,f4(a3))+E(f777(f777(f90(a3,f857(a3,a3)),f777(f777(a214,x93192),x93191)),f777(f777(f22(a3,a3,f857(a3,a3)),f777(f777(f12(a3,f858(a3,f857(a3,a3)),a3),f243(a3,a3)),f777(f45(a3),x93192))),f777(f45(a3),x93191))),f212(x93192,x93191))+P1(f777(f777(f235(a3),x93191),f4(a3))) % 174.01/173.90 [8170]~P88(x81702)+~P110(x81702)+~P1(f777(f777(f235(x81702),f777(f108(x81702),x81701)),f82(x81702)))+P1(f777(f777(f235(a3),x81701),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))) % 174.01/173.90 [8171]~P88(x81712)+~P110(x81712)+~P1(f777(f777(f234(x81712),f777(f108(x81712),x81711)),f82(x81712)))+P1(f777(f777(f234(a3),x81711),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))) % 174.01/173.90 [8445]~P110(x84451)+~P88(x84451)+P1(f777(f777(f235(x84451),f777(f108(x84451),x84452)),f82(x84451)))+~P1(f777(f777(f235(a3),x84452),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))) % 174.01/173.90 [8446]~P110(x84461)+~P88(x84461)+P1(f777(f777(f234(x84461),f777(f108(x84461),x84462)),f82(x84461)))+~P1(f777(f777(f234(a3),x84462),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))) % 174.01/173.90 [8630]~P88(x86302)+~P110(x86302)+~P1(f777(f777(f235(x86302),f82(x86302)),f777(f108(x86302),x86301)))+P1(f777(f777(f235(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),x86301)) % 174.01/173.90 [8631]~P88(x86312)+~P110(x86312)+~P1(f777(f777(f234(x86312),f82(x86312)),f777(f108(x86312),x86311)))+P1(f777(f777(f234(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),x86311)) % 174.01/173.90 [8963]~P110(x89631)+~P88(x89631)+P1(f777(f777(f235(x89631),f82(x89631)),f777(f108(x89631),x89632)))+~P1(f777(f777(f235(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),x89632)) % 174.01/173.90 [8964]~P110(x89641)+~P88(x89641)+P1(f777(f777(f234(x89641),f82(x89641)),f777(f108(x89641),x89642)))+~P1(f777(f777(f234(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),x89642)) % 174.01/173.90 [9442]~P120(x94422)+E(x94421,f82(x94422))+E(x94421,f777(f83(x94422),f82(x94422)))+~E(f777(f777(f244(x94422),x94421),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f82(x94422)) % 174.01/173.90 [9687]~P62(x96871)+~P88(x96871)+~P1(f777(f777(f235(x96871),f4(x96871)),x96872))+P1(f777(f777(f235(x96871),f4(x96871)),f777(f777(f285(x96871),x96872),f777(f108(x96871),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))) % 174.01/173.90 [9742]~P62(x97421)+~P88(x97421)+P1(f777(f777(f235(x97421),f4(x97421)),x97422))+~P1(f777(f777(f235(x97421),f4(x97421)),f777(f777(f285(x97421),x97422),f777(f108(x97421),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))) % 174.01/173.90 [10017]~P133(x100172)+E(x100171,f4(a3))+P1(f777(f777(f235(a3),x100171),f4(a3)))+E(f777(f777(f253(a3,a3,x100172),f777(f777(f11(a3,f858(a3,f858(x100172,x100172)),f858(a3,x100172)),f777(f777(f12(f858(f858(x100172,x100172),x100172),f858(f858(a3,f858(x100172,x100172)),f858(a3,x100172)),a3),f12(f858(x100172,x100172),x100172,a3)),f777(f777(f12(x100172,f858(f858(x100172,x100172),x100172),a3),f90(x100172,x100172)),f107(x100172)))),f777(f777(f11(a3,f858(x100172,x100172),f858(x100172,x100172)),f777(f777(f12(f858(x100172,f858(x100172,x100172)),f858(f858(x100172,x100172),f858(x100172,x100172)),a3),f22(x100172,x100172,x100172)),f777(f777(f11(a3,f858(x100172,x100172),f858(x100172,f858(x100172,x100172))),f777(f777(f12(f858(x100172,f858(x100172,x100172)),f858(f858(x100172,x100172),f858(x100172,f858(x100172,x100172))),a3),f12(x100172,f858(x100172,x100172),x100172)),f777(f777(f12(a845,f858(x100172,f858(x100172,x100172)),a3),f100(x100172)),f777(f777(f11(a3,a3,a845),a332),f4(a3))))),f777(f777(f22(x100172,x100172,x100172),f84(x100172)),f9(x100172))))),f777(f777(f11(x100172,x100172,x100172),f777(f777(f12(x100172,f858(x100172,x100172),x100172),f84(x100172)),f777(f777(f22(x100172,x100172,x100172),f84(x100172)),f9(x100172)))),f82(x100172))))),f55(x100171,f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f107(x100172),x100171)) % 174.01/173.90 [4761]~P87(x47613)+~P88(x47613)+E(x47611,x47612)+~E(f777(f108(x47613),x47611),f777(f108(x47613),x47612)) % 174.01/173.90 [5906]~P1(f777(x59061,x59062))+~P1(f777(x59061,x59063))+~P1(f777(f777(f234(a851),x59063),f793(x59062,x59061)))+P1(f777(x59061,f4(a851))) % 174.01/173.90 [6338]P140(x63382,x63381,x63383)+E(x63381,f4(a3))+P1(f777(f777(f234(a3),f4(a3)),f784(x63383,x63381,x63382)))+P1(f777(f777(f235(a3),x63381),f4(a3))) % 174.01/173.90 [6339]P141(x63392,x63391,x63393)+E(x63391,f4(a3))+P1(f777(f777(f234(a3),f4(a3)),f787(x63393,x63391,x63392)))+P1(f777(f777(f235(a3),x63391),f4(a3))) % 174.01/173.90 [6471]P140(x64711,x64712,x64713)+~P1(f777(x64711,x64713))+P1(f777(f777(f234(a3),f4(a3)),f784(x64713,x64712,x64711)))+P1(f777(f777(f235(a3),x64712),f4(a3))) % 174.01/173.90 [6496]P141(x64961,x64962,x64963)+P1(f777(f777(f234(a3),f4(a3)),f787(x64963,x64962,x64961)))+~P1(f777(x64961,f4(a3)))+P1(f777(f777(f235(a3),x64962),f4(a3))) % 174.01/173.90 [6528]P140(x65282,x65281,x65283)+E(x65281,f4(a3))+~P1(f777(x65282,f784(x65283,x65281,x65282)))+P1(f777(f777(f235(a3),x65281),f4(a3))) % 174.01/173.90 [6529]P141(x65292,x65291,x65293)+E(x65291,f4(a3))+~P1(f777(x65292,f788(x65293,x65291,x65292)))+P1(f777(f777(f235(a3),x65291),f4(a3))) % 174.01/173.90 [6633]~P100(x66331)+~P9(x66331)+~P1(f777(f777(f235(x66331),x66332),f46(x66331,x66333)))+P1(f777(f777(f235(x66331),x66332),f673(x66333,x66332,x66331))) % 174.01/173.90 [6643]P140(x66431,x66432,x66433)+~P1(f777(x66431,x66433))+~P1(f777(x66431,f784(x66433,x66432,x66431)))+P1(f777(f777(f235(a3),x66432),f4(a3))) % 174.01/173.90 [6676]P141(x66761,x66762,x66763)+~P1(f777(x66761,f788(x66763,x66762,x66761)))+~P1(f777(x66761,f4(a3)))+P1(f777(f777(f235(a3),x66762),f4(a3))) % 174.01/173.90 [6939]P140(x69392,x69391,x69393)+E(x69391,f4(a3))+P1(f777(f777(f234(a3),f4(a3)),f784(x69393,x69391,x69392)))+P1(f777(f777(f235(a3),x69391),f782(x69393,x69391,x69392))) % 174.01/173.90 [6940]P141(x69402,x69401,x69403)+E(x69401,f4(a3))+P1(f777(f777(f234(a3),f4(a3)),f787(x69403,x69401,x69402)))+P1(f777(f777(f235(a3),x69401),f786(x69403,x69401,x69402))) % 174.01/173.90 [7057]P140(x70571,x70572,x70573)+~P1(f777(x70571,x70573))+P1(f777(f777(f234(a3),f4(a3)),f784(x70573,x70572,x70571)))+P1(f777(f777(f235(a3),x70572),f782(x70573,x70572,x70571))) % 174.01/173.90 [7078]P141(x70781,x70782,x70783)+P1(f777(f777(f234(a3),f4(a3)),f787(x70783,x70782,x70781)))+P1(f777(f777(f235(a3),x70782),f786(x70783,x70782,x70781)))+~P1(f777(x70781,f4(a3))) % 174.01/173.90 [7109]P140(x71092,x71091,x71093)+E(x71091,f4(a3))+~P1(f777(x71092,f784(x71093,x71091,x71092)))+P1(f777(f777(f235(a3),x71091),f782(x71093,x71091,x71092))) % 174.01/173.90 [7110]P141(x71102,x71101,x71103)+E(x71101,f4(a3))+~P1(f777(x71102,f788(x71103,x71101,x71102)))+P1(f777(f777(f235(a3),x71101),f786(x71103,x71101,x71102))) % 174.01/173.90 [7150]P140(x71502,x71501,x71503)+E(x71501,f4(a3))+P1(f777(f777(f234(a3),f4(a3)),f784(x71503,x71501,x71502)))+~P1(f777(x71502,f782(x71503,x71501,x71502))) % 174.01/173.90 [7151]P141(x71512,x71511,x71513)+E(x71511,f4(a3))+P1(f777(f777(f234(a3),f4(a3)),f787(x71513,x71511,x71512)))+~P1(f777(x71512,f789(x71513,x71511,x71512))) % 174.01/173.90 [7256]P140(x72561,x72562,x72563)+~P1(f777(x72561,x72563))+~P1(f777(x72561,f784(x72563,x72562,x72561)))+P1(f777(f777(f235(a3),x72562),f782(x72563,x72562,x72561))) % 174.01/173.90 [7272]P141(x72721,x72722,x72723)+~P1(f777(x72721,f788(x72723,x72722,x72721)))+P1(f777(f777(f235(a3),x72722),f786(x72723,x72722,x72721)))+~P1(f777(x72721,f4(a3))) % 174.01/173.90 [7278]P140(x72781,x72782,x72783)+~P1(f777(x72781,x72783))+P1(f777(f777(f234(a3),f4(a3)),f784(x72783,x72782,x72781)))+~P1(f777(x72781,f782(x72783,x72782,x72781))) % 174.01/173.90 [7296]P141(x72961,x72962,x72963)+P1(f777(f777(f234(a3),f4(a3)),f787(x72963,x72962,x72961)))+~P1(f777(x72961,f789(x72963,x72962,x72961)))+~P1(f777(x72961,f4(a3))) % 174.01/173.90 [7320]P140(x73202,x73201,x73203)+E(x73201,f4(a3))+~P1(f777(x73202,f784(x73203,x73201,x73202)))+~P1(f777(x73202,f782(x73203,x73201,x73202))) % 174.01/173.90 [7321]P141(x73212,x73211,x73213)+E(x73211,f4(a3))+~P1(f777(x73212,f788(x73213,x73211,x73212)))+~P1(f777(x73212,f789(x73213,x73211,x73212))) % 174.01/173.90 [7417]P140(x74171,x74172,x74173)+~P1(f777(x74171,x74173))+~P1(f777(x74171,f784(x74173,x74172,x74171)))+~P1(f777(x74171,f782(x74173,x74172,x74171))) % 174.01/173.90 [7432]P141(x74321,x74322,x74323)+~P1(f777(x74321,f788(x74323,x74322,x74321)))+~P1(f777(x74321,f789(x74323,x74322,x74321)))+~P1(f777(x74321,f4(a3))) % 174.01/173.90 [7483]P140(x74832,x74831,x74833)+E(x74831,f4(a3))+P1(f777(f777(f234(a3),f4(a3)),f784(x74833,x74831,x74832)))+P1(f777(f777(f234(a3),f782(x74833,x74831,x74832)),f4(a3))) % 174.01/173.90 [7484]P141(x74842,x74841,x74843)+E(x74841,f4(a3))+P1(f777(f777(f234(a3),f4(a3)),f787(x74843,x74841,x74842)))+P1(f777(f777(f234(a3),f786(x74843,x74841,x74842)),f4(a3))) % 174.01/173.90 [7485]~P2(x74851)+~P1(f777(f777(f336(x74851),x74853),f178(x74851)))+~P1(f777(f777(f336(x74851),x74852),f178(x74851)))+P1(f777(f777(f336(x74851),f777(f777(f84(x74851),x74852),x74853)),f178(x74851))) % 174.01/173.90 [7486]~P133(x74861)+~P1(f777(f777(f336(x74861),x74863),f114(x74861)))+~P1(f777(f777(f336(x74861),x74862),f114(x74861)))+P1(f777(f777(f336(x74861),f777(f777(f84(x74861),x74862),x74863)),f114(x74861))) % 174.01/173.90 [7487]~P2(x74871)+~P1(f777(f777(f336(x74871),x74873),f178(x74871)))+~P1(f777(f777(f336(x74871),x74872),f178(x74871)))+P1(f777(f777(f336(x74871),f777(f777(f85(x74871),x74872),x74873)),f178(x74871))) % 174.01/173.90 [7488]~P133(x74881)+~P1(f777(f777(f336(x74881),x74883),f114(x74881)))+~P1(f777(f777(f336(x74881),x74882),f114(x74881)))+P1(f777(f777(f336(x74881),f777(f777(f85(x74881),x74882),x74883)),f114(x74881))) % 174.01/173.90 [7489]~P133(x74891)+~P1(f777(f777(f336(x74891),x74893),f114(x74891)))+~P1(f777(f777(f336(x74891),x74892),f114(x74891)))+P1(f777(f777(f336(x74891),f777(f777(f5(x74891),x74892),x74893)),f114(x74891))) % 174.01/173.90 [7490]~P81(x74901)+~P1(f777(f777(f235(x74901),x74903),f4(x74901)))+~P1(f777(f777(f235(x74901),x74902),f4(x74901)))+P1(f777(f777(f235(x74901),f777(f777(f84(x74901),x74902),x74903)),f4(x74901))) % 174.01/173.90 [7491]~P81(x74911)+~P1(f777(f777(f234(x74911),x74912),f4(x74911)))+~P1(f777(f777(f235(x74911),x74913),f4(x74911)))+P1(f777(f777(f235(x74911),f777(f777(f84(x74911),x74912),x74913)),f4(x74911))) % 174.01/173.90 [7492]~P81(x74921)+~P1(f777(f777(f234(x74921),x74923),f4(x74921)))+~P1(f777(f777(f235(x74921),x74922),f4(x74921)))+P1(f777(f777(f235(x74921),f777(f777(f84(x74921),x74922),x74923)),f4(x74921))) % 174.01/173.90 [7493]~P81(x74931)+~P1(f777(f777(f234(x74931),x74933),f4(x74931)))+~P1(f777(f777(f234(x74931),x74932),f4(x74931)))+P1(f777(f777(f234(x74931),f777(f777(f84(x74931),x74932),x74933)),f4(x74931))) % 174.01/173.90 [7519]P140(x75193,x75191,x75192)+E(x75191,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x75191),f781(x75192,x75191,x75193))),f784(x75192,x75191,x75193)),x75192)+P1(f777(f777(f235(a3),x75191),f4(a3))) % 174.01/173.90 [7520]P141(x75203,x75201,x75202)+E(x75201,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x75201),f788(x75202,x75201,x75203))),f787(x75202,x75201,x75203)),x75202)+P1(f777(f777(f235(a3),x75201),f4(a3))) % 174.01/173.90 [7605]P140(x76051,x76052,x76053)+~P1(f777(x76051,x76053))+P1(f777(f777(f234(a3),f4(a3)),f784(x76053,x76052,x76051)))+P1(f777(f777(f234(a3),f782(x76053,x76052,x76051)),f4(a3))) % 174.01/173.90 [7636]P141(x76361,x76362,x76363)+P1(f777(f777(f234(a3),f4(a3)),f787(x76363,x76362,x76361)))+~P1(f777(x76361,f4(a3)))+P1(f777(f777(f234(a3),f786(x76363,x76362,x76361)),f4(a3))) % 174.01/173.90 [7644]P140(x76443,x76441,x76442)+~P1(f777(x76443,x76442))+E(f777(f777(f84(a3),f777(f777(f85(a3),x76441),f781(x76442,x76441,x76443))),f784(x76442,x76441,x76443)),x76442)+P1(f777(f777(f235(a3),x76441),f4(a3))) % 174.01/173.90 [7649]P140(x76492,x76491,x76493)+E(x76491,f4(a3))+~P1(f777(x76492,f784(x76493,x76491,x76492)))+P1(f777(f777(f234(a3),f782(x76493,x76491,x76492)),f4(a3))) % 174.01/173.90 [7650]P141(x76502,x76501,x76503)+E(x76501,f4(a3))+~P1(f777(x76502,f788(x76503,x76501,x76502)))+P1(f777(f777(f234(a3),f786(x76503,x76501,x76502)),f4(a3))) % 174.01/173.90 [7655]P141(x76553,x76551,x76552)+E(f777(f777(f84(a3),f777(f777(f85(a3),x76551),f788(x76552,x76551,x76553))),f787(x76552,x76551,x76553)),x76552)+~P1(f777(x76553,f4(a3)))+P1(f777(f777(f235(a3),x76551),f4(a3))) % 174.01/173.90 [7708]P140(x77081,x77082,x77083)+~P1(f777(x77081,x77083))+~P1(f777(x77081,f784(x77083,x77082,x77081)))+P1(f777(f777(f234(a3),f782(x77083,x77082,x77081)),f4(a3))) % 174.01/173.90 [7713]P141(x77131,x77132,x77133)+~P1(f777(x77131,f788(x77133,x77132,x77131)))+~P1(f777(x77131,f4(a3)))+P1(f777(f777(f234(a3),f786(x77133,x77132,x77131)),f4(a3))) % 174.01/173.90 [7787]~P62(x77871)+~P1(f777(f777(f235(x77871),f777(f777(f285(x77871),x77873),x77872)),f4(x77871)))+P1(f777(f777(f235(x77871),x77872),f4(x77871)))+P1(f777(f777(f235(x77871),x77873),f4(x77871))) % 174.01/173.90 [7788]~P119(x77881)+~P1(f777(f777(f234(x77881),f777(f777(f85(x77881),x77883),x77882)),f4(x77881)))+P1(f777(f777(f234(x77881),x77882),f4(x77881)))+P1(f777(f777(f234(x77881),x77883),f4(x77881))) % 174.01/173.90 [7789]~P62(x77891)+~P1(f777(f777(f234(x77891),f777(f777(f285(x77891),x77893),x77892)),f4(x77891)))+P1(f777(f777(f234(x77891),x77892),f4(x77891)))+P1(f777(f777(f234(x77891),x77893),f4(x77891))) % 174.01/173.90 [7901]P140(x79013,x79011,x79012)+E(x79011,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x79011),f781(x79012,x79011,x79013))),f784(x79012,x79011,x79013)),x79012)+P1(f777(f777(f235(a3),x79011),f782(x79012,x79011,x79013))) % 174.01/173.90 [7902]P141(x79023,x79021,x79022)+E(x79021,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x79021),f788(x79022,x79021,x79023))),f787(x79022,x79021,x79023)),x79022)+P1(f777(f777(f235(a3),x79021),f786(x79022,x79021,x79023))) % 174.01/173.90 [7913]P140(x79133,x79131,x79132)+E(x79131,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x79131),f785(x79132,x79131,x79133))),f782(x79132,x79131,x79133)),x79132)+P1(f777(f777(f234(a3),f4(a3)),f784(x79132,x79131,x79133))) % 174.01/173.90 [7914]P141(x79143,x79141,x79142)+E(x79141,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x79141),f789(x79142,x79141,x79143))),f786(x79142,x79141,x79143)),x79142)+P1(f777(f777(f234(a3),f4(a3)),f787(x79142,x79141,x79143))) % 174.01/173.90 [7961]P140(x79613,x79611,x79612)+~P1(f777(x79613,x79612))+E(f777(f777(f84(a3),f777(f777(f85(a3),x79611),f781(x79612,x79611,x79613))),f784(x79612,x79611,x79613)),x79612)+P1(f777(f777(f235(a3),x79611),f782(x79612,x79611,x79613))) % 174.01/173.90 [7972]P141(x79723,x79721,x79722)+E(f777(f777(f84(a3),f777(f777(f85(a3),x79721),f788(x79722,x79721,x79723))),f787(x79722,x79721,x79723)),x79722)+P1(f777(f777(f235(a3),x79721),f786(x79722,x79721,x79723)))+~P1(f777(x79723,f4(a3))) % 174.01/173.90 [7978]P140(x79783,x79781,x79782)+~P1(f777(x79783,x79782))+E(f777(f777(f84(a3),f777(f777(f85(a3),x79781),f785(x79782,x79781,x79783))),f782(x79782,x79781,x79783)),x79782)+P1(f777(f777(f234(a3),f4(a3)),f784(x79782,x79781,x79783))) % 174.01/173.90 [7985]P141(x79853,x79851,x79852)+E(f777(f777(f84(a3),f777(f777(f85(a3),x79851),f789(x79852,x79851,x79853))),f786(x79852,x79851,x79853)),x79852)+P1(f777(f777(f234(a3),f4(a3)),f787(x79852,x79851,x79853)))+~P1(f777(x79853,f4(a3))) % 174.01/173.90 [7995]P140(x79953,x79951,x79952)+E(x79951,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x79951),f781(x79952,x79951,x79953))),f784(x79952,x79951,x79953)),x79952)+~P1(f777(x79953,f782(x79952,x79951,x79953))) % 174.01/173.90 [7996]P141(x79963,x79961,x79962)+E(x79961,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x79961),f788(x79962,x79961,x79963))),f787(x79962,x79961,x79963)),x79962)+~P1(f777(x79963,f789(x79962,x79961,x79963))) % 174.01/173.90 [7997]P140(x79973,x79971,x79972)+E(x79971,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x79971),f785(x79972,x79971,x79973))),f782(x79972,x79971,x79973)),x79972)+~P1(f777(x79973,f784(x79972,x79971,x79973))) % 174.01/173.90 [7998]P141(x79983,x79981,x79982)+E(x79981,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x79981),f789(x79982,x79981,x79983))),f786(x79982,x79981,x79983)),x79982)+~P1(f777(x79983,f788(x79982,x79981,x79983))) % 174.01/173.90 [8051]P140(x80513,x80511,x80512)+~P1(f777(x80513,x80512))+E(f777(f777(f84(a3),f777(f777(f85(a3),x80511),f781(x80512,x80511,x80513))),f784(x80512,x80511,x80513)),x80512)+~P1(f777(x80513,f782(x80512,x80511,x80513))) % 174.01/173.90 [8052]P140(x80523,x80521,x80522)+~P1(f777(x80523,x80522))+E(f777(f777(f84(a3),f777(f777(f85(a3),x80521),f785(x80522,x80521,x80523))),f782(x80522,x80521,x80523)),x80522)+~P1(f777(x80523,f784(x80522,x80521,x80523))) % 174.01/173.90 [8064]P141(x80643,x80641,x80642)+E(f777(f777(f84(a3),f777(f777(f85(a3),x80641),f788(x80642,x80641,x80643))),f787(x80642,x80641,x80643)),x80642)+~P1(f777(x80643,f789(x80642,x80641,x80643)))+~P1(f777(x80643,f4(a3))) % 174.01/173.90 [8065]P141(x80653,x80651,x80652)+E(f777(f777(f84(a3),f777(f777(f85(a3),x80651),f789(x80652,x80651,x80653))),f786(x80652,x80651,x80653)),x80652)+~P1(f777(x80653,f788(x80652,x80651,x80653)))+~P1(f777(x80653,f4(a3))) % 174.01/173.90 [8163]P140(x81633,x81631,x81632)+E(x81631,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x81631),f781(x81632,x81631,x81633))),f784(x81632,x81631,x81633)),x81632)+P1(f777(f777(f234(a3),f782(x81632,x81631,x81633)),f4(a3))) % 174.01/173.90 [8164]P141(x81643,x81641,x81642)+E(x81641,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x81641),f788(x81642,x81641,x81643))),f787(x81642,x81641,x81643)),x81642)+P1(f777(f777(f234(a3),f786(x81642,x81641,x81643)),f4(a3))) % 174.01/173.90 [8202]P140(x82023,x82021,x82022)+~P1(f777(x82023,x82022))+E(f777(f777(f84(a3),f777(f777(f85(a3),x82021),f781(x82022,x82021,x82023))),f784(x82022,x82021,x82023)),x82022)+P1(f777(f777(f234(a3),f782(x82022,x82021,x82023)),f4(a3))) % 174.01/173.90 [8207]P141(x82073,x82071,x82072)+E(f777(f777(f84(a3),f777(f777(f85(a3),x82071),f788(x82072,x82071,x82073))),f787(x82072,x82071,x82073)),x82072)+~P1(f777(x82073,f4(a3)))+P1(f777(f777(f234(a3),f786(x82072,x82071,x82073)),f4(a3))) % 174.01/173.90 [8338]P140(x83383,x83381,x83382)+E(x83381,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x83381),f785(x83382,x83381,x83383))),f782(x83382,x83381,x83383)),x83382)+E(f777(f777(f84(a3),f777(f777(f85(a3),x83381),f781(x83382,x83381,x83383))),f784(x83382,x83381,x83383)),x83382) % 174.01/173.90 [8339]P141(x83393,x83391,x83392)+E(x83391,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x83391),f789(x83392,x83391,x83393))),f786(x83392,x83391,x83393)),x83392)+E(f777(f777(f84(a3),f777(f777(f85(a3),x83391),f788(x83392,x83391,x83393))),f787(x83392,x83391,x83393)),x83392) % 174.01/173.90 [8362]P140(x83623,x83621,x83622)+~P1(f777(x83623,x83622))+E(f777(f777(f84(a3),f777(f777(f85(a3),x83621),f785(x83622,x83621,x83623))),f782(x83622,x83621,x83623)),x83622)+E(f777(f777(f84(a3),f777(f777(f85(a3),x83621),f781(x83622,x83621,x83623))),f784(x83622,x83621,x83623)),x83622) % 174.01/173.90 [8374]P141(x83743,x83741,x83742)+E(f777(f777(f84(a3),f777(f777(f85(a3),x83741),f789(x83742,x83741,x83743))),f786(x83742,x83741,x83743)),x83742)+E(f777(f777(f84(a3),f777(f777(f85(a3),x83741),f788(x83742,x83741,x83743))),f787(x83742,x83741,x83743)),x83742)+~P1(f777(x83743,f4(a3))) % 174.01/173.90 [8968]~P119(x89681)+~E(x89683,f4(x89681))+~E(x89682,f4(x89681))+P1(f777(f777(f234(x89681),f777(f777(f84(x89681),f777(f777(f85(x89681),x89682),x89682)),f777(f777(f85(x89681),x89683),x89683))),f4(x89681))) % 174.01/173.90 [9967]~P110(x99671)+~E(x99673,f4(x99671))+~E(x99672,f4(x99671))+P1(f777(f777(f234(x99671),f777(f777(f84(x99671),f777(f777(f244(x99671),x99672),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x99671),x99673),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))),f4(x99671))) % 174.01/173.90 [4711]~E(x47113,x47111)+~P113(x47112)+E(x47111,f4(x47112))+E(f777(f777(f285(x47112),x47113),x47111),f82(x47112)) % 174.01/173.90 [4762]~P95(x47621)+~E(x47623,f182(x47621))+~E(x47622,f182(x47621))+E(f777(f777(f105(x47621),x47622),x47623),f182(x47621)) % 174.01/173.90 [4763]~P94(x47631)+~E(x47633,f241(x47631))+~E(x47632,f241(x47631))+E(f777(f777(f106(x47631),x47632),x47633),f241(x47631)) % 174.01/173.90 [4849]~P113(x48493)+E(x48491,x48492)+E(x48492,f4(x48493))+~E(f777(f777(f285(x48493),x48491),x48492),f82(x48493)) % 174.01/173.90 [4865]~P134(x48652)+E(x48651,f4(x48652))+E(x48653,f4(x48652))+~E(f777(f777(f85(x48652),x48653),x48651),f4(x48652)) % 174.01/173.90 [4867]~P127(x48672)+E(x48671,f4(x48672))+E(x48673,f4(x48672))+~E(f777(f777(f85(x48672),x48673),x48671),f4(x48672)) % 174.01/173.90 [5242]~P111(x52423)+E(x52421,x52422)+E(x52421,f777(f83(x52423),x52422))+~E(f777(f777(f85(x52423),x52421),x52421),f777(f777(f85(x52423),x52422),x52422)) % 174.01/173.90 [5279]~P90(x52791)+E(f777(f83(x52791),x52792),x52793)+~E(f777(f777(f105(x52791),x52792),x52793),f241(x52791))+~E(f777(f777(f106(x52791),x52792),x52793),f182(x52791)) % 174.01/173.90 [5355]~P110(x53553)+E(x53551,x53552)+P1(f777(f777(f235(x53553),x53552),x53551))+P1(f777(f777(f235(x53553),x53551),x53552)) % 174.01/173.90 [5361]~P100(x53613)+E(x53611,x53612)+P1(f777(f777(f235(x53613),x53612),x53611))+P1(f777(f777(f235(x53613),x53611),x53612)) % 174.01/173.90 [5362]~E(x53622,x53623)+~P100(x53621)+P1(f777(f777(f234(x53621),x53622),x53623))+P1(f777(f777(f235(x53621),x53622),x53623)) % 174.01/173.90 [5608]~P99(x56083)+E(x56081,x56082)+~P1(f777(f777(f234(x56083),x56082),x56081))+P1(f777(f777(f235(x56083),x56082),x56081)) % 174.01/173.90 [5614]~P99(x56143)+E(x56141,x56142)+~P1(f777(f777(f234(x56143),x56141),x56142))+P1(f777(f777(f235(x56143),x56141),x56142)) % 174.01/173.90 [5616]~P100(x56163)+E(x56161,x56162)+~P1(f777(f777(f234(x56163),x56161),x56162))+P1(f777(f777(f235(x56163),x56161),x56162)) % 174.01/173.90 [5728]P140(x57281,x57282,x57283)+~P1(f777(x57281,x57283))+P1(f777(f777(f235(a3),x57282),f4(a3)))+P1(f777(f777(f235(a3),f4(a3)),x57282)) % 174.01/173.90 [5779]P141(x57791,x57792,x57793)+~P1(f777(x57791,f4(a3)))+P1(f777(f777(f235(a3),x57792),f4(a3)))+P1(f777(f777(f235(a3),f4(a3)),x57792)) % 174.01/173.90 [5783]~P93(x57831)+E(f777(f777(f105(x57831),x57832),f14(x57831,x57833)),x57832)+~P1(f777(f65(x57831),x57833))+~P1(f777(f777(f336(x57831),x57832),x57833)) % 174.01/173.90 [5784]~P93(x57841)+E(f777(f777(f106(x57841),x57842),f17(x57841,x57843)),x57842)+~P1(f777(f65(x57841),x57843))+~P1(f777(f777(f336(x57841),x57842),x57843)) % 174.01/173.90 [5817]~P100(x58171)+E(f777(f777(f238(x58171),x58172),f19(x58171,x58173)),f19(x58171,x58173))+~P1(f777(f65(x58171),x58173))+~P1(f777(f777(f336(x58171),x58172),x58173)) % 174.01/173.90 [5818]~P100(x58181)+E(f777(f777(f181(x58181),x58182),f18(x58181,x58183)),f18(x58181,x58183))+~P1(f777(f65(x58181),x58183))+~P1(f777(f777(f336(x58181),x58182),x58183)) % 174.01/173.90 [5819]~P93(x58191)+E(f777(f777(f105(x58191),x58192),f17(x58191,x58193)),f17(x58191,x58193))+~P1(f777(f65(x58191),x58193))+~P1(f777(f777(f336(x58191),x58192),x58193)) % 174.01/173.90 [5820]~P93(x58201)+E(f777(f777(f106(x58201),x58202),f14(x58201,x58203)),f14(x58201,x58203))+~P1(f777(f65(x58201),x58203))+~P1(f777(f777(f336(x58201),x58202),x58203)) % 174.01/173.90 [5860]E(x58601,x58602)+~P99(x58603)+~P1(f777(f777(f234(x58603),x58602),x58601))+~P1(f777(f777(f234(x58603),x58601),x58602)) % 174.01/173.90 [6002]~P103(x60021)+P1(f777(f777(f234(x60021),x60023),x60022))+~P1(f777(f777(f234(x60021),x60022),x60023))+P1(f777(f777(f235(x60021),x60022),x60023)) % 174.01/173.90 [6026]~P100(x60261)+~P1(f777(f65(x60261),x60263))+P1(f777(f777(f234(x60261),x60262),f18(x60261,x60263)))+~P1(f777(f777(f336(x60261),x60262),x60263)) % 174.01/173.90 [6080]~P100(x60801)+E(f777(f777(f238(x60801),x60802),f15(x60801,f181(x60801),x60803)),x60802)+~P1(f777(f65(x60801),x60803))+~P1(f777(f777(f336(x60801),x60802),x60803)) % 174.01/173.90 [6081]~P100(x60811)+E(f777(f777(f181(x60811),x60812),f16(x60811,f238(x60811),x60813)),x60812)+~P1(f777(f65(x60811),x60813))+~P1(f777(f777(f336(x60811),x60812),x60813)) % 174.01/173.90 [6222]E(x62221,x62222)+~E(f777(f777(f5(a851),x62221),x62223),f777(f777(f5(a851),x62222),x62223))+~P1(f777(f777(f234(a851),x62223),x62221))+~P1(f777(f777(f234(a851),x62223),x62222)) % 174.01/173.90 [6250]~P100(x62501)+~P1(f777(f65(x62501),x62502))+~P1(f777(f777(f336(x62501),x62503),x62502))+P1(f777(f777(f234(x62501),f19(x62501,x62502)),x62503)) % 174.01/173.90 [6317]P140(x63172,x63171,x63173)+E(x63171,f4(a3))+P1(f777(f777(f235(a3),x63171),f782(x63173,x63171,x63172)))+P1(f777(f777(f235(a3),f4(a3)),x63171)) % 174.01/173.90 [6318]P141(x63182,x63181,x63183)+E(x63181,f4(a3))+P1(f777(f777(f235(a3),x63181),f786(x63183,x63181,x63182)))+P1(f777(f777(f235(a3),f4(a3)),x63181)) % 174.01/173.90 [6319]~P100(x63191)+E(f777(f777(f238(x63191),x63192),f16(x63191,f238(x63191),x63193)),f16(x63191,f238(x63191),x63193))+~P1(f777(f65(x63191),x63193))+~P1(f777(f777(f336(x63191),x63192),x63193)) % 174.01/173.90 [6320]~P100(x63201)+E(f777(f777(f181(x63201),x63202),f15(x63201,f181(x63201),x63203)),f15(x63201,f181(x63201),x63203))+~P1(f777(f65(x63201),x63203))+~P1(f777(f777(f336(x63201),x63202),x63203)) % 174.01/173.90 [6327]~P1(f777(x63271,x63272))+P1(f777(x63271,f811(x63272,x63271,x63273)))+P1(f777(x63271,f4(a851)))+~P1(f777(f777(f235(a851),x63272),x63273)) % 174.01/173.90 [6386]~P1(f777(x63861,x63862))+~P1(f777(f65(x63863),x63862))+P1(f777(x63861,f484(x63861,x63862,x63863)))+P1(f777(x63861,f182(f858(x63863,a845)))) % 174.01/173.90 [6401]~P110(x64011)+~P88(x64011)+P1(f777(f777(f235(x64011),f777(f108(x64011),x64012)),f777(f108(x64011),x64013)))+~P1(f777(f777(f235(a3),x64012),x64013)) % 174.01/173.90 [6402]~P110(x64021)+~P88(x64021)+P1(f777(f777(f234(x64021),f777(f108(x64021),x64022)),f777(f108(x64021),x64023)))+~P1(f777(f777(f234(a3),x64022),x64023)) % 174.01/173.90 [6405]~P1(f777(x64051,x64053))+~P1(f777(f65(x64052),x64053))+P1(f777(f65(x64052),f484(x64051,x64053,x64052)))+P1(f777(x64051,f182(f858(x64052,a845)))) % 174.01/173.90 [6439]P140(x64391,x64392,x64393)+~P1(f777(x64391,x64393))+P1(f777(f777(f235(a3),x64392),f782(x64393,x64392,x64391)))+P1(f777(f777(f235(a3),f4(a3)),x64392)) % 174.01/173.90 [6479]P141(x64791,x64792,x64793)+P1(f777(f777(f235(a3),x64792),f786(x64793,x64792,x64791)))+~P1(f777(x64791,f4(a3)))+P1(f777(f777(f235(a3),f4(a3)),x64792)) % 174.01/173.90 [6507]~P102(x65071)+~P89(x65071)+E(f777(f777(f238(x65071),f777(f108(x65071),x65072)),f777(f108(x65071),x65073)),f777(f108(x65071),x65073))+P1(f777(f777(f234(x65071),f777(f108(x65071),x65072)),f777(f108(x65071),x65073))) % 174.01/173.90 [6508]~P102(x65081)+~P89(x65081)+E(f777(f777(f181(x65081),f777(f108(x65081),x65082)),f777(f108(x65081),x65083)),f777(f108(x65081),x65082))+P1(f777(f777(f234(x65081),f777(f108(x65081),x65082)),f777(f108(x65081),x65083))) % 174.01/173.90 [6570]P140(x65702,x65701,x65703)+E(x65701,f4(a3))+~P1(f777(x65702,f782(x65703,x65701,x65702)))+P1(f777(f777(f235(a3),f4(a3)),x65701)) % 174.01/173.90 [6571]P141(x65712,x65711,x65713)+E(x65711,f4(a3))+~P1(f777(x65712,f789(x65713,x65711,x65712)))+P1(f777(f777(f235(a3),f4(a3)),x65711)) % 174.01/173.90 [6666]P140(x66661,x66662,x66663)+~P1(f777(x66661,x66663))+~P1(f777(x66661,f782(x66663,x66662,x66661)))+P1(f777(f777(f235(a3),f4(a3)),x66662)) % 174.01/173.90 [6696]P141(x66961,x66962,x66963)+~P1(f777(x66961,f789(x66963,x66962,x66961)))+~P1(f777(x66961,f4(a3)))+P1(f777(f777(f235(a3),f4(a3)),x66962)) % 174.01/173.90 [6813]~P88(x68133)+~P110(x68133)+~P1(f777(f777(f235(x68133),f777(f108(x68133),x68131)),f777(f108(x68133),x68132)))+P1(f777(f777(f235(a3),x68131),x68132)) % 174.01/173.90 [6814]~P88(x68143)+~P110(x68143)+~P1(f777(f777(f234(x68143),f777(f108(x68143),x68141)),f777(f108(x68143),x68142)))+P1(f777(f777(f234(a3),x68141),x68142)) % 174.01/173.90 [6843]~P100(x68431)+~P18(x68431,x68433)+P18(x68431,f777(f777(f142(x68431),x68432),x68433))+~P1(f777(f777(f234(x68431),x68432),f765(x68433,x68432,x68431))) % 174.01/173.90 [6844]~P100(x68441)+~P18(x68441,x68443)+P18(x68441,f777(f777(f142(x68441),x68442),x68443))+~P1(f777(f777(f234(x68441),x68442),f766(x68443,x68442,x68441))) % 174.01/173.90 [6931]P140(x69312,x69311,x69313)+E(x69311,f4(a3))+P1(f777(f777(f235(a3),x69311),f4(a3)))+P1(f777(f777(f235(a3),f784(x69313,x69311,x69312)),x69311)) % 174.01/173.90 [6932]P141(x69322,x69321,x69323)+E(x69321,f4(a3))+P1(f777(f777(f235(a3),x69321),f4(a3)))+P1(f777(f777(f235(a3),f787(x69323,x69321,x69322)),x69321)) % 174.01/173.90 [6971]P140(x69712,x69711,x69713)+E(x69711,f4(a3))+P1(f777(f777(f234(a3),f782(x69713,x69711,x69712)),f4(a3)))+P1(f777(f777(f235(a3),f4(a3)),x69711)) % 174.01/173.90 [6972]P141(x69722,x69721,x69723)+E(x69721,f4(a3))+P1(f777(f777(f234(a3),f786(x69723,x69721,x69722)),f4(a3)))+P1(f777(f777(f235(a3),f4(a3)),x69721)) % 174.01/173.90 [6990]~P100(x69901)+~P18(x69901,x69903)+E(f777(f777(f140(x69901,x69901,f9(x69901)),x69902),f153(x69901,x69902,x69903)),x69903)+~P1(f777(f777(f336(x69901),x69902),f777(f160(x69901),x69903))) % 174.01/173.90 [7040]P140(x70401,x70402,x70403)+~P1(f777(x70401,x70403))+P1(f777(f777(f235(a3),x70402),f4(a3)))+P1(f777(f777(f235(a3),f784(x70403,x70402,x70401)),x70402)) % 174.01/173.90 [7046]~P102(x70461)+~P89(x70461)+E(f777(f777(f238(x70461),f777(f108(x70461),x70462)),f777(f108(x70461),x70463)),f777(f108(x70461),x70462))+~P1(f777(f777(f234(x70461),f777(f108(x70461),x70462)),f777(f108(x70461),x70463))) % 174.01/173.90 [7047]~P102(x70471)+~P89(x70471)+E(f777(f777(f181(x70471),f777(f108(x70471),x70472)),f777(f108(x70471),x70473)),f777(f108(x70471),x70473))+~P1(f777(f777(f234(x70471),f777(f108(x70471),x70472)),f777(f108(x70471),x70473))) % 174.01/173.90 [7060]P141(x70601,x70602,x70603)+~P1(f777(x70601,f4(a3)))+P1(f777(f777(f235(a3),x70602),f4(a3)))+P1(f777(f777(f235(a3),f787(x70603,x70602,x70601)),x70602)) % 174.01/173.90 [7070]P140(x70701,x70702,x70703)+~P1(f777(x70701,x70703))+P1(f777(f777(f234(a3),f782(x70703,x70702,x70701)),f4(a3)))+P1(f777(f777(f235(a3),f4(a3)),x70702)) % 174.01/173.90 [7094]P141(x70941,x70942,x70943)+~P1(f777(x70941,f4(a3)))+P1(f777(f777(f234(a3),f786(x70943,x70942,x70941)),f4(a3)))+P1(f777(f777(f235(a3),f4(a3)),x70942)) % 174.01/173.90 [7121]~P1(f777(x71211,x71212))+P1(f777(x71211,f4(a851)))+~P1(f777(f777(f235(a851),x71212),x71213))+P1(f777(f777(f235(a851),f811(x71212,x71211,x71213)),x71213)) % 174.01/173.90 [7138]~P100(x71381)+~P18(x71381,x71383)+P18(x71381,f777(f777(f142(x71381),x71382),x71383))+P1(f777(f777(f336(x71381),f765(x71383,x71382,x71381)),f777(f160(x71381),x71383))) % 174.01/173.90 [7139]~P100(x71391)+~P18(x71391,x71393)+P18(x71391,f777(f777(f142(x71391),x71392),x71393))+P1(f777(f777(f336(x71391),f766(x71393,x71392,x71391)),f777(f160(x71391),x71393))) % 174.01/173.90 [7261]~P100(x72611)+~P9(x72611)+~P1(f777(f777(f235(x72611),x72613),f46(x72611,x72612)))+P1(f777(f777(f336(x72611),f673(x72612,x72613,x72611)),x72612)) % 174.01/173.90 [7430]~P100(x74301)+~P9(x74301)+~P1(f777(f777(f235(x74301),f47(x74301,x74303)),x74302))+P1(f777(f777(f336(x74301),f676(x74302,x74303,x74301)),x74303)) % 174.01/173.90 [7431]~P100(x74311)+~P9(x74311)+~P1(f777(f777(f235(x74311),f47(x74311,x74313)),x74312))+P1(f777(f777(f235(x74311),f676(x74312,x74313,x74311)),x74312)) % 174.01/173.90 [7445]P140(x74452,x74451,x74453)+E(x74451,f4(a3))+P1(f777(f777(f235(a3),x74451),f782(x74453,x74451,x74452)))+P1(f777(f777(f235(a3),f784(x74453,x74451,x74452)),x74451)) % 174.01/173.90 [7446]P141(x74462,x74461,x74463)+E(x74461,f4(a3))+P1(f777(f777(f235(a3),x74461),f786(x74463,x74461,x74462)))+P1(f777(f777(f235(a3),f787(x74463,x74461,x74462)),x74461)) % 174.01/173.90 [7542]P140(x75423,x75421,x75422)+E(x75421,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x75421),f785(x75422,x75421,x75423))),f782(x75422,x75421,x75423)),x75422)+P1(f777(f777(f235(a3),f4(a3)),x75421)) % 174.01/173.90 [7543]P141(x75433,x75431,x75432)+E(x75431,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x75431),f789(x75432,x75431,x75433))),f786(x75432,x75431,x75433)),x75432)+P1(f777(f777(f235(a3),f4(a3)),x75431)) % 174.01/173.90 [7545]~P123(x75451)+~P1(f777(f777(f235(x75451),x75453),f4(x75451)))+P1(f777(f777(f235(x75451),f777(f777(f85(x75451),x75452),x75453)),f4(x75451)))+~P1(f777(f777(f235(x75451),f4(x75451)),x75452)) % 174.01/173.90 [7546]~P123(x75461)+~P1(f777(f777(f235(x75461),x75462),f4(x75461)))+P1(f777(f777(f235(x75461),f777(f777(f85(x75461),x75462),x75463)),f4(x75461)))+~P1(f777(f777(f235(x75461),f4(x75461)),x75463)) % 174.01/173.90 [7547]~P62(x75471)+~P1(f777(f777(f235(x75471),x75473),f4(x75471)))+P1(f777(f777(f235(x75471),f777(f777(f285(x75471),x75472),x75473)),f4(x75471)))+~P1(f777(f777(f235(x75471),f4(x75471)),x75472)) % 174.01/173.90 [7548]~P62(x75481)+~P1(f777(f777(f235(x75481),x75482),f4(x75481)))+P1(f777(f777(f235(x75481),f777(f777(f285(x75481),x75482),x75483)),f4(x75481)))+~P1(f777(f777(f235(x75481),f4(x75481)),x75483)) % 174.01/173.90 [7549]~P63(x75491)+~P1(f777(f777(f235(x75491),x75493),f4(x75491)))+P1(f777(f777(f235(x75491),f777(f777(f285(x75491),x75492),x75493)),f4(x75491)))+~P1(f777(f777(f235(x75491),f4(x75491)),x75492)) % 174.01/173.90 [7550]~P63(x75501)+~P1(f777(f777(f235(x75501),x75502),f4(x75501)))+P1(f777(f777(f235(x75501),f777(f777(f285(x75501),x75502),x75503)),f4(x75501)))+~P1(f777(f777(f235(x75501),f4(x75501)),x75503)) % 174.01/173.90 [7552]~P119(x75521)+~P1(f777(f777(f234(x75521),x75523),f4(x75521)))+P1(f777(f777(f234(x75521),f777(f777(f85(x75521),x75522),x75523)),f4(x75521)))+~P1(f777(f777(f234(x75521),f4(x75521)),x75522)) % 174.01/173.90 [7553]~P119(x75531)+~P1(f777(f777(f234(x75531),x75532),f4(x75531)))+P1(f777(f777(f234(x75531),f777(f777(f85(x75531),x75532),x75533)),f4(x75531)))+~P1(f777(f777(f234(x75531),f4(x75531)),x75533)) % 174.01/173.90 [7555]~P128(x75551)+~P1(f777(f777(f234(x75551),x75553),f4(x75551)))+P1(f777(f777(f234(x75551),f777(f777(f85(x75551),x75552),x75553)),f4(x75551)))+~P1(f777(f777(f234(x75551),f4(x75551)),x75552)) % 174.01/173.90 [7557]~P128(x75571)+~P1(f777(f777(f234(x75571),x75572),f4(x75571)))+P1(f777(f777(f234(x75571),f777(f777(f85(x75571),x75572),x75573)),f4(x75571)))+~P1(f777(f777(f234(x75571),f4(x75571)),x75573)) % 174.01/173.90 [7558]~P62(x75581)+~P1(f777(f777(f234(x75581),x75583),f4(x75581)))+P1(f777(f777(f234(x75581),f777(f777(f285(x75581),x75582),x75583)),f4(x75581)))+~P1(f777(f777(f234(x75581),f4(x75581)),x75582)) % 174.01/173.90 [7559]~P62(x75591)+~P1(f777(f777(f234(x75591),x75592),f4(x75591)))+P1(f777(f777(f234(x75591),f777(f777(f285(x75591),x75592),x75593)),f4(x75591)))+~P1(f777(f777(f234(x75591),f4(x75591)),x75593)) % 174.01/173.90 [7560]~P63(x75601)+~P1(f777(f777(f235(x75601),x75603),f4(x75601)))+P1(f777(f777(f234(x75601),f777(f777(f285(x75601),x75602),x75603)),f4(x75601)))+~P1(f777(f777(f234(x75601),f4(x75601)),x75602)) % 174.01/173.90 [7561]~P63(x75611)+~P1(f777(f777(f234(x75611),x75612),f4(x75611)))+P1(f777(f777(f234(x75611),f777(f777(f285(x75611),x75612),x75613)),f4(x75611)))+~P1(f777(f777(f235(x75611),f4(x75611)),x75613)) % 174.01/173.90 [7577]P140(x75771,x75772,x75773)+~P1(f777(x75771,x75773))+P1(f777(f777(f235(a3),x75772),f782(x75773,x75772,x75771)))+P1(f777(f777(f235(a3),f784(x75773,x75772,x75771)),x75772)) % 174.01/173.90 [7590]P141(x75901,x75902,x75903)+P1(f777(f777(f235(a3),x75902),f786(x75903,x75902,x75901)))+~P1(f777(x75901,f4(a3)))+P1(f777(f777(f235(a3),f787(x75903,x75902,x75901)),x75902)) % 174.01/173.90 [7642]P140(x76422,x76421,x76423)+E(x76421,f4(a3))+~P1(f777(x76422,f782(x76423,x76421,x76422)))+P1(f777(f777(f235(a3),f784(x76423,x76421,x76422)),x76421)) % 174.01/173.90 [7643]P141(x76432,x76431,x76433)+E(x76431,f4(a3))+~P1(f777(x76432,f789(x76433,x76431,x76432)))+P1(f777(f777(f235(a3),f787(x76433,x76431,x76432)),x76431)) % 174.01/173.90 [7652]P140(x76523,x76521,x76522)+~P1(f777(x76523,x76522))+E(f777(f777(f84(a3),f777(f777(f85(a3),x76521),f785(x76522,x76521,x76523))),f782(x76522,x76521,x76523)),x76522)+P1(f777(f777(f235(a3),f4(a3)),x76521)) % 174.01/173.90 [7670]P141(x76703,x76701,x76702)+E(f777(f777(f84(a3),f777(f777(f85(a3),x76701),f789(x76702,x76701,x76703))),f786(x76702,x76701,x76703)),x76702)+~P1(f777(x76703,f4(a3)))+P1(f777(f777(f235(a3),f4(a3)),x76701)) % 174.01/173.90 [7694]~P1(f777(x76941,x76943))+~P1(f777(f65(x76942),x76943))+P1(f777(f777(f336(x76942),f485(x76941,x76943,x76942)),f484(x76941,x76943,x76942)))+P1(f777(x76941,f182(f858(x76942,a845)))) % 174.01/173.90 [7704]P140(x77041,x77042,x77043)+~P1(f777(x77041,x77043))+~P1(f777(x77041,f782(x77043,x77042,x77041)))+P1(f777(f777(f235(a3),f784(x77043,x77042,x77041)),x77042)) % 174.01/173.90 [7710]P141(x77101,x77102,x77103)+~P1(f777(x77101,f789(x77103,x77102,x77101)))+~P1(f777(x77101,f4(a3)))+P1(f777(f777(f235(a3),f787(x77103,x77102,x77101)),x77102)) % 174.01/173.90 [7818]~P62(x78181)+~P1(f777(f777(f235(x78181),f777(f777(f285(x78181),x78183),x78182)),f4(x78181)))+P1(f777(f777(f235(x78181),x78182),f4(x78181)))+P1(f777(f777(f235(x78181),f4(x78181)),x78182)) % 174.01/173.90 [7819]~P62(x78191)+~P1(f777(f777(f235(x78191),f777(f777(f285(x78191),x78192),x78193)),f4(x78191)))+P1(f777(f777(f235(x78191),x78192),f4(x78191)))+P1(f777(f777(f235(x78191),f4(x78191)),x78192)) % 174.01/173.90 [7820]~P119(x78201)+~P1(f777(f777(f234(x78201),f777(f777(f85(x78201),x78203),x78202)),f4(x78201)))+P1(f777(f777(f234(x78201),x78202),f4(x78201)))+P1(f777(f777(f234(x78201),f4(x78201)),x78202)) % 174.01/173.90 [7821]~P119(x78211)+~P1(f777(f777(f234(x78211),f777(f777(f85(x78211),x78212),x78213)),f4(x78211)))+P1(f777(f777(f234(x78211),x78212),f4(x78211)))+P1(f777(f777(f234(x78211),f4(x78211)),x78212)) % 174.01/173.90 [7822]~P62(x78221)+~P1(f777(f777(f234(x78221),f777(f777(f285(x78221),x78223),x78222)),f4(x78221)))+P1(f777(f777(f234(x78221),x78222),f4(x78221)))+P1(f777(f777(f234(x78221),f4(x78221)),x78222)) % 174.01/173.90 [7823]~P62(x78231)+~P1(f777(f777(f234(x78231),f777(f777(f285(x78231),x78232),x78233)),f4(x78231)))+P1(f777(f777(f234(x78231),x78232),f4(x78231)))+P1(f777(f777(f234(x78231),f4(x78231)),x78232)) % 174.01/173.90 [7849]~P62(x78491)+~P1(f777(f777(f235(x78491),f777(f777(f285(x78491),x78492),x78493)),f4(x78491)))+P1(f777(f777(f235(x78491),f4(x78491)),x78492))+P1(f777(f777(f235(x78491),f4(x78491)),x78493)) % 174.01/173.90 [7850]~P119(x78501)+~P1(f777(f777(f234(x78501),f777(f777(f85(x78501),x78502),x78503)),f4(x78501)))+P1(f777(f777(f234(x78501),f4(x78501)),x78502))+P1(f777(f777(f234(x78501),f4(x78501)),x78503)) % 174.01/173.90 [7851]~P62(x78511)+~P1(f777(f777(f234(x78511),f777(f777(f285(x78511),x78512),x78513)),f4(x78511)))+P1(f777(f777(f234(x78511),f4(x78511)),x78512))+P1(f777(f777(f234(x78511),f4(x78511)),x78513)) % 174.01/173.90 [7870]P140(x78702,x78701,x78703)+E(x78701,f4(a3))+P1(f777(f777(f234(a3),f782(x78703,x78701,x78702)),f4(a3)))+P1(f777(f777(f235(a3),f784(x78703,x78701,x78702)),x78701)) % 174.01/173.90 [7871]P141(x78712,x78711,x78713)+E(x78711,f4(a3))+P1(f777(f777(f234(a3),f786(x78713,x78711,x78712)),f4(a3)))+P1(f777(f777(f235(a3),f787(x78713,x78711,x78712)),x78711)) % 174.01/173.90 [7877]~P117(x78771)+~P1(f777(f777(f235(x78771),x78772),f82(x78771)))+P1(f777(f777(f235(x78771),f777(f777(f244(x78771),x78772),f777(a116,x78773))),f82(x78771)))+~P1(f777(f777(f235(x78771),f4(x78771)),x78772)) % 174.01/173.90 [7931]~P100(x79311)+~E(x79313,f117(x79311))+~P18(x79311,f777(f144(x79311),x79313))+E(f777(f134(x79311,x79311,f777(f11(x79311,x79311,x79311),f181(x79311)),x79312),f777(f144(x79311),x79313)),x79312) % 174.01/173.90 [7933]P140(x79331,x79332,x79333)+~P1(f777(x79331,x79333))+P1(f777(f777(f234(a3),f782(x79333,x79332,x79331)),f4(a3)))+P1(f777(f777(f235(a3),f784(x79333,x79332,x79331)),x79332)) % 174.01/173.90 [7945]P141(x79451,x79452,x79453)+~P1(f777(x79451,f4(a3)))+P1(f777(f777(f234(a3),f786(x79453,x79452,x79451)),f4(a3)))+P1(f777(f777(f235(a3),f787(x79453,x79452,x79451)),x79452)) % 174.01/173.90 [8158]P140(x81583,x81581,x81582)+E(x81581,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x81581),f785(x81582,x81581,x81583))),f782(x81582,x81581,x81583)),x81582)+P1(f777(f777(f235(a3),f784(x81582,x81581,x81583)),x81581)) % 174.01/173.90 [8159]P141(x81593,x81591,x81592)+E(x81591,f4(a3))+E(f777(f777(f84(a3),f777(f777(f85(a3),x81591),f789(x81592,x81591,x81593))),f786(x81592,x81591,x81593)),x81592)+P1(f777(f777(f235(a3),f787(x81592,x81591,x81593)),x81591)) % 174.01/173.90 [8194]P140(x81943,x81941,x81942)+~P1(f777(x81943,x81942))+E(f777(f777(f84(a3),f777(f777(f85(a3),x81941),f785(x81942,x81941,x81943))),f782(x81942,x81941,x81943)),x81942)+P1(f777(f777(f235(a3),f784(x81942,x81941,x81943)),x81941)) % 174.01/173.90 [8195]~P66(x81951)+~P70(x81951)+~P38(x81953)+E(f777(f777(f10(a851,x81951),f777(f777(f12(a3,x81951,a851),x81952),f104(a3))),f777(f305(a3,a851,a109),x81953)),f777(f777(f10(a3,x81951),x81952),x81953)) % 174.01/173.90 [8196]~P66(x81961)+~P70(x81961)+~P38(x81963)+E(f777(f777(f13(a851,x81961),f777(f777(f12(a3,x81961,a851),x81962),f104(a3))),f777(f305(a3,a851,a109),x81963)),f777(f777(f13(a3,x81961),x81962),x81963)) % 174.01/173.90 [8204]P141(x82043,x82041,x82042)+E(f777(f777(f84(a3),f777(f777(f85(a3),x82041),f789(x82042,x82041,x82043))),f786(x82042,x82041,x82043)),x82042)+~P1(f777(x82043,f4(a3)))+P1(f777(f777(f235(a3),f787(x82042,x82041,x82043)),x82041)) % 174.01/173.90 [8222]~E(x82222,f4(a851))+~E(f777(f242(a851,a851),x82223),f4(a851))+~E(x82221,f777(f777(f84(a851),f777(f777(f85(a851),f777(f242(a851,a851),x82223)),x82222)),f777(f252(a851,a851),x82223)))+P1(f777(f57(x82221,x82222),x82223)) % 174.01/173.90 [9070]P1(f777(f777(f234(a3),x90701),f4(a3)))+~P1(f777(f777(f235(a3),f777(f777(f84(a3),f777(f777(f85(a3),x90702),x90701)),x90703)),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x90702))+~P1(f777(f777(f234(a3),f4(a3)),x90703)) % 174.01/173.90 [5677]~P93(x56772)+E(x56771,f182(f858(x56772,a845)))+~P1(f777(f65(x56772),x56771))+E(f17(x56772,f777(f777(f304(x56772),x56773),x56771)),f777(f777(f105(x56772),x56773),f17(x56772,x56771))) % 174.01/173.90 [5678]~P100(x56782)+E(x56781,f182(f858(x56782,a845)))+~P1(f777(f65(x56782),x56781))+E(f18(x56782,f777(f777(f304(x56782),x56783),x56781)),f777(f777(f181(x56782),x56783),f18(x56782,x56781))) % 174.01/173.90 [5679]~P100(x56792)+E(x56791,f182(f858(x56792,a845)))+~P1(f777(f65(x56792),x56791))+E(f19(x56792,f777(f777(f304(x56792),x56793),x56791)),f777(f777(f238(x56792),x56793),f19(x56792,x56791))) % 174.01/173.90 [5680]~P93(x56802)+E(x56801,f182(f858(x56802,a845)))+~P1(f777(f65(x56802),x56801))+E(f14(x56802,f777(f777(f304(x56802),x56803),x56801)),f777(f777(f106(x56802),x56803),f14(x56802,x56801))) % 174.01/173.90 [5999]~P119(x59991)+~E(x59993,f4(x59991))+~E(x59992,f4(x59991))+E(f777(f777(f84(x59991),f777(f777(f85(x59991),x59992),x59992)),f777(f777(f85(x59991),x59993),x59993)),f4(x59991)) % 174.01/173.90 [6074]~P91(x60742)+E(x60741,f182(f858(x60742,a845)))+~P1(f777(f65(x60742),x60741))+E(f777(f67(x60742,f85(x60742)),f777(f777(f304(x60742),x60743),x60741)),f777(f777(f85(x60742),x60743),f777(f67(x60742,f85(x60742)),x60741))) % 174.01/173.90 [6200]~P100(x62002)+E(x62001,f182(f858(x62002,a845)))+~P1(f777(f65(x62002),x62001))+E(f15(x62002,f181(x62002),f777(f777(f304(x62002),x62003),x62001)),f777(f777(f181(x62002),x62003),f15(x62002,f181(x62002),x62001))) % 174.01/173.90 [6201]~P100(x62012)+E(x62011,f182(f858(x62012,a845)))+~P1(f777(f65(x62012),x62011))+E(f16(x62012,f238(x62012),f777(f777(f304(x62012),x62013),x62011)),f777(f777(f238(x62012),x62013),f16(x62012,f238(x62012),x62011))) % 174.01/173.90 [6731]~P64(x67311)+~P1(f777(f65(x67311),x67313))+E(f777(f67(x67311,f85(x67311)),f777(f777(f304(x67311),x67312),x67313)),f777(f777(f68(x67311,x67311,f85(x67311)),x67312),x67313))+P1(f777(f777(f336(x67311),x67312),x67313)) % 174.01/173.90 [6818]~E(f777(f777(f84(a3),x68182),f777(f777(f85(a3),x68183),x68181)),x68183)+~P1(f777(f777(f235(a3),f4(a3)),x68183))+P1(f777(f777(f234(a3),f82(a3)),x68181))+~P1(f777(f777(f235(a3),x68182),x68183)) % 174.01/173.90 [6849]~E(f777(f777(f84(a3),x68492),f777(f777(f85(a3),x68493),x68491)),x68493)+P1(f777(f777(f234(a3),x68491),f82(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x68493))+~P1(f777(f777(f234(a3),f4(a3)),x68492)) % 174.01/173.90 [6867]E(x68671,f4(a851))+~P1(f777(f57(x68673,x68671),x68672))+~P1(f777(f777(f235(a851),f4(a851)),x68671))+P1(f777(f777(f235(a851),f777(f252(a851,a851),x68672)),x68671)) % 174.01/173.90 [6896]~P132(x68961)+~P1(f777(f777(f234(x68961),x68962),f4(x68961)))+~P1(f777(f777(f234(x68961),x68963),f4(x68961)))+E(f777(f777(f85(x68961),f777(f79(x68961),x68962)),f777(f79(x68961),x68963)),f777(f79(x68961),f777(f777(f85(x68961),x68962),x68963))) % 174.01/173.90 [6948]~P132(x69481)+~P1(f777(f777(f234(x69481),x69482),f4(x69481)))+E(f777(f777(f85(x69481),f777(f79(x69481),x69482)),f777(f79(x69481),x69483)),f777(f79(x69481),f777(f777(f85(x69481),x69482),x69483)))+~P1(f777(f777(f234(x69481),f4(x69481)),x69483)) % 174.01/173.90 [6949]~P132(x69491)+~P1(f777(f777(f234(x69491),x69493),f4(x69491)))+E(f777(f777(f85(x69491),f777(f79(x69491),x69492)),f777(f79(x69491),x69493)),f777(f79(x69491),f777(f777(f85(x69491),x69492),x69493)))+~P1(f777(f777(f234(x69491),f4(x69491)),x69492)) % 174.01/173.90 [6999]~P132(x69991)+E(f777(f777(f85(x69991),f777(f79(x69991),x69992)),f777(f79(x69991),x69993)),f777(f79(x69991),f777(f777(f85(x69991),x69992),x69993)))+~P1(f777(f777(f234(x69991),f4(x69991)),x69992))+~P1(f777(f777(f234(x69991),f4(x69991)),x69993)) % 174.01/173.90 [7017]~P119(x70171)+~P1(f777(f777(f235(x70171),x70173),f4(x70171)))+~P1(f777(f777(f235(x70171),x70172),f4(x70171)))+P1(f777(f777(f235(x70171),f4(x70171)),f777(f777(f85(x70171),x70172),x70173))) % 174.01/173.90 [7018]~P62(x70181)+~P1(f777(f777(f235(x70181),x70183),f4(x70181)))+~P1(f777(f777(f235(x70181),x70182),f4(x70181)))+P1(f777(f777(f235(x70181),f4(x70181)),f777(f777(f285(x70181),x70182),x70183))) % 174.01/173.90 [7019]~P63(x70191)+~P1(f777(f777(f235(x70191),x70193),f4(x70191)))+~P1(f777(f777(f235(x70191),x70192),f4(x70191)))+P1(f777(f777(f235(x70191),f4(x70191)),f777(f777(f285(x70191),x70192),x70193))) % 174.01/173.90 [7020]~P119(x70201)+~P1(f777(f777(f234(x70201),x70203),f4(x70201)))+~P1(f777(f777(f234(x70201),x70202),f4(x70201)))+P1(f777(f777(f234(x70201),f4(x70201)),f777(f777(f85(x70201),x70202),x70203))) % 174.01/173.90 [7022]~P129(x70221)+~P1(f777(f777(f234(x70221),x70223),f4(x70221)))+~P1(f777(f777(f234(x70221),x70222),f4(x70221)))+P1(f777(f777(f234(x70221),f4(x70221)),f777(f777(f85(x70221),x70222),x70223))) % 174.01/173.90 [7023]~P62(x70231)+~P1(f777(f777(f234(x70231),x70233),f4(x70231)))+~P1(f777(f777(f234(x70231),x70232),f4(x70231)))+P1(f777(f777(f234(x70231),f4(x70231)),f777(f777(f285(x70231),x70232),x70233))) % 174.01/173.90 [7024]~P63(x70241)+~P1(f777(f777(f235(x70241),x70243),f4(x70241)))+~P1(f777(f777(f234(x70241),x70242),f4(x70241)))+P1(f777(f777(f234(x70241),f4(x70241)),f777(f777(f285(x70241),x70242),x70243))) % 174.01/173.90 [7025]~P117(x70251)+~P1(f777(f777(f235(a851),f4(a851)),x70253))+~P1(f777(f777(f235(x70251),f82(x70251)),x70252))+P1(f777(f777(f235(x70251),f82(x70251)),f777(f777(f244(x70251),x70252),x70253))) % 174.01/173.90 [7122]~P81(x71221)+~P1(f777(f777(f235(x71221),f4(x71221)),x71223))+~P1(f777(f777(f235(x71221),f4(x71221)),x71222))+P1(f777(f777(f235(x71221),f4(x71221)),f777(f777(f84(x71221),x71222),x71223))) % 174.01/173.90 [7125]~P123(x71251)+~P1(f777(f777(f235(x71251),f4(x71251)),x71253))+~P1(f777(f777(f235(x71251),f4(x71251)),x71252))+P1(f777(f777(f235(x71251),f4(x71251)),f777(f777(f85(x71251),x71252),x71253))) % 174.01/173.90 [7126]~P62(x71261)+~P1(f777(f777(f235(x71261),f4(x71261)),x71263))+~P1(f777(f777(f235(x71261),f4(x71261)),x71262))+P1(f777(f777(f235(x71261),f4(x71261)),f777(f777(f285(x71261),x71262),x71263))) % 174.01/173.90 [7127]~P63(x71271)+~P1(f777(f777(f235(x71271),f4(x71271)),x71273))+~P1(f777(f777(f235(x71271),f4(x71271)),x71272))+P1(f777(f777(f235(x71271),f4(x71271)),f777(f777(f285(x71271),x71272),x71273))) % 174.01/173.90 [7128]~P117(x71281)+~P1(f777(f777(f235(x71281),f82(x71281)),x71283))+~P1(f777(f777(f235(x71281),f82(x71281)),x71282))+P1(f777(f777(f235(x71281),f82(x71281)),f777(f777(f85(x71281),x71282),x71283))) % 174.01/173.90 [7130]~P119(x71301)+~P1(f777(f777(f234(x71301),f4(x71301)),x71303))+~P1(f777(f777(f234(x71301),f4(x71301)),x71302))+P1(f777(f777(f234(x71301),f4(x71301)),f777(f777(f85(x71301),x71302),x71303))) % 174.01/173.90 [7131]~P128(x71311)+~P1(f777(f777(f234(x71311),f4(x71311)),x71313))+~P1(f777(f777(f234(x71311),f4(x71311)),x71312))+P1(f777(f777(f234(x71311),f4(x71311)),f777(f777(f85(x71311),x71312),x71313))) % 174.01/173.90 [7132]~P129(x71321)+~P1(f777(f777(f234(x71321),f4(x71321)),x71323))+~P1(f777(f777(f234(x71321),f4(x71321)),x71322))+P1(f777(f777(f234(x71321),f4(x71321)),f777(f777(f85(x71321),x71322),x71323))) % 174.01/173.90 [7133]~P62(x71331)+~P1(f777(f777(f234(x71331),f4(x71331)),x71333))+~P1(f777(f777(f234(x71331),f4(x71331)),x71332))+P1(f777(f777(f234(x71331),f4(x71331)),f777(f777(f285(x71331),x71332),x71333))) % 174.01/173.90 [7134]~P63(x71341)+~P1(f777(f777(f235(x71341),f4(x71341)),x71343))+~P1(f777(f777(f234(x71341),f4(x71341)),x71342))+P1(f777(f777(f234(x71341),f4(x71341)),f777(f777(f285(x71341),x71342),x71343))) % 174.01/173.90 [7212]~P93(x72121)+~P1(f777(f65(x72121),x72123))+E(f17(x72121,f777(f777(f304(x72121),x72122),x72123)),x72122)+~E(f777(f777(f5(f858(x72121,a845)),x72123),f777(f777(f304(x72121),x72122),f182(f858(x72121,a845)))),f182(f858(x72121,a845))) % 174.01/173.90 [7213]~P100(x72131)+~P1(f777(f65(x72131),x72133))+E(f18(x72131,f777(f777(f304(x72131),x72132),x72133)),x72132)+~E(f777(f777(f5(f858(x72131,a845)),x72133),f777(f777(f304(x72131),x72132),f182(f858(x72131,a845)))),f182(f858(x72131,a845))) % 174.01/173.90 [7214]~P100(x72141)+~P1(f777(f65(x72141),x72143))+E(f19(x72141,f777(f777(f304(x72141),x72142),x72143)),x72142)+~E(f777(f777(f5(f858(x72141,a845)),x72143),f777(f777(f304(x72141),x72142),f182(f858(x72141,a845)))),f182(f858(x72141,a845))) % 174.01/173.90 [7215]~P93(x72151)+~P1(f777(f65(x72151),x72153))+E(f14(x72151,f777(f777(f304(x72151),x72152),x72153)),x72152)+~E(f777(f777(f5(f858(x72151,a845)),x72153),f777(f777(f304(x72151),x72152),f182(f858(x72151,a845)))),f182(f858(x72151,a845))) % 174.01/173.90 [7216]~P62(x72161)+P1(f777(f777(f235(x72161),x72162),f4(x72161)))+P1(f777(f777(f235(x72161),f4(x72161)),x72163))+~P1(f777(f777(f235(x72161),f4(x72161)),f777(f777(f285(x72161),x72163),x72162))) % 174.01/173.90 [7217]~P62(x72171)+P1(f777(f777(f235(x72171),x72172),f4(x72171)))+P1(f777(f777(f235(x72171),f4(x72171)),x72173))+~P1(f777(f777(f235(x72171),f4(x72171)),f777(f777(f285(x72171),x72172),x72173))) % 174.01/173.90 [7218]~P62(x72181)+P1(f777(f777(f235(x72181),x72182),f4(x72181)))+P1(f777(f777(f235(x72181),f4(x72181)),x72182))+~P1(f777(f777(f235(x72181),f4(x72181)),f777(f777(f285(x72181),x72183),x72182))) % 174.01/173.90 [7219]~P62(x72191)+P1(f777(f777(f235(x72191),x72192),f4(x72191)))+P1(f777(f777(f235(x72191),f4(x72191)),x72192))+~P1(f777(f777(f235(x72191),f4(x72191)),f777(f777(f285(x72191),x72192),x72193))) % 174.01/173.90 [7220]~P119(x72201)+P1(f777(f777(f234(x72201),x72202),f4(x72201)))+P1(f777(f777(f234(x72201),f4(x72201)),x72203))+~P1(f777(f777(f234(x72201),f4(x72201)),f777(f777(f85(x72201),x72203),x72202))) % 174.01/173.90 [7221]~P119(x72211)+P1(f777(f777(f234(x72211),x72212),f4(x72211)))+P1(f777(f777(f234(x72211),f4(x72211)),x72213))+~P1(f777(f777(f234(x72211),f4(x72211)),f777(f777(f85(x72211),x72212),x72213))) % 174.01/173.90 [7222]~P62(x72221)+P1(f777(f777(f234(x72221),x72222),f4(x72221)))+P1(f777(f777(f234(x72221),f4(x72221)),x72223))+~P1(f777(f777(f234(x72221),f4(x72221)),f777(f777(f285(x72221),x72223),x72222))) % 174.01/173.90 [7223]~P62(x72231)+P1(f777(f777(f234(x72231),x72232),f4(x72231)))+P1(f777(f777(f234(x72231),f4(x72231)),x72233))+~P1(f777(f777(f234(x72231),f4(x72231)),f777(f777(f285(x72231),x72232),x72233))) % 174.01/173.90 [7224]~P119(x72241)+P1(f777(f777(f234(x72241),x72242),f4(x72241)))+P1(f777(f777(f234(x72241),f4(x72241)),x72242))+~P1(f777(f777(f234(x72241),f4(x72241)),f777(f777(f85(x72241),x72243),x72242))) % 174.01/173.90 [7225]~P119(x72251)+P1(f777(f777(f234(x72251),x72252),f4(x72251)))+P1(f777(f777(f234(x72251),f4(x72251)),x72252))+~P1(f777(f777(f234(x72251),f4(x72251)),f777(f777(f85(x72251),x72252),x72253))) % 174.01/173.90 [7226]~P62(x72261)+P1(f777(f777(f234(x72261),x72262),f4(x72261)))+P1(f777(f777(f234(x72261),f4(x72261)),x72262))+~P1(f777(f777(f234(x72261),f4(x72261)),f777(f777(f285(x72261),x72263),x72262))) % 174.01/173.90 [7227]~P62(x72271)+P1(f777(f777(f234(x72271),x72272),f4(x72271)))+P1(f777(f777(f234(x72271),f4(x72271)),x72272))+~P1(f777(f777(f234(x72271),f4(x72271)),f777(f777(f285(x72271),x72272),x72273))) % 174.01/173.90 [7312]~P1(f777(f777(f281(a851),x73121),x73123))+P1(f777(f777(f281(a851),x73121),x73122))+~P1(f777(f777(f234(a851),x73122),x73123))+~P1(f777(f777(f281(a851),x73121),f777(f777(f5(a851),x73123),x73122))) % 174.01/173.90 [7313]~P1(f777(f777(f281(a851),x73131),x73133))+P1(f777(f777(f281(a851),x73131),x73132))+~P1(f777(f777(f234(a851),x73133),x73132))+~P1(f777(f777(f281(a851),x73131),f777(f777(f5(a851),x73132),x73133))) % 174.01/173.90 [7328]~E(f777(f777(f106(f858(x73281,a845)),f777(f160(x73281),x73282)),f777(f160(x73281),x73283)),f182(f858(x73281,a845)))+~P1(f777(f129(x73281),x73283))+~P1(f777(f129(x73281),x73282))+P1(f777(f129(x73281),f777(f777(f127(x73281),x73282),x73283))) % 174.01/173.90 [7329]~P100(x73291)+~P1(f777(f65(x73291),x73293))+E(f15(x73291,f181(x73291),f777(f777(f304(x73291),x73292),x73293)),x73292)+~E(f777(f777(f5(f858(x73291,a845)),x73293),f777(f777(f304(x73291),x73292),f182(f858(x73291,a845)))),f182(f858(x73291,a845))) % 174.01/173.90 [7330]~P100(x73301)+~P1(f777(f65(x73301),x73303))+E(f16(x73301,f238(x73301),f777(f777(f304(x73301),x73302),x73303)),x73302)+~E(f777(f777(f5(f858(x73301,a845)),x73303),f777(f777(f304(x73301),x73302),f182(f858(x73301,a845)))),f182(f858(x73301,a845))) % 174.01/173.90 [7348]~P110(x73481)+~P1(f777(f777(f235(x73481),x73482),x73483))+~P1(f777(f777(f235(x73481),f777(f83(x73481),x73482)),x73483))+P1(f777(f777(f235(x73481),f777(f79(x73481),x73482)),x73483)) % 174.01/173.90 [7350]~P79(x73501)+~P1(f777(f777(f234(x73501),x73502),x73503))+~P1(f777(f777(f234(x73501),f777(f83(x73501),x73502)),x73503))+P1(f777(f777(f234(x73501),f777(f79(x73501),x73502)),x73503)) % 174.01/173.90 [7419]~P123(x74191)+P1(f777(f777(f235(x74191),f4(x74191)),x74192))+~P1(f777(f777(f235(x74191),f4(x74191)),x74193))+~P1(f777(f777(f235(x74191),f4(x74191)),f777(f777(f85(x74191),x74193),x74192))) % 174.01/173.90 [7420]~P123(x74201)+P1(f777(f777(f235(x74201),f4(x74201)),x74202))+~P1(f777(f777(f235(x74201),f4(x74201)),x74203))+~P1(f777(f777(f235(x74201),f4(x74201)),f777(f777(f85(x74201),x74202),x74203))) % 174.01/173.90 [7727]E(x77271,x77272)+~P1(f777(f65(x77273),x77271))+~P1(f777(f777(f234(a851),f777(f44(x77273),x77271)),f777(f44(x77273),x77272)))+~P1(f777(f777(f234(f858(x77273,a845)),x77272),x77271)) % 174.01/173.90 [7874]~P1(f777(f777(f235(a3),x78741),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x78742))+~P1(f777(f777(f234(a3),x78742),x78743))+P1(f777(f777(f234(a3),f777(f777(f45(a3),x78741),x78742)),f777(f777(f45(a3),x78741),x78743))) % 174.01/173.90 [7885]~P1(f777(f777(f235(a3),f4(a3)),x78853))+~P1(f777(f777(f234(a3),f4(a3)),x78851))+~P1(f777(f777(f234(a3),x78853),x78852))+P1(f777(f777(f234(a3),f777(f777(f45(a3),x78851),x78852)),f777(f777(f45(a3),x78851),x78853))) % 174.01/173.90 [8020]E(f777(x80201,f815(x80202,x80201,x80203)),x80202)+~P1(f777(f777(f234(a3),x80202),f777(x80201,x80203)))+P1(f777(f777(f235(a851),f816(x80202,x80201,x80203)),x80203))+~P1(f777(f777(f234(a3),f777(x80201,f4(a851))),x80202)) % 174.01/173.90 [8021]E(f777(x80211,f817(x80212,x80211,x80213)),x80212)+~P1(f777(f777(f234(a3),x80212),f777(x80211,x80213)))+P1(f777(f777(f235(a851),f818(x80212,x80211,x80213)),x80213))+~P1(f777(f777(f234(a3),f777(x80211,f4(a851))),x80212)) % 174.01/173.90 [8118]~P1(f777(f65(x81181),x81183))+~P1(f777(f777(f235(a851),f777(f44(x81181),x81182)),f777(f44(x81181),x81183)))+~P1(f777(f777(f234(f858(x81181,a845)),x81182),x81183))+P1(f777(f777(f235(f858(x81181,a845)),x81182),x81183)) % 174.01/173.90 [8147]E(f777(f777(f5(a3),f420(x81473,x81471,x81472)),f421(x81473,x81471,x81472)),x81471)+E(f777(f777(f84(a3),x81471),x81472),x81471)+~P1(f777(f777(f235(a3),f4(a3)),x81472))+~P1(f777(f777(f336(a3),f777(f777(f84(a3),x81471),f82(a3))),x81473)) % 174.01/173.90 [8148]E(f777(f777(f84(a3),f422(x81483,x81481,x81482)),f423(x81483,x81481,x81482)),x81481)+E(f777(f777(f5(a3),x81481),x81482),x81481)+~P1(f777(f777(f235(a3),f4(a3)),x81482))+~P1(f777(f777(f336(a3),f777(f777(f5(a3),x81481),f82(a3))),x81483)) % 174.01/173.90 [8200]~P1(f777(f777(f234(a851),x82003),x82001))+P1(f777(f777(f235(a851),x82001),x82002))+~P1(f777(f777(f234(a851),x82003),x82002))+~P1(f777(f777(f235(a851),f777(f777(f5(a851),x82001),x82003)),f777(f777(f5(a851),x82002),x82003))) % 174.01/173.90 [8201]~P1(f777(f777(f234(a851),x82013),x82011))+P1(f777(f777(f234(a851),x82011),x82012))+~P1(f777(f777(f234(a851),x82013),x82012))+~P1(f777(f777(f234(a851),f777(f777(f5(a851),x82011),x82013)),f777(f777(f5(a851),x82012),x82013))) % 174.01/173.90 [8215]~P100(x82152)+E(x82151,f117(x82152))+~P18(x82152,f777(f144(x82152),x82151))+E(f777(f134(x82152,x82152,f777(f11(x82152,x82152,x82152),f181(x82152)),x82153),f777(f144(x82152),x82151)),f777(f777(f181(x82152),f777(f777(f155(x82152),x82151),f4(a851))),x82153)) % 174.01/173.90 [8280]E(f777(f777(f84(a3),x82801),x82802),x82801)+~P1(f777(f777(f235(a3),f4(a3)),x82802))+P1(f777(f777(f336(a3),f420(x82803,x82801,x82802)),x82803))+~P1(f777(f777(f336(a3),f777(f777(f84(a3),x82801),f82(a3))),x82803)) % 174.01/173.90 [8281]E(f777(f777(f5(a3),x82811),x82812),x82811)+~P1(f777(f777(f235(a3),f4(a3)),x82812))+P1(f777(f777(f336(a3),f422(x82813,x82811,x82812)),x82813))+~P1(f777(f777(f336(a3),f777(f777(f5(a3),x82811),f82(a3))),x82813)) % 174.01/173.90 [8360]~P1(f777(f777(f234(a3),x83601),f777(x83602,x83603)))+P1(f777(f777(f234(a851),f815(x83601,x83602,x83603)),x83603))+P1(f777(f777(f235(a851),f816(x83601,x83602,x83603)),x83603))+~P1(f777(f777(f234(a3),f777(x83602,f4(a851))),x83601)) % 174.01/173.90 [8361]~P1(f777(f777(f234(a3),x83611),f777(x83612,x83613)))+P1(f777(f777(f234(a851),f817(x83611,x83612,x83613)),x83613))+P1(f777(f777(f235(a851),f818(x83611,x83612,x83613)),x83613))+~P1(f777(f777(f234(a3),f777(x83612,f4(a851))),x83611)) % 174.01/173.90 [8436]E(f777(f777(f84(a3),x84361),x84362),x84361)+~P1(f777(f777(f235(a3),f4(a3)),x84362))+P1(f777(f777(f336(a3),f421(x84363,x84361,x84362)),f297(a3,f82(a3),x84362)))+~P1(f777(f777(f336(a3),f777(f777(f84(a3),x84361),f82(a3))),x84363)) % 174.01/173.90 [8437]E(f777(f777(f5(a3),x84371),x84372),x84371)+~P1(f777(f777(f235(a3),f4(a3)),x84372))+P1(f777(f777(f336(a3),f423(x84373,x84371,x84372)),f297(a3,f82(a3),x84372)))+~P1(f777(f777(f336(a3),f777(f777(f5(a3),x84371),f82(a3))),x84373)) % 174.01/173.90 [8562]~P117(x85621)+~P1(f777(f777(f235(x85621),x85622),f82(x85621)))+~P1(f777(f777(f235(x85621),f4(x85621)),x85622))+P1(f777(f777(f235(x85621),f777(f777(f85(x85621),x85622),f777(f777(f244(x85621),x85622),x85623))),f777(f777(f244(x85621),x85622),x85623))) % 174.01/173.90 [8637]~P1(f777(x86371,x86372))+P1(f777(x86371,f4(a851)))+~P1(f777(f777(f235(a851),x86372),x86373))+~P1(f777(x86371,f54(a851,f777(a116,f811(x86372,x86371,x86373)),x86373))) % 174.01/173.90 [8767]E(f836(x87671,x87672,x87673),f4(a851))+P1(f777(f777(x87671,x87673),x87672))+P1(f777(f777(x87671,f836(x87671,x87672,x87673)),f54(a851,f834(x87671,x87672,x87673),f836(x87671,x87672,x87673))))+~P1(f777(f323(f857(a851,a851),a216),f777(f777(f243(a851,a851),x87673),x87672))) % 174.01/173.90 [8799]~P29(x87991,x87991,x87992,x87993)+E(f777(f305(x87991,x87991,x87992),x87993),x87993)+~P1(f777(f65(x87991),x87993))+~P1(f777(f777(f234(f858(x87991,a845)),f777(f305(x87991,x87991,x87992),x87993)),x87993)) % 174.01/173.90 [9019]P1(f777(f777(x90191,x90192),x90193))+~P1(f777(f777(f235(a3),f833(x90191,x90193,x90192)),f4(a3)))+P1(f777(f777(x90191,f777(f83(a3),f830(x90191,x90193,x90192))),f777(f83(a3),f833(x90191,x90193,x90192))))+~P1(f777(f323(f857(a3,a3),a218),f777(f777(f243(a3,a3),x90192),x90193))) % 174.01/173.90 [9177]P1(f777(f777(x91771,x91772),x91773))+P1(f777(f777(x91771,f777(f777(f84(a3),f396(x91771,x91773,x91772)),f82(a3))),f397(x91771,x91773,x91772)))+~P1(f777(f777(f234(a3),f396(x91771,x91773,x91772)),f397(x91771,x91773,x91772)))+~P1(f777(f323(f857(a3,a3),a170),f777(f777(f243(a3,a3),x91772),x91773))) % 174.01/173.90 [9850]E(f777(x98501,f815(x98502,x98501,x98503)),x98502)+~P1(f777(f777(f234(a3),x98502),f777(x98501,x98503)))+~P1(f777(f777(f234(a3),f777(f79(a3),f777(f777(f5(a3),f777(x98501,f777(f777(f84(a851),f816(x98502,x98501,x98503)),f82(a851)))),f777(x98501,f816(x98502,x98501,x98503))))),f82(a3)))+~P1(f777(f777(f234(a3),f777(x98501,f4(a851))),x98502)) % 174.01/173.90 [9851]E(f777(x98511,f817(x98512,x98511,x98513)),x98512)+~P1(f777(f777(f234(a3),x98512),f777(x98511,x98513)))+~P1(f777(f777(f234(a3),f777(f79(a3),f777(f777(f5(a3),f777(x98511,f777(f777(f84(a851),f818(x98512,x98511,x98513)),f82(a851)))),f777(x98511,f818(x98512,x98511,x98513))))),f82(a3)))+~P1(f777(f777(f234(a3),f777(x98511,f4(a851))),x98512)) % 174.01/173.90 [9855]~P1(f777(f777(f234(a3),x98551),f777(x98552,x98553)))+~P1(f777(f777(f234(a3),f777(f79(a3),f777(f777(f5(a3),f777(x98552,f777(f777(f84(a851),f816(x98551,x98552,x98553)),f82(a851)))),f777(x98552,f816(x98551,x98552,x98553))))),f82(a3)))+P1(f777(f777(f234(a851),f815(x98551,x98552,x98553)),x98553))+~P1(f777(f777(f234(a3),f777(x98552,f4(a851))),x98551)) % 174.01/173.90 [9856]~P1(f777(f777(f234(a3),x98561),f777(x98562,x98563)))+~P1(f777(f777(f234(a3),f777(f79(a3),f777(f777(f5(a3),f777(x98562,f777(f777(f84(a851),f818(x98561,x98562,x98563)),f82(a851)))),f777(x98562,f818(x98561,x98562,x98563))))),f82(a3)))+P1(f777(f777(f234(a851),f817(x98561,x98562,x98563)),x98563))+~P1(f777(f777(f234(a3),f777(x98562,f4(a851))),x98561)) % 174.01/173.90 [9910]E(x99101,x99102)+~E(f777(f134(f852(x99103),f852(x99103),f127(x99103),f117(x99103)),x99101),f777(f134(f852(x99103),f852(x99103),f127(x99103),f117(x99103)),x99102))+~E(f777(f183(f852(f852(x99103))),x99101),f777(f183(f852(f852(x99103))),x99102))+~P1(f777(f777(f253(f852(x99103),f852(x99103),a845),f777(f777(f11(f852(x99103),f858(f852(x99103),a851),f858(f852(x99103),a845)),f777(f777(f12(f858(a851,a845),f858(f858(f852(x99103),a851),f858(f852(x99103),a845)),f852(x99103)),f12(a851,a845,f852(x99103))),f777(f777(f12(a851,f858(a851,a845),f852(x99103)),a332),f183(f852(x99103))))),f183(f852(x99103)))),f773(x99101,x99102,x99103))) % 174.01/173.90 [9911]E(x99111,x99112)+~E(f777(f134(f852(x99113),f852(x99113),f127(x99113),f117(x99113)),x99111),f777(f134(f852(x99113),f852(x99113),f127(x99113),f117(x99113)),x99112))+~E(f777(f183(f852(f852(x99113))),x99111),f777(f183(f852(f852(x99113))),x99112))+~P1(f777(f777(f253(f852(x99113),f852(x99113),a845),f777(f777(f11(f852(x99113),f858(f852(x99113),a851),f858(f852(x99113),a845)),f777(f777(f12(f858(a851,a845),f858(f858(f852(x99113),a851),f858(f852(x99113),a845)),f852(x99113)),f12(a851,a845,f852(x99113))),f777(f777(f12(a851,f858(a851,a845),f852(x99113)),a332),f183(f852(x99113))))),f183(f852(x99113)))),f774(x99112,x99111,x99113))) % 174.01/173.90 [6720]~E(f82(a851),f4(a851))+~P1(f777(f65(x67201),x67203))+~P1(f777(f65(x67201),x67202))+E(f777(f777(f84(a851),f777(f44(x67201),x67202)),f777(f44(x67201),x67203)),f777(f44(x67201),f777(f777(f105(f858(x67201,a845)),x67202),x67203))) % 174.01/173.90 [7140]~P100(x71401)+~P1(f777(f65(x71401),x71402))+~P1(f777(f777(f336(x71401),x71403),x71402))+P1(f777(f777(f234(x71401),f777(f67(x71401,f238(x71401)),x71402)),x71403)) % 174.01/173.90 [7141]~P98(x71411)+~P1(f777(f65(x71411),x71412))+~P1(f777(f777(f336(x71411),x71413),x71412))+P1(f777(f777(f234(x71411),f777(f67(x71411,f106(x71411)),x71412)),x71413)) % 174.01/173.90 [7416]~P1(f777(f65(x74161),x74163))+~P1(f777(f65(x74161),x74162))+~E(f777(f777(f106(f858(x74161,a845)),x74162),x74163),f182(f858(x74161,a845)))+E(f777(f777(f84(a851),f777(f44(x74161),x74162)),f777(f44(x74161),x74163)),f777(f44(x74161),f777(f777(f105(f858(x74161,a845)),x74162),x74163))) % 174.01/173.90 [8205]~P36(x82051,x82053)+~P36(x82051,x82052)+~E(f777(f777(f106(f858(x82051,a845)),f777(f263(x82051,x82051),x82052)),f777(f261(x82051,x82051),x82053)),f182(f858(x82051,a845)))+P36(x82051,f777(f777(f105(f858(f857(x82051,x82051),a845)),x82052),x82053)) % 174.01/173.90 [8293]E(x82931,f777(f777(f45(a851),x82932),x82933))+~P1(f777(f777(f235(a851),f4(a851)),x82933))+~P1(f777(f777(f235(a851),x82932),f777(f777(f85(a851),x82933),f777(a116,x82931))))+~P1(f777(f777(f234(a851),f777(f777(f85(a851),x82933),x82931)),x82932)) % 174.01/173.90 [8434]~P1(f777(f65(x84341),x84342))+~P1(f777(f65(x84341),x84343))+E(f777(f777(f84(a851),f777(f44(x84341),x84342)),f777(f44(x84341),x84343)),f777(f44(x84341),f777(f777(f105(f858(x84341,a845)),x84342),x84343)))+P1(f777(f777(f336(x84341),f510(x84343,x84342,x84341)),f777(f777(f106(f858(x84341,a845)),x84342),x84343))) % 174.01/173.90 [8778]~P119(x87782)+~E(x87781,f4(x87782))+~E(x87783,f4(x87782))+~P1(f777(f777(f235(x87782),f4(x87782)),f777(f777(f84(x87782),f777(f777(f85(x87782),x87783),x87783)),f777(f777(f85(x87782),x87781),x87781)))) % 174.01/173.90 [9249]~P36(x92491,x92493)+~P36(x92491,x92492)+P36(x92491,f777(f777(f105(f858(f857(x92491,x92491),a845)),x92492),x92493))+~P1(f777(f777(f234(f858(f857(x92491,x92491),a845)),f777(f777(f283(x92491,x92491,x92491),x92492),x92493)),x92492)) % 174.01/173.90 [9375]~P1(f777(x93751,x93753))+~P1(f777(f65(x93752),x93753))+P1(f777(x93751,f182(f858(x93752,a845))))+~P1(f777(x93751,f777(f777(f5(f858(x93752,a845)),f484(x93751,x93753,x93752)),f777(f777(f304(x93752),f485(x93751,x93753,x93752)),f182(f858(x93752,a845)))))) % 174.01/173.90 [8591]~P1(f777(f777(f235(a3),f4(a3)),x85913))+P1(f777(f777(f234(a3),f4(a3)),x85911))+~P1(f777(f777(f235(a3),x85912),x85913))+~P1(f777(f777(f234(a3),f4(a3)),f777(f777(f84(a3),f777(f777(f85(a3),x85913),x85911)),x85912))) % 174.01/173.90 [8611]~P93(x86111)+~P1(f777(f65(x86111),x86112))+E(f777(f777(f5(f858(x86111,a845)),x86112),f777(f777(f304(x86111),x86113),f182(f858(x86111,a845)))),f182(f858(x86111,a845)))+E(f777(f777(f105(x86111),x86113),f17(x86111,f777(f777(f5(f858(x86111,a845)),x86112),f777(f777(f304(x86111),x86113),f182(f858(x86111,a845)))))),f17(x86111,f777(f777(f304(x86111),x86113),x86112))) % 174.01/173.90 [8612]~P100(x86121)+~P1(f777(f65(x86121),x86122))+E(f777(f777(f5(f858(x86121,a845)),x86122),f777(f777(f304(x86121),x86123),f182(f858(x86121,a845)))),f182(f858(x86121,a845)))+E(f777(f777(f181(x86121),x86123),f18(x86121,f777(f777(f5(f858(x86121,a845)),x86122),f777(f777(f304(x86121),x86123),f182(f858(x86121,a845)))))),f18(x86121,f777(f777(f304(x86121),x86123),x86122))) % 174.01/173.90 [8613]~P100(x86131)+~P1(f777(f65(x86131),x86132))+E(f777(f777(f5(f858(x86131,a845)),x86132),f777(f777(f304(x86131),x86133),f182(f858(x86131,a845)))),f182(f858(x86131,a845)))+E(f777(f777(f238(x86131),x86133),f19(x86131,f777(f777(f5(f858(x86131,a845)),x86132),f777(f777(f304(x86131),x86133),f182(f858(x86131,a845)))))),f19(x86131,f777(f777(f304(x86131),x86133),x86132))) % 174.01/173.90 [8614]~P93(x86141)+~P1(f777(f65(x86141),x86142))+E(f777(f777(f5(f858(x86141,a845)),x86142),f777(f777(f304(x86141),x86143),f182(f858(x86141,a845)))),f182(f858(x86141,a845)))+E(f777(f777(f106(x86141),x86143),f14(x86141,f777(f777(f5(f858(x86141,a845)),x86142),f777(f777(f304(x86141),x86143),f182(f858(x86141,a845)))))),f14(x86141,f777(f777(f304(x86141),x86143),x86142))) % 174.01/173.90 [8676]~P100(x86761)+~P1(f777(f65(x86761),x86762))+E(f777(f777(f5(f858(x86761,a845)),x86762),f777(f777(f304(x86761),x86763),f182(f858(x86761,a845)))),f182(f858(x86761,a845)))+E(f777(f777(f181(x86761),x86763),f15(x86761,f181(x86761),f777(f777(f5(f858(x86761,a845)),x86762),f777(f777(f304(x86761),x86763),f182(f858(x86761,a845)))))),f15(x86761,f181(x86761),f777(f777(f304(x86761),x86763),x86762))) % 174.01/173.90 [8677]~P100(x86771)+~P1(f777(f65(x86771),x86772))+E(f777(f777(f5(f858(x86771,a845)),x86772),f777(f777(f304(x86771),x86773),f182(f858(x86771,a845)))),f182(f858(x86771,a845)))+E(f777(f777(f238(x86771),x86773),f16(x86771,f238(x86771),f777(f777(f5(f858(x86771,a845)),x86772),f777(f777(f304(x86771),x86773),f182(f858(x86771,a845)))))),f16(x86771,f238(x86771),f777(f777(f304(x86771),x86773),x86772))) % 174.01/173.90 [9191]E(x91911,x91912)+~E(f777(f134(f852(x91913),f852(x91913),f127(x91913),f117(x91913)),x91911),f777(f134(f852(x91913),f852(x91913),f127(x91913),f117(x91913)),x91912))+~E(f777(f183(f852(f852(x91913))),x91911),f777(f183(f852(f852(x91913))),x91912))+P1(f777(f777(f336(f857(f852(x91913),f852(x91913))),f773(x91911,x91912,x91913)),f777(f160(f857(f852(x91913),f852(x91913))),f777(f777(f169(f852(x91913),f852(x91913)),x91912),x91911)))) % 174.01/173.90 [9192]E(x91921,x91922)+~E(f777(f134(f852(x91923),f852(x91923),f127(x91923),f117(x91923)),x91921),f777(f134(f852(x91923),f852(x91923),f127(x91923),f117(x91923)),x91922))+~E(f777(f183(f852(f852(x91923))),x91921),f777(f183(f852(f852(x91923))),x91922))+P1(f777(f777(f336(f857(f852(x91923),f852(x91923))),f774(x91922,x91921,x91923)),f777(f160(f857(f852(x91923),f852(x91923))),f777(f777(f169(f852(x91923),f852(x91923)),x91921),x91922)))) % 174.01/173.90 [10001]~P72(x100012)+E(x100011,f182(f858(x100012,a845)))+~P1(f777(f65(x100012),x100011))+E(f18(x100012,f777(f258(x100012),f777(f777(f12(f858(x100012,a845),a845,x100012),f91(x100012)),f777(f777(f11(x100012,f858(x100012,a845),f858(x100012,a845)),f777(f777(f12(f858(x100012,f858(a845,a845)),f858(f858(x100012,a845),f858(x100012,a845)),x100012),f22(x100012,a845,a845)),f777(f777(f12(f858(x100012,a845),f858(x100012,f858(a845,a845)),x100012),f777(f12(a845,f858(a845,a845),x100012),a333)),f777(f777(f11(x100012,f858(x100012,x100012),f858(x100012,a845)),f777(f777(f12(f858(x100012,a845),f858(f858(x100012,x100012),f858(x100012,a845)),x100012),f12(x100012,a845,x100012)),a332)),f777(f84(x100012),x100013))))),f777(f777(f11(x100012,f858(x100012,a845),a845),f336(x100012)),x100011))))),f777(f777(f84(x100012),x100013),f18(x100012,x100011))) % 174.01/173.90 [10002]~P72(x100022)+E(x100021,f182(f858(x100022,a845)))+~P1(f777(f65(x100022),x100021))+E(f19(x100022,f777(f258(x100022),f777(f777(f12(f858(x100022,a845),a845,x100022),f91(x100022)),f777(f777(f11(x100022,f858(x100022,a845),f858(x100022,a845)),f777(f777(f12(f858(x100022,f858(a845,a845)),f858(f858(x100022,a845),f858(x100022,a845)),x100022),f22(x100022,a845,a845)),f777(f777(f12(f858(x100022,a845),f858(x100022,f858(a845,a845)),x100022),f777(f12(a845,f858(a845,a845),x100022),a333)),f777(f777(f11(x100022,f858(x100022,x100022),f858(x100022,a845)),f777(f777(f12(f858(x100022,a845),f858(f858(x100022,x100022),f858(x100022,a845)),x100022),f12(x100022,a845,x100022)),a332)),f777(f84(x100022),x100023))))),f777(f777(f11(x100022,f858(x100022,a845),a845),f336(x100022)),x100021))))),f777(f777(f84(x100022),x100023),f19(x100022,x100021))) % 174.01/173.90 [10003]~P97(x100032)+E(x100031,f182(f858(x100032,a845)))+~P1(f777(f65(x100032),x100031))+E(f14(x100032,f777(f258(x100032),f777(f777(f12(f858(x100032,a845),a845,x100032),f91(x100032)),f777(f777(f11(x100032,f858(x100032,a845),f858(x100032,a845)),f777(f777(f12(f858(x100032,f858(a845,a845)),f858(f858(x100032,a845),f858(x100032,a845)),x100032),f22(x100032,a845,a845)),f777(f777(f12(f858(x100032,a845),f858(x100032,f858(a845,a845)),x100032),f777(f12(a845,f858(a845,a845),x100032),a333)),f777(f777(f11(x100032,f858(x100032,x100032),f858(x100032,a845)),f777(f777(f12(f858(x100032,a845),f858(f858(x100032,x100032),f858(x100032,a845)),x100032),f12(x100032,a845,x100032)),a332)),f777(f105(x100032),x100033))))),f777(f777(f11(x100032,f858(x100032,a845),a845),f336(x100032)),x100031))))),f777(f777(f105(x100032),x100033),f14(x100032,x100031))) % 174.01/173.90 [10004]~P97(x100042)+E(x100041,f182(f858(x100042,a845)))+~P1(f777(f65(x100042),x100041))+E(f17(x100042,f777(f258(x100042),f777(f777(f12(f858(x100042,a845),a845,x100042),f91(x100042)),f777(f777(f11(x100042,f858(x100042,a845),f858(x100042,a845)),f777(f777(f12(f858(x100042,f858(a845,a845)),f858(f858(x100042,a845),f858(x100042,a845)),x100042),f22(x100042,a845,a845)),f777(f777(f12(f858(x100042,a845),f858(x100042,f858(a845,a845)),x100042),f777(f12(a845,f858(a845,a845),x100042),a333)),f777(f777(f11(x100042,f858(x100042,x100042),f858(x100042,a845)),f777(f777(f12(f858(x100042,a845),f858(f858(x100042,x100042),f858(x100042,a845)),x100042),f12(x100042,a845,x100042)),a332)),f777(f106(x100042),x100043))))),f777(f777(f11(x100042,f858(x100042,a845),a845),f336(x100042)),x100041))))),f777(f777(f106(x100042),x100043),f17(x100042,x100041))) % 174.01/173.90 [10005]~P100(x100052)+E(x100051,f182(f858(x100052,a845)))+~P1(f777(f65(x100052),x100051))+E(f15(x100052,f181(x100052),f777(f258(x100052),f777(f777(f12(f858(x100052,a845),a845,x100052),f91(x100052)),f777(f777(f11(x100052,f858(x100052,a845),f858(x100052,a845)),f777(f777(f12(f858(x100052,f858(a845,a845)),f858(f858(x100052,a845),f858(x100052,a845)),x100052),f22(x100052,a845,a845)),f777(f777(f12(f858(x100052,a845),f858(x100052,f858(a845,a845)),x100052),f777(f12(a845,f858(a845,a845),x100052),a333)),f777(f777(f11(x100052,f858(x100052,x100052),f858(x100052,a845)),f777(f777(f12(f858(x100052,a845),f858(f858(x100052,x100052),f858(x100052,a845)),x100052),f12(x100052,a845,x100052)),a332)),f777(f238(x100052),x100053))))),f777(f777(f11(x100052,f858(x100052,a845),a845),f336(x100052)),x100051))))),f777(f777(f238(x100052),x100053),f15(x100052,f181(x100052),x100051))) % 174.01/173.90 [10006]~P100(x100062)+E(x100061,f182(f858(x100062,a845)))+~P1(f777(f65(x100062),x100061))+E(f16(x100062,f238(x100062),f777(f258(x100062),f777(f777(f12(f858(x100062,a845),a845,x100062),f91(x100062)),f777(f777(f11(x100062,f858(x100062,a845),f858(x100062,a845)),f777(f777(f12(f858(x100062,f858(a845,a845)),f858(f858(x100062,a845),f858(x100062,a845)),x100062),f22(x100062,a845,a845)),f777(f777(f12(f858(x100062,a845),f858(x100062,f858(a845,a845)),x100062),f777(f12(a845,f858(a845,a845),x100062),a333)),f777(f777(f11(x100062,f858(x100062,x100062),f858(x100062,a845)),f777(f777(f12(f858(x100062,a845),f858(f858(x100062,x100062),f858(x100062,a845)),x100062),f12(x100062,a845,x100062)),a332)),f777(f181(x100062),x100063))))),f777(f777(f11(x100062,f858(x100062,a845),a845),f336(x100062)),x100061))))),f777(f777(f181(x100062),x100063),f16(x100062,f238(x100062),x100061))) % 174.01/173.90 [9735]~P110(x97351)+~E(x97353,f4(x97351))+~E(x97352,f4(x97351))+E(f777(f777(f84(x97351),f777(f777(f244(x97351),x97352),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x97351),x97353),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f4(x97351)) % 174.01/173.90 [9895]~P117(x98951)+~P1(f777(f777(f234(x98951),f4(x98951)),x98953))+P1(f777(f777(f234(x98951),x98952),x98953))+~P1(f777(f777(f234(x98951),f777(f777(f244(x98951),x98952),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x98951),x98953),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))))) % 174.01/173.90 [9941]~P110(x99412)+~E(x99411,f4(x99412))+~E(x99413,f4(x99412))+~P1(f777(f777(f235(x99412),f4(x99412)),f777(f777(f84(x99412),f777(f777(f244(x99412),x99413),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))),f777(f777(f244(x99412),x99411),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))))) % 174.01/173.90 [9165]E(x91651,x91652)+~E(f753(x91651,x91652,x91654,x91653),f755(x91651,x91652,x91654,x91653))+P1(f777(f777(f336(f857(f852(x91653),f852(x91653))),f777(f777(f243(f852(x91653),f852(x91653)),x91652),x91651)),f139(x91653,x91654)))+P1(f777(f777(f336(f857(f852(x91653),f852(x91653))),f777(f777(f243(f852(x91653),f852(x91653)),x91651),x91652)),f139(x91653,x91654))) % 174.01/173.90 [4748]~P60(x47482)+~E(x47484,f4(x47482))+~E(x47481,f4(x47482))+E(x47481,f777(f777(f285(x47482),x47483),x47484)) % 174.01/173.90 [4749]~P60(x47491)+~E(x47493,f4(x47491))+~E(x47494,f4(x47491))+E(f777(f777(f285(x47491),x47492),x47493),x47494) % 174.01/173.90 [4856]~P60(x48562)+E(x48561,f4(x48562))+~E(x48563,f4(x48562))+~E(x48561,f777(f777(f285(x48562),x48564),x48563)) % 174.01/173.90 [4857]~P60(x48572)+E(x48571,f4(x48572))+~E(x48573,f4(x48572))+~E(f777(f777(f285(x48572),x48574),x48573),x48571) % 174.01/173.90 [5038]~P113(x50382)+E(x50381,f4(x50382))+~E(f777(f777(f285(x50382),x50383),x50381),x50384)+E(x50383,f777(f777(f85(x50382),x50384),x50381)) % 174.01/173.90 [5040]~P113(x50402)+E(x50401,f4(x50402))+~E(f777(f777(f85(x50402),x50403),x50401),x50404)+E(x50403,f777(f777(f285(x50402),x50404),x50401)) % 174.01/173.90 [5041]~P60(x50412)+E(x50411,f4(x50412))+~E(f777(f777(f285(x50412),x50413),x50411),x50414)+E(x50413,f777(f777(f85(x50412),x50414),x50411)) % 174.01/173.90 [5042]~P60(x50422)+E(x50421,f4(x50422))+~E(f777(f777(f85(x50422),x50423),x50421),x50424)+E(x50423,f777(f777(f285(x50422),x50424),x50421)) % 174.01/173.90 [5043]~P113(x50432)+E(x50431,f4(x50432))+~E(x50433,f777(f777(f285(x50432),x50434),x50431))+E(f777(f777(f85(x50432),x50433),x50431),x50434) % 174.01/173.90 [5045]~P113(x50452)+E(x50451,f4(x50452))+~E(x50453,f777(f777(f85(x50452),x50454),x50451))+E(f777(f777(f285(x50452),x50453),x50451),x50454) % 174.01/173.90 [5046]~P60(x50462)+E(x50461,f4(x50462))+~E(x50463,f777(f777(f285(x50462),x50464),x50461))+E(f777(f777(f85(x50462),x50463),x50461),x50464) % 174.01/173.90 [5047]~P60(x50472)+E(x50471,f4(x50472))+~E(x50473,f777(f777(f85(x50472),x50474),x50471))+E(f777(f777(f285(x50472),x50473),x50471),x50474) % 174.01/173.90 [5080]~P60(x50802)+~E(x50801,f4(x50802))+~E(f777(f777(f85(x50802),x50801),x50804),x50803)+E(x50801,f777(f777(f285(x50802),x50803),x50804)) % 174.01/173.90 [5081]~P60(x50811)+~E(x50814,f4(x50811))+~E(x50812,f777(f777(f85(x50811),x50814),x50813))+E(f777(f777(f285(x50811),x50812),x50813),x50814) % 174.01/173.90 [5150]~E(x51503,x51504)+~E(x51502,x51503)+~P99(x51501)+E(f297(x51501,x51502,x51503),f777(f777(f304(x51501),x51504),f182(f858(x51501,a845)))) % 174.01/173.90 [5349]~E(f136(x53492,x53491),x53494)+~E(f118(x53492,x53491),x53493)+E(x53491,f117(x53492))+E(f777(f777(f127(x53492),x53493),f777(f777(f142(x53492),x53494),f117(x53492))),x53491) % 174.01/173.90 [5967]~P117(x59673)+E(x59671,x59672)+~E(f777(f777(f244(x59673),x59674),x59671),f777(f777(f244(x59673),x59674),x59672))+~P1(f777(f777(f235(x59673),f82(x59673)),x59674)) % 174.01/173.90 [5968]E(x59681,x59682)+~E(f777(f777(f304(x59683),x59684),x59681),f777(f777(f304(x59683),x59684),x59682))+P1(f777(f777(f336(x59683),x59684),x59682))+P1(f777(f777(f336(x59683),x59684),x59681)) % 174.01/173.90 [6006]E(f777(x60061,x60062),f4(a851))+~E(f777(f777(f10(x60063,a851),x60061),x60064),f4(a851))+~P1(f777(f65(x60063),x60064))+~P1(f777(f777(f336(x60063),x60062),x60064)) % 174.01/173.90 [6007]E(f777(x60071,x60072),f82(a851))+~E(f777(f777(f13(x60073,a851),x60071),x60074),f82(a851))+~P1(f777(f65(x60073),x60074))+~P1(f777(f777(f336(x60073),x60072),x60074)) % 174.01/173.90 [6232]~P99(x62321)+~P1(f777(f777(f235(x62321),x62324),x62323))+P1(f777(f777(f235(x62321),x62322),x62323))+~P1(f777(f777(f235(x62321),x62322),x62324)) % 174.01/173.90 [6233]~P99(x62331)+~P1(f777(f777(f234(x62331),x62334),x62333))+P1(f777(f777(f235(x62331),x62332),x62333))+~P1(f777(f777(f235(x62331),x62332),x62334)) % 174.01/173.90 [6234]~P99(x62341)+~P1(f777(f777(f234(x62341),x62342),x62344))+P1(f777(f777(f235(x62341),x62342),x62343))+~P1(f777(f777(f235(x62341),x62344),x62343)) % 174.01/173.90 [6235]~P103(x62351)+~P1(f777(f777(f235(x62351),x62352),x62354))+P1(f777(f777(f235(x62351),x62352),x62353))+~P1(f777(f777(f235(x62351),x62354),x62353)) % 174.01/173.90 [6236]~P103(x62361)+~P1(f777(f777(f234(x62361),x62362),x62364))+P1(f777(f777(f235(x62361),x62362),x62363))+~P1(f777(f777(f235(x62361),x62364),x62363)) % 174.01/173.90 [6237]~P103(x62371)+~P1(f777(f777(f234(x62371),x62374),x62373))+P1(f777(f777(f235(x62371),x62372),x62373))+~P1(f777(f777(f235(x62371),x62372),x62374)) % 174.01/173.90 [6238]~P99(x62381)+~P1(f777(f777(f234(x62381),x62384),x62383))+P1(f777(f777(f234(x62381),x62382),x62383))+~P1(f777(f777(f234(x62381),x62382),x62384)) % 174.01/173.90 [6239]~P103(x62391)+~P1(f777(f777(f234(x62391),x62392),x62394))+P1(f777(f777(f234(x62391),x62392),x62393))+~P1(f777(f777(f234(x62391),x62394),x62393)) % 174.01/173.90 [6240]~P85(x62401)+~P1(f777(f777(f281(x62401),x62402),x62404))+P1(f777(f777(f281(x62401),x62402),x62403))+~P1(f777(f777(f281(x62401),x62404),x62403)) % 174.01/173.90 [6485]~P9(x64851)+~P1(f777(f777(f234(x64851),x64852),f47(x64851,x64854)))+P1(f777(f777(f234(x64851),x64852),x64853))+~P1(f777(f777(f336(x64851),x64853),x64854)) % 174.01/173.90 [6636]~P100(x66361)+~P18(x66361,f777(f777(f142(x66361),x66362),x66364))+~P1(f777(f777(f336(x66361),x66363),f777(f160(x66361),x66364)))+P1(f777(f777(f234(x66361),x66362),x66363)) % 174.01/173.90 [6729]~P9(x67291)+~P1(f777(f777(f234(x67291),f46(x67291,x67294)),x67293))+P1(f777(f777(f234(x67291),x67292),x67293))+~P1(f777(f777(f336(x67291),x67292),x67294)) % 174.01/173.90 [6882]~P7(x68821)+P1(f777(f777(f281(x68821),x68822),f54(x68821,x68823,x68824)))+~P1(f777(f777(f281(x68821),x68822),x68824))+~P1(f777(f777(f281(x68821),x68822),x68823)) % 174.01/173.90 [7143]~P100(x71431)+E(f777(f777(f105(f858(x71431,a845)),f777(f296(x71431,x71432),x71433)),f777(f296(x71431,x71433),x71434)),f777(f296(x71431,x71432),x71434))+~P1(f777(f777(f234(x71431),x71433),x71434))+~P1(f777(f777(f234(x71431),x71432),x71433)) % 174.01/173.90 [7230]~P7(x72301)+~P1(f777(f777(f281(x72301),x72302),f54(x72301,x72303,x72304)))+P1(f777(f777(f281(x72301),x72302),x72303))+~P1(f777(f777(f281(x72301),x72302),x72304)) % 174.01/173.90 [7271]~P100(x72711)+E(f777(f777(f105(f858(x72711,a845)),f777(f296(x72711,x72712),x72713)),f297(x72711,x72713,x72714)),f297(x72711,x72712,x72714))+~P1(f777(f777(f234(x72711),x72713),x72714))+~P1(f777(f777(f234(x72711),x72712),x72713)) % 174.01/173.90 [7285]~P99(x72851)+~P50(a851,x72851,f281(a851),x72852)+P1(f777(f777(f234(x72851),f777(x72852,x72853)),f777(x72852,x72854)))+~P1(f777(f777(f281(a851),x72853),x72854)) % 174.01/173.90 [7339]~P100(x73391)+E(f777(f777(f105(f858(x73391,a845)),f300(x73391,x73392,x73393)),f777(f296(x73391,x73393),x73394)),f300(x73391,x73392,x73394))+~P1(f777(f777(f235(x73391),x73392),x73393))+~P1(f777(f777(f234(x73391),x73393),x73394)) % 174.01/173.90 [7362]~P100(x73621)+E(f777(f777(f105(f858(x73621,a845)),f297(x73621,x73622,x73623)),f300(x73621,x73623,x73624)),f777(f296(x73621,x73622),x73624))+~P1(f777(f777(f235(x73621),x73623),x73624))+~P1(f777(f777(f234(x73621),x73622),x73623)) % 174.01/173.90 [7397]~P100(x73971)+E(f777(f777(f105(f858(x73971,a845)),f297(x73971,x73972,x73973)),f299(x73971,x73973,x73974)),f297(x73971,x73972,x73974))+~P1(f777(f777(f234(x73971),x73973),x73974))+~P1(f777(f777(f234(x73971),x73972),x73973)) % 174.01/173.90 [7398]~P100(x73981)+E(f777(f777(f105(f858(x73981,a845)),f299(x73981,x73982,x73983)),f299(x73981,x73983,x73984)),f299(x73981,x73982,x73984))+~P1(f777(f777(f234(x73981),x73983),x73984))+~P1(f777(f777(f234(x73981),x73982),x73983)) % 174.01/173.90 [7399]~P100(x73991)+E(f777(f777(f105(f858(x73991,a845)),f299(x73991,x73992,x73993)),f300(x73991,x73993,x73994)),f300(x73991,x73992,x73994))+~P1(f777(f777(f235(x73991),x73993),x73994))+~P1(f777(f777(f234(x73991),x73992),x73993)) % 174.01/173.90 [7400]~P100(x74001)+E(f777(f777(f105(f858(x74001,a845)),f300(x74001,x74002,x74003)),f297(x74001,x74003,x74004)),f299(x74001,x74002,x74004))+~P1(f777(f777(f235(x74001),x74002),x74003))+~P1(f777(f777(f234(x74001),x74003),x74004)) % 174.01/173.90 [8190]P29(x81901,x81902,f529(x81903,x81902,x81904,x81901),x81904)+~P1(f777(f65(x81902),x81903))+~P1(f777(f65(x81901),x81904))+~P1(f777(f777(f234(a851),f777(f44(x81901),x81904)),f777(f44(x81902),x81903))) % 174.01/173.90 [8260]~P70(x82601)+~E(f777(x82603,f624(x82603,x82604,x82602,x82601)),f82(x82601))+E(f777(f777(f777(f69(x82601,x82602,f85(x82601)),x82603),f82(x82601)),x82604),f82(x82601))+~P1(f777(f65(x82602),x82604)) % 174.01/173.90 [8534]~P117(x85341)+~P1(f777(f777(f234(x85341),f4(x85341)),x85343))+P1(f777(f777(f234(x85341),x85342),x85343))+~P1(f777(f777(f234(x85341),f777(f777(f244(x85341),x85342),f777(a116,x85344))),f777(f777(f244(x85341),x85343),f777(a116,x85344)))) % 174.01/173.90 [8864]~P70(x88641)+E(f777(f777(f777(f69(x88641,x88642,f85(x88641)),x88643),f82(x88641)),x88644),f82(x88641))+~P1(f777(f65(x88642),x88644))+P1(f777(f777(f336(x88642),f624(x88643,x88644,x88642,x88641)),x88644)) % 174.01/173.90 [9116]~P12(x91162,x91163,x91164)+~P1(f777(f65(x91162),x91163))+~P1(f777(f777(f281(a851),x91161),f777(f44(x91162),f519(x91161,x91164,x91163,x91162))))+P1(f777(f777(f281(a851),x91161),f777(f44(x91162),x91163))) % 174.01/173.90 [9314]~P1(f777(f777(f281(a851),x93141),x93143))+~P1(f777(f777(f281(a851),x93141),x93142))+~P1(f777(f777(f281(a851),x93144),x93143))+~P1(f777(f777(f235(f858(a851,a845)),f284(a851,f281(a851),x93141,x93143)),f284(a851,f281(a851),x93142,x93144))) % 174.01/173.90 [9320]~P1(f777(f777(f234(a3),x93204),f4(a3)))+P1(f777(f777(f234(a3),f777(f777(f84(a3),f777(f777(f85(a3),x93201),f54(a3,x93202,x93203))),x93204)),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x93203))+~P1(f777(f777(f235(a3),x93201),x93204)) % 174.01/173.90 [9726]~P1(f777(f65(x97261),x97262))+~P1(f777(f777(f336(x97261),x97264),x97262))+~P1(f777(f777(f336(x97261),x97263),x97262))+P1(f777(f777(f235(a851),f777(f44(x97261),f777(f777(f5(f858(x97261,a845)),f777(f777(f5(f858(x97261,a845)),x97262),f777(f777(f304(x97261),x97263),f182(f858(x97261,a845))))),f777(f777(f304(x97261),x97264),f182(f858(x97261,a845)))))),f777(f44(x97261),x97262))) % 174.01/173.90 [6792]~P136(x67923)+~P112(x67923)+P1(f777(x67921,f839(x67922,x67921,x67923)))+~P1(f777(x67921,f777(f777(f85(x67923),x67922),x67924))) % 174.01/173.90 [6852]~P100(x68521)+~P1(f777(f777(f235(x68521),x68522),x68524))+~P1(f777(f777(f235(x68521),x68522),x68523))+P1(f777(f777(f235(x68521),x68522),f777(f777(f238(x68521),x68523),x68524))) % 174.01/173.90 [6855]~P100(x68551)+~P1(f777(f777(f234(x68551),x68552),x68554))+~P1(f777(f777(f234(x68551),x68552),x68553))+P1(f777(f777(f234(x68551),x68552),f777(f777(f238(x68551),x68553),x68554))) % 174.01/173.90 [6858]~P98(x68581)+~P1(f777(f777(f234(x68581),x68582),x68584))+~P1(f777(f777(f234(x68581),x68582),x68583))+P1(f777(f777(f234(x68581),x68582),f777(f777(f106(x68581),x68583),x68584))) % 174.01/173.90 [6859]~P85(x68591)+~P1(f777(f777(f281(x68591),x68592),x68594))+~P1(f777(f777(f281(x68591),x68592),x68593))+P1(f777(f777(f281(x68591),x68592),f777(f777(f84(x68591),x68593),x68594))) % 174.01/173.90 [6860]~P104(x68601)+~P1(f777(f777(f281(x68601),x68602),x68604))+~P1(f777(f777(f281(x68601),x68602),x68603))+P1(f777(f777(f281(x68601),x68602),f777(f777(f5(x68601),x68603),x68604))) % 174.01/173.90 [6880]~P61(x68802)+E(x68801,f4(x68802))+E(f777(f777(f285(x68802),f777(f777(f244(x68802),x68801),x68803)),f777(f777(f244(x68802),x68801),x68804)),f777(f777(f244(x68802),x68801),f777(f777(f5(a851),x68803),x68804)))+~P1(f777(f777(f234(a851),x68804),x68803)) % 174.01/173.90 [6925]~P100(x69251)+~P18(x69251,f777(f777(f142(x69251),x69253),x69254))+P18(x69251,f777(f777(f142(x69251),x69252),f777(f777(f142(x69251),x69253),x69254)))+~P1(f777(f777(f234(x69251),x69252),x69253)) % 174.01/173.90 [6965]~P81(x69651)+~P1(f777(f777(f234(x69651),f4(x69651)),x69653))+~P1(f777(f777(f235(x69651),x69652),x69654))+P1(f777(f777(f235(x69651),x69652),f777(f777(f84(x69651),x69653),x69654))) % 174.01/173.90 [6966]~P81(x69661)+~P1(f777(f777(f234(x69661),x69662),x69664))+~P1(f777(f777(f235(x69661),f4(x69661)),x69663))+P1(f777(f777(f235(x69661),x69662),f777(f777(f84(x69661),x69663),x69664))) % 174.01/173.90 [6967]~P117(x69671)+~P1(f777(f777(f235(x69671),f4(x69671)),x69673))+~P1(f777(f777(f235(x69671),x69672),x69674))+P1(f777(f777(f235(x69671),x69672),f777(f777(f84(x69671),x69673),x69674))) % 174.01/173.90 [6968]~P81(x69681)+~P1(f777(f777(f234(x69681),f4(x69681)),x69684))+~P1(f777(f777(f234(x69681),x69682),x69683))+P1(f777(f777(f234(x69681),x69682),f777(f777(f84(x69681),x69683),x69684))) % 174.01/173.90 [6969]~P81(x69691)+~P1(f777(f777(f234(x69691),f4(x69691)),x69693))+~P1(f777(f777(f234(x69691),x69692),x69694))+P1(f777(f777(f234(x69691),x69692),f777(f777(f84(x69691),x69693),x69694))) % 174.01/173.90 [7003]~P100(x70031)+P1(f777(f777(f235(x70031),x70032),x70033))+P1(f777(f777(f235(x70031),x70032),x70034))+~P1(f777(f777(f235(x70031),x70032),f777(f777(f181(x70031),x70034),x70033))) % 174.01/173.90 [7004]~P100(x70041)+P1(f777(f777(f234(x70041),x70042),x70043))+P1(f777(f777(f234(x70041),x70042),x70044))+~P1(f777(f777(f234(x70041),x70042),f777(f777(f181(x70041),x70044),x70043))) % 174.01/173.90 [7688]~P63(x76881)+~P1(f777(f777(f235(x76881),x76884),f4(x76881)))+~P1(f777(f777(f235(x76881),x76883),f777(f777(f285(x76881),x76882),x76884)))+P1(f777(f777(f235(x76881),x76882),f777(f777(f85(x76881),x76883),x76884))) % 174.01/173.90 [7689]~P63(x76891)+~P1(f777(f777(f235(x76891),x76894),f4(x76891)))+~P1(f777(f777(f235(x76891),x76893),f777(f777(f85(x76891),x76892),x76894)))+P1(f777(f777(f235(x76891),x76892),f777(f777(f285(x76891),x76893),x76894))) % 174.01/173.90 [7690]~P63(x76901)+~P1(f777(f777(f235(x76901),x76904),f4(x76901)))+~P1(f777(f777(f234(x76901),x76903),f777(f777(f285(x76901),x76902),x76904)))+P1(f777(f777(f234(x76901),x76902),f777(f777(f85(x76901),x76903),x76904))) % 174.01/173.90 [7691]~P63(x76911)+~P1(f777(f777(f235(x76911),x76914),f4(x76911)))+~P1(f777(f777(f234(x76911),x76913),f777(f777(f85(x76911),x76912),x76914)))+P1(f777(f777(f234(x76911),x76912),f777(f777(f285(x76911),x76913),x76914))) % 174.01/173.90 [7804]~P119(x78041)+~P1(f777(f777(f235(x78041),x78043),f4(x78041)))+~P1(f777(f777(f235(x78041),x78044),x78042))+P1(f777(f777(f235(x78041),f777(f777(f85(x78041),x78042),x78043)),f777(f777(f85(x78041),x78044),x78043))) % 174.01/173.90 [7805]~P119(x78051)+~P1(f777(f777(f235(x78051),x78052),f4(x78051)))+~P1(f777(f777(f235(x78051),x78054),x78053))+P1(f777(f777(f235(x78051),f777(f777(f85(x78051),x78052),x78053)),f777(f777(f85(x78051),x78052),x78054))) % 174.01/173.90 [7806]~P63(x78061)+~P1(f777(f777(f235(x78061),x78063),f4(x78061)))+~P1(f777(f777(f235(x78061),x78064),x78062))+P1(f777(f777(f235(x78061),f777(f777(f285(x78061),x78062),x78063)),f777(f777(f285(x78061),x78064),x78063))) % 174.01/173.90 [7807]~P119(x78071)+~P1(f777(f777(f235(x78071),x78072),f4(x78071)))+~P1(f777(f777(f234(x78071),x78074),x78073))+P1(f777(f777(f234(x78071),f777(f777(f85(x78071),x78072),x78073)),f777(f777(f85(x78071),x78072),x78074))) % 174.01/173.90 [7808]~P129(x78081)+~P1(f777(f777(f234(x78081),x78082),f4(x78081)))+~P1(f777(f777(f234(x78081),x78084),x78083))+P1(f777(f777(f234(x78081),f777(f777(f85(x78081),x78082),x78083)),f777(f777(f85(x78081),x78082),x78084))) % 174.01/173.90 [7809]~P129(x78091)+~P1(f777(f777(f234(x78091),x78093),f4(x78091)))+~P1(f777(f777(f234(x78091),x78094),x78092))+P1(f777(f777(f234(x78091),f777(f777(f85(x78091),x78092),x78093)),f777(f777(f85(x78091),x78094),x78093))) % 174.01/173.90 [7810]~P62(x78101)+~P1(f777(f777(f234(x78101),x78103),f4(x78101)))+~P1(f777(f777(f234(x78101),x78104),x78102))+P1(f777(f777(f234(x78101),f777(f777(f285(x78101),x78102),x78103)),f777(f777(f285(x78101),x78104),x78103))) % 174.01/173.90 [7812]~P117(x78121)+~P1(f777(f777(f235(x78121),f82(x78121)),x78122))+~P1(f777(f777(f235(a851),x78123),x78124))+P1(f777(f777(f235(x78121),f777(f777(f244(x78121),x78122),x78123)),f777(f777(f244(x78121),x78122),x78124))) % 174.01/173.90 [7813]~P117(x78131)+~P1(f777(f777(f235(x78131),f82(x78131)),x78132))+~P1(f777(f777(f234(a851),x78133),x78134))+P1(f777(f777(f234(x78131),f777(f777(f244(x78131),x78132),x78133)),f777(f777(f244(x78131),x78132),x78134))) % 174.01/173.90 [7814]~P117(x78141)+~P1(f777(f777(f234(x78141),f82(x78141)),x78142))+~P1(f777(f777(f234(a851),x78143),x78144))+P1(f777(f777(f234(x78141),f777(f777(f244(x78141),x78142),x78143)),f777(f777(f244(x78141),x78142),x78144))) % 174.01/173.90 [7841]P1(f777(f777(f235(a851),f4(a851)),f777(x78411,x78412)))+~P1(f777(f65(x78413),x78414))+~P1(f777(f777(f336(x78413),x78412),x78414))+~P1(f777(f777(f235(a851),f4(a851)),f777(f777(f13(x78413,a851),x78411),x78414))) % 174.01/173.90 [7853]~P123(x78531)+~P1(f777(f777(f235(x78531),x78533),x78534))+~P1(f777(f777(f235(x78531),f4(x78531)),x78532))+P1(f777(f777(f235(x78531),f777(f777(f85(x78531),x78532),x78533)),f777(f777(f85(x78531),x78532),x78534))) % 174.01/173.90 [7854]~P115(x78541)+~P1(f777(f777(f235(x78541),x78543),x78544))+~P1(f777(f777(f235(x78541),f4(x78541)),x78542))+P1(f777(f777(f235(x78541),f777(f777(f85(x78541),x78542),x78543)),f777(f777(f85(x78541),x78542),x78544))) % 174.01/173.90 [7855]~P119(x78551)+~P1(f777(f777(f235(x78551),x78552),x78554))+~P1(f777(f777(f235(x78551),f4(x78551)),x78553))+P1(f777(f777(f235(x78551),f777(f777(f85(x78551),x78552),x78553)),f777(f777(f85(x78551),x78554),x78553))) % 174.01/173.90 [7856]~P123(x78561)+~P1(f777(f777(f235(x78561),x78562),x78564))+~P1(f777(f777(f235(x78561),f4(x78561)),x78563))+P1(f777(f777(f235(x78561),f777(f777(f85(x78561),x78562),x78563)),f777(f777(f85(x78561),x78564),x78563))) % 174.01/173.90 [7857]~P119(x78571)+~P1(f777(f777(f235(x78571),x78573),x78574))+~P1(f777(f777(f235(x78571),f4(x78571)),x78572))+P1(f777(f777(f235(x78571),f777(f777(f85(x78571),x78572),x78573)),f777(f777(f85(x78571),x78572),x78574))) % 174.01/173.90 [7858]~P63(x78581)+~P1(f777(f777(f235(x78581),x78582),x78584))+~P1(f777(f777(f235(x78581),f4(x78581)),x78583))+P1(f777(f777(f235(x78581),f777(f777(f285(x78581),x78582),x78583)),f777(f777(f285(x78581),x78584),x78583))) % 174.01/173.90 [7859]~P119(x78591)+~P1(f777(f777(f235(x78591),f4(x78591)),x78592))+~P1(f777(f777(f234(x78591),x78593),x78594))+P1(f777(f777(f234(x78591),f777(f777(f85(x78591),x78592),x78593)),f777(f777(f85(x78591),x78592),x78594))) % 174.01/173.90 [7860]~P131(x78601)+~P1(f777(f777(f234(x78601),x78603),x78604))+~P1(f777(f777(f234(x78601),f4(x78601)),x78602))+P1(f777(f777(f234(x78601),f777(f777(f85(x78601),x78602),x78603)),f777(f777(f85(x78601),x78602),x78604))) % 174.01/173.90 [7861]~P130(x78611)+~P1(f777(f777(f234(x78611),x78613),x78614))+~P1(f777(f777(f234(x78611),f4(x78611)),x78612))+P1(f777(f777(f234(x78611),f777(f777(f85(x78611),x78612),x78613)),f777(f777(f85(x78611),x78612),x78614))) % 174.01/173.90 [7862]~P131(x78621)+~P1(f777(f777(f234(x78621),x78622),x78624))+~P1(f777(f777(f234(x78621),f4(x78621)),x78623))+P1(f777(f777(f234(x78621),f777(f777(f85(x78621),x78622),x78623)),f777(f777(f85(x78621),x78624),x78623))) % 174.01/173.90 [7863]~P117(x78631)+~P1(f777(f777(f234(x78631),x78632),x78634))+~P1(f777(f777(f234(x78631),f4(x78631)),x78632))+P1(f777(f777(f234(x78631),f777(f777(f244(x78631),x78632),x78633)),f777(f777(f244(x78631),x78634),x78633))) % 174.01/173.90 [7864]~P62(x78641)+~P1(f777(f777(f234(x78641),x78642),x78644))+~P1(f777(f777(f234(x78641),f4(x78641)),x78643))+P1(f777(f777(f234(x78641),f777(f777(f285(x78641),x78642),x78643)),f777(f777(f285(x78641),x78644),x78643))) % 174.01/173.90 [7903]~P102(x79032)+P1(f777(f777(f234(f858(x79031,x79032)),x79034),x79033))+~P1(f777(f777(f234(f858(x79031,x79032)),x79033),x79034))+P1(f777(f777(f235(f858(x79031,x79032)),x79033),x79034)) % 174.01/173.90 [7947]P1(f777(f777(f336(x79471),x79472),x79473))+P1(f777(f777(f336(x79471),x79472),x79474))+~P1(f777(f777(f234(f858(x79471,a845)),x79474),x79473))+P1(f777(f777(f235(f858(x79471,a845)),x79474),f777(f777(f304(x79471),x79472),x79473))) % 174.01/173.90 [8054]~P111(x80542)+E(x80541,f4(x80542))+P1(f777(f777(f281(x80542),x80543),x80544))+~P1(f777(f777(f281(x80542),f777(f777(f85(x80542),x80543),x80541)),f777(f777(f85(x80542),x80544),x80541))) % 174.01/173.90 [8055]~P111(x80552)+E(x80551,f4(x80552))+P1(f777(f777(f281(x80552),x80553),x80554))+~P1(f777(f777(f281(x80552),f777(f777(f85(x80552),x80551),x80553)),f777(f777(f85(x80552),x80551),x80554))) % 174.01/173.90 [8099]P1(f777(f777(f336(x80991),x80992),x80993))+P1(f777(f777(f336(x80991),x80992),x80994))+~P1(f777(f777(f235(f858(x80991,a845)),x80994),f777(f777(f304(x80991),x80992),x80993)))+P1(f777(f777(f234(f858(x80991,a845)),x80994),x80993)) % 174.01/173.90 [8168]~P119(x81681)+P1(f777(f777(f235(x81681),x81683),x81682))+P1(f777(f777(f235(x81681),x81682),x81683))+~P1(f777(f777(f235(x81681),f777(f777(f85(x81681),x81684),x81682)),f777(f777(f85(x81681),x81684),x81683))) % 174.01/173.90 [8169]~P119(x81691)+P1(f777(f777(f235(x81691),x81693),x81692))+P1(f777(f777(f235(x81691),x81692),x81693))+~P1(f777(f777(f235(x81691),f777(f777(f85(x81691),x81692),x81694)),f777(f777(f85(x81691),x81693),x81694))) % 174.01/173.90 [8180]~P119(x81801)+P1(f777(f777(f235(x81801),x81804),f4(x81801)))+P1(f777(f777(f235(x81801),x81802),x81803))+~P1(f777(f777(f235(x81801),f777(f777(f85(x81801),x81802),x81804)),f777(f777(f85(x81801),x81803),x81804))) % 174.01/173.90 [8181]~P119(x81811)+P1(f777(f777(f235(x81811),x81814),f4(x81811)))+P1(f777(f777(f235(x81811),x81812),x81813))+~P1(f777(f777(f235(x81811),f777(f777(f85(x81811),x81814),x81812)),f777(f777(f85(x81811),x81814),x81813))) % 174.01/173.90 [8184]~P119(x81841)+P1(f777(f777(f235(x81841),x81842),x81843))+P1(f777(f777(f235(x81841),f4(x81841)),x81844))+~P1(f777(f777(f235(x81841),f777(f777(f85(x81841),x81844),x81843)),f777(f777(f85(x81841),x81844),x81842))) % 174.01/173.90 [8185]~P119(x81851)+P1(f777(f777(f235(x81851),x81852),x81853))+P1(f777(f777(f235(x81851),f4(x81851)),x81854))+~P1(f777(f777(f235(x81851),f777(f777(f85(x81851),x81853),x81854)),f777(f777(f85(x81851),x81852),x81854))) % 174.01/173.90 [8198]~P119(x81981)+P1(f777(f777(f235(x81981),x81982),f4(x81981)))+P1(f777(f777(f235(x81981),f4(x81981)),x81982))+~P1(f777(f777(f235(x81981),f777(f777(f85(x81981),x81983),x81982)),f777(f777(f85(x81981),x81984),x81982))) % 174.01/173.90 [8199]~P119(x81991)+P1(f777(f777(f235(x81991),x81992),f4(x81991)))+P1(f777(f777(f235(x81991),f4(x81991)),x81992))+~P1(f777(f777(f235(x81991),f777(f777(f85(x81991),x81992),x81993)),f777(f777(f85(x81991),x81992),x81994))) % 174.01/173.90 [8223]~P119(x82231)+~P1(f777(f777(f235(x82231),x82234),f4(x82231)))+P1(f777(f777(f235(x82231),x82232),x82233))+~P1(f777(f777(f235(x82231),f777(f777(f85(x82231),x82234),x82233)),f777(f777(f85(x82231),x82234),x82232))) % 174.01/173.90 [8224]~P119(x82241)+~P1(f777(f777(f235(x82241),x82244),f4(x82241)))+P1(f777(f777(f234(x82241),x82242),x82243))+~P1(f777(f777(f234(x82241),f777(f777(f85(x82241),x82244),x82243)),f777(f777(f85(x82241),x82244),x82242))) % 174.01/173.90 [8236]~P117(x82363)+~P1(f777(f777(f235(x82363),f82(x82363)),x82364))+P1(f777(f777(f235(a851),x82361),x82362))+~P1(f777(f777(f235(x82363),f777(f777(f244(x82363),x82364),x82361)),f777(f777(f244(x82363),x82364),x82362))) % 174.01/173.90 [8238]~P117(x82383)+~P1(f777(f777(f235(x82383),f82(x82383)),x82384))+P1(f777(f777(f234(a851),x82381),x82382))+~P1(f777(f777(f234(x82383),f777(f777(f244(x82383),x82384),x82381)),f777(f777(f244(x82383),x82384),x82382))) % 174.01/173.90 [8248]~P119(x82481)+P1(f777(f777(f235(x82481),x82482),x82483))+~P1(f777(f777(f235(x82481),f4(x82481)),x82484))+~P1(f777(f777(f235(x82481),f777(f777(f85(x82481),x82484),x82482)),f777(f777(f85(x82481),x82484),x82483))) % 174.01/173.90 [8249]~P123(x82491)+P1(f777(f777(f235(x82491),x82492),x82493))+~P1(f777(f777(f234(x82491),f4(x82491)),x82494))+~P1(f777(f777(f235(x82491),f777(f777(f85(x82491),x82494),x82492)),f777(f777(f85(x82491),x82494),x82493))) % 174.01/173.90 [8250]~P125(x82501)+P1(f777(f777(f235(x82501),x82502),x82503))+~P1(f777(f777(f234(x82501),f4(x82501)),x82504))+~P1(f777(f777(f235(x82501),f777(f777(f85(x82501),x82504),x82502)),f777(f777(f85(x82501),x82504),x82503))) % 174.01/173.90 [8251]~P117(x82511)+~P1(f777(f777(f234(x82511),f4(x82511)),x82513))+P1(f777(f777(f235(x82511),x82512),x82513))+~P1(f777(f777(f235(x82511),f777(f777(f244(x82511),x82512),x82514)),f777(f777(f244(x82511),x82513),x82514))) % 174.01/173.90 [8252]~P123(x82521)+P1(f777(f777(f235(x82521),x82522),x82523))+~P1(f777(f777(f234(x82521),f4(x82521)),x82524))+~P1(f777(f777(f235(x82521),f777(f777(f85(x82521),x82522),x82524)),f777(f777(f85(x82521),x82523),x82524))) % 174.01/173.90 [8253]~P125(x82531)+P1(f777(f777(f235(x82531),x82532),x82533))+~P1(f777(f777(f234(x82531),f4(x82531)),x82534))+~P1(f777(f777(f235(x82531),f777(f777(f85(x82531),x82532),x82534)),f777(f777(f85(x82531),x82533),x82534))) % 174.01/173.90 [8254]~P119(x82541)+P1(f777(f777(f234(x82541),x82542),x82543))+~P1(f777(f777(f235(x82541),f4(x82541)),x82544))+~P1(f777(f777(f234(x82541),f777(f777(f85(x82541),x82544),x82542)),f777(f777(f85(x82541),x82544),x82543))) % 174.01/173.90 [8255]~P123(x82551)+P1(f777(f777(f234(x82551),x82552),x82553))+~P1(f777(f777(f235(x82551),f4(x82551)),x82554))+~P1(f777(f777(f234(x82551),f777(f777(f85(x82551),x82554),x82552)),f777(f777(f85(x82551),x82554),x82553))) % 174.01/173.90 [8256]~P123(x82561)+P1(f777(f777(f234(x82561),x82562),x82563))+~P1(f777(f777(f235(x82561),f4(x82561)),x82564))+~P1(f777(f777(f234(x82561),f777(f777(f85(x82561),x82562),x82564)),f777(f777(f85(x82561),x82563),x82564))) % 174.01/173.90 [8296]P1(f777(f777(f336(x82961),x82962),x82963))+~P1(f777(f777(f234(f858(x82961,a845)),x82963),x82964))+~P1(f777(f777(f235(f858(x82961,a845)),x82963),x82964))+P1(f777(f777(f235(f858(x82961,a845)),x82963),f777(f777(f304(x82961),x82962),x82964))) % 174.01/173.90 [8331]~P136(x83311)+~P112(x83311)+P1(f777(f777(f281(x83311),x83312),f777(f777(f84(x83311),f839(x83312,x83313,x83311)),f4(x83311))))+~P1(f777(x83313,f777(f777(f85(x83311),x83312),x83314))) % 174.01/173.90 [8657]E(f777(f777(f5(a3),f348(x86571,x86572,x86573,x86574)),f349(x86571,x86572,x86573,x86574)),x86574)+~P1(f777(f777(f235(a3),f4(a3)),x86573))+~P1(f777(f777(f234(a3),x86571),x86574))+P1(f777(f777(f234(a3),x86571),f777(f777(f84(a3),x86574),x86573))) % 174.01/173.90 [8658]E(f777(f777(f5(a3),f356(x86581,x86582,x86583,x86584)),f357(x86581,x86582,x86583,x86584)),x86584)+~P1(f777(f777(f235(a3),f4(a3)),x86583))+~P1(f777(f777(f235(a3),x86581),x86584))+P1(f777(f777(f235(a3),x86581),f777(f777(f84(a3),x86584),x86583))) % 174.01/173.90 [8784]~E(f777(f777(f155(x87841),x87843),f758(x87844,x87843,x87841,x87842)),f777(f777(f155(x87841),x87844),f758(x87844,x87843,x87841,x87842)))+E(f777(f777(f161(x87841),x87842),x87843),f777(f777(f161(x87841),x87842),x87844))+~P1(f777(f777(f234(a851),x87842),f777(f183(f852(x87841)),x87843)))+~P1(f777(f777(f234(a851),x87842),f777(f183(f852(x87841)),x87844))) % 174.01/173.90 [8835]~P1(f777(f777(f235(a3),f4(a3)),x88353))+~P1(f777(f777(f234(a3),x88351),x88354))+P1(f777(f777(f336(a3),f348(x88351,x88352,x88353,x88354)),x88352))+P1(f777(f777(f234(a3),x88351),f777(f777(f84(a3),x88354),x88353))) % 174.01/173.90 [8836]~P1(f777(f777(f235(a3),f4(a3)),x88363))+~P1(f777(f777(f235(a3),x88361),x88364))+P1(f777(f777(f336(a3),f356(x88361,x88362,x88363,x88364)),x88362))+P1(f777(f777(f235(a3),x88361),f777(f777(f84(a3),x88364),x88363))) % 174.01/173.90 [8873]~P100(x88731)+~P1(f777(f65(x88731),x88733))+~P1(f777(f777(f336(x88731),x88734),x88733))+P1(f777(f777(f234(x88731),f777(f777(f68(x88731,x88731,f238(x88731)),x88732),x88733)),f777(f777(f238(x88731),x88734),x88732))) % 174.01/173.90 [8874]~P98(x88741)+~P1(f777(f65(x88741),x88743))+~P1(f777(f777(f336(x88741),x88744),x88743))+P1(f777(f777(f234(x88741),f777(f777(f68(x88741,x88741,f106(x88741)),x88742),x88743)),f777(f777(f106(x88741),x88744),x88742))) % 174.01/173.90 [8883]~P12(x88832,x88833,x88834)+~P1(f777(f65(x88832),x88833))+P1(f777(f777(f281(a851),x88831),f777(f44(x88832),x88833)))+P1(f777(f777(f336(f858(x88832,a845)),f519(x88831,x88834,x88833,x88832)),f777(f777(f63(x88832),x88833),x88834))) % 174.01/173.90 [8922]E(f777(f777(f161(x89221),x89222),x89223),f777(f777(f161(x89221),x89222),x89224))+P1(f777(f777(f235(a851),f758(x89223,x89224,x89221,x89222)),x89222))+~P1(f777(f777(f234(a851),x89222),f777(f183(f852(x89221)),x89223)))+~P1(f777(f777(f234(a851),x89222),f777(f183(f852(x89221)),x89224))) % 174.01/173.90 [8927]~P1(f777(f777(f235(a3),f4(a3)),x89273))+~P1(f777(f777(f235(a3),x89271),x89272))+P1(f777(f777(f336(a3),f357(x89271,x89274,x89273,x89272)),f297(a3,f82(a3),x89273)))+P1(f777(f777(f235(a3),x89271),f777(f777(f84(a3),x89272),x89273))) % 174.01/173.90 [8928]~P1(f777(f777(f235(a3),f4(a3)),x89283))+~P1(f777(f777(f234(a3),x89281),x89282))+P1(f777(f777(f336(a3),f349(x89281,x89284,x89283,x89282)),f297(a3,f82(a3),x89283)))+P1(f777(f777(f234(a3),x89281),f777(f777(f84(a3),x89282),x89283))) % 174.01/173.90 [9091]~E(f168(x90911,x90912,x90913),f168(x90911,x90912,x90914))+E(f777(f160(f857(x90911,x90912)),x90913),f777(f160(f857(x90911,x90912)),x90914))+~P1(f777(f129(x90911),f777(f777(f145(f857(x90911,x90912),x90911),f242(x90911,x90912)),x90914)))+~P1(f777(f129(x90911),f777(f777(f145(f857(x90911,x90912),x90911),f242(x90911,x90912)),x90913))) % 174.01/173.90 [9094]E(f168(x90941,x90942,x90943),f168(x90941,x90942,x90944))+~E(f777(f160(f857(x90941,x90942)),x90943),f777(f160(f857(x90941,x90942)),x90944))+~P1(f777(f129(x90941),f777(f777(f145(f857(x90941,x90942),x90941),f242(x90941,x90942)),x90944)))+~P1(f777(f129(x90941),f777(f777(f145(f857(x90941,x90942),x90941),f242(x90941,x90942)),x90943))) % 174.01/173.90 [9211]~P100(x92111)+~P1(f777(f65(x92111),x92114))+P1(f777(f777(f336(x92111),f691(x92112,x92113,x92114,x92111)),x92114))+P1(f777(f777(f234(x92111),f777(f777(f68(x92111,x92111,f181(x92111)),x92112),x92114)),f777(f777(f181(x92111),x92113),x92112))) % 174.01/173.90 [9212]~P92(x92121)+~P1(f777(f65(x92121),x92124))+P1(f777(f777(f336(x92121),f695(x92122,x92123,x92124,x92121)),x92124))+P1(f777(f777(f234(x92121),f777(f777(f68(x92121,x92121,f105(x92121)),x92122),x92124)),f777(f777(f105(x92121),x92123),x92122))) % 174.01/173.90 [9338]~P100(x93381)+~P1(f777(f65(x93381),x93383))+~P1(f777(f777(f234(x93381),f691(x93382,x93384,x93383,x93381)),x93384))+P1(f777(f777(f234(x93381),f777(f777(f68(x93381,x93381,f181(x93381)),x93382),x93383)),f777(f777(f181(x93381),x93384),x93382))) % 174.01/173.90 [9339]~P92(x93391)+~P1(f777(f65(x93391),x93393))+~P1(f777(f777(f234(x93391),f695(x93392,x93394,x93393,x93391)),x93394))+P1(f777(f777(f234(x93391),f777(f777(f68(x93391,x93391,f105(x93391)),x93392),x93393)),f777(f777(f105(x93391),x93394),x93392))) % 174.01/173.90 [9341]~P1(f777(f777(f235(a3),f4(a3)),x93413))+~P1(f777(f777(f234(a3),f4(a3)),x93414))+~P1(f777(f777(f235(a3),x93414),x93411))+P1(f777(f777(f235(a3),f777(f777(f84(a3),f777(f777(f85(a3),x93411),f54(a3,x93412,x93413))),x93414)),f777(f777(f85(a3),x93411),x93413))) % 174.01/173.90 [9601]~P99(x96011)+P1(f777(f777(f235(x96011),f777(x96012,x96013)),f777(x96012,x96014)))+~P1(f777(f777(f235(a851),x96013),x96014))+~P1(f777(f777(f235(x96011),f777(x96012,f651(x96014,x96013,x96012,x96011))),f777(x96012,f777(a116,f651(x96014,x96013,x96012,x96011))))) % 174.01/173.90 [9602]~P99(x96021)+P1(f777(f777(f235(x96021),f777(x96022,x96023)),f777(x96022,x96024)))+~P1(f777(f777(f235(a851),x96023),x96024))+~P1(f777(f777(f235(x96021),f777(x96022,f664(x96024,x96023,x96022,x96021))),f777(x96022,f777(a116,f664(x96024,x96023,x96022,x96021))))) % 174.01/173.90 [9603]~P99(x96033)+~P1(f777(f777(f235(x96033),f777(x96034,x96031)),f777(x96034,x96032)))+P1(f777(f777(f235(a851),x96031),x96032))+~P1(f777(f777(f235(x96033),f777(x96034,f651(x96032,x96031,x96034,x96033))),f777(x96034,f777(a116,f651(x96032,x96031,x96034,x96033))))) % 174.01/173.90 [9696]E(x96961,x96962)+P1(f777(f777(f336(f857(f852(x96963),f852(x96963))),f777(f777(f243(f852(x96963),f852(x96963)),x96962),x96961)),f139(x96963,x96964)))+P1(f777(f777(f336(f857(f852(x96963),f852(x96963))),f777(f777(f243(f852(x96963),f852(x96963)),x96961),x96962)),f139(x96963,x96964)))+~P1(f777(f777(f336(f857(x96963,x96963)),f777(f777(f243(x96963,x96963),f753(x96961,x96962,x96964,x96963)),f755(x96961,x96962,x96964,x96963))),x96964)) % 174.01/173.90 [9697]E(x96971,x96972)+P1(f777(f777(f336(f857(f852(x96973),f852(x96973))),f777(f777(f243(f852(x96973),f852(x96973)),x96972),x96971)),f139(x96973,x96974)))+P1(f777(f777(f336(f857(f852(x96973),f852(x96973))),f777(f777(f243(f852(x96973),f852(x96973)),x96971),x96972)),f139(x96973,x96974)))+~P1(f777(f777(f336(f857(x96973,x96973)),f777(f777(f243(x96973,x96973),f755(x96971,x96972,x96974,x96973)),f753(x96971,x96972,x96974,x96973))),x96974)) % 174.01/173.90 [7386]~P100(x73861)+~P1(f777(f777(f235(x73861),x73863),x73864))+~P1(f777(f777(f235(x73861),x73862),x73864))+P1(f777(f777(f235(x73861),f777(f777(f181(x73861),x73862),x73863)),x73864)) % 174.01/173.90 [7389]~P100(x73891)+~P1(f777(f777(f234(x73891),x73893),x73894))+~P1(f777(f777(f234(x73891),x73892),x73894))+P1(f777(f777(f234(x73891),f777(f777(f181(x73891),x73892),x73893)),x73894)) % 174.01/173.90 [7392]~P92(x73921)+~P1(f777(f777(f234(x73921),x73923),x73924))+~P1(f777(f777(f234(x73921),x73922),x73924))+P1(f777(f777(f234(x73921),f777(f777(f105(x73921),x73922),x73923)),x73924)) % 174.01/173.90 [7633]~P7(x76331)+E(f777(f777(f84(x76331),f777(f777(f45(x76331),x76332),x76333)),f777(f777(f45(x76331),x76334),x76333)),f777(f777(f45(x76331),f777(f777(f84(x76331),x76332),x76334)),x76333))+~P1(f777(f777(f281(x76331),x76333),x76334))+~P1(f777(f777(f281(x76331),x76333),x76332)) % 174.01/173.90 [7711]~E(x77111,x77113)+E(f132(a851,f777(f296(a851,x77111),x77112)),f777(f777(f142(a851),x77113),x77114))+~E(f132(a851,f777(f296(a851,f777(f777(f84(a851),x77111),f82(a851))),x77112)),x77114)+~P1(f777(f777(f235(a851),x77111),x77112)) % 174.01/173.90 [7722]~P100(x77221)+P1(f777(f777(f235(x77221),x77222),x77223))+P1(f777(f777(f235(x77221),x77224),x77223))+~P1(f777(f777(f235(x77221),f777(f777(f238(x77221),x77224),x77222)),x77223)) % 174.01/173.90 [7723]~P100(x77231)+P1(f777(f777(f234(x77231),x77232),x77233))+P1(f777(f777(f234(x77231),x77234),x77233))+~P1(f777(f777(f234(x77231),f777(f777(f238(x77231),x77234),x77232)),x77233)) % 174.01/173.90 [8004]~P62(x80041)+~P1(f777(f777(f235(x80041),f4(x80041)),x80043))+~P1(f777(f777(f235(x80041),x80042),f777(f777(f285(x80041),x80044),x80043)))+P1(f777(f777(f235(x80041),f777(f777(f85(x80041),x80042),x80043)),x80044)) % 174.01/173.90 [8005]~P63(x80051)+~P1(f777(f777(f235(x80051),f4(x80051)),x80053))+~P1(f777(f777(f235(x80051),x80052),f777(f777(f285(x80051),x80054),x80053)))+P1(f777(f777(f235(x80051),f777(f777(f85(x80051),x80052),x80053)),x80054)) % 174.01/173.90 [8006]~P62(x80061)+~P1(f777(f777(f235(x80061),f4(x80061)),x80063))+~P1(f777(f777(f235(x80061),x80062),f777(f777(f85(x80061),x80064),x80063)))+P1(f777(f777(f235(x80061),f777(f777(f285(x80061),x80062),x80063)),x80064)) % 174.01/173.90 [8008]~P63(x80081)+~P1(f777(f777(f235(x80081),f4(x80081)),x80083))+~P1(f777(f777(f235(x80081),x80082),f777(f777(f85(x80081),x80084),x80083)))+P1(f777(f777(f235(x80081),f777(f777(f285(x80081),x80082),x80083)),x80084)) % 174.01/173.90 [8009]~P62(x80091)+~P1(f777(f777(f235(x80091),f4(x80091)),x80093))+~P1(f777(f777(f234(x80091),x80092),f777(f777(f285(x80091),x80094),x80093)))+P1(f777(f777(f234(x80091),f777(f777(f85(x80091),x80092),x80093)),x80094)) % 174.01/173.90 [8010]~P63(x80101)+~P1(f777(f777(f235(x80101),f4(x80101)),x80103))+~P1(f777(f777(f234(x80101),x80102),f777(f777(f285(x80101),x80104),x80103)))+P1(f777(f777(f234(x80101),f777(f777(f85(x80101),x80102),x80103)),x80104)) % 174.01/173.90 [8011]~P62(x80111)+~P1(f777(f777(f235(x80111),f4(x80111)),x80113))+~P1(f777(f777(f234(x80111),x80112),f777(f777(f85(x80111),x80114),x80113)))+P1(f777(f777(f234(x80111),f777(f777(f285(x80111),x80112),x80113)),x80114)) % 174.01/173.90 [8013]~P63(x80131)+~P1(f777(f777(f235(x80131),f4(x80131)),x80133))+~P1(f777(f777(f234(x80131),x80132),f777(f777(f85(x80131),x80134),x80133)))+P1(f777(f777(f234(x80131),f777(f777(f285(x80131),x80132),x80133)),x80134)) % 174.01/173.90 [8137]~P62(x81371)+~P1(f777(f777(f235(x81371),f4(x81371)),x81374))+P1(f777(f777(f235(x81371),x81372),f777(f777(f85(x81371),x81373),x81374)))+~P1(f777(f777(f235(x81371),f777(f777(f285(x81371),x81372),x81374)),x81373)) % 174.01/173.90 [8138]~P62(x81381)+~P1(f777(f777(f235(x81381),f4(x81381)),x81384))+P1(f777(f777(f235(x81381),x81382),f777(f777(f285(x81381),x81383),x81384)))+~P1(f777(f777(f235(x81381),f777(f777(f85(x81381),x81382),x81384)),x81383)) % 174.01/173.90 [8140]~P63(x81401)+~P1(f777(f777(f235(x81401),f4(x81401)),x81404))+P1(f777(f777(f235(x81401),x81402),f777(f777(f85(x81401),x81403),x81404)))+~P1(f777(f777(f235(x81401),f777(f777(f285(x81401),x81402),x81404)),x81403)) % 174.01/173.90 [8141]~P63(x81411)+~P1(f777(f777(f235(x81411),f4(x81411)),x81414))+P1(f777(f777(f235(x81411),x81412),f777(f777(f285(x81411),x81413),x81414)))+~P1(f777(f777(f235(x81411),f777(f777(f85(x81411),x81412),x81414)),x81413)) % 174.01/173.90 [8142]~P62(x81421)+~P1(f777(f777(f235(x81421),f4(x81421)),x81424))+P1(f777(f777(f234(x81421),x81422),f777(f777(f85(x81421),x81423),x81424)))+~P1(f777(f777(f234(x81421),f777(f777(f285(x81421),x81422),x81424)),x81423)) % 174.01/173.90 [8143]~P62(x81431)+~P1(f777(f777(f235(x81431),f4(x81431)),x81434))+P1(f777(f777(f234(x81431),x81432),f777(f777(f285(x81431),x81433),x81434)))+~P1(f777(f777(f234(x81431),f777(f777(f85(x81431),x81432),x81434)),x81433)) % 174.01/173.90 [8145]~P63(x81451)+~P1(f777(f777(f235(x81451),f4(x81451)),x81454))+P1(f777(f777(f234(x81451),x81452),f777(f777(f85(x81451),x81453),x81454)))+~P1(f777(f777(f234(x81451),f777(f777(f285(x81451),x81452),x81454)),x81453)) % 174.01/173.90 [8146]~P63(x81461)+~P1(f777(f777(f235(x81461),f4(x81461)),x81464))+P1(f777(f777(f234(x81461),x81462),f777(f777(f285(x81461),x81463),x81464)))+~P1(f777(f777(f234(x81461),f777(f777(f85(x81461),x81462),x81464)),x81463)) % 174.01/173.90 [8301]~P63(x83011)+~P1(f777(f777(f235(x83011),x83013),f4(x83011)))+~P1(f777(f777(f235(x83011),f777(f777(f285(x83011),x83014),x83013)),x83012))+P1(f777(f777(f235(x83011),f777(f777(f85(x83011),x83012),x83013)),x83014)) % 174.01/173.90 [8302]~P63(x83021)+~P1(f777(f777(f235(x83021),x83023),f4(x83021)))+~P1(f777(f777(f235(x83021),f777(f777(f85(x83021),x83024),x83023)),x83022))+P1(f777(f777(f235(x83021),f777(f777(f285(x83021),x83022),x83023)),x83024)) % 174.01/173.90 [8303]~P63(x83031)+~P1(f777(f777(f235(x83031),x83033),f4(x83031)))+~P1(f777(f777(f234(x83031),f777(f777(f285(x83031),x83034),x83033)),x83032))+P1(f777(f777(f234(x83031),f777(f777(f85(x83031),x83032),x83033)),x83034)) % 174.01/173.90 [8304]~P63(x83041)+~P1(f777(f777(f235(x83041),x83043),f4(x83041)))+~P1(f777(f777(f234(x83041),f777(f777(f85(x83041),x83044),x83043)),x83042))+P1(f777(f777(f234(x83041),f777(f777(f285(x83041),x83042),x83043)),x83044)) % 174.01/173.90 [8317]~P1(f777(x83171,x83174))+~P1(f777(f777(f235(a851),x83172),f777(f777(f85(a851),x83173),f777(a116,x83174))))+P1(f777(x83171,f777(f777(f45(a851),x83172),x83173)))+~P1(f777(f777(f234(a851),f777(f777(f85(a851),x83173),x83174)),x83172)) % 174.01/173.90 [8532]~P100(x85321)+~P1(f777(f65(x85321),x85324))+~P1(f777(f777(f336(x85321),x85322),x85324))+P1(f777(f777(f234(x85321),f777(f777(f181(x85321),x85322),x85323)),f777(f777(f68(x85321,x85321,f181(x85321)),x85323),x85324))) % 174.01/173.90 [8533]~P92(x85331)+~P1(f777(f65(x85331),x85334))+~P1(f777(f777(f336(x85331),x85332),x85334))+P1(f777(f777(f234(x85331),f777(f777(f105(x85331),x85332),x85333)),f777(f777(f68(x85331,x85331,f105(x85331)),x85333),x85334))) % 174.01/173.90 [8659]~P1(f777(f65(x86591),x86592))+E(f777(f44(x86591),f777(f777(f5(f858(x86591,a845)),x86592),f777(f777(f304(x86591),x86593),x86594))),f777(f777(f5(a851),f777(f44(x86591),f777(f777(f5(f858(x86591,a845)),x86592),x86594))),f82(a851)))+P1(f777(f777(f336(x86591),x86593),x86594))+~P1(f777(f777(f336(x86591),x86593),x86592)) % 174.01/173.90 [8723]E(f777(f777(f84(a3),f350(x87231,x87232,x87233,x87234)),f351(x87231,x87232,x87233,x87234)),x87234)+~P1(f777(f777(f235(a3),f4(a3)),x87233))+~P1(f777(f777(f234(a3),x87234),x87231))+P1(f777(f777(f234(a3),f777(f777(f5(a3),x87234),x87233)),x87231)) % 174.01/173.90 [8724]E(f777(f777(f84(a3),f359(x87241,x87242,x87243,x87244)),f360(x87241,x87242,x87243,x87244)),x87244)+~P1(f777(f777(f235(a3),f4(a3)),x87243))+~P1(f777(f777(f235(a3),x87244),x87241))+P1(f777(f777(f235(a3),f777(f777(f5(a3),x87244),x87243)),x87241)) % 174.01/173.90 [8907]~P1(f777(f777(f235(a3),f4(a3)),x89073))+~P1(f777(f777(f234(a3),x89074),x89071))+P1(f777(f777(f336(a3),f350(x89071,x89072,x89073,x89074)),x89072))+P1(f777(f777(f234(a3),f777(f777(f5(a3),x89074),x89073)),x89071)) % 174.01/173.90 [8908]~P1(f777(f777(f235(a3),f4(a3)),x89083))+~P1(f777(f777(f235(a3),x89084),x89081))+P1(f777(f777(f336(a3),f359(x89081,x89082,x89083,x89084)),x89082))+P1(f777(f777(f235(a3),f777(f777(f5(a3),x89084),x89083)),x89081)) % 174.01/173.90 [8987]~P1(f777(f777(f235(a3),f4(a3)),x89872))+~P1(f777(f777(f235(a3),x89871),x89873))+P1(f777(f777(f336(a3),f360(x89873,x89874,x89872,x89871)),f297(a3,f82(a3),x89872)))+P1(f777(f777(f235(a3),f777(f777(f5(a3),x89871),x89872)),x89873)) % 174.01/173.90 [8988]~P1(f777(f777(f235(a3),f4(a3)),x89882))+~P1(f777(f777(f234(a3),x89881),x89883))+P1(f777(f777(f336(a3),f351(x89883,x89884,x89882,x89881)),f297(a3,f82(a3),x89882)))+P1(f777(f777(f234(a3),f777(f777(f5(a3),x89881),x89882)),x89883)) % 174.01/173.90 [9009]~P1(f777(f777(f235(a3),f4(a3)),x90093))+~P1(f777(f777(f234(a3),f4(a3)),x90094))+~P1(f777(f777(f235(a3),x90094),x90091))+P1(f777(f777(f234(a3),f4(a3)),f777(f777(f84(a3),f777(f777(f85(a3),x90091),f54(a3,x90092,x90093))),x90094))) % 174.01/173.90 [9067]~P100(x90671)+~P1(f777(f65(x90671),x90674))+~P1(f777(f777(f234(x90671),x90672),f690(x90673,x90672,x90674,x90671)))+P1(f777(f777(f234(x90671),f777(f777(f238(x90671),x90672),x90673)),f777(f777(f68(x90671,x90671,f238(x90671)),x90673),x90674))) % 174.01/173.90 [9068]~P98(x90681)+~P1(f777(f65(x90681),x90684))+~P1(f777(f777(f234(x90681),x90682),f694(x90683,x90682,x90684,x90681)))+P1(f777(f777(f234(x90681),f777(f777(f106(x90681),x90682),x90683)),f777(f777(f68(x90681,x90681,f106(x90681)),x90683),x90684))) % 174.01/173.90 [9081]~P1(f777(f777(f234(a3),x90814),f4(a3)))+~P1(f777(f777(f235(a3),f4(a3)),x90812))+~P1(f777(f777(f235(a3),x90811),x90814))+P1(f777(f777(f235(a3),f777(f777(f85(a3),x90811),x90812)),f777(f777(f84(a3),f777(f777(f85(a3),x90811),f54(a3,x90813,x90812))),x90814))) % 174.01/173.90 [9103]P1(f777(f65(x91031),x91032))+~P1(f777(f65(x91031),x91033))+~P1(f777(f777(f336(f858(x91031,a845)),x91032),f777(f777(f63(x91031),x91033),x91034)))+~P1(f777(f777(f234(f858(f857(x91031,x91031),a845)),x91034),f777(f777(f250(x91031,x91031),x91033),f777(f20(f858(x91031,a845),x91031),x91033)))) % 174.01/173.90 [9126]~P100(x91261)+~P1(f777(f65(x91261),x91264))+P1(f777(f777(f336(x91261),f690(x91262,x91263,x91264,x91261)),x91264))+P1(f777(f777(f234(x91261),f777(f777(f238(x91261),x91263),x91262)),f777(f777(f68(x91261,x91261,f238(x91261)),x91262),x91264))) % 174.01/173.90 [9127]~P98(x91271)+~P1(f777(f65(x91271),x91274))+P1(f777(f777(f336(x91271),f694(x91272,x91273,x91274,x91271)),x91274))+P1(f777(f777(f234(x91271),f777(f777(f106(x91271),x91273),x91272)),f777(f777(f68(x91271,x91271,f106(x91271)),x91272),x91274))) % 174.01/173.90 [9499]~P1(f777(f65(x94992),x94994))+~P1(f777(f65(x94991),x94993))+~P1(f777(f777(f234(a851),f777(f44(x94992),x94994)),f777(f44(x94991),x94993)))+P1(f777(f777(f234(f858(x94991,a845)),f777(f305(x94992,x94991,f529(x94993,x94991,x94994,x94992)),x94994)),x94993)) % 174.01/173.90 [9164]~P1(f777(f777(f336(x91641),x91642),x91644))+P1(f777(f777(f336(x91641),x91642),x91643))+~P1(f777(f777(f235(f858(x91641,a845)),x91644),f777(f777(f304(x91641),x91642),x91643)))+P1(f777(f777(f235(f858(x91641,a845)),f777(f777(f5(f858(x91641,a845)),x91644),f777(f777(f304(x91641),x91642),f182(f858(x91641,a845))))),x91643)) % 174.01/173.90 [9316]~P1(f777(f777(f336(x93161),x93162),x93164))+P1(f777(f777(f336(x93161),x93162),x93163))+P1(f777(f777(f235(f858(x93161,a845)),x93164),f777(f777(f304(x93161),x93162),x93163)))+~P1(f777(f777(f235(f858(x93161,a845)),f777(f777(f5(f858(x93161,a845)),x93164),f777(f777(f304(x93161),x93162),f182(f858(x93161,a845))))),x93163)) % 174.01/173.90 [9344]P1(f777(f777(f336(x93441),x93442),x93443))+~P1(f777(f777(f234(f858(x93441,a845)),x93444),x93443))+P1(f777(f777(f235(f858(x93441,a845)),x93444),f777(f777(f304(x93441),x93442),x93443)))+~P1(f777(f777(f235(f858(x93441,a845)),f777(f777(f5(f858(x93441,a845)),x93444),f777(f777(f304(x93441),x93442),f182(f858(x93441,a845))))),x93443)) % 174.01/173.90 [9349]~P1(f777(f777(f336(x93491),x93493),x93492))+~P1(f777(f777(f235(f858(x93491,a845)),x93492),x93494))+P1(f777(f777(f235(f858(x93491,a845)),x93492),f777(f777(f304(x93491),x93493),x93494)))+~P1(f777(f777(f235(f858(x93491,a845)),f777(f777(f5(f858(x93491,a845)),x93492),f777(f777(f304(x93491),x93493),f182(f858(x93491,a845))))),x93494)) % 174.01/173.90 [9361]~P1(f777(f777(f234(f858(x93611,a845)),x93612),x93614))+~P1(f777(f777(f235(f858(x93611,a845)),x93612),x93614))+P1(f777(f777(f235(f858(x93611,a845)),x93612),f777(f777(f304(x93611),x93613),x93614)))+~P1(f777(f777(f235(f858(x93611,a845)),f777(f777(f5(f858(x93611,a845)),x93612),f777(f777(f304(x93611),x93613),f182(f858(x93611,a845))))),x93614)) % 174.01/173.90 [9688]E(f777(f777(f155(x96881),f777(f777(f155(f852(x96881)),f166(x96881,x96882)),x96883)),x96884),f777(f777(f155(x96881),f777(f777(f155(f852(x96881)),x96882),x96884)),x96883))+~P1(f777(f777(f235(a851),x96883),f777(f183(f852(f852(x96881))),f166(x96881,x96882))))+~P18(a851,f777(f144(a851),f777(f777(f145(f852(x96881),a851),f183(f852(x96881))),x96882)))+~P1(f777(f777(f235(a851),x96884),f777(f183(f852(f852(x96881))),f777(f128(f852(x96881),f777(f777(f12(a851,a845,f852(x96881)),f777(f235(a851),x96883)),f183(f852(x96881)))),x96882)))) % 174.01/173.90 [9709]~P1(f777(f777(f336(f857(a851,a851)),x97094),x97091))+~P1(f777(f777(f336(f857(f857(a851,a851),f857(a851,a851))),f777(f777(f243(f857(a851,a851),f857(a851,a851)),x97094),x97092)),a42))+~P1(f777(f777(f336(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),x97091),x97093)),a72))+P1(f777(f777(f336(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),x97091),f777(f777(f304(f857(a851,a851)),x97092),x97093))),a72)) % 174.01/173.90 [9710]~P1(f777(f777(f336(f857(a851,a851)),x97104),x97101))+~P1(f777(f777(f336(f857(f857(a851,a851),f857(a851,a851))),f777(f777(f243(f857(a851,a851),f857(a851,a851)),x97104),x97102)),a74))+~P1(f777(f777(f336(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),x97101),x97103)),a75))+P1(f777(f777(f336(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),x97101),f777(f777(f304(f857(a851,a851)),x97102),x97103))),a75)) % 174.01/173.90 [9722]~P1(f777(f777(f336(f857(a851,a851)),x97224),x97223))+~P1(f777(f777(f336(f857(f857(a851,a851),f857(a851,a851))),f777(f777(f243(f857(a851,a851),f857(a851,a851)),x97221),x97224)),a42))+~P1(f777(f777(f336(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),x97222),x97223)),a43))+P1(f777(f777(f336(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),f777(f777(f304(f857(a851,a851)),x97221),x97222)),x97223)),a43)) % 174.01/173.90 [9723]~P1(f777(f777(f336(f857(a851,a851)),x97234),x97233))+~P1(f777(f777(f336(f857(f857(a851,a851),f857(a851,a851))),f777(f777(f243(f857(a851,a851),f857(a851,a851)),x97231),x97234)),a74))+~P1(f777(f777(f336(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),x97232),x97233)),a73))+P1(f777(f777(f336(f857(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845))),f777(f777(f243(f858(f857(a851,a851),a845),f858(f857(a851,a851),a845)),f777(f777(f304(f857(a851,a851)),x97231),x97232)),x97233)),a73)) % 174.01/173.90 [5915]~P11(x59154,x59151)+~P1(f777(f777(x59151,x59152),x59155))+P1(f777(f777(x59151,x59152),x59153))+~P1(f777(f777(x59151,x59155),x59153)) % 174.01/173.90 [5179]~P6(x51795)+E(x51791,x51792)+~E(x51793,x51794)+~E(f777(f777(f5(x51795),x51793),x51794),f777(f777(f5(x51795),x51791),x51792)) % 174.01/173.90 [6027]~P21(x60275,x60271,x60273)+E(f777(f777(x60271,x60272),f777(x60273,x60274)),f777(x60273,x60274))+~P1(f777(f65(x60275),x60274))+~P1(f777(f777(f336(x60275),x60272),x60274)) % 174.01/173.90 [6224]~P77(x62241)+~E(f777(f777(f5(x62241),x62244),x62245),f777(f777(f5(x62241),x62242),x62243))+~P1(f777(f777(f235(x62241),x62244),x62245))+P1(f777(f777(f235(x62241),x62242),x62243)) % 174.01/173.90 [6226]~P77(x62261)+~E(f777(f777(f5(x62261),x62264),x62265),f777(f777(f5(x62261),x62262),x62263))+~P1(f777(f777(f234(x62261),x62264),x62265))+P1(f777(f777(f234(x62261),x62262),x62263)) % 174.01/173.90 [7231]~E(x72312,f777(f777(f142(x72311),x72314),x72315))+P1(f777(f777(f336(f852(x72311)),x72312),f151(x72311,x72313)))+~P1(f777(f777(f336(f852(x72311)),x72315),f151(x72311,x72313)))+~P1(f777(f777(f336(x72311),x72314),x72313)) % 174.01/173.90 [7665]~E(f777(f183(f852(x76651)),x76653),f777(f183(f852(x76652)),x76654))+~E(f777(f777(f145(f857(x76651,x76652),x76652),f252(x76651,x76652)),x76655),x76654)+~E(f777(f777(f145(f857(x76651,x76652),x76651),f242(x76651,x76652)),x76655),x76653)+E(f777(f777(f169(x76651,x76652),x76653),x76654),x76655) % 174.01/173.90 [8001]~P99(x80011)+P1(f777(f777(f235(f858(x80011,a845)),f297(x80011,x80012,x80013)),f297(x80011,x80014,x80015)))+~P1(f777(f777(f234(x80011),x80014),x80015))+P1(f777(f777(f234(x80011),x80012),x80013)) % 174.01/173.90 [8093]~P99(x80931)+P1(f777(f777(f234(f858(x80931,a845)),f297(x80931,x80932,x80933)),f297(x80931,x80934,x80935)))+~P1(f777(f777(f234(x80931),x80933),x80935))+~P1(f777(f777(f234(x80931),x80934),x80932)) % 174.01/173.90 [8211]~P100(x82111)+P1(f777(f777(f234(x82111),x82112),x82113))+P1(f777(f777(f234(x82111),x82114),x82113))+~P1(f777(f777(f234(f858(x82111,a845)),f777(f296(x82111,x82113),x82112)),f777(f296(x82111,x82114),x82115))) % 174.01/173.90 [8212]~P100(x82121)+P1(f777(f777(f234(x82121),x82122),x82123))+P1(f777(f777(f234(x82121),x82122),x82124))+~P1(f777(f777(f234(f858(x82121,a845)),f777(f296(x82121,x82123),x82122)),f777(f296(x82121,x82125),x82124))) % 174.01/173.90 [8452]~P99(x84521)+~P1(f777(f777(f235(f858(x84521,a845)),f297(x84521,x84524,x84522)),f297(x84521,x84525,x84523)))+P1(f777(f777(f234(x84521),x84522),x84523))+~P1(f777(f777(f234(x84521),x84524),x84522)) % 174.01/173.90 [8453]~P99(x84531)+~P1(f777(f777(f234(f858(x84531,a845)),f297(x84531,x84534,x84532)),f297(x84531,x84535,x84533)))+P1(f777(f777(f234(x84531),x84532),x84533))+~P1(f777(f777(f234(x84531),x84534),x84532)) % 174.01/173.90 [8454]~P99(x84541)+~P1(f777(f777(f235(f858(x84541,a845)),f297(x84541,x84543,x84544)),f297(x84541,x84542,x84545)))+P1(f777(f777(f234(x84541),x84542),x84543))+~P1(f777(f777(f234(x84541),x84543),x84544)) % 174.01/173.90 [8455]~P99(x84551)+~P1(f777(f777(f234(f858(x84551,a845)),f297(x84551,x84553,x84554)),f297(x84551,x84552,x84555)))+P1(f777(f777(f234(x84551),x84552),x84553))+~P1(f777(f777(f234(x84551),x84553),x84554)) % 174.01/173.90 [5914]~P21(x59142,x59145,x59143)+E(x59141,f182(f858(x59142,a845)))+~P1(f777(f65(x59142),x59141))+E(f777(x59143,f777(f777(f304(x59142),x59144),x59141)),f777(f777(x59145,x59144),f777(x59143,x59141))) % 174.01/173.90 [6718]~E(x67181,x67182)+~E(f777(f777(f106(f858(x67183,a845)),x67184),x67185),f182(f858(x67183,a845)))+~P1(f777(f777(f336(x67183),x67182),x67185))+~P1(f777(f777(f336(x67183),x67181),x67184)) % 174.01/173.90 [6805]~P22(x68052,x68055,x68051)+~P1(f777(f65(x68052),x68054))+E(f777(x68051,f777(f777(f304(x68052),x68053),x68054)),f777(f777(f68(x68052,x68052,x68055),x68053),x68054))+P1(f777(f777(f336(x68052),x68053),x68054)) % 174.01/173.90 [6876]~P66(x68762)+~P1(f777(f65(x68761),x68765))+E(f777(f777(f10(x68761,x68762),x68763),f777(f777(f304(x68761),x68764),x68765)),f777(f777(f84(x68762),f777(x68763,x68764)),f777(f777(f10(x68761,x68762),x68763),x68765)))+P1(f777(f777(f336(x68761),x68764),x68765)) % 174.01/173.90 [6878]~P70(x68782)+~P1(f777(f65(x68781),x68785))+E(f777(f777(f13(x68781,x68782),x68783),f777(f777(f304(x68781),x68784),x68785)),f777(f777(f85(x68782),f777(x68783,x68784)),f777(f777(f13(x68781,x68782),x68783),x68785)))+P1(f777(f777(f336(x68781),x68784),x68785)) % 174.01/173.90 [7289]~P85(x72891)+~P1(f777(f65(x72894),x72895))+~P1(f777(f777(f336(x72894),x72893),x72895))+P1(f777(f777(f281(x72891),f777(x72892,x72893)),f777(f777(f13(x72894,x72891),x72892),x72895))) % 174.01/173.90 [7402]~P22(x74022,x74025,x74021)+~P1(f777(f65(x74022),x74024))+E(f777(x74021,f777(f777(f304(x74022),x74023),x74024)),x74023)+~E(f777(f777(f5(f858(x74022,a845)),x74024),f777(f777(f304(x74022),x74023),f182(f858(x74022,a845)))),f182(f858(x74022,a845))) % 174.01/173.90 [7715]~P1(f777(x77151,x77153))+~P1(f777(f777(f189(x77152),x77153),x77155))+~P1(f777(f777(f189(f37(x77151,x77152)),x77155),x77154))+P1(f777(f777(f189(f37(x77151,x77152)),x77153),x77154)) % 174.01/173.90 [7733]~P85(x77331)+~P1(f777(f777(f281(x77331),x77332),x77334))+~P1(f777(f777(f234(a851),x77333),x77335))+P1(f777(f777(f281(x77331),f777(f777(f244(x77331),x77332),x77333)),f777(f777(f244(x77331),x77334),x77335))) % 174.01/173.90 [7767]~P7(x77671)+E(f777(f777(f45(x77671),f777(f777(f85(x77671),x77672),x77673)),f777(f777(f85(x77671),x77674),x77675)),f777(f777(f85(x77671),f777(f777(f45(x77671),x77672),x77674)),f777(f777(f45(x77671),x77673),x77675)))+~P1(f777(f777(f281(x77671),x77675),x77673))+~P1(f777(f777(f281(x77671),x77674),x77672)) % 174.01/173.90 [7771]~P80(x77711)+~P1(f777(f777(f235(x77711),x77713),x77715))+~P1(f777(f777(f235(x77711),x77712),x77714))+P1(f777(f777(f235(x77711),f777(f777(f84(x77711),x77712),x77713)),f777(f777(f84(x77711),x77714),x77715))) % 174.01/173.90 [7772]~P80(x77721)+~P1(f777(f777(f234(x77721),x77722),x77724))+~P1(f777(f777(f235(x77721),x77723),x77725))+P1(f777(f777(f235(x77721),f777(f777(f84(x77721),x77722),x77723)),f777(f777(f84(x77721),x77724),x77725))) % 174.01/173.90 [7773]~P80(x77731)+~P1(f777(f777(f234(x77731),x77733),x77735))+~P1(f777(f777(f235(x77731),x77732),x77734))+P1(f777(f777(f235(x77731),f777(f777(f84(x77731),x77732),x77733)),f777(f777(f84(x77731),x77734),x77735))) % 174.01/173.90 [7774]~P78(x77741)+~P1(f777(f777(f234(x77741),x77743),x77745))+~P1(f777(f777(f234(x77741),x77742),x77744))+P1(f777(f777(f234(x77741),f777(f777(f84(x77741),x77742),x77743)),f777(f777(f84(x77741),x77744),x77745))) % 174.01/173.90 [7775]~P100(x77751)+~P1(f777(f777(f234(x77751),x77753),x77755))+~P1(f777(f777(f234(x77751),x77752),x77754))+P1(f777(f777(f234(x77751),f777(f777(f238(x77751),x77752),x77753)),f777(f777(f238(x77751),x77754),x77755))) % 174.01/173.90 [7776]~P100(x77761)+~P1(f777(f777(f234(x77761),x77763),x77765))+~P1(f777(f777(f234(x77761),x77762),x77764))+P1(f777(f777(f234(x77761),f777(f777(f181(x77761),x77762),x77763)),f777(f777(f181(x77761),x77764),x77765))) % 174.01/173.90 [7777]~P92(x77771)+~P1(f777(f777(f234(x77771),x77773),x77775))+~P1(f777(f777(f234(x77771),x77772),x77774))+P1(f777(f777(f234(x77771),f777(f777(f105(x77771),x77772),x77773)),f777(f777(f105(x77771),x77774),x77775))) % 174.01/173.90 [7778]~P98(x77781)+~P1(f777(f777(f234(x77781),x77783),x77785))+~P1(f777(f777(f234(x77781),x77782),x77784))+P1(f777(f777(f234(x77781),f777(f777(f106(x77781),x77782),x77783)),f777(f777(f106(x77781),x77784),x77785))) % 174.01/173.90 [7779]~P85(x77791)+~P1(f777(f777(f281(x77791),x77793),x77795))+~P1(f777(f777(f281(x77791),x77792),x77794))+P1(f777(f777(f281(x77791),f777(f777(f85(x77791),x77792),x77793)),f777(f777(f85(x77791),x77794),x77795))) % 174.01/173.90 [7912]~P137(x79125)+E(x79121,x79122)+E(x79123,x79124)+~E(f777(f777(f84(x79125),f777(f777(f85(x79125),x79123),x79121)),f777(f777(f85(x79125),x79124),x79122)),f777(f777(f84(x79125),f777(f777(f85(x79125),x79123),x79122)),f777(f777(f85(x79125),x79124),x79121))) % 174.01/173.90 [8050]P31(x80501,x80502,x80503)+~P32(x80501,x80504,x80505)+~P31(x80501,x80502,f562(x80505,x80504,x80501,x80502))+~P1(f777(f777(f336(f850(x80501)),x80503),x80505)) % 174.01/173.90 [8113]~P100(x81134)+~P1(f777(f129(x81131),x81133))+P1(f777(f777(f336(x81131),x81132),f777(f160(x81131),x81133)))+P1(f777(f129(x81131),f777(f777(f140(x81131,x81134,x81135),x81132),x81133))) % 174.01/173.90 [8257]~P66(x82571)+E(f777(f777(f84(x82571),f777(f777(f10(a851,x82571),x82572),f777(f296(a851,x82573),x82574))),f777(f777(f10(a851,x82571),x82572),f777(f296(a851,x82574),x82575))),f777(f777(f10(a851,x82571),x82572),f777(f296(a851,x82573),x82575)))+~P1(f777(f777(f234(a851),x82574),x82575))+~P1(f777(f777(f234(a851),x82573),x82574)) % 174.01/173.90 [8258]~P6(x82581)+E(f777(f777(f5(x82581),f777(f777(f10(a851,x82581),x82582),f777(f296(a851,x82583),x82584))),f777(f777(f10(a851,x82581),x82582),f777(f296(a851,x82583),x82585))),f777(f777(f10(a851,x82581),x82582),f777(f296(a851,x82585),x82584)))+~P1(f777(f777(f234(a851),x82585),x82584))+~P1(f777(f777(f234(a851),x82583),x82585)) % 174.01/173.90 [8577]~P61(x85772)+E(x85771,f4(x85772))+E(x85773,f4(x85772))+E(f777(f777(f285(x85772),f777(f777(f84(x85772),f777(f777(f85(x85772),x85774),x85771)),f777(f777(f85(x85772),x85775),x85773))),f777(f777(f85(x85772),x85773),x85771)),f777(f777(f84(x85772),f777(f777(f285(x85772),x85774),x85773)),f777(f777(f285(x85772),x85775),x85771))) % 174.01/173.90 [8578]~P61(x85782)+E(x85781,f4(x85782))+E(x85783,f4(x85782))+E(f777(f777(f285(x85782),f777(f777(f5(x85782),f777(f777(f85(x85782),x85784),x85781)),f777(f777(f85(x85782),x85785),x85783))),f777(f777(f85(x85782),x85783),x85781)),f777(f777(f5(x85782),f777(f777(f285(x85782),x85784),x85783)),f777(f777(f285(x85782),x85785),x85781))) % 174.01/173.90 [8587]~E(x85872,f777(x85873,x85871))+E(x85871,f525(x85872,x85873,x85874,x85875))+~P29(x85875,x85874,x85873,f241(f858(x85875,a845)))+~P1(f777(f777(f336(x85874),x85872),f777(f305(x85875,x85874,x85873),f241(f858(x85875,a845))))) % 174.01/173.90 [8771]~P110(x87711)+~P1(f777(f777(f235(x87711),f777(f79(x87711),x87712)),x87714))+P1(f777(f777(f235(x87711),f777(f777(f85(x87711),f777(f79(x87711),x87712)),f777(f79(x87711),x87713))),f777(f777(f85(x87711),x87714),x87715)))+~P1(f777(f777(f235(x87711),f777(f79(x87711),x87713)),x87715)) % 174.01/173.90 [8785]~P32(x87851,x87855,x87854)+P31(x87851,x87852,x87853)+P1(f777(f777(f336(f850(x87851)),f562(x87854,x87855,x87851,x87852)),x87855))+~P1(f777(f777(f336(f850(x87851)),x87853),x87854)) % 174.01/173.90 [8865]~P29(x88651,x88653,x88655,x88652)+~P1(f777(f65(x88653),x88654))+P1(f777(f777(f234(a851),f777(f44(x88651),x88652)),f777(f44(x88653),x88654)))+~P1(f777(f777(f234(f858(x88653,a845)),f777(f305(x88651,x88653,x88655),x88652)),x88654)) % 174.01/173.90 [8934]~P66(x89342)+~P29(x89341,x89341,x89344,x89345)+~P1(f777(f65(x89341),x89345))+E(f777(f777(f10(x89341,x89342),f777(f77(x89341,x89342,x89341,x89343),x89344)),x89345),f777(f777(f10(x89341,x89342),x89343),f777(f305(x89341,x89341,x89344),x89345))) % 174.01/173.90 [8935]~P70(x89352)+~P29(x89351,x89351,x89354,x89355)+~P1(f777(f65(x89351),x89355))+E(f777(f777(f13(x89351,x89352),f777(f77(x89351,x89352,x89351,x89353),x89354)),x89355),f777(f777(f13(x89351,x89352),x89353),f777(f305(x89351,x89351,x89354),x89355))) % 174.01/173.90 [9047]~P36(x90471,x90472)+~P1(f777(f777(f336(x90471),x90473),x90474))+~P1(f777(f777(f336(x90471),x90475),x90474))+~P1(f777(f777(f336(f857(x90471,x90471)),f777(f777(f243(x90471,x90471),x90475),f696(x90472,x90471,x90474))),x90472)) % 174.01/173.90 [9080]~P29(x90802,x90803,x90805,x90801)+E(x90801,f182(f858(x90802,a845)))+E(f777(f305(x90803,x90802,f527(x90804,x90803,x90802,x90801)),x90804),x90801)+~P1(f777(f777(f234(f858(x90803,a845)),f777(f305(x90802,x90803,x90805),x90801)),x90804)) % 174.01/173.90 [9522]~P100(x95225)+~P9(x95225)+P1(f777(f777(f336(x95221),f392(x95222,x95223,x95221,x95224,x95225)),x95223))+~P1(f777(f777(f235(x95225),x95224),f777(f777(f48(x95221,x95225),x95223),x95222))) % 174.01/173.90 [9527]~P100(x95271)+~P9(x95271)+P1(f777(f777(f235(x95271),x95272),f777(x95273,f392(x95273,x95274,x95275,x95272,x95271))))+~P1(f777(f777(f235(x95271),x95272),f777(f777(f48(x95275,x95271),x95274),x95273))) % 174.01/173.90 [9596]~P64(x95961)+~P1(f777(f70(x95961,x95961,f85(x95961),x95962,x95963),x95965))+P1(f777(f777(f336(x95961),x95962),x95963))+P1(f777(f70(x95961,x95961,f85(x95961),x95964,f777(f777(f304(x95961),x95962),x95963)),f777(f777(f85(x95961),x95964),x95965))) % 174.01/173.90 [9805]~P66(x98052)+~P1(f777(f65(x98051),x98055))+E(f777(f777(f10(x98051,x98052),f777(f777(f11(x98051,x98052,x98052),f777(f777(f22(x98051,x98052,f858(x98052,x98052)),f777(f777(f12(a845,f858(x98052,f858(x98052,x98052)),x98051),f100(x98052)),f777(a332,x98053))),x98054)),f4(x98052))),x98055),f4(x98052))+P1(f777(f777(f336(x98051),x98053),x98055)) % 174.01/173.90 [9806]~P70(x98062)+~P1(f777(f65(x98061),x98065))+E(f777(f777(f13(x98061,x98062),f777(f777(f11(x98061,x98062,x98062),f777(f777(f22(x98061,x98062,f858(x98062,x98062)),f777(f777(f12(a845,f858(x98062,f858(x98062,x98062)),x98061),f100(x98062)),f777(a332,x98063))),x98064)),f82(x98062))),x98065),f82(x98062))+P1(f777(f777(f336(x98061),x98063),x98065)) % 174.01/173.90 [9807]~P66(x98072)+~P1(f777(f65(x98071),x98075))+E(f777(f777(f10(x98071,x98072),f777(f777(f11(x98071,x98072,x98072),f777(f777(f22(x98071,x98072,f858(x98072,x98072)),f777(f777(f12(a845,f858(x98072,f858(x98072,x98072)),x98071),f100(x98072)),f777(a332,x98073))),x98074)),f4(x98072))),x98075),f777(x98074,x98073))+~P1(f777(f777(f336(x98071),x98073),x98075)) % 174.01/173.90 [9808]~P70(x98082)+~P1(f777(f65(x98081),x98085))+E(f777(f777(f13(x98081,x98082),f777(f777(f11(x98081,x98082,x98082),f777(f777(f22(x98081,x98082,f858(x98082,x98082)),f777(f777(f12(a845,f858(x98082,f858(x98082,x98082)),x98081),f100(x98082)),f777(a332,x98083))),x98084)),f82(x98082))),x98085),f777(x98084,x98083))+~P1(f777(f777(f336(x98081),x98083),x98085)) % 174.01/173.90 [9869]~P66(x98692)+~P1(f777(f65(x98691),x98695))+E(f777(f777(f10(x98691,x98692),f777(f777(f11(x98691,x98692,x98692),f777(f777(f22(x98691,x98692,f858(x98692,x98692)),f777(f777(f12(a845,f858(x98692,f858(x98692,x98692)),x98691),f100(x98692)),f777(f777(f11(x98691,x98691,a845),a332),x98693))),x98694)),f4(x98692))),x98695),f4(x98692))+P1(f777(f777(f336(x98691),x98693),x98695)) % 174.01/173.90 [9870]~P70(x98702)+~P1(f777(f65(x98701),x98705))+E(f777(f777(f13(x98701,x98702),f777(f777(f11(x98701,x98702,x98702),f777(f777(f22(x98701,x98702,f858(x98702,x98702)),f777(f777(f12(a845,f858(x98702,f858(x98702,x98702)),x98701),f100(x98702)),f777(f777(f11(x98701,x98701,a845),a332),x98703))),x98704)),f82(x98702))),x98705),f82(x98702))+P1(f777(f777(f336(x98701),x98703),x98705)) % 174.01/173.90 [9872]~P66(x98722)+~P1(f777(f65(x98721),x98725))+E(f777(f777(f10(x98721,x98722),f777(f777(f11(x98721,x98722,x98722),f777(f777(f22(x98721,x98722,f858(x98722,x98722)),f777(f777(f12(a845,f858(x98722,f858(x98722,x98722)),x98721),f100(x98722)),f777(f777(f11(x98721,x98721,a845),a332),x98723))),x98724)),f4(x98722))),x98725),f777(x98724,x98723))+~P1(f777(f777(f336(x98721),x98723),x98725)) % 174.01/173.90 [9873]~P70(x98732)+~P1(f777(f65(x98731),x98735))+E(f777(f777(f13(x98731,x98732),f777(f777(f11(x98731,x98732,x98732),f777(f777(f22(x98731,x98732,f858(x98732,x98732)),f777(f777(f12(a845,f858(x98732,f858(x98732,x98732)),x98731),f100(x98732)),f777(f777(f11(x98731,x98731,a845),a332),x98733))),x98734)),f82(x98732))),x98735),f777(x98734,x98733))+~P1(f777(f777(f336(x98731),x98733),x98735)) % 174.01/173.90 [7770]~P6(x77702)+~P1(f777(f65(x77701),x77704))+E(f777(f777(f10(x77701,x77702),x77703),f777(f777(f5(f858(x77701,a845)),x77704),f777(f777(f304(x77701),x77705),f182(f858(x77701,a845))))),f777(f777(f10(x77701,x77702),x77703),x77704))+P1(f777(f777(f336(x77701),x77705),x77704)) % 174.01/173.90 [8263]~P121(x82632)+~P1(f777(f65(x82631),x82634))+E(f777(f777(f10(x82631,x82632),x82633),f777(f777(f5(f858(x82631,a845)),x82634),f777(f777(f304(x82631),x82635),f182(f858(x82631,a845))))),f777(f777(f5(x82632),f777(f777(f10(x82631,x82632),x82633),x82634)),f777(x82633,x82635)))+~P1(f777(f777(f336(x82631),x82635),x82634)) % 174.01/173.90 [8264]~P6(x82642)+~P1(f777(f65(x82641),x82644))+E(f777(f777(f10(x82641,x82642),x82643),f777(f777(f5(f858(x82641,a845)),x82644),f777(f777(f304(x82641),x82645),f182(f858(x82641,a845))))),f777(f777(f5(x82642),f777(f777(f10(x82641,x82642),x82643),x82644)),f777(x82643,x82645)))+~P1(f777(f777(f336(x82641),x82645),x82644)) % 174.01/173.90 [8275]~P85(x82751)+~P1(f777(f777(f234(a851),x82753),x82755))+~P1(f777(f777(f281(x82751),f777(f777(f244(x82751),x82752),x82755)),x82754))+P1(f777(f777(f281(x82751),f777(f777(f244(x82751),x82752),x82753)),x82754)) % 174.01/173.90 [8292]~P6(x82921)+~P1(f777(f65(x82922),x82924))+E(f777(f777(f5(x82921),f777(f777(f10(x82922,x82921),x82923),x82924)),f777(f777(f10(x82922,x82921),x82923),x82925)),f777(f777(f10(x82922,x82921),x82923),f777(f777(f5(f858(x82922,a845)),x82924),x82925)))+~P1(f777(f777(f234(f858(x82922,a845)),x82925),x82924)) % 174.01/173.90 [8313]P1(f777(f65(x83131),f777(x83132,x83133)))+~P1(f777(f65(x83134),x83135))+~P1(f777(f777(f336(x83134),x83133),x83135))+~P1(f777(f65(x83131),f777(f777(f48(x83134,f858(x83131,a845)),x83135),x83132))) % 174.01/173.90 [8736]~P12(x87361,x87365,x87364)+~E(f777(f279(x87361,x87361,x87364),f777(f777(f304(x87361),x87362),f182(f858(x87361,a845)))),f777(f279(x87361,x87361,x87364),f777(f777(f304(x87361),x87363),f182(f858(x87361,a845)))))+~P1(f777(f777(f336(x87361),x87363),x87365))+P1(f777(f777(f336(f857(x87361,x87361)),f777(f777(f243(x87361,x87361),x87362),x87363)),x87364)) % 174.01/173.90 [9007]~P1(f777(x90071,x90075))+P1(f777(x90071,f383(x90071,x90072,x90073,x90074)))+P1(f777(x90071,f381(x90071,x90072,x90073,x90074)))+~P1(f777(f777(f336(x90074),x90075),f777(f777(f105(f858(x90074,a845)),x90073),x90072))) % 174.01/173.90 [9168]~P1(f777(x91681,x91685))+P1(f777(x91681,f381(x91681,x91682,x91683,x91684)))+P1(f777(f777(f336(x91684),f383(x91681,x91682,x91683,x91684)),x91682))+~P1(f777(f777(f336(x91684),x91685),f777(f777(f105(f858(x91684,a845)),x91683),x91682))) % 174.01/173.90 [9169]~P1(f777(x91691,x91695))+P1(f777(x91691,f383(x91691,x91692,x91693,x91694)))+P1(f777(f777(f336(x91694),f381(x91691,x91692,x91693,x91694)),x91693))+~P1(f777(f777(f336(x91694),x91695),f777(f777(f105(f858(x91694,a845)),x91693),x91692))) % 174.01/173.90 [9173]P1(f777(x91731,x91732))+~P1(f777(x91731,f387(x91731,x91733,x91734,x91735)))+~P1(f777(x91731,f386(x91731,x91733,x91734,x91735)))+~P1(f777(f777(f336(x91735),x91732),f777(f777(f105(f858(x91735,a845)),x91734),x91733))) % 174.01/173.90 [9206]E(x92061,x92062)+~P1(f777(f777(f336(f857(x92063,x92063)),f777(f777(f243(x92063,x92063),x92061),x92062)),f302(x92063,x92065)))+P1(f777(f777(f336(x92063),x92061),x92064))+~P1(f777(f777(f234(f858(f857(x92063,x92063),a845)),x92065),f777(f777(f250(x92063,x92063),x92064),f777(f20(f858(x92063,a845),x92063),x92064)))) % 174.01/173.90 [9223]P1(f777(x92231,x92232))+~P1(f777(x92231,f386(x92231,x92234,x92235,x92233)))+P1(f777(f777(f336(x92233),f387(x92231,x92234,x92235,x92233)),x92234))+~P1(f777(f777(f336(x92233),x92232),f777(f777(f105(f858(x92233,a845)),x92235),x92234))) % 174.01/173.90 [9224]P1(f777(x92241,x92242))+~P1(f777(x92241,f387(x92241,x92244,x92245,x92243)))+P1(f777(f777(f336(x92243),f386(x92241,x92244,x92245,x92243)),x92245))+~P1(f777(f777(f336(x92243),x92242),f777(f777(f105(f858(x92243,a845)),x92245),x92244))) % 174.01/173.90 [9286]P1(f777(x92861,x92862))+P1(f777(f777(f336(x92863),f387(x92861,x92864,x92865,x92863)),x92864))+P1(f777(f777(f336(x92863),f386(x92861,x92864,x92865,x92863)),x92865))+~P1(f777(f777(f336(x92863),x92862),f777(f777(f105(f858(x92863,a845)),x92865),x92864))) % 174.01/173.90 [9288]~P1(f777(x92882,x92885))+P1(f777(f777(f336(x92881),f383(x92882,x92883,x92884,x92881)),x92883))+P1(f777(f777(f336(x92881),f381(x92882,x92883,x92884,x92881)),x92884))+~P1(f777(f777(f336(x92881),x92885),f777(f777(f105(f858(x92881,a845)),x92884),x92883))) % 174.01/173.90 [9435]~P12(x94351,x94355,x94354)+~P1(f777(f777(f336(x94351),x94353),x94355))+P1(f777(f777(f336(f857(x94351,x94351)),f777(f777(f243(x94351,x94351),x94352),x94353)),x94354))+~P1(f777(f777(f234(f858(x94351,a845)),f777(f279(x94351,x94351,x94354),f777(f777(f304(x94351),x94353),f182(f858(x94351,a845))))),f777(f279(x94351,x94351,x94354),f777(f777(f304(x94351),x94352),f182(f858(x94351,a845)))))) % 174.01/173.90 [9551]~P100(x95515)+~P9(x95515)+P1(f777(f777(f336(x95511),f663(x95512,x95513,x95514,x95511,x95515)),x95514))+~P1(f777(f777(f235(x95515),f777(f777(f49(x95511,x95515),x95514),x95513)),x95512)) % 174.01/173.90 [9583]~P67(x95835)+~P78(x95835)+P1(f777(f777(f336(x95831),f754(x95832,x95833,x95834,x95831,x95835)),f777(f160(x95831),x95834)))+P1(f777(f777(f234(x95835),f777(f157(x95835),f777(f777(f145(x95831,x95835),x95833),x95834))),f777(f157(x95835),f777(f777(f145(x95831,x95835),x95832),x95834)))) % 174.01/173.90 [9678]~P100(x96781)+~P9(x96781)+P1(f777(f777(f235(x96781),f777(x96782,f663(x96783,x96782,x96784,x96785,x96781))),x96783))+~P1(f777(f777(f235(x96781),f777(f777(f49(x96785,x96781),x96784),x96782)),x96783)) % 174.01/173.90 [9822]~P67(x98221)+~P78(x98221)+~P1(f777(f777(f234(x98221),f777(x98223,f754(x98225,x98223,x98224,x98222,x98221))),f777(x98225,f754(x98225,x98223,x98224,x98222,x98221))))+P1(f777(f777(f234(x98221),f777(f157(x98221),f777(f777(f145(x98222,x98221),x98223),x98224))),f777(f157(x98221),f777(f777(f145(x98222,x98221),x98225),x98224)))) % 174.01/173.90 [8595]~P66(x85951)+~P1(f777(f65(x85954),x85955))+~P1(f777(f777(f336(x85954),x85953),x85955))+E(f777(f777(f84(x85951),f777(x85952,x85953)),f777(f777(f10(x85954,x85951),x85952),f777(f777(f5(f858(x85954,a845)),x85955),f777(f777(f304(x85954),x85953),f182(f858(x85954,a845)))))),f777(f777(f10(x85954,x85951),x85952),x85955)) % 174.01/173.90 [8596]~P70(x85961)+~P1(f777(f65(x85964),x85965))+~P1(f777(f777(f336(x85964),x85963),x85965))+E(f777(f777(f85(x85961),f777(x85962,x85963)),f777(f777(f13(x85964,x85961),x85962),f777(f777(f5(f858(x85964,a845)),x85965),f777(f777(f304(x85964),x85963),f182(f858(x85964,a845)))))),f777(f777(f13(x85964,x85961),x85962),x85965)) % 174.01/173.90 [8649]~P22(x86491,x86494,x86495)+~P1(f777(f65(x86491),x86492))+E(f777(f777(f5(f858(x86491,a845)),x86492),f777(f777(f304(x86491),x86493),f182(f858(x86491,a845)))),f182(f858(x86491,a845)))+E(f777(f777(x86494,x86493),f777(x86495,f777(f777(f5(f858(x86491,a845)),x86492),f777(f777(f304(x86491),x86493),f182(f858(x86491,a845)))))),f777(x86495,f777(f777(f304(x86491),x86493),x86492))) % 174.01/173.90 [8982]~P66(x89821)+~P1(f777(f65(x89822),x89825))+~P1(f777(f65(x89822),x89824))+E(f777(f777(f84(x89821),f777(f777(f10(x89822,x89821),x89823),f777(f777(f105(f858(x89822,a845)),x89824),x89825))),f777(f777(f10(x89822,x89821),x89823),f777(f777(f106(f858(x89822,a845)),x89824),x89825))),f777(f777(f84(x89821),f777(f777(f10(x89822,x89821),x89823),x89824)),f777(f777(f10(x89822,x89821),x89823),x89825))) % 174.01/173.90 [8984]~P70(x89841)+~P1(f777(f65(x89842),x89845))+~P1(f777(f65(x89842),x89844))+E(f777(f777(f85(x89841),f777(f777(f13(x89842,x89841),x89843),f777(f777(f105(f858(x89842,a845)),x89844),x89845))),f777(f777(f13(x89842,x89841),x89843),f777(f777(f106(f858(x89842,a845)),x89844),x89845))),f777(f777(f85(x89841),f777(f777(f13(x89842,x89841),x89843),x89844)),f777(f777(f13(x89842,x89841),x89843),x89845))) % 174.01/173.90 [9118]~P6(x91181)+~P1(f777(f65(x91182),x91185))+~P1(f777(f65(x91182),x91184))+E(f777(f777(f5(x91181),f777(f777(f84(x91181),f777(f777(f10(x91182,x91181),x91183),x91184)),f777(f777(f10(x91182,x91181),x91183),x91185))),f777(f777(f10(x91182,x91181),x91183),f777(f777(f106(f858(x91182,a845)),x91184),x91185))),f777(f777(f10(x91182,x91181),x91183),f777(f777(f105(f858(x91182,a845)),x91184),x91185))) % 174.01/173.90 [9300]~P29(x93001,x93002,x93003,x93005)+~P29(x93001,x93002,x93003,x93004)+P29(x93001,x93002,x93003,f777(f777(f105(f858(x93001,a845)),x93004),x93005))+~E(f777(f777(f106(f858(x93002,a845)),f777(f305(x93001,x93002,x93003),f777(f777(f5(f858(x93001,a845)),x93004),x93005))),f777(f305(x93001,x93002,x93003),f777(f777(f5(f858(x93001,a845)),x93005),x93004))),f182(f858(x93002,a845))) % 174.01/173.90 [9407]E(x94071,f4(a3))+~P1(f777(f777(f235(a3),f4(a3)),x94073))+~P1(f777(f58(x94072,x94071),f777(f777(f243(a3,a3),x94074),x94075)))+P1(f777(f58(x94072,f777(f777(f85(a3),x94071),x94073)),f777(f777(f243(a3,a3),f777(f777(f45(a3),x94074),x94073)),f777(f777(f84(a3),f777(f777(f85(a3),x94071),f54(a3,x94074,x94073))),x94075)))) % 174.01/173.90 [9415]~P1(f777(f777(f235(a851),f4(a851)),x94153))+~P1(f777(f777(f235(a851),f4(a851)),x94152))+~P1(f777(f57(x94151,x94152),f777(f777(f243(a851,a851),x94154),x94155)))+P1(f777(f57(x94151,f777(f777(f85(a851),x94152),x94153)),f777(f777(f243(a851,a851),f777(f777(f45(a851),x94154),x94153)),f777(f777(f84(a851),f777(f777(f85(a851),x94152),f54(a851,x94154,x94153))),x94155)))) % 174.01/173.90 [9465]E(f777(f777(f84(a3),f365(x94651,x94652,x94653,x94654,x94655)),f366(x94651,x94652,x94653,x94654,x94655)),x94655)+~P1(f777(f777(f281(a3),x94654),x94653))+~P1(f777(f777(f281(a3),x94654),f777(f777(f84(a3),x94655),x94651)))+P1(f777(f777(f281(a3),x94654),f777(f777(f84(a3),f777(f777(f5(a3),x94655),x94653)),x94651))) % 174.01/173.90 [9466]E(f777(f777(f5(a3),f367(x94661,x94662,x94663,x94664,x94665)),f368(x94661,x94662,x94663,x94664,x94665)),x94665)+~P1(f777(f777(f281(a3),x94664),x94663))+~P1(f777(f777(f281(a3),x94664),f777(f777(f84(a3),x94665),x94661)))+P1(f777(f777(f281(a3),x94664),f777(f777(f84(a3),f777(f777(f84(a3),x94665),x94663)),x94661))) % 174.01/173.90 [9467]~P70(x94671)+~P1(f777(f65(x94672),x94675))+~P1(f777(f65(x94672),x94674))+E(f777(f777(f85(x94671),f777(f777(f777(f69(x94671,x94672,f85(x94671)),x94673),f82(x94671)),f777(f777(f105(f858(x94672,a845)),x94674),x94675))),f777(f777(f777(f69(x94671,x94672,f85(x94671)),x94673),f82(x94671)),f777(f777(f106(f858(x94672,a845)),x94674),x94675))),f777(f777(f85(x94671),f777(f777(f777(f69(x94671,x94672,f85(x94671)),x94673),f82(x94671)),x94674)),f777(f777(f777(f69(x94671,x94672,f85(x94671)),x94673),f82(x94671)),x94675))) % 174.01/173.90 [9469]~E(f777(f777(f161(x94691),x94695),x94692),f777(f777(f161(x94691),x94695),x94693))+P1(f777(f777(f336(f857(f852(x94691),f852(x94691))),f777(f777(f243(f852(x94691),f852(x94691)),x94692),x94693)),f139(x94691,x94694)))+~P1(f777(f777(f235(a851),x94695),f777(f777(f238(a851),f777(f183(f852(x94691)),x94692)),f777(f183(f852(x94691)),x94693))))+~P1(f777(f777(f336(f857(x94691,x94691)),f777(f777(f243(x94691,x94691),f777(f777(f155(x94691),x94692),x94695)),f777(f777(f155(x94691),x94693),x94695))),x94694)) % 174.01/173.90 [9478]E(f777(f777(f84(a3),f369(x94781,x94782,x94783,x94784,x94785)),f370(x94781,x94782,x94783,x94784,x94785)),x94785)+~P1(f777(f777(f281(a3),x94784),x94783))+P1(f777(f777(f281(a3),x94784),f777(f777(f84(a3),x94785),x94781)))+~P1(f777(f777(f281(a3),x94784),f777(f777(f84(a3),f777(f777(f5(a3),x94785),x94783)),x94781))) % 174.01/173.90 [9479]E(f777(f777(f5(a3),f362(x94791,x94792,x94793,x94794,x94795)),f363(x94791,x94792,x94793,x94794,x94795)),x94795)+~P1(f777(f777(f281(a3),x94794),x94793))+P1(f777(f777(f281(a3),x94794),f777(f777(f84(a3),x94795),x94791)))+~P1(f777(f777(f281(a3),x94794),f777(f777(f84(a3),f777(f777(f84(a3),x94795),x94793)),x94791))) % 174.01/173.90 [9560]~P1(f777(f777(f281(a3),x95604),x95603))+P1(f777(f777(f336(a3),f367(x95601,x95602,x95603,x95604,x95605)),x95602))+~P1(f777(f777(f281(a3),x95604),f777(f777(f84(a3),x95605),x95601)))+P1(f777(f777(f281(a3),x95604),f777(f777(f84(a3),f777(f777(f84(a3),x95605),x95603)),x95601))) % 174.01/173.90 [9561]~P1(f777(f777(f281(a3),x95614),x95613))+P1(f777(f777(f336(a3),f365(x95611,x95612,x95613,x95614,x95615)),x95612))+~P1(f777(f777(f281(a3),x95614),f777(f777(f84(a3),x95615),x95611)))+P1(f777(f777(f281(a3),x95614),f777(f777(f84(a3),f777(f777(f5(a3),x95615),x95613)),x95611))) % 174.01/173.90 [9568]~P1(f777(f777(f281(a3),x95684),x95683))+P1(f777(f777(f336(a3),f368(x95681,x95682,x95683,x95684,x95685)),f297(a3,f82(a3),x95683)))+~P1(f777(f777(f281(a3),x95684),f777(f777(f84(a3),x95685),x95681)))+P1(f777(f777(f281(a3),x95684),f777(f777(f84(a3),f777(f777(f84(a3),x95685),x95683)),x95681))) % 174.01/173.90 [9569]~P1(f777(f777(f281(a3),x95694),x95693))+P1(f777(f777(f336(a3),f366(x95691,x95692,x95693,x95694,x95695)),f297(a3,f82(a3),x95693)))+~P1(f777(f777(f281(a3),x95694),f777(f777(f84(a3),x95695),x95691)))+P1(f777(f777(f281(a3),x95694),f777(f777(f84(a3),f777(f777(f5(a3),x95695),x95693)),x95691))) % 174.01/173.90 [9570]~P2(x95705)+~P78(x95705)+P1(f777(f777(f336(x95701),f442(x95702,x95703,x95704,x95701,x95705)),x95704))+P1(f777(f777(f234(x95705),f777(f777(f10(x95701,x95705),x95703),x95704)),f777(f777(f85(x95705),f777(f104(x95705),f777(f44(x95701),x95704))),x95702))) % 174.01/173.90 [9571]~P1(f777(f777(f281(a3),x95714),x95713))+P1(f777(f777(f336(a3),f362(x95711,x95712,x95713,x95714,x95715)),x95712))+P1(f777(f777(f281(a3),x95714),f777(f777(f84(a3),x95715),x95711)))+~P1(f777(f777(f281(a3),x95714),f777(f777(f84(a3),f777(f777(f84(a3),x95715),x95713)),x95711))) % 174.01/173.90 [9572]~P1(f777(f777(f281(a3),x95724),x95723))+P1(f777(f777(f336(a3),f369(x95721,x95722,x95723,x95724,x95725)),x95722))+P1(f777(f777(f281(a3),x95724),f777(f777(f84(a3),x95725),x95721)))+~P1(f777(f777(f281(a3),x95724),f777(f777(f84(a3),f777(f777(f5(a3),x95725),x95723)),x95721))) % 174.01/173.90 [9573]~P1(f777(f777(f281(a3),x95731),x95735))+P1(f777(f777(f336(a3),f363(x95733,x95734,x95735,x95731,x95732)),f297(a3,f82(a3),x95735)))+P1(f777(f777(f281(a3),x95731),f777(f777(f84(a3),x95732),x95733)))+~P1(f777(f777(f281(a3),x95731),f777(f777(f84(a3),f777(f777(f84(a3),x95732),x95735)),x95733))) % 174.01/173.90 [9574]~P1(f777(f777(f281(a3),x95741),x95745))+P1(f777(f777(f336(a3),f370(x95743,x95744,x95745,x95741,x95742)),f297(a3,f82(a3),x95745)))+P1(f777(f777(f281(a3),x95741),f777(f777(f84(a3),x95742),x95743)))+~P1(f777(f777(f281(a3),x95741),f777(f777(f84(a3),f777(f777(f5(a3),x95742),x95745)),x95743))) % 174.01/173.90 [9738]~P2(x97381)+~P78(x97381)+~P1(f777(f777(f234(x97381),f777(x97383,f442(x97385,x97383,x97384,x97382,x97381))),x97385))+P1(f777(f777(f234(x97381),f777(f777(f10(x97382,x97381),x97383),x97384)),f777(f777(f85(x97381),f777(f104(x97381),f777(f44(x97382),x97384))),x97385))) % 174.01/173.90 [8621]E(f777(f777(f127(x86211),x86212),x86213),f777(f777(f127(x86211),x86214),x86215))+~E(f777(f777(f161(x86211),f777(f183(f852(x86211)),x86212)),x86214),x86212)+~E(f777(f777(f127(x86211),f777(f777(f130(x86211),f777(f183(f852(x86211)),x86212)),x86214)),x86215),x86213)+P1(f777(f777(f234(a851),f777(f183(f852(x86211)),x86214)),f777(f183(f852(x86211)),x86212))) % 174.01/173.90 [8734]E(f777(f777(f127(x87341),x87342),x87343),f777(f777(f127(x87341),x87344),x87345))+~E(f777(f777(f161(x87341),f777(f183(f852(x87341)),x87342)),x87344),x87342)+~E(x87343,f777(f777(f127(x87341),f777(f777(f130(x87341),f777(f183(f852(x87341)),x87342)),x87344)),x87345))+~P1(f777(f777(f234(a851),f777(f183(f852(x87341)),x87342)),f777(f183(f852(x87341)),x87344))) % 174.01/173.90 [9890]~P1(f777(x98905,x98904))+~P1(f777(f65(x98902),f777(f258(x98902),x98905)))+P1(f777(f65(x98901),f777(f258(x98901),f777(f777(f11(x98901,x98902,a845),x98903),x98904))))+~P1(f777(f65(x98901),f777(f258(x98901),f777(f777(f12(f858(x98902,a845),a845,x98901),f91(x98902)),f777(f777(f12(f858(x98902,a845),f858(x98902,a845),x98901),f777(f22(x98902,a845,a845),f777(f777(f12(a845,f858(a845,a845),x98902),a333),x98905))),x98903))))) % 174.01/173.90 [7916]~P39(x79162,x79163,x79164,x79166)+~P39(f37(x79161,x79162),x79166,x79164,x79165)+P39(f37(x79161,x79162),x79163,x79164,x79165)+~P1(f777(x79161,x79163)) % 174.01/173.90 [8428]~P23(x84285,x84281,x84286,x84282)+E(f777(f77(x84281,x84281,x84281,f777(x84282,x84283)),f777(x84282,x84284)),f777(f77(x84281,x84281,x84281,f777(x84282,x84284)),f777(x84282,x84283)))+~P1(f777(f65(x84285),x84284))+~P1(f777(f65(x84285),x84283)) % 174.01/173.90 [7826]~P29(x78261,x78262,x78264,x78263)+~E(f777(x78264,x78266),x78265)+E(f777(f81(x78261,x78262,x78263,x78264),x78265),x78266)+~P1(f777(f777(f336(x78261),x78266),x78263)) % 174.01/173.90 [8019]~P24(x80196,x80191,x80194,x80192)+E(f777(f77(x80191,x80191,x80191,f777(x80192,x80193)),f777(x80194,x80195)),f777(x80192,x80193))+~P1(f777(f65(x80196),x80193))+~P1(f777(f777(f336(x80196),x80195),x80193)) % 174.01/173.90 [9156]~P23(x91563,x91561,x91566,x91562)+E(f777(f77(x91561,x91561,x91561,f777(x91562,f777(f777(f5(f858(x91563,a845)),x91564),f777(f777(f304(x91563),x91565),f182(f858(x91563,a845)))))),f777(x91566,x91565)),f777(x91562,x91564))+~P1(f777(f65(x91563),x91564))+~P1(f777(f777(f336(x91563),x91565),x91564)) % 174.01/173.90 [6883]~P7(x68831)+~E(f54(x68831,x68833,x68834),f54(x68831,x68836,x68834))+~E(f54(x68831,x68832,x68834),f54(x68831,x68835,x68834))+E(f54(x68831,f777(f777(f84(x68831),x68832),x68833),x68834),f54(x68831,f777(f777(f84(x68831),x68835),x68836),x68834)) % 174.01/173.90 [6884]~P7(x68841)+~E(f54(x68841,x68843,x68844),f54(x68841,x68846,x68844))+~E(f54(x68841,x68842,x68844),f54(x68841,x68845,x68844))+E(f54(x68841,f777(f777(f85(x68841),x68842),x68843),x68844),f54(x68841,f777(f777(f85(x68841),x68845),x68846),x68844)) % 174.01/173.90 [6885]~P8(x68851)+~E(f54(x68851,x68853,x68854),f54(x68851,x68856,x68854))+~E(f54(x68851,x68852,x68854),f54(x68851,x68855,x68854))+E(f54(x68851,f777(f777(f5(x68851),x68852),x68853),x68854),f54(x68851,f777(f777(f5(x68851),x68855),x68856),x68854)) % 174.01/173.90 [7717]~P20(x77171,x77172,x77173)+~P1(f777(f65(x77171),x77176))+E(f777(f777(f68(x77171,x77172,x77173),x77174),f777(f777(f304(x77171),x77175),x77176)),f777(f777(f68(x77171,x77172,x77173),f777(f777(x77173,x77175),x77174)),x77176))+P1(f777(f777(f336(x77171),x77175),x77176)) % 174.01/173.90 [7784]~P9(x77841)+P1(f777(f777(f234(x77841),x77842),f777(x77843,x77844)))+~P1(f777(f777(f336(x77845),x77844),x77846))+~P1(f777(f777(f234(x77841),x77842),f777(f777(f49(x77845,x77841),x77846),x77843))) % 174.01/173.90 [7944]~P20(x79441,x79442,x79443)+~P1(f777(f65(x79441),x79446))+E(f777(f777(f68(x79441,x79442,x79443),x79444),f777(f777(f304(x79441),x79445),x79446)),f777(f777(x79443,x79445),f777(f777(f68(x79441,x79442,x79443),x79444),x79446)))+P1(f777(f777(f336(x79441),x79445),x79446)) % 174.01/173.90 [8035]~P100(x80353)+~P1(f777(x80352,x80355))+~P18(x80353,f777(f777(f145(x80351,x80353),x80354),x80356))+E(f777(f128(x80351,x80352),f777(f777(f140(x80351,x80353,x80354),x80355),x80356)),f777(f777(f140(x80351,x80353,x80354),x80355),f777(f128(x80351,x80352),x80356))) % 174.01/173.90 [8058]E(x80581,x80582)+E(x80583,f4(a3))+~P1(f777(f58(x80584,x80583),f777(f777(f243(a3,a3),x80585),x80582)))+~P1(f777(f58(x80584,x80583),f777(f777(f243(a3,a3),x80586),x80581))) % 174.01/173.90 [8059]E(x80591,x80592)+E(x80593,f4(a3))+~P1(f777(f58(x80594,x80593),f777(f777(f243(a3,a3),x80592),x80595)))+~P1(f777(f58(x80594,x80593),f777(f777(f243(a3,a3),x80591),x80596))) % 174.01/173.90 [8081]~P23(x80812,x80815,x80816,x80811)+~P1(f777(f65(x80812),x80814))+E(f777(x80811,f777(f777(f304(x80812),x80813),x80814)),f777(f77(x80815,x80815,x80815,f777(x80811,x80814)),f777(x80816,x80813)))+P1(f777(f777(f336(x80812),x80813),x80814)) % 174.01/173.90 [8295]~P24(x82955,x82951,x82956,x82952)+E(f777(f77(x82951,x82951,x82951,f777(x82952,x82953)),f777(x82952,x82954)),f777(x82952,x82953))+~P1(f777(f65(x82955),x82953))+~P1(f777(f777(f234(f858(x82955,a845)),x82954),x82953)) % 174.01/173.90 [9346]~P29(x93461,x93462,x93464,x93463)+~P1(f777(f777(f336(x93462),x93465),f777(f305(x93461,x93462,x93464),x93463)))+P1(f777(f777(f336(x93461),f777(f81(x93461,x93462,x93463,x93464),x93465)),x93466))+~P1(f777(f777(f234(f858(x93461,a845)),x93463),x93466)) % 174.01/173.90 [9689]~P66(x96892)+~E(f497(x96891,x96893,x96895,x96896,x96894,x96892),f498(x96891,x96893,x96895,x96896,x96894,x96892))+~P1(f777(f65(x96894),x96896))+E(f777(f777(f10(x96891,x96892),x96893),f777(f305(x96894,x96891,x96895),x96896)),f777(f777(f10(x96894,x96892),f777(f77(x96891,x96892,x96894,x96893),x96895)),x96896)) % 174.01/173.90 [9718]~P66(x97186)+E(f777(x97181,f497(x97182,x97183,x97181,x97184,x97185,x97186)),f777(x97181,f498(x97182,x97183,x97181,x97184,x97185,x97186)))+E(f777(f777(f10(x97182,x97186),x97183),f777(f305(x97185,x97182,x97181),x97184)),f777(f777(f10(x97185,x97186),f777(f77(x97182,x97186,x97185,x97183),x97181)),x97184))+~P1(f777(f65(x97185),x97184)) % 174.01/173.90 [9772]~P66(x97722)+~E(f777(x97723,f777(x97725,f498(x97721,x97723,x97725,x97726,x97724,x97722))),f4(x97722))+~P1(f777(f65(x97724),x97726))+E(f777(f777(f10(x97721,x97722),x97723),f777(f305(x97724,x97721,x97725),x97726)),f777(f777(f10(x97724,x97722),f777(f77(x97721,x97722,x97724,x97723),x97725)),x97726)) % 174.01/173.90 [9832]~P66(x98322)+~P1(f777(f65(x98324),x98326))+E(f777(f777(f10(x98321,x98322),x98323),f777(f305(x98324,x98321,x98325),x98326)),f777(f777(f10(x98324,x98322),f777(f77(x98321,x98322,x98324,x98323),x98325)),x98326))+P1(f777(f777(f336(x98324),f498(x98321,x98323,x98325,x98326,x98324,x98322)),x98326)) % 174.01/173.90 [9833]~P66(x98332)+~P1(f777(f65(x98334),x98336))+E(f777(f777(f10(x98331,x98332),x98333),f777(f305(x98334,x98331,x98335),x98336)),f777(f777(f10(x98334,x98332),f777(f77(x98331,x98332,x98334,x98333),x98335)),x98336))+P1(f777(f777(f336(x98334),f497(x98331,x98333,x98335,x98336,x98334,x98332)),x98336)) % 174.01/173.90 [9955]~P70(x99551)+~P1(f777(f65(x99552),x99556))+E(f777(f777(f777(f69(x99551,x99552,f85(x99551)),f777(f777(f22(x99552,f858(x99553,a845),x99551),f777(f777(f11(x99552,x99551,f858(f858(x99553,a845),x99551)),f777(f777(f12(f858(x99553,x99551),f858(x99551,f858(f858(x99553,a845),x99551)),x99552),f69(x99551,x99553,f85(x99551))),x99554)),f82(x99551))),x99555)),f82(x99551)),x99556),f777(f777(f777(f69(x99551,f857(x99552,x99553),f85(x99551)),f777(f253(x99552,x99553,x99551),x99554)),f82(x99551)),f777(f777(f250(x99552,x99553),x99556),x99555)))+P1(f777(f777(f336(x99552),f566(x99554,x99555,x99553,x99556,x99552,x99551)),x99556)) % 174.01/173.90 [9971]~P70(x99711)+~P1(f777(f65(x99712),x99716))+E(f777(f777(f777(f69(x99711,x99712,f85(x99711)),f777(f777(f22(x99712,f858(x99713,a845),x99711),f777(f777(f11(x99712,x99711,f858(f858(x99713,a845),x99711)),f777(f777(f12(f858(x99713,x99711),f858(x99711,f858(f858(x99713,a845),x99711)),x99712),f69(x99711,x99713,f85(x99711))),x99714)),f82(x99711))),x99715)),f82(x99711)),x99716),f777(f777(f777(f69(x99711,f857(x99712,x99713),f85(x99711)),f777(f253(x99712,x99713,x99711),x99714)),f82(x99711)),f777(f777(f250(x99712,x99713),x99716),x99715)))+~P1(f777(f65(x99713),f777(x99715,f566(x99714,x99715,x99713,x99716,x99712,x99711)))) % 174.01/173.90 [8210]~P24(x82102,x82105,x82106,x82101)+~P1(f777(f65(x82102),x82104))+~P1(f777(f65(x82102),x82103))+E(f777(x82101,f777(f777(f105(f858(x82102,a845)),x82103),x82104)),f777(f77(x82105,x82105,x82105,f777(x82101,x82103)),f777(x82101,x82104))) % 174.01/173.90 [8430]~P9(x84301)+P1(f777(f777(f234(x84301),f777(x84302,x84303)),x84304))+~P1(f777(f777(f336(x84305),x84303),x84306))+~P1(f777(f777(f234(x84301),f777(f777(f48(x84305,x84301),x84306),x84302)),x84304)) % 174.01/173.90 [8804]~P29(x88042,x88041,x88043,x88046)+E(f777(f777(f5(f858(x88041,a845)),f777(f305(x88042,x88041,x88043),x88044)),f777(f305(x88042,x88041,x88043),x88045)),f777(f305(x88042,x88041,x88043),f777(f777(f5(f858(x88042,a845)),x88044),x88045)))+~P1(f777(f777(f234(f858(x88042,a845)),x88045),x88046))+~P1(f777(f777(f234(f858(x88042,a845)),x88044),x88046)) % 174.01/173.90 [8805]~P29(x88052,x88051,x88053,x88056)+E(f777(f777(f106(f858(x88051,a845)),f777(f305(x88052,x88051,x88053),x88054)),f777(f305(x88052,x88051,x88053),x88055)),f777(f305(x88052,x88051,x88053),f777(f777(f106(f858(x88052,a845)),x88054),x88055)))+~P1(f777(f777(f234(f858(x88052,a845)),x88055),x88056))+~P1(f777(f777(f234(f858(x88052,a845)),x88054),x88056)) % 174.01/173.90 [9049]E(x90491,x90492)+~P53(x90493,x90494,x90495)+~P1(f777(f777(f336(f857(x90493,x90494)),f777(f777(f243(x90493,x90494),x90496),x90492)),x90495))+~P1(f777(f777(f336(f857(x90493,x90494)),f777(f777(f243(x90493,x90494),x90496),x90491)),x90495)) % 174.01/173.90 [9629]~P66(x96291)+~P1(f777(f65(x96293),x96296))+~P1(f777(f65(x96292),x96295))+E(f777(f777(f84(x96291),f777(f777(f10(x96292,x96291),f777(f77(f859(x96292,x96293),x96291,x96292,x96294),f306(x96292,x96293))),x96295)),f777(f777(f10(x96293,x96291),f777(f77(f859(x96292,x96293),x96291,x96293,x96294),f315(x96293,x96292))),x96296)),f777(f777(f10(f859(x96292,x96293),x96291),x96294),f316(x96292,x96293,x96295,x96296))) % 174.01/173.90 [9768]~P64(x97681)+~E(f777(x97683,f632(x97684,x97686,x97683,x97685,x97682,x97681)),f777(x97686,f632(x97684,x97686,x97683,x97685,x97682,x97681)))+~P1(f777(f65(x97682),x97685))+E(f777(f777(f777(f69(x97681,x97682,f85(x97681)),x97683),x97684),x97685),f777(f777(f777(f69(x97681,x97682,f85(x97681)),x97686),x97684),x97685)) % 174.01/173.90 [9829]~P64(x98291)+~P1(f777(f65(x98292),x98295))+E(f777(f777(f777(f69(x98291,x98292,f85(x98291)),x98293),x98294),x98295),f777(f777(f777(f69(x98291,x98292,f85(x98291)),x98296),x98294),x98295))+P1(f777(f777(f336(x98292),f632(x98294,x98293,x98296,x98295,x98292,x98291)),x98295)) % 174.01/173.90 [8634]~P64(x86341)+~P1(f777(f65(x86342),x86346))+P1(f777(f777(f336(x86342),x86345),x86346))+E(f777(f777(f777(f69(x86341,x86342,f85(x86341)),x86343),x86344),f777(f777(f304(x86342),x86345),x86346)),f777(f777(f85(x86341),f777(x86343,x86345)),f777(f777(f777(f69(x86341,x86342,f85(x86341)),x86343),x86344),x86346))) % 174.01/173.90 [8678]~P12(x86781,x86786,x86783)+~P16(x86781,f858(x86782,a845),x86783,x86785)+~P1(f777(f777(f336(x86781),x86784),x86786))+E(f777(f777(f48(x86781,f858(x86782,a845)),f777(f279(x86781,x86781,x86783),f777(f777(f304(x86781),x86784),f182(f858(x86781,a845))))),x86785),f777(x86785,x86784)) % 174.01/173.90 [8786]~P20(x87863,x87864,x87861)+~P1(f777(f65(x87863),x87866))+~P1(f777(f777(f336(x87863),x87862),x87866))+E(f777(f777(x87861,x87862),f777(f777(f68(x87863,x87864,x87861),x87865),f777(f777(f5(f858(x87863,a845)),x87866),f777(f777(f304(x87863),x87862),f182(f858(x87863,a845)))))),f777(f777(f68(x87863,x87864,x87861),x87865),x87866)) % 174.01/173.90 [9059]~P23(x90593,x90591,x90596,x90592)+~P1(f777(f65(x90593),x90595))+~P1(f777(f65(x90593),x90594))+E(f777(f77(x90591,x90591,x90591,f777(x90592,f777(f777(f105(f858(x90593,a845)),x90594),x90595))),f777(x90592,f777(f777(f106(f858(x90593,a845)),x90594),x90595))),f777(f77(x90591,x90591,x90591,f777(x90592,x90594)),f777(x90592,x90595))) % 174.01/173.90 [9366]~E(x93663,f777(f777(f150(x93661,x93662),x93665),x93666))+P1(f777(f777(f336(f857(f852(x93661),f852(x93661))),f777(f777(f243(f852(x93661),f852(x93661)),x93662),x93663)),f148(x93661,x93664)))+~P1(f777(f777(f235(a851),x93665),f777(f183(f852(x93661)),x93662)))+~P1(f777(f777(f336(f857(x93661,x93661)),f777(f777(f243(x93661,x93661),f777(f777(f155(x93661),x93662),x93665)),x93666)),x93664)) % 174.01/173.90 [9848]~P66(x98482)+~P1(f777(f65(x98481),x98486))+P1(f777(f777(f336(x98481),f565(x98484,x98485,x98483,x98486,x98481,x98482)),x98486))+E(f777(f777(f10(x98481,x98482),f777(f777(f22(x98481,f858(x98483,a845),x98482),f777(f777(f12(f858(x98483,x98482),f858(f858(x98483,a845),x98482),x98481),f10(x98483,x98482)),x98484)),x98485)),x98486),f777(f777(f10(f857(x98481,x98483),x98482),f777(f253(x98481,x98483,x98482),x98484)),f777(f777(f250(x98481,x98483),x98486),x98485))) % 174.01/173.90 [9849]~P70(x98492)+~P1(f777(f65(x98491),x98496))+P1(f777(f777(f336(x98491),f558(x98494,x98495,x98493,x98496,x98491,x98492)),x98496))+E(f777(f777(f13(x98491,x98492),f777(f777(f22(x98491,f858(x98493,a845),x98492),f777(f777(f12(f858(x98493,x98492),f858(f858(x98493,a845),x98492),x98491),f13(x98493,x98492)),x98494)),x98495)),x98496),f777(f777(f13(f857(x98491,x98493),x98492),f777(f253(x98491,x98493,x98492),x98494)),f777(f777(f250(x98491,x98493),x98496),x98495))) % 174.01/173.90 [9888]~P66(x98882)+~P1(f777(f65(x98881),x98886))+~P1(f777(f65(x98883),f777(x98885,f565(x98884,x98885,x98883,x98886,x98881,x98882))))+E(f777(f777(f10(x98881,x98882),f777(f777(f22(x98881,f858(x98883,a845),x98882),f777(f777(f12(f858(x98883,x98882),f858(f858(x98883,a845),x98882),x98881),f10(x98883,x98882)),x98884)),x98885)),x98886),f777(f777(f10(f857(x98881,x98883),x98882),f777(f253(x98881,x98883,x98882),x98884)),f777(f777(f250(x98881,x98883),x98886),x98885))) % 174.01/173.90 [9889]~P70(x98892)+~P1(f777(f65(x98891),x98896))+~P1(f777(f65(x98893),f777(x98895,f558(x98894,x98895,x98893,x98896,x98891,x98892))))+E(f777(f777(f13(x98891,x98892),f777(f777(f22(x98891,f858(x98893,a845),x98892),f777(f777(f12(f858(x98893,x98892),f858(f858(x98893,a845),x98892),x98891),f13(x98893,x98892)),x98894)),x98895)),x98896),f777(f777(f13(f857(x98891,x98893),x98892),f777(f253(x98891,x98893,x98892),x98894)),f777(f777(f250(x98891,x98893),x98896),x98895))) % 174.01/173.90 [9871]~P70(x98712)+~P1(f777(f65(x98711),x98716))+P1(f777(f777(f336(x98711),x98713),x98716))+E(f777(f777(f13(x98711,x98712),f777(f777(f11(x98711,x98712,x98712),f777(f777(f22(x98711,x98712,f858(x98712,x98712)),f777(f777(f12(a845,f858(x98712,f858(x98712,x98712)),x98711),f100(x98712)),f777(f777(f11(x98711,x98711,a845),a332),x98713))),x98714)),x98715)),x98716),f777(f777(f244(x98712),x98715),f777(f44(x98711),x98716))) % 174.01/173.90 [9876]~P70(x98762)+~P1(f777(f65(x98761),x98766))+~P1(f777(f777(f336(x98761),x98763),x98766))+E(f777(f777(f13(x98761,x98762),f777(f777(f11(x98761,x98762,x98762),f777(f777(f22(x98761,x98762,f858(x98762,x98762)),f777(f777(f12(a845,f858(x98762,f858(x98762,x98762)),x98761),f100(x98762)),f777(f777(f11(x98761,x98761,a845),a332),x98763))),x98764)),x98765)),x98766),f777(f777(f85(x98762),f777(x98764,x98763)),f777(f777(f244(x98762),x98765),f777(f777(f5(a851),f777(f44(x98761),x98766)),f82(a851))))) % 174.01/173.90 [9942]~P1(f777(f65(x99421),x99425))+~P1(f777(f65(x99422),x99423))+P1(f777(f777(f336(x99422),f588(x99426,x99424,x99423,x99422,x99425,x99421)),x99423))+E(f777(f777(f10(x99421,a851),f777(f777(f12(f858(x99422,a845),a851,x99421),f44(x99422)),f777(f777(f12(f858(x99422,a845),f858(x99422,a845),x99421),f258(x99422)),f777(f777(f12(f858(x99422,a845),f858(x99422,a845),x99421),f777(f22(x99422,a845,a845),f777(f777(f12(a845,f858(a845,a845),x99422),a333),f777(f777(f11(x99422,f858(x99422,a845),a845),f336(x99422)),x99423)))),x99424)))),x99425),f777(f777(f85(a851),x99426),f777(f44(x99422),x99423))) % 174.01/173.90 [9943]~P1(f777(f65(x99431),x99435))+~P1(f777(f65(x99432),x99433))+P1(f777(f777(f336(x99432),f589(x99436,x99434,x99433,x99432,x99435,x99431)),x99433))+E(f777(f777(f10(x99431,a851),f777(f777(f12(f858(x99432,a845),a851,x99431),f44(x99432)),f777(f777(f12(f858(x99432,a845),f858(x99432,a845),x99431),f258(x99432)),f777(f777(f12(f858(x99432,a845),f858(x99432,a845),x99431),f777(f22(x99432,a845,a845),f777(f777(f12(a845,f858(a845,a845),x99432),a333),f777(f777(f11(x99432,f858(x99432,a845),a845),f336(x99432)),x99433)))),x99434)))),x99435),f777(f777(f10(x99432,a851),x99436),x99433)) % 174.01/173.90 [9977]~P1(f777(f65(x99772),x99773))+~P1(f777(f65(x99771),x99775))+~E(f777(f44(x99771),f777(f258(x99771),f777(f777(f22(x99771,a845,a845),f777(f777(f12(a845,f858(a845,a845),x99771),a333),f777(f777(f11(x99771,f858(x99771,a845),a845),f336(x99771)),x99775))),f777(f777(f11(x99771,x99772,a845),x99774),f588(x99776,x99774,x99773,x99772,x99775,x99771))))),x99776)+E(f777(f777(f10(x99771,a851),f777(f777(f12(f858(x99772,a845),a851,x99771),f44(x99772)),f777(f777(f12(f858(x99772,a845),f858(x99772,a845),x99771),f258(x99772)),f777(f777(f12(f858(x99772,a845),f858(x99772,a845),x99771),f777(f22(x99772,a845,a845),f777(f777(f12(a845,f858(a845,a845),x99772),a333),f777(f777(f11(x99772,f858(x99772,a845),a845),f336(x99772)),x99773)))),x99774)))),x99775),f777(f777(f85(a851),x99776),f777(f44(x99772),x99773))) % 174.01/173.90 [9979]~P1(f777(f65(x99792),x99793))+~P1(f777(f65(x99791),x99795))+~E(f777(f44(x99791),f777(f258(x99791),f777(f777(f22(x99791,a845,a845),f777(f777(f12(a845,f858(a845,a845),x99791),a333),f777(f777(f11(x99791,f858(x99791,a845),a845),f336(x99791)),x99795))),f777(f777(f11(x99791,x99792,a845),x99794),f589(x99796,x99794,x99793,x99792,x99795,x99791))))),f777(x99796,f589(x99796,x99794,x99793,x99792,x99795,x99791)))+E(f777(f777(f10(x99791,a851),f777(f777(f12(f858(x99792,a845),a851,x99791),f44(x99792)),f777(f777(f12(f858(x99792,a845),f858(x99792,a845),x99791),f258(x99792)),f777(f777(f12(f858(x99792,a845),f858(x99792,a845),x99791),f777(f22(x99792,a845,a845),f777(f777(f12(a845,f858(a845,a845),x99792),a333),f777(f777(f11(x99792,f858(x99792,a845),a845),f336(x99792)),x99793)))),x99794)))),x99795),f777(f777(f10(x99792,a851),x99796),x99793)) % 174.01/173.90 [9628]E(x96281,x96282)+~P20(x96283,x96284,x96285)+~P1(f777(f70(x96283,x96284,x96285,x96286,x96287),x96282))+~P1(f777(f70(x96283,x96284,x96285,x96286,x96287),x96281)) % 174.01/173.90 [9438]P1(f777(x94381,x94382))+~P1(f777(f777(f336(x94387),x94382),f777(x94386,x94384)))+~P1(f777(x94381,f389(x94381,x94386,x94385,x94383,x94387)))+~P1(f777(f777(f336(x94383),x94384),x94385)) % 174.01/173.90 [9863]~P20(x98637,x98636,x98631)+E(f777(f777(x98631,x98632),f665(x98632,x98633,x98634,x98635,x98631,x98636,x98637)),x98633)+~P1(f777(f70(x98637,x98636,x98631,x98635,x98634),x98633))+~P1(f777(f777(f336(x98637),x98632),x98634)) % 174.01/173.90 [9927]~P20(x99271,x99272,x99273)+~P1(f777(f70(x99271,x99272,x99273,x99274,x99275),x99277))+P1(f777(f70(x99271,x99272,x99273,x99274,f777(f777(f5(f858(x99271,a845)),x99275),f777(f777(f304(x99271),x99276),f182(f858(x99271,a845))))),f665(x99276,x99277,x99275,x99274,x99273,x99272,x99271)))+~P1(f777(f777(f336(x99271),x99276),x99275)) % 174.01/173.90 [9342]~P64(x93421)+~P29(x93425,x93422,x93426,x93427)+~P1(f777(f65(x93425),x93427))+E(f777(f777(f777(f69(x93421,x93422,f85(x93421)),x93423),x93424),f777(f305(x93425,x93422,x93426),x93427)),f777(f777(f777(f69(x93421,x93425,f85(x93421)),f777(f77(x93422,x93421,x93425,x93423),x93426)),x93424),x93427)) % 174.01/173.90 [9460]~E(f777(f777(f304(x94601),x94605),x94606),f777(f777(f304(x94601),x94602),x94603))+~P1(f777(f70(x94601,x94601,x94604,x94602,x94603),x94607))+P1(f777(f777(f336(x94601),x94602),x94603))+P1(f777(f66(x94601,x94604,f777(f777(f304(x94601),x94605),x94606)),x94607)) % 174.01/173.90 [9539]P1(f777(x95391,x95392))+~P1(f777(f777(f336(x95393),x95392),f777(x95394,x95397)))+~P1(f777(f777(f336(x95396),x95397),x95395))+P1(f777(f777(f336(x95393),f389(x95391,x95394,x95395,x95396,x95393)),f777(f777(f48(x95396,f858(x95393,a845)),x95395),x95394))) % 174.01/173.90 [9552]~P29(x95522,x95521,x95525,x95524)+~P29(x95521,x95523,x95526,f777(f305(x95522,x95521,x95525),x95524))+E(f777(f777(f77(x95521,x95522,x95523,f81(x95522,x95521,x95524,x95525)),f81(x95521,x95523,f777(f305(x95522,x95521,x95525),x95524),x95526)),x95527),f777(f81(x95522,x95523,x95524,f777(f77(x95521,x95523,x95522,x95526),x95525)),x95527))+~P1(f777(f777(f336(x95523),x95527),f777(f305(x95521,x95523,x95526),f777(f305(x95522,x95521,x95525),x95524)))) % 174.01/173.90 [9864]~P20(x98647,x98646,x98641)+E(f777(f777(x98641,x98642),f693(x98643,x98644,x98642,x98645,x98641,x98646,x98647)),x98643)+P1(f777(f777(f336(x98647),x98642),x98644))+~P1(f777(f70(x98647,x98646,x98641,x98645,f777(f777(f304(x98647),x98642),x98644)),x98643)) % 174.01/173.90 [9926]~P20(x99261,x99264,x99265)+P1(f777(f70(x99261,x99264,x99265,x99266,x99263),f693(x99267,x99263,x99262,x99266,x99265,x99264,x99261)))+P1(f777(f777(f336(x99261),x99262),x99263))+~P1(f777(f70(x99261,x99264,x99265,x99266,f777(f777(f304(x99261),x99262),x99263)),x99267)) % 174.01/173.90 [9611]E(x96111,f4(a3))+~P1(f777(f58(x96113,x96111),f777(f777(f243(a3,a3),x96115),x96117)))+~P1(f777(f58(x96112,x96111),f777(f777(f243(a3,a3),x96114),x96116)))+P1(f777(f58(f777(f777(f84(a3),x96112),x96113),x96111),f777(f777(f243(a3,a3),f777(f777(f84(a3),f777(f777(f84(a3),x96114),x96115)),f777(f777(f45(a3),f777(f777(f84(a3),x96116),x96117)),x96111))),f54(a3,f777(f777(f84(a3),x96116),x96117),x96111)))) % 174.01/173.90 [9613]~P1(f777(f777(f235(a851),f4(a851)),x96133))+~P1(f777(f57(x96132,x96133),f777(f777(f243(a851,a851),x96135),x96137)))+~P1(f777(f57(x96131,x96133),f777(f777(f243(a851,a851),x96134),x96136)))+P1(f777(f57(f777(f777(f84(a851),x96131),x96132),x96133),f777(f777(f243(a851,a851),f777(f777(f84(a851),f777(f777(f84(a851),x96134),x96135)),f777(f777(f45(a851),f777(f777(f84(a851),x96136),x96137)),x96133))),f54(a851,f777(f777(f84(a851),x96136),x96137),x96133)))) % 174.01/173.90 [9976]~P66(x99762)+~P1(f777(f65(x99763),x99765))+~P1(f777(f65(x99761),x99767))+E(f777(f777(f10(x99761,x99762),f777(f777(f22(x99761,f858(x99763,a845),x99762),f777(f777(f12(f858(x99763,x99762),f858(f858(x99763,a845),x99762),x99761),f10(x99763,x99762)),x99764)),f777(f777(f12(f858(x99763,a845),f858(x99763,a845),x99761),f258(x99763)),f777(f777(f12(f858(x99763,a845),f858(x99763,a845),x99761),f777(f22(x99763,a845,a845),f777(f777(f12(a845,f858(a845,a845),x99763),a333),f777(f777(f11(x99763,f858(x99763,a845),a845),f336(x99763)),x99765)))),x99766)))),x99767),f777(f777(f10(x99763,x99762),f777(f777(f22(x99763,f858(x99761,a845),x99762),f777(f777(f12(f858(x99761,x99762),f858(f858(x99761,a845),x99762),x99763),f10(x99761,x99762)),f777(f11(x99761,x99763,x99762),x99764))),f777(f777(f12(f858(x99761,a845),f858(x99761,a845),x99763),f258(x99761)),f777(f777(f12(f858(x99761,a845),f858(x99761,a845),x99763),f777(f22(x99761,a845,a845),f777(f777(f12(a845,f858(a845,a845),x99761),a333),f777(f777(f11(x99761,f858(x99761,a845),a845),f336(x99761)),x99767)))),f777(f11(x99761,x99763,a845),x99766))))),x99765)) % 174.01/173.90 [9498]~P26(x94987,x94986,x94981,x94988,x94982,x94984)+E(f777(f777(x94981,f777(x94982,x94983)),f777(x94984,x94985)),f777(x94984,x94985))+~P1(f777(f65(x94986),x94985))+~P1(f777(f777(f336(x94986),x94983),x94985)) % 174.01/173.90 [9502]~P17(x95026,x95021,x95022,x95028,x95023,x95024)+~P12(x95026,x95027,x95028)+P16(x95021,x95022,x95023,f777(x95024,x95025))+~P1(f777(f777(f336(x95026),x95025),x95027)) % 174.01/173.90 [7744]~P39(x77444,x77445,x77446,x77443)+~P31(x77448,x77446,f777(f777(f777(f95(x77448),x77447),x77444),x77441))+P1(f777(f777(x77441,x77442),x77443))+~P1(f777(f777(x77447,x77442),x77445)) % 174.01/173.90 [9146]~P23(x91467,x91461,x91468,x91463)+~P1(f777(f65(x91467),x91465))+~P1(f777(f65(x91467),x91464))+E(f777(f77(x91461,x91461,x91462,f777(x91463,x91464)),f777(f77(x91461,x91461,x91462,f777(x91463,x91465)),x91466)),f777(f77(x91461,x91461,x91462,f777(x91463,x91465)),f777(f77(x91461,x91461,x91462,f777(x91463,x91464)),x91466))) % 174.01/173.90 [9213]~P29(x92132,x92132,x92135,x92136)+~P25(x92133,x92132,x92137,x92138,x92131)+~P1(f777(f65(x92132),x92136))+E(f777(f777(x92131,f777(f77(x92132,x92133,x92132,x92134),x92135)),x92136),f777(f777(x92131,x92134),f777(f305(x92132,x92132,x92135),x92136))) % 174.01/173.90 [9500]~P27(x95007,x95002,x95005,x95008,x95006,x95001)+~P1(f777(f65(x95002),x95004))+E(f777(x95001,f777(f777(f304(x95002),x95003),x95004)),f777(f777(x95005,f777(x95006,x95003)),f777(x95001,x95004)))+P1(f777(f777(f336(x95002),x95003),x95004)) % 174.01/173.90 [9507]~P26(x95076,x95075,x95071,x95077,x95078,x95072)+E(f777(f777(x95071,f777(x95072,x95073)),f777(x95072,x95074)),f777(x95072,x95074))+~P1(f777(f65(x95075),x95074))+~P1(f777(f777(f234(f858(x95075,a845)),x95073),x95074)) % 174.01/173.90 [9133]P1(f777(f777(f336(f857(f852(x91331),f852(x91331))),f777(f777(f243(f852(x91331),f852(x91331)),x91332),x91333)),f148(x91331,x91334)))+~E(x91333,f777(f777(f127(x91331),x91335),f777(f777(f142(x91331),x91336),x91337)))+~E(x91332,f777(f777(f127(x91331),x91335),f777(f777(f142(x91331),x91338),x91337)))+~P1(f777(f777(f336(f857(x91331,x91331)),f777(f777(f243(x91331,x91331),x91338),x91336)),x91334)) % 174.01/173.90 [9503]~P26(x95036,x95032,x95035,x95037,x95038,x95031)+~P1(f777(f65(x95032),x95034))+~P1(f777(f65(x95032),x95033))+E(f777(x95031,f777(f777(f105(f858(x95032,a845)),x95033),x95034)),f777(f777(x95035,f777(x95031,x95033)),f777(x95031,x95034))) % 174.01/173.90 [10016]~P29(x100164,x100162,x100165,x100168)+E(f777(f777(f49(x100161,f858(x100162,a845)),x100163),f777(f777(f12(f858(x100164,a845),f858(x100162,a845),x100161),f305(x100164,x100162,x100165)),x100166)),f777(f305(x100164,x100162,x100165),f777(f777(f49(x100161,f858(x100164,a845)),x100163),x100166)))+~P1(f777(f777(f336(x100161),x100167),x100163))+P1(f777(f777(f336(x100161),f680(x100167,x100166,x100163,x100161,x100168,x100165,x100162,x100164)),x100163)) % 174.01/173.90 [10034]~P29(x100344,x100342,x100345,x100347)+E(f777(f777(f49(x100341,f858(x100342,a845)),x100343),f777(f777(f12(f858(x100344,a845),f858(x100342,a845),x100341),f305(x100344,x100342,x100345)),x100346)),f777(f305(x100344,x100342,x100345),f777(f777(f49(x100341,f858(x100344,a845)),x100343),x100346)))+~P1(f777(f777(f336(x100341),x100348),x100343))+~P1(f777(f777(f234(f858(x100344,a845)),f777(x100346,f680(x100348,x100346,x100343,x100341,x100347,x100345,x100342,x100344))),x100347)) % 174.01/173.90 [9557]~P27(x95577,x95575,x95571,x95578,x95572,x95574)+~P1(f777(f65(x95575),x95576))+~P1(f777(f777(f336(x95575),x95573),x95576))+E(f777(f777(x95571,f777(x95572,x95573)),f777(x95574,f777(f777(f5(f858(x95575,a845)),x95576),f777(f777(f304(x95575),x95573),f182(f858(x95575,a845)))))),f777(x95574,x95576)) % 174.01/173.90 [9566]~P27(x95666,x95663,x95661,x95667,x95668,x95662)+~P1(f777(f65(x95663),x95665))+~P1(f777(f65(x95663),x95664))+E(f777(f777(x95661,f777(x95662,f777(f777(f105(f858(x95663,a845)),x95664),x95665))),f777(x95662,f777(f777(f106(f858(x95663,a845)),x95664),x95665))),f777(f777(x95661,f777(x95662,x95664)),f777(x95662,x95665))) % 174.01/173.90 [9648]P41(x96481,x96482,x96483,x96484,x96485,f777(f777(x96483,x96486),x96487))+~P41(x96481,x96482,x96483,x96484,f777(f777(f5(f858(x96481,a845)),x96485),f777(f777(f304(x96481),x96488),f182(f858(x96481,a845)))),x96489)+~E(f777(f777(x96483,x96486),x96487),f777(f777(x96483,x96488),x96489))+~P1(f777(f777(f336(x96481),x96488),x96485)) % 174.01/173.90 [10045]P28(x100451,x100452,f777(f777(f304(f850(x100451)),f777(f777(f777(f95(x100451),f777(x100453,f428(x100454,x100455,x100456,x100457,x100453,x100452,x100451,x100458,x100459))),f777(x100457,f428(x100454,x100455,x100456,x100457,x100453,x100452,x100451,x100458,x100459))),f777(x100456,f428(x100454,x100455,x100456,x100457,x100453,x100452,x100451,x100458,x100459)))),f182(f858(f850(x100451),a845))))+~P1(f777(f65(x100459),x100458))+~P28(x100451,x100452,f777(f305(x100459,f850(x100451),f777(f777(f22(x100459,f858(x100451,f858(a848,a845)),f850(x100451)),f777(f777(f22(x100459,a846,f858(f858(x100451,f858(a848,a845)),f850(x100451))),f777(f777(f12(f858(x100451,f858(a848,a845)),f858(a846,f858(f858(x100451,f858(a848,a845)),f850(x100451))),x100459),f95(x100451)),x100453)),x100457)),x100456)),x100458))+P28(x100451,x100452,f777(f305(x100459,f850(x100451),f777(f777(f22(x100459,f858(x100451,f858(a848,a845)),f850(x100451)),f777(f777(f22(x100459,a846,f858(f858(x100451,f858(a848,a845)),f850(x100451))),f777(f777(f12(f858(x100451,f858(a848,a845)),f858(a846,f858(f858(x100451,f858(a848,a845)),f850(x100451))),x100459),f95(x100451)),x100455)),x100457)),x100454)),x100458)) % 174.01/173.90 [10046]~P28(x100461,x100462,f777(f777(f304(f850(x100461)),f777(f777(f777(f95(x100461),f777(x100464,f428(x100466,x100464,x100468,x100465,x100469,x100462,x100461,x100467,x100463))),f777(x100465,f428(x100466,x100464,x100468,x100465,x100469,x100462,x100461,x100467,x100463))),f777(x100466,f428(x100466,x100464,x100468,x100465,x100469,x100462,x100461,x100467,x100463)))),f182(f858(f850(x100461),a845))))+~P1(f777(f65(x100463),x100467))+~P28(x100461,x100462,f777(f305(x100463,f850(x100461),f777(f777(f22(x100463,f858(x100461,f858(a848,a845)),f850(x100461)),f777(f777(f22(x100463,a846,f858(f858(x100461,f858(a848,a845)),f850(x100461))),f777(f777(f12(f858(x100461,f858(a848,a845)),f858(a846,f858(f858(x100461,f858(a848,a845)),f850(x100461))),x100463),f95(x100461)),x100469)),x100465)),x100468)),x100467))+P28(x100461,x100462,f777(f305(x100463,f850(x100461),f777(f777(f22(x100463,f858(x100461,f858(a848,a845)),f850(x100461)),f777(f777(f22(x100463,a846,f858(f858(x100461,f858(a848,a845)),f850(x100461))),f777(f777(f12(f858(x100461,f858(a848,a845)),f858(a846,f858(f858(x100461,f858(a848,a845)),f850(x100461))),x100463),f95(x100461)),x100464)),x100465)),x100466)),x100467)) % 174.01/173.90 [9590]~P17(x95906,x95907,x95908,x95909,x959010,x95901)+E(f777(f777(x95901,x95902),x95903),f777(f777(x95901,x95904),x95905))+~P1(f777(f777(f336(f857(x95907,x95907)),f777(f777(f243(x95907,x95907),x95903),x95905)),x959010))+~P1(f777(f777(f336(f857(x95906,x95906)),f777(f777(f243(x95906,x95906),x95902),x95904)),x95909)) % 174.01/173.90 [6812]E(x68121,x68122)+~P1(f777(f777(f234(a3),f4(a3)),x68122))+~P1(f777(f777(f234(a3),f4(a3)),x68121))+~P1(f777(f777(f281(a3),x68122),x68121))+~P1(f777(f777(f281(a3),x68121),x68122)) % 174.01/173.90 [9215]~P93(x92152)+E(x92151,f182(f858(x92152,a845)))+~P1(f777(f65(x92152),x92151))+P1(f777(f777(f336(x92152),f17(x92152,x92151)),x92151))+~P1(f777(f777(f336(x92152),f777(f777(f105(x92152),f445(x92151,x92152)),f446(x92151,x92152))),f777(f777(f304(x92152),f445(x92151,x92152)),f777(f777(f304(x92152),f446(x92151,x92152)),f182(f858(x92152,a845)))))) % 174.01/173.90 [9218]~P93(x92182)+E(x92181,f182(f858(x92182,a845)))+~P1(f777(f65(x92182),x92181))+P1(f777(f777(f336(x92182),f14(x92182,x92181)),x92181))+~P1(f777(f777(f336(x92182),f777(f777(f106(x92182),f518(x92181,x92182)),f520(x92181,x92182))),f777(f777(f304(x92182),f518(x92181,x92182)),f777(f777(f304(x92182),f520(x92181,x92182)),f182(f858(x92182,a845)))))) % 174.01/173.90 [9246]~P64(x92462)+E(x92461,f182(f858(x92462,a845)))+~P1(f777(f65(x92462),x92461))+P1(f777(f777(f336(x92462),f777(f67(x92462,f85(x92462)),x92461)),x92461))+~P1(f777(f777(f336(x92462),f777(f777(f85(x92462),f567(x92461,x92462)),f568(x92461,x92462))),f777(f777(f304(x92462),f567(x92461,x92462)),f777(f777(f304(x92462),f568(x92461,x92462)),f182(f858(x92462,a845)))))) % 174.01/173.90 [9252]~P100(x92522)+E(x92521,f182(f858(x92522,a845)))+~P1(f777(f65(x92522),x92521))+P1(f777(f777(f336(x92522),f15(x92522,f181(x92522),x92521)),x92521))+~P1(f777(f777(f336(x92522),f777(f777(f181(x92522),f454(x92521,x92522)),f457(x92521,x92522))),f777(f777(f304(x92522),f454(x92521,x92522)),f777(f777(f304(x92522),f457(x92521,x92522)),f182(f858(x92522,a845)))))) % 174.01/173.90 [9253]~P100(x92532)+E(x92531,f182(f858(x92532,a845)))+~P1(f777(f65(x92532),x92531))+P1(f777(f777(f336(x92532),f16(x92532,f238(x92532),x92531)),x92531))+~P1(f777(f777(f336(x92532),f777(f777(f238(x92532),f458(x92531,x92532)),f459(x92531,x92532))),f777(f777(f304(x92532),f458(x92531,x92532)),f777(f777(f304(x92532),f459(x92531,x92532)),f182(f858(x92532,a845)))))) % 174.01/173.90 [6424]~P81(x64242)+E(x64241,f4(x64242))+~E(f777(f777(f84(x64242),x64243),x64241),f4(x64242))+~P1(f777(f777(f234(x64242),f4(x64242)),x64243))+~P1(f777(f777(f234(x64242),f4(x64242)),x64241)) % 174.01/173.90 [6425]~P81(x64252)+E(x64251,f4(x64252))+~E(f777(f777(f84(x64252),x64251),x64253),f4(x64252))+~P1(f777(f777(f234(x64252),f4(x64252)),x64253))+~P1(f777(f777(f234(x64252),f4(x64252)),x64251)) % 174.01/173.90 [7145]~P100(x71451)+E(f19(x71451,x71452),x71453)+~P1(f777(f65(x71451),x71452))+~P1(f777(f777(f234(x71451),x71453),f631(x71453,x71452,x71451)))+~P1(f777(f777(f336(x71451),x71453),x71452)) % 174.01/173.90 [7180]~P100(x71801)+~P18(x71801,x71802)+~P18(x71801,x71803)+P18(x71801,f777(f777(f127(x71801),x71802),x71803))+P1(f777(f777(f336(x71801),f767(x71803,x71802,x71801)),f777(f160(x71801),x71802))) % 174.01/173.90 [7181]~P100(x71811)+~P18(x71811,x71812)+~P18(x71811,x71813)+P18(x71811,f777(f777(f127(x71811),x71812),x71813))+P1(f777(f777(f336(x71811),f768(x71813,x71812,x71811)),f777(f160(x71811),x71813))) % 174.01/173.90 [7247]~P100(x72471)+E(f18(x72471,x72472),x72473)+~P1(f777(f65(x72471),x72472))+P1(f777(f777(f336(x72471),f634(x72473,x72472,x72471)),x72472))+~P1(f777(f777(f336(x72471),x72473),x72472)) % 174.01/173.90 [7248]~P100(x72481)+E(f19(x72481,x72482),x72483)+~P1(f777(f65(x72481),x72482))+P1(f777(f777(f336(x72481),f631(x72483,x72482,x72481)),x72482))+~P1(f777(f777(f336(x72481),x72483),x72482)) % 174.01/173.90 [7847]~P100(x78471)+E(f18(x78471,x78472),x78473)+~P1(f777(f65(x78471),x78472))+~P1(f777(f777(f336(x78471),x78473),x78472))+~P1(f777(f777(f234(x78471),f634(x78473,x78472,x78471)),x78473)) % 174.01/173.90 [8161]~P100(x81611)+~P18(x81611,x81612)+~P18(x81611,x81613)+P18(x81611,f777(f777(f127(x81611),x81612),x81613))+~P1(f777(f777(f234(x81611),f767(x81613,x81612,x81611)),f768(x81613,x81612,x81611))) % 174.01/173.90 [8890]~P93(x88902)+E(x88901,f182(f858(x88902,a845)))+~E(f777(f777(f105(x88902),f777(x88903,f476(x88901,x88903,x88902))),f777(x88903,f479(x88901,x88903,x88902))),f777(x88903,f777(f777(f105(x88902),f476(x88901,x88903,x88902)),f479(x88901,x88903,x88902))))+E(f17(x88902,f777(f305(x88902,x88902,x88903),x88901)),f777(x88903,f17(x88902,x88901)))+~P1(f777(f65(x88902),x88901)) % 174.01/173.90 [8891]~P100(x88912)+E(x88911,f182(f858(x88912,a845)))+~E(f777(f777(f181(x88912),f777(x88913,f467(x88911,x88913,x88912))),f777(x88913,f472(x88911,x88913,x88912))),f777(x88913,f777(f777(f181(x88912),f467(x88911,x88913,x88912)),f472(x88911,x88913,x88912))))+E(f18(x88912,f777(f305(x88912,x88912,x88913),x88911)),f777(x88913,f18(x88912,x88911)))+~P1(f777(f65(x88912),x88911)) % 174.01/173.90 [8892]~P100(x88922)+E(x88921,f182(f858(x88922,a845)))+~E(f777(f777(f238(x88922),f777(x88923,f477(x88921,x88923,x88922))),f777(x88923,f478(x88921,x88923,x88922))),f777(x88923,f777(f777(f238(x88922),f477(x88921,x88923,x88922)),f478(x88921,x88923,x88922))))+E(f19(x88922,f777(f305(x88922,x88922,x88923),x88921)),f777(x88923,f19(x88922,x88921)))+~P1(f777(f65(x88922),x88921)) % 174.01/173.90 [8893]~P93(x88932)+E(x88931,f182(f858(x88932,a845)))+~E(f777(f777(f106(x88932),f777(x88933,f532(x88931,x88933,x88932))),f777(x88933,f534(x88931,x88933,x88932))),f777(x88933,f777(f777(f106(x88932),f532(x88931,x88933,x88932)),f534(x88931,x88933,x88932))))+E(f14(x88932,f777(f305(x88932,x88932,x88933),x88931)),f777(x88933,f14(x88932,x88931)))+~P1(f777(f65(x88932),x88931)) % 174.01/173.90 [8957]~P100(x89572)+E(x89571,f182(f858(x89572,a845)))+~E(f777(f777(f181(x89572),f777(x89573,f468(x89571,x89573,x89572))),f777(x89573,f469(x89571,x89573,x89572))),f777(x89573,f777(f777(f181(x89572),f468(x89571,x89573,x89572)),f469(x89571,x89573,x89572))))+E(f15(x89572,f181(x89572),f777(f305(x89572,x89572,x89573),x89571)),f777(x89573,f15(x89572,f181(x89572),x89571)))+~P1(f777(f65(x89572),x89571)) % 174.01/173.90 [8958]~P100(x89582)+E(x89581,f182(f858(x89582,a845)))+~E(f777(f777(f238(x89582),f777(x89583,f470(x89581,x89583,x89582))),f777(x89583,f471(x89581,x89583,x89582))),f777(x89583,f777(f777(f238(x89582),f470(x89581,x89583,x89582)),f471(x89581,x89583,x89582))))+E(f16(x89582,f238(x89582),f777(f305(x89582,x89582,x89583),x89581)),f777(x89583,f16(x89582,f238(x89582),x89581)))+~P1(f777(f65(x89582),x89581)) % 174.01/173.90 [6441]~P64(x64412)+E(x64411,f182(f858(x64412,a845)))+~P1(f777(f65(x64412),x64411))+E(f777(f67(x64412,f85(x64412)),f777(f777(f304(x64412),x64413),x64411)),f777(f777(f85(x64412),x64413),f777(f67(x64412,f85(x64412)),x64411)))+P1(f777(f777(f336(x64412),x64413),x64411)) % 174.01/173.90 [6983]~P100(x69832)+E(f777(f777(f238(x69832),f19(x69832,x69831)),f19(x69832,x69833)),f19(x69832,x69833))+E(x69831,f182(f858(x69832,a845)))+~P1(f777(f65(x69832),x69833))+~P1(f777(f777(f234(f858(x69832,a845)),x69831),x69833)) % 174.01/173.90 [6984]~P100(x69842)+E(f777(f777(f181(x69842),f18(x69842,x69841)),f18(x69842,x69843)),f18(x69842,x69843))+E(x69841,f182(f858(x69842,a845)))+~P1(f777(f65(x69842),x69843))+~P1(f777(f777(f234(f858(x69842,a845)),x69841),x69843)) % 174.01/173.90 [6985]~P93(x69852)+E(f777(f777(f105(x69852),f17(x69852,x69851)),f17(x69852,x69853)),f17(x69852,x69853))+E(x69851,f182(f858(x69852,a845)))+~P1(f777(f65(x69852),x69853))+~P1(f777(f777(f234(f858(x69852,a845)),x69851),x69853)) % 174.01/173.90 [6986]~P93(x69862)+E(f777(f777(f106(x69862),f14(x69862,x69861)),f14(x69862,x69863)),f14(x69862,x69863))+E(x69861,f182(f858(x69862,a845)))+~P1(f777(f65(x69862),x69863))+~P1(f777(f777(f234(f858(x69862,a845)),x69861),x69863)) % 174.01/173.90 [7303]~P100(x73032)+E(x73031,f182(f858(x73032,a845)))+~P1(f777(f65(x73032),x73033))+P1(f777(f777(f234(x73032),f18(x73032,x73031)),f18(x73032,x73033)))+~P1(f777(f777(f234(f858(x73032,a845)),x73031),x73033)) % 174.01/173.90 [7304]~P100(x73042)+E(x73041,f182(f858(x73042,a845)))+~P1(f777(f65(x73042),x73043))+P1(f777(f777(f234(x73042),f19(x73042,x73043)),f19(x73042,x73041)))+~P1(f777(f777(f234(f858(x73042,a845)),x73041),x73043)) % 174.01/173.90 [7366]~P93(x73661)+E(f17(x73661,x73662),x73663)+~P1(f777(f65(x73661),x73662))+~E(f777(f777(f5(f858(x73661,a845)),x73662),f777(f777(f304(x73661),x73663),f182(f858(x73661,a845)))),f182(f858(x73661,a845)))+~P1(f777(f777(f336(x73661),x73663),x73662)) % 174.01/173.90 [7367]~P100(x73671)+E(f18(x73671,x73672),x73673)+~P1(f777(f65(x73671),x73672))+~E(f777(f777(f5(f858(x73671,a845)),x73672),f777(f777(f304(x73671),x73673),f182(f858(x73671,a845)))),f182(f858(x73671,a845)))+~P1(f777(f777(f336(x73671),x73673),x73672)) % 174.01/173.90 [7368]~P100(x73681)+E(f19(x73681,x73682),x73683)+~P1(f777(f65(x73681),x73682))+~E(f777(f777(f5(f858(x73681,a845)),x73682),f777(f777(f304(x73681),x73683),f182(f858(x73681,a845)))),f182(f858(x73681,a845)))+~P1(f777(f777(f336(x73681),x73683),x73682)) % 174.01/173.90 [7369]~P93(x73691)+E(f14(x73691,x73692),x73693)+~P1(f777(f65(x73691),x73692))+~E(f777(f777(f5(f858(x73691,a845)),x73692),f777(f777(f304(x73691),x73693),f182(f858(x73691,a845)))),f182(f858(x73691,a845)))+~P1(f777(f777(f336(x73691),x73693),x73692)) % 174.01/173.90 [7469]~P100(x74691)+E(f15(x74691,f181(x74691),x74692),x74693)+~P1(f777(f65(x74691),x74692))+~E(f777(f777(f5(f858(x74691,a845)),x74692),f777(f777(f304(x74691),x74693),f182(f858(x74691,a845)))),f182(f858(x74691,a845)))+~P1(f777(f777(f336(x74691),x74693),x74692)) % 174.01/173.90 [7470]~P100(x74701)+E(f16(x74701,f238(x74701),x74702),x74703)+~P1(f777(f65(x74701),x74702))+~E(f777(f777(f5(f858(x74701,a845)),x74702),f777(f777(f304(x74701),x74703),f182(f858(x74701,a845)))),f182(f858(x74701,a845)))+~P1(f777(f777(f336(x74701),x74703),x74702)) % 174.01/173.90 [7507]~P100(x75072)+E(x75071,f182(f858(x75072,a845)))+~P1(f777(f65(x75072),x75071))+~P1(f777(f777(f235(x75072),x75073),f549(x75073,x75071,x75072)))+P1(f777(f777(f235(x75072),x75073),f777(f67(x75072,f238(x75072)),x75071))) % 174.01/173.90 [7508]~P100(x75082)+E(x75081,f182(f858(x75082,a845)))+~P1(f777(f65(x75082),x75081))+~P1(f777(f777(f234(x75082),x75083),f550(x75083,x75081,x75082)))+P1(f777(f777(f234(x75082),x75083),f777(f67(x75082,f238(x75082)),x75081))) % 174.01/173.90 [7509]~P98(x75092)+E(x75091,f182(f858(x75092,a845)))+~P1(f777(f65(x75092),x75091))+~P1(f777(f777(f234(x75092),x75093),f551(x75093,x75091,x75092)))+P1(f777(f777(f234(x75092),x75093),f777(f67(x75092,f106(x75092)),x75091))) % 174.01/173.90 [7597]~P98(x75972)+E(x75971,f182(f858(x75972,a845)))+~P1(f777(f65(x75972),x75971))+P1(f777(f777(f336(x75972),f551(x75973,x75971,x75972)),x75971))+P1(f777(f777(f234(x75972),x75973),f777(f67(x75972,f106(x75972)),x75971))) % 174.01/173.90 [7598]~P100(x75982)+E(x75981,f182(f858(x75982,a845)))+~P1(f777(f65(x75982),x75981))+P1(f777(f777(f336(x75982),f550(x75983,x75981,x75982)),x75981))+P1(f777(f777(f234(x75982),x75983),f777(f67(x75982,f238(x75982)),x75981))) % 174.01/173.90 [7599]~P100(x75992)+E(x75991,f182(f858(x75992,a845)))+~P1(f777(f65(x75992),x75991))+P1(f777(f777(f336(x75992),f549(x75993,x75991,x75992)),x75991))+P1(f777(f777(f235(x75992),x75993),f777(f67(x75992,f238(x75992)),x75991))) % 174.01/173.90 [7719]~P100(x77192)+E(x77191,f182(f858(x77192,a845)))+E(f777(f777(f238(x77192),f16(x77192,f238(x77192),x77191)),f16(x77192,f238(x77192),x77193)),f16(x77192,f238(x77192),x77193))+~P1(f777(f65(x77192),x77193))+~P1(f777(f777(f234(f858(x77192,a845)),x77191),x77193)) % 174.01/173.90 [7720]~P100(x77202)+E(x77201,f182(f858(x77202,a845)))+E(f777(f777(f181(x77202),f15(x77202,f181(x77202),x77201)),f15(x77202,f181(x77202),x77203)),f15(x77202,f181(x77202),x77203))+~P1(f777(f65(x77202),x77203))+~P1(f777(f777(f234(f858(x77202,a845)),x77201),x77203)) % 174.01/173.90 [7922]~E(f677(x79221,x79223,x79222),f678(x79221,x79223,x79222))+~E(f777(f44(x79222),f679(x79221,x79223,x79222)),x79221)+E(f777(f777(f85(a851),x79221),f777(f44(f858(x79222,a845)),x79223)),f777(f44(x79222),f46(f858(x79222,a845),x79223)))+~P1(f777(f65(x79222),f46(f858(x79222,a845),x79223)))+~P1(f777(f65(f858(x79222,a845)),x79223)) % 174.01/173.90 [8097]~P100(x80972)+E(x80971,f182(f858(x80972,a845)))+~P1(f777(f65(x80972),x80973))+P1(f777(f777(f234(x80972),f777(f67(x80972,f238(x80972)),x80973)),f777(f67(x80972,f238(x80972)),x80971)))+~P1(f777(f777(f234(f858(x80972,a845)),x80971),x80973)) % 174.01/173.90 [8401]~E(f677(x84011,x84013,x84012),f678(x84011,x84013,x84012))+E(f777(f777(f85(a851),x84011),f777(f44(f858(x84012,a845)),x84013)),f777(f44(x84012),f46(f858(x84012,a845),x84013)))+P1(f777(f777(f336(f858(x84012,a845)),f679(x84011,x84013,x84012)),x84013))+~P1(f777(f65(x84012),f46(f858(x84012,a845),x84013)))+~P1(f777(f65(f858(x84012,a845)),x84013)) % 174.01/173.90 [8425]~E(f777(f44(x84252),f679(x84251,x84253,x84252)),x84251)+E(f777(f777(f85(a851),x84251),f777(f44(f858(x84252,a845)),x84253)),f777(f44(x84252),f46(f858(x84252,a845),x84253)))+P1(f777(f777(f336(f858(x84252,a845)),f678(x84251,x84253,x84252)),x84253))+~P1(f777(f65(x84252),f46(f858(x84252,a845),x84253)))+~P1(f777(f65(f858(x84252,a845)),x84253)) % 174.01/173.90 [8426]~E(f777(f44(x84262),f679(x84261,x84263,x84262)),x84261)+E(f777(f777(f85(a851),x84261),f777(f44(f858(x84262,a845)),x84263)),f777(f44(x84262),f46(f858(x84262,a845),x84263)))+P1(f777(f777(f336(f858(x84262,a845)),f677(x84261,x84263,x84262)),x84263))+~P1(f777(f65(x84262),f46(f858(x84262,a845),x84263)))+~P1(f777(f65(f858(x84262,a845)),x84263)) % 174.01/173.90 [8456]~E(f777(f44(x84562),f679(x84561,x84563,x84562)),x84561)+~E(f777(f777(f106(f858(x84562,a845)),f678(x84561,x84563,x84562)),f677(x84561,x84563,x84562)),f182(f858(x84562,a845)))+E(f777(f777(f85(a851),x84561),f777(f44(f858(x84562,a845)),x84563)),f777(f44(x84562),f46(f858(x84562,a845),x84563)))+~P1(f777(f65(f858(x84562,a845)),x84563))+~P1(f777(f65(x84562),f46(f858(x84562,a845),x84563))) % 174.01/173.90 [8682]E(f777(f777(f85(a851),x86821),f777(f44(f858(x86822,a845)),x86823)),f777(f44(x86822),f46(f858(x86822,a845),x86823)))+P1(f777(f777(f336(f858(x86822,a845)),f679(x86821,x86823,x86822)),x86823))+P1(f777(f777(f336(f858(x86822,a845)),f678(x86821,x86823,x86822)),x86823))+~P1(f777(f65(f858(x86822,a845)),x86823))+~P1(f777(f65(x86822),f46(f858(x86822,a845),x86823))) % 174.01/173.90 [8683]E(f777(f777(f85(a851),x86831),f777(f44(f858(x86832,a845)),x86833)),f777(f44(x86832),f46(f858(x86832,a845),x86833)))+P1(f777(f777(f336(f858(x86832,a845)),f679(x86831,x86833,x86832)),x86833))+P1(f777(f777(f336(f858(x86832,a845)),f677(x86831,x86833,x86832)),x86833))+~P1(f777(f65(f858(x86832,a845)),x86833))+~P1(f777(f65(x86832),f46(f858(x86832,a845),x86833))) % 174.01/173.90 [8708]~E(f777(f777(f106(f858(x87082,a845)),f678(x87081,x87083,x87082)),f677(x87081,x87083,x87082)),f182(f858(x87082,a845)))+E(f777(f777(f85(a851),x87081),f777(f44(f858(x87082,a845)),x87083)),f777(f44(x87082),f46(f858(x87082,a845),x87083)))+~P1(f777(f65(f858(x87082,a845)),x87083))+P1(f777(f777(f336(f858(x87082,a845)),f679(x87081,x87083,x87082)),x87083))+~P1(f777(f65(x87082),f46(f858(x87082,a845),x87083))) % 174.01/173.90 [8936]~P91(x89362)+E(x89361,f182(f858(x89362,a845)))+~E(f777(f777(f85(x89362),f777(x89363,f569(x89361,x89363,x89362))),f777(x89363,f570(x89361,x89363,x89362))),f777(x89363,f777(f777(f85(x89362),f569(x89361,x89363,x89362)),f570(x89361,x89363,x89362))))+~P1(f777(f65(x89362),x89361))+E(f777(f67(x89362,f85(x89362)),f777(f305(x89362,x89362,x89363),x89361)),f777(x89363,f777(f67(x89362,f85(x89362)),x89361))) % 174.01/173.90 [9803]P1(f777(f777(x98031,x98032),x98033))+P1(f777(f777(f235(a3),f828(x98031,x98033,x98032)),f829(x98031,x98033,x98032)))+P1(f777(f777(f234(a3),f829(x98031,x98033,x98032)),f4(a3)))+P1(f777(f777(x98031,f828(x98031,x98033,x98032)),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f829(x98031,x98033,x98032))))+~P1(f777(f323(f857(a3,a3),a64),f777(f777(f243(a3,a3),x98032),x98033))) % 174.01/173.90 [9809]P1(f777(f777(x98091,x98092),x98093))+P1(f777(f777(f234(a3),f827(x98091,x98093,x98092)),f4(a3)))+P1(f777(f777(x98091,f826(x98091,x98093,x98092)),f777(f777(f85(a3),f777(f108(a3),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f827(x98091,x98093,x98092))))+P1(f777(f777(f234(a3),f4(a3)),f777(f777(f84(a3),f826(x98091,x98093,x98092)),f827(x98091,x98093,x98092))))+~P1(f777(f323(f857(a3,a3),a61),f777(f777(f243(a3,a3),x98092),x98093))) % 174.01/173.90 [7892]~P110(x78921)+~P1(f777(f777(f234(x78921),x78922),f82(x78921)))+~P1(f777(f777(f234(x78921),f4(x78921)),x78922))+~P1(f777(f777(f234(x78921),f4(x78921)),x78923))+P1(f777(f777(f234(x78921),f777(f777(f85(x78921),x78922),x78923)),x78923)) % 174.01/173.90 [7893]~P110(x78931)+~P1(f777(f777(f234(x78931),x78933),f82(x78931)))+~P1(f777(f777(f234(x78931),f4(x78931)),x78933))+~P1(f777(f777(f234(x78931),f4(x78931)),x78932))+P1(f777(f777(f234(x78931),f777(f777(f85(x78931),x78932),x78933)),x78932)) % 174.01/173.90 [8242]~P100(x82422)+E(x82421,f182(f858(x82422,a845)))+~P1(f777(f65(x82422),x82421))+P1(f777(f777(f336(x82422),f554(x82423,x82421,x82422)),x82421))+~P1(f777(f777(f234(x82422),f777(f67(x82422,f238(x82422)),x82421)),x82423)) % 174.01/173.90 [8243]~P100(x82432)+E(x82431,f182(f858(x82432,a845)))+~P1(f777(f65(x82432),x82431))+P1(f777(f777(f336(x82432),f555(x82433,x82431,x82432)),x82431))+~P1(f777(f777(f235(x82432),f777(f67(x82432,f238(x82432)),x82431)),x82433)) % 174.01/173.90 [8244]~P100(x82442)+E(x82441,f182(f858(x82442,a845)))+~P1(f777(f65(x82442),x82441))+P1(f777(f777(f235(x82442),f555(x82443,x82441,x82442)),x82443))+~P1(f777(f777(f235(x82442),f777(f67(x82442,f238(x82442)),x82441)),x82443)) % 174.01/173.90 [8245]~P100(x82452)+E(x82451,f182(f858(x82452,a845)))+~P1(f777(f65(x82452),x82451))+P1(f777(f777(f234(x82452),f554(x82453,x82451,x82452)),x82453))+~P1(f777(f777(f234(x82452),f777(f67(x82452,f238(x82452)),x82451)),x82453)) % 174.01/173.90 [8330]~P1(f777(x83301,x83303))+P1(f777(x83301,f353(x83301,x83302)))+P1(f777(x83301,f352(x83301,x83302)))+~P1(f777(f777(f235(a3),f4(a3)),x83302))+P1(f777(x83301,f777(f777(f5(a3),f352(x83301,x83302)),f777(f777(f85(a3),f354(x83301,x83302)),x83302)))) % 174.01/173.90 [8548]~P1(f777(x85481,x85483))+P1(f777(x85481,f352(x85481,x85482)))+~P1(f777(f777(f235(a3),f4(a3)),x85482))+P1(f777(f777(f336(a3),f353(x85481,x85482)),f297(a3,f82(a3),x85482)))+P1(f777(x85481,f777(f777(f5(a3),f352(x85481,x85482)),f777(f777(f85(a3),f354(x85481,x85482)),x85482)))) % 174.01/173.90 [8726]~P1(f777(x87261,x87263))+~P1(f777(x87261,f352(x87261,x87262)))+P1(f777(x87261,f353(x87261,x87262)))+~P1(f777(f777(f235(a3),f4(a3)),x87262))+~P1(f777(x87261,f777(f777(f5(a3),f352(x87261,x87262)),f777(f777(f85(a3),f354(x87261,x87262)),x87262)))) % 174.01/173.90 [8829]~P1(f777(x88291,x88293))+~P1(f777(x88291,f352(x88291,x88292)))+~P1(f777(f777(f235(a3),f4(a3)),x88292))+P1(f777(f777(f336(a3),f353(x88291,x88292)),f297(a3,f82(a3),x88292)))+~P1(f777(x88291,f777(f777(f5(a3),f352(x88291,x88292)),f777(f777(f85(a3),f354(x88291,x88292)),x88292)))) % 174.01/173.90 [8645]~P93(x86451)+~P1(f777(f65(x86451),x86452))+E(f777(f777(f5(f858(x86451,a845)),x86452),f777(f777(f304(x86451),x86453),f182(f858(x86451,a845)))),f182(f858(x86451,a845)))+~P1(f777(f777(f336(x86451),x86453),x86452))+E(f777(f777(f105(x86451),x86453),f17(x86451,f777(f777(f5(f858(x86451,a845)),x86452),f777(f777(f304(x86451),x86453),f182(f858(x86451,a845)))))),f17(x86451,x86452)) % 174.01/173.90 [8646]~P100(x86461)+~P1(f777(f65(x86461),x86462))+E(f777(f777(f5(f858(x86461,a845)),x86462),f777(f777(f304(x86461),x86463),f182(f858(x86461,a845)))),f182(f858(x86461,a845)))+~P1(f777(f777(f336(x86461),x86463),x86462))+E(f777(f777(f181(x86461),x86463),f18(x86461,f777(f777(f5(f858(x86461,a845)),x86462),f777(f777(f304(x86461),x86463),f182(f858(x86461,a845)))))),f18(x86461,x86462)) % 174.01/173.90 [8647]~P100(x86471)+~P1(f777(f65(x86471),x86472))+E(f777(f777(f5(f858(x86471,a845)),x86472),f777(f777(f304(x86471),x86473),f182(f858(x86471,a845)))),f182(f858(x86471,a845)))+~P1(f777(f777(f336(x86471),x86473),x86472))+E(f777(f777(f238(x86471),x86473),f19(x86471,f777(f777(f5(f858(x86471,a845)),x86472),f777(f777(f304(x86471),x86473),f182(f858(x86471,a845)))))),f19(x86471,x86472)) % 174.01/173.90 [8648]~P93(x86481)+~P1(f777(f65(x86481),x86482))+E(f777(f777(f5(f858(x86481,a845)),x86482),f777(f777(f304(x86481),x86483),f182(f858(x86481,a845)))),f182(f858(x86481,a845)))+~P1(f777(f777(f336(x86481),x86483),x86482))+E(f777(f777(f106(x86481),x86483),f14(x86481,f777(f777(f5(f858(x86481,a845)),x86482),f777(f777(f304(x86481),x86483),f182(f858(x86481,a845)))))),f14(x86481,x86482)) % 174.01/173.90 [8703]~P100(x87031)+~P1(f777(f65(x87031),x87032))+E(f777(f777(f5(f858(x87031,a845)),x87032),f777(f777(f304(x87031),x87033),f182(f858(x87031,a845)))),f182(f858(x87031,a845)))+~P1(f777(f777(f336(x87031),x87033),x87032))+E(f777(f777(f181(x87031),x87033),f15(x87031,f181(x87031),f777(f777(f5(f858(x87031,a845)),x87032),f777(f777(f304(x87031),x87033),f182(f858(x87031,a845)))))),f15(x87031,f181(x87031),x87032)) % 174.01/173.90 [8704]~P100(x87041)+~P1(f777(f65(x87041),x87042))+E(f777(f777(f5(f858(x87041,a845)),x87042),f777(f777(f304(x87041),x87043),f182(f858(x87041,a845)))),f182(f858(x87041,a845)))+~P1(f777(f777(f336(x87041),x87043),x87042))+E(f777(f777(f238(x87041),x87043),f16(x87041,f238(x87041),f777(f777(f5(f858(x87041,a845)),x87042),f777(f777(f304(x87041),x87043),f182(f858(x87041,a845)))))),f16(x87041,f238(x87041),x87042)) % 174.01/173.90 [8714]~P100(x87141)+~P1(f777(f65(x87141),x87143))+~P1(f777(f65(x87141),x87142))+E(f777(f777(f106(f858(x87141,a845)),x87142),x87143),f182(f858(x87141,a845)))+E(f777(f777(f238(x87141),f19(x87141,f777(f777(f105(f858(x87141,a845)),x87142),x87143))),f19(x87141,f777(f777(f106(f858(x87141,a845)),x87142),x87143))),f777(f777(f238(x87141),f19(x87141,x87142)),f19(x87141,x87143))) % 174.01/173.90 [8715]~P100(x87151)+~P1(f777(f65(x87151),x87153))+~P1(f777(f65(x87151),x87152))+E(f777(f777(f106(f858(x87151,a845)),x87152),x87153),f182(f858(x87151,a845)))+E(f777(f777(f181(x87151),f18(x87151,f777(f777(f105(f858(x87151,a845)),x87152),x87153))),f18(x87151,f777(f777(f106(f858(x87151,a845)),x87152),x87153))),f777(f777(f181(x87151),f18(x87151,x87152)),f18(x87151,x87153))) % 174.01/173.90 [8716]~P93(x87161)+~P1(f777(f65(x87161),x87163))+~P1(f777(f65(x87161),x87162))+E(f777(f777(f106(f858(x87161,a845)),x87162),x87163),f182(f858(x87161,a845)))+E(f777(f777(f105(x87161),f17(x87161,f777(f777(f105(f858(x87161,a845)),x87162),x87163))),f17(x87161,f777(f777(f106(f858(x87161,a845)),x87162),x87163))),f777(f777(f105(x87161),f17(x87161,x87162)),f17(x87161,x87163))) % 174.01/173.90 [8717]~P93(x87171)+~P1(f777(f65(x87171),x87173))+~P1(f777(f65(x87171),x87172))+E(f777(f777(f106(f858(x87171,a845)),x87172),x87173),f182(f858(x87171,a845)))+E(f777(f777(f106(x87171),f14(x87171,f777(f777(f105(f858(x87171,a845)),x87172),x87173))),f14(x87171,f777(f777(f106(f858(x87171,a845)),x87172),x87173))),f777(f777(f106(x87171),f14(x87171,x87172)),f14(x87171,x87173))) % 174.01/173.90 [8910]~P100(x89101)+~P1(f777(f65(x89101),x89103))+~P1(f777(f65(x89101),x89102))+E(f777(f777(f106(f858(x89101,a845)),x89102),x89103),f182(f858(x89101,a845)))+E(f777(f777(f238(x89101),f16(x89101,f238(x89101),f777(f777(f105(f858(x89101,a845)),x89102),x89103))),f16(x89101,f238(x89101),f777(f777(f106(f858(x89101,a845)),x89102),x89103))),f777(f777(f238(x89101),f16(x89101,f238(x89101),x89102)),f16(x89101,f238(x89101),x89103))) % 174.01/173.90 [8911]~P100(x89111)+~P1(f777(f65(x89111),x89113))+~P1(f777(f65(x89111),x89112))+E(f777(f777(f106(f858(x89111,a845)),x89112),x89113),f182(f858(x89111,a845)))+E(f777(f777(f181(x89111),f15(x89111,f181(x89111),f777(f777(f105(f858(x89111,a845)),x89112),x89113))),f15(x89111,f181(x89111),f777(f777(f106(f858(x89111,a845)),x89112),x89113))),f777(f777(f181(x89111),f15(x89111,f181(x89111),x89112)),f15(x89111,f181(x89111),x89113))) % 174.01/173.90 [9645]~P117(x96453)+E(x96451,x96452)+~P1(f777(f777(f234(x96453),f4(x96453)),x96452))+~P1(f777(f777(f234(x96453),f4(x96453)),x96451))+~E(f777(f777(f244(x96453),x96451),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)))),f777(f777(f244(x96453),x96452),f777(f108(a851),f777(f777(f84(a3),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101)),f777(f777(f5(a3),f777(f777(f84(a3),a87),a87)),a101))))) % 174.01/173.90 [6589]P142(x65891,x65892)+~P142(x65891,x65893)+~P39(a861,x65893,x65894,x65892)+~P31(a843,x65894,f775(x65894))+~P1(f777(a2,x65893)) % 174.01/173.90 [5763]~P7(x57632)+E(x57631,f4(x57632))+~E(f777(f777(f45(x57632),x57633),x57631),x57634)+E(x57633,f777(f777(f85(x57632),x57634),x57631))+~P1(f777(f777(f281(x57632),x57631),x57633)) % 174.01/173.90 [5764]~P7(x57642)+E(x57641,f4(x57642))+~E(x57643,f777(f777(f85(x57642),x57644),x57641))+E(f777(f777(f45(x57642),x57643),x57641),x57644)+~P1(f777(f777(f281(x57642),x57641),x57643)) % 174.01/173.90 [6228]E(f406(x62281,x62282,x62283),x62284)+E(f777(x62281,x62284),f4(a851))+~E(f777(f777(f10(x62283,a851),x62281),x62282),f82(a851))+~P1(f777(f65(x62283),x62282))+~P1(f777(f777(f336(x62283),x62284),x62282)) % 174.01/173.90 [6296]E(f408(x62961,x62962,x62963),x62964)+E(f777(x62961,x62964),f4(a851))+~E(f777(f777(f10(x62963,a851),x62961),x62962),f777(a116,f4(a851)))+~P1(f777(f65(x62963),x62962))+~P1(f777(f777(f336(x62963),x62964),x62962)) % 174.01/173.90 [6410]~P100(x64101)+~P9(x64101)+P1(f777(f777(f235(x64101),x64102),f46(x64101,x64103)))+~P1(f777(f777(f235(x64101),x64102),x64104))+~P1(f777(f777(f336(x64101),x64104),x64103)) % 174.01/173.90 [6588]~P100(x65881)+~P9(x65881)+~P1(f777(f777(f235(x65881),x65884),x65883))+P1(f777(f777(f235(x65881),f47(x65881,x65882)),x65883))+~P1(f777(f777(f336(x65881),x65884),x65882)) % 174.01/173.90 [6746]P142(x67461,x67462)+~P142(x67461,x67464)+~P39(a861,x67464,x67463,x67462)+~P1(f777(a2,x67464))+P1(f777(f777(f336(f850(a843)),f775(x67463)),a860)) % 174.01/173.90 [6866]~P117(x68663)+E(x68661,x68662)+~E(f777(f777(f244(x68663),x68661),f777(a116,x68664)),f777(f777(f244(x68663),x68662),f777(a116,x68664)))+~P1(f777(f777(f234(x68663),f4(x68663)),x68662))+~P1(f777(f777(f234(x68663),f4(x68663)),x68661)) % 174.01/173.90 [7077]~E(f411(x70772,x70773,x70771,x70774),x70774)+~E(f777(x70772,x70774),f82(a851))+E(f777(f777(f10(x70771,a851),x70772),x70773),f82(a851))+~P1(f777(f65(x70771),x70773))+~P1(f777(f777(f336(x70771),x70774),x70773)) % 174.01/173.90 [7084]~P85(x70844)+~P127(x70844)+E(f777(x70841,f453(x70841,x70842,x70843,x70844)),f4(x70844))+~E(f777(f777(f13(x70843,x70844),x70841),x70842),f4(x70844))+~P1(f777(f65(x70843),x70842)) % 174.01/173.90 [7167]~E(f410(x71672,x71673,x71671,x71674),x71674)+~E(f777(x71672,x71674),f777(a116,f4(a851)))+E(f777(f777(f10(x71671,a851),x71672),x71673),f777(a116,f4(a851)))+~P1(f777(f65(x71671),x71673))+~P1(f777(f777(f336(x71671),x71674),x71673)) % 174.01/173.90 [7932]~E(f777(x79322,x79324),f82(a851))+~E(f777(x79322,f411(x79322,x79323,x79321,x79324)),f4(a851))+E(f777(f777(f10(x79321,a851),x79322),x79323),f82(a851))+~P1(f777(f65(x79321),x79323))+~P1(f777(f777(f336(x79321),x79324),x79323)) % 174.01/173.90 [7977]~E(f777(x79772,x79774),f777(a116,f4(a851)))+~E(f777(x79772,f410(x79772,x79773,x79771,x79774)),f4(a851))+E(f777(f777(f10(x79771,a851),x79772),x79773),f777(a116,f4(a851)))+~P1(f777(f65(x79771),x79773))+~P1(f777(f777(f336(x79771),x79774),x79773)) % 174.01/173.90 [8056]~P136(x80562)+~P112(x80562)+~P1(f777(x80561,x80564))+~P1(f777(f777(f281(x80562),x80563),f777(f777(f84(x80562),x80564),f4(x80562))))+P1(f777(x80561,f777(f777(f85(x80562),x80563),f841(x80563,x80561,x80562)))) % 174.01/173.90 [8551]E(x85511,x85512)+E(f777(f777(f84(a3),f435(x85513,x85512,x85514,x85511)),f436(x85513,x85512,x85514,x85511)),x85511)+~E(f777(f777(f5(a3),x85511),x85514),x85512)+~P1(f777(f777(f235(a3),f4(a3)),x85514))+~P1(f777(f777(f336(a3),x85512),x85513)) % 174.01/173.90 [8552]E(x85521,x85522)+E(f777(f777(f5(a3),f425(x85523,x85522,x85524,x85521)),f426(x85523,x85522,x85524,x85521)),x85521)+~E(f777(f777(f84(a3),x85521),x85524),x85522)+~P1(f777(f777(f235(a3),f4(a3)),x85524))+~P1(f777(f777(f336(a3),x85522),x85523)) % 174.01/173.90 [8713]E(f777(x87131,f819(x87132,x87131,x87133,x87134)),x87132)+P1(f777(f777(f234(a851),x87134),f820(x87132,x87131,x87133,x87134)))+~P1(f777(f777(f234(a3),x87132),f777(x87131,x87133)))+~P1(f777(f777(f235(a851),x87134),x87133))+~P1(f777(f777(f234(a3),f777(x87131,x87134)),x87132)) % 174.01/173.90 [8730]~P85(x87304)+~P127(x87304)+~E(f777(f777(f13(x87301,x87304),x87302),x87303),f4(x87304))+~P1(f777(f65(x87301),x87303))+P1(f777(f777(f336(x87301),f453(x87302,x87303,x87301,x87304)),x87303)) % 174.01/173.90 [8763]~E(f777(x87632,x87634),f82(a851))+E(f777(f777(f10(x87631,a851),x87632),x87633),f82(a851))+~P1(f777(f65(x87631),x87633))+~P1(f777(f777(f336(x87631),x87634),x87633))+P1(f777(f777(f336(x87631),f411(x87632,x87633,x87631,x87634)),x87633)) % 174.01/173.90 [8772]E(x87721,x87722)+~E(f777(f777(f84(a3),x87722),x87724),x87721)+~P1(f777(f777(f235(a3),f4(a3)),x87724))+~P1(f777(f777(f336(a3),x87721),x87723))+P1(f777(f777(f336(a3),f425(x87723,x87721,x87724,x87722)),x87723)) % 174.01/173.90 [8773]E(x87731,x87732)+~E(f777(f777(f5(a3),x87732),x87734),x87731)+~P1(f777(f777(f235(a3),f4(a3)),x87734))+~P1(f777(f777(f336(a3),x87731),x87733))+P1(f777(f777(f336(a3),f435(x87733,x87731,x87734,x87732)),x87733)) % 174.01/173.90 [8775]~E(f777(x87752,x87754),f777(a116,f4(a851)))+E(f777(f777(f10(x87751,a851),x87752),x87753),f777(a116,f4(a851)))+~P1(f777(f65(x87751),x87753))+~P1(f777(f777(f336(x87751),x87754),x87753))+P1(f777(f777(f336(x87751),f410(x87752,x87753,x87751,x87754)),x87753)) % 174.01/173.90 [8779]P57(x87792,x87793,x87794,x87791)+E(x87791,f182(f858(x87792,a845)))+~P1(f777(f65(x87792),x87794))+~P1(f777(f65(x87792),x87791))+P1(f777(f777(f336(x87792),f539(x87791,x87794,x87793,x87792)),x87794)) % 174.01/173.90 [8842]E(x88421,x88422)+~E(f777(f777(f84(a3),x88422),x88424),x88421)+~P1(f777(f777(f235(a3),f4(a3)),x88424))+~P1(f777(f777(f336(a3),x88421),x88423))+P1(f777(f777(f336(a3),f426(x88423,x88421,x88424,x88422)),f297(a3,f82(a3),x88424))) % 174.01/173.90 [8843]E(x88431,x88432)+~E(f777(f777(f5(a3),x88432),x88434),x88431)+~P1(f777(f777(f235(a3),f4(a3)),x88434))+~P1(f777(f777(f336(a3),x88431),x88433))+P1(f777(f777(f336(a3),f436(x88433,x88431,x88434,x88432)),f297(a3,f82(a3),x88434))) % 174.01/173.90 [8916]P1(f777(f777(f234(a851),x89161),f819(x89162,x89163,x89164,x89161)))+~P1(f777(f777(f234(a3),x89162),f777(x89163,x89164)))+P1(f777(f777(f234(a851),x89161),f820(x89162,x89163,x89164,x89161)))+~P1(f777(f777(f235(a851),x89161),x89164))+~P1(f777(f777(f234(a3),f777(x89163,x89161)),x89162)) % 174.01/173.90 [9023]E(f777(x90231,f819(x90232,x90231,x90233,x90234)),x90232)+~P1(f777(f777(f234(a3),x90232),f777(x90231,x90233)))+P1(f777(f777(f235(a851),f820(x90232,x90231,x90233,x90234)),x90233))+~P1(f777(f777(f235(a851),x90234),x90233))+~P1(f777(f777(f234(a3),f777(x90231,x90234)),x90232)) % 174.01/173.90 [9128]~P1(f777(f777(f281(a851),x91284),x91281))+~P1(f777(f777(f281(a851),x91284),x91283))+~P1(f777(f777(f281(a851),x91282),x91281))+P1(f777(f777(f281(a851),x91281),x91282))+P1(f777(f777(f235(f858(a851,a845)),f284(a851,f281(a851),x91283,x91282)),f284(a851,f281(a851),x91284,x91281))) % 174.01/173.90 [9129]~P1(f777(f777(f281(a851),x91292),x91291))+~P1(f777(f777(f281(a851),x91293),x91294))+~P1(f777(f777(f281(a851),x91292),x91294))+P1(f777(f777(f281(a851),x91291),x91292))+P1(f777(f777(f235(f858(a851,a845)),f284(a851,f281(a851),x91291,x91293)),f284(a851,f281(a851),x91292,x91294))) % 174.01/173.90 [9140]~P1(f777(f777(f234(a3),x91402),f777(x91403,x91404)))+P1(f777(f777(f234(a851),x91401),f820(x91402,x91403,x91404,x91401)))+P1(f777(f777(f234(a851),f819(x91402,x91403,x91404,x91401)),x91404))+~P1(f777(f777(f235(a851),x91401),x91404))+~P1(f777(f777(f234(a3),f777(x91403,x91401)),x91402)) % 174.01/173.90 [9141]~P1(f777(f777(f234(a3),x91412),f777(x91413,x91414)))+P1(f777(f777(f234(a851),x91411),f819(x91412,x91413,x91414,x91411)))+P1(f777(f777(f235(a851),f820(x91412,x91413,x91414,x91411)),x91414))+~P1(f777(f777(f235(a851),x91411),x91414))+~P1(f777(f777(f234(a3),f777(x91413,x91411)),x91412)) % 174.01/173.90 [9228]~P1(f777(f777(f234(a3),x92281),f777(x92282,x92283)))+P1(f777(f777(f234(a851),f819(x92281,x92282,x92283,x92284)),x92283))+~P1(f777(f777(f235(a851),x92284),x92283))+~P1(f777(f777(f234(a3),f777(x92282,x92284)),x92281))+P1(f777(f777(f235(a851),f820(x92281,x92282,x92283,x92284)),x92283)) % 174.01/173.90 [9312]E(x93121,f182(f858(x93122,a845)))+~P1(f777(f65(x93122),x93124))+~P1(f777(f65(x93122),x93121))+P1(f777(f777(f336(f857(f858(x93122,a845),f858(x93122,a845))),f777(f777(f243(f858(x93122,a845),f858(x93122,a845)),x93124),x93121)),f326(x93122,x93123)))+P1(f777(f777(f336(x93122),f541(x93123,x93121,x93124,x93122)),x93124)) % 174.01/173.90 [9313]E(x93131,f182(f858(x93132,a845)))+~P1(f777(f65(x93132),x93134))+~P1(f777(f65(x93132),x93131))+P1(f777(f777(f336(f857(f858(x93132,a845),f858(x93132,a845))),f777(f777(f243(f858(x93132,a845),f858(x93132,a845)),x93134),x93131)),f326(x93132,x93133)))+P1(f777(f777(f336(x93132),f625(x93133,x93131,x93134,x93132)),x93134)) % 174.01/173.90 [9956]E(f777(x99561,f819(x99562,x99561,x99563,x99564)),x99562)+~P1(f777(f777(f234(a3),x99562),f777(x99561,x99563)))+~P1(f777(f777(f234(a3),f777(f79(a3),f777(f777(f5(a3),f777(x99561,f777(f777(f84(a851),f820(x99562,x99561,x99563,x99564)),f82(a851)))),f777(x99561,f820(x99562,x99561,x99563,x99564))))),f82(a3)))+~P1(f777(f777(f235(a851),x99564),x99563))+~P1(f777(f777(f234(a3),f777(x99561,x99564)),x99562)) % 174.01/173.90 [9957]~P1(f777(f777(f234(a3),x99572),f777(x99573,x99574)))+P1(f777(f777(f234(a851),x99571),f819(x99572,x99573,x99574,x99571)))+~P1(f777(f777(f234(a3),f777(f79(a3),f777(f777(f5(a3),f777(x99573,f777(f777(f84(a851),f820(x99572,x99573,x99574,x99571)),f82(a851)))),f777(x99573,f820(x99572,x99573,x99574,x99571))))),f82(a3)))+~P1(f777(f777(f235(a851),x99571),x99574))+~P1(f777(f777(f234(a3),f777(x99573,x99571)),x99572)) % 174.01/173.90 [9958]~P1(f777(f777(f234(a3),x99581),f777(x99582,x99583)))+~P1(f777(f777(f234(a3),f777(f79(a3),f777(f777(f5(a3),f777(x99582,f777(f777(f84(a851),f820(x99581,x99582,x99583,x99584)),f82(a851)))),f777(x99582,f820(x99581,x99582,x99583,x99584))))),f82(a3)))+~P1(f777(f777(f235(a851),x99584),x99583))+~P1(f777(f777(f234(a3),f777(x99582,x99584)),x99581))+P1(f777(f777(f234(a851),f819(x99581,x99582,x99583,x99584)),x99583)) % 174.01/173.90 [7135]~P62(x71351)+P1(f777(f777(f235(x71351),x71352),f4(x71351)))+~P1(f777(f777(f235(x71351),x71353),f4(x71351)))+P1(f777(f777(f235(x71351),f4(x71351)),x71352))+P1(f777(f777(f235(x71351),x71353),f777(f777(f285(x71351),x71354),x71352))) % 174.01/173.90 [7136]~P62(x71361)+P1(f777(f777(f235(x71361),x71362),f4(x71361)))+~P1(f777(f777(f234(x71361),x71363),f4(x71361)))+P1(f777(f777(f235(x71361),f4(x71361)),x71362))+P1(f777(f777(f234(x71361),x71363),f777(f777(f285(x71361),x71364),x71362))) % 174.01/173.90 [7407]~P62(x74071)+P1(f777(f777(f235(x74071),x74072),f4(x74071)))+P1(f777(f777(f235(x74071),x74073),f4(x74071)))+P1(f777(f777(f235(x74071),f4(x74071)),x74073))+~P1(f777(f777(f235(x74071),x74072),f777(f777(f285(x74071),x74074),x74073))) % 174.01/173.90 [7408]~P62(x74081)+P1(f777(f777(f235(x74081),x74082),f4(x74081)))+P1(f777(f777(f234(x74081),x74083),f4(x74081)))+P1(f777(f777(f235(x74081),f4(x74081)),x74082))+~P1(f777(f777(f234(x74081),x74083),f777(f777(f285(x74081),x74084),x74082))) % 174.01/173.90 [7527]E(x75271,x75272)+~E(f777(f777(f155(x75273),x75274),x75271),f777(f777(f155(x75273),x75274),x75272))+~P1(f777(f129(x75273),x75274))+~P1(f777(f777(f235(a851),x75272),f777(f183(f852(x75273)),x75274)))+~P1(f777(f777(f235(a851),x75271),f777(f183(f852(x75273)),x75274))) % 174.01/173.90 [7894]~P62(x78941)+~P1(f777(f777(f235(x78941),x78943),f4(x78941)))+P1(f777(f777(f235(x78941),f4(x78941)),x78942))+~P1(f777(f777(f235(x78941),x78944),f777(f777(f85(x78941),x78943),x78942)))+P1(f777(f777(f235(x78941),x78943),f777(f777(f285(x78941),x78944),x78942))) % 174.01/173.90 [7895]~P62(x78951)+~P1(f777(f777(f234(x78951),x78953),f4(x78951)))+P1(f777(f777(f235(x78951),f4(x78951)),x78952))+~P1(f777(f777(f234(x78951),x78954),f777(f777(f85(x78951),x78953),x78952)))+P1(f777(f777(f234(x78951),x78953),f777(f777(f285(x78951),x78954),x78952))) % 174.01/173.90 [7896]~P62(x78961)+~P1(f777(f777(f235(x78961),x78962),f4(x78961)))+P1(f777(f777(f235(x78961),f4(x78961)),x78962))+~P1(f777(f777(f235(x78961),x78964),f777(f777(f85(x78961),x78963),x78962)))+P1(f777(f777(f235(x78961),x78963),f777(f777(f285(x78961),x78964),x78962))) % 174.01/173.90 [7897]~P62(x78971)+~P1(f777(f777(f235(x78971),x78972),f4(x78971)))+P1(f777(f777(f235(x78971),f4(x78971)),x78972))+~P1(f777(f777(f235(x78971),x78974),f777(f777(f285(x78971),x78973),x78972)))+P1(f777(f777(f235(x78971),x78973),f777(f777(f85(x78971),x78974),x78972))) % 174.01/173.90 [7898]~P62(x78981)+~P1(f777(f777(f235(x78981),x78982),f4(x78981)))+P1(f777(f777(f235(x78981),f4(x78981)),x78982))+~P1(f777(f777(f234(x78981),x78984),f777(f777(f85(x78981),x78983),x78982)))+P1(f777(f777(f234(x78981),x78983),f777(f777(f285(x78981),x78984),x78982))) % 174.01/173.90 [7899]~P62(x78991)+~P1(f777(f777(f235(x78991),x78992),f4(x78991)))+P1(f777(f777(f235(x78991),f4(x78991)),x78992))+~P1(f777(f777(f234(x78991),x78994),f777(f777(f285(x78991),x78993),x78992)))+P1(f777(f777(f234(x78991),x78993),f777(f777(f85(x78991),x78994),x78992))) % 174.01/173.90 [8024]~P7(x80241)+~P1(f777(f777(f281(x80241),x80243),x80244))+~P1(f777(f777(f281(x80241),x80243),x80242))+~P1(f777(f777(f281(x80241),x80242),x80244))+P1(f777(f777(f281(x80241),f777(f777(f45(x80241),x80242),x80243)),f777(f777(f45(x80241),x80244),x80243))) % 174.01/173.90 [8039]~P100(x80391)+~P18(x80391,x80392)+~P1(f777(f777(f234(a851),x80393),x80394))+P1(f777(f777(f234(x80391),f777(f777(f155(x80391),x80392),x80393)),f777(f777(f155(x80391),x80392),x80394)))+~P1(f777(f777(f235(a851),x80394),f777(f183(f852(x80391)),x80392))) % 174.01/173.90 [8089]~P117(x80891)+~P1(f777(f777(f235(x80891),x80892),f82(x80891)))+~P1(f777(f777(f235(x80891),f4(x80891)),x80892))+~P1(f777(f777(f235(a851),x80894),x80893))+P1(f777(f777(f235(x80891),f777(f777(f244(x80891),x80892),x80893)),f777(f777(f244(x80891),x80892),x80894))) % 174.01/173.90 [8090]~P117(x80901)+~P1(f777(f777(f234(x80901),x80902),f82(x80901)))+~P1(f777(f777(f234(x80901),f4(x80901)),x80902))+~P1(f777(f777(f234(a851),x80904),x80903))+P1(f777(f777(f234(x80901),f777(f777(f244(x80901),x80902),x80903)),f777(f777(f244(x80901),x80902),x80904))) % 174.01/173.90 [8091]~P117(x80911)+~P1(f777(f777(f234(x80911),f4(x80911)),x80912))+~P1(f777(f777(f235(a851),f4(a851)),x80913))+~P1(f777(f777(f235(x80911),x80912),x80914))+P1(f777(f777(f235(x80911),f777(f777(f244(x80911),x80912),x80913)),f777(f777(f244(x80911),x80914),x80913))) % 174.01/173.90 [8109]~P100(x81091)+~P18(x81091,f777(f144(x81091),x81092))+~P1(f777(f777(f234(a851),x81094),x81093))+P1(f777(f777(f234(x81091),f777(f777(f155(x81091),x81092),x81093)),f777(f777(f155(x81091),x81092),x81094)))+~P1(f777(f777(f235(a851),x81093),f777(f183(f852(x81091)),x81092))) % 174.01/173.90 [8337]~P7(x83371)+P1(f777(f777(f281(x83371),x83372),x83373))+~P1(f777(f777(f281(x83371),x83374),x83373))+~P1(f777(f777(f281(x83371),x83374),x83372))+~P1(f777(f777(f281(x83371),f777(f777(f45(x83371),x83372),x83374)),f777(f777(f45(x83371),x83373),x83374))) % 174.01/173.90 [8354]~P63(x83541)+~P1(f777(f777(f235(x83541),x83542),f4(x83541)))+~P1(f777(f777(f235(x83541),x83543),x83544))+~P1(f777(f777(f235(x83541),f4(x83541)),f777(f777(f85(x83541),x83543),x83544)))+P1(f777(f777(f235(x83541),f777(f777(f285(x83541),x83542),x83543)),f777(f777(f285(x83541),x83542),x83544))) % 174.01/173.90 [8355]~P62(x83551)+~P1(f777(f777(f234(x83551),x83552),f4(x83551)))+~P1(f777(f777(f234(x83551),x83553),x83554))+~P1(f777(f777(f235(x83551),f4(x83551)),f777(f777(f85(x83551),x83553),x83554)))+P1(f777(f777(f234(x83551),f777(f777(f285(x83551),x83552),x83553)),f777(f777(f285(x83551),x83552),x83554))) % 174.01/173.90 [8365]~P63(x83651)+~P1(f777(f777(f235(x83651),x83654),x83653))+~P1(f777(f777(f235(x83651),f4(x83651)),x83652))+~P1(f777(f777(f235(x83651),f4(x83651)),f777(f777(f85(x83651),x83653),x83654)))+P1(f777(f777(f235(x83651),f777(f777(f285(x83651),x83652),x83653)),f777(f777(f285(x83651),x83652),x83654))) % 174.01/173.90 [8366]~P63(x83661)+~P1(f777(f777(f234(x83661),x83664),x83663))+~P1(f777(f777(f234(x83661),f4(x83661)),x83662))+~P1(f777(f777(f235(x83661),f4(x83661)),f777(f777(f85(x83661),x83663),x83664)))+P1(f777(f777(f234(x83661),f777(f777(f285(x83661),x83662),x83663)),f777(f777(f285(x83661),x83662),x83664))) % 174.01/173.90 [8474]P1(f777(x84741,x84742))+~P1(f777(f65(x84744),x84742))+P1(f777(x84741,f488(x84741,x84743,x84742,x84744)))+~P1(f777(x84741,f182(f858(x84744,a845))))+~P1(f777(f777(f234(f858(x84744,a845)),x84742),x84743)) % 174.01/173.90 [8482]P1(f777(x84821,x84822))+P1(f777(f65(x84823),f488(x84821,x84824,x84822,x84823)))+~P1(f777(f65(x84823),x84822))+~P1(f777(x84821,f182(f858(x84823,a845))))+~P1(f777(f777(f234(f858(x84823,a845)),x84822),x84824)) % 174.01/173.90 [8710]E(f777(f777(f84(a3),f438(x87101,x87102,x87103,x87104)),f439(x87101,x87102,x87103,x87104)),x87104)+~P1(f777(f777(f235(a3),f4(a3)),x87103))+~P1(f777(f777(f235(a3),x87102),x87104))+~P1(f777(f777(f336(a3),x87102),x87101))+P1(f777(f777(f235(a3),x87102),f777(f777(f5(a3),x87104),x87103))) % 174.01/173.90 [8896]~P1(f777(f777(f235(a3),f4(a3)),x88963))+~P1(f777(f777(f235(a3),x88962),x88964))+~P1(f777(f777(f336(a3),x88962),x88961))+P1(f777(f777(f336(a3),f438(x88961,x88962,x88963,x88964)),x88961))+P1(f777(f777(f235(a3),x88962),f777(f777(f5(a3),x88964),x88963))) % 174.01/173.90 [8909]P1(f777(x89091,x89092))+~P1(f777(f65(x89093),x89092))+P1(f777(f777(f336(x89093),f489(x89091,x89094,x89092,x89093)),x89094))+~P1(f777(x89091,f182(f858(x89093,a845))))+~P1(f777(f777(f234(f858(x89093,a845)),x89092),x89094)) % 174.01/173.90 [8926]E(f777(f777(f84(a3),f430(x89261,x89262,x89263,x89264)),f431(x89261,x89262,x89263,x89264)),x89264)+~P1(f777(f777(f235(a3),f4(a3)),x89263))+~P1(f777(f777(f234(a3),x89262),x89264))+P1(f777(f777(f234(a3),x89262),f777(f777(f5(a3),x89264),x89263)))+~P1(f777(f777(f336(a3),f777(f777(f5(a3),x89262),f82(a3))),x89261)) % 174.01/173.90 [8973]~P1(f777(f777(f235(a3),f4(a3)),x89733))+~P1(f777(f777(f235(a3),x89731),x89732))+~P1(f777(f777(f336(a3),x89731),x89734))+P1(f777(f777(f336(a3),f439(x89734,x89731,x89733,x89732)),f297(a3,f82(a3),x89733)))+P1(f777(f777(f235(a3),x89731),f777(f777(f5(a3),x89732),x89733))) % 174.01/173.90 [9066]~P1(f777(f777(f235(a3),f4(a3)),x90663))+~P1(f777(f777(f234(a3),x90662),x90664))+P1(f777(f777(f336(a3),f430(x90661,x90662,x90663,x90664)),x90661))+P1(f777(f777(f234(a3),x90662),f777(f777(f5(a3),x90664),x90663)))+~P1(f777(f777(f336(a3),f777(f777(f5(a3),x90662),f82(a3))),x90661)) % 174.01/173.90 [9104]~P1(f777(f777(f235(a3),f4(a3)),x91043))+~P1(f777(f777(f234(a3),x91041),x91042))+P1(f777(f777(f336(a3),f431(x91044,x91041,x91043,x91042)),f297(a3,f82(a3),x91043)))+P1(f777(f777(f234(a3),x91041),f777(f777(f5(a3),x91042),x91043)))+~P1(f777(f777(f336(a3),f777(f777(f5(a3),x91041),f82(a3))),x91044)) % 174.01/173.90 [9315]P1(f777(x93151,x93152))+~P1(f777(f777(f336(x93153),f489(x93151,x93154,x93152,x93153)),f488(x93151,x93154,x93152,x93153)))+~P1(f777(f65(x93153),x93152))+~P1(f777(x93151,f182(f858(x93153,a845))))+~P1(f777(f777(f234(f858(x93153,a845)),x93152),x93154)) % 174.01/173.90 [9519]P1(f777(x95191,x95192))+~P1(f777(f65(x95193),x95192))+~P1(f777(x95191,f777(f777(f304(x95193),f489(x95191,x95194,x95192,x95193)),f488(x95191,x95194,x95192,x95193))))+~P1(f777(x95191,f182(f858(x95193,a845))))+~P1(f777(f777(f234(f858(x95193,a845)),x95192),x95194)) % 174.01/173.90 [9838]~P99(x98383)+~P52(a851,x98383,f777(f777(f22(a851,f858(a851,a845),f858(a851,a845)),f777(f777(f12(f858(a851,f858(a845,a845)),f858(f858(a851,a845),f858(a851,a845)),a851),f22(a851,a845,a845)),f777(f777(f12(f858(a851,a845),f858(a851,f858(a845,a845)),a851),f777(f12(a845,f858(a845,a845),a851),a333)),f281(a851)))),f777(f777(f12(f858(a851,a845),f858(a851,a845),a851),f777(f12(a845,a845,a851),a330)),f777(f11(a851,a851,a845),f281(a851)))),x98384)+P1(f777(f777(f235(x98383),f777(x98384,x98382)),f777(x98384,x98381)))+~P1(f777(f777(f281(a851),x98382),x98381))+P1(f777(f777(f281(a851),x98381),x98382)) % 174.01/173.90 [7666]~P62(x76661)+P1(f777(f777(f235(x76661),x76662),f4(x76661)))+P1(f777(f777(f235(x76661),f4(x76661)),x76662))+~P1(f777(f777(f235(x76661),f4(x76661)),x76664))+P1(f777(f777(f235(x76661),f777(f777(f285(x76661),x76663),x76662)),x76664)) % 174.01/173.90 [7667]~P62(x76671)+P1(f777(f777(f235(x76671),x76672),f4(x76671)))+~P1(f777(f777(f234(x76671),f4(x76671)),x76674))+P1(f777(f777(f235(x76671),f4(x76671)),x76672))+P1(f777(f777(f234(x76671),f777(f777(f285(x76671),x76673),x76672)),x76674)) % 174.01/173.90 [7950]~P1(f777(f777(f234(a3),x79504),f4(a3)))+~E(x79502,f777(f777(f84(a3),f777(f777(f85(a3),x79501),x79503)),x79504))+P1(f777(f777(f235(a3),f4(a3)),x79501))+~P1(f777(f777(f235(a3),x79501),x79504))+P1(f777(f58(x79502,x79501),f777(f777(f243(a3,a3),x79503),x79504))) % 174.01/173.90 [7987]~P1(f777(x79871,x79874))+P1(f777(x79871,f808(x79872,x79871,x79873)))+~P1(f777(f777(f235(a3),f4(a3)),x79873))+~P1(f777(f777(f234(a3),f4(a3)),x79872))+P1(f777(x79871,f777(f777(f84(a3),x79874),f777(f777(f85(a3),x79872),x79873)))) % 174.01/173.90 [7988]~P1(f777(x79881,x79884))+P1(f777(x79881,f813(x79882,x79881,x79883)))+~P1(f777(f777(f235(a3),f4(a3)),x79883))+~P1(f777(f777(f234(a3),f4(a3)),x79882))+P1(f777(x79881,f777(f777(f5(a3),x79884),f777(f777(f85(a3),x79882),x79883)))) % 174.01/173.90 [7989]~P62(x79891)+P1(f777(f777(f235(x79891),x79892),f4(x79891)))+P1(f777(f777(f235(x79891),f4(x79891)),x79892))+P1(f777(f777(f235(x79891),f4(x79891)),x79893))+~P1(f777(f777(f235(x79891),f777(f777(f285(x79891),x79894),x79892)),x79893)) % 174.01/173.90 [7990]~P62(x79901)+P1(f777(f777(f235(x79901),x79902),f4(x79901)))+P1(f777(f777(f235(x79901),f4(x79901)),x79902))+P1(f777(f777(f234(x79901),f4(x79901)),x79903))+~P1(f777(f777(f234(x79901),f777(f777(f285(x79901),x79904),x79902)),x79903)) % 174.01/173.90 [8034]~E(x80341,f777(f777(f84(a3),f777(f777(f85(a3),x80342),x80343)),x80344))+~P1(f777(f777(f235(a3),f4(a3)),x80342))+~P1(f777(f777(f234(a3),f4(a3)),x80344))+~P1(f777(f777(f235(a3),x80344),x80342))+P1(f777(f58(x80341,x80342),f777(f777(f243(a3,a3),x80343),x80344))) % 174.01/173.90 [8151]~P62(x81511)+P1(f777(f777(f235(x81511),x81512),f4(x81511)))+~P1(f777(f777(f235(x81511),f4(x81511)),x81514))+~P1(f777(f777(f235(x81511),x81513),f777(f777(f85(x81511),x81514),x81512)))+P1(f777(f777(f235(x81511),f777(f777(f285(x81511),x81513),x81512)),x81514)) % 174.01/173.90 [8152]~P62(x81521)+P1(f777(f777(f235(x81521),x81522),f4(x81521)))+~P1(f777(f777(f234(x81521),f4(x81521)),x81524))+~P1(f777(f777(f234(x81521),x81523),f777(f777(f85(x81521),x81524),x81522)))+P1(f777(f777(f234(x81521),f777(f777(f285(x81521),x81523),x81522)),x81524)) % 174.01/173.90 [8230]~P62(x82301)+P1(f777(f777(f235(x82301),x82302),f4(x82301)))+~P1(f777(f777(f235(x82301),x82303),f4(x82301)))+P1(f777(f777(f235(x82301),x82303),f777(f777(f285(x82301),x82304),x82302)))+~P1(f777(f777(f235(x82301),f777(f777(f85(x82301),x82303),x82302)),x82304)) % 174.01/173.90 [8231]~P62(x82311)+P1(f777(f777(f235(x82311),x82312),f4(x82311)))+~P1(f777(f777(f234(x82311),x82313),f4(x82311)))+P1(f777(f777(f234(x82311),x82313),f777(f777(f285(x82311),x82314),x82312)))+~P1(f777(f777(f234(x82311),f777(f777(f85(x82311),x82313),x82312)),x82314)) % 174.01/173.90 [8390]~P62(x83901)+~P1(f777(f777(f235(x83901),x83902),f4(x83901)))+P1(f777(f777(f235(x83901),f4(x83901)),x83902))+~P1(f777(f777(f235(x83901),f777(f777(f285(x83901),x83904),x83902)),x83903))+P1(f777(f777(f235(x83901),f777(f777(f85(x83901),x83903),x83902)),x83904)) % 174.01/173.90 [8391]~P62(x83911)+~P1(f777(f777(f235(x83911),x83912),f4(x83911)))+P1(f777(f777(f235(x83911),f4(x83911)),x83912))+~P1(f777(f777(f235(x83911),f777(f777(f85(x83911),x83914),x83912)),x83913))+P1(f777(f777(f235(x83911),f777(f777(f285(x83911),x83913),x83912)),x83914)) % 174.01/173.90 [8392]~P62(x83921)+~P1(f777(f777(f235(x83921),x83922),f4(x83921)))+P1(f777(f777(f235(x83921),f4(x83921)),x83922))+~P1(f777(f777(f234(x83921),f777(f777(f285(x83921),x83924),x83922)),x83923))+P1(f777(f777(f234(x83921),f777(f777(f85(x83921),x83923),x83922)),x83924)) % 174.01/173.90 [8393]~P62(x83931)+~P1(f777(f777(f235(x83931),x83932),f4(x83931)))+P1(f777(f777(f235(x83931),f4(x83931)),x83932))+~P1(f777(f777(f234(x83931),f777(f777(f85(x83931),x83934),x83932)),x83933))+P1(f777(f777(f234(x83931),f777(f777(f285(x83931),x83933),x83932)),x83934)) % 174.01/173.90 [8412]~P62(x84121)+~P1(f777(f777(f235(x84121),f4(x84121)),x84124))+P1(f777(f777(f235(x84121),f4(x84121)),x84122))+~P1(f777(f777(f235(x84121),f777(f777(f85(x84121),x84124),x84122)),x84123))+P1(f777(f777(f235(x84121),f777(f777(f285(x84121),x84123),x84122)),x84124)) % 174.01/173.90 [8413]~P62(x84131)+~P1(f777(f777(f234(x84131),f4(x84131)),x84134))+P1(f777(f777(f235(x84131),f4(x84131)),x84132))+~P1(f777(f777(f234(x84131),f777(f777(f85(x84131),x84134),x84132)),x84133))+P1(f777(f777(f234(x84131),f777(f777(f285(x84131),x84133),x84132)),x84134)) % 174.01/173.90 [8490]~P62(x84901)+~P1(f777(f777(f235(x84901),x84904),f4(x84901)))+~P1(f777(f777(f235(x84901),x84903),f777(f777(f85(x84901),x84902),x84904)))+P1(f777(f777(f235(x84901),x84902),f777(f777(f285(x84901),x84903),x84904)))+~P1(f777(f777(f235(x84901),f777(f777(f85(x84901),x84902),x84904)),x84903)) % 174.01/173.90 [8491]~P62(x84911)+~P1(f777(f777(f235(x84911),x84912),f4(x84911)))+~P1(f777(f777(f235(x84911),x84913),f777(f777(f85(x84911),x84912),x84914)))+P1(f777(f777(f235(x84911),x84912),f777(f777(f285(x84911),x84913),x84914)))+~P1(f777(f777(f235(x84911),f777(f777(f85(x84911),x84912),x84914)),x84913)) % 174.01/173.90 [8492]~P62(x84921)+~P1(f777(f777(f235(x84921),x84924),f4(x84921)))+~P1(f777(f777(f234(x84921),x84923),f777(f777(f85(x84921),x84922),x84924)))+P1(f777(f777(f234(x84921),x84922),f777(f777(f285(x84921),x84923),x84924)))+~P1(f777(f777(f234(x84921),f777(f777(f85(x84921),x84922),x84924)),x84923)) % 174.01/173.90 [8493]~P62(x84931)+~P1(f777(f777(f234(x84931),x84932),f4(x84931)))+~P1(f777(f777(f234(x84931),x84933),f777(f777(f85(x84931),x84932),x84934)))+P1(f777(f777(f234(x84931),x84932),f777(f777(f285(x84931),x84933),x84934)))+~P1(f777(f777(f234(x84931),f777(f777(f85(x84931),x84932),x84934)),x84933)) % 174.01/173.90 [8592]~P62(x85921)+~P1(f777(f777(f235(x85921),x85923),f4(x85921)))+~P1(f777(f777(f235(x85921),x85922),f777(f777(f85(x85921),x85924),x85923)))+~P1(f777(f777(f235(x85921),f777(f777(f85(x85921),x85924),x85923)),x85922))+P1(f777(f777(f235(x85921),f777(f777(f285(x85921),x85922),x85923)),x85924)) % 174.01/173.90 [8593]~P62(x85931)+~P1(f777(f777(f235(x85931),x85933),f4(x85931)))+~P1(f777(f777(f234(x85931),x85932),f777(f777(f85(x85931),x85934),x85933)))+~P1(f777(f777(f234(x85931),f777(f777(f85(x85931),x85934),x85933)),x85932))+P1(f777(f777(f234(x85931),f777(f777(f285(x85931),x85932),x85933)),x85934)) % 174.01/173.90 [8607]~P62(x86071)+~P1(f777(f777(f235(x86071),f4(x86071)),x86074))+~P1(f777(f777(f235(x86071),x86072),f777(f777(f85(x86071),x86074),x86073)))+~P1(f777(f777(f235(x86071),f777(f777(f85(x86071),x86074),x86073)),x86072))+P1(f777(f777(f235(x86071),f777(f777(f285(x86071),x86072),x86073)),x86074)) % 174.01/173.90 [8608]~P62(x86081)+~P1(f777(f777(f234(x86081),f4(x86081)),x86084))+~P1(f777(f777(f234(x86081),x86082),f777(f777(f85(x86081),x86084),x86083)))+~P1(f777(f777(f234(x86081),f777(f777(f85(x86081),x86084),x86083)),x86082))+P1(f777(f777(f234(x86081),f777(f777(f285(x86081),x86082),x86083)),x86084)) % 174.01/173.90 [8765]E(f777(f777(f5(a3),f440(x87651,x87652,x87653,x87654)),f441(x87651,x87652,x87653,x87654)),x87654)+~P1(f777(f777(f235(a3),f4(a3)),x87653))+~P1(f777(f777(f336(a3),x87652),x87651))+~P1(f777(f777(f235(a3),x87654),x87652))+P1(f777(f777(f235(a3),f777(f777(f84(a3),x87654),x87653)),x87652)) % 174.01/173.90 [8826]~P1(f777(x88261,x88262))+~P1(f777(f777(f235(a3),f4(a3)),x88264))+~P1(f777(f777(f234(a3),f4(a3)),x88263))+~P1(f777(x88261,f777(f777(f84(a3),f808(x88263,x88261,x88264)),x88264)))+P1(f777(x88261,f777(f777(f84(a3),x88262),f777(f777(f85(a3),x88263),x88264)))) % 174.01/173.90 [8827]~P1(f777(x88271,x88272))+~P1(f777(f777(f235(a3),f4(a3)),x88274))+~P1(f777(f777(f234(a3),f4(a3)),x88273))+~P1(f777(x88271,f777(f777(f5(a3),f813(x88273,x88271,x88274)),x88274)))+P1(f777(x88271,f777(f777(f5(a3),x88272),f777(f777(f85(a3),x88273),x88274)))) % 174.01/173.90 [8966]~P1(f777(f777(f235(a3),f4(a3)),x89663))+~P1(f777(f777(f336(a3),x89662),x89661))+~P1(f777(f777(f235(a3),x89664),x89662))+P1(f777(f777(f336(a3),f440(x89661,x89662,x89663,x89664)),x89661))+P1(f777(f777(f235(a3),f777(f777(f84(a3),x89664),x89663)),x89662)) % 174.01/173.90 [8986]E(f777(f777(f5(a3),f433(x89861,x89862,x89863,x89864)),f434(x89861,x89862,x89863,x89864)),x89864)+~P1(f777(f777(f235(a3),f4(a3)),x89863))+~P1(f777(f777(f234(a3),x89864),x89862))+~P1(f777(f777(f336(a3),f777(f777(f84(a3),x89862),f82(a3))),x89861))+P1(f777(f777(f234(a3),f777(f777(f84(a3),x89864),x89863)),x89862)) % 174.01/173.90 [9018]~P1(f777(f777(f235(a3),f4(a3)),x90182))+~P1(f777(f777(f336(a3),x90183),x90184))+~P1(f777(f777(f235(a3),x90181),x90183))+P1(f777(f777(f336(a3),f441(x90184,x90183,x90182,x90181)),f297(a3,f82(a3),x90182)))+P1(f777(f777(f235(a3),f777(f777(f84(a3),x90181),x90182)),x90183)) % 174.01/173.90 [9097]~P1(f777(f777(f235(a3),f4(a3)),x90973))+~P1(f777(f777(f234(a3),x90974),x90972))+P1(f777(f777(f336(a3),f433(x90971,x90972,x90973,x90974)),x90971))+~P1(f777(f777(f336(a3),f777(f777(f84(a3),x90972),f82(a3))),x90971))+P1(f777(f777(f234(a3),f777(f777(f84(a3),x90974),x90973)),x90972)) % 174.01/173.90 [9136]~P1(f777(f777(f235(a3),f4(a3)),x91362))+~P1(f777(f777(f234(a3),x91361),x91363))+P1(f777(f777(f336(a3),f434(x91364,x91363,x91362,x91361)),f297(a3,f82(a3),x91362)))+~P1(f777(f777(f336(a3),f777(f777(f84(a3),x91363),f82(a3))),x91364))+P1(f777(f777(f234(a3),f777(f777(f84(a3),x91361),x91362)),x91363)) % 174.01/173.90 [9402]~P36(x94021,x94023)+~P30(x94021,x94024)+P36(x94021,f777(f777(f105(f858(f857(x94021,x94021),a845)),x94022),x94023))+~P1(f777(f777(f234(f858(f857(x94021,x94021),a845)),x94022),f777(f242(f858(f857(x94021,x94021),a845),f858(f857(x94021,x94021),a845)),x94024)))+~P1(f777(f777(f234(f858(f857(x94021,x94021),a845)),x94023),f777(f252(f858(f857(x94021,x94021),a845),f858(f857(x94021,x94021),a845)),x94024))) % 174.01/173.90 [9670]~E(f777(f709(x96701,x96704,x96703,x96702),f713(x96701,x96704,x96703,x96702)),f185(f852(a844)))+P1(f777(f777(f235(a3),f712(x96701,x96704,x96703,x96702)),f713(x96701,x96704,x96703,x96702)))+P1(f777(f777(f777(x96701,x96702),x96703),x96704))+P1(f777(f777(f777(x96701,f709(x96701,x96704,x96703,x96702)),f712(x96701,x96704,x96703,x96702)),f777(f777(f84(a3),f713(x96701,x96704,x96703,x96702)),f82(a3))))+~P1(f777(f323(f857(f858(a3,f855(f852(a844))),f857(a3,a3)),a313),f777(f777(f243(f858(a3,f855(f852(a844))),f857(a3,a3)),x96702),f777(f777(f243(a3,a3),x96703),x96704)))) % 174.01/173.90 [9771]~P22(x97712,x97714,x97713)+E(x97711,f182(f858(x97712,a845)))+~P1(f777(f65(x97712),x97711))+P1(f777(f777(f336(x97712),f777(x97713,x97711)),x97711))+~P1(f777(f777(f336(x97712),f777(f777(x97714,f460(x97711,x97713,x97714,x97712)),f461(x97711,x97713,x97714,x97712))),f777(f777(f304(x97712),f460(x97711,x97713,x97714,x97712)),f777(f777(f304(x97712),f461(x97711,x97713,x97714,x97712)),f182(f858(x97712,a845)))))) % 174.01/173.90 [9322]~P53(x93221,x93221,x93224)+P1(f777(f777(f336(f857(x93221,x93221)),f777(f777(f243(x93221,x93221),x93222),x93223)),f302(x93221,x93224)))+P1(f777(f777(f336(f857(x93221,x93221)),f777(f777(f243(x93221,x93221),x93223),x93222)),f302(x93221,x93224)))+~P1(f777(f777(f336(f857(x93221,x93221)),f777(f777(f243(x93221,x93221),x93225),x93222)),f302(x93221,x93224)))+~P1(f777(f777(f336(f857(x93221,x93221)),f777(f777(f243(x93221,x93221),x93225),x93223)),f302(x93221,x93224))) % 174.01/173.90 [5502]E(x55021,f4(a851))+~E(f777(f44(x55022),x55025),x55021)+E(f777(f44(x55022),x55023),f777(a116,x55021))+~E(x55023,f777(f777(f304(x55022),x55024),x55025))+P1(f777(f777(f336(x55022),x55024),x55025)) % 174.01/173.90 [5623]~P61(x56232)+E(x56231,f4(x56232))+E(x56233,f4(x56232))+~E(f777(f777(f285(x56232),x56234),x56233),f777(f777(f285(x56232),x56235),x56231))+E(f777(f777(f85(x56232),x56234),x56231),f777(f777(f85(x56232),x56235),x56233)) % 174.01/173.90 [5624]~P61(x56242)+E(x56241,f4(x56242))+E(x56243,f4(x56242))+~E(f777(f777(f85(x56242),x56244),x56243),f777(f777(f85(x56242),x56245),x56241))+E(f777(f777(f285(x56242),x56244),x56241),f777(f777(f285(x56242),x56245),x56243)) % 174.01/173.90 [5697]~E(f777(f44(x56971),x56975),x56973)+~E(x56975,f182(f858(x56971,a845)))+E(f777(f44(x56971),x56972),f777(a116,x56973))+~E(x56972,f777(f777(f304(x56971),x56974),x56975))+P1(f777(f777(f336(x56971),x56974),x56975)) % 174.01/173.90 [5924]~P85(x59242)+~E(f777(x59243,x59245),f4(x59242))+E(f777(f777(f13(x59241,x59242),x59243),x59244),f4(x59242))+~P1(f777(f65(x59241),x59244))+~P1(f777(f777(f336(x59241),x59245),x59244)) % 174.01/173.90 [6309]~P100(x63093)+E(x63091,x63092)+~E(f777(f296(x63093,x63094),x63091),f777(f296(x63093,x63095),x63092))+~P1(f777(f777(f235(x63093),x63095),x63092))+~P1(f777(f777(f235(x63093),x63094),x63091)) % 174.01/173.90 [6310]~P100(x63103)+E(x63101,x63102)+~E(f777(f296(x63103,x63101),x63104),f777(f296(x63103,x63102),x63105))+~P1(f777(f777(f235(x63103),x63102),x63105))+~P1(f777(f777(f235(x63103),x63101),x63104)) % 174.01/173.90 [7421]~P100(x74211)+~P18(x74211,f777(f777(f127(x74211),x74214),x74215))+~P1(f777(f777(f336(x74211),x74213),f777(f160(x74211),x74215)))+~P1(f777(f777(f336(x74211),x74212),f777(f160(x74211),x74214)))+P1(f777(f777(f234(x74211),x74212),x74213)) % 174.01/173.90 [8524]~P99(x85241)+~P1(f777(f777(f235(f858(x85241,a845)),f297(x85241,x85245,x85242)),f297(x85241,x85244,x85243)))+~P1(f777(f777(f234(x85241),x85245),x85242))+P1(f777(f777(f235(x85241),x85242),x85243))+P1(f777(f777(f235(x85241),x85244),x85245)) % 174.01/173.90 [9815]~P21(x98152,x98155,x98153)+E(x98151,f182(f858(x98152,a845)))+~E(f777(f777(x98155,f777(x98154,f578(x98151,x98154,x98153,x98155,x98152))),f777(x98154,f579(x98151,x98154,x98153,x98155,x98152))),f777(x98154,f777(f777(x98155,f578(x98151,x98154,x98153,x98155,x98152)),f579(x98151,x98154,x98153,x98155,x98152))))+E(f777(x98153,f777(f305(x98152,x98152,x98154),x98151)),f777(x98154,f777(x98153,x98151)))+~P1(f777(f65(x98152),x98151)) % 174.01/173.90 [6306]~P22(x63062,x63065,x63063)+E(x63061,f182(f858(x63062,a845)))+~P1(f777(f65(x63062),x63061))+E(f777(x63063,f777(f777(f304(x63062),x63064),x63061)),f777(f777(x63065,x63064),f777(x63063,x63061)))+P1(f777(f777(f336(x63062),x63064),x63061)) % 174.01/173.90 [7158]~P21(x71582,x71583,x71584)+E(f777(f777(x71583,f777(x71584,x71581)),f777(x71584,x71585)),f777(x71584,x71585))+E(x71581,f182(f858(x71582,a845)))+~P1(f777(f65(x71582),x71585))+~P1(f777(f777(f234(f858(x71582,a845)),x71581),x71585)) % 174.01/173.90 [7562]~P22(x75624,x75625,x75621)+E(f777(x75621,x75622),x75623)+~P1(f777(f65(x75624),x75622))+~E(f777(f777(f5(f858(x75624,a845)),x75622),f777(f777(f304(x75624),x75623),f182(f858(x75624,a845)))),f182(f858(x75624,a845)))+~P1(f777(f777(f336(x75624),x75623),x75622)) % 174.01/173.90 [7709]E(x77091,x77092)+~E(f777(f183(f852(x77093)),x77092),f777(f183(f852(x77094)),x77095))+~E(f777(f183(f852(x77093)),x77091),f777(f183(f852(x77094)),x77095))+~E(f168(x77094,x77093,f777(f777(f169(x77094,x77093),x77095),x77091)),f168(x77094,x77093,f777(f777(f169(x77094,x77093),x77095),x77092)))+~P1(f777(f129(x77094),x77095)) % 174.01/173.90 [8447]~P70(x84471)+~P112(x84471)+~P1(f777(f65(x84472),x84475))+P1(f777(f777(f281(x84471),f777(f777(f13(x84472,x84471),x84473),x84474)),f777(f777(f13(x84472,x84471),x84473),x84475)))+~P1(f777(f777(f234(f858(x84472,a845)),x84474),x84475)) % 174.01/173.90 [8497]E(x84971,x84972)+~P12(x84973,x84974,x84975)+E(f777(f777(f106(f858(x84973,a845)),x84971),x84972),f182(f858(x84973,a845)))+~P1(f777(f777(f336(f858(x84973,a845)),x84972),f777(f777(f63(x84973),x84974),x84975)))+~P1(f777(f777(f336(f858(x84973,a845)),x84971),f777(f777(f63(x84973),x84974),x84975))) % 174.01/173.90 [9200]~P66(x92002)+~E(f777(x92003,f480(x92003,x92004,x92005,x92001,x92002)),f4(x92002))+E(f777(f777(f10(x92001,x92002),x92003),x92004),f777(f777(f10(x92001,x92002),x92003),x92005))+~P1(f777(f65(x92001),x92005))+~P1(f777(f777(f234(f858(x92001,a845)),x92004),x92005)) % 174.01/173.90 [9201]~P66(x92012)+~E(f777(x92013,f483(x92013,x92014,x92015,x92011,x92012)),f4(x92012))+E(f777(f777(f10(x92011,x92012),x92013),x92014),f777(f777(f10(x92011,x92012),x92013),x92015))+~P1(f777(f65(x92011),x92015))+~P1(f777(f777(f234(f858(x92011,a845)),x92014),x92015)) % 174.01/173.90 [9202]~P70(x92022)+~E(f777(x92023,f481(x92023,x92024,x92025,x92021,x92022)),f82(x92022))+E(f777(f777(f13(x92021,x92022),x92023),x92024),f777(f777(f13(x92021,x92022),x92023),x92025))+~P1(f777(f65(x92021),x92025))+~P1(f777(f777(f234(f858(x92021,a845)),x92024),x92025)) % 174.01/173.90 [9203]~P70(x92032)+~E(f777(x92033,f482(x92033,x92034,x92035,x92031,x92032)),f82(x92032))+E(f777(f777(f13(x92031,x92032),x92033),x92034),f777(f777(f13(x92031,x92032),x92033),x92035))+~P1(f777(f65(x92031),x92035))+~P1(f777(f777(f234(f858(x92031,a845)),x92034),x92035)) % 174.01/173.90 [9653]~P81(x96531)+~P1(f777(f65(x96532),x96535))+~P1(f777(f777(f234(x96531),f4(x96531)),f777(x96533,f443(x96533,x96534,x96535,x96532,x96531))))+P1(f777(f777(f234(x96531),f777(f777(f10(x96532,x96531),x96533),x96534)),f777(f777(f10(x96532,x96531),x96533),x96535)))+~P1(f777(f777(f234(f858(x96532,a845)),x96534),x96535)) % 174.01/173.90 [7418]E(x74181,f4(a851))+P1(f777(x74182,x74183))+~E(x74184,f777(f777(f84(a851),f777(f777(f85(a851),x74181),x74183)),x74185))+~P1(f777(f777(f235(a851),x74185),x74181))+~P1(f777(x74182,f777(f777(f45(a851),x74184),x74181))) % 174.01/173.90 [7501]E(x75011,f4(a851))+P1(f777(x75012,x75013))+~P1(f777(x75012,f54(a851,x75014,x75011)))+~E(x75014,f777(f777(f84(a851),f777(f777(f85(a851),x75011),x75015)),x75013))+~P1(f777(f777(f235(a851),x75013),x75011)) % 174.01/173.90 [7797]~P61(x77973)+E(f777(x77971,x77972),f4(x77973))+~P1(f777(f65(x77974),x77975))+E(f777(f777(f13(x77974,x77973),x77971),f777(f777(f5(f858(x77974,a845)),x77975),f777(f777(f304(x77974),x77972),f182(f858(x77974,a845))))),f777(f777(f13(x77974,x77973),x77971),x77975))+P1(f777(f777(f336(x77974),x77972),x77975)) % 174.01/173.90 [8191]~P66(x81911)+~P1(f777(f65(x81912),x81915))+~P1(f777(f65(x81912),x81914))+~E(f777(f777(f106(f858(x81912,a845)),x81914),x81915),f182(f858(x81912,a845)))+E(f777(f777(f84(x81911),f777(f777(f10(x81912,x81911),x81913),x81914)),f777(f777(f10(x81912,x81911),x81913),x81915)),f777(f777(f10(x81912,x81911),x81913),f777(f777(f105(f858(x81912,a845)),x81914),x81915))) % 174.01/173.90 [8193]~P70(x81931)+~P1(f777(f65(x81932),x81935))+~P1(f777(f65(x81932),x81934))+~E(f777(f777(f106(f858(x81932,a845)),x81934),x81935),f182(f858(x81932,a845)))+E(f777(f777(f85(x81931),f777(f777(f13(x81932,x81931),x81933),x81934)),f777(f777(f13(x81932,x81931),x81933),x81935)),f777(f777(f13(x81932,x81931),x81933),f777(f777(f105(f858(x81932,a845)),x81934),x81935))) % 174.01/173.90 [8283]~P61(x82833)+E(f777(x82831,x82832),f4(x82833))+~P1(f777(f65(x82834),x82835))+E(f777(f777(f13(x82834,x82833),x82831),f777(f777(f5(f858(x82834,a845)),x82835),f777(f777(f304(x82834),x82832),f182(f858(x82834,a845))))),f777(f777(f285(x82833),f777(f777(f13(x82834,x82833),x82831),x82835)),f777(x82831,x82832)))+~P1(f777(f777(f336(x82834),x82832),x82835)) % 174.01/173.90 [8948]~P12(x89481,x89485,x89484)+~E(f777(f777(f63(x89481),f777(f777(f304(x89481),x89482),f182(f858(x89481,a845)))),x89484),f777(f777(f63(x89481),f777(f777(f304(x89481),x89483),f182(f858(x89481,a845)))),x89484))+~P1(f777(f777(f336(x89481),x89483),x89485))+~P1(f777(f777(f336(x89481),x89482),x89485))+P1(f777(f777(f336(f857(x89481,x89481)),f777(f777(f243(x89481,x89481),x89482),x89483)),x89484)) % 174.01/173.90 [8965]~P12(x89651,x89655,x89653)+E(f777(f777(f63(x89651),f777(f777(f304(x89651),x89652),f182(f858(x89651,a845)))),x89653),f777(f777(f63(x89651),f777(f777(f304(x89651),x89654),f182(f858(x89651,a845)))),x89653))+~P1(f777(f777(f336(x89651),x89654),x89655))+~P1(f777(f777(f336(x89651),x89652),x89655))+~P1(f777(f777(f336(f857(x89651,x89651)),f777(f777(f243(x89651,x89651),x89652),x89654)),x89653)) % 174.01/173.90 [9227]~P70(x92271)+~P1(f777(f65(x92272),x92275))+~P1(f777(f65(x92272),x92274))+~E(f777(f777(f106(f858(x92272,a845)),x92274),x92275),f182(f858(x92272,a845)))+E(f777(f777(f85(x92271),f777(f777(f777(f69(x92271,x92272,f85(x92271)),x92273),f82(x92271)),x92274)),f777(f777(f777(f69(x92271,x92272,f85(x92271)),x92273),f82(x92271)),x92275)),f777(f777(f777(f69(x92271,x92272,f85(x92271)),x92273),f82(x92271)),f777(f777(f105(f858(x92272,a845)),x92274),x92275))) % 174.01/173.90 [9237]~P66(x92371)+~E(f777(x92373,f512(x92373,x92375,x92374,x92372,x92371)),f4(x92371))+~P1(f777(f65(x92372),x92374))+~P1(f777(f65(x92372),x92375))+E(f777(f777(f84(x92371),f777(f777(f10(x92372,x92371),x92373),x92374)),f777(f777(f10(x92372,x92371),x92373),x92375)),f777(f777(f10(x92372,x92371),x92373),f777(f777(f105(f858(x92372,a845)),x92374),x92375))) % 174.01/173.90 [9238]~P66(x92381)+~E(f777(x92383,f516(x92383,x92385,x92384,x92382,x92381)),f4(x92381))+~P1(f777(f65(x92382),x92384))+~P1(f777(f65(x92382),x92385))+E(f777(f777(f84(x92381),f777(f777(f10(x92382,x92381),x92383),x92384)),f777(f777(f10(x92382,x92381),x92383),x92385)),f777(f777(f10(x92382,x92381),x92383),f777(f777(f105(f858(x92382,a845)),x92384),x92385))) % 174.01/173.90 [9239]~P70(x92391)+~E(f777(x92393,f513(x92393,x92395,x92394,x92392,x92391)),f82(x92391))+~P1(f777(f65(x92392),x92394))+~P1(f777(f65(x92392),x92395))+E(f777(f777(f85(x92391),f777(f777(f13(x92392,x92391),x92393),x92394)),f777(f777(f13(x92392,x92391),x92393),x92395)),f777(f777(f13(x92392,x92391),x92393),f777(f777(f105(f858(x92392,a845)),x92394),x92395))) % 174.01/173.90 [9240]~P70(x92401)+~E(f777(x92403,f515(x92403,x92405,x92404,x92402,x92401)),f82(x92401))+~P1(f777(f65(x92402),x92404))+~P1(f777(f65(x92402),x92405))+E(f777(f777(f85(x92401),f777(f777(f13(x92402,x92401),x92403),x92404)),f777(f777(f13(x92402,x92401),x92403),x92405)),f777(f777(f13(x92402,x92401),x92403),f777(f777(f105(f858(x92402,a845)),x92404),x92405))) % 174.01/173.90 [9444]~P70(x94441)+~E(f777(x94443,f533(x94443,x94445,x94444,x94442,x94441)),f82(x94441))+~P1(f777(f65(x94442),x94444))+~P1(f777(f65(x94442),x94445))+E(f777(f777(f85(x94441),f777(f777(f777(f69(x94441,x94442,f85(x94441)),x94443),f82(x94441)),x94444)),f777(f777(f777(f69(x94441,x94442,f85(x94441)),x94443),f82(x94441)),x94445)),f777(f777(f777(f69(x94441,x94442,f85(x94441)),x94443),f82(x94441)),f777(f777(f105(f858(x94442,a845)),x94444),x94445))) % 174.01/173.90 [9545]~P66(x95452)+E(f777(f777(f10(x95451,x95452),x95453),x95454),f777(f777(f10(x95451,x95452),x95453),x95455))+~P1(f777(f65(x95451),x95455))+~P1(f777(f777(f234(f858(x95451,a845)),x95454),x95455))+P1(f777(f777(f336(x95451),f480(x95453,x95454,x95455,x95451,x95452)),f777(f777(f5(f858(x95451,a845)),x95455),x95454))) % 174.01/173.90 [9546]~P66(x95462)+E(f777(f777(f10(x95461,x95462),x95463),x95464),f777(f777(f10(x95461,x95462),x95463),x95465))+~P1(f777(f65(x95461),x95465))+~P1(f777(f777(f234(f858(x95461,a845)),x95464),x95465))+P1(f777(f777(f336(x95461),f483(x95463,x95464,x95465,x95461,x95462)),f777(f777(f5(f858(x95461,a845)),x95465),x95464))) % 174.01/173.90 [9547]~P70(x95472)+E(f777(f777(f13(x95471,x95472),x95473),x95474),f777(f777(f13(x95471,x95472),x95473),x95475))+~P1(f777(f65(x95471),x95475))+~P1(f777(f777(f234(f858(x95471,a845)),x95474),x95475))+P1(f777(f777(f336(x95471),f481(x95473,x95474,x95475,x95471,x95472)),f777(f777(f5(f858(x95471,a845)),x95475),x95474))) % 174.01/173.90 [9548]~P70(x95482)+E(f777(f777(f13(x95481,x95482),x95483),x95484),f777(f777(f13(x95481,x95482),x95483),x95485))+~P1(f777(f65(x95481),x95485))+~P1(f777(f777(f234(f858(x95481,a845)),x95484),x95485))+P1(f777(f777(f336(x95481),f482(x95483,x95484,x95485,x95481,x95482)),f777(f777(f5(f858(x95481,a845)),x95485),x95484))) % 174.01/173.90 [9562]~P66(x95621)+~P1(f777(f65(x95622),x95624))+~P1(f777(f65(x95622),x95625))+E(f777(f777(f84(x95621),f777(f777(f10(x95622,x95621),x95623),x95624)),f777(f777(f10(x95622,x95621),x95623),x95625)),f777(f777(f10(x95622,x95621),x95623),f777(f777(f105(f858(x95622,a845)),x95624),x95625)))+P1(f777(f777(f336(x95622),f512(x95623,x95625,x95624,x95622,x95621)),f777(f777(f106(f858(x95622,a845)),x95624),x95625))) % 174.01/173.90 [9563]~P66(x95631)+~P1(f777(f65(x95632),x95634))+~P1(f777(f65(x95632),x95635))+E(f777(f777(f84(x95631),f777(f777(f10(x95632,x95631),x95633),x95634)),f777(f777(f10(x95632,x95631),x95633),x95635)),f777(f777(f10(x95632,x95631),x95633),f777(f777(f105(f858(x95632,a845)),x95634),x95635)))+P1(f777(f777(f336(x95632),f516(x95633,x95635,x95634,x95632,x95631)),f777(f777(f106(f858(x95632,a845)),x95634),x95635))) % 174.01/173.90 [9564]~P70(x95641)+~P1(f777(f65(x95642),x95644))+~P1(f777(f65(x95642),x95645))+E(f777(f777(f85(x95641),f777(f777(f13(x95642,x95641),x95643),x95644)),f777(f777(f13(x95642,x95641),x95643),x95645)),f777(f777(f13(x95642,x95641),x95643),f777(f777(f105(f858(x95642,a845)),x95644),x95645)))+P1(f777(f777(f336(x95642),f513(x95643,x95645,x95644,x95642,x95641)),f777(f777(f106(f858(x95642,a845)),x95644),x95645))) % 174.01/173.90 [9565]~P70(x95651)+~P1(f777(f65(x95652),x95654))+~P1(f777(f65(x95652),x95655))+E(f777(f777(f85(x95651),f777(f777(f13(x95652,x95651),x95653),x95654)),f777(f777(f13(x95652,x95651),x95653),x95655)),f777(f777(f13(x95652,x95651),x95653),f777(f777(f105(f858(x95652,a845)),x95654),x95655)))+P1(f777(f777(f336(x95652),f515(x95653,x95655,x95654,x95652,x95651)),f777(f777(f106(f858(x95652,a845)),x95654),x95655))) % 174.01/173.90 [9577]~P81(x95775)+~P1(f777(f65(x95771),x95774))+P1(f777(f777(f234(x95775),f777(f777(f10(x95771,x95775),x95772),x95773)),f777(f777(f10(x95771,x95775),x95772),x95774)))+~P1(f777(f777(f234(f858(x95771,a845)),x95773),x95774))+P1(f777(f777(f336(x95771),f443(x95772,x95773,x95774,x95771,x95775)),f777(f777(f5(f858(x95771,a845)),x95774),x95773))) % 174.01/173.90 [9619]~P70(x96191)+~P1(f777(f65(x96192),x96194))+~P1(f777(f65(x96192),x96195))+E(f777(f777(f85(x96191),f777(f777(f777(f69(x96191,x96192,f85(x96191)),x96193),f82(x96191)),x96194)),f777(f777(f777(f69(x96191,x96192,f85(x96191)),x96193),f82(x96191)),x96195)),f777(f777(f777(f69(x96191,x96192,f85(x96191)),x96193),f82(x96191)),f777(f777(f105(f858(x96192,a845)),x96194),x96195)))+P1(f777(f777(f336(x96192),f533(x96193,x96195,x96194,x96192,x96191)),f777(f777(f106(f858(x96192,a845)),x96194),x96195))) % 174.01/173.90 [8674]~P22(x86741,x86744,x86745)+~P1(f777(f65(x86741),x86742))+E(f777(f777(f5(f858(x86741,a845)),x86742),f777(f777(f304(x86741),x86743),f182(f858(x86741,a845)))),f182(f858(x86741,a845)))+~P1(f777(f777(f336(x86741),x86743),x86742))+E(f777(f777(x86744,x86743),f777(x86745,f777(f777(f5(f858(x86741,a845)),x86742),f777(f777(f304(x86741),x86743),f182(f858(x86741,a845)))))),f777(x86745,x86742)) % 174.01/173.90 [8741]~P22(x87411,x87414,x87415)+~P1(f777(f65(x87411),x87413))+~P1(f777(f65(x87411),x87412))+E(f777(f777(f106(f858(x87411,a845)),x87412),x87413),f182(f858(x87411,a845)))+E(f777(f777(x87414,f777(x87415,f777(f777(f105(f858(x87411,a845)),x87412),x87413))),f777(x87415,f777(f777(f106(f858(x87411,a845)),x87412),x87413))),f777(f777(x87414,f777(x87415,x87412)),f777(x87415,x87413))) % 174.01/173.90 [9242]~P1(f777(f777(f234(a3),x92424),f4(a3)))+~P1(f777(f777(f235(a3),x92423),x92425))+P1(f777(f777(f234(a3),x92421),x92422))+~P1(f777(f777(f235(a3),x92423),x92424))+~P1(f777(f777(f234(a3),f777(f777(f84(a3),f777(f777(f85(a3),x92423),x92422)),x92425)),f777(f777(f84(a3),f777(f777(f85(a3),x92423),x92421)),x92424))) % 174.01/173.90 [9244]~P1(f777(f777(f234(a3),f4(a3)),x92445))+P1(f777(f777(f234(a3),x92441),x92442))+~P1(f777(f777(f235(a3),x92443),x92444))+~P1(f777(f777(f235(a3),x92445),x92444))+~P1(f777(f777(f234(a3),f777(f777(f84(a3),f777(f777(f85(a3),x92444),x92441)),x92445)),f777(f777(f84(a3),f777(f777(f85(a3),x92444),x92442)),x92443))) % 174.01/173.90 [9357]~P61(x93575)+E(f777(x93571,f514(x93571,x93572,x93573,x93574,x93575)),f4(x93575))+~P1(f777(f65(x93574),x93573))+~P1(f777(f65(x93574),x93572))+E(f777(f777(f285(x93575),f777(f777(f85(x93575),f777(f777(f13(x93574,x93575),x93571),x93573)),f777(f777(f13(x93574,x93575),x93571),x93572))),f777(f777(f13(x93574,x93575),x93571),f777(f777(f106(f858(x93574,a845)),x93573),x93572))),f777(f777(f13(x93574,x93575),x93571),f777(f777(f105(f858(x93574,a845)),x93573),x93572))) % 174.01/173.90 [9612]~P61(x96121)+~P1(f777(f65(x96122),x96124))+~P1(f777(f65(x96122),x96125))+E(f777(f777(f285(x96121),f777(f777(f85(x96121),f777(f777(f13(x96122,x96121),x96123),x96124)),f777(f777(f13(x96122,x96121),x96123),x96125))),f777(f777(f13(x96122,x96121),x96123),f777(f777(f106(f858(x96122,a845)),x96124),x96125))),f777(f777(f13(x96122,x96121),x96123),f777(f777(f105(f858(x96122,a845)),x96124),x96125)))+P1(f777(f777(f336(x96122),f514(x96123,x96125,x96124,x96122,x96121)),f777(f777(f106(f858(x96122,a845)),x96124),x96125))) % 174.01/173.90 [8985]E(f777(f777(f127(x89851),x89852),x89853),f777(f777(f127(x89851),x89854),x89855))+~E(f777(f777(f161(x89851),f777(f183(f852(x89851)),x89854)),x89852),x89854)+~E(f777(f777(f161(x89851),f777(f183(f852(x89851)),x89852)),x89854),x89852)+~E(x89855,f777(f777(f127(x89851),f777(f777(f130(x89851),f777(f183(f852(x89851)),x89854)),x89852)),x89853))+~E(f777(f777(f127(x89851),f777(f777(f130(x89851),f777(f183(f852(x89851)),x89852)),x89854)),x89855),x89853) % 174.01/173.90 [9355]~P100(x93552)+E(f777(f777(f140(x93551,x93552,x93553),x93554),f153(x93551,x93554,x93555)),x93555)+~P18(x93552,f777(f777(f145(x93551,x93552),x93553),x93555))+~P1(f777(f777(f336(x93551),x93554),f777(f160(x93551),x93555)))+~E(f777(f133(x93551),f777(f128(x93551,f777(f777(f12(x93552,a845,x93551),f777(a332,f777(x93553,x93554))),x93553)),x93555)),x93554) % 174.01/173.90 [9667]~P64(x96671)+~P1(f777(f70(x96671,x96671,f85(x96671),x96672,x96673),x96675))+~P1(f777(f777(f336(x96671),x96674),x96673))+P1(f777(f777(f336(x96671),x96672),x96673))+P1(f777(f70(x96671,x96671,f85(x96671),x96674,f777(f777(f304(x96671),x96672),f777(f777(f5(f858(x96671,a845)),x96673),f777(f777(f304(x96671),x96674),f182(f858(x96671,a845)))))),x96675)) % 174.01/173.90 [7165]E(x71651,x71652)+~P29(x71654,x71655,x71653,x71656)+~E(f777(x71653,x71651),f777(x71653,x71652))+~P1(f777(f777(f336(x71654),x71652),x71656))+~P1(f777(f777(f336(x71654),x71651),x71656)) % 174.01/173.90 [6404]~P137(x64044)+E(x64041,x64042)+~E(x64045,x64046)+E(x64043,f4(x64044))+~E(f777(f777(f84(x64044),x64045),f777(f777(f85(x64044),x64043),x64041)),f777(f777(f84(x64044),x64046),f777(f777(f85(x64044),x64043),x64042))) % 174.01/173.90 [7481]~P100(x74811)+~P9(x74811)+~P1(f777(f777(f235(x74811),x74812),f777(x74815,x74816)))+~P1(f777(f777(f336(x74813),x74816),x74814))+P1(f777(f777(f235(x74811),x74812),f777(f777(f48(x74813,x74811),x74814),x74815))) % 174.01/173.90 [9830]~P85(x98306)+~P1(f777(f65(x98301),x98305))+P1(f777(f777(f336(x98301),f633(x98302,x98303,x98304,x98305,x98301,x98306)),x98304))+P1(f777(f777(f281(x98306),f777(f777(f13(x98301,x98306),x98303),x98304)),f777(f777(f13(x98301,x98306),x98302),x98305)))+~P1(f777(f777(f234(f858(x98301,a845)),x98304),x98305)) % 174.01/173.90 [9953]~P85(x99531)+~P1(f777(f65(x99532),x99536))+~P1(f777(f777(f281(x99531),f777(x99533,f633(x99535,x99533,x99534,x99536,x99532,x99531))),f777(x99535,f633(x99535,x99533,x99534,x99536,x99532,x99531))))+P1(f777(f777(f281(x99531),f777(f777(f13(x99532,x99531),x99533),x99534)),f777(f777(f13(x99532,x99531),x99535),x99536)))+~P1(f777(f777(f234(f858(x99532,a845)),x99534),x99536)) % 174.01/173.90 [8162]~P100(x81621)+~P9(x81621)+~P1(f777(f777(f235(x81621),f777(x81624,x81626)),x81625))+~P1(f777(f777(f336(x81622),x81626),x81623))+P1(f777(f777(f235(x81621),f777(f777(f49(x81622,x81621),x81623),x81624)),x81625)) % 174.01/173.90 [8419]~P23(x84192,x84195,x84196,x84191)+~P1(f777(f65(x84192),x84194))+~P1(f777(f65(x84192),x84193))+~E(f777(f777(f106(f858(x84192,a845)),x84193),x84194),f182(f858(x84192,a845)))+E(f777(x84191,f777(f777(f105(f858(x84192,a845)),x84193),x84194)),f777(f77(x84195,x84195,x84195,f777(x84191,x84193)),f777(x84191,x84194))) % 174.01/173.90 [9072]~P112(x90721)+~P108(x90721)+~P1(f777(f777(f281(x90721),x90722),x90725))+~P1(f777(f777(f281(x90721),x90722),f777(f777(f84(x90721),x90723),x90726)))+P1(f777(f777(f281(x90721),x90722),f777(f777(f84(x90721),f777(f777(f5(x90721),x90723),f777(f777(f85(x90721),x90724),x90725))),x90726))) % 174.01/173.90 [9232]~P112(x92321)+~P108(x92321)+~P1(f777(f777(f281(x92321),x92322),x92325))+P1(f777(f777(f281(x92321),x92322),f777(f777(f84(x92321),x92323),x92324)))+~P1(f777(f777(f281(x92321),x92322),f777(f777(f84(x92321),f777(f777(f5(x92321),x92323),f777(f777(f85(x92321),x92326),x92325))),x92324))) % 174.01/173.90 [8712]E(x87121,x87122)+~P55(x87124,x87125,x87126,x87123,x87127)+~E(f777(x87123,x87121),f777(x87123,x87122))+~P1(f777(f777(f336(x87125),x87122),x87127))+~P1(f777(f777(f336(x87125),x87121),x87127)) % 174.01/173.90 [9961]~P12(x99611,x99617,x99616)+~P16(x99611,f858(x99615,a845),x99616,x99614)+P1(f777(f777(f336(x99611),f511(x99612,x99613,x99614,x99615,x99616,x99617,x99611)),x99617))+~P1(f777(f777(f336(f858(x99611,a845)),x99613),f777(f777(f63(x99611),x99617),x99616)))+P1(f777(f777(f336(f858(x99615,a845)),f777(f777(f48(x99611,f858(x99615,a845)),x99613),x99614)),x99612)) % 174.01/173.90 [10008]~P12(x100082,x100086,x100087)+~P16(x100082,f858(x100081,a845),x100087,x100084)+~P1(f777(f777(f336(f858(x100082,a845)),x100083),f777(f777(f63(x100082),x100086),x100087)))+~P1(f777(f777(f336(f858(x100081,a845)),f777(x100084,f511(x100085,x100083,x100084,x100081,x100087,x100086,x100082))),x100085))+P1(f777(f777(f336(f858(x100081,a845)),f777(f777(f48(x100082,f858(x100081,a845)),x100083),x100084)),x100085)) % 174.01/173.90 [8329]~P70(x83292)+~P29(x83291,x83295,x83298,x83294)+~E(x83293,f777(f77(x83295,x83292,x83291,x83296),x83298))+~E(x83297,f777(f305(x83291,x83295,x83298),x83294))+E(f777(f777(f13(x83291,x83292),x83293),x83294),f777(f777(f13(x83295,x83292),x83296),x83297)) % 174.01/173.90 [10011]~P70(x100112)+~P29(x100115,x100111,x100118,x100117)+~E(f777(x100116,f537(x100113,x100116,x100114,x100117,x100118,x100111,x100115,x100112)),f777(f777(f77(x100111,x100112,x100115,x100113),x100118),f537(x100113,x100116,x100114,x100117,x100118,x100111,x100115,x100112)))+~E(x100114,f777(f305(x100115,x100111,x100118),x100117))+E(f777(f777(f13(x100111,x100112),x100113),x100114),f777(f777(f13(x100115,x100112),x100116),x100117)) % 174.01/173.90 [10014]~P66(x100142)+~P29(x100141,x100145,x100148,x100144)+~E(x100147,f777(f305(x100141,x100145,x100148),x100144))+E(f777(f777(f10(x100141,x100142),x100143),x100144),f777(f777(f10(x100145,x100142),x100146),x100147))+P1(f777(f777(f336(x100141),f638(x100146,x100143,x100147,x100144,x100148,x100145,x100141,x100142)),x100144)) % 174.01/173.90 [10015]~P70(x100152)+~P29(x100151,x100155,x100158,x100154)+~E(x100157,f777(f305(x100151,x100155,x100158),x100154))+E(f777(f777(f13(x100151,x100152),x100153),x100154),f777(f777(f13(x100155,x100152),x100156),x100157))+P1(f777(f777(f336(x100151),f537(x100156,x100153,x100157,x100154,x100158,x100155,x100151,x100152)),x100154)) % 174.01/173.90 [10019]~P66(x100192)+~P29(x100195,x100191,x100198,x100197)+~E(x100194,f777(f305(x100195,x100191,x100198),x100197))+~E(f777(x100196,f638(x100193,x100196,x100194,x100197,x100198,x100191,x100195,x100192)),f777(x100193,f777(x100198,f638(x100193,x100196,x100194,x100197,x100198,x100191,x100195,x100192))))+E(f777(f777(f10(x100191,x100192),x100193),x100194),f777(f777(f10(x100195,x100192),x100196),x100197)) % 174.01/173.90 [9420]~E(f777(f183(f852(x94202)),x94205),f777(f183(f852(x94201)),x94203))+~E(f777(f183(f852(x94202)),x94204),f777(f183(f852(x94201)),x94203))+~E(f777(f777(f777(f76(x94201,f855(x94202)),f168(x94201,x94202,f777(f777(f169(x94201,x94202),x94203),x94204))),x94206),f777(f229(x94202),x94207)),f777(f777(f777(f76(x94201,f855(x94202)),f168(x94201,x94202,f777(f777(f169(x94201,x94202),x94203),x94205))),x94206),f777(f229(x94202),x94208)))+E(f168(x94201,x94202,f777(f777(f169(x94201,x94202),x94203),x94204)),f168(x94201,x94202,f777(f777(f169(x94201,x94202),x94203),x94205)))+P1(f777(f777(f336(x94201),x94206),f777(f160(x94201),x94203))) % 174.01/173.90 [9515]~P27(x95156,x95152,x95155,x95157,x95158,x95151)+~P1(f777(f65(x95152),x95154))+~P1(f777(f65(x95152),x95153))+~E(f777(f777(f106(f858(x95152,a845)),x95153),x95154),f182(f858(x95152,a845)))+E(f777(x95151,f777(f777(f105(f858(x95152,a845)),x95153),x95154)),f777(f777(x95155,f777(x95151,x95153)),f777(x95151,x95154))) % 174.01/173.90 [9905]~P27(x99058,x99052,x99055,x99057,x99056,x99051)+~E(f777(x99056,f580(x99054,x99053,x99051,x99056,x99057,x99055,x99052)),x99057)+~P1(f777(f65(x99052),x99053))+~P1(f777(f65(x99052),x99054))+E(f777(x99051,f777(f777(f105(f858(x99052,a845)),x99053),x99054)),f777(f777(x99055,f777(x99051,x99053)),f777(x99051,x99054))) % 174.01/173.90 [9966]~P27(x99668,x99662,x99665,x99667,x99666,x99661)+~P1(f777(f65(x99662),x99663))+~P1(f777(f65(x99662),x99664))+E(f777(x99661,f777(f777(f105(f858(x99662,a845)),x99663),x99664)),f777(f777(x99665,f777(x99661,x99663)),f777(x99661,x99664)))+P1(f777(f777(f336(x99662),f580(x99664,x99663,x99661,x99666,x99667,x99665,x99662)),f777(f777(f106(f858(x99662,a845)),x99663),x99664))) % 174.01/173.90 [9658]~P12(x96584,x96588,x96585)+~P12(x96581,x96589,x96583)+~P17(x96581,x96584,f858(x96582,a845),x96583,x96585,x96587)+P16(x96581,f858(x96582,a845),x96583,f777(f777(f12(f858(x96584,f858(x96582,a845)),f858(x96582,a845),x96581),f777(f48(x96584,f858(x96582,a845)),f777(f279(x96584,x96584,x96585),f777(f777(f304(x96584),x96586),f182(f858(x96584,a845)))))),x96587))+~P1(f777(f777(f336(x96584),x96586),x96588)) % 174.01/173.90 [4935]~P122(x49352)+~P127(x49352)+~P138(x49352)+~P105(x49352)+E(x49351,f4(x49352))+~E(f777(f777(f244(x49352),x49351),x49353),f4(x49352)) % 174.01/173.90 [4936]~P122(x49362)+~P127(x49362)+~P138(x49362)+~P105(x49362)+~E(x49361,f4(a851))+~E(f777(f777(f244(x49362),x49363),x49361),f4(x49362)) % 174.01/173.90 [6384]~P81(x63841)+~E(x63843,f4(x63841))+~E(x63842,f4(x63841))+E(f777(f777(f84(x63841),x63842),x63843),f4(x63841))+~P1(f777(f777(f234(x63841),f4(x63841)),x63843))+~P1(f777(f777(f234(x63841),f4(x63841)),x63842)) % 174.01/173.90 [8770]~E(f777(f242(a851,a851),x87703),f4(a851))+~E(x87701,f777(f777(f84(a851),f777(f777(f85(a851),f777(f242(a851,a851),x87703)),x87702)),f777(f252(a851,a851),x87703)))+P1(f777(f57(x87701,x87702),x87703))+~P1(f777(f777(f234(a851),f777(f252(a851,a851),x87703)),f4(a851)))+P1(f777(f777(f235(a851),f4(a851)),x87702))+~P1(f777(f777(f235(a851),x87702),f777(f252(a851,a851),x87703))) % 174.01/173.90 [8777]E(x87771,f4(a851))+~E(x87772,f777(f777(f84(a851),f777(f777(f85(a851),f777(f242(a851,a851),x87773)),x87771)),f777(f252(a851,a851),x87773)))+P1(f777(f57(x87772,x87771),x87773))+~P1(f777(f777(f235(a851),f4(a851)),x87771))+~P1(f777(f777(f234(a851),f4(a851)),f777(f252(a851,a851),x87773)))+~P1(f777(f777(f235(a851),f777(f252(a851,a851),x87773)),x87771)) % 174.01/173.90 [8791]~E(f777(f242(a851,a851),x87913),f4(a851))+~E(x87911,f777(f777(f84(a851),f777(f777(f85(a851),f777(f242(a851,a851),x87913)),x87912)),f777(f252(a851,a851),x87913)))+P1(f777(f57(x87911,x87912),x87913))+~P1(f777(f777(f235(a851),f4(a851)),x87912))+~P1(f777(f777(f234(a851),f4(a851)),f777(f252(a851,a851),x87913)))+~P1(f777(f777(f235(a851),f777(f252(a851,a851),x87913)),x87912)) % 174.01/173.90 [6786]~P93(x67862)+E(x67861,f182(f858(x67862,a845)))+E(x67863,f182(f858(x67862,a845)))+~P1(f777(f65(x67862),x67861))+~P1(f777(f65(x67862),x67863))+E(f17(x67862,f777(f777(f105(f858(x67862,a845)),x67863),x67861)),f777(f777(f105(x67862),f17(x67862,x67863)),f17(x67862,x67861))) % 174.01/173.90 [6787]~P100(x67872)+E(x67871,f182(f858(x67872,a845)))+E(x67873,f182(f858(x67872,a845)))+~P1(f777(f65(x67872),x67871))+~P1(f777(f65(x67872),x67873))+E(f18(x67872,f777(f777(f105(f858(x67872,a845)),x67873),x67871)),f777(f777(f181(x67872),f18(x67872,x67873)),f18(x67872,x67871))) % 174.01/173.90 [6788]~P100(x67882)+E(x67881,f182(f858(x67882,a845)))+E(x67883,f182(f858(x67882,a845)))+~P1(f777(f65(x67882),x67881))+~P1(f777(f65(x67882),x67883))+E(f19(x67882,f777(f777(f105(f858(x67882,a845)),x67883),x67881)),f777(f777(f238(x67882),f19(x67882,x67883)),f19(x67882,x67881))) % 174.01/173.90 [6789]~P93(x67892)+E(x67891,f182(f858(x67892,a845)))+E(x67893,f182(f858(x67892,a845)))+~P1(f777(f65(x67892),x67891))+~P1(f777(f65(x67892),x67893))+E(f14(x67892,f777(f777(f105(f858(x67892,a845)),x67893),x67891)),f777(f777(f106(x67892),f14(x67892,x67893)),f14(x67892,x67891))) % 174.01/173.90 [7453]~P91(x74532)+E(x74531,f182(f858(x74532,a845)))+E(x74533,f182(f858(x74532,a845)))+~P1(f777(f65(x74532),x74531))+~P1(f777(f65(x74532),x74533))+E(f777(f777(f85(x74532),f777(f67(x74532,f85(x74532)),x74533)),f777(f67(x74532,f85(x74532)),x74531)),f777(f67(x74532,f85(x74532)),f777(f777(f105(f858(x74532,a845)),x74533),x74531))) % 174.01/173.90 [7618]~P100(x76182)+E(x76181,f182(f858(x76182,a845)))+E(x76183,f182(f858(x76182,a845)))+~P1(f777(f65(x76182),x76181))+~P1(f777(f65(x76182),x76183))+E(f777(f777(f181(x76182),f15(x76182,f181(x76182),x76183)),f15(x76182,f181(x76182),x76181)),f15(x76182,f181(x76182),f777(f777(f105(f858(x76182,a845)),x76183),x76181))) % 174.01/173.90 [7619]~P100(x76192)+E(x76191,f182(f858(x76192,a845)))+E(x76193,f182(f858(x76192,a845)))+~P1(f777(f65(x76192),x76191))+~P1(f777(f65(x76192),x76193))+E(f777(f777(f238(x76192),f16(x76192,f238(x76192),x76193)),f16(x76192,f238(x76192),x76191)),f16(x76192,f238(x76192),f777(f777(f105(f858(x76192,a845)),x76193),x76191))) % 174.01/173.90 [8627]~P1(f777(x86271,x86273))+P1(f777(x86271,f355(x86271,x86272)))+P1(f777(x86271,f352(x86271,x86272)))+~P1(f777(f777(f235(a3),f4(a3)),x86272))+~P1(f777(f777(f336(a3),x86273),f297(a3,f82(a3),x86272)))+P1(f777(x86271,f777(f777(f5(a3),f352(x86271,x86272)),f777(f777(f85(a3),f354(x86271,x86272)),x86272)))) % 174.01/173.90 [8889]~P1(f777(x88891,x88893))+~P1(f777(x88891,f352(x88891,x88892)))+P1(f777(x88891,f355(x88891,x88892)))+~P1(f777(f777(f235(a3),f4(a3)),x88892))+~P1(f777(f777(f336(a3),x88893),f297(a3,f82(a3),x88892)))+~P1(f777(x88891,f777(f777(f5(a3),f352(x88891,x88892)),f777(f777(f85(a3),f354(x88891,x88892)),x88892)))) % 174.01/173.90 [10038]~P97(x100382)+E(x100381,f182(f858(x100382,a845)))+E(x100383,f182(f858(x100382,a845)))+~P1(f777(f65(x100382),x100381))+~P1(f777(f65(x100382),x100383))+E(f14(x100382,f777(f258(x100382),f777(f777(f12(f858(x100382,a845),a845,x100382),f91(x100382)),f777(f777(f12(f858(x100382,f858(x100382,a845)),f858(x100382,a845),x100382),f777(f12(f858(x100382,a845),a845,x100382),f91(x100382))),f777(f777(f11(x100382,f858(x100382,f858(x100382,a845)),f858(x100382,f858(x100382,a845))),f777(f777(f12(f858(x100382,f858(f858(x100382,a845),f858(x100382,a845))),f858(f858(x100382,f858(x100382,a845)),f858(x100382,f858(x100382,a845))),x100382),f22(x100382,f858(x100382,a845),f858(x100382,a845))),f777(f777(f12(f858(x100382,f858(x100382,f858(a845,a845))),f858(x100382,f858(f858(x100382,a845),f858(x100382,a845))),x100382),f777(f12(f858(x100382,f858(a845,a845)),f858(f858(x100382,a845),f858(x100382,a845)),x100382),f22(x100382,a845,a845))),f777(f777(f12(f858(x100382,f858(x100382,a845)),f858(x100382,f858(x100382,f858(a845,a845))),x100382),f777(f12(f858(x100382,a845),f858(x100382,f858(a845,a845)),x100382),f777(f12(a845,f858(a845,a845),x100382),a333))),f777(f777(f11(x100382,f858(x100382,f858(x100382,x100382)),f858(x100382,f858(x100382,a845))),f777(f777(f12(f858(f858(x100382,x100382),f858(x100382,a845)),f858(f858(x100382,f858(x100382,x100382)),f858(x100382,f858(x100382,a845))),x100382),f12(f858(x100382,x100382),f858(x100382,a845),x100382)),f777(f777(f12(f858(x100382,a845),f858(f858(x100382,x100382),f858(x100382,a845)),x100382),f12(x100382,a845,x100382)),a332))),f105(x100382)))))),f777(f777(f11(x100382,f858(x100382,a845),f858(x100382,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x100382,a845),f858(x100382,a845)),x100382),f12(a845,a845,x100382)),f777(f777(f12(a845,f858(a845,a845),x100382),a333),f777(f777(f11(x100382,f858(x100382,a845),a845),f336(x100382)),x100383)))),f777(f777(f11(x100382,f858(x100382,a845),a845),f336(x100382)),x100381))))))),f777(f777(f105(x100382),f14(x100382,x100383)),f14(x100382,x100381))) % 174.01/173.90 [10039]~P97(x100392)+E(x100391,f182(f858(x100392,a845)))+E(x100393,f182(f858(x100392,a845)))+~P1(f777(f65(x100392),x100391))+~P1(f777(f65(x100392),x100393))+E(f17(x100392,f777(f258(x100392),f777(f777(f12(f858(x100392,a845),a845,x100392),f91(x100392)),f777(f777(f12(f858(x100392,f858(x100392,a845)),f858(x100392,a845),x100392),f777(f12(f858(x100392,a845),a845,x100392),f91(x100392))),f777(f777(f11(x100392,f858(x100392,f858(x100392,a845)),f858(x100392,f858(x100392,a845))),f777(f777(f12(f858(x100392,f858(f858(x100392,a845),f858(x100392,a845))),f858(f858(x100392,f858(x100392,a845)),f858(x100392,f858(x100392,a845))),x100392),f22(x100392,f858(x100392,a845),f858(x100392,a845))),f777(f777(f12(f858(x100392,f858(x100392,f858(a845,a845))),f858(x100392,f858(f858(x100392,a845),f858(x100392,a845))),x100392),f777(f12(f858(x100392,f858(a845,a845)),f858(f858(x100392,a845),f858(x100392,a845)),x100392),f22(x100392,a845,a845))),f777(f777(f12(f858(x100392,f858(x100392,a845)),f858(x100392,f858(x100392,f858(a845,a845))),x100392),f777(f12(f858(x100392,a845),f858(x100392,f858(a845,a845)),x100392),f777(f12(a845,f858(a845,a845),x100392),a333))),f777(f777(f11(x100392,f858(x100392,f858(x100392,x100392)),f858(x100392,f858(x100392,a845))),f777(f777(f12(f858(f858(x100392,x100392),f858(x100392,a845)),f858(f858(x100392,f858(x100392,x100392)),f858(x100392,f858(x100392,a845))),x100392),f12(f858(x100392,x100392),f858(x100392,a845),x100392)),f777(f777(f12(f858(x100392,a845),f858(f858(x100392,x100392),f858(x100392,a845)),x100392),f12(x100392,a845,x100392)),a332))),f106(x100392)))))),f777(f777(f11(x100392,f858(x100392,a845),f858(x100392,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x100392,a845),f858(x100392,a845)),x100392),f12(a845,a845,x100392)),f777(f777(f12(a845,f858(a845,a845),x100392),a333),f777(f777(f11(x100392,f858(x100392,a845),a845),f336(x100392)),x100393)))),f777(f777(f11(x100392,f858(x100392,a845),a845),f336(x100392)),x100391))))))),f777(f777(f106(x100392),f17(x100392,x100393)),f17(x100392,x100391))) % 174.01/173.90 [10040]~P100(x100402)+E(x100401,f182(f858(x100402,a845)))+E(x100403,f182(f858(x100402,a845)))+~P1(f777(f65(x100402),x100401))+~P1(f777(f65(x100402),x100403))+E(f15(x100402,f181(x100402),f777(f258(x100402),f777(f777(f12(f858(x100402,a845),a845,x100402),f91(x100402)),f777(f777(f12(f858(x100402,f858(x100402,a845)),f858(x100402,a845),x100402),f777(f12(f858(x100402,a845),a845,x100402),f91(x100402))),f777(f777(f11(x100402,f858(x100402,f858(x100402,a845)),f858(x100402,f858(x100402,a845))),f777(f777(f12(f858(x100402,f858(f858(x100402,a845),f858(x100402,a845))),f858(f858(x100402,f858(x100402,a845)),f858(x100402,f858(x100402,a845))),x100402),f22(x100402,f858(x100402,a845),f858(x100402,a845))),f777(f777(f12(f858(x100402,f858(x100402,f858(a845,a845))),f858(x100402,f858(f858(x100402,a845),f858(x100402,a845))),x100402),f777(f12(f858(x100402,f858(a845,a845)),f858(f858(x100402,a845),f858(x100402,a845)),x100402),f22(x100402,a845,a845))),f777(f777(f12(f858(x100402,f858(x100402,a845)),f858(x100402,f858(x100402,f858(a845,a845))),x100402),f777(f12(f858(x100402,a845),f858(x100402,f858(a845,a845)),x100402),f777(f12(a845,f858(a845,a845),x100402),a333))),f777(f777(f11(x100402,f858(x100402,f858(x100402,x100402)),f858(x100402,f858(x100402,a845))),f777(f777(f12(f858(f858(x100402,x100402),f858(x100402,a845)),f858(f858(x100402,f858(x100402,x100402)),f858(x100402,f858(x100402,a845))),x100402),f12(f858(x100402,x100402),f858(x100402,a845),x100402)),f777(f777(f12(f858(x100402,a845),f858(f858(x100402,x100402),f858(x100402,a845)),x100402),f12(x100402,a845,x100402)),a332))),f238(x100402)))))),f777(f777(f11(x100402,f858(x100402,a845),f858(x100402,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x100402,a845),f858(x100402,a845)),x100402),f12(a845,a845,x100402)),f777(f777(f12(a845,f858(a845,a845),x100402),a333),f777(f777(f11(x100402,f858(x100402,a845),a845),f336(x100402)),x100403)))),f777(f777(f11(x100402,f858(x100402,a845),a845),f336(x100402)),x100401))))))),f777(f777(f238(x100402),f15(x100402,f181(x100402),x100403)),f15(x100402,f181(x100402),x100401))) % 174.01/173.90 [10041]~P100(x100412)+E(x100411,f182(f858(x100412,a845)))+E(x100413,f182(f858(x100412,a845)))+~P1(f777(f65(x100412),x100411))+~P1(f777(f65(x100412),x100413))+E(f16(x100412,f238(x100412),f777(f258(x100412),f777(f777(f12(f858(x100412,a845),a845,x100412),f91(x100412)),f777(f777(f12(f858(x100412,f858(x100412,a845)),f858(x100412,a845),x100412),f777(f12(f858(x100412,a845),a845,x100412),f91(x100412))),f777(f777(f11(x100412,f858(x100412,f858(x100412,a845)),f858(x100412,f858(x100412,a845))),f777(f777(f12(f858(x100412,f858(f858(x100412,a845),f858(x100412,a845))),f858(f858(x100412,f858(x100412,a845)),f858(x100412,f858(x100412,a845))),x100412),f22(x100412,f858(x100412,a845),f858(x100412,a845))),f777(f777(f12(f858(x100412,f858(x100412,f858(a845,a845))),f858(x100412,f858(f858(x100412,a845),f858(x100412,a845))),x100412),f777(f12(f858(x100412,f858(a845,a845)),f858(f858(x100412,a845),f858(x100412,a845)),x100412),f22(x100412,a845,a845))),f777(f777(f12(f858(x100412,f858(x100412,a845)),f858(x100412,f858(x100412,f858(a845,a845))),x100412),f777(f12(f858(x100412,a845),f858(x100412,f858(a845,a845)),x100412),f777(f12(a845,f858(a845,a845),x100412),a333))),f777(f777(f11(x100412,f858(x100412,f858(x100412,x100412)),f858(x100412,f858(x100412,a845))),f777(f777(f12(f858(f858(x100412,x100412),f858(x100412,a845)),f858(f858(x100412,f858(x100412,x100412)),f858(x100412,f858(x100412,a845))),x100412),f12(f858(x100412,x100412),f858(x100412,a845),x100412)),f777(f777(f12(f858(x100412,a845),f858(f858(x100412,x100412),f858(x100412,a845)),x100412),f12(x100412,a845,x100412)),a332))),f181(x100412)))))),f777(f777(f11(x100412,f858(x100412,a845),f858(x100412,a845)),f777(f777(f12(f858(a845,a845),f858(f858(x100412,a845),f858(x100412,a845)),x100412),f12(a845,a845,x100412)),f777(f777(f12(a845,f858(a845,a845),x100412),a333),f777(f777(f11(x100412,f858(x100412,a845),a845),f336(x100412)),x100413)))),f777(f777(f11(x100412,f858(x100412,a845),a845),f336(x100412)),x100411))))))),f777(f777(f181(x100412),f16(x100412,f238(x100412),x100413)),f16(x100412,f238(x100412),x100411))) % 174.01/173.90 [7118]~P117(x71183)+E(x71181,x71182)+~E(f777(f777(f244(x71183),x71181),x71184),f777(f777(f244(x71183),x71182),x71184))+~P1(f777(f777(f234(x71183),f4(x71183)),x71182))+~P1(f777(f777(f234(x71183),f4(x71183)),x71181))+~P1(f777(f777(f235(a851),f4(a851)),x71184)) % 174.01/173.90 [7413]~P100(x74132)+E(x74131,f182(f858(x74132,a845)))+~P1(f777(f65(x74132),x74131))+~P1(f777(f777(f336(x74132),x74134),x74131))+P1(f777(f777(f235(x74132),x74133),x74134))+~P1(f777(f777(f235(x74132),x74133),f777(f67(x74132,f238(x74132)),x74131))) % 174.01/173.90 [7414]~P100(x74142)+E(x74141,f182(f858(x74142,a845)))+~P1(f777(f65(x74142),x74141))+~P1(f777(f777(f336(x74142),x74144),x74141))+P1(f777(f777(f234(x74142),x74143),x74144))+~P1(f777(f777(f234(x74142),x74143),f777(f67(x74142,f238(x74142)),x74141))) % 174.01/173.90 [7415]~P98(x74152)+E(x74151,f182(f858(x74152,a845)))+~P1(f777(f65(x74152),x74151))+~P1(f777(f777(f336(x74152),x74154),x74151))+P1(f777(f777(f234(x74152),x74153),x74154))+~P1(f777(f777(f234(x74152),x74153),f777(f67(x74152,f106(x74152)),x74151))) % 174.01/173.90 [7309]E(x73091,f4(a3))+E(f777(f777(f45(a3),x73092),x73091),x73093)+~P1(f777(f777(f234(a3),x73094),f4(a3)))+~E(x73092,f777(f777(f84(a3),f777(f777(f85(a3),x73091),x73093)),x73094))+P1(f777(f777(f235(a3),f4(a3)),x73091))+~P1(f777(f777(f235(a3),x73091),x73094)) % 174.01/173.90 [7325]E(f54(a3,x73252,x73251),x73253)+E(x73251,f4(a3))+~P1(f777(f777(f234(a3),x73253),f4(a3)))+~E(x73252,f777(f777(f84(a3),f777(f777(f85(a3),x73251),x73254)),x73253))+P1(f777(f777(f235(a3),f4(a3)),x73251))+~P1(f777(f777(f235(a3),x73251),x73253)) % 174.01/173.90 [7452]E(x74521,f4(a3))+E(f777(f777(f45(a3),x74522),x74521),x74523)+~E(x74522,f777(f777(f84(a3),f777(f777(f85(a3),x74521),x74523)),x74524))+~P1(f777(f777(f235(a3),f4(a3)),x74521))+~P1(f777(f777(f234(a3),f4(a3)),x74524))+~P1(f777(f777(f235(a3),x74524),x74521)) % 174.01/173.90 [7477]E(f54(a3,x74772,x74771),x74773)+E(x74771,f4(a3))+~E(x74772,f777(f777(f84(a3),f777(f777(f85(a3),x74771),x74774)),x74773))+~P1(f777(f777(f235(a3),f4(a3)),x74771))+~P1(f777(f777(f234(a3),f4(a3)),x74773))+~P1(f777(f777(f235(a3),x74773),x74771)) % 174.01/173.90 [7622]~P100(x76222)+E(x76221,f182(f858(x76222,a845)))+~P1(f777(f65(x76222),x76221))+~P1(f777(f777(f235(x76222),x76224),x76223))+~P1(f777(f777(f336(x76222),x76224),x76221))+P1(f777(f777(f235(x76222),f777(f67(x76222,f238(x76222)),x76221)),x76223)) % 174.01/173.90 [7623]~P100(x76232)+E(x76231,f182(f858(x76232,a845)))+~P1(f777(f65(x76232),x76231))+~P1(f777(f777(f234(x76232),x76234),x76233))+~P1(f777(f777(f336(x76232),x76234),x76231))+P1(f777(f777(f234(x76232),f777(f67(x76232,f238(x76232)),x76231)),x76233)) % 174.01/173.90 [8186]~P1(f777(f777(f234(a3),x81864),f4(a3)))+~E(x81861,f777(f777(f84(a3),f777(f777(f85(a3),x81862),x81863)),x81864))+~P1(f777(f777(f234(a3),f4(a3)),x81864))+~P1(f777(f777(f235(a3),x81864),x81862))+~P1(f777(f777(f235(a3),x81862),x81864))+P1(f777(f58(x81861,x81862),f777(f777(f243(a3,a3),x81863),x81864))) % 174.01/173.90 [8352]~P99(x83521)+P1(f777(f777(f235(f858(x83521,a845)),f297(x83521,x83522,x83523)),f297(x83521,x83524,x83525)))+~P1(f777(f777(f235(x83521),x83523),x83525))+~P1(f777(f777(f234(x83521),x83524),x83522))+~P1(f777(f777(f234(x83521),x83524),x83525))+~P1(f777(f777(f234(x83521),x83523),x83525)) % 174.01/173.90 [8353]~P99(x83531)+P1(f777(f777(f235(f858(x83531,a845)),f297(x83531,x83532,x83533)),f297(x83531,x83534,x83535)))+~P1(f777(f777(f235(x83531),x83534),x83532))+~P1(f777(f777(f234(x83531),x83533),x83535))+~P1(f777(f777(f234(x83531),x83534),x83535))+~P1(f777(f777(f234(x83531),x83534),x83532)) % 174.01/173.90 [9135]P57(x91352,x91353,x91354,x91351)+E(x91351,f182(f858(x91352,a845)))+~P1(f777(f65(x91352),x91354))+~P1(f777(f65(x91352),x91351))+~P1(f777(f777(x91353,f539(x91351,x91354,x91353,x91352)),x91355))+~P1(f777(f777(f336(x91352),x91355),x91351)) % 174.01/173.90 [9261]~E(x92613,x92615)+~P66(x92611)+~P70(x92611)+~P38(x92613)+E(f777(f777(f10(a3,x92611),x92612),x92613),f777(f777(f10(a3,x92611),x92614),x92615))+P1(f777(f777(f234(a3),f4(a3)),f382(x92612,x92614,x92613,x92615,x92611))) % 174.01/173.90 [9262]~E(x92623,x92625)+~P66(x92621)+~P70(x92621)+~P38(x92623)+E(f777(f777(f13(a3,x92621),x92622),x92623),f777(f777(f13(a3,x92621),x92624),x92625))+P1(f777(f777(f234(a3),f4(a3)),f535(x92622,x92624,x92623,x92625,x92621))) % 174.01/173.90 [9427]~E(x94275,x94273)+~P66(x94271)+~P70(x94271)+~P38(x94275)+~E(f777(x94272,f382(x94274,x94272,x94275,x94273,x94271)),f777(x94274,f382(x94274,x94272,x94275,x94273,x94271)))+E(f777(f777(f10(a3,x94271),x94272),x94273),f777(f777(f10(a3,x94271),x94274),x94275)) % 174.01/173.90 [9428]~E(x94285,x94283)+~P66(x94281)+~P70(x94281)+~P38(x94285)+~E(f777(x94282,f535(x94284,x94282,x94285,x94283,x94281)),f777(x94284,f535(x94284,x94282,x94285,x94283,x94281)))+E(f777(f777(f13(a3,x94281),x94282),x94283),f777(f777(f13(a3,x94281),x94284),x94285)) % 174.01/173.90 [9512]~P77(x95123)+E(f777(x95121,x95122),f4(x95123))+~E(f777(f777(f10(x95124,x95123),x95121),x95125),f4(x95123))+~P1(f777(f65(x95124),x95125))+P1(f777(f777(f336(x95124),f465(x95122,x95121,x95125,x95124,x95123)),x95125))+~P1(f777(f777(f336(x95124),x95122),x95125)) % 174.01/173.90 [9634]~P77(x96343)+E(f777(x96341,x96342),f4(x96343))+~E(f777(f777(f10(x96344,x96343),x96341),x96345),f4(x96343))+~P1(f777(f65(x96344),x96345))+~P1(f777(f777(f336(x96344),x96342),x96345))+~P1(f777(f777(f234(x96343),f4(x96343)),f777(x96341,f465(x96342,x96341,x96345,x96344,x96343)))) % 174.01/173.90 [8265]~P123(x82651)+~P1(f777(f777(f234(x82651),f4(x82651)),x82653))+~P1(f777(f777(f235(x82651),x82653),x82655))+~P1(f777(f777(f235(x82651),x82652),x82654))+~P1(f777(f777(f235(x82651),f4(x82651)),x82654))+P1(f777(f777(f235(x82651),f777(f777(f85(x82651),x82652),x82653)),f777(f777(f85(x82651),x82654),x82655))) % 174.01/173.90 [8266]~P123(x82661)+~P1(f777(f777(f234(x82661),f4(x82661)),x82663))+~P1(f777(f777(f234(x82661),f4(x82661)),x82662))+~P1(f777(f777(f235(x82661),x82663),x82665))+~P1(f777(f777(f235(x82661),x82662),x82664))+P1(f777(f777(f235(x82661),f777(f777(f85(x82661),x82662),x82663)),f777(f777(f85(x82661),x82664),x82665))) % 174.01/173.90 [8267]~P123(x82671)+~P1(f777(f777(f234(x82671),x82672),x82674))+~P1(f777(f777(f234(x82671),f4(x82671)),x82673))+~P1(f777(f777(f235(x82671),x82673),x82675))+~P1(f777(f777(f235(x82671),f4(x82671)),x82672))+P1(f777(f777(f235(x82671),f777(f777(f85(x82671),x82672),x82673)),f777(f777(f85(x82671),x82674),x82675))) % 174.01/173.90 [8268]~P123(x82681)+~P1(f777(f777(f234(x82681),x82683),x82685))+~P1(f777(f777(f234(x82681),f4(x82681)),x82682))+~P1(f777(f777(f235(x82681),x82682),x82684))+~P1(f777(f777(f235(x82681),f4(x82681)),x82683))+P1(f777(f777(f235(x82681),f777(f777(f85(x82681),x82682),x82683)),f777(f777(f85(x82681),x82684),x82685))) % 174.01/173.90 [8269]~P63(x82691)+~P1(f777(f777(f234(x82691),x82692),x82694))+~P1(f777(f777(f235(x82691),x82695),x82693))+~P1(f777(f777(f235(x82691),f4(x82691)),x82695))+~P1(f777(f777(f235(x82691),f4(x82691)),x82692))+P1(f777(f777(f235(x82691),f777(f777(f285(x82691),x82692),x82693)),f777(f777(f285(x82691),x82694),x82695))) % 174.01/173.90 [8270]~P63(x82701)+~P1(f777(f777(f234(x82701),x82705),x82703))+~P1(f777(f777(f234(x82701),f4(x82701)),x82702))+~P1(f777(f777(f235(x82701),x82702),x82704))+~P1(f777(f777(f235(x82701),f4(x82701)),x82705))+P1(f777(f777(f235(x82701),f777(f777(f285(x82701),x82702),x82703)),f777(f777(f285(x82701),x82704),x82705))) % 174.01/173.90 [8271]~P131(x82711)+~P1(f777(f777(f234(x82711),x82713),x82715))+~P1(f777(f777(f234(x82711),x82712),x82714))+~P1(f777(f777(f234(x82711),f4(x82711)),x82713))+~P1(f777(f777(f234(x82711),f4(x82711)),x82714))+P1(f777(f777(f234(x82711),f777(f777(f85(x82711),x82712),x82713)),f777(f777(f85(x82711),x82714),x82715))) % 174.01/173.90 [8272]~P131(x82721)+~P1(f777(f777(f234(x82721),x82723),x82725))+~P1(f777(f777(f234(x82721),x82722),x82724))+~P1(f777(f777(f234(x82721),f4(x82721)),x82723))+~P1(f777(f777(f234(x82721),f4(x82721)),x82722))+P1(f777(f777(f234(x82721),f777(f777(f85(x82721),x82722),x82723)),f777(f777(f85(x82721),x82724),x82725))) % 174.01/173.90 [8273]~P63(x82731)+~P1(f777(f777(f235(x82731),f4(x82731)),x82735))+~P1(f777(f777(f234(x82731),x82735),x82733))+~P1(f777(f777(f234(x82731),x82732),x82734))+~P1(f777(f777(f234(x82731),f4(x82731)),x82732))+P1(f777(f777(f234(x82731),f777(f777(f285(x82731),x82732),x82733)),f777(f777(f285(x82731),x82734),x82735))) % 174.01/173.90 [9549]~P66(x95495)+~P80(x95495)+E(x95491,f182(f858(x95492,a845)))+~P1(f777(f65(x95492),x95491))+P1(f777(f777(f336(x95492),f491(x95493,x95494,x95491,x95492,x95495)),x95491))+P1(f777(f777(f235(x95495),f777(f777(f10(x95492,x95495),x95494),x95491)),f777(f777(f10(x95492,x95495),x95493),x95491))) % 174.01/173.90 [9654]~P66(x96541)+~P78(x96541)+~P1(f777(f65(x96542),x96545))+~P1(f777(f777(f234(x96541),f4(x96541)),f777(x96543,f415(x96543,x96544,x96545,x96542,x96541))))+P1(f777(f777(f234(x96541),f777(f777(f10(x96542,x96541),x96543),x96544)),f777(f777(f10(x96542,x96541),x96543),x96545)))+~P1(f777(f777(f234(f858(x96542,a845)),x96544),x96545)) % 174.01/173.90 [9820]~P66(x98203)+~P80(x98203)+E(x98201,f182(f858(x98202,a845)))+~P1(f777(f65(x98202),x98201))+~P1(f777(f777(f235(x98203),f777(x98204,f491(x98205,x98204,x98201,x98202,x98203))),f777(x98205,f491(x98205,x98204,x98201,x98202,x98203))))+P1(f777(f777(f235(x98203),f777(f777(f10(x98202,x98203),x98204),x98201)),f777(f777(f10(x98202,x98203),x98205),x98201))) % 174.01/173.90 [6978]~P21(x69782,x69785,x69784)+E(x69781,f182(f858(x69782,a845)))+E(x69783,f182(f858(x69782,a845)))+~P1(f777(f65(x69782),x69781))+~P1(f777(f65(x69782),x69783))+E(f777(x69784,f777(f777(f105(f858(x69782,a845)),x69783),x69781)),f777(f777(x69785,f777(x69784,x69783)),f777(x69784,x69781))) % 174.01/173.90 [7587]~P141(x75871,x75874,x75873)+P1(f777(x75871,x75872))+~P1(f777(f777(f235(a3),x75874),f4(a3)))+~P1(f777(f777(f234(a3),x75875),f4(a3)))+~E(x75873,f777(f777(f84(a3),f777(f777(f85(a3),x75874),x75872)),x75875))+~P1(f777(f777(f235(a3),x75874),x75875)) % 174.01/173.90 [7588]~P140(x75881,x75884,x75883)+P1(f777(x75881,x75882))+~P1(f777(f777(f235(a3),x75884),f4(a3)))+~P1(f777(f777(f234(a3),x75882),f4(a3)))+~E(x75883,f777(f777(f84(a3),f777(f777(f85(a3),x75884),x75885)),x75882))+~P1(f777(f777(f235(a3),x75884),x75882)) % 174.01/173.90 [7631]~P141(x76311,x76314,x76313)+P1(f777(x76311,x76312))+~E(x76313,f777(f777(f84(a3),f777(f777(f85(a3),x76314),x76312)),x76315))+~P1(f777(f777(f235(a3),f4(a3)),x76314))+~P1(f777(f777(f234(a3),f4(a3)),x76315))+~P1(f777(f777(f235(a3),x76315),x76314)) % 174.01/173.90 [7632]~P140(x76321,x76324,x76323)+P1(f777(x76321,x76322))+~E(x76323,f777(f777(f84(a3),f777(f777(f85(a3),x76324),x76325)),x76322))+~P1(f777(f777(f235(a3),f4(a3)),x76324))+~P1(f777(f777(f234(a3),f4(a3)),x76322))+~P1(f777(f777(f235(a3),x76322),x76324)) % 174.01/173.90 [8557]P1(f777(f777(x85571,x85572),x85573))+~P1(f777(f777(x85571,f777(f777(f45(a3),x85574),x85575)),f54(a3,x85574,x85575)))+~P1(f777(f777(f235(a3),x85575),f4(a3)))+~P1(f777(f777(f234(a3),x85573),f4(a3)))+~E(x85574,f777(f777(f84(a3),f777(f777(f85(a3),x85575),x85572)),x85573))+~P1(f777(f777(f235(a3),x85575),x85573)) % 174.01/173.90 [8564]P1(f777(f777(x85641,x85642),x85643))+~P1(f777(f777(x85641,f777(f777(f45(a3),x85644),x85645)),f54(a3,x85644,x85645)))+~E(x85644,f777(f777(f84(a3),f777(f777(f85(a3),x85645),x85642)),x85643))+~P1(f777(f777(f235(a3),f4(a3)),x85645))+~P1(f777(f777(f234(a3),f4(a3)),x85643))+~P1(f777(f777(f235(a3),x85643),x85645)) % 174.01/173.90 [8783]E(x87831,x87832)+~P54(x87833,x87835,x87834)+~P1(f777(f777(f336(x87833),x87832),x87835))+~P1(f777(f777(f336(x87833),x87831),x87835))+P1(f777(f777(f336(f857(x87833,x87833)),f777(f777(f243(x87833,x87833),x87831),x87832)),x87834))+P1(f777(f777(f336(f857(x87833,x87833)),f777(f777(f243(x87833,x87833),x87832),x87831)),x87834)) % 174.01/173.90 [9578]~P66(x95785)+~P78(x95785)+~P1(f777(f65(x95781),x95784))+P1(f777(f777(f234(x95785),f777(f777(f10(x95781,x95785),x95782),x95783)),f777(f777(f10(x95781,x95785),x95782),x95784)))+~P1(f777(f777(f234(f858(x95781,a845)),x95783),x95784))+P1(f777(f777(f336(x95781),f415(x95782,x95783,x95784,x95781,x95785)),f777(f777(f5(f858(x95781,a845)),x95784),x95783))) % 174.01/173.90 [9661]E(x96611,f182(f858(x96612,a845)))+~P1(f777(f65(x96612),x96613))+~P1(f777(f65(x96612),x96611))+P1(f777(f777(f336(f857(f858(x96612,a845),f858(x96612,a845))),f777(f777(f243(f858(x96612,a845),f858(x96612,a845)),x96613),x96611)),f326(x96612,x96614)))+~P1(f777(f777(f336(x96612),x96615),x96611))+~P1(f777(f777(f336(f857(x96612,x96612)),f777(f777(f243(x96612,x96612),f541(x96614,x96611,x96613,x96612)),x96615)),x96614)) % 174.01/173.90 [9662]E(x96621,f182(f858(x96622,a845)))+~P1(f777(f65(x96622),x96623))+~P1(f777(f65(x96622),x96621))+P1(f777(f777(f336(f857(f858(x96622,a845),f858(x96622,a845))),f777(f777(f243(f858(x96622,a845),f858(x96622,a845)),x96623),x96621)),f326(x96622,x96624)))+~P1(f777(f777(f336(x96622),x96625),x96621))+~P1(f777(f777(f336(f857(x96622,x96622)),f777(f777(f243(x96622,x96622),f625(x96624,x96621,x96623,x96622)),x96625)),x96624)) % 174.01/173.90 [9823]~P77(x98231)+~E(f777(f777(f10(x98235,x98231),x98232),x98236),x98234)+~P1(f777(f65(x98235),x98236))+P1(f777(f777(f336(x98235),f466(x98233,x98234,x98232,x98236,x98235,x98231)),x98236))+P1(f777(f777(f234(x98231),f777(x98232,x98233)),x98234))+~P1(f777(f777(f336(x98235),x98233),x98236)) % 174.01/173.90 [9877]~P77(x98771)+~E(f777(f777(f10(x98775,x98771),x98772),x98776),x98774)+~P1(f777(f65(x98775),x98776))+~P1(f777(f777(f336(x98775),x98773),x98776))+~P1(f777(f777(f234(x98771),f4(x98771)),f777(x98772,f466(x98773,x98774,x98772,x98776,x98775,x98771))))+P1(f777(f777(f234(x98771),f777(x98772,x98773)),x98774)) % 174.01/173.90 [9994]~E(x99945,x99948)+~E(x99944,x99947)+~P66(x99942)+~P102(x99941)+E(f777(f777(f10(x99941,x99942),x99943),f777(f296(x99941,x99944),x99945)),f777(f777(f10(x99941,x99942),x99946),f777(f296(x99941,x99947),x99948)))+P1(f777(f777(f234(x99941),x99944),f374(x99943,x99946,x99945,x99948,x99944,x99947,x99941,x99942))) % 174.01/173.90 [10010]~E(x100107,x100104)+~E(x100108,x100105)+~P66(x100102)+~P102(x100101)+~E(f777(x100103,f374(x100106,x100103,x100108,x100105,x100107,x100104,x100101,x100102)),f777(x100106,f374(x100106,x100103,x100108,x100105,x100107,x100104,x100101,x100102)))+E(f777(f777(f10(x100101,x100102),x100103),f777(f296(x100101,x100104),x100105)),f777(f777(f10(x100101,x100102),x100106),f777(f296(x100101,x100107),x100108))) % 174.01/173.90 [10013]~E(x100134,x100137)+~E(x100135,x100138)+~P66(x100132)+~P102(x100131)+E(f777(f777(f10(x100131,x100132),x100133),f777(f296(x100131,x100134),x100135)),f777(f777(f10(x100131,x100132),x100136),f777(f296(x100131,x100137),x100138)))+P1(f777(f777(f235(x100131),f374(x100133,x100136,x100135,x100138,x100134,x100137,x100131,x100132)),x100135)) % 174.01/173.90 [9666]~P12(x96665,x96669,x96666)+~P12(x96661,x966610,x96663)+~P17(x96661,x96665,f858(x96662,a845),x96663,x96666,x96668)+~P1(f777(f777(f336(x96665),x96667),x96669))+~P1(f777(f777(f336(x96661),x96664),x966610))+E(f777(f777(f48(x96661,f858(x96662,a845)),f777(f279(x96661,x96661,x96663),f777(f777(f304(x96661),x96664),f182(f858(x96661,a845))))),f777(f777(f12(f858(x96665,f858(x96662,a845)),f858(x96662,a845),x96661),f777(f48(x96665,f858(x96662,a845)),f777(f279(x96665,x96665,x96666),f777(f777(f304(x96665),x96667),f182(f858(x96665,a845)))))),x96668)),f777(f777(x96668,x96664),x96667)) % 174.01/173.90 [5473]~P100(x54733)+~P18(x54733,x54732)+~P18(x54733,x54731)+E(x54731,x54732)+~E(f777(f160(x54733),x54731),f777(f160(x54733),x54732))+~P1(f777(f129(x54733),x54732))+~P1(f777(f129(x54733),x54731)) % 174.01/173.90 [4819]~P122(x48192)+~P127(x48192)+~P138(x48192)+~P105(x48192)+~E(x48193,f4(x48192))+E(x48191,f4(a851))+E(f777(f777(f244(x48192),x48193),x48191),f4(x48192)) % 174.01/173.90 [9021]E(x90211,f4(a851))+~E(x90212,f777(f777(f84(a851),f777(f777(f85(a851),f777(f242(a851,a851),x90213)),x90211)),f777(f252(a851,a851),x90213)))+P1(f777(f57(x90212,x90211),x90213))+~P1(f777(f777(f234(a851),f777(f252(a851,a851),x90213)),f4(a851)))+~P1(f777(f777(f234(a851),f4(a851)),f777(f252(a851,a851),x90213)))+~P1(f777(f777(f235(a851),x90211),f777(f252(a851,a851),x90213)))+~P1(f777(f777(f235(a851),f777(f252(a851,a851),x90213)),x90211)) % 174.01/173.90 [9029]~E(f777(f242(a851,a851),x90293),f4(a851))+~E(x90291,f777(f777(f84(a851),f777(f777(f85(a851),f777(f242(a851,a851),x90293)),x90292)),f777(f252(a851,a851),x90293)))+P1(f777(f57(x90291,x90292),x90293))+~P1(f777(f777(f234(a851),f777(f252(a851,a851),x90293)),f4(a851)))+~P1(f777(f777(f234(a851),f4(a851)),f777(f252(a851,a851),x90293)))+~P1(f777(f777(f235(a851),x90292),f777(f252(a851,a851),x90293)))+~P1(f777(f777(f235(a851),f777(f252(a851,a851),x90293)),x90292)) % 174.01/173.90 [7946]~P64(x79462)+E(x79461,f182(f858(x79462,a845)))+E(x79463,f182(f858(x79462,a845)))+~P1(f777(f65(x79462),x79461))+~P1(f777(f65(x79462),x79463))+~E(f777(f777(f106(f858(x79462,a845)),x79463),x79461),f182(f858(x79462,a845)))+E(f777(f777(f85(x79462),f777(f67(x79462,f85(x79462)),x79463)),f777(f67(x79462,f85(x79462)),x79461)),f777(f67(x79462,f85(x79462)),f777(f777(f105(f858(x79462,a845)),x79463),x79461))) % 174.01/173.90 [7725]E(x77251,f4(a3))+E(f777(f777(f45(a3),x77252),x77251),x77253)+~P1(f777(f777(f234(a3),x77254),f4(a3)))+~E(x77252,f777(f777(f84(a3),f777(f777(f85(a3),x77251),x77253)),x77254))+~P1(f777(f777(f234(a3),f4(a3)),x77254))+~P1(f777(f777(f235(a3),x77254),x77251))+~P1(f777(f777(f235(a3),x77251),x77254)) % 174.01/173.90 [7731]E(f54(a3,x77312,x77311),x77313)+E(x77311,f4(a3))+~P1(f777(f777(f234(a3),x77313),f4(a3)))+~E(x77312,f777(f777(f84(a3),f777(f777(f85(a3),x77311),x77314)),x77313))+~P1(f777(f777(f234(a3),f4(a3)),x77313))+~P1(f777(f777(f235(a3),x77313),x77311))+~P1(f777(f777(f235(a3),x77311),x77313)) % 174.01/173.90 [6752]~P7(x67522)+E(x67521,f4(x67522))+E(x67523,f4(x67522))+~E(f777(f777(f45(x67522),x67524),x67523),f777(f777(f45(x67522),x67525),x67521))+E(f777(f777(f85(x67522),x67524),x67521),f777(f777(f85(x67522),x67523),x67525))+~P1(f777(f777(f281(x67522),x67521),x67525))+~P1(f777(f777(f281(x67522),x67523),x67524)) % 174.01/173.90 [6753]~P7(x67532)+E(x67531,f4(x67532))+E(x67533,f4(x67532))+~E(f777(f777(f85(x67532),x67534),x67533),f777(f777(f85(x67532),x67531),x67535))+E(f777(f777(f45(x67532),x67534),x67531),f777(f777(f45(x67532),x67535),x67533))+~P1(f777(f777(f281(x67532),x67531),x67534))+~P1(f777(f777(f281(x67532),x67533),x67535)) % 174.01/173.90 [7640]~P22(x76402,x76405,x76404)+E(x76401,f182(f858(x76402,a845)))+E(x76403,f182(f858(x76402,a845)))+~P1(f777(f65(x76402),x76401))+~P1(f777(f65(x76402),x76403))+~E(f777(f777(f106(f858(x76402,a845)),x76403),x76401),f182(f858(x76402,a845)))+E(f777(x76404,f777(f777(f105(f858(x76402,a845)),x76403),x76401)),f777(f777(x76405,f777(x76404,x76403)),f777(x76404,x76401))) % 174.01/173.90 [9233]~P29(x92333,x92331,x92335,x92334)+~P29(x92331,x92333,x92336,x92332)+E(f777(f44(x92331),x92332),f777(f44(x92333),x92334))+~P1(f777(f65(x92333),x92334))+~P1(f777(f65(x92331),x92332))+~P1(f777(f777(f234(f858(x92333,a845)),f777(f305(x92331,x92333,x92336),x92332)),x92334))+~P1(f777(f777(f234(f858(x92331,a845)),f777(f305(x92333,x92331,x92335),x92334)),x92332)) % 174.01/173.90 [9181]~P1(f777(f777(f235(a3),f777(f777(f84(a3),f777(f777(f85(a3),x91815),x91811)),x91816)),f4(a3)))+~E(f777(f777(f84(a3),f777(f777(f85(a3),x91813),x91812)),x91814),f777(f777(f84(a3),f777(f777(f85(a3),x91815),x91811)),x91816))+~P1(f777(f777(f235(a3),f4(a3)),x91815))+~P1(f777(f777(f234(a3),f4(a3)),x91816))+~P1(f777(f777(f235(a3),x91814),x91813))+~P1(f777(f777(f234(a3),x91815),x91813))+P1(f777(f777(f234(a3),x91811),x91812)) % 174.01/173.90 [8972]~E(f777(f777(f84(a3),f777(f777(f85(a3),x89723),x89721)),x89724),f777(f777(f84(a3),f777(f777(f85(a3),x89725),x89722)),x89726))+~P1(f777(f777(f235(a3),f4(a3)),x89725))+~P1(f777(f777(f234(a3),f4(a3)),x89724))+~P1(f777(f777(f235(a3),x89726),x89725))+~P1(f777(f777(f234(a3),x89725),x89723))+P1(f777(f777(f234(a3),x89721),x89722))+~P1(f777(f777(f234(a3),f4(a3)),f777(f777(f84(a3),f777(f777(f85(a3),x89725),x89722)),x89726))) % 174.01/173.90 [9137]~P124(x91371)+~E(f777(f777(f84(x91371),x91372),x91374),f82(x91371))+~P1(f777(f777(f234(x91371),f4(x91371)),x91374))+~P1(f777(f777(f234(x91371),f4(x91371)),x91372))+~P1(f777(f777(f235(x91371),x91375),x91376))+~P1(f777(f777(f235(x91371),x91373),x91376))+P1(f777(f777(f235(x91371),f777(f777(f84(x91371),f777(f777(f85(x91371),x91372),x91373)),f777(f777(f85(x91371),x91374),x91375))),x91376)) % 174.01/173.90 [9138]~P126(x91381)+~E(f777(f777(f84(x91381),x91382),x91384),f82(x91381))+~P1(f777(f777(f234(x91381),x91385),x91386))+~P1(f777(f777(f234(x91381),x91383),x91386))+~P1(f777(f777(f234(x91381),f4(x91381)),x91384))+~P1(f777(f777(f234(x91381),f4(x91381)),x91382))+P1(f777(f777(f234(x91381),f777(f777(f84(x91381),f777(f777(f85(x91381),x91382),x91383)),f777(f777(f85(x91381),x91384),x91385))),x91386)) % 174.01/173.90 [9919]~P12(x99197,x99196,x99195)+E(x99191,x99192)+~P16(x99197,f858(x99194,a845),x99195,x99193)+E(f777(x99193,f501(x99191,x99192,x99193,x99194,x99195,x99196,x99197)),f777(x99193,f502(x99191,x99192,x99193,x99194,x99195,x99196,x99197)))+~E(f777(f777(f48(x99197,f858(x99194,a845)),x99191),x99193),f777(f777(f48(x99197,f858(x99194,a845)),x99192),x99193))+~P1(f777(f777(f336(f858(x99197,a845)),x99192),f777(f777(f63(x99197),x99196),x99195)))+~P1(f777(f777(f336(f858(x99197,a845)),x99191),f777(f777(f63(x99197),x99196),x99195))) % 174.01/173.90 [9959]~P12(x99593,x99597,x99596)+E(x99591,x99592)+~P16(x99593,f858(x99595,a845),x99596,x99594)+~E(f777(f777(f48(x99593,f858(x99595,a845)),x99591),x99594),f777(f777(f48(x99593,f858(x99595,a845)),x99592),x99594))+P1(f777(f777(f336(x99593),f502(x99591,x99592,x99594,x99595,x99596,x99597,x99593)),x99597))+~P1(f777(f777(f336(f858(x99593,a845)),x99592),f777(f777(f63(x99593),x99597),x99596)))+~P1(f777(f777(f336(f858(x99593,a845)),x99591),f777(f777(f63(x99593),x99597),x99596))) % 174.01/173.90 [9960]~P12(x99603,x99607,x99606)+E(x99601,x99602)+~P16(x99603,f858(x99605,a845),x99606,x99604)+~E(f777(f777(f48(x99603,f858(x99605,a845)),x99601),x99604),f777(f777(f48(x99603,f858(x99605,a845)),x99602),x99604))+P1(f777(f777(f336(x99603),f501(x99601,x99602,x99604,x99605,x99606,x99607,x99603)),x99607))+~P1(f777(f777(f336(f858(x99603,a845)),x99602),f777(f777(f63(x99603),x99607),x99606)))+~P1(f777(f777(f336(f858(x99603,a845)),x99601),f777(f777(f63(x99603),x99607),x99606))) % 174.01/173.90 [10026]E(x100261,x100262)+~P12(x100263,x100266,x100267)+~P16(x100263,f858(x100264,a845),x100267,x100265)+~E(f777(f777(f48(x100263,f858(x100264,a845)),x100261),x100265),f777(f777(f48(x100263,f858(x100264,a845)),x100262),x100265))+~P1(f777(f777(f336(f857(x100263,x100263)),f777(f777(f243(x100263,x100263),f502(x100261,x100262,x100265,x100264,x100267,x100266,x100263)),f501(x100261,x100262,x100265,x100264,x100267,x100266,x100263))),x100267))+~P1(f777(f777(f336(f858(x100263,a845)),x100262),f777(f777(f63(x100263),x100266),x100267)))+~P1(f777(f777(f336(f858(x100263,a845)),x100261),f777(f777(f63(x100263),x100266),x100267))) % 174.01/173.90 [8971]~P12(x89711,x89717,x89714)+~E(x89715,x89716)+~P1(f777(f777(f336(x89711),x89713),x89716))+~P1(f777(f777(f336(x89711),x89712),x89715))+~P1(f777(f777(f336(f858(x89711,a845)),x89716),f777(f777(f63(x89711),x89717),x89714)))+~P1(f777(f777(f336(f858(x89711,a845)),x89715),f777(f777(f63(x89711),x89717),x89714)))+P1(f777(f777(f336(f857(x89711,x89711)),f777(f777(f243(x89711,x89711),x89712),x89713)),x89714)) % 174.01/173.90 [9102]E(x91021,x91022)+~P12(x91023,x91024,x91025)+~P1(f777(f777(f336(x91023),x91026),x91022))+~P1(f777(f777(f336(x91023),x91027),x91021))+~P1(f777(f777(f336(f858(x91023,a845)),x91022),f777(f777(f63(x91023),x91024),x91025)))+~P1(f777(f777(f336(f858(x91023,a845)),x91021),f777(f777(f63(x91023),x91024),x91025)))+~P1(f777(f777(f336(f857(x91023,x91023)),f777(f777(f243(x91023,x91023),x91027),x91026)),x91025)) % 174.01/173.90 [10043]~P12(x100439,x100438,x100437)+~P12(x100431,x1004311,x1004310)+~P17(x100431,x100439,f858(x100436,a845),x1004310,x100437,x100435)+P1(f777(f777(f336(x100431),f503(x100432,x100433,x100434,x100435,x100436,x100437,x100438,x100439,x1004310,x1004311,x100431)),x1004311))+~P1(f777(f777(f336(f858(x100439,a845)),x100433),f777(f777(f63(x100439),x100438),x100437)))+~P1(f777(f777(f336(f858(x100431,a845)),x100434),f777(f777(f63(x100431),x1004311),x1004310)))+P1(f777(f777(f336(f858(x100436,a845)),f777(f777(f48(x100431,f858(x100436,a845)),x100434),f777(f777(f12(f858(x100439,f858(x100436,a845)),f858(x100436,a845),x100431),f777(f48(x100439,f858(x100436,a845)),x100433)),x100435))),x100432)) % 174.01/173.90 [10044]~P12(x1004411,x1004410,x100449)+~P12(x100441,x100448,x100447)+~P17(x1004411,x100441,f858(x100446,a845),x100449,x100447,x100445)+P1(f777(f777(f336(x100441),f504(x100442,x100443,x100444,x100445,x100446,x100447,x100448,x100441,x100449,x1004410,x1004411)),x100448))+~P1(f777(f777(f336(f858(x1004411,a845)),x100444),f777(f777(f63(x1004411),x1004410),x100449)))+~P1(f777(f777(f336(f858(x100441,a845)),x100443),f777(f777(f63(x100441),x100448),x100447)))+P1(f777(f777(f336(f858(x100446,a845)),f777(f777(f48(x1004411,f858(x100446,a845)),x100444),f777(f777(f12(f858(x100441,f858(x100446,a845)),f858(x100446,a845),x1004411),f777(f48(x100441,f858(x100446,a845)),x100443)),x100445))),x100442)) % 174.01/173.90 [10047]~P12(x100472,x100478,x100479)+~P12(x100474,x1004710,x1004711)+~P17(x100472,x100474,f858(x100471,a845),x100479,x1004711,x100476)+~P1(f777(f777(f336(f858(x100472,a845)),x100473),f777(f777(f63(x100472),x100478),x100479)))+~P1(f777(f777(f336(f858(x100474,a845)),x100475),f777(f777(f63(x100474),x1004710),x1004711)))+~P1(f777(f777(f336(f858(x100471,a845)),f777(f777(x100476,f503(x100477,x100475,x100473,x100476,x100471,x1004711,x1004710,x100474,x100479,x100478,x100472)),f504(x100477,x100475,x100473,x100476,x100471,x1004711,x1004710,x100474,x100479,x100478,x100472))),x100477))+P1(f777(f777(f336(f858(x100471,a845)),f777(f777(f48(x100472,f858(x100471,a845)),x100473),f777(f777(f12(f858(x100474,f858(x100471,a845)),f858(x100471,a845),x100472),f777(f48(x100474,f858(x100471,a845)),x100475)),x100476))),x100477)) % 174.01/173.90 [9014]E(x90141,x90142)+~P100(x90144)+~P29(x90143,x90144,x90145,f777(f777(f105(f858(x90143,a845)),f777(f160(x90143),x90141)),f777(f160(x90143),x90142)))+~E(f777(f160(x90143),x90141),f777(f160(x90143),x90142))+~P18(x90144,f777(f777(f145(x90143,x90144),x90145),x90142))+~P18(x90144,f777(f777(f145(x90143,x90144),x90145),x90141))+~P1(f777(f129(x90144),f777(f777(f145(x90143,x90144),x90145),x90142)))+~P1(f777(f129(x90144),f777(f777(f145(x90143,x90144),x90145),x90141))) % 174.01/173.90 %EqnAxiom % 174.01/173.90 [1]E(x11,x11) % 174.01/173.90 [2]E(x22,x21)+~E(x21,x22) % 174.01/173.90 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 174.01/173.90 [4]~E(x41,x42)+E(f4(x41),f4(x42)) % 174.01/173.90 [5]~E(x51,x52)+E(f5(x51),f5(x52)) % 174.01/173.90 [6]~E(x61,x62)+E(f104(x61),f104(x62)) % 174.01/173.90 [7]~E(x71,x72)+E(f36(x71),f36(x72)) % 174.01/173.90 [8]~E(x81,x82)+E(f777(x81,x83),f777(x82,x83)) % 174.01/173.90 [9]~E(x91,x92)+E(f777(x93,x91),f777(x93,x92)) % 174.01/173.90 [10]~E(x101,x102)+E(f88(x101),f88(x102)) % 174.01/173.90 [11]~E(x111,x112)+E(f588(x111,x113,x114,x115,x116,x117),f588(x112,x113,x114,x115,x116,x117)) % 174.01/173.90 [12]~E(x121,x122)+E(f588(x123,x121,x124,x125,x126,x127),f588(x123,x122,x124,x125,x126,x127)) % 174.01/173.90 [13]~E(x131,x132)+E(f588(x133,x134,x131,x135,x136,x137),f588(x133,x134,x132,x135,x136,x137)) % 174.01/173.90 [14]~E(x141,x142)+E(f588(x143,x144,x145,x141,x146,x147),f588(x143,x144,x145,x142,x146,x147)) % 174.01/173.90 [15]~E(x151,x152)+E(f588(x153,x154,x155,x156,x151,x157),f588(x153,x154,x155,x156,x152,x157)) % 174.01/173.90 [16]~E(x161,x162)+E(f588(x163,x164,x165,x166,x167,x161),f588(x163,x164,x165,x166,x167,x162)) % 174.01/173.90 [17]~E(x171,x172)+E(f47(x171,x173),f47(x172,x173)) % 174.01/173.90 [18]~E(x181,x182)+E(f47(x183,x181),f47(x183,x182)) % 174.01/173.90 [19]~E(x191,x192)+E(f11(x191,x193,x194),f11(x192,x193,x194)) % 174.01/173.90 [20]~E(x201,x202)+E(f11(x203,x201,x204),f11(x203,x202,x204)) % 174.01/173.90 [21]~E(x211,x212)+E(f11(x213,x214,x211),f11(x213,x214,x212)) % 174.01/173.90 [22]~E(x221,x222)+E(f181(x221),f181(x222)) % 174.01/173.90 [23]~E(x231,x232)+E(f105(x231),f105(x232)) % 174.01/173.90 [24]~E(x241,x242)+E(f182(x241),f182(x242)) % 174.01/173.90 [25]~E(x251,x252)+E(f504(x251,x253,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512),f504(x252,x253,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512)) % 174.01/173.90 [26]~E(x261,x262)+E(f504(x263,x261,x264,x265,x266,x267,x268,x269,x2610,x2611,x2612),f504(x263,x262,x264,x265,x266,x267,x268,x269,x2610,x2611,x2612)) % 174.01/173.90 [27]~E(x271,x272)+E(f504(x273,x274,x271,x275,x276,x277,x278,x279,x2710,x2711,x2712),f504(x273,x274,x272,x275,x276,x277,x278,x279,x2710,x2711,x2712)) % 174.01/173.90 [28]~E(x281,x282)+E(f504(x283,x284,x285,x281,x286,x287,x288,x289,x2810,x2811,x2812),f504(x283,x284,x285,x282,x286,x287,x288,x289,x2810,x2811,x2812)) % 174.01/173.90 [29]~E(x291,x292)+E(f504(x293,x294,x295,x296,x291,x297,x298,x299,x2910,x2911,x2912),f504(x293,x294,x295,x296,x292,x297,x298,x299,x2910,x2911,x2912)) % 174.01/173.90 [30]~E(x301,x302)+E(f504(x303,x304,x305,x306,x307,x301,x308,x309,x3010,x3011,x3012),f504(x303,x304,x305,x306,x307,x302,x308,x309,x3010,x3011,x3012)) % 174.01/173.90 [31]~E(x311,x312)+E(f504(x313,x314,x315,x316,x317,x318,x311,x319,x3110,x3111,x3112),f504(x313,x314,x315,x316,x317,x318,x312,x319,x3110,x3111,x3112)) % 174.01/173.90 [32]~E(x321,x322)+E(f504(x323,x324,x325,x326,x327,x328,x329,x321,x3210,x3211,x3212),f504(x323,x324,x325,x326,x327,x328,x329,x322,x3210,x3211,x3212)) % 174.01/173.90 [33]~E(x331,x332)+E(f504(x333,x334,x335,x336,x337,x338,x339,x3310,x331,x3311,x3312),f504(x333,x334,x335,x336,x337,x338,x339,x3310,x332,x3311,x3312)) % 174.01/173.90 [34]~E(x341,x342)+E(f504(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x341,x3412),f504(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x342,x3412)) % 174.01/173.90 [35]~E(x351,x352)+E(f504(x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512,x351),f504(x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512,x352)) % 174.01/173.90 [36]~E(x361,x362)+E(f238(x361),f238(x362)) % 174.01/173.90 [37]~E(x371,x372)+E(f106(x371),f106(x372)) % 174.01/173.90 [38]~E(x381,x382)+E(f107(x381),f107(x382)) % 174.01/173.90 [39]~E(x391,x392)+E(f41(x391),f41(x392)) % 174.01/173.90 [40]~E(x401,x402)+E(f336(x401),f336(x402)) % 174.01/173.90 [41]~E(x411,x412)+E(f82(x411),f82(x412)) % 174.01/173.90 [42]~E(x421,x422)+E(f503(x421,x423,x424,x425,x426,x427,x428,x429,x4210,x4211,x4212),f503(x422,x423,x424,x425,x426,x427,x428,x429,x4210,x4211,x4212)) % 174.01/173.90 [43]~E(x431,x432)+E(f503(x433,x431,x434,x435,x436,x437,x438,x439,x4310,x4311,x4312),f503(x433,x432,x434,x435,x436,x437,x438,x439,x4310,x4311,x4312)) % 174.01/173.90 [44]~E(x441,x442)+E(f503(x443,x444,x441,x445,x446,x447,x448,x449,x4410,x4411,x4412),f503(x443,x444,x442,x445,x446,x447,x448,x449,x4410,x4411,x4412)) % 174.01/173.90 [45]~E(x451,x452)+E(f503(x453,x454,x455,x451,x456,x457,x458,x459,x4510,x4511,x4512),f503(x453,x454,x455,x452,x456,x457,x458,x459,x4510,x4511,x4512)) % 174.01/173.90 [46]~E(x461,x462)+E(f503(x463,x464,x465,x466,x461,x467,x468,x469,x4610,x4611,x4612),f503(x463,x464,x465,x466,x462,x467,x468,x469,x4610,x4611,x4612)) % 174.01/173.90 [47]~E(x471,x472)+E(f503(x473,x474,x475,x476,x477,x471,x478,x479,x4710,x4711,x4712),f503(x473,x474,x475,x476,x477,x472,x478,x479,x4710,x4711,x4712)) % 174.01/173.90 [48]~E(x481,x482)+E(f503(x483,x484,x485,x486,x487,x488,x481,x489,x4810,x4811,x4812),f503(x483,x484,x485,x486,x487,x488,x482,x489,x4810,x4811,x4812)) % 174.01/173.90 [49]~E(x491,x492)+E(f503(x493,x494,x495,x496,x497,x498,x499,x491,x4910,x4911,x4912),f503(x493,x494,x495,x496,x497,x498,x499,x492,x4910,x4911,x4912)) % 174.01/173.90 [50]~E(x501,x502)+E(f503(x503,x504,x505,x506,x507,x508,x509,x5010,x501,x5011,x5012),f503(x503,x504,x505,x506,x507,x508,x509,x5010,x502,x5011,x5012)) % 174.01/173.90 [51]~E(x511,x512)+E(f503(x513,x514,x515,x516,x517,x518,x519,x5110,x5111,x511,x5112),f503(x513,x514,x515,x516,x517,x518,x519,x5110,x5111,x512,x5112)) % 174.01/173.90 [52]~E(x521,x522)+E(f503(x523,x524,x525,x526,x527,x528,x529,x5210,x5211,x5212,x521),f503(x523,x524,x525,x526,x527,x528,x529,x5210,x5211,x5212,x522)) % 174.01/173.90 [53]~E(x531,x532)+E(f115(x531),f115(x532)) % 174.01/173.90 [54]~E(x541,x542)+E(f235(x541),f235(x542)) % 174.01/173.90 [55]~E(x551,x552)+E(f858(x551,x553),f858(x552,x553)) % 174.01/173.90 [56]~E(x561,x562)+E(f858(x563,x561),f858(x563,x562)) % 174.01/173.90 [57]~E(x571,x572)+E(f8(x571),f8(x572)) % 174.01/173.90 [58]~E(x581,x582)+E(f145(x581,x583),f145(x582,x583)) % 174.01/173.90 [59]~E(x591,x592)+E(f145(x593,x591),f145(x593,x592)) % 174.01/173.90 [60]~E(x601,x602)+E(f83(x601),f83(x602)) % 174.01/173.90 [61]~E(x611,x612)+E(f304(x611),f304(x612)) % 174.01/173.90 [62]~E(x621,x622)+E(f183(x621),f183(x622)) % 174.01/173.90 [63]~E(x631,x632)+E(f12(x631,x633,x634),f12(x632,x633,x634)) % 174.01/173.90 [64]~E(x641,x642)+E(f12(x643,x641,x644),f12(x643,x642,x644)) % 174.01/173.90 [65]~E(x651,x652)+E(f12(x653,x654,x651),f12(x653,x654,x652)) % 174.01/173.90 [66]~E(x661,x662)+E(f108(x661),f108(x662)) % 174.01/173.90 [67]~E(x671,x672)+E(f84(x671),f84(x672)) % 174.01/173.90 [68]~E(x681,x682)+E(f22(x681,x683,x684),f22(x682,x683,x684)) % 174.01/173.90 [69]~E(x691,x692)+E(f22(x693,x691,x694),f22(x693,x692,x694)) % 174.01/173.90 [70]~E(x701,x702)+E(f22(x703,x704,x701),f22(x703,x704,x702)) % 174.01/173.90 [71]~E(x711,x712)+E(f258(x711),f258(x712)) % 174.01/173.90 [72]~E(x721,x722)+E(f44(x721),f44(x722)) % 174.01/173.90 [73]~E(x731,x732)+E(f63(x731),f63(x732)) % 174.01/173.90 [74]~E(x741,x742)+E(f481(x741,x743,x744,x745,x746),f481(x742,x743,x744,x745,x746)) % 174.01/173.90 [75]~E(x751,x752)+E(f481(x753,x751,x754,x755,x756),f481(x753,x752,x754,x755,x756)) % 174.01/173.90 [76]~E(x761,x762)+E(f481(x763,x764,x761,x765,x766),f481(x763,x764,x762,x765,x766)) % 174.01/173.90 [77]~E(x771,x772)+E(f481(x773,x774,x775,x771,x776),f481(x773,x774,x775,x772,x776)) % 174.01/173.90 [78]~E(x781,x782)+E(f481(x783,x784,x785,x786,x781),f481(x783,x784,x785,x786,x782)) % 174.01/173.90 [79]~E(x791,x792)+E(f85(x791),f85(x792)) % 174.01/173.90 [80]~E(x801,x802)+E(f76(x801,x803),f76(x802,x803)) % 174.01/173.90 [81]~E(x811,x812)+E(f76(x813,x811),f76(x813,x812)) % 174.01/173.90 [82]~E(x821,x822)+E(f234(x821),f234(x822)) % 174.01/173.90 [83]~E(x831,x832)+E(f281(x831),f281(x832)) % 174.01/173.90 [84]~E(x841,x842)+E(f323(x841,x843),f323(x842,x843)) % 174.01/173.90 [85]~E(x851,x852)+E(f323(x853,x851),f323(x853,x852)) % 174.01/173.90 [86]~E(x861,x862)+E(f852(x861),f852(x862)) % 174.01/173.90 [87]~E(x871,x872)+E(f857(x871,x873),f857(x872,x873)) % 174.01/173.90 [88]~E(x881,x882)+E(f857(x883,x881),f857(x883,x882)) % 174.01/173.90 [89]~E(x891,x892)+E(f127(x891),f127(x892)) % 174.01/173.90 [90]~E(x901,x902)+E(f160(x901),f160(x902)) % 174.01/173.90 [91]~E(x911,x912)+E(f243(x911,x913),f243(x912,x913)) % 174.01/173.90 [92]~E(x921,x922)+E(f243(x923,x921),f243(x923,x922)) % 174.01/173.90 [93]~E(x931,x932)+E(f418(x931,x933,x934,x935),f418(x932,x933,x934,x935)) % 174.01/173.90 [94]~E(x941,x942)+E(f418(x943,x941,x944,x945),f418(x943,x942,x944,x945)) % 174.01/173.90 [95]~E(x951,x952)+E(f418(x953,x954,x951,x955),f418(x953,x954,x952,x955)) % 174.01/173.90 [96]~E(x961,x962)+E(f418(x963,x964,x965,x961),f418(x963,x964,x965,x962)) % 174.01/173.90 [97]~E(x971,x972)+E(f94(x971,x973),f94(x972,x973)) % 174.01/173.90 [98]~E(x981,x982)+E(f94(x983,x981),f94(x983,x982)) % 174.01/173.90 [99]~E(x991,x992)+E(f35(x991,x993,x994),f35(x992,x993,x994)) % 174.01/173.90 [100]~E(x1001,x1002)+E(f35(x1003,x1001,x1004),f35(x1003,x1002,x1004)) % 174.01/173.90 [101]~E(x1011,x1012)+E(f35(x1013,x1014,x1011),f35(x1013,x1014,x1012)) % 174.01/173.90 [102]~E(x1021,x1022)+E(f295(x1021),f295(x1022)) % 174.01/173.90 [103]~E(x1031,x1032)+E(f65(x1031),f65(x1032)) % 174.01/173.90 [104]~E(x1041,x1042)+E(f45(x1041),f45(x1042)) % 174.01/173.90 [105]~E(x1051,x1052)+E(f305(x1051,x1053,x1054),f305(x1052,x1053,x1054)) % 174.01/173.90 [106]~E(x1061,x1062)+E(f305(x1063,x1061,x1064),f305(x1063,x1062,x1064)) % 174.01/173.90 [107]~E(x1071,x1072)+E(f305(x1073,x1074,x1071),f305(x1073,x1074,x1072)) % 174.01/173.90 [108]~E(x1081,x1082)+E(f723(x1081,x1083),f723(x1082,x1083)) % 174.01/173.90 [109]~E(x1091,x1092)+E(f723(x1093,x1091),f723(x1093,x1092)) % 174.01/173.90 [110]~E(x1101,x1102)+E(f298(x1101),f298(x1102)) % 174.01/173.90 [111]~E(x1111,x1112)+E(f10(x1111,x1113),f10(x1112,x1113)) % 174.01/173.90 [112]~E(x1121,x1122)+E(f10(x1123,x1121),f10(x1123,x1122)) % 174.01/173.90 [113]~E(x1131,x1132)+E(f253(x1131,x1133,x1134),f253(x1132,x1133,x1134)) % 174.01/173.90 [114]~E(x1141,x1142)+E(f253(x1143,x1141,x1144),f253(x1143,x1142,x1144)) % 174.01/173.90 [115]~E(x1151,x1152)+E(f253(x1153,x1154,x1151),f253(x1153,x1154,x1152)) % 174.01/173.90 [116]~E(x1161,x1162)+E(f581(x1161),f581(x1162)) % 174.01/173.90 [117]~E(x1171,x1172)+E(f54(x1171,x1173,x1174),f54(x1172,x1173,x1174)) % 174.01/173.90 [118]~E(x1181,x1182)+E(f54(x1183,x1181,x1184),f54(x1183,x1182,x1184)) % 174.01/173.90 [119]~E(x1191,x1192)+E(f54(x1193,x1194,x1191),f54(x1193,x1194,x1192)) % 174.01/173.90 [120]~E(x1201,x1202)+E(f57(x1201,x1203),f57(x1202,x1203)) % 174.01/173.90 [121]~E(x1211,x1212)+E(f57(x1213,x1211),f57(x1213,x1212)) % 174.01/173.90 [122]~E(x1221,x1222)+E(f155(x1221),f155(x1222)) % 174.01/173.90 [123]~E(x1231,x1232)+E(f244(x1231),f244(x1232)) % 174.01/173.90 [124]~E(x1241,x1242)+E(f140(x1241,x1243,x1244),f140(x1242,x1243,x1244)) % 174.01/173.90 [125]~E(x1251,x1252)+E(f140(x1253,x1251,x1254),f140(x1253,x1252,x1254)) % 174.01/173.90 [126]~E(x1261,x1262)+E(f140(x1263,x1264,x1261),f140(x1263,x1264,x1262)) % 174.01/173.90 [127]~E(x1271,x1272)+E(f46(x1271,x1273),f46(x1272,x1273)) % 174.01/173.90 [128]~E(x1281,x1282)+E(f46(x1283,x1281),f46(x1283,x1282)) % 174.01/173.90 [129]~E(x1291,x1292)+E(f228(x1291,x1293),f228(x1292,x1293)) % 174.01/173.90 [130]~E(x1301,x1302)+E(f228(x1303,x1301),f228(x1303,x1302)) % 174.01/173.90 [131]~E(x1311,x1312)+E(f819(x1311,x1313,x1314,x1315),f819(x1312,x1313,x1314,x1315)) % 174.01/173.90 [132]~E(x1321,x1322)+E(f819(x1323,x1321,x1324,x1325),f819(x1323,x1322,x1324,x1325)) % 174.01/173.90 [133]~E(x1331,x1332)+E(f819(x1333,x1334,x1331,x1335),f819(x1333,x1334,x1332,x1335)) % 174.01/173.90 [134]~E(x1341,x1342)+E(f819(x1343,x1344,x1345,x1341),f819(x1343,x1344,x1345,x1342)) % 174.01/173.90 [135]~E(x1351,x1352)+E(f727(x1351,x1353,x1354),f727(x1352,x1353,x1354)) % 174.01/173.90 [136]~E(x1361,x1362)+E(f727(x1363,x1361,x1364),f727(x1363,x1362,x1364)) % 174.01/173.90 [137]~E(x1371,x1372)+E(f727(x1373,x1374,x1371),f727(x1373,x1374,x1372)) % 174.01/173.90 [138]~E(x1381,x1382)+E(f169(x1381,x1383),f169(x1382,x1383)) % 174.01/173.90 [139]~E(x1391,x1392)+E(f169(x1393,x1391),f169(x1393,x1392)) % 174.01/173.90 [140]~E(x1401,x1402)+E(f284(x1401,x1403,x1404,x1405),f284(x1402,x1403,x1404,x1405)) % 174.01/173.90 [141]~E(x1411,x1412)+E(f284(x1413,x1411,x1414,x1415),f284(x1413,x1412,x1414,x1415)) % 174.01/173.90 [142]~E(x1421,x1422)+E(f284(x1423,x1424,x1421,x1425),f284(x1423,x1424,x1422,x1425)) % 174.01/173.90 [143]~E(x1431,x1432)+E(f284(x1433,x1434,x1435,x1431),f284(x1433,x1434,x1435,x1432)) % 174.01/173.90 [144]~E(x1441,x1442)+E(f13(x1441,x1443),f13(x1442,x1443)) % 174.01/173.91 [145]~E(x1451,x1452)+E(f13(x1453,x1451),f13(x1453,x1452)) % 174.01/173.91 [146]~E(x1461,x1462)+E(f110(x1461),f110(x1462)) % 174.01/173.91 [147]~E(x1471,x1472)+E(f112(x1471),f112(x1472)) % 174.01/173.91 [148]~E(x1481,x1482)+E(f335(x1481),f335(x1482)) % 174.01/173.91 [149]~E(x1491,x1492)+E(f33(x1491,x1493,x1494),f33(x1492,x1493,x1494)) % 174.01/173.91 [150]~E(x1501,x1502)+E(f33(x1503,x1501,x1504),f33(x1503,x1502,x1504)) % 174.01/173.91 [151]~E(x1511,x1512)+E(f33(x1513,x1514,x1511),f33(x1513,x1514,x1512)) % 174.01/173.91 [152]~E(x1521,x1522)+E(f855(x1521),f855(x1522)) % 174.01/173.91 [153]~E(x1531,x1532)+E(f240(x1531,x1533),f240(x1532,x1533)) % 174.01/173.91 [154]~E(x1541,x1542)+E(f240(x1543,x1541),f240(x1543,x1542)) % 174.01/173.91 [155]~E(x1551,x1552)+E(f241(x1551),f241(x1552)) % 174.01/173.91 [156]~E(x1561,x1562)+E(f185(x1561),f185(x1562)) % 174.01/173.91 [157]~E(x1571,x1572)+E(f252(x1571,x1573),f252(x1572,x1573)) % 174.01/173.91 [158]~E(x1581,x1582)+E(f252(x1583,x1581),f252(x1583,x1582)) % 174.01/173.91 [159]~E(x1591,x1592)+E(f395(x1591,x1593),f395(x1592,x1593)) % 174.01/173.91 [160]~E(x1601,x1602)+E(f395(x1603,x1601),f395(x1603,x1602)) % 174.01/173.91 [161]~E(x1611,x1612)+E(f128(x1611,x1613),f128(x1612,x1613)) % 174.01/173.91 [162]~E(x1621,x1622)+E(f128(x1623,x1621),f128(x1623,x1622)) % 174.01/173.91 [163]~E(x1631,x1632)+E(f9(x1631),f9(x1632)) % 174.01/173.91 [164]~E(x1641,x1642)+E(f157(x1641),f157(x1642)) % 174.01/173.91 [165]~E(x1651,x1652)+E(f126(x1651),f126(x1652)) % 174.01/173.91 [166]~E(x1661,x1662)+E(f782(x1661,x1663,x1664),f782(x1662,x1663,x1664)) % 174.01/173.91 [167]~E(x1671,x1672)+E(f782(x1673,x1671,x1674),f782(x1673,x1672,x1674)) % 174.01/173.91 [168]~E(x1681,x1682)+E(f782(x1683,x1684,x1681),f782(x1683,x1684,x1682)) % 174.01/173.91 [169]~E(x1691,x1692)+E(f189(x1691),f189(x1692)) % 174.01/173.91 [170]~E(x1701,x1702)+E(f48(x1701,x1703),f48(x1702,x1703)) % 174.01/173.91 [171]~E(x1711,x1712)+E(f48(x1713,x1711),f48(x1713,x1712)) % 174.01/173.91 [172]~E(x1721,x1722)+E(f30(x1721,x1723),f30(x1722,x1723)) % 174.01/173.91 [173]~E(x1731,x1732)+E(f30(x1733,x1731),f30(x1733,x1732)) % 174.01/173.91 [174]~E(x1741,x1742)+E(f229(x1741),f229(x1742)) % 174.01/173.91 [175]~E(x1751,x1752)+E(f79(x1751),f79(x1752)) % 174.01/173.91 [176]~E(x1761,x1762)+E(f172(x1761,x1763,x1764,x1765),f172(x1762,x1763,x1764,x1765)) % 174.01/173.91 [177]~E(x1771,x1772)+E(f172(x1773,x1771,x1774,x1775),f172(x1773,x1772,x1774,x1775)) % 174.01/173.91 [178]~E(x1781,x1782)+E(f172(x1783,x1784,x1781,x1785),f172(x1783,x1784,x1782,x1785)) % 174.01/173.91 [179]~E(x1791,x1792)+E(f172(x1793,x1794,x1795,x1791),f172(x1793,x1794,x1795,x1792)) % 174.01/173.91 [180]~E(x1801,x1802)+E(f142(x1801),f142(x1802)) % 174.01/173.91 [181]~E(x1811,x1812)+E(f144(x1811),f144(x1812)) % 174.01/173.91 [182]~E(x1821,x1822)+E(f62(x1821,x1823),f62(x1822,x1823)) % 174.01/173.91 [183]~E(x1831,x1832)+E(f62(x1833,x1831),f62(x1833,x1832)) % 174.01/173.91 [184]~E(x1841,x1842)+E(f168(x1841,x1843,x1844),f168(x1842,x1843,x1844)) % 174.01/173.91 [185]~E(x1851,x1852)+E(f168(x1853,x1851,x1854),f168(x1853,x1852,x1854)) % 174.01/173.91 [186]~E(x1861,x1862)+E(f168(x1863,x1864,x1861),f168(x1863,x1864,x1862)) % 174.01/173.91 [187]~E(x1871,x1872)+E(f250(x1871,x1873),f250(x1872,x1873)) % 174.01/173.91 [188]~E(x1881,x1882)+E(f250(x1883,x1881),f250(x1883,x1882)) % 174.01/173.91 [189]~E(x1891,x1892)+E(f291(x1891,x1893,x1894,x1895,x1896),f291(x1892,x1893,x1894,x1895,x1896)) % 174.01/173.91 [190]~E(x1901,x1902)+E(f291(x1903,x1901,x1904,x1905,x1906),f291(x1903,x1902,x1904,x1905,x1906)) % 174.01/173.91 [191]~E(x1911,x1912)+E(f291(x1913,x1914,x1911,x1915,x1916),f291(x1913,x1914,x1912,x1915,x1916)) % 174.01/173.91 [192]~E(x1921,x1922)+E(f291(x1923,x1924,x1925,x1921,x1926),f291(x1923,x1924,x1925,x1922,x1926)) % 174.01/173.91 [193]~E(x1931,x1932)+E(f291(x1933,x1934,x1935,x1936,x1931),f291(x1933,x1934,x1935,x1936,x1932)) % 174.01/173.91 [194]~E(x1941,x1942)+E(f285(x1941),f285(x1942)) % 174.01/173.91 [195]~E(x1951,x1952)+E(f242(x1951,x1953),f242(x1952,x1953)) % 174.01/173.91 [196]~E(x1961,x1962)+E(f242(x1963,x1961),f242(x1963,x1962)) % 174.01/173.91 [197]~E(x1971,x1972)+E(f77(x1971,x1973,x1974,x1975),f77(x1972,x1973,x1974,x1975)) % 174.01/173.91 [198]~E(x1981,x1982)+E(f77(x1983,x1981,x1984,x1985),f77(x1983,x1982,x1984,x1985)) % 174.01/173.91 [199]~E(x1991,x1992)+E(f77(x1993,x1994,x1991,x1995),f77(x1993,x1994,x1992,x1995)) % 174.01/173.91 [200]~E(x2001,x2002)+E(f77(x2003,x2004,x2005,x2001),f77(x2003,x2004,x2005,x2002)) % 174.01/173.91 [201]~E(x2011,x2012)+E(f630(x2011,x2013),f630(x2012,x2013)) % 174.01/173.91 [202]~E(x2021,x2022)+E(f630(x2023,x2021),f630(x2023,x2022)) % 174.01/173.91 [203]~E(x2031,x2032)+E(f34(x2031,x2033,x2034),f34(x2032,x2033,x2034)) % 174.01/173.91 [204]~E(x2041,x2042)+E(f34(x2043,x2041,x2044),f34(x2043,x2042,x2044)) % 174.01/173.91 [205]~E(x2051,x2052)+E(f34(x2053,x2054,x2051),f34(x2053,x2054,x2052)) % 174.01/173.91 [206]~E(x2061,x2062)+E(f81(x2061,x2063,x2064,x2065),f81(x2062,x2063,x2064,x2065)) % 174.01/173.91 [207]~E(x2071,x2072)+E(f81(x2073,x2071,x2074,x2075),f81(x2073,x2072,x2074,x2075)) % 174.01/173.91 [208]~E(x2081,x2082)+E(f81(x2083,x2084,x2081,x2085),f81(x2083,x2084,x2082,x2085)) % 174.01/173.91 [209]~E(x2091,x2092)+E(f81(x2093,x2094,x2095,x2091),f81(x2093,x2094,x2095,x2092)) % 174.01/173.91 [210]~E(x2101,x2102)+E(f40(x2101,x2103,x2104,x2105,x2106,x2107,x2108,x2109,x21010,x21011),f40(x2102,x2103,x2104,x2105,x2106,x2107,x2108,x2109,x21010,x21011)) % 174.01/173.91 [211]~E(x2111,x2112)+E(f40(x2113,x2111,x2114,x2115,x2116,x2117,x2118,x2119,x21110,x21111),f40(x2113,x2112,x2114,x2115,x2116,x2117,x2118,x2119,x21110,x21111)) % 174.01/173.91 [212]~E(x2121,x2122)+E(f40(x2123,x2124,x2121,x2125,x2126,x2127,x2128,x2129,x21210,x21211),f40(x2123,x2124,x2122,x2125,x2126,x2127,x2128,x2129,x21210,x21211)) % 174.01/173.91 [213]~E(x2131,x2132)+E(f40(x2133,x2134,x2135,x2131,x2136,x2137,x2138,x2139,x21310,x21311),f40(x2133,x2134,x2135,x2132,x2136,x2137,x2138,x2139,x21310,x21311)) % 174.01/173.91 [214]~E(x2141,x2142)+E(f40(x2143,x2144,x2145,x2146,x2141,x2147,x2148,x2149,x21410,x21411),f40(x2143,x2144,x2145,x2146,x2142,x2147,x2148,x2149,x21410,x21411)) % 174.01/173.91 [215]~E(x2151,x2152)+E(f40(x2153,x2154,x2155,x2156,x2157,x2151,x2158,x2159,x21510,x21511),f40(x2153,x2154,x2155,x2156,x2157,x2152,x2158,x2159,x21510,x21511)) % 174.01/173.91 [216]~E(x2161,x2162)+E(f40(x2163,x2164,x2165,x2166,x2167,x2168,x2161,x2169,x21610,x21611),f40(x2163,x2164,x2165,x2166,x2167,x2168,x2162,x2169,x21610,x21611)) % 174.01/173.91 [217]~E(x2171,x2172)+E(f40(x2173,x2174,x2175,x2176,x2177,x2178,x2179,x2171,x21710,x21711),f40(x2173,x2174,x2175,x2176,x2177,x2178,x2179,x2172,x21710,x21711)) % 174.01/173.91 [218]~E(x2181,x2182)+E(f40(x2183,x2184,x2185,x2186,x2187,x2188,x2189,x21810,x2181,x21811),f40(x2183,x2184,x2185,x2186,x2187,x2188,x2189,x21810,x2182,x21811)) % 174.01/173.91 [219]~E(x2191,x2192)+E(f40(x2193,x2194,x2195,x2196,x2197,x2198,x2199,x21910,x21911,x2191),f40(x2193,x2194,x2195,x2196,x2197,x2198,x2199,x21910,x21911,x2192)) % 174.01/173.91 [220]~E(x2201,x2202)+E(f265(x2201,x2203),f265(x2202,x2203)) % 174.01/173.91 [221]~E(x2211,x2212)+E(f265(x2213,x2211),f265(x2213,x2212)) % 174.01/173.91 [222]~E(x2221,x2222)+E(f59(x2221,x2223),f59(x2222,x2223)) % 174.01/173.91 [223]~E(x2231,x2232)+E(f59(x2233,x2231),f59(x2233,x2232)) % 174.01/173.91 [224]~E(x2241,x2242)+E(f37(x2241,x2243),f37(x2242,x2243)) % 174.01/173.91 [225]~E(x2251,x2252)+E(f37(x2253,x2251),f37(x2253,x2252)) % 174.01/173.91 [226]~E(x2261,x2262)+E(f764(x2261,x2263),f764(x2262,x2263)) % 174.01/173.91 [227]~E(x2271,x2272)+E(f764(x2273,x2271),f764(x2273,x2272)) % 174.01/173.91 [228]~E(x2281,x2282)+E(f282(x2281,x2283),f282(x2282,x2283)) % 174.01/173.91 [229]~E(x2291,x2292)+E(f282(x2293,x2291),f282(x2293,x2292)) % 174.01/173.91 [230]~E(x2301,x2302)+E(f296(x2301,x2303),f296(x2302,x2303)) % 174.01/173.91 [231]~E(x2311,x2312)+E(f296(x2313,x2311),f296(x2313,x2312)) % 174.01/173.91 [232]~E(x2321,x2322)+E(f49(x2321,x2323),f49(x2322,x2323)) % 174.01/173.91 [233]~E(x2331,x2332)+E(f49(x2333,x2331),f49(x2333,x2332)) % 174.01/173.91 [234]~E(x2341,x2342)+E(f158(x2341,x2343,x2344),f158(x2342,x2343,x2344)) % 174.01/173.91 [235]~E(x2351,x2352)+E(f158(x2353,x2351,x2354),f158(x2353,x2352,x2354)) % 174.01/173.91 [236]~E(x2361,x2362)+E(f158(x2363,x2364,x2361),f158(x2363,x2364,x2362)) % 174.01/173.91 [237]~E(x2371,x2372)+E(f688(x2371,x2373,x2374),f688(x2372,x2373,x2374)) % 174.01/173.91 [238]~E(x2381,x2382)+E(f688(x2383,x2381,x2384),f688(x2383,x2382,x2384)) % 174.01/173.91 [239]~E(x2391,x2392)+E(f688(x2393,x2394,x2391),f688(x2393,x2394,x2392)) % 174.01/173.91 [240]~E(x2401,x2402)+E(f117(x2401),f117(x2402)) % 174.01/173.91 [241]~E(x2411,x2412)+E(f622(x2411,x2413,x2414,x2415,x2416,x2417),f622(x2412,x2413,x2414,x2415,x2416,x2417)) % 174.01/173.91 [242]~E(x2421,x2422)+E(f622(x2423,x2421,x2424,x2425,x2426,x2427),f622(x2423,x2422,x2424,x2425,x2426,x2427)) % 174.01/173.91 [243]~E(x2431,x2432)+E(f622(x2433,x2434,x2431,x2435,x2436,x2437),f622(x2433,x2434,x2432,x2435,x2436,x2437)) % 174.01/173.91 [244]~E(x2441,x2442)+E(f622(x2443,x2444,x2445,x2441,x2446,x2447),f622(x2443,x2444,x2445,x2442,x2446,x2447)) % 174.01/173.91 [245]~E(x2451,x2452)+E(f622(x2453,x2454,x2455,x2456,x2451,x2457),f622(x2453,x2454,x2455,x2456,x2452,x2457)) % 174.01/173.91 [246]~E(x2461,x2462)+E(f622(x2463,x2464,x2465,x2466,x2467,x2461),f622(x2463,x2464,x2465,x2466,x2467,x2462)) % 174.01/173.91 [247]~E(x2471,x2472)+E(f260(x2471),f260(x2472)) % 174.01/173.91 [248]~E(x2481,x2482)+E(f20(x2481,x2483),f20(x2482,x2483)) % 174.01/173.91 [249]~E(x2491,x2492)+E(f20(x2493,x2491),f20(x2493,x2492)) % 174.01/173.91 [250]~E(x2501,x2502)+E(f147(x2501,x2503,x2504,x2505),f147(x2502,x2503,x2504,x2505)) % 174.01/173.91 [251]~E(x2511,x2512)+E(f147(x2513,x2511,x2514,x2515),f147(x2513,x2512,x2514,x2515)) % 174.01/173.91 [252]~E(x2521,x2522)+E(f147(x2523,x2524,x2521,x2525),f147(x2523,x2524,x2522,x2525)) % 174.01/173.91 [253]~E(x2531,x2532)+E(f147(x2533,x2534,x2535,x2531),f147(x2533,x2534,x2535,x2532)) % 174.01/173.91 [254]~E(x2541,x2542)+E(f118(x2541,x2543),f118(x2542,x2543)) % 174.01/173.91 [255]~E(x2551,x2552)+E(f118(x2553,x2551),f118(x2553,x2552)) % 174.01/173.91 [256]~E(x2561,x2562)+E(f456(x2561,x2563,x2564,x2565,x2566,x2567,x2568),f456(x2562,x2563,x2564,x2565,x2566,x2567,x2568)) % 174.01/173.91 [257]~E(x2571,x2572)+E(f456(x2573,x2571,x2574,x2575,x2576,x2577,x2578),f456(x2573,x2572,x2574,x2575,x2576,x2577,x2578)) % 174.01/173.91 [258]~E(x2581,x2582)+E(f456(x2583,x2584,x2581,x2585,x2586,x2587,x2588),f456(x2583,x2584,x2582,x2585,x2586,x2587,x2588)) % 174.01/173.91 [259]~E(x2591,x2592)+E(f456(x2593,x2594,x2595,x2591,x2596,x2597,x2598),f456(x2593,x2594,x2595,x2592,x2596,x2597,x2598)) % 174.01/173.91 [260]~E(x2601,x2602)+E(f456(x2603,x2604,x2605,x2606,x2601,x2607,x2608),f456(x2603,x2604,x2605,x2606,x2602,x2607,x2608)) % 174.01/173.91 [261]~E(x2611,x2612)+E(f456(x2613,x2614,x2615,x2616,x2617,x2611,x2618),f456(x2613,x2614,x2615,x2616,x2617,x2612,x2618)) % 174.01/173.91 [262]~E(x2621,x2622)+E(f456(x2623,x2624,x2625,x2626,x2627,x2628,x2621),f456(x2623,x2624,x2625,x2626,x2627,x2628,x2622)) % 174.01/173.91 [263]~E(x2631,x2632)+E(f186(x2631),f186(x2632)) % 174.01/173.91 [264]~E(x2641,x2642)+E(f132(x2641,x2643),f132(x2642,x2643)) % 174.01/173.91 [265]~E(x2651,x2652)+E(f132(x2653,x2651),f132(x2653,x2652)) % 174.01/173.91 [266]~E(x2661,x2662)+E(f119(x2661),f119(x2662)) % 174.01/173.91 [267]~E(x2671,x2672)+E(f67(x2671,x2673),f67(x2672,x2673)) % 174.01/173.91 [268]~E(x2681,x2682)+E(f67(x2683,x2681),f67(x2683,x2682)) % 174.01/173.91 [269]~E(x2691,x2692)+E(f137(x2691,x2693),f137(x2692,x2693)) % 174.01/173.91 [270]~E(x2701,x2702)+E(f137(x2703,x2701),f137(x2703,x2702)) % 174.01/173.91 [271]~E(x2711,x2712)+E(f129(x2711),f129(x2712)) % 174.01/173.91 [272]~E(x2721,x2722)+E(f212(x2721,x2723),f212(x2722,x2723)) % 174.01/173.91 [273]~E(x2731,x2732)+E(f212(x2733,x2731),f212(x2733,x2732)) % 174.01/173.91 [274]~E(x2741,x2742)+E(f792(x2741,x2743),f792(x2742,x2743)) % 174.01/173.91 [275]~E(x2751,x2752)+E(f792(x2753,x2751),f792(x2753,x2752)) % 174.01/173.91 [276]~E(x2761,x2762)+E(f279(x2761,x2763,x2764),f279(x2762,x2763,x2764)) % 174.01/173.91 [277]~E(x2771,x2772)+E(f279(x2773,x2771,x2774),f279(x2773,x2772,x2774)) % 174.01/173.91 [278]~E(x2781,x2782)+E(f279(x2783,x2784,x2781),f279(x2783,x2784,x2782)) % 174.01/173.91 [279]~E(x2791,x2792)+E(f143(x2791),f143(x2792)) % 174.01/173.91 [280]~E(x2801,x2802)+E(f297(x2801,x2803,x2804),f297(x2802,x2803,x2804)) % 174.01/173.91 [281]~E(x2811,x2812)+E(f297(x2813,x2811,x2814),f297(x2813,x2812,x2814)) % 174.01/173.91 [282]~E(x2821,x2822)+E(f297(x2823,x2824,x2821),f297(x2823,x2824,x2822)) % 174.01/173.91 [283]~E(x2831,x2832)+E(f283(x2831,x2833,x2834),f283(x2832,x2833,x2834)) % 174.01/173.91 [284]~E(x2841,x2842)+E(f283(x2843,x2841,x2844),f283(x2843,x2842,x2844)) % 174.01/173.91 [285]~E(x2851,x2852)+E(f283(x2853,x2854,x2851),f283(x2853,x2854,x2852)) % 174.01/173.91 [286]~E(x2861,x2862)+E(f834(x2861,x2863,x2864),f834(x2862,x2863,x2864)) % 174.01/173.91 [287]~E(x2871,x2872)+E(f834(x2873,x2871,x2874),f834(x2873,x2872,x2874)) % 174.01/173.91 [288]~E(x2881,x2882)+E(f834(x2883,x2884,x2881),f834(x2883,x2884,x2882)) % 174.01/173.91 [289]~E(x2891,x2892)+E(f159(x2891),f159(x2892)) % 174.01/173.91 [290]~E(x2901,x2902)+E(f647(x2901,x2903,x2904,x2905,x2906),f647(x2902,x2903,x2904,x2905,x2906)) % 174.01/173.91 [291]~E(x2911,x2912)+E(f647(x2913,x2911,x2914,x2915,x2916),f647(x2913,x2912,x2914,x2915,x2916)) % 174.01/173.91 [292]~E(x2921,x2922)+E(f647(x2923,x2924,x2921,x2925,x2926),f647(x2923,x2924,x2922,x2925,x2926)) % 174.01/173.91 [293]~E(x2931,x2932)+E(f647(x2933,x2934,x2935,x2931,x2936),f647(x2933,x2934,x2935,x2932,x2936)) % 174.01/173.91 [294]~E(x2941,x2942)+E(f647(x2943,x2944,x2945,x2946,x2941),f647(x2943,x2944,x2945,x2946,x2942)) % 174.01/173.91 [295]~E(x2951,x2952)+E(f535(x2951,x2953,x2954,x2955,x2956),f535(x2952,x2953,x2954,x2955,x2956)) % 174.01/173.91 [296]~E(x2961,x2962)+E(f535(x2963,x2961,x2964,x2965,x2966),f535(x2963,x2962,x2964,x2965,x2966)) % 174.01/173.91 [297]~E(x2971,x2972)+E(f535(x2973,x2974,x2971,x2975,x2976),f535(x2973,x2974,x2972,x2975,x2976)) % 174.01/173.91 [298]~E(x2981,x2982)+E(f535(x2983,x2984,x2985,x2981,x2986),f535(x2983,x2984,x2985,x2982,x2986)) % 174.01/173.91 [299]~E(x2991,x2992)+E(f535(x2993,x2994,x2995,x2996,x2991),f535(x2993,x2994,x2995,x2996,x2992)) % 174.01/173.91 [300]~E(x3001,x3002)+E(f489(x3001,x3003,x3004,x3005),f489(x3002,x3003,x3004,x3005)) % 174.01/173.91 [301]~E(x3011,x3012)+E(f489(x3013,x3011,x3014,x3015),f489(x3013,x3012,x3014,x3015)) % 174.01/173.91 [302]~E(x3021,x3022)+E(f489(x3023,x3024,x3021,x3025),f489(x3023,x3024,x3022,x3025)) % 174.01/173.91 [303]~E(x3031,x3032)+E(f489(x3033,x3034,x3035,x3031),f489(x3033,x3034,x3035,x3032)) % 174.01/173.91 [304]~E(x3041,x3042)+E(f148(x3041,x3043),f148(x3042,x3043)) % 174.01/173.91 [305]~E(x3051,x3052)+E(f148(x3053,x3051),f148(x3053,x3052)) % 174.01/173.91 [306]~E(x3061,x3062)+E(f198(x3061,x3063),f198(x3062,x3063)) % 174.01/173.91 [307]~E(x3071,x3072)+E(f198(x3073,x3071),f198(x3073,x3072)) % 174.01/173.91 [308]~E(x3081,x3082)+E(f850(x3081),f850(x3082)) % 174.01/173.91 [309]~E(x3091,x3092)+E(f784(x3091,x3093,x3094),f784(x3092,x3093,x3094)) % 174.01/173.91 [310]~E(x3101,x3102)+E(f784(x3103,x3101,x3104),f784(x3103,x3102,x3104)) % 174.01/173.91 [311]~E(x3111,x3112)+E(f784(x3113,x3114,x3111),f784(x3113,x3114,x3112)) % 174.01/173.91 [312]~E(x3121,x3122)+E(f156(x3121,x3123,x3124,x3125),f156(x3122,x3123,x3124,x3125)) % 174.01/173.91 [313]~E(x3131,x3132)+E(f156(x3133,x3131,x3134,x3135),f156(x3133,x3132,x3134,x3135)) % 174.01/173.91 [314]~E(x3141,x3142)+E(f156(x3143,x3144,x3141,x3145),f156(x3143,x3144,x3142,x3145)) % 174.01/173.91 [315]~E(x3151,x3152)+E(f156(x3153,x3154,x3155,x3151),f156(x3153,x3154,x3155,x3152)) % 174.01/173.91 [316]~E(x3161,x3162)+E(f811(x3161,x3163,x3164),f811(x3162,x3163,x3164)) % 174.01/173.91 [317]~E(x3171,x3172)+E(f811(x3173,x3171,x3174),f811(x3173,x3172,x3174)) % 174.01/173.91 [318]~E(x3181,x3182)+E(f811(x3183,x3184,x3181),f811(x3183,x3184,x3182)) % 174.01/173.91 [319]~E(x3191,x3192)+E(f309(x3191,x3193,x3194),f309(x3192,x3193,x3194)) % 174.01/173.91 [320]~E(x3201,x3202)+E(f309(x3203,x3201,x3204),f309(x3203,x3202,x3204)) % 174.01/173.91 [321]~E(x3211,x3212)+E(f309(x3213,x3214,x3211),f309(x3213,x3214,x3212)) % 174.01/173.91 [322]~E(x3221,x3222)+E(f139(x3221,x3223),f139(x3222,x3223)) % 174.01/173.91 [323]~E(x3231,x3232)+E(f139(x3233,x3231),f139(x3233,x3232)) % 174.01/173.91 [324]~E(x3241,x3242)+E(f58(x3241,x3243),f58(x3242,x3243)) % 174.01/173.91 [325]~E(x3251,x3252)+E(f58(x3253,x3251),f58(x3253,x3252)) % 174.01/173.91 [326]~E(x3261,x3262)+E(f69(x3261,x3263,x3264),f69(x3262,x3263,x3264)) % 174.01/173.91 [327]~E(x3271,x3272)+E(f69(x3273,x3271,x3274),f69(x3273,x3272,x3274)) % 174.01/173.91 [328]~E(x3281,x3282)+E(f69(x3283,x3284,x3281),f69(x3283,x3284,x3282)) % 174.01/173.91 [329]~E(x3291,x3292)+E(f434(x3291,x3293,x3294,x3295),f434(x3292,x3293,x3294,x3295)) % 174.01/173.91 [330]~E(x3301,x3302)+E(f434(x3303,x3301,x3304,x3305),f434(x3303,x3302,x3304,x3305)) % 174.01/173.91 [331]~E(x3311,x3312)+E(f434(x3313,x3314,x3311,x3315),f434(x3313,x3314,x3312,x3315)) % 174.01/173.91 [332]~E(x3321,x3322)+E(f434(x3323,x3324,x3325,x3321),f434(x3323,x3324,x3325,x3322)) % 174.01/173.91 [333]~E(x3331,x3332)+E(f423(x3331,x3333,x3334),f423(x3332,x3333,x3334)) % 174.01/173.91 [334]~E(x3341,x3342)+E(f423(x3343,x3341,x3344),f423(x3343,x3342,x3344)) % 174.01/173.91 [335]~E(x3351,x3352)+E(f423(x3353,x3354,x3351),f423(x3353,x3354,x3352)) % 174.01/173.91 [336]~E(x3361,x3362)+E(f326(x3361,x3363),f326(x3362,x3363)) % 174.01/173.91 [337]~E(x3371,x3372)+E(f326(x3373,x3371),f326(x3373,x3372)) % 174.01/173.91 [338]~E(x3381,x3382)+E(f408(x3381,x3383,x3384),f408(x3382,x3383,x3384)) % 174.01/173.91 [339]~E(x3391,x3392)+E(f408(x3393,x3391,x3394),f408(x3393,x3392,x3394)) % 174.01/173.91 [340]~E(x3401,x3402)+E(f408(x3403,x3404,x3401),f408(x3403,x3404,x3402)) % 174.01/173.91 [341]~E(x3411,x3412)+E(f328(x3411,x3413),f328(x3412,x3413)) % 174.01/173.91 [342]~E(x3421,x3422)+E(f328(x3423,x3421),f328(x3423,x3422)) % 174.01/173.91 [343]~E(x3431,x3432)+E(f828(x3431,x3433,x3434),f828(x3432,x3433,x3434)) % 174.01/173.91 [344]~E(x3441,x3442)+E(f828(x3443,x3441,x3444),f828(x3443,x3442,x3444)) % 174.01/173.91 [345]~E(x3451,x3452)+E(f828(x3453,x3454,x3451),f828(x3453,x3454,x3452)) % 174.01/173.91 [346]~E(x3461,x3462)+E(f606(x3461,x3463),f606(x3462,x3463)) % 174.01/173.91 [347]~E(x3471,x3472)+E(f606(x3473,x3471),f606(x3473,x3472)) % 174.01/173.91 [348]~E(x3481,x3482)+E(f756(x3481,x3483,x3484),f756(x3482,x3483,x3484)) % 174.01/173.91 [349]~E(x3491,x3492)+E(f756(x3493,x3491,x3494),f756(x3493,x3492,x3494)) % 174.01/173.91 [350]~E(x3501,x3502)+E(f756(x3503,x3504,x3501),f756(x3503,x3504,x3502)) % 174.01/173.91 [351]~E(x3511,x3512)+E(f68(x3511,x3513,x3514),f68(x3512,x3513,x3514)) % 174.01/173.91 [352]~E(x3521,x3522)+E(f68(x3523,x3521,x3524),f68(x3523,x3522,x3524)) % 174.01/173.91 [353]~E(x3531,x3532)+E(f68(x3533,x3534,x3531),f68(x3533,x3534,x3532)) % 174.01/173.91 [354]~E(x3541,x3542)+E(f315(x3541,x3543),f315(x3542,x3543)) % 174.01/173.91 [355]~E(x3551,x3552)+E(f315(x3553,x3551),f315(x3553,x3552)) % 174.01/173.91 [356]~E(x3561,x3562)+E(f15(x3561,x3563,x3564),f15(x3562,x3563,x3564)) % 174.01/173.91 [357]~E(x3571,x3572)+E(f15(x3573,x3571,x3574),f15(x3573,x3572,x3574)) % 174.01/173.91 [358]~E(x3581,x3582)+E(f15(x3583,x3584,x3581),f15(x3583,x3584,x3582)) % 174.01/173.91 [359]~E(x3591,x3592)+E(f255(x3591,x3593,x3594,x3595),f255(x3592,x3593,x3594,x3595)) % 174.01/173.91 [360]~E(x3601,x3602)+E(f255(x3603,x3601,x3604,x3605),f255(x3603,x3602,x3604,x3605)) % 174.01/173.91 [361]~E(x3611,x3612)+E(f255(x3613,x3614,x3611,x3615),f255(x3613,x3614,x3612,x3615)) % 174.01/173.91 [362]~E(x3621,x3622)+E(f255(x3623,x3624,x3625,x3621),f255(x3623,x3624,x3625,x3622)) % 174.01/173.91 [363]~E(x3631,x3632)+E(f678(x3631,x3633,x3634),f678(x3632,x3633,x3634)) % 174.01/173.91 [364]~E(x3641,x3642)+E(f678(x3643,x3641,x3644),f678(x3643,x3642,x3644)) % 174.01/173.91 [365]~E(x3651,x3652)+E(f678(x3653,x3654,x3651),f678(x3653,x3654,x3652)) % 174.01/173.91 [366]~E(x3661,x3662)+E(f136(x3661,x3663),f136(x3662,x3663)) % 174.01/173.91 [367]~E(x3671,x3672)+E(f136(x3673,x3671),f136(x3673,x3672)) % 174.01/173.91 [368]~E(x3681,x3682)+E(f175(x3681,x3683),f175(x3682,x3683)) % 174.01/173.91 [369]~E(x3691,x3692)+E(f175(x3693,x3691),f175(x3693,x3692)) % 174.01/173.91 [370]~E(x3701,x3702)+E(f217(x3701,x3703,x3704,x3705),f217(x3702,x3703,x3704,x3705)) % 174.01/173.91 [371]~E(x3711,x3712)+E(f217(x3713,x3711,x3714,x3715),f217(x3713,x3712,x3714,x3715)) % 174.01/173.91 [372]~E(x3721,x3722)+E(f217(x3723,x3724,x3721,x3725),f217(x3723,x3724,x3722,x3725)) % 174.01/173.91 [373]~E(x3731,x3732)+E(f217(x3733,x3734,x3735,x3731),f217(x3733,x3734,x3735,x3732)) % 174.01/173.91 [374]~E(x3741,x3742)+E(f788(x3741,x3743,x3744),f788(x3742,x3743,x3744)) % 174.01/173.91 [375]~E(x3751,x3752)+E(f788(x3753,x3751,x3754),f788(x3753,x3752,x3754)) % 174.01/173.91 [376]~E(x3761,x3762)+E(f788(x3763,x3764,x3761),f788(x3763,x3764,x3762)) % 174.01/173.91 [377]~E(x3771,x3772)+E(f302(x3771,x3773),f302(x3772,x3773)) % 174.01/173.91 [378]~E(x3781,x3782)+E(f302(x3783,x3781),f302(x3783,x3782)) % 174.01/173.91 [379]~E(x3791,x3792)+E(f146(x3791,x3793,x3794),f146(x3792,x3793,x3794)) % 174.01/173.91 [380]~E(x3801,x3802)+E(f146(x3803,x3801,x3804),f146(x3803,x3802,x3804)) % 174.01/173.91 [381]~E(x3811,x3812)+E(f146(x3813,x3814,x3811),f146(x3813,x3814,x3812)) % 174.01/173.91 [382]~E(x3821,x3822)+E(f728(x3821,x3823),f728(x3822,x3823)) % 174.01/173.91 [383]~E(x3831,x3832)+E(f728(x3833,x3831),f728(x3833,x3832)) % 174.01/173.91 [384]~E(x3841,x3842)+E(f38(x3841,x3843),f38(x3842,x3843)) % 174.01/173.91 [385]~E(x3851,x3852)+E(f38(x3853,x3851),f38(x3853,x3852)) % 174.01/173.91 [386]~E(x3861,x3862)+E(f89(x3861,x3863),f89(x3862,x3863)) % 174.01/173.91 [387]~E(x3871,x3872)+E(f89(x3873,x3871),f89(x3873,x3872)) % 174.01/173.91 [388]~E(x3881,x3882)+E(f150(x3881,x3883),f150(x3882,x3883)) % 174.01/173.91 [389]~E(x3891,x3892)+E(f150(x3893,x3891),f150(x3893,x3892)) % 174.01/173.91 [390]~E(x3901,x3902)+E(f91(x3901),f91(x3902)) % 174.01/173.91 [391]~E(x3911,x3912)+E(f165(x3911,x3913),f165(x3912,x3913)) % 174.01/173.91 [392]~E(x3921,x3922)+E(f165(x3923,x3921),f165(x3923,x3922)) % 174.01/173.91 [393]~E(x3931,x3932)+E(f829(x3931,x3933,x3934),f829(x3932,x3933,x3934)) % 174.01/173.91 [394]~E(x3941,x3942)+E(f829(x3943,x3941,x3944),f829(x3943,x3942,x3944)) % 174.01/173.91 [395]~E(x3951,x3952)+E(f829(x3953,x3954,x3951),f829(x3953,x3954,x3952)) % 174.01/173.91 [396]~E(x3961,x3962)+E(f786(x3961,x3963,x3964),f786(x3962,x3963,x3964)) % 174.01/173.91 [397]~E(x3971,x3972)+E(f786(x3973,x3971,x3974),f786(x3973,x3972,x3974)) % 174.01/173.91 [398]~E(x3981,x3982)+E(f786(x3983,x3984,x3981),f786(x3983,x3984,x3982)) % 174.01/173.91 [399]~E(x3991,x3992)+E(f303(x3991),f303(x3992)) % 174.01/173.91 [400]~E(x4001,x4002)+E(f820(x4001,x4003,x4004,x4005),f820(x4002,x4003,x4004,x4005)) % 174.01/173.91 [401]~E(x4011,x4012)+E(f820(x4013,x4011,x4014,x4015),f820(x4013,x4012,x4014,x4015)) % 174.01/173.91 [402]~E(x4021,x4022)+E(f820(x4023,x4024,x4021,x4025),f820(x4023,x4024,x4022,x4025)) % 174.01/173.91 [403]~E(x4031,x4032)+E(f820(x4033,x4034,x4035,x4031),f820(x4033,x4034,x4035,x4032)) % 174.01/173.91 [404]~E(x4041,x4042)+E(f164(x4041,x4043,x4044),f164(x4042,x4043,x4044)) % 174.01/173.91 [405]~E(x4051,x4052)+E(f164(x4053,x4051,x4054),f164(x4053,x4052,x4054)) % 174.01/173.91 [406]~E(x4061,x4062)+E(f164(x4063,x4064,x4061),f164(x4063,x4064,x4062)) % 174.01/173.91 [407]~E(x4071,x4072)+E(f39(x4071,x4073,x4074,x4075,x4076,x4077,x4078,x4079,x40710,x40711),f39(x4072,x4073,x4074,x4075,x4076,x4077,x4078,x4079,x40710,x40711)) % 174.01/173.91 [408]~E(x4081,x4082)+E(f39(x4083,x4081,x4084,x4085,x4086,x4087,x4088,x4089,x40810,x40811),f39(x4083,x4082,x4084,x4085,x4086,x4087,x4088,x4089,x40810,x40811)) % 174.01/173.91 [409]~E(x4091,x4092)+E(f39(x4093,x4094,x4091,x4095,x4096,x4097,x4098,x4099,x40910,x40911),f39(x4093,x4094,x4092,x4095,x4096,x4097,x4098,x4099,x40910,x40911)) % 174.01/173.91 [410]~E(x4101,x4102)+E(f39(x4103,x4104,x4105,x4101,x4106,x4107,x4108,x4109,x41010,x41011),f39(x4103,x4104,x4105,x4102,x4106,x4107,x4108,x4109,x41010,x41011)) % 174.01/173.91 [411]~E(x4111,x4112)+E(f39(x4113,x4114,x4115,x4116,x4111,x4117,x4118,x4119,x41110,x41111),f39(x4113,x4114,x4115,x4116,x4112,x4117,x4118,x4119,x41110,x41111)) % 174.01/173.91 [412]~E(x4121,x4122)+E(f39(x4123,x4124,x4125,x4126,x4127,x4121,x4128,x4129,x41210,x41211),f39(x4123,x4124,x4125,x4126,x4127,x4122,x4128,x4129,x41210,x41211)) % 174.01/173.91 [413]~E(x4131,x4132)+E(f39(x4133,x4134,x4135,x4136,x4137,x4138,x4131,x4139,x41310,x41311),f39(x4133,x4134,x4135,x4136,x4137,x4138,x4132,x4139,x41310,x41311)) % 174.01/173.91 [414]~E(x4141,x4142)+E(f39(x4143,x4144,x4145,x4146,x4147,x4148,x4149,x4141,x41410,x41411),f39(x4143,x4144,x4145,x4146,x4147,x4148,x4149,x4142,x41410,x41411)) % 174.01/173.91 [415]~E(x4151,x4152)+E(f39(x4153,x4154,x4155,x4156,x4157,x4158,x4159,x41510,x4151,x41511),f39(x4153,x4154,x4155,x4156,x4157,x4158,x4159,x41510,x4152,x41511)) % 174.01/173.91 [416]~E(x4161,x4162)+E(f39(x4163,x4164,x4165,x4166,x4167,x4168,x4169,x41610,x41611,x4161),f39(x4163,x4164,x4165,x4166,x4167,x4168,x4169,x41610,x41611,x4162)) % 174.01/173.91 [417]~E(x4171,x4172)+E(f161(x4171),f161(x4172)) % 174.01/173.91 [418]~E(x4181,x4182)+E(f454(x4181,x4183),f454(x4182,x4183)) % 174.01/173.91 [419]~E(x4191,x4192)+E(f454(x4193,x4191),f454(x4193,x4192)) % 174.01/173.91 [420]~E(x4201,x4202)+E(f56(x4201,x4203),f56(x4202,x4203)) % 174.01/173.91 [421]~E(x4211,x4212)+E(f56(x4213,x4211),f56(x4213,x4212)) % 174.01/173.91 [422]~E(x4221,x4222)+E(f789(x4221,x4223,x4224),f789(x4222,x4223,x4224)) % 174.01/173.91 [423]~E(x4231,x4232)+E(f789(x4233,x4231,x4234),f789(x4233,x4232,x4234)) % 174.01/173.91 [424]~E(x4241,x4242)+E(f789(x4243,x4244,x4241),f789(x4243,x4244,x4242)) % 174.01/173.91 [425]~E(x4251,x4252)+E(f200(x4251,x4253),f200(x4252,x4253)) % 174.01/173.91 [426]~E(x4261,x4262)+E(f200(x4263,x4261),f200(x4263,x4262)) % 174.01/173.91 [427]~E(x4271,x4272)+E(f263(x4271,x4273),f263(x4272,x4273)) % 174.01/173.91 [428]~E(x4281,x4282)+E(f263(x4283,x4281),f263(x4283,x4282)) % 174.01/173.91 [429]~E(x4291,x4292)+E(f178(x4291),f178(x4292)) % 174.01/173.91 [430]~E(x4301,x4302)+E(f474(x4301,x4303,x4304),f474(x4302,x4303,x4304)) % 174.01/173.91 [431]~E(x4311,x4312)+E(f474(x4313,x4311,x4314),f474(x4313,x4312,x4314)) % 174.01/173.91 [432]~E(x4321,x4322)+E(f474(x4323,x4324,x4321),f474(x4323,x4324,x4322)) % 174.01/173.91 [433]~E(x4331,x4332)+E(f626(x4331,x4333,x4334,x4335,x4336),f626(x4332,x4333,x4334,x4335,x4336)) % 174.01/173.91 [434]~E(x4341,x4342)+E(f626(x4343,x4341,x4344,x4345,x4346),f626(x4343,x4342,x4344,x4345,x4346)) % 174.01/173.91 [435]~E(x4351,x4352)+E(f626(x4353,x4354,x4351,x4355,x4356),f626(x4353,x4354,x4352,x4355,x4356)) % 174.01/173.91 [436]~E(x4361,x4362)+E(f626(x4363,x4364,x4365,x4361,x4366),f626(x4363,x4364,x4365,x4362,x4366)) % 174.01/173.91 [437]~E(x4371,x4372)+E(f626(x4373,x4374,x4375,x4376,x4371),f626(x4373,x4374,x4375,x4376,x4372)) % 174.01/173.91 [438]~E(x4381,x4382)+E(f16(x4381,x4383,x4384),f16(x4382,x4383,x4384)) % 174.01/173.91 [439]~E(x4391,x4392)+E(f16(x4393,x4391,x4394),f16(x4393,x4392,x4394)) % 174.01/173.91 [440]~E(x4401,x4402)+E(f16(x4403,x4404,x4401),f16(x4403,x4404,x4402)) % 174.01/173.91 [441]~E(x4411,x4412)+E(f754(x4411,x4413,x4414,x4415,x4416),f754(x4412,x4413,x4414,x4415,x4416)) % 174.01/173.91 [442]~E(x4421,x4422)+E(f754(x4423,x4421,x4424,x4425,x4426),f754(x4423,x4422,x4424,x4425,x4426)) % 174.01/173.91 [443]~E(x4431,x4432)+E(f754(x4433,x4434,x4431,x4435,x4436),f754(x4433,x4434,x4432,x4435,x4436)) % 174.01/173.91 [444]~E(x4441,x4442)+E(f754(x4443,x4444,x4445,x4441,x4446),f754(x4443,x4444,x4445,x4442,x4446)) % 174.01/173.91 [445]~E(x4451,x4452)+E(f754(x4453,x4454,x4455,x4456,x4451),f754(x4453,x4454,x4455,x4456,x4452)) % 174.01/173.91 [446]~E(x4461,x4462)+E(f639(x4461,x4463,x4464,x4465,x4466),f639(x4462,x4463,x4464,x4465,x4466)) % 174.01/173.91 [447]~E(x4471,x4472)+E(f639(x4473,x4471,x4474,x4475,x4476),f639(x4473,x4472,x4474,x4475,x4476)) % 174.01/173.91 [448]~E(x4481,x4482)+E(f639(x4483,x4484,x4481,x4485,x4486),f639(x4483,x4484,x4482,x4485,x4486)) % 174.01/173.91 [449]~E(x4491,x4492)+E(f639(x4493,x4494,x4495,x4491,x4496),f639(x4493,x4494,x4495,x4492,x4496)) % 174.01/173.91 [450]~E(x4501,x4502)+E(f639(x4503,x4504,x4505,x4506,x4501),f639(x4503,x4504,x4505,x4506,x4502)) % 174.01/173.91 [451]~E(x4511,x4512)+E(f506(x4511),f506(x4512)) % 174.01/173.91 [452]~E(x4521,x4522)+E(f100(x4521),f100(x4522)) % 174.01/173.91 [453]~E(x4531,x4532)+E(f353(x4531,x4533),f353(x4532,x4533)) % 174.01/173.91 [454]~E(x4541,x4542)+E(f353(x4543,x4541),f353(x4543,x4542)) % 174.01/173.91 [455]~E(x4551,x4552)+E(f166(x4551,x4553),f166(x4552,x4553)) % 174.01/173.91 [456]~E(x4561,x4562)+E(f166(x4563,x4561),f166(x4563,x4562)) % 174.01/173.91 [457]~E(x4571,x4572)+E(f435(x4571,x4573,x4574,x4575),f435(x4572,x4573,x4574,x4575)) % 174.01/173.91 [458]~E(x4581,x4582)+E(f435(x4583,x4581,x4584,x4585),f435(x4583,x4582,x4584,x4585)) % 174.01/173.91 [459]~E(x4591,x4592)+E(f435(x4593,x4594,x4591,x4595),f435(x4593,x4594,x4592,x4595)) % 174.01/173.91 [460]~E(x4601,x4602)+E(f435(x4603,x4604,x4605,x4601),f435(x4603,x4604,x4605,x4602)) % 174.01/173.91 [461]~E(x4611,x4612)+E(f455(x4611,x4613,x4614,x4615,x4616,x4617,x4618),f455(x4612,x4613,x4614,x4615,x4616,x4617,x4618)) % 174.01/173.91 [462]~E(x4621,x4622)+E(f455(x4623,x4621,x4624,x4625,x4626,x4627,x4628),f455(x4623,x4622,x4624,x4625,x4626,x4627,x4628)) % 174.01/173.91 [463]~E(x4631,x4632)+E(f455(x4633,x4634,x4631,x4635,x4636,x4637,x4638),f455(x4633,x4634,x4632,x4635,x4636,x4637,x4638)) % 174.01/173.91 [464]~E(x4641,x4642)+E(f455(x4643,x4644,x4645,x4641,x4646,x4647,x4648),f455(x4643,x4644,x4645,x4642,x4646,x4647,x4648)) % 174.01/173.91 [465]~E(x4651,x4652)+E(f455(x4653,x4654,x4655,x4656,x4651,x4657,x4658),f455(x4653,x4654,x4655,x4656,x4652,x4657,x4658)) % 174.01/173.91 [466]~E(x4661,x4662)+E(f455(x4663,x4664,x4665,x4666,x4667,x4661,x4668),f455(x4663,x4664,x4665,x4666,x4667,x4662,x4668)) % 174.01/173.91 [467]~E(x4671,x4672)+E(f455(x4673,x4674,x4675,x4676,x4677,x4678,x4671),f455(x4673,x4674,x4675,x4676,x4677,x4678,x4672)) % 174.01/173.91 [468]~E(x4681,x4682)+E(f859(x4681,x4683),f859(x4682,x4683)) % 174.01/173.91 [469]~E(x4691,x4692)+E(f859(x4693,x4691),f859(x4693,x4692)) % 174.01/173.91 [470]~E(x4701,x4702)+E(f18(x4701,x4703),f18(x4702,x4703)) % 174.01/173.91 [471]~E(x4711,x4712)+E(f18(x4713,x4711),f18(x4713,x4712)) % 174.01/173.91 [472]~E(x4721,x4722)+E(f17(x4721,x4723),f17(x4722,x4723)) % 174.01/173.91 [473]~E(x4731,x4732)+E(f17(x4733,x4731),f17(x4733,x4732)) % 174.01/173.91 [474]~E(x4741,x4742)+E(f66(x4741,x4743,x4744),f66(x4742,x4743,x4744)) % 174.01/173.91 [475]~E(x4751,x4752)+E(f66(x4753,x4751,x4754),f66(x4753,x4752,x4754)) % 174.01/173.91 [476]~E(x4761,x4762)+E(f66(x4763,x4764,x4761),f66(x4763,x4764,x4762)) % 174.01/173.91 [477]~E(x4771,x4772)+E(f130(x4771),f130(x4772)) % 174.01/173.91 [478]~E(x4781,x4782)+E(f301(x4781),f301(x4782)) % 174.01/173.91 [479]~E(x4791,x4792)+E(f390(x4791,x4793,x4794,x4795,x4796),f390(x4792,x4793,x4794,x4795,x4796)) % 174.01/173.91 [480]~E(x4801,x4802)+E(f390(x4803,x4801,x4804,x4805,x4806),f390(x4803,x4802,x4804,x4805,x4806)) % 174.01/173.91 [481]~E(x4811,x4812)+E(f390(x4813,x4814,x4811,x4815,x4816),f390(x4813,x4814,x4812,x4815,x4816)) % 174.01/173.91 [482]~E(x4821,x4822)+E(f390(x4823,x4824,x4825,x4821,x4826),f390(x4823,x4824,x4825,x4822,x4826)) % 174.01/173.91 [483]~E(x4831,x4832)+E(f390(x4833,x4834,x4835,x4836,x4831),f390(x4833,x4834,x4835,x4836,x4832)) % 174.01/173.91 [484]~E(x4841,x4842)+E(f736(x4841,x4843,x4844,x4845,x4846),f736(x4842,x4843,x4844,x4845,x4846)) % 174.01/173.91 [485]~E(x4851,x4852)+E(f736(x4853,x4851,x4854,x4855,x4856),f736(x4853,x4852,x4854,x4855,x4856)) % 174.01/173.91 [486]~E(x4861,x4862)+E(f736(x4863,x4864,x4861,x4865,x4866),f736(x4863,x4864,x4862,x4865,x4866)) % 174.01/173.91 [487]~E(x4871,x4872)+E(f736(x4873,x4874,x4875,x4871,x4876),f736(x4873,x4874,x4875,x4872,x4876)) % 174.01/173.91 [488]~E(x4881,x4882)+E(f736(x4883,x4884,x4885,x4886,x4881),f736(x4883,x4884,x4885,x4886,x4882)) % 174.01/173.91 [489]~E(x4891,x4892)+E(f290(x4891,x4893,x4894),f290(x4892,x4893,x4894)) % 174.01/173.91 [490]~E(x4901,x4902)+E(f290(x4903,x4901,x4904),f290(x4903,x4902,x4904)) % 174.01/173.91 [491]~E(x4911,x4912)+E(f290(x4913,x4914,x4911),f290(x4913,x4914,x4912)) % 174.01/173.91 [492]~E(x4921,x4922)+E(f341(x4921,x4923),f341(x4922,x4923)) % 174.01/173.91 [493]~E(x4931,x4932)+E(f341(x4933,x4931),f341(x4933,x4932)) % 174.01/173.91 [494]~E(x4941,x4942)+E(f254(x4941,x4943,x4944,x4945,x4946,x4947),f254(x4942,x4943,x4944,x4945,x4946,x4947)) % 174.01/173.91 [495]~E(x4951,x4952)+E(f254(x4953,x4951,x4954,x4955,x4956,x4957),f254(x4953,x4952,x4954,x4955,x4956,x4957)) % 174.01/173.91 [496]~E(x4961,x4962)+E(f254(x4963,x4964,x4961,x4965,x4966,x4967),f254(x4963,x4964,x4962,x4965,x4966,x4967)) % 174.01/173.91 [497]~E(x4971,x4972)+E(f254(x4973,x4974,x4975,x4971,x4976,x4977),f254(x4973,x4974,x4975,x4972,x4976,x4977)) % 174.01/173.91 [498]~E(x4981,x4982)+E(f254(x4983,x4984,x4985,x4986,x4981,x4987),f254(x4983,x4984,x4985,x4986,x4982,x4987)) % 174.01/173.91 [499]~E(x4991,x4992)+E(f254(x4993,x4994,x4995,x4996,x4997,x4991),f254(x4993,x4994,x4995,x4996,x4997,x4992)) % 174.01/173.91 [500]~E(x5001,x5002)+E(f545(x5001,x5003,x5004,x5005,x5006,x5007),f545(x5002,x5003,x5004,x5005,x5006,x5007)) % 174.01/173.91 [501]~E(x5011,x5012)+E(f545(x5013,x5011,x5014,x5015,x5016,x5017),f545(x5013,x5012,x5014,x5015,x5016,x5017)) % 174.01/173.91 [502]~E(x5021,x5022)+E(f545(x5023,x5024,x5021,x5025,x5026,x5027),f545(x5023,x5024,x5022,x5025,x5026,x5027)) % 174.01/173.91 [503]~E(x5031,x5032)+E(f545(x5033,x5034,x5035,x5031,x5036,x5037),f545(x5033,x5034,x5035,x5032,x5036,x5037)) % 174.01/173.91 [504]~E(x5041,x5042)+E(f545(x5043,x5044,x5045,x5046,x5041,x5047),f545(x5043,x5044,x5045,x5046,x5042,x5047)) % 174.01/173.91 [505]~E(x5051,x5052)+E(f545(x5053,x5054,x5055,x5056,x5057,x5051),f545(x5053,x5054,x5055,x5056,x5057,x5052)) % 174.01/173.91 [506]~E(x5061,x5062)+E(f259(x5061),f259(x5062)) % 174.01/173.91 [507]~E(x5071,x5072)+E(f400(x5071,x5073,x5074,x5075),f400(x5072,x5073,x5074,x5075)) % 174.01/173.91 [508]~E(x5081,x5082)+E(f400(x5083,x5081,x5084,x5085),f400(x5083,x5082,x5084,x5085)) % 174.01/173.91 [509]~E(x5091,x5092)+E(f400(x5093,x5094,x5091,x5095),f400(x5093,x5094,x5092,x5095)) % 174.01/173.91 [510]~E(x5101,x5102)+E(f400(x5103,x5104,x5105,x5101),f400(x5103,x5104,x5105,x5102)) % 174.01/173.91 [511]~E(x5111,x5112)+E(f627(x5111),f627(x5112)) % 174.01/173.91 [512]~E(x5121,x5122)+E(f231(x5121,x5123,x5124,x5125),f231(x5122,x5123,x5124,x5125)) % 174.01/173.91 [513]~E(x5131,x5132)+E(f231(x5133,x5131,x5134,x5135),f231(x5133,x5132,x5134,x5135)) % 174.01/173.91 [514]~E(x5141,x5142)+E(f231(x5143,x5144,x5141,x5145),f231(x5143,x5144,x5142,x5145)) % 174.01/173.91 [515]~E(x5151,x5152)+E(f231(x5153,x5154,x5155,x5151),f231(x5153,x5154,x5155,x5152)) % 174.01/173.91 [516]~E(x5161,x5162)+E(f802(x5161,x5163,x5164),f802(x5162,x5163,x5164)) % 174.01/173.91 [517]~E(x5171,x5172)+E(f802(x5173,x5171,x5174),f802(x5173,x5172,x5174)) % 174.01/173.91 [518]~E(x5181,x5182)+E(f802(x5183,x5184,x5181),f802(x5183,x5184,x5182)) % 174.01/173.91 [519]~E(x5191,x5192)+E(f70(x5191,x5193,x5194,x5195,x5196),f70(x5192,x5193,x5194,x5195,x5196)) % 174.01/173.91 [520]~E(x5201,x5202)+E(f70(x5203,x5201,x5204,x5205,x5206),f70(x5203,x5202,x5204,x5205,x5206)) % 174.01/173.91 [521]~E(x5211,x5212)+E(f70(x5213,x5214,x5211,x5215,x5216),f70(x5213,x5214,x5212,x5215,x5216)) % 174.01/173.91 [522]~E(x5221,x5222)+E(f70(x5223,x5224,x5225,x5221,x5226),f70(x5223,x5224,x5225,x5222,x5226)) % 174.01/173.91 [523]~E(x5231,x5232)+E(f70(x5233,x5234,x5235,x5236,x5231),f70(x5233,x5234,x5235,x5236,x5232)) % 174.01/173.91 [524]~E(x5241,x5242)+E(f251(x5241,x5243,x5244,x5245),f251(x5242,x5243,x5244,x5245)) % 174.01/173.91 [525]~E(x5251,x5252)+E(f251(x5253,x5251,x5254,x5255),f251(x5253,x5252,x5254,x5255)) % 174.01/173.91 [526]~E(x5261,x5262)+E(f251(x5263,x5264,x5261,x5265),f251(x5263,x5264,x5262,x5265)) % 174.01/173.91 [527]~E(x5271,x5272)+E(f251(x5273,x5274,x5275,x5271),f251(x5273,x5274,x5275,x5272)) % 174.01/173.91 [528]~E(x5281,x5282)+E(f393(x5281,x5283,x5284,x5285,x5286),f393(x5282,x5283,x5284,x5285,x5286)) % 174.01/173.91 [529]~E(x5291,x5292)+E(f393(x5293,x5291,x5294,x5295,x5296),f393(x5293,x5292,x5294,x5295,x5296)) % 174.01/173.91 [530]~E(x5301,x5302)+E(f393(x5303,x5304,x5301,x5305,x5306),f393(x5303,x5304,x5302,x5305,x5306)) % 174.01/173.91 [531]~E(x5311,x5312)+E(f393(x5313,x5314,x5315,x5311,x5316),f393(x5313,x5314,x5315,x5312,x5316)) % 174.01/173.91 [532]~E(x5321,x5322)+E(f393(x5323,x5324,x5325,x5326,x5321),f393(x5323,x5324,x5325,x5326,x5322)) % 174.01/173.91 [533]~E(x5331,x5332)+E(f55(x5331,x5333),f55(x5332,x5333)) % 174.01/173.91 [534]~E(x5341,x5342)+E(f55(x5343,x5341),f55(x5343,x5342)) % 174.01/173.91 [535]~E(x5351,x5352)+E(f266(x5351),f266(x5352)) % 174.01/173.91 [536]~E(x5361,x5362)+E(f209(x5361),f209(x5362)) % 174.01/173.91 [537]~E(x5371,x5372)+E(f299(x5371,x5373,x5374),f299(x5372,x5373,x5374)) % 174.01/173.91 [538]~E(x5381,x5382)+E(f299(x5383,x5381,x5384),f299(x5383,x5382,x5384)) % 174.01/173.91 [539]~E(x5391,x5392)+E(f299(x5393,x5394,x5391),f299(x5393,x5394,x5392)) % 174.01/173.91 [540]~E(x5401,x5402)+E(f710(x5401,x5403,x5404,x5405,x5406,x5407),f710(x5402,x5403,x5404,x5405,x5406,x5407)) % 174.01/173.91 [541]~E(x5411,x5412)+E(f710(x5413,x5411,x5414,x5415,x5416,x5417),f710(x5413,x5412,x5414,x5415,x5416,x5417)) % 174.01/173.91 [542]~E(x5421,x5422)+E(f710(x5423,x5424,x5421,x5425,x5426,x5427),f710(x5423,x5424,x5422,x5425,x5426,x5427)) % 174.01/173.91 [543]~E(x5431,x5432)+E(f710(x5433,x5434,x5435,x5431,x5436,x5437),f710(x5433,x5434,x5435,x5432,x5436,x5437)) % 174.01/173.91 [544]~E(x5441,x5442)+E(f710(x5443,x5444,x5445,x5446,x5441,x5447),f710(x5443,x5444,x5445,x5446,x5442,x5447)) % 174.01/173.91 [545]~E(x5451,x5452)+E(f710(x5453,x5454,x5455,x5456,x5457,x5451),f710(x5453,x5454,x5455,x5456,x5457,x5452)) % 174.01/173.91 [546]~E(x5461,x5462)+E(f517(x5461,x5463,x5464,x5465),f517(x5462,x5463,x5464,x5465)) % 174.01/173.91 [547]~E(x5471,x5472)+E(f517(x5473,x5471,x5474,x5475),f517(x5473,x5472,x5474,x5475)) % 174.01/173.91 [548]~E(x5481,x5482)+E(f517(x5483,x5484,x5481,x5485),f517(x5483,x5484,x5482,x5485)) % 174.01/173.91 [549]~E(x5491,x5492)+E(f517(x5493,x5494,x5495,x5491),f517(x5493,x5494,x5495,x5492)) % 174.01/173.91 [550]~E(x5501,x5502)+E(f711(x5501,x5503,x5504,x5505,x5506,x5507),f711(x5502,x5503,x5504,x5505,x5506,x5507)) % 174.01/173.91 [551]~E(x5511,x5512)+E(f711(x5513,x5511,x5514,x5515,x5516,x5517),f711(x5513,x5512,x5514,x5515,x5516,x5517)) % 174.01/173.91 [552]~E(x5521,x5522)+E(f711(x5523,x5524,x5521,x5525,x5526,x5527),f711(x5523,x5524,x5522,x5525,x5526,x5527)) % 174.01/173.91 [553]~E(x5531,x5532)+E(f711(x5533,x5534,x5535,x5531,x5536,x5537),f711(x5533,x5534,x5535,x5532,x5536,x5537)) % 174.01/173.91 [554]~E(x5541,x5542)+E(f711(x5543,x5544,x5545,x5546,x5541,x5547),f711(x5543,x5544,x5545,x5546,x5542,x5547)) % 174.01/173.91 [555]~E(x5551,x5552)+E(f711(x5553,x5554,x5555,x5556,x5557,x5551),f711(x5553,x5554,x5555,x5556,x5557,x5552)) % 174.01/173.91 [556]~E(x5561,x5562)+E(f162(x5561,x5563,x5564),f162(x5562,x5563,x5564)) % 174.01/173.91 [557]~E(x5571,x5572)+E(f162(x5573,x5571,x5574),f162(x5573,x5572,x5574)) % 174.01/173.91 [558]~E(x5581,x5582)+E(f162(x5583,x5584,x5581),f162(x5583,x5584,x5582)) % 174.01/173.91 [559]~E(x5591,x5592)+E(f578(x5591,x5593,x5594,x5595,x5596),f578(x5592,x5593,x5594,x5595,x5596)) % 174.01/173.91 [560]~E(x5601,x5602)+E(f578(x5603,x5601,x5604,x5605,x5606),f578(x5603,x5602,x5604,x5605,x5606)) % 174.01/173.91 [561]~E(x5611,x5612)+E(f578(x5613,x5614,x5611,x5615,x5616),f578(x5613,x5614,x5612,x5615,x5616)) % 174.01/173.91 [562]~E(x5621,x5622)+E(f578(x5623,x5624,x5625,x5621,x5626),f578(x5623,x5624,x5625,x5622,x5626)) % 174.01/173.91 [563]~E(x5631,x5632)+E(f578(x5633,x5634,x5635,x5636,x5631),f578(x5633,x5634,x5635,x5636,x5632)) % 174.01/173.91 [564]~E(x5641,x5642)+E(f579(x5641,x5643,x5644,x5645,x5646),f579(x5642,x5643,x5644,x5645,x5646)) % 174.01/173.91 [565]~E(x5651,x5652)+E(f579(x5653,x5651,x5654,x5655,x5656),f579(x5653,x5652,x5654,x5655,x5656)) % 174.01/173.91 [566]~E(x5661,x5662)+E(f579(x5663,x5664,x5661,x5665,x5666),f579(x5663,x5664,x5662,x5665,x5666)) % 174.01/173.91 [567]~E(x5671,x5672)+E(f579(x5673,x5674,x5675,x5671,x5676),f579(x5673,x5674,x5675,x5672,x5676)) % 174.01/173.91 [568]~E(x5681,x5682)+E(f579(x5683,x5684,x5685,x5686,x5681),f579(x5683,x5684,x5685,x5686,x5682)) % 174.01/173.91 [569]~E(x5691,x5692)+E(f533(x5691,x5693,x5694,x5695,x5696),f533(x5692,x5693,x5694,x5695,x5696)) % 174.01/173.91 [570]~E(x5701,x5702)+E(f533(x5703,x5701,x5704,x5705,x5706),f533(x5703,x5702,x5704,x5705,x5706)) % 174.01/173.91 [571]~E(x5711,x5712)+E(f533(x5713,x5714,x5711,x5715,x5716),f533(x5713,x5714,x5712,x5715,x5716)) % 174.01/173.91 [572]~E(x5721,x5722)+E(f533(x5723,x5724,x5725,x5721,x5726),f533(x5723,x5724,x5725,x5722,x5726)) % 174.01/173.91 [573]~E(x5731,x5732)+E(f533(x5733,x5734,x5735,x5736,x5731),f533(x5733,x5734,x5735,x5736,x5732)) % 174.01/173.91 [574]~E(x5741,x5742)+E(f379(x5741,x5743),f379(x5742,x5743)) % 174.01/173.91 [575]~E(x5751,x5752)+E(f379(x5753,x5751),f379(x5753,x5752)) % 174.01/173.91 [576]~E(x5761,x5762)+E(f286(x5761,x5763),f286(x5762,x5763)) % 174.01/173.91 [577]~E(x5771,x5772)+E(f286(x5773,x5771),f286(x5773,x5772)) % 174.01/173.91 [578]~E(x5781,x5782)+E(f414(x5781,x5783,x5784,x5785),f414(x5782,x5783,x5784,x5785)) % 174.01/173.91 [579]~E(x5791,x5792)+E(f414(x5793,x5791,x5794,x5795),f414(x5793,x5792,x5794,x5795)) % 174.01/173.91 [580]~E(x5801,x5802)+E(f414(x5803,x5804,x5801,x5805),f414(x5803,x5804,x5802,x5805)) % 174.01/173.91 [581]~E(x5811,x5812)+E(f414(x5813,x5814,x5815,x5811),f414(x5813,x5814,x5815,x5812)) % 174.01/173.91 [582]~E(x5821,x5822)+E(f86(x5821,x5823),f86(x5822,x5823)) % 174.01/173.91 [583]~E(x5831,x5832)+E(f86(x5833,x5831),f86(x5833,x5832)) % 174.01/173.91 [584]~E(x5841,x5842)+E(f149(x5841,x5843),f149(x5842,x5843)) % 174.01/173.91 [585]~E(x5851,x5852)+E(f149(x5853,x5851),f149(x5853,x5852)) % 174.01/173.91 [586]~E(x5861,x5862)+E(f798(x5861,x5863,x5864),f798(x5862,x5863,x5864)) % 174.01/173.91 [587]~E(x5871,x5872)+E(f798(x5873,x5871,x5874),f798(x5873,x5872,x5874)) % 174.01/173.91 [588]~E(x5881,x5882)+E(f798(x5883,x5884,x5881),f798(x5883,x5884,x5882)) % 174.01/173.91 [589]~E(x5891,x5892)+E(f665(x5891,x5893,x5894,x5895,x5896,x5897,x5898),f665(x5892,x5893,x5894,x5895,x5896,x5897,x5898)) % 174.01/173.91 [590]~E(x5901,x5902)+E(f665(x5903,x5901,x5904,x5905,x5906,x5907,x5908),f665(x5903,x5902,x5904,x5905,x5906,x5907,x5908)) % 174.01/173.91 [591]~E(x5911,x5912)+E(f665(x5913,x5914,x5911,x5915,x5916,x5917,x5918),f665(x5913,x5914,x5912,x5915,x5916,x5917,x5918)) % 174.01/173.91 [592]~E(x5921,x5922)+E(f665(x5923,x5924,x5925,x5921,x5926,x5927,x5928),f665(x5923,x5924,x5925,x5922,x5926,x5927,x5928)) % 174.01/173.91 [593]~E(x5931,x5932)+E(f665(x5933,x5934,x5935,x5936,x5931,x5937,x5938),f665(x5933,x5934,x5935,x5936,x5932,x5937,x5938)) % 174.01/173.91 [594]~E(x5941,x5942)+E(f665(x5943,x5944,x5945,x5946,x5947,x5941,x5948),f665(x5943,x5944,x5945,x5946,x5947,x5942,x5948)) % 174.01/173.91 [595]~E(x5951,x5952)+E(f665(x5953,x5954,x5955,x5956,x5957,x5958,x5951),f665(x5953,x5954,x5955,x5956,x5957,x5958,x5952)) % 174.01/173.91 [596]~E(x5961,x5962)+E(f744(x5961,x5963,x5964,x5965),f744(x5962,x5963,x5964,x5965)) % 174.01/173.91 [597]~E(x5971,x5972)+E(f744(x5973,x5971,x5974,x5975),f744(x5973,x5972,x5974,x5975)) % 174.01/173.91 [598]~E(x5981,x5982)+E(f744(x5983,x5984,x5981,x5985),f744(x5983,x5984,x5982,x5985)) % 174.01/173.91 [599]~E(x5991,x5992)+E(f744(x5993,x5994,x5995,x5991),f744(x5993,x5994,x5995,x5992)) % 174.01/173.91 [600]~E(x6001,x6002)+E(f176(x6001,x6003,x6004),f176(x6002,x6003,x6004)) % 174.01/173.91 [601]~E(x6011,x6012)+E(f176(x6013,x6011,x6014),f176(x6013,x6012,x6014)) % 174.01/173.91 [602]~E(x6021,x6022)+E(f176(x6023,x6024,x6021),f176(x6023,x6024,x6022)) % 174.01/173.91 [603]~E(x6031,x6032)+E(f19(x6031,x6033),f19(x6032,x6033)) % 174.01/173.91 [604]~E(x6041,x6042)+E(f19(x6043,x6041),f19(x6043,x6042)) % 174.01/173.91 [605]~E(x6051,x6052)+E(f707(x6051,x6053,x6054,x6055,x6056,x6057),f707(x6052,x6053,x6054,x6055,x6056,x6057)) % 174.01/173.91 [606]~E(x6061,x6062)+E(f707(x6063,x6061,x6064,x6065,x6066,x6067),f707(x6063,x6062,x6064,x6065,x6066,x6067)) % 174.01/173.91 [607]~E(x6071,x6072)+E(f707(x6073,x6074,x6071,x6075,x6076,x6077),f707(x6073,x6074,x6072,x6075,x6076,x6077)) % 174.01/173.91 [608]~E(x6081,x6082)+E(f707(x6083,x6084,x6085,x6081,x6086,x6087),f707(x6083,x6084,x6085,x6082,x6086,x6087)) % 174.01/173.91 [609]~E(x6091,x6092)+E(f707(x6093,x6094,x6095,x6096,x6091,x6097),f707(x6093,x6094,x6095,x6096,x6092,x6097)) % 174.01/173.91 [610]~E(x6101,x6102)+E(f707(x6103,x6104,x6105,x6106,x6107,x6101),f707(x6103,x6104,x6105,x6106,x6107,x6102)) % 174.01/173.91 [611]~E(x6111,x6112)+E(f356(x6111,x6113,x6114,x6115),f356(x6112,x6113,x6114,x6115)) % 174.01/173.91 [612]~E(x6121,x6122)+E(f356(x6123,x6121,x6124,x6125),f356(x6123,x6122,x6124,x6125)) % 174.01/173.91 [613]~E(x6131,x6132)+E(f356(x6133,x6134,x6131,x6135),f356(x6133,x6134,x6132,x6135)) % 174.01/173.91 [614]~E(x6141,x6142)+E(f356(x6143,x6144,x6145,x6141),f356(x6143,x6144,x6145,x6142)) % 174.01/173.91 [615]~E(x6151,x6152)+E(f174(x6151,x6153,x6154,x6155),f174(x6152,x6153,x6154,x6155)) % 174.01/173.91 [616]~E(x6161,x6162)+E(f174(x6163,x6161,x6164,x6165),f174(x6163,x6162,x6164,x6165)) % 174.01/173.91 [617]~E(x6171,x6172)+E(f174(x6173,x6174,x6171,x6175),f174(x6173,x6174,x6172,x6175)) % 174.01/173.91 [618]~E(x6181,x6182)+E(f174(x6183,x6184,x6185,x6181),f174(x6183,x6184,x6185,x6182)) % 174.01/173.91 [619]~E(x6191,x6192)+E(f361(x6191,x6193,x6194,x6195,x6196),f361(x6192,x6193,x6194,x6195,x6196)) % 174.01/173.91 [620]~E(x6201,x6202)+E(f361(x6203,x6201,x6204,x6205,x6206),f361(x6203,x6202,x6204,x6205,x6206)) % 174.01/173.91 [621]~E(x6211,x6212)+E(f361(x6213,x6214,x6211,x6215,x6216),f361(x6213,x6214,x6212,x6215,x6216)) % 174.01/173.91 [622]~E(x6221,x6222)+E(f361(x6223,x6224,x6225,x6221,x6226),f361(x6223,x6224,x6225,x6222,x6226)) % 174.01/173.91 [623]~E(x6231,x6232)+E(f361(x6233,x6234,x6235,x6236,x6231),f361(x6233,x6234,x6235,x6236,x6232)) % 174.01/173.91 [624]~E(x6241,x6242)+E(f280(x6241,x6243),f280(x6242,x6243)) % 174.01/173.91 [625]~E(x6251,x6252)+E(f280(x6253,x6251),f280(x6253,x6252)) % 174.01/173.91 [626]~E(x6261,x6262)+E(f134(x6261,x6263,x6264,x6265),f134(x6262,x6263,x6264,x6265)) % 174.01/173.91 [627]~E(x6271,x6272)+E(f134(x6273,x6271,x6274,x6275),f134(x6273,x6272,x6274,x6275)) % 174.01/173.91 [628]~E(x6281,x6282)+E(f134(x6283,x6284,x6281,x6285),f134(x6283,x6284,x6282,x6285)) % 174.01/173.91 [629]~E(x6291,x6292)+E(f134(x6293,x6294,x6295,x6291),f134(x6293,x6294,x6295,x6292)) % 174.01/173.91 [630]~E(x6301,x6302)+E(f609(x6301,x6303),f609(x6302,x6303)) % 174.01/173.91 [631]~E(x6311,x6312)+E(f609(x6313,x6311),f609(x6313,x6312)) % 174.01/173.91 [632]~E(x6321,x6322)+E(f247(x6321,x6323),f247(x6322,x6323)) % 174.01/173.91 [633]~E(x6331,x6332)+E(f247(x6333,x6331),f247(x6333,x6332)) % 174.01/173.91 [634]~E(x6341,x6342)+E(f95(x6341),f95(x6342)) % 174.01/173.91 [635]~E(x6351,x6352)+E(f223(x6351,x6353),f223(x6352,x6353)) % 174.01/173.91 [636]~E(x6361,x6362)+E(f223(x6363,x6361),f223(x6363,x6362)) % 174.01/173.91 [637]~E(x6371,x6372)+E(f460(x6371,x6373,x6374,x6375),f460(x6372,x6373,x6374,x6375)) % 174.01/173.91 [638]~E(x6381,x6382)+E(f460(x6383,x6381,x6384,x6385),f460(x6383,x6382,x6384,x6385)) % 174.01/173.91 [639]~E(x6391,x6392)+E(f460(x6393,x6394,x6391,x6395),f460(x6393,x6394,x6392,x6395)) % 174.01/173.91 [640]~E(x6401,x6402)+E(f460(x6403,x6404,x6405,x6401),f460(x6403,x6404,x6405,x6402)) % 174.01/173.91 [641]~E(x6411,x6412)+E(f498(x6411,x6413,x6414,x6415,x6416,x6417),f498(x6412,x6413,x6414,x6415,x6416,x6417)) % 174.01/173.91 [642]~E(x6421,x6422)+E(f498(x6423,x6421,x6424,x6425,x6426,x6427),f498(x6423,x6422,x6424,x6425,x6426,x6427)) % 174.01/173.91 [643]~E(x6431,x6432)+E(f498(x6433,x6434,x6431,x6435,x6436,x6437),f498(x6433,x6434,x6432,x6435,x6436,x6437)) % 174.01/173.91 [644]~E(x6441,x6442)+E(f498(x6443,x6444,x6445,x6441,x6446,x6447),f498(x6443,x6444,x6445,x6442,x6446,x6447)) % 174.01/173.91 [645]~E(x6451,x6452)+E(f498(x6453,x6454,x6455,x6456,x6451,x6457),f498(x6453,x6454,x6455,x6456,x6452,x6457)) % 174.01/173.91 [646]~E(x6461,x6462)+E(f498(x6463,x6464,x6465,x6466,x6467,x6461),f498(x6463,x6464,x6465,x6466,x6467,x6462)) % 174.01/173.91 [647]~E(x6471,x6472)+E(f539(x6471,x6473,x6474,x6475),f539(x6472,x6473,x6474,x6475)) % 174.01/173.91 [648]~E(x6481,x6482)+E(f539(x6483,x6481,x6484,x6485),f539(x6483,x6482,x6484,x6485)) % 174.01/173.91 [649]~E(x6491,x6492)+E(f539(x6493,x6494,x6491,x6495),f539(x6493,x6494,x6492,x6495)) % 174.01/173.91 [650]~E(x6501,x6502)+E(f539(x6503,x6504,x6505,x6501),f539(x6503,x6504,x6505,x6502)) % 174.01/173.91 [651]~E(x6511,x6512)+E(f793(x6511,x6513),f793(x6512,x6513)) % 174.01/173.91 [652]~E(x6521,x6522)+E(f793(x6523,x6521),f793(x6523,x6522)) % 174.01/173.91 [653]~E(x6531,x6532)+E(f410(x6531,x6533,x6534,x6535),f410(x6532,x6533,x6534,x6535)) % 174.01/173.91 [654]~E(x6541,x6542)+E(f410(x6543,x6541,x6544,x6545),f410(x6543,x6542,x6544,x6545)) % 174.01/173.91 [655]~E(x6551,x6552)+E(f410(x6553,x6554,x6551,x6555),f410(x6553,x6554,x6552,x6555)) % 174.01/173.91 [656]~E(x6561,x6562)+E(f410(x6563,x6564,x6565,x6561),f410(x6563,x6564,x6565,x6562)) % 174.01/173.91 [657]~E(x6571,x6572)+E(f133(x6571),f133(x6572)) % 174.01/173.91 [658]~E(x6581,x6582)+E(f327(x6581,x6583,x6584,x6585),f327(x6582,x6583,x6584,x6585)) % 174.01/173.91 [659]~E(x6591,x6592)+E(f327(x6593,x6591,x6594,x6595),f327(x6593,x6592,x6594,x6595)) % 174.01/173.91 [660]~E(x6601,x6602)+E(f327(x6603,x6604,x6601,x6605),f327(x6603,x6604,x6602,x6605)) % 174.01/173.91 [661]~E(x6611,x6612)+E(f327(x6613,x6614,x6615,x6611),f327(x6613,x6614,x6615,x6612)) % 174.01/173.91 [662]~E(x6621,x6622)+E(f90(x6621,x6623),f90(x6622,x6623)) % 174.01/173.91 [663]~E(x6631,x6632)+E(f90(x6633,x6631),f90(x6633,x6632)) % 174.01/173.91 [664]~E(x6641,x6642)+E(f300(x6641,x6643,x6644),f300(x6642,x6643,x6644)) % 174.01/173.91 [665]~E(x6651,x6652)+E(f300(x6653,x6651,x6654),f300(x6653,x6652,x6654)) % 174.01/173.91 [666]~E(x6661,x6662)+E(f300(x6663,x6664,x6661),f300(x6663,x6664,x6662)) % 174.01/173.91 [667]~E(x6671,x6672)+E(f153(x6671,x6673,x6674),f153(x6672,x6673,x6674)) % 174.01/173.91 [668]~E(x6681,x6682)+E(f153(x6683,x6681,x6684),f153(x6683,x6682,x6684)) % 174.01/173.91 [669]~E(x6691,x6692)+E(f153(x6693,x6694,x6691),f153(x6693,x6694,x6692)) % 174.01/173.91 [670]~E(x6701,x6702)+E(f171(x6701,x6703,x6704),f171(x6702,x6703,x6704)) % 174.01/173.91 [671]~E(x6711,x6712)+E(f171(x6713,x6711,x6714),f171(x6713,x6712,x6714)) % 174.01/173.91 [672]~E(x6721,x6722)+E(f171(x6723,x6724,x6721),f171(x6723,x6724,x6722)) % 174.01/173.91 [673]~E(x6731,x6732)+E(f270(x6731,x6733,x6734,x6735),f270(x6732,x6733,x6734,x6735)) % 174.01/173.91 [674]~E(x6741,x6742)+E(f270(x6743,x6741,x6744,x6745),f270(x6743,x6742,x6744,x6745)) % 174.01/173.91 [675]~E(x6751,x6752)+E(f270(x6753,x6754,x6751,x6755),f270(x6753,x6754,x6752,x6755)) % 174.01/173.91 [676]~E(x6761,x6762)+E(f270(x6763,x6764,x6765,x6761),f270(x6763,x6764,x6765,x6762)) % 174.01/173.91 [677]~E(x6771,x6772)+E(f307(x6771,x6773,x6774),f307(x6772,x6773,x6774)) % 174.01/173.91 [678]~E(x6781,x6782)+E(f307(x6783,x6781,x6784),f307(x6783,x6782,x6784)) % 174.01/173.91 [679]~E(x6791,x6792)+E(f307(x6793,x6794,x6791),f307(x6793,x6794,x6792)) % 174.01/173.91 [680]~E(x6801,x6802)+E(f357(x6801,x6803,x6804,x6805),f357(x6802,x6803,x6804,x6805)) % 174.01/173.91 [681]~E(x6811,x6812)+E(f357(x6813,x6811,x6814,x6815),f357(x6813,x6812,x6814,x6815)) % 174.01/173.91 [682]~E(x6821,x6822)+E(f357(x6823,x6824,x6821,x6825),f357(x6823,x6824,x6822,x6825)) % 174.01/173.91 [683]~E(x6831,x6832)+E(f357(x6833,x6834,x6835,x6831),f357(x6833,x6834,x6835,x6832)) % 174.01/173.91 [684]~E(x6841,x6842)+E(f248(x6841,x6843,x6844),f248(x6842,x6843,x6844)) % 174.01/173.91 [685]~E(x6851,x6852)+E(f248(x6853,x6851,x6854),f248(x6853,x6852,x6854)) % 174.01/173.91 [686]~E(x6861,x6862)+E(f248(x6863,x6864,x6861),f248(x6863,x6864,x6862)) % 174.01/173.91 [687]~E(x6871,x6872)+E(f14(x6871,x6873),f14(x6872,x6873)) % 174.01/173.91 [688]~E(x6881,x6882)+E(f14(x6883,x6881),f14(x6883,x6882)) % 174.01/173.91 [689]~E(x6891,x6892)+E(f779(x6891),f779(x6892)) % 174.01/173.91 [690]~E(x6901,x6902)+E(f757(x6901,x6903,x6904),f757(x6902,x6903,x6904)) % 174.01/173.91 [691]~E(x6911,x6912)+E(f757(x6913,x6911,x6914),f757(x6913,x6912,x6914)) % 174.01/173.91 [692]~E(x6921,x6922)+E(f757(x6923,x6924,x6921),f757(x6923,x6924,x6922)) % 174.01/173.91 [693]~E(x6931,x6932)+E(f151(x6931,x6933),f151(x6932,x6933)) % 174.01/173.91 [694]~E(x6941,x6942)+E(f151(x6943,x6941),f151(x6943,x6942)) % 174.01/173.91 [695]~E(x6951,x6952)+E(f557(x6951,x6953,x6954),f557(x6952,x6953,x6954)) % 174.01/173.91 [696]~E(x6961,x6962)+E(f557(x6963,x6961,x6964),f557(x6963,x6962,x6964)) % 174.01/173.91 [697]~E(x6971,x6972)+E(f557(x6973,x6974,x6971),f557(x6973,x6974,x6972)) % 174.01/173.91 [698]~E(x6981,x6982)+E(f853(x6981),f853(x6982)) % 174.01/173.91 [699]~E(x6991,x6992)+E(f278(x6991),f278(x6992)) % 174.01/173.91 [700]~E(x7001,x7002)+E(f616(x7001,x7003,x7004,x7005,x7006,x7007),f616(x7002,x7003,x7004,x7005,x7006,x7007)) % 174.01/173.91 [701]~E(x7011,x7012)+E(f616(x7013,x7011,x7014,x7015,x7016,x7017),f616(x7013,x7012,x7014,x7015,x7016,x7017)) % 174.01/173.91 [702]~E(x7021,x7022)+E(f616(x7023,x7024,x7021,x7025,x7026,x7027),f616(x7023,x7024,x7022,x7025,x7026,x7027)) % 174.01/173.91 [703]~E(x7031,x7032)+E(f616(x7033,x7034,x7035,x7031,x7036,x7037),f616(x7033,x7034,x7035,x7032,x7036,x7037)) % 174.01/173.91 [704]~E(x7041,x7042)+E(f616(x7043,x7044,x7045,x7046,x7041,x7047),f616(x7043,x7044,x7045,x7046,x7042,x7047)) % 174.01/173.91 [705]~E(x7051,x7052)+E(f616(x7053,x7054,x7055,x7056,x7057,x7051),f616(x7053,x7054,x7055,x7056,x7057,x7052)) % 174.01/173.91 [706]~E(x7061,x7062)+E(f306(x7061,x7063),f306(x7062,x7063)) % 174.01/173.91 [707]~E(x7071,x7072)+E(f306(x7073,x7071),f306(x7073,x7072)) % 174.01/173.91 [708]~E(x7081,x7082)+E(f806(x7081,x7083,x7084),f806(x7082,x7083,x7084)) % 174.01/173.91 [709]~E(x7091,x7092)+E(f806(x7093,x7091,x7094),f806(x7093,x7092,x7094)) % 174.01/173.91 [710]~E(x7101,x7102)+E(f806(x7103,x7104,x7101),f806(x7103,x7104,x7102)) % 174.01/173.91 [711]~E(x7111,x7112)+E(f800(x7111,x7113),f800(x7112,x7113)) % 174.01/173.91 [712]~E(x7121,x7122)+E(f800(x7123,x7121),f800(x7123,x7122)) % 174.01/173.91 [713]~E(x7131,x7132)+E(f484(x7131,x7133,x7134),f484(x7132,x7133,x7134)) % 174.01/173.91 [714]~E(x7141,x7142)+E(f484(x7143,x7141,x7144),f484(x7143,x7142,x7144)) % 174.01/173.91 [715]~E(x7151,x7152)+E(f484(x7153,x7154,x7151),f484(x7153,x7154,x7152)) % 174.01/173.91 [716]~E(x7161,x7162)+E(f466(x7161,x7163,x7164,x7165,x7166,x7167),f466(x7162,x7163,x7164,x7165,x7166,x7167)) % 174.01/173.91 [717]~E(x7171,x7172)+E(f466(x7173,x7171,x7174,x7175,x7176,x7177),f466(x7173,x7172,x7174,x7175,x7176,x7177)) % 174.01/173.91 [718]~E(x7181,x7182)+E(f466(x7183,x7184,x7181,x7185,x7186,x7187),f466(x7183,x7184,x7182,x7185,x7186,x7187)) % 174.01/173.91 [719]~E(x7191,x7192)+E(f466(x7193,x7194,x7195,x7191,x7196,x7197),f466(x7193,x7194,x7195,x7192,x7196,x7197)) % 174.01/173.91 [720]~E(x7201,x7202)+E(f466(x7203,x7204,x7205,x7206,x7201,x7207),f466(x7203,x7204,x7205,x7206,x7202,x7207)) % 174.01/173.91 [721]~E(x7211,x7212)+E(f466(x7213,x7214,x7215,x7216,x7217,x7211),f466(x7213,x7214,x7215,x7216,x7217,x7212)) % 174.01/173.91 [722]~E(x7221,x7222)+E(f644(x7221,x7223,x7224,x7225,x7226),f644(x7222,x7223,x7224,x7225,x7226)) % 174.01/173.91 [723]~E(x7231,x7232)+E(f644(x7233,x7231,x7234,x7235,x7236),f644(x7233,x7232,x7234,x7235,x7236)) % 174.01/173.91 [724]~E(x7241,x7242)+E(f644(x7243,x7244,x7241,x7245,x7246),f644(x7243,x7244,x7242,x7245,x7246)) % 174.01/173.91 [725]~E(x7251,x7252)+E(f644(x7253,x7254,x7255,x7251,x7256),f644(x7253,x7254,x7255,x7252,x7256)) % 174.01/173.91 [726]~E(x7261,x7262)+E(f644(x7263,x7264,x7265,x7266,x7261),f644(x7263,x7264,x7265,x7266,x7262)) % 174.01/173.91 [727]~E(x7271,x7272)+E(f397(x7271,x7273,x7274),f397(x7272,x7273,x7274)) % 174.01/173.91 [728]~E(x7281,x7282)+E(f397(x7283,x7281,x7284),f397(x7283,x7282,x7284)) % 174.01/173.91 [729]~E(x7291,x7292)+E(f397(x7293,x7294,x7291),f397(x7293,x7294,x7292)) % 174.01/173.91 [730]~E(x7301,x7302)+E(f382(x7301,x7303,x7304,x7305,x7306),f382(x7302,x7303,x7304,x7305,x7306)) % 174.01/173.91 [731]~E(x7311,x7312)+E(f382(x7313,x7311,x7314,x7315,x7316),f382(x7313,x7312,x7314,x7315,x7316)) % 174.01/173.91 [732]~E(x7321,x7322)+E(f382(x7323,x7324,x7321,x7325,x7326),f382(x7323,x7324,x7322,x7325,x7326)) % 174.01/173.91 [733]~E(x7331,x7332)+E(f382(x7333,x7334,x7335,x7331,x7336),f382(x7333,x7334,x7335,x7332,x7336)) % 174.01/173.91 [734]~E(x7341,x7342)+E(f382(x7343,x7344,x7345,x7346,x7341),f382(x7343,x7344,x7345,x7346,x7342)) % 174.01/173.91 [735]~E(x7351,x7352)+E(f662(x7351,x7353,x7354,x7355,x7356),f662(x7352,x7353,x7354,x7355,x7356)) % 174.01/173.91 [736]~E(x7361,x7362)+E(f662(x7363,x7361,x7364,x7365,x7366),f662(x7363,x7362,x7364,x7365,x7366)) % 174.01/173.91 [737]~E(x7371,x7372)+E(f662(x7373,x7374,x7371,x7375,x7376),f662(x7373,x7374,x7372,x7375,x7376)) % 174.01/173.91 [738]~E(x7381,x7382)+E(f662(x7383,x7384,x7385,x7381,x7386),f662(x7383,x7384,x7385,x7382,x7386)) % 174.01/173.91 [739]~E(x7391,x7392)+E(f662(x7393,x7394,x7395,x7396,x7391),f662(x7393,x7394,x7395,x7396,x7392)) % 174.01/173.91 [740]~E(x7401,x7402)+E(f659(x7401,x7403,x7404,x7405,x7406),f659(x7402,x7403,x7404,x7405,x7406)) % 174.01/173.91 [741]~E(x7411,x7412)+E(f659(x7413,x7411,x7414,x7415,x7416),f659(x7413,x7412,x7414,x7415,x7416)) % 174.01/173.91 [742]~E(x7421,x7422)+E(f659(x7423,x7424,x7421,x7425,x7426),f659(x7423,x7424,x7422,x7425,x7426)) % 174.01/173.91 [743]~E(x7431,x7432)+E(f659(x7433,x7434,x7435,x7431,x7436),f659(x7433,x7434,x7435,x7432,x7436)) % 174.01/173.91 [744]~E(x7441,x7442)+E(f659(x7443,x7444,x7445,x7446,x7441),f659(x7443,x7444,x7445,x7446,x7442)) % 174.01/173.91 [745]~E(x7451,x7452)+E(f436(x7451,x7453,x7454,x7455),f436(x7452,x7453,x7454,x7455)) % 174.01/173.91 [746]~E(x7461,x7462)+E(f436(x7463,x7461,x7464,x7465),f436(x7463,x7462,x7464,x7465)) % 174.01/173.91 [747]~E(x7471,x7472)+E(f436(x7473,x7474,x7471,x7475),f436(x7473,x7474,x7472,x7475)) % 174.01/173.91 [748]~E(x7481,x7482)+E(f436(x7483,x7484,x7485,x7481),f436(x7483,x7484,x7485,x7482)) % 174.01/173.91 [749]~E(x7491,x7492)+E(f293(x7491,x7493,x7494,x7495),f293(x7492,x7493,x7494,x7495)) % 174.01/173.91 [750]~E(x7501,x7502)+E(f293(x7503,x7501,x7504,x7505),f293(x7503,x7502,x7504,x7505)) % 174.01/173.91 [751]~E(x7511,x7512)+E(f293(x7513,x7514,x7511,x7515),f293(x7513,x7514,x7512,x7515)) % 174.01/173.91 [752]~E(x7521,x7522)+E(f293(x7523,x7524,x7525,x7521),f293(x7523,x7524,x7525,x7522)) % 174.01/173.91 [753]~E(x7531,x7532)+E(f135(x7531,x7533),f135(x7532,x7533)) % 174.01/173.91 [754]~E(x7541,x7542)+E(f135(x7543,x7541),f135(x7543,x7542)) % 174.01/173.91 [755]~E(x7551,x7552)+E(f261(x7551,x7553),f261(x7552,x7553)) % 174.01/173.91 [756]~E(x7561,x7562)+E(f261(x7563,x7561),f261(x7563,x7562)) % 174.01/173.91 [757]~E(x7571,x7572)+E(f512(x7571,x7573,x7574,x7575,x7576),f512(x7572,x7573,x7574,x7575,x7576)) % 174.01/173.91 [758]~E(x7581,x7582)+E(f512(x7583,x7581,x7584,x7585,x7586),f512(x7583,x7582,x7584,x7585,x7586)) % 174.01/173.91 [759]~E(x7591,x7592)+E(f512(x7593,x7594,x7591,x7595,x7596),f512(x7593,x7594,x7592,x7595,x7596)) % 174.01/173.91 [760]~E(x7601,x7602)+E(f512(x7603,x7604,x7605,x7601,x7606),f512(x7603,x7604,x7605,x7602,x7606)) % 174.01/173.91 [761]~E(x7611,x7612)+E(f512(x7613,x7614,x7615,x7616,x7611),f512(x7613,x7614,x7615,x7616,x7612)) % 174.01/173.91 [762]~E(x7621,x7622)+E(f374(x7621,x7623,x7624,x7625,x7626,x7627,x7628,x7629),f374(x7622,x7623,x7624,x7625,x7626,x7627,x7628,x7629)) % 174.01/173.91 [763]~E(x7631,x7632)+E(f374(x7633,x7631,x7634,x7635,x7636,x7637,x7638,x7639),f374(x7633,x7632,x7634,x7635,x7636,x7637,x7638,x7639)) % 174.01/173.91 [764]~E(x7641,x7642)+E(f374(x7643,x7644,x7641,x7645,x7646,x7647,x7648,x7649),f374(x7643,x7644,x7642,x7645,x7646,x7647,x7648,x7649)) % 174.01/173.91 [765]~E(x7651,x7652)+E(f374(x7653,x7654,x7655,x7651,x7656,x7657,x7658,x7659),f374(x7653,x7654,x7655,x7652,x7656,x7657,x7658,x7659)) % 174.01/173.91 [766]~E(x7661,x7662)+E(f374(x7663,x7664,x7665,x7666,x7661,x7667,x7668,x7669),f374(x7663,x7664,x7665,x7666,x7662,x7667,x7668,x7669)) % 174.01/173.91 [767]~E(x7671,x7672)+E(f374(x7673,x7674,x7675,x7676,x7677,x7671,x7678,x7679),f374(x7673,x7674,x7675,x7676,x7677,x7672,x7678,x7679)) % 174.01/173.91 [768]~E(x7681,x7682)+E(f374(x7683,x7684,x7685,x7686,x7687,x7688,x7681,x7689),f374(x7683,x7684,x7685,x7686,x7687,x7688,x7682,x7689)) % 174.01/173.91 [769]~E(x7691,x7692)+E(f374(x7693,x7694,x7695,x7696,x7697,x7698,x7699,x7691),f374(x7693,x7694,x7695,x7696,x7697,x7698,x7699,x7692)) % 174.01/173.91 [770]~E(x7701,x7702)+E(f52(x7701),f52(x7702)) % 174.01/173.91 [771]~E(x7711,x7712)+E(f542(x7711,x7713,x7714,x7715,x7716),f542(x7712,x7713,x7714,x7715,x7716)) % 174.01/173.91 [772]~E(x7721,x7722)+E(f542(x7723,x7721,x7724,x7725,x7726),f542(x7723,x7722,x7724,x7725,x7726)) % 174.01/173.91 [773]~E(x7731,x7732)+E(f542(x7733,x7734,x7731,x7735,x7736),f542(x7733,x7734,x7732,x7735,x7736)) % 174.01/173.91 [774]~E(x7741,x7742)+E(f542(x7743,x7744,x7745,x7741,x7746),f542(x7743,x7744,x7745,x7742,x7746)) % 174.01/173.91 [775]~E(x7751,x7752)+E(f542(x7753,x7754,x7755,x7756,x7751),f542(x7753,x7754,x7755,x7756,x7752)) % 174.01/173.91 [776]~E(x7761,x7762)+E(f696(x7761,x7763,x7764),f696(x7762,x7763,x7764)) % 174.01/173.91 [777]~E(x7771,x7772)+E(f696(x7773,x7771,x7774),f696(x7773,x7772,x7774)) % 174.01/173.91 [778]~E(x7781,x7782)+E(f696(x7783,x7784,x7781),f696(x7783,x7784,x7782)) % 174.01/173.91 [779]~E(x7791,x7792)+E(f121(x7791,x7793,x7794,x7795),f121(x7792,x7793,x7794,x7795)) % 174.01/173.91 [780]~E(x7801,x7802)+E(f121(x7803,x7801,x7804,x7805),f121(x7803,x7802,x7804,x7805)) % 174.01/173.91 [781]~E(x7811,x7812)+E(f121(x7813,x7814,x7811,x7815),f121(x7813,x7814,x7812,x7815)) % 174.01/173.91 [782]~E(x7821,x7822)+E(f121(x7823,x7824,x7825,x7821),f121(x7823,x7824,x7825,x7822)) % 174.01/173.91 [783]~E(x7831,x7832)+E(f546(x7831,x7833,x7834,x7835,x7836,x7837),f546(x7832,x7833,x7834,x7835,x7836,x7837)) % 174.01/173.91 [784]~E(x7841,x7842)+E(f546(x7843,x7841,x7844,x7845,x7846,x7847),f546(x7843,x7842,x7844,x7845,x7846,x7847)) % 174.01/173.91 [785]~E(x7851,x7852)+E(f546(x7853,x7854,x7851,x7855,x7856,x7857),f546(x7853,x7854,x7852,x7855,x7856,x7857)) % 174.01/173.91 [786]~E(x7861,x7862)+E(f546(x7863,x7864,x7865,x7861,x7866,x7867),f546(x7863,x7864,x7865,x7862,x7866,x7867)) % 174.01/173.91 [787]~E(x7871,x7872)+E(f546(x7873,x7874,x7875,x7876,x7871,x7877),f546(x7873,x7874,x7875,x7876,x7872,x7877)) % 174.01/173.91 [788]~E(x7881,x7882)+E(f546(x7883,x7884,x7885,x7886,x7887,x7881),f546(x7883,x7884,x7885,x7886,x7887,x7882)) % 174.01/173.91 [789]~E(x7891,x7892)+E(f566(x7891,x7893,x7894,x7895,x7896,x7897),f566(x7892,x7893,x7894,x7895,x7896,x7897)) % 174.01/173.91 [790]~E(x7901,x7902)+E(f566(x7903,x7901,x7904,x7905,x7906,x7907),f566(x7903,x7902,x7904,x7905,x7906,x7907)) % 174.01/173.91 [791]~E(x7911,x7912)+E(f566(x7913,x7914,x7911,x7915,x7916,x7917),f566(x7913,x7914,x7912,x7915,x7916,x7917)) % 174.01/173.91 [792]~E(x7921,x7922)+E(f566(x7923,x7924,x7925,x7921,x7926,x7927),f566(x7923,x7924,x7925,x7922,x7926,x7927)) % 174.01/173.91 [793]~E(x7931,x7932)+E(f566(x7933,x7934,x7935,x7936,x7931,x7937),f566(x7933,x7934,x7935,x7936,x7932,x7937)) % 174.01/173.91 [794]~E(x7941,x7942)+E(f566(x7943,x7944,x7945,x7946,x7947,x7941),f566(x7943,x7944,x7945,x7946,x7947,x7942)) % 174.01/173.91 [795]~E(x7951,x7952)+E(f666(x7951,x7953,x7954,x7955,x7956),f666(x7952,x7953,x7954,x7955,x7956)) % 174.01/173.91 [796]~E(x7961,x7962)+E(f666(x7963,x7961,x7964,x7965,x7966),f666(x7963,x7962,x7964,x7965,x7966)) % 174.01/173.91 [797]~E(x7971,x7972)+E(f666(x7973,x7974,x7971,x7975,x7976),f666(x7973,x7974,x7972,x7975,x7976)) % 174.01/173.91 [798]~E(x7981,x7982)+E(f666(x7983,x7984,x7985,x7981,x7986),f666(x7983,x7984,x7985,x7982,x7986)) % 174.01/173.91 [799]~E(x7991,x7992)+E(f666(x7993,x7994,x7995,x7996,x7991),f666(x7993,x7994,x7995,x7996,x7992)) % 174.01/173.91 [800]~E(x8001,x8002)+E(f524(x8001,x8003,x8004,x8005),f524(x8002,x8003,x8004,x8005)) % 174.01/173.91 [801]~E(x8011,x8012)+E(f524(x8013,x8011,x8014,x8015),f524(x8013,x8012,x8014,x8015)) % 174.01/173.91 [802]~E(x8021,x8022)+E(f524(x8023,x8024,x8021,x8025),f524(x8023,x8024,x8022,x8025)) % 174.01/173.91 [803]~E(x8031,x8032)+E(f524(x8033,x8034,x8035,x8031),f524(x8033,x8034,x8035,x8032)) % 174.01/173.91 [804]~E(x8041,x8042)+E(f372(x8041,x8043),f372(x8042,x8043)) % 174.01/173.91 [805]~E(x8051,x8052)+E(f372(x8053,x8051),f372(x8053,x8052)) % 174.01/173.91 [806]~E(x8061,x8062)+E(f547(x8061,x8063,x8064,x8065,x8066),f547(x8062,x8063,x8064,x8065,x8066)) % 174.01/173.91 [807]~E(x8071,x8072)+E(f547(x8073,x8071,x8074,x8075,x8076),f547(x8073,x8072,x8074,x8075,x8076)) % 174.01/173.91 [808]~E(x8081,x8082)+E(f547(x8083,x8084,x8081,x8085,x8086),f547(x8083,x8084,x8082,x8085,x8086)) % 174.01/173.91 [809]~E(x8091,x8092)+E(f547(x8093,x8094,x8095,x8091,x8096),f547(x8093,x8094,x8095,x8092,x8096)) % 174.01/173.91 [810]~E(x8101,x8102)+E(f547(x8103,x8104,x8105,x8106,x8101),f547(x8103,x8104,x8105,x8106,x8102)) % 174.01/173.91 [811]~E(x8111,x8112)+E(f558(x8111,x8113,x8114,x8115,x8116,x8117),f558(x8112,x8113,x8114,x8115,x8116,x8117)) % 174.01/173.91 [812]~E(x8121,x8122)+E(f558(x8123,x8121,x8124,x8125,x8126,x8127),f558(x8123,x8122,x8124,x8125,x8126,x8127)) % 174.01/173.91 [813]~E(x8131,x8132)+E(f558(x8133,x8134,x8131,x8135,x8136,x8137),f558(x8133,x8134,x8132,x8135,x8136,x8137)) % 174.01/173.91 [814]~E(x8141,x8142)+E(f558(x8143,x8144,x8145,x8141,x8146,x8147),f558(x8143,x8144,x8145,x8142,x8146,x8147)) % 174.01/173.91 [815]~E(x8151,x8152)+E(f558(x8153,x8154,x8155,x8156,x8151,x8157),f558(x8153,x8154,x8155,x8156,x8152,x8157)) % 174.01/173.91 [816]~E(x8161,x8162)+E(f558(x8163,x8164,x8165,x8166,x8167,x8161),f558(x8163,x8164,x8165,x8166,x8167,x8162)) % 174.01/173.91 [817]~E(x8171,x8172)+E(f394(x8171,x8173,x8174,x8175,x8176),f394(x8172,x8173,x8174,x8175,x8176)) % 174.01/173.91 [818]~E(x8181,x8182)+E(f394(x8183,x8181,x8184,x8185,x8186),f394(x8183,x8182,x8184,x8185,x8186)) % 174.01/173.91 [819]~E(x8191,x8192)+E(f394(x8193,x8194,x8191,x8195,x8196),f394(x8193,x8194,x8192,x8195,x8196)) % 174.01/173.91 [820]~E(x8201,x8202)+E(f394(x8203,x8204,x8205,x8201,x8206),f394(x8203,x8204,x8205,x8202,x8206)) % 174.01/173.91 [821]~E(x8211,x8212)+E(f394(x8213,x8214,x8215,x8216,x8211),f394(x8213,x8214,x8215,x8216,x8212)) % 174.01/173.91 [822]~E(x8221,x8222)+E(f732(x8221,x8223,x8224),f732(x8222,x8223,x8224)) % 174.01/173.91 [823]~E(x8231,x8232)+E(f732(x8233,x8231,x8234),f732(x8233,x8232,x8234)) % 174.01/173.91 [824]~E(x8241,x8242)+E(f732(x8243,x8244,x8241),f732(x8243,x8244,x8242)) % 174.01/173.91 [825]~E(x8251,x8252)+E(f702(x8251,x8253,x8254,x8255),f702(x8252,x8253,x8254,x8255)) % 174.01/173.91 [826]~E(x8261,x8262)+E(f702(x8263,x8261,x8264,x8265),f702(x8263,x8262,x8264,x8265)) % 174.01/173.91 [827]~E(x8271,x8272)+E(f702(x8273,x8274,x8271,x8275),f702(x8273,x8274,x8272,x8275)) % 174.01/173.91 [828]~E(x8281,x8282)+E(f702(x8283,x8284,x8285,x8281),f702(x8283,x8284,x8285,x8282)) % 174.01/173.91 [829]~E(x8291,x8292)+E(f706(x8291,x8293,x8294,x8295),f706(x8292,x8293,x8294,x8295)) % 174.01/173.91 [830]~E(x8301,x8302)+E(f706(x8303,x8301,x8304,x8305),f706(x8303,x8302,x8304,x8305)) % 174.01/173.91 [831]~E(x8311,x8312)+E(f706(x8313,x8314,x8311,x8315),f706(x8313,x8314,x8312,x8315)) % 174.01/173.91 [832]~E(x8321,x8322)+E(f706(x8323,x8324,x8325,x8321),f706(x8323,x8324,x8325,x8322)) % 174.01/173.91 [833]~E(x8331,x8332)+E(f365(x8331,x8333,x8334,x8335,x8336),f365(x8332,x8333,x8334,x8335,x8336)) % 174.01/173.91 [834]~E(x8341,x8342)+E(f365(x8343,x8341,x8344,x8345,x8346),f365(x8343,x8342,x8344,x8345,x8346)) % 174.01/173.91 [835]~E(x8351,x8352)+E(f365(x8353,x8354,x8351,x8355,x8356),f365(x8353,x8354,x8352,x8355,x8356)) % 174.01/173.91 [836]~E(x8361,x8362)+E(f365(x8363,x8364,x8365,x8361,x8366),f365(x8363,x8364,x8365,x8362,x8366)) % 174.01/173.91 [837]~E(x8371,x8372)+E(f365(x8373,x8374,x8375,x8376,x8371),f365(x8373,x8374,x8375,x8376,x8372)) % 174.01/173.91 [838]~E(x8381,x8382)+E(f406(x8381,x8383,x8384),f406(x8382,x8383,x8384)) % 174.01/173.91 [839]~E(x8391,x8392)+E(f406(x8393,x8391,x8394),f406(x8393,x8392,x8394)) % 174.01/173.91 [840]~E(x8401,x8402)+E(f406(x8403,x8404,x8401),f406(x8403,x8404,x8402)) % 174.01/173.91 [841]~E(x8411,x8412)+E(f461(x8411,x8413,x8414,x8415),f461(x8412,x8413,x8414,x8415)) % 174.01/173.91 [842]~E(x8421,x8422)+E(f461(x8423,x8421,x8424,x8425),f461(x8423,x8422,x8424,x8425)) % 174.01/173.91 [843]~E(x8431,x8432)+E(f461(x8433,x8434,x8431,x8435),f461(x8433,x8434,x8432,x8435)) % 174.01/173.91 [844]~E(x8441,x8442)+E(f461(x8443,x8444,x8445,x8441),f461(x8443,x8444,x8445,x8442)) % 174.01/173.91 [845]~E(x8451,x8452)+E(f373(x8451,x8453,x8454,x8455,x8456),f373(x8452,x8453,x8454,x8455,x8456)) % 174.01/173.91 [846]~E(x8461,x8462)+E(f373(x8463,x8461,x8464,x8465,x8466),f373(x8463,x8462,x8464,x8465,x8466)) % 174.01/173.91 [847]~E(x8471,x8472)+E(f373(x8473,x8474,x8471,x8475,x8476),f373(x8473,x8474,x8472,x8475,x8476)) % 174.01/173.91 [848]~E(x8481,x8482)+E(f373(x8483,x8484,x8485,x8481,x8486),f373(x8483,x8484,x8485,x8482,x8486)) % 174.01/173.91 [849]~E(x8491,x8492)+E(f373(x8493,x8494,x8495,x8496,x8491),f373(x8493,x8494,x8495,x8496,x8492)) % 174.01/173.91 [850]~E(x8501,x8502)+E(f324(x8501,x8503),f324(x8502,x8503)) % 174.01/173.91 [851]~E(x8511,x8512)+E(f324(x8513,x8511),f324(x8513,x8512)) % 174.01/173.91 [852]~E(x8521,x8522)+E(f249(x8521,x8523,x8524),f249(x8522,x8523,x8524)) % 174.01/173.91 [853]~E(x8531,x8532)+E(f249(x8533,x8531,x8534),f249(x8533,x8532,x8534)) % 174.01/173.91 [854]~E(x8541,x8542)+E(f249(x8543,x8544,x8541),f249(x8543,x8544,x8542)) % 174.01/173.91 [855]~E(x8551,x8552)+E(f760(x8551,x8553,x8554),f760(x8552,x8553,x8554)) % 174.01/173.91 [856]~E(x8561,x8562)+E(f760(x8563,x8561,x8564),f760(x8563,x8562,x8564)) % 174.01/173.91 [857]~E(x8571,x8572)+E(f760(x8573,x8574,x8571),f760(x8573,x8574,x8572)) % 174.01/173.91 [858]~E(x8581,x8582)+E(f429(x8581,x8583),f429(x8582,x8583)) % 174.01/173.91 [859]~E(x8591,x8592)+E(f429(x8593,x8591),f429(x8593,x8592)) % 174.01/173.91 [860]~E(x8601,x8602)+E(f650(x8601,x8603,x8604,x8605,x8606),f650(x8602,x8603,x8604,x8605,x8606)) % 174.01/173.91 [861]~E(x8611,x8612)+E(f650(x8613,x8611,x8614,x8615,x8616),f650(x8613,x8612,x8614,x8615,x8616)) % 174.01/173.91 [862]~E(x8621,x8622)+E(f650(x8623,x8624,x8621,x8625,x8626),f650(x8623,x8624,x8622,x8625,x8626)) % 174.01/173.91 [863]~E(x8631,x8632)+E(f650(x8633,x8634,x8635,x8631,x8636),f650(x8633,x8634,x8635,x8632,x8636)) % 174.01/173.91 [864]~E(x8641,x8642)+E(f650(x8643,x8644,x8645,x8646,x8641),f650(x8643,x8644,x8645,x8646,x8642)) % 174.01/173.91 [865]~E(x8651,x8652)+E(f387(x8651,x8653,x8654,x8655),f387(x8652,x8653,x8654,x8655)) % 174.01/173.91 [866]~E(x8661,x8662)+E(f387(x8663,x8661,x8664,x8665),f387(x8663,x8662,x8664,x8665)) % 174.01/173.91 [867]~E(x8671,x8672)+E(f387(x8673,x8674,x8671,x8675),f387(x8673,x8674,x8672,x8675)) % 174.01/173.91 [868]~E(x8681,x8682)+E(f387(x8683,x8684,x8685,x8681),f387(x8683,x8684,x8685,x8682)) % 174.01/173.91 [869]~E(x8691,x8692)+E(f338(x8691,x8693,x8694,x8695),f338(x8692,x8693,x8694,x8695)) % 174.01/173.91 [870]~E(x8701,x8702)+E(f338(x8703,x8701,x8704,x8705),f338(x8703,x8702,x8704,x8705)) % 174.01/173.91 [871]~E(x8711,x8712)+E(f338(x8713,x8714,x8711,x8715),f338(x8713,x8714,x8712,x8715)) % 174.01/173.91 [872]~E(x8721,x8722)+E(f338(x8723,x8724,x8725,x8721),f338(x8723,x8724,x8725,x8722)) % 174.01/173.91 [873]~E(x8731,x8732)+E(f173(x8731,x8733,x8734),f173(x8732,x8733,x8734)) % 174.01/173.91 [874]~E(x8741,x8742)+E(f173(x8743,x8741,x8744),f173(x8743,x8742,x8744)) % 174.01/173.91 [875]~E(x8751,x8752)+E(f173(x8753,x8754,x8751),f173(x8753,x8754,x8752)) % 174.01/173.91 [876]~E(x8761,x8762)+E(f475(x8761,x8763),f475(x8762,x8763)) % 174.01/173.91 [877]~E(x8771,x8772)+E(f475(x8773,x8771),f475(x8773,x8772)) % 174.01/173.91 [878]~E(x8781,x8782)+E(f645(x8781,x8783,x8784,x8785,x8786),f645(x8782,x8783,x8784,x8785,x8786)) % 174.01/173.91 [879]~E(x8791,x8792)+E(f645(x8793,x8791,x8794,x8795,x8796),f645(x8793,x8792,x8794,x8795,x8796)) % 174.01/173.91 [880]~E(x8801,x8802)+E(f645(x8803,x8804,x8801,x8805,x8806),f645(x8803,x8804,x8802,x8805,x8806)) % 174.01/173.91 [881]~E(x8811,x8812)+E(f645(x8813,x8814,x8815,x8811,x8816),f645(x8813,x8814,x8815,x8812,x8816)) % 174.01/173.91 [882]~E(x8821,x8822)+E(f645(x8823,x8824,x8825,x8826,x8821),f645(x8823,x8824,x8825,x8826,x8822)) % 174.01/173.91 [883]~E(x8831,x8832)+E(f272(x8831,x8833),f272(x8832,x8833)) % 174.01/173.91 [884]~E(x8841,x8842)+E(f272(x8843,x8841),f272(x8843,x8842)) % 174.01/173.91 [885]~E(x8851,x8852)+E(f316(x8851,x8853,x8854,x8855),f316(x8852,x8853,x8854,x8855)) % 174.01/173.91 [886]~E(x8861,x8862)+E(f316(x8863,x8861,x8864,x8865),f316(x8863,x8862,x8864,x8865)) % 174.01/173.91 [887]~E(x8871,x8872)+E(f316(x8873,x8874,x8871,x8875),f316(x8873,x8874,x8872,x8875)) % 174.01/173.91 [888]~E(x8881,x8882)+E(f316(x8883,x8884,x8885,x8881),f316(x8883,x8884,x8885,x8882)) % 174.01/173.91 [889]~E(x8891,x8892)+E(f294(x8891,x8893,x8894,x8895,x8896),f294(x8892,x8893,x8894,x8895,x8896)) % 174.01/173.91 [890]~E(x8901,x8902)+E(f294(x8903,x8901,x8904,x8905,x8906),f294(x8903,x8902,x8904,x8905,x8906)) % 174.01/173.91 [891]~E(x8911,x8912)+E(f294(x8913,x8914,x8911,x8915,x8916),f294(x8913,x8914,x8912,x8915,x8916)) % 174.01/173.91 [892]~E(x8921,x8922)+E(f294(x8923,x8924,x8925,x8921,x8926),f294(x8923,x8924,x8925,x8922,x8926)) % 174.01/173.91 [893]~E(x8931,x8932)+E(f294(x8933,x8934,x8935,x8936,x8931),f294(x8933,x8934,x8935,x8936,x8932)) % 174.01/173.91 [894]~E(x8941,x8942)+E(f755(x8941,x8943,x8944,x8945),f755(x8942,x8943,x8944,x8945)) % 174.01/173.91 [895]~E(x8951,x8952)+E(f755(x8953,x8951,x8954,x8955),f755(x8953,x8952,x8954,x8955)) % 174.01/173.91 [896]~E(x8961,x8962)+E(f755(x8963,x8964,x8961,x8965),f755(x8963,x8964,x8962,x8965)) % 174.01/173.91 [897]~E(x8971,x8972)+E(f755(x8973,x8974,x8975,x8971),f755(x8973,x8974,x8975,x8972)) % 174.01/173.91 [898]~E(x8981,x8982)+E(f23(x8981,x8983,x8984,x8985),f23(x8982,x8983,x8984,x8985)) % 174.01/173.91 [899]~E(x8991,x8992)+E(f23(x8993,x8991,x8994,x8995),f23(x8993,x8992,x8994,x8995)) % 174.01/173.91 [900]~E(x9001,x9002)+E(f23(x9003,x9004,x9001,x9005),f23(x9003,x9004,x9002,x9005)) % 174.01/173.91 [901]~E(x9011,x9012)+E(f23(x9013,x9014,x9015,x9011),f23(x9013,x9014,x9015,x9012)) % 174.01/173.91 [902]~E(x9021,x9022)+E(f287(x9021,x9023),f287(x9022,x9023)) % 174.01/173.91 [903]~E(x9031,x9032)+E(f287(x9033,x9031),f287(x9033,x9032)) % 174.01/173.91 [904]~E(x9041,x9042)+E(f422(x9041,x9043,x9044),f422(x9042,x9043,x9044)) % 174.01/173.91 [905]~E(x9051,x9052)+E(f422(x9053,x9051,x9054),f422(x9053,x9052,x9054)) % 174.01/173.91 [906]~E(x9061,x9062)+E(f422(x9063,x9064,x9061),f422(x9063,x9064,x9062)) % 174.01/173.91 [907]~E(x9071,x9072)+E(f26(x9071,x9073),f26(x9072,x9073)) % 174.01/173.91 [908]~E(x9081,x9082)+E(f26(x9083,x9081),f26(x9083,x9082)) % 174.01/173.91 [909]~E(x9091,x9092)+E(f424(x9091,x9093,x9094,x9095),f424(x9092,x9093,x9094,x9095)) % 174.01/173.91 [910]~E(x9101,x9102)+E(f424(x9103,x9101,x9104,x9105),f424(x9103,x9102,x9104,x9105)) % 174.01/173.91 [911]~E(x9111,x9112)+E(f424(x9113,x9114,x9111,x9115),f424(x9113,x9114,x9112,x9115)) % 174.01/173.91 [912]~E(x9121,x9122)+E(f424(x9123,x9124,x9125,x9121),f424(x9123,x9124,x9125,x9122)) % 174.01/173.91 [913]~E(x9131,x9132)+E(f467(x9131,x9133,x9134),f467(x9132,x9133,x9134)) % 174.01/173.91 [914]~E(x9141,x9142)+E(f467(x9143,x9141,x9144),f467(x9143,x9142,x9144)) % 174.01/173.91 [915]~E(x9151,x9152)+E(f467(x9153,x9154,x9151),f467(x9153,x9154,x9152)) % 174.01/173.91 [916]~E(x9161,x9162)+E(f701(x9161,x9163,x9164,x9165,x9166),f701(x9162,x9163,x9164,x9165,x9166)) % 174.01/173.91 [917]~E(x9171,x9172)+E(f701(x9173,x9171,x9174,x9175,x9176),f701(x9173,x9172,x9174,x9175,x9176)) % 174.01/173.91 [918]~E(x9181,x9182)+E(f701(x9183,x9184,x9181,x9185,x9186),f701(x9183,x9184,x9182,x9185,x9186)) % 174.01/173.91 [919]~E(x9191,x9192)+E(f701(x9193,x9194,x9195,x9191,x9196),f701(x9193,x9194,x9195,x9192,x9196)) % 174.01/173.91 [920]~E(x9201,x9202)+E(f701(x9203,x9204,x9205,x9206,x9201),f701(x9203,x9204,x9205,x9206,x9202)) % 174.01/173.91 [921]~E(x9211,x9212)+E(f187(x9211,x9213),f187(x9212,x9213)) % 174.01/173.91 [922]~E(x9221,x9222)+E(f187(x9223,x9221),f187(x9223,x9222)) % 174.01/173.91 [923]~E(x9231,x9232)+E(f267(x9231,x9233),f267(x9232,x9233)) % 174.01/173.91 [924]~E(x9241,x9242)+E(f267(x9243,x9241),f267(x9243,x9242)) % 174.01/173.91 [925]~E(x9251,x9252)+E(f122(x9251,x9253),f122(x9252,x9253)) % 174.01/173.91 [926]~E(x9261,x9262)+E(f122(x9263,x9261),f122(x9263,x9262)) % 174.01/173.91 [927]~E(x9271,x9272)+E(f196(x9271,x9273),f196(x9272,x9273)) % 174.01/173.91 [928]~E(x9281,x9282)+E(f196(x9283,x9281),f196(x9283,x9282)) % 174.01/173.91 [929]~E(x9291,x9292)+E(f750(x9291,x9293,x9294),f750(x9292,x9293,x9294)) % 174.01/173.91 [930]~E(x9301,x9302)+E(f750(x9303,x9301,x9304),f750(x9303,x9302,x9304)) % 174.01/173.91 [931]~E(x9311,x9312)+E(f750(x9313,x9314,x9311),f750(x9313,x9314,x9312)) % 174.01/173.91 [932]~E(x9321,x9322)+E(f125(x9321,x9323),f125(x9322,x9323)) % 174.01/173.91 [933]~E(x9331,x9332)+E(f125(x9333,x9331),f125(x9333,x9332)) % 174.01/173.91 [934]~E(x9341,x9342)+E(f738(x9341,x9343),f738(x9342,x9343)) % 174.01/173.91 [935]~E(x9351,x9352)+E(f738(x9353,x9351),f738(x9353,x9352)) % 174.01/173.91 [936]~E(x9361,x9362)+E(f51(x9361),f51(x9362)) % 174.01/173.91 [937]~E(x9371,x9372)+E(f794(x9371,x9373,x9374),f794(x9372,x9373,x9374)) % 174.01/173.91 [938]~E(x9381,x9382)+E(f794(x9383,x9381,x9384),f794(x9383,x9382,x9384)) % 174.01/173.91 [939]~E(x9391,x9392)+E(f794(x9393,x9394,x9391),f794(x9393,x9394,x9392)) % 174.01/173.91 [940]~E(x9401,x9402)+E(f445(x9401,x9403),f445(x9402,x9403)) % 174.01/173.91 [941]~E(x9411,x9412)+E(f445(x9413,x9411),f445(x9413,x9412)) % 174.01/173.91 [942]~E(x9421,x9422)+E(f491(x9421,x9423,x9424,x9425,x9426),f491(x9422,x9423,x9424,x9425,x9426)) % 174.01/173.91 [943]~E(x9431,x9432)+E(f491(x9433,x9431,x9434,x9435,x9436),f491(x9433,x9432,x9434,x9435,x9436)) % 174.01/173.91 [944]~E(x9441,x9442)+E(f491(x9443,x9444,x9441,x9445,x9446),f491(x9443,x9444,x9442,x9445,x9446)) % 174.01/173.91 [945]~E(x9451,x9452)+E(f491(x9453,x9454,x9455,x9451,x9456),f491(x9453,x9454,x9455,x9452,x9456)) % 174.01/173.91 [946]~E(x9461,x9462)+E(f491(x9463,x9464,x9465,x9466,x9461),f491(x9463,x9464,x9465,x9466,x9462)) % 174.01/173.91 [947]~E(x9471,x9472)+E(f651(x9471,x9473,x9474,x9475),f651(x9472,x9473,x9474,x9475)) % 174.01/173.91 [948]~E(x9481,x9482)+E(f651(x9483,x9481,x9484,x9485),f651(x9483,x9482,x9484,x9485)) % 174.01/173.91 [949]~E(x9491,x9492)+E(f651(x9493,x9494,x9491,x9495),f651(x9493,x9494,x9492,x9495)) % 174.01/173.91 [950]~E(x9501,x9502)+E(f651(x9503,x9504,x9505,x9501),f651(x9503,x9504,x9505,x9502)) % 174.01/173.91 [951]~E(x9511,x9512)+E(f530(x9511,x9513,x9514,x9515),f530(x9512,x9513,x9514,x9515)) % 174.01/173.91 [952]~E(x9521,x9522)+E(f530(x9523,x9521,x9524,x9525),f530(x9523,x9522,x9524,x9525)) % 174.01/173.91 [953]~E(x9531,x9532)+E(f530(x9533,x9534,x9531,x9535),f530(x9533,x9534,x9532,x9535)) % 174.01/173.91 [954]~E(x9541,x9542)+E(f530(x9543,x9544,x9545,x9541),f530(x9543,x9544,x9545,x9542)) % 174.01/173.91 [955]~E(x9551,x9552)+E(f515(x9551,x9553,x9554,x9555,x9556),f515(x9552,x9553,x9554,x9555,x9556)) % 174.01/173.91 [956]~E(x9561,x9562)+E(f515(x9563,x9561,x9564,x9565,x9566),f515(x9563,x9562,x9564,x9565,x9566)) % 174.01/173.91 [957]~E(x9571,x9572)+E(f515(x9573,x9574,x9571,x9575,x9576),f515(x9573,x9574,x9572,x9575,x9576)) % 174.01/173.91 [958]~E(x9581,x9582)+E(f515(x9583,x9584,x9585,x9581,x9586),f515(x9583,x9584,x9585,x9582,x9586)) % 174.01/173.91 [959]~E(x9591,x9592)+E(f515(x9593,x9594,x9595,x9596,x9591),f515(x9593,x9594,x9595,x9596,x9592)) % 174.01/173.91 [960]~E(x9601,x9602)+E(f704(x9601,x9603,x9604,x9605,x9606),f704(x9602,x9603,x9604,x9605,x9606)) % 174.01/173.91 [961]~E(x9611,x9612)+E(f704(x9613,x9611,x9614,x9615,x9616),f704(x9613,x9612,x9614,x9615,x9616)) % 174.01/173.91 [962]~E(x9621,x9622)+E(f704(x9623,x9624,x9621,x9625,x9626),f704(x9623,x9624,x9622,x9625,x9626)) % 174.01/173.91 [963]~E(x9631,x9632)+E(f704(x9633,x9634,x9635,x9631,x9636),f704(x9633,x9634,x9635,x9632,x9636)) % 174.01/173.91 [964]~E(x9641,x9642)+E(f704(x9643,x9644,x9645,x9646,x9641),f704(x9643,x9644,x9645,x9646,x9642)) % 174.01/173.91 [965]~E(x9651,x9652)+E(f446(x9651,x9653),f446(x9652,x9653)) % 174.01/173.91 [966]~E(x9661,x9662)+E(f446(x9663,x9661),f446(x9663,x9662)) % 174.01/173.91 [967]~E(x9671,x9672)+E(f571(x9671,x9673,x9674,x9675,x9676),f571(x9672,x9673,x9674,x9675,x9676)) % 174.01/173.91 [968]~E(x9681,x9682)+E(f571(x9683,x9681,x9684,x9685,x9686),f571(x9683,x9682,x9684,x9685,x9686)) % 174.01/173.91 [969]~E(x9691,x9692)+E(f571(x9693,x9694,x9691,x9695,x9696),f571(x9693,x9694,x9692,x9695,x9696)) % 174.01/173.91 [970]~E(x9701,x9702)+E(f571(x9703,x9704,x9705,x9701,x9706),f571(x9703,x9704,x9705,x9702,x9706)) % 174.01/173.91 [971]~E(x9711,x9712)+E(f571(x9713,x9714,x9715,x9716,x9711),f571(x9713,x9714,x9715,x9716,x9712)) % 174.01/173.91 [972]~E(x9721,x9722)+E(f485(x9721,x9723,x9724),f485(x9722,x9723,x9724)) % 174.01/173.91 [973]~E(x9731,x9732)+E(f485(x9733,x9731,x9734),f485(x9733,x9732,x9734)) % 174.01/173.91 [974]~E(x9741,x9742)+E(f485(x9743,x9744,x9741),f485(x9743,x9744,x9742)) % 174.01/173.91 [975]~E(x9751,x9752)+E(f739(x9751,x9753,x9754,x9755),f739(x9752,x9753,x9754,x9755)) % 174.01/173.91 [976]~E(x9761,x9762)+E(f739(x9763,x9761,x9764,x9765),f739(x9763,x9762,x9764,x9765)) % 174.01/173.91 [977]~E(x9771,x9772)+E(f739(x9773,x9774,x9771,x9775),f739(x9773,x9774,x9772,x9775)) % 174.01/173.91 [978]~E(x9781,x9782)+E(f739(x9783,x9784,x9785,x9781),f739(x9783,x9784,x9785,x9782)) % 174.01/173.91 [979]~E(x9791,x9792)+E(f570(x9791,x9793,x9794),f570(x9792,x9793,x9794)) % 174.01/173.91 [980]~E(x9801,x9802)+E(f570(x9803,x9801,x9804),f570(x9803,x9802,x9804)) % 174.01/173.91 [981]~E(x9811,x9812)+E(f570(x9813,x9814,x9811),f570(x9813,x9814,x9812)) % 174.01/173.91 [982]~E(x9821,x9822)+E(f568(x9821,x9823),f568(x9822,x9823)) % 174.01/173.91 [983]~E(x9831,x9832)+E(f568(x9833,x9831),f568(x9833,x9832)) % 174.01/173.91 [984]~E(x9841,x9842)+E(f384(x9841,x9843,x9844,x9845),f384(x9842,x9843,x9844,x9845)) % 174.01/173.91 [985]~E(x9851,x9852)+E(f384(x9853,x9851,x9854,x9855),f384(x9853,x9852,x9854,x9855)) % 174.01/173.91 [986]~E(x9861,x9862)+E(f384(x9863,x9864,x9861,x9865),f384(x9863,x9864,x9862,x9865)) % 174.01/173.91 [987]~E(x9871,x9872)+E(f384(x9873,x9874,x9875,x9871),f384(x9873,x9874,x9875,x9872)) % 174.01/173.91 [988]~E(x9881,x9882)+E(f715(x9881,x9883,x9884),f715(x9882,x9883,x9884)) % 174.01/173.91 [989]~E(x9891,x9892)+E(f715(x9893,x9891,x9894),f715(x9893,x9892,x9894)) % 174.01/173.91 [990]~E(x9901,x9902)+E(f715(x9903,x9904,x9901),f715(x9903,x9904,x9902)) % 174.01/173.91 [991]~E(x9911,x9912)+E(f494(x9911,x9913),f494(x9912,x9913)) % 174.01/173.91 [992]~E(x9921,x9922)+E(f494(x9923,x9921),f494(x9923,x9922)) % 174.01/173.91 [993]~E(x9931,x9932)+E(f369(x9931,x9933,x9934,x9935,x9936),f369(x9932,x9933,x9934,x9935,x9936)) % 174.01/173.91 [994]~E(x9941,x9942)+E(f369(x9943,x9941,x9944,x9945,x9946),f369(x9943,x9942,x9944,x9945,x9946)) % 174.01/173.91 [995]~E(x9951,x9952)+E(f369(x9953,x9954,x9951,x9955,x9956),f369(x9953,x9954,x9952,x9955,x9956)) % 174.01/173.91 [996]~E(x9961,x9962)+E(f369(x9963,x9964,x9965,x9961,x9966),f369(x9963,x9964,x9965,x9962,x9966)) % 174.01/173.91 [997]~E(x9971,x9972)+E(f369(x9973,x9974,x9975,x9976,x9971),f369(x9973,x9974,x9975,x9976,x9972)) % 174.01/173.91 [998]~E(x9981,x9982)+E(f735(x9981,x9983,x9984,x9985,x9986),f735(x9982,x9983,x9984,x9985,x9986)) % 174.01/173.91 [999]~E(x9991,x9992)+E(f735(x9993,x9991,x9994,x9995,x9996),f735(x9993,x9992,x9994,x9995,x9996)) % 174.01/173.91 [1000]~E(x10001,x10002)+E(f735(x10003,x10004,x10001,x10005,x10006),f735(x10003,x10004,x10002,x10005,x10006)) % 174.01/173.91 [1001]~E(x10011,x10012)+E(f735(x10013,x10014,x10015,x10011,x10016),f735(x10013,x10014,x10015,x10012,x10016)) % 174.01/173.91 [1002]~E(x10021,x10022)+E(f735(x10023,x10024,x10025,x10026,x10021),f735(x10023,x10024,x10025,x10026,x10022)) % 174.01/173.91 [1003]~E(x10031,x10032)+E(f477(x10031,x10033,x10034),f477(x10032,x10033,x10034)) % 174.01/173.91 [1004]~E(x10041,x10042)+E(f477(x10043,x10041,x10044),f477(x10043,x10042,x10044)) % 174.01/173.91 [1005]~E(x10051,x10052)+E(f477(x10053,x10054,x10051),f477(x10053,x10054,x10052)) % 174.01/173.91 [1006]~E(x10061,x10062)+E(f741(x10061,x10063,x10064,x10065),f741(x10062,x10063,x10064,x10065)) % 174.01/173.91 [1007]~E(x10071,x10072)+E(f741(x10073,x10071,x10074,x10075),f741(x10073,x10072,x10074,x10075)) % 174.01/173.91 [1008]~E(x10081,x10082)+E(f741(x10083,x10084,x10081,x10085),f741(x10083,x10084,x10082,x10085)) % 174.01/173.91 [1009]~E(x10091,x10092)+E(f741(x10093,x10094,x10095,x10091),f741(x10093,x10094,x10095,x10092)) % 174.01/173.91 [1010]~E(x10101,x10102)+E(f680(x10101,x10103,x10104,x10105,x10106,x10107,x10108,x10109),f680(x10102,x10103,x10104,x10105,x10106,x10107,x10108,x10109)) % 174.01/173.91 [1011]~E(x10111,x10112)+E(f680(x10113,x10111,x10114,x10115,x10116,x10117,x10118,x10119),f680(x10113,x10112,x10114,x10115,x10116,x10117,x10118,x10119)) % 174.01/173.91 [1012]~E(x10121,x10122)+E(f680(x10123,x10124,x10121,x10125,x10126,x10127,x10128,x10129),f680(x10123,x10124,x10122,x10125,x10126,x10127,x10128,x10129)) % 174.01/173.91 [1013]~E(x10131,x10132)+E(f680(x10133,x10134,x10135,x10131,x10136,x10137,x10138,x10139),f680(x10133,x10134,x10135,x10132,x10136,x10137,x10138,x10139)) % 174.01/173.91 [1014]~E(x10141,x10142)+E(f680(x10143,x10144,x10145,x10146,x10141,x10147,x10148,x10149),f680(x10143,x10144,x10145,x10146,x10142,x10147,x10148,x10149)) % 174.01/173.91 [1015]~E(x10151,x10152)+E(f680(x10153,x10154,x10155,x10156,x10157,x10151,x10158,x10159),f680(x10153,x10154,x10155,x10156,x10157,x10152,x10158,x10159)) % 174.01/173.91 [1016]~E(x10161,x10162)+E(f680(x10163,x10164,x10165,x10166,x10167,x10168,x10161,x10169),f680(x10163,x10164,x10165,x10166,x10167,x10168,x10162,x10169)) % 174.01/173.91 [1017]~E(x10171,x10172)+E(f680(x10173,x10174,x10175,x10176,x10177,x10178,x10179,x10171),f680(x10173,x10174,x10175,x10176,x10177,x10178,x10179,x10172)) % 174.01/173.91 [1018]~E(x10181,x10182)+E(f177(x10181,x10183,x10184,x10185),f177(x10182,x10183,x10184,x10185)) % 174.01/173.91 [1019]~E(x10191,x10192)+E(f177(x10193,x10191,x10194,x10195),f177(x10193,x10192,x10194,x10195)) % 174.01/173.91 [1020]~E(x10201,x10202)+E(f177(x10203,x10204,x10201,x10205),f177(x10203,x10204,x10202,x10205)) % 174.01/173.91 [1021]~E(x10211,x10212)+E(f177(x10213,x10214,x10215,x10211),f177(x10213,x10214,x10215,x10212)) % 174.01/173.91 [1022]~E(x10221,x10222)+E(f381(x10221,x10223,x10224,x10225),f381(x10222,x10223,x10224,x10225)) % 174.01/173.91 [1023]~E(x10231,x10232)+E(f381(x10233,x10231,x10234,x10235),f381(x10233,x10232,x10234,x10235)) % 174.01/173.91 [1024]~E(x10241,x10242)+E(f381(x10243,x10244,x10241,x10245),f381(x10243,x10244,x10242,x10245)) % 174.01/173.91 [1025]~E(x10251,x10252)+E(f381(x10253,x10254,x10255,x10251),f381(x10253,x10254,x10255,x10252)) % 174.01/173.91 [1026]~E(x10261,x10262)+E(f708(x10261,x10263,x10264,x10265,x10266,x10267),f708(x10262,x10263,x10264,x10265,x10266,x10267)) % 174.01/173.91 [1027]~E(x10271,x10272)+E(f708(x10273,x10271,x10274,x10275,x10276,x10277),f708(x10273,x10272,x10274,x10275,x10276,x10277)) % 174.01/173.91 [1028]~E(x10281,x10282)+E(f708(x10283,x10284,x10281,x10285,x10286,x10287),f708(x10283,x10284,x10282,x10285,x10286,x10287)) % 174.01/173.91 [1029]~E(x10291,x10292)+E(f708(x10293,x10294,x10295,x10291,x10296,x10297),f708(x10293,x10294,x10295,x10292,x10296,x10297)) % 174.01/173.91 [1030]~E(x10301,x10302)+E(f708(x10303,x10304,x10305,x10306,x10301,x10307),f708(x10303,x10304,x10305,x10306,x10302,x10307)) % 174.01/173.91 [1031]~E(x10311,x10312)+E(f708(x10313,x10314,x10315,x10316,x10317,x10311),f708(x10313,x10314,x10315,x10316,x10317,x10312)) % 174.01/173.91 [1032]~E(x10321,x10322)+E(f577(x10321,x10323),f577(x10322,x10323)) % 174.01/173.91 [1033]~E(x10331,x10332)+E(f577(x10333,x10331),f577(x10333,x10332)) % 174.01/173.91 [1034]~E(x10341,x10342)+E(f123(x10341,x10343,x10344,x10345),f123(x10342,x10343,x10344,x10345)) % 174.01/173.91 [1035]~E(x10351,x10352)+E(f123(x10353,x10351,x10354,x10355),f123(x10353,x10352,x10354,x10355)) % 174.01/173.91 [1036]~E(x10361,x10362)+E(f123(x10363,x10364,x10361,x10365),f123(x10363,x10364,x10362,x10365)) % 174.01/173.91 [1037]~E(x10371,x10372)+E(f123(x10373,x10374,x10375,x10371),f123(x10373,x10374,x10375,x10372)) % 174.01/173.91 [1038]~E(x10381,x10382)+E(f213(x10381,x10383),f213(x10382,x10383)) % 174.01/173.91 [1039]~E(x10391,x10392)+E(f213(x10393,x10391),f213(x10393,x10392)) % 174.01/173.91 [1040]~E(x10401,x10402)+E(f836(x10401,x10403,x10404),f836(x10402,x10403,x10404)) % 174.01/173.91 [1041]~E(x10411,x10412)+E(f836(x10413,x10411,x10414),f836(x10413,x10412,x10414)) % 174.01/173.91 [1042]~E(x10421,x10422)+E(f836(x10423,x10424,x10421),f836(x10423,x10424,x10422)) % 174.01/173.91 [1043]~E(x10431,x10432)+E(f584(x10431,x10433),f584(x10432,x10433)) % 174.01/173.91 [1044]~E(x10441,x10442)+E(f584(x10443,x10441),f584(x10443,x10442)) % 174.01/173.91 [1045]~E(x10451,x10452)+E(f812(x10451,x10453,x10454),f812(x10452,x10453,x10454)) % 174.01/173.91 [1046]~E(x10461,x10462)+E(f812(x10463,x10461,x10464),f812(x10463,x10462,x10464)) % 174.01/173.91 [1047]~E(x10471,x10472)+E(f812(x10473,x10474,x10471),f812(x10473,x10474,x10472)) % 174.01/173.91 [1048]~E(x10481,x10482)+E(f114(x10481),f114(x10482)) % 174.01/173.91 [1049]~E(x10491,x10492)+E(f343(x10491,x10493,x10494),f343(x10492,x10493,x10494)) % 174.01/173.91 [1050]~E(x10501,x10502)+E(f343(x10503,x10501,x10504),f343(x10503,x10502,x10504)) % 174.01/173.91 [1051]~E(x10511,x10512)+E(f343(x10513,x10514,x10511),f343(x10513,x10514,x10512)) % 174.01/173.91 [1052]~E(x10521,x10522)+E(f693(x10521,x10523,x10524,x10525,x10526,x10527,x10528),f693(x10522,x10523,x10524,x10525,x10526,x10527,x10528)) % 174.01/173.91 [1053]~E(x10531,x10532)+E(f693(x10533,x10531,x10534,x10535,x10536,x10537,x10538),f693(x10533,x10532,x10534,x10535,x10536,x10537,x10538)) % 174.01/173.91 [1054]~E(x10541,x10542)+E(f693(x10543,x10544,x10541,x10545,x10546,x10547,x10548),f693(x10543,x10544,x10542,x10545,x10546,x10547,x10548)) % 174.01/173.91 [1055]~E(x10551,x10552)+E(f693(x10553,x10554,x10555,x10551,x10556,x10557,x10558),f693(x10553,x10554,x10555,x10552,x10556,x10557,x10558)) % 174.01/173.91 [1056]~E(x10561,x10562)+E(f693(x10563,x10564,x10565,x10566,x10561,x10567,x10568),f693(x10563,x10564,x10565,x10566,x10562,x10567,x10568)) % 174.01/173.91 [1057]~E(x10571,x10572)+E(f693(x10573,x10574,x10575,x10576,x10577,x10571,x10578),f693(x10573,x10574,x10575,x10576,x10577,x10572,x10578)) % 174.01/173.91 [1058]~E(x10581,x10582)+E(f693(x10583,x10584,x10585,x10586,x10587,x10588,x10581),f693(x10583,x10584,x10585,x10586,x10587,x10588,x10582)) % 174.01/173.91 [1059]~E(x10591,x10592)+E(f472(x10591,x10593,x10594),f472(x10592,x10593,x10594)) % 174.01/173.91 [1060]~E(x10601,x10602)+E(f472(x10603,x10601,x10604),f472(x10603,x10602,x10604)) % 174.01/173.91 [1061]~E(x10611,x10612)+E(f472(x10613,x10614,x10611),f472(x10613,x10614,x10612)) % 174.01/173.91 [1062]~E(x10621,x10622)+E(f516(x10621,x10623,x10624,x10625,x10626),f516(x10622,x10623,x10624,x10625,x10626)) % 174.01/173.91 [1063]~E(x10631,x10632)+E(f516(x10633,x10631,x10634,x10635,x10636),f516(x10633,x10632,x10634,x10635,x10636)) % 174.01/173.91 [1064]~E(x10641,x10642)+E(f516(x10643,x10644,x10641,x10645,x10646),f516(x10643,x10644,x10642,x10645,x10646)) % 174.01/173.91 [1065]~E(x10651,x10652)+E(f516(x10653,x10654,x10655,x10651,x10656),f516(x10653,x10654,x10655,x10652,x10656)) % 174.01/173.91 [1066]~E(x10661,x10662)+E(f516(x10663,x10664,x10665,x10666,x10661),f516(x10663,x10664,x10665,x10666,x10662)) % 174.01/173.91 [1067]~E(x10671,x10672)+E(f787(x10671,x10673,x10674),f787(x10672,x10673,x10674)) % 174.01/173.91 [1068]~E(x10681,x10682)+E(f787(x10683,x10681,x10684),f787(x10683,x10682,x10684)) % 174.01/173.91 [1069]~E(x10691,x10692)+E(f787(x10693,x10694,x10691),f787(x10693,x10694,x10692)) % 174.01/173.91 [1070]~E(x10701,x10702)+E(f729(x10701),f729(x10702)) % 174.01/173.91 [1071]~E(x10711,x10712)+E(f815(x10711,x10713,x10714),f815(x10712,x10713,x10714)) % 174.01/173.91 [1072]~E(x10721,x10722)+E(f815(x10723,x10721,x10724),f815(x10723,x10722,x10724)) % 174.01/173.91 [1073]~E(x10731,x10732)+E(f815(x10733,x10734,x10731),f815(x10733,x10734,x10732)) % 174.01/173.91 [1074]~E(x10741,x10742)+E(f628(x10741,x10743,x10744),f628(x10742,x10743,x10744)) % 174.01/173.91 [1075]~E(x10751,x10752)+E(f628(x10753,x10751,x10754),f628(x10753,x10752,x10754)) % 174.01/173.91 [1076]~E(x10761,x10762)+E(f628(x10763,x10764,x10761),f628(x10763,x10764,x10762)) % 174.01/173.91 [1077]~E(x10771,x10772)+E(f190(x10771,x10773),f190(x10772,x10773)) % 174.01/173.91 [1078]~E(x10781,x10782)+E(f190(x10783,x10781),f190(x10783,x10782)) % 174.01/173.91 [1079]~E(x10791,x10792)+E(f502(x10791,x10793,x10794,x10795,x10796,x10797,x10798),f502(x10792,x10793,x10794,x10795,x10796,x10797,x10798)) % 174.01/173.91 [1080]~E(x10801,x10802)+E(f502(x10803,x10801,x10804,x10805,x10806,x10807,x10808),f502(x10803,x10802,x10804,x10805,x10806,x10807,x10808)) % 174.01/173.91 [1081]~E(x10811,x10812)+E(f502(x10813,x10814,x10811,x10815,x10816,x10817,x10818),f502(x10813,x10814,x10812,x10815,x10816,x10817,x10818)) % 174.01/173.91 [1082]~E(x10821,x10822)+E(f502(x10823,x10824,x10825,x10821,x10826,x10827,x10828),f502(x10823,x10824,x10825,x10822,x10826,x10827,x10828)) % 174.01/173.91 [1083]~E(x10831,x10832)+E(f502(x10833,x10834,x10835,x10836,x10831,x10837,x10838),f502(x10833,x10834,x10835,x10836,x10832,x10837,x10838)) % 174.01/173.91 [1084]~E(x10841,x10842)+E(f502(x10843,x10844,x10845,x10846,x10847,x10841,x10848),f502(x10843,x10844,x10845,x10846,x10847,x10842,x10848)) % 174.01/173.91 [1085]~E(x10851,x10852)+E(f502(x10853,x10854,x10855,x10856,x10857,x10858,x10851),f502(x10853,x10854,x10855,x10856,x10857,x10858,x10852)) % 174.01/173.91 [1086]~E(x10861,x10862)+E(f753(x10861,x10863,x10864,x10865),f753(x10862,x10863,x10864,x10865)) % 174.01/173.91 [1087]~E(x10871,x10872)+E(f753(x10873,x10871,x10874,x10875),f753(x10873,x10872,x10874,x10875)) % 174.01/173.91 [1088]~E(x10881,x10882)+E(f753(x10883,x10884,x10881,x10885),f753(x10883,x10884,x10882,x10885)) % 174.01/173.91 [1089]~E(x10891,x10892)+E(f753(x10893,x10894,x10895,x10891),f753(x10893,x10894,x10895,x10892)) % 174.01/173.91 [1090]~E(x10901,x10902)+E(f78(x10901,x10903),f78(x10902,x10903)) % 174.01/173.91 [1091]~E(x10911,x10912)+E(f78(x10913,x10911),f78(x10913,x10912)) % 174.01/173.91 [1092]~E(x10921,x10922)+E(f534(x10921,x10923,x10924),f534(x10922,x10923,x10924)) % 174.01/173.91 [1093]~E(x10931,x10932)+E(f534(x10933,x10931,x10934),f534(x10933,x10932,x10934)) % 174.01/173.91 [1094]~E(x10941,x10942)+E(f534(x10943,x10944,x10941),f534(x10943,x10944,x10942)) % 174.01/173.91 [1095]~E(x10951,x10952)+E(f724(x10951,x10953),f724(x10952,x10953)) % 174.01/173.91 [1096]~E(x10961,x10962)+E(f724(x10963,x10961),f724(x10963,x10962)) % 174.01/173.91 [1097]~E(x10971,x10972)+E(f671(x10971,x10973,x10974),f671(x10972,x10973,x10974)) % 174.01/173.91 [1098]~E(x10981,x10982)+E(f671(x10983,x10981,x10984),f671(x10983,x10982,x10984)) % 174.01/173.91 [1099]~E(x10991,x10992)+E(f671(x10993,x10994,x10991),f671(x10993,x10994,x10992)) % 174.01/173.91 [1100]~E(x11001,x11002)+E(f163(x11001,x11003,x11004),f163(x11002,x11003,x11004)) % 174.01/173.91 [1101]~E(x11011,x11012)+E(f163(x11013,x11011,x11014),f163(x11013,x11012,x11014)) % 174.01/173.91 [1102]~E(x11021,x11022)+E(f163(x11023,x11024,x11021),f163(x11023,x11024,x11022)) % 174.01/173.91 [1103]~E(x11031,x11032)+E(f822(x11031,x11033,x11034),f822(x11032,x11033,x11034)) % 174.01/173.91 [1104]~E(x11041,x11042)+E(f822(x11043,x11041,x11044),f822(x11043,x11042,x11044)) % 174.01/173.91 [1105]~E(x11051,x11052)+E(f822(x11053,x11054,x11051),f822(x11053,x11054,x11052)) % 174.01/173.91 [1106]~E(x11061,x11062)+E(f354(x11061,x11063),f354(x11062,x11063)) % 174.01/173.91 [1107]~E(x11071,x11072)+E(f354(x11073,x11071),f354(x11073,x11072)) % 174.01/173.91 [1108]~E(x11081,x11082)+E(f457(x11081,x11083),f457(x11082,x11083)) % 174.01/173.91 [1109]~E(x11091,x11092)+E(f457(x11093,x11091),f457(x11093,x11092)) % 174.01/173.91 [1110]~E(x11101,x11102)+E(f362(x11101,x11103,x11104,x11105,x11106),f362(x11102,x11103,x11104,x11105,x11106)) % 174.01/173.91 [1111]~E(x11111,x11112)+E(f362(x11113,x11111,x11114,x11115,x11116),f362(x11113,x11112,x11114,x11115,x11116)) % 174.01/173.91 [1112]~E(x11121,x11122)+E(f362(x11123,x11124,x11121,x11125,x11126),f362(x11123,x11124,x11122,x11125,x11126)) % 174.01/173.91 [1113]~E(x11131,x11132)+E(f362(x11133,x11134,x11135,x11131,x11136),f362(x11133,x11134,x11135,x11132,x11136)) % 174.01/173.91 [1114]~E(x11141,x11142)+E(f362(x11143,x11144,x11145,x11146,x11141),f362(x11143,x11144,x11145,x11146,x11142)) % 174.01/173.91 [1115]~E(x11151,x11152)+E(f497(x11151,x11153,x11154,x11155,x11156,x11157),f497(x11152,x11153,x11154,x11155,x11156,x11157)) % 174.01/173.91 [1116]~E(x11161,x11162)+E(f497(x11163,x11161,x11164,x11165,x11166,x11167),f497(x11163,x11162,x11164,x11165,x11166,x11167)) % 174.01/173.91 [1117]~E(x11171,x11172)+E(f497(x11173,x11174,x11171,x11175,x11176,x11177),f497(x11173,x11174,x11172,x11175,x11176,x11177)) % 174.01/173.91 [1118]~E(x11181,x11182)+E(f497(x11183,x11184,x11185,x11181,x11186,x11187),f497(x11183,x11184,x11185,x11182,x11186,x11187)) % 174.01/173.91 [1119]~E(x11191,x11192)+E(f497(x11193,x11194,x11195,x11196,x11191,x11197),f497(x11193,x11194,x11195,x11196,x11192,x11197)) % 174.01/173.91 [1120]~E(x11201,x11202)+E(f497(x11203,x11204,x11205,x11206,x11207,x11201),f497(x11203,x11204,x11205,x11206,x11207,x11202)) % 174.01/173.91 [1121]~E(x11211,x11212)+E(f226(x11211,x11213,x11214),f226(x11212,x11213,x11214)) % 174.01/173.91 [1122]~E(x11221,x11222)+E(f226(x11223,x11221,x11224),f226(x11223,x11222,x11224)) % 174.01/173.91 [1123]~E(x11231,x11232)+E(f226(x11233,x11234,x11231),f226(x11233,x11234,x11232)) % 174.01/173.91 [1124]~E(x11241,x11242)+E(f657(x11241,x11243,x11244,x11245),f657(x11242,x11243,x11244,x11245)) % 174.01/173.91 [1125]~E(x11251,x11252)+E(f657(x11253,x11251,x11254,x11255),f657(x11253,x11252,x11254,x11255)) % 174.01/173.91 [1126]~E(x11261,x11262)+E(f657(x11263,x11264,x11261,x11265),f657(x11263,x11264,x11262,x11265)) % 174.01/173.91 [1127]~E(x11271,x11272)+E(f657(x11273,x11274,x11275,x11271),f657(x11273,x11274,x11275,x11272)) % 174.01/173.91 [1128]~E(x11281,x11282)+E(f92(x11281),f92(x11282)) % 174.01/173.91 [1129]~E(x11291,x11292)+E(f742(x11291,x11293,x11294,x11295,x11296),f742(x11292,x11293,x11294,x11295,x11296)) % 174.01/173.91 [1130]~E(x11301,x11302)+E(f742(x11303,x11301,x11304,x11305,x11306),f742(x11303,x11302,x11304,x11305,x11306)) % 174.01/173.91 [1131]~E(x11311,x11312)+E(f742(x11313,x11314,x11311,x11315,x11316),f742(x11313,x11314,x11312,x11315,x11316)) % 174.01/173.91 [1132]~E(x11321,x11322)+E(f742(x11323,x11324,x11325,x11321,x11326),f742(x11323,x11324,x11325,x11322,x11326)) % 174.01/173.91 [1133]~E(x11331,x11332)+E(f742(x11333,x11334,x11335,x11336,x11331),f742(x11333,x11334,x11335,x11336,x11332)) % 174.01/173.91 [1134]~E(x11341,x11342)+E(f536(x11341,x11343,x11344,x11345,x11346),f536(x11342,x11343,x11344,x11345,x11346)) % 174.01/173.91 [1135]~E(x11351,x11352)+E(f536(x11353,x11351,x11354,x11355,x11356),f536(x11353,x11352,x11354,x11355,x11356)) % 174.01/173.91 [1136]~E(x11361,x11362)+E(f536(x11363,x11364,x11361,x11365,x11366),f536(x11363,x11364,x11362,x11365,x11366)) % 174.01/173.91 [1137]~E(x11371,x11372)+E(f536(x11373,x11374,x11375,x11371,x11376),f536(x11373,x11374,x11375,x11372,x11376)) % 174.01/173.91 [1138]~E(x11381,x11382)+E(f536(x11383,x11384,x11385,x11386,x11381),f536(x11383,x11384,x11385,x11386,x11382)) % 174.01/173.91 [1139]~E(x11391,x11392)+E(f552(x11391,x11393,x11394),f552(x11392,x11393,x11394)) % 174.01/173.91 [1140]~E(x11401,x11402)+E(f552(x11403,x11401,x11404),f552(x11403,x11402,x11404)) % 174.01/173.91 [1141]~E(x11411,x11412)+E(f552(x11413,x11414,x11411),f552(x11413,x11414,x11412)) % 174.01/173.91 [1142]~E(x11421,x11422)+E(f692(x11421,x11423,x11424,x11425,x11426,x11427),f692(x11422,x11423,x11424,x11425,x11426,x11427)) % 174.01/173.91 [1143]~E(x11431,x11432)+E(f692(x11433,x11431,x11434,x11435,x11436,x11437),f692(x11433,x11432,x11434,x11435,x11436,x11437)) % 174.01/173.91 [1144]~E(x11441,x11442)+E(f692(x11443,x11444,x11441,x11445,x11446,x11447),f692(x11443,x11444,x11442,x11445,x11446,x11447)) % 174.01/173.91 [1145]~E(x11451,x11452)+E(f692(x11453,x11454,x11455,x11451,x11456,x11457),f692(x11453,x11454,x11455,x11452,x11456,x11457)) % 174.01/173.91 [1146]~E(x11461,x11462)+E(f692(x11463,x11464,x11465,x11466,x11461,x11467),f692(x11463,x11464,x11465,x11466,x11462,x11467)) % 174.01/173.91 [1147]~E(x11471,x11472)+E(f692(x11473,x11474,x11475,x11476,x11477,x11471),f692(x11473,x11474,x11475,x11476,x11477,x11472)) % 174.01/173.91 [1148]~E(x11481,x11482)+E(f509(x11481,x11483,x11484),f509(x11482,x11483,x11484)) % 174.01/173.91 [1149]~E(x11491,x11492)+E(f509(x11493,x11491,x11494),f509(x11493,x11492,x11494)) % 174.01/173.91 [1150]~E(x11501,x11502)+E(f509(x11503,x11504,x11501),f509(x11503,x11504,x11502)) % 174.01/173.91 [1151]~E(x11511,x11512)+E(f803(x11511,x11513,x11514),f803(x11512,x11513,x11514)) % 174.01/173.91 [1152]~E(x11521,x11522)+E(f803(x11523,x11521,x11524),f803(x11523,x11522,x11524)) % 174.01/173.91 [1153]~E(x11531,x11532)+E(f803(x11533,x11534,x11531),f803(x11533,x11534,x11532)) % 174.01/173.91 [1154]~E(x11541,x11542)+E(f318(x11541,x11543,x11544,x11545),f318(x11542,x11543,x11544,x11545)) % 174.01/173.91 [1155]~E(x11551,x11552)+E(f318(x11553,x11551,x11554,x11555),f318(x11553,x11552,x11554,x11555)) % 174.01/173.91 [1156]~E(x11561,x11562)+E(f318(x11563,x11564,x11561,x11565),f318(x11563,x11564,x11562,x11565)) % 174.01/173.91 [1157]~E(x11571,x11572)+E(f318(x11573,x11574,x11575,x11571),f318(x11573,x11574,x11575,x11572)) % 174.01/173.91 [1158]~E(x11581,x11582)+E(f648(x11581,x11583,x11584),f648(x11582,x11583,x11584)) % 174.01/173.91 [1159]~E(x11591,x11592)+E(f648(x11593,x11591,x11594),f648(x11593,x11592,x11594)) % 174.01/173.91 [1160]~E(x11601,x11602)+E(f648(x11603,x11604,x11601),f648(x11603,x11604,x11602)) % 174.01/173.91 [1161]~E(x11611,x11612)+E(f496(x11611,x11613,x11614,x11615),f496(x11612,x11613,x11614,x11615)) % 174.01/173.91 [1162]~E(x11621,x11622)+E(f496(x11623,x11621,x11624,x11625),f496(x11623,x11622,x11624,x11625)) % 174.01/173.91 [1163]~E(x11631,x11632)+E(f496(x11633,x11634,x11631,x11635),f496(x11633,x11634,x11632,x11635)) % 174.01/173.91 [1164]~E(x11641,x11642)+E(f496(x11643,x11644,x11645,x11641),f496(x11643,x11644,x11645,x11642)) % 174.01/173.91 [1165]~E(x11651,x11652)+E(f468(x11651,x11653,x11654),f468(x11652,x11653,x11654)) % 174.01/173.91 [1166]~E(x11661,x11662)+E(f468(x11663,x11661,x11664),f468(x11663,x11662,x11664)) % 174.01/173.91 [1167]~E(x11671,x11672)+E(f468(x11673,x11674,x11671),f468(x11673,x11674,x11672)) % 174.01/173.91 [1168]~E(x11681,x11682)+E(f349(x11681,x11683,x11684,x11685),f349(x11682,x11683,x11684,x11685)) % 174.01/173.91 [1169]~E(x11691,x11692)+E(f349(x11693,x11691,x11694,x11695),f349(x11693,x11692,x11694,x11695)) % 174.01/173.91 [1170]~E(x11701,x11702)+E(f349(x11703,x11704,x11701,x11705),f349(x11703,x11704,x11702,x11705)) % 174.01/173.91 [1171]~E(x11711,x11712)+E(f349(x11713,x11714,x11715,x11711),f349(x11713,x11714,x11715,x11712)) % 174.01/173.91 [1172]~E(x11721,x11722)+E(f371(x11721,x11723),f371(x11722,x11723)) % 174.01/173.91 [1173]~E(x11731,x11732)+E(f371(x11733,x11731),f371(x11733,x11732)) % 174.01/173.91 [1174]~E(x11741,x11742)+E(f522(x11741),f522(x11742)) % 174.01/173.91 [1175]~E(x11751,x11752)+E(f71(x11751,x11753,x11754),f71(x11752,x11753,x11754)) % 174.01/173.91 [1176]~E(x11761,x11762)+E(f71(x11763,x11761,x11764),f71(x11763,x11762,x11764)) % 174.01/173.91 [1177]~E(x11771,x11772)+E(f71(x11773,x11774,x11771),f71(x11773,x11774,x11772)) % 174.01/173.91 [1178]~E(x11781,x11782)+E(f233(x11781),f233(x11782)) % 174.01/173.91 [1179]~E(x11791,x11792)+E(f618(x11791,x11793),f618(x11792,x11793)) % 174.01/173.91 [1180]~E(x11801,x11802)+E(f618(x11803,x11801),f618(x11803,x11802)) % 174.01/173.91 [1181]~E(x11811,x11812)+E(f591(x11811,x11813),f591(x11812,x11813)) % 174.01/173.91 [1182]~E(x11821,x11822)+E(f591(x11823,x11821),f591(x11823,x11822)) % 174.01/173.91 [1183]~E(x11831,x11832)+E(f548(x11831,x11833,x11834,x11835,x11836),f548(x11832,x11833,x11834,x11835,x11836)) % 174.01/173.91 [1184]~E(x11841,x11842)+E(f548(x11843,x11841,x11844,x11845,x11846),f548(x11843,x11842,x11844,x11845,x11846)) % 174.01/173.91 [1185]~E(x11851,x11852)+E(f548(x11853,x11854,x11851,x11855,x11856),f548(x11853,x11854,x11852,x11855,x11856)) % 174.01/173.91 [1186]~E(x11861,x11862)+E(f548(x11863,x11864,x11865,x11861,x11866),f548(x11863,x11864,x11865,x11862,x11866)) % 174.01/173.91 [1187]~E(x11871,x11872)+E(f548(x11873,x11874,x11875,x11876,x11871),f548(x11873,x11874,x11875,x11876,x11872)) % 174.01/173.91 [1188]~E(x11881,x11882)+E(f507(x11881,x11883,x11884,x11885),f507(x11882,x11883,x11884,x11885)) % 174.01/173.91 [1189]~E(x11891,x11892)+E(f507(x11893,x11891,x11894,x11895),f507(x11893,x11892,x11894,x11895)) % 174.01/173.91 [1190]~E(x11901,x11902)+E(f507(x11903,x11904,x11901,x11905),f507(x11903,x11904,x11902,x11905)) % 174.01/173.91 [1191]~E(x11911,x11912)+E(f507(x11913,x11914,x11915,x11911),f507(x11913,x11914,x11915,x11912)) % 174.01/173.91 [1192]~E(x11921,x11922)+E(f96(x11921,x11923,x11924),f96(x11922,x11923,x11924)) % 174.01/173.91 [1193]~E(x11931,x11932)+E(f96(x11933,x11931,x11934),f96(x11933,x11932,x11934)) % 174.01/173.91 [1194]~E(x11941,x11942)+E(f96(x11943,x11944,x11941),f96(x11943,x11944,x11942)) % 174.01/173.91 [1195]~E(x11951,x11952)+E(f652(x11951,x11953,x11954),f652(x11952,x11953,x11954)) % 174.01/173.91 [1196]~E(x11961,x11962)+E(f652(x11963,x11961,x11964),f652(x11963,x11962,x11964)) % 174.01/173.91 [1197]~E(x11971,x11972)+E(f652(x11973,x11974,x11971),f652(x11973,x11974,x11972)) % 174.01/173.91 [1198]~E(x11981,x11982)+E(f531(x11981,x11983,x11984,x11985),f531(x11982,x11983,x11984,x11985)) % 174.01/173.91 [1199]~E(x11991,x11992)+E(f531(x11993,x11991,x11994,x11995),f531(x11993,x11992,x11994,x11995)) % 174.01/173.91 [1200]~E(x12001,x12002)+E(f531(x12003,x12004,x12001,x12005),f531(x12003,x12004,x12002,x12005)) % 174.01/173.91 [1201]~E(x12011,x12012)+E(f531(x12013,x12014,x12015,x12011),f531(x12013,x12014,x12015,x12012)) % 174.01/173.91 [1202]~E(x12021,x12022)+E(f758(x12021,x12023,x12024,x12025),f758(x12022,x12023,x12024,x12025)) % 174.01/173.91 [1203]~E(x12031,x12032)+E(f758(x12033,x12031,x12034,x12035),f758(x12033,x12032,x12034,x12035)) % 174.01/173.91 [1204]~E(x12041,x12042)+E(f758(x12043,x12044,x12041,x12045),f758(x12043,x12044,x12042,x12045)) % 174.01/173.91 [1205]~E(x12051,x12052)+E(f758(x12053,x12054,x12055,x12051),f758(x12053,x12054,x12055,x12052)) % 174.01/173.91 [1206]~E(x12061,x12062)+E(f603(x12061,x12063),f603(x12062,x12063)) % 174.01/173.91 [1207]~E(x12071,x12072)+E(f603(x12073,x12071),f603(x12073,x12072)) % 174.01/173.91 [1208]~E(x12081,x12082)+E(f321(x12081,x12083,x12084,x12085,x12086),f321(x12082,x12083,x12084,x12085,x12086)) % 174.01/173.91 [1209]~E(x12091,x12092)+E(f321(x12093,x12091,x12094,x12095,x12096),f321(x12093,x12092,x12094,x12095,x12096)) % 174.01/173.91 [1210]~E(x12101,x12102)+E(f321(x12103,x12104,x12101,x12105,x12106),f321(x12103,x12104,x12102,x12105,x12106)) % 174.01/173.91 [1211]~E(x12111,x12112)+E(f321(x12113,x12114,x12115,x12111,x12116),f321(x12113,x12114,x12115,x12112,x12116)) % 174.01/173.91 [1212]~E(x12121,x12122)+E(f321(x12123,x12124,x12125,x12126,x12121),f321(x12123,x12124,x12125,x12126,x12122)) % 174.01/173.91 [1213]~E(x12131,x12132)+E(f560(x12131),f560(x12132)) % 174.01/173.91 [1214]~E(x12141,x12142)+E(f403(x12141),f403(x12142)) % 174.01/173.91 [1215]~E(x12151,x12152)+E(f276(x12151,x12153,x12154,x12155),f276(x12152,x12153,x12154,x12155)) % 174.01/173.91 [1216]~E(x12161,x12162)+E(f276(x12163,x12161,x12164,x12165),f276(x12163,x12162,x12164,x12165)) % 174.01/173.91 [1217]~E(x12171,x12172)+E(f276(x12173,x12174,x12171,x12175),f276(x12173,x12174,x12172,x12175)) % 174.01/173.91 [1218]~E(x12181,x12182)+E(f276(x12183,x12184,x12185,x12181),f276(x12183,x12184,x12185,x12182)) % 174.01/173.91 [1219]~E(x12191,x12192)+E(f541(x12191,x12193,x12194,x12195),f541(x12192,x12193,x12194,x12195)) % 174.01/173.91 [1220]~E(x12201,x12202)+E(f541(x12203,x12201,x12204,x12205),f541(x12203,x12202,x12204,x12205)) % 174.01/173.91 [1221]~E(x12211,x12212)+E(f541(x12213,x12214,x12211,x12215),f541(x12213,x12214,x12212,x12215)) % 174.01/173.91 [1222]~E(x12221,x12222)+E(f541(x12223,x12224,x12225,x12221),f541(x12223,x12224,x12225,x12222)) % 174.01/173.91 [1223]~E(x12231,x12232)+E(f184(x12231,x12233,x12234,x12235),f184(x12232,x12233,x12234,x12235)) % 174.01/173.91 [1224]~E(x12241,x12242)+E(f184(x12243,x12241,x12244,x12245),f184(x12243,x12242,x12244,x12245)) % 174.01/173.91 [1225]~E(x12251,x12252)+E(f184(x12253,x12254,x12251,x12255),f184(x12253,x12254,x12252,x12255)) % 174.01/173.91 [1226]~E(x12261,x12262)+E(f184(x12263,x12264,x12265,x12261),f184(x12263,x12264,x12265,x12262)) % 174.01/173.91 [1227]~E(x12271,x12272)+E(f428(x12271,x12273,x12274,x12275,x12276,x12277,x12278,x12279,x122710),f428(x12272,x12273,x12274,x12275,x12276,x12277,x12278,x12279,x122710)) % 174.01/173.91 [1228]~E(x12281,x12282)+E(f428(x12283,x12281,x12284,x12285,x12286,x12287,x12288,x12289,x122810),f428(x12283,x12282,x12284,x12285,x12286,x12287,x12288,x12289,x122810)) % 174.01/173.91 [1229]~E(x12291,x12292)+E(f428(x12293,x12294,x12291,x12295,x12296,x12297,x12298,x12299,x122910),f428(x12293,x12294,x12292,x12295,x12296,x12297,x12298,x12299,x122910)) % 174.01/173.91 [1230]~E(x12301,x12302)+E(f428(x12303,x12304,x12305,x12301,x12306,x12307,x12308,x12309,x123010),f428(x12303,x12304,x12305,x12302,x12306,x12307,x12308,x12309,x123010)) % 174.01/173.91 [1231]~E(x12311,x12312)+E(f428(x12313,x12314,x12315,x12316,x12311,x12317,x12318,x12319,x123110),f428(x12313,x12314,x12315,x12316,x12312,x12317,x12318,x12319,x123110)) % 174.01/173.91 [1232]~E(x12321,x12322)+E(f428(x12323,x12324,x12325,x12326,x12327,x12321,x12328,x12329,x123210),f428(x12323,x12324,x12325,x12326,x12327,x12322,x12328,x12329,x123210)) % 174.01/173.91 [1233]~E(x12331,x12332)+E(f428(x12333,x12334,x12335,x12336,x12337,x12338,x12331,x12339,x123310),f428(x12333,x12334,x12335,x12336,x12337,x12338,x12332,x12339,x123310)) % 174.01/173.91 [1234]~E(x12341,x12342)+E(f428(x12343,x12344,x12345,x12346,x12347,x12348,x12349,x12341,x123410),f428(x12343,x12344,x12345,x12346,x12347,x12348,x12349,x12342,x123410)) % 174.01/173.91 [1235]~E(x12351,x12352)+E(f428(x12353,x12354,x12355,x12356,x12357,x12358,x12359,x123510,x12351),f428(x12353,x12354,x12355,x12356,x12357,x12358,x12359,x123510,x12352)) % 174.01/173.91 [1236]~E(x12361,x12362)+E(f712(x12361,x12363,x12364,x12365),f712(x12362,x12363,x12364,x12365)) % 174.01/173.91 [1237]~E(x12371,x12372)+E(f712(x12373,x12371,x12374,x12375),f712(x12373,x12372,x12374,x12375)) % 174.01/173.91 [1238]~E(x12381,x12382)+E(f712(x12383,x12384,x12381,x12385),f712(x12383,x12384,x12382,x12385)) % 174.01/173.91 [1239]~E(x12391,x12392)+E(f712(x12393,x12394,x12395,x12391),f712(x12393,x12394,x12395,x12392)) % 174.01/173.91 [1240]~E(x12401,x12402)+E(f832(x12401,x12403,x12404),f832(x12402,x12403,x12404)) % 174.01/173.91 [1241]~E(x12411,x12412)+E(f832(x12413,x12411,x12414),f832(x12413,x12412,x12414)) % 174.01/173.91 [1242]~E(x12421,x12422)+E(f832(x12423,x12424,x12421),f832(x12423,x12424,x12422)) % 174.01/173.91 [1243]~E(x12431,x12432)+E(f610(x12431,x12433,x12434,x12435),f610(x12432,x12433,x12434,x12435)) % 174.01/173.91 [1244]~E(x12441,x12442)+E(f610(x12443,x12441,x12444,x12445),f610(x12443,x12442,x12444,x12445)) % 174.01/173.91 [1245]~E(x12451,x12452)+E(f610(x12453,x12454,x12451,x12455),f610(x12453,x12454,x12452,x12455)) % 174.01/173.91 [1246]~E(x12461,x12462)+E(f610(x12463,x12464,x12465,x12461),f610(x12463,x12464,x12465,x12462)) % 174.01/173.91 [1247]~E(x12471,x12472)+E(f575(x12471,x12473,x12474,x12475,x12476,x12477,x12478,x12479),f575(x12472,x12473,x12474,x12475,x12476,x12477,x12478,x12479)) % 174.01/173.91 [1248]~E(x12481,x12482)+E(f575(x12483,x12481,x12484,x12485,x12486,x12487,x12488,x12489),f575(x12483,x12482,x12484,x12485,x12486,x12487,x12488,x12489)) % 174.01/173.91 [1249]~E(x12491,x12492)+E(f575(x12493,x12494,x12491,x12495,x12496,x12497,x12498,x12499),f575(x12493,x12494,x12492,x12495,x12496,x12497,x12498,x12499)) % 174.01/173.91 [1250]~E(x12501,x12502)+E(f575(x12503,x12504,x12505,x12501,x12506,x12507,x12508,x12509),f575(x12503,x12504,x12505,x12502,x12506,x12507,x12508,x12509)) % 174.01/173.91 [1251]~E(x12511,x12512)+E(f575(x12513,x12514,x12515,x12516,x12511,x12517,x12518,x12519),f575(x12513,x12514,x12515,x12516,x12512,x12517,x12518,x12519)) % 174.01/173.91 [1252]~E(x12521,x12522)+E(f575(x12523,x12524,x12525,x12526,x12527,x12521,x12528,x12529),f575(x12523,x12524,x12525,x12526,x12527,x12522,x12528,x12529)) % 174.01/173.91 [1253]~E(x12531,x12532)+E(f575(x12533,x12534,x12535,x12536,x12537,x12538,x12531,x12539),f575(x12533,x12534,x12535,x12536,x12537,x12538,x12532,x12539)) % 174.01/173.91 [1254]~E(x12541,x12542)+E(f575(x12543,x12544,x12545,x12546,x12547,x12548,x12549,x12541),f575(x12543,x12544,x12545,x12546,x12547,x12548,x12549,x12542)) % 174.01/173.91 [1255]~E(x12551,x12552)+E(f580(x12551,x12553,x12554,x12555,x12556,x12557,x12558),f580(x12552,x12553,x12554,x12555,x12556,x12557,x12558)) % 174.01/173.91 [1256]~E(x12561,x12562)+E(f580(x12563,x12561,x12564,x12565,x12566,x12567,x12568),f580(x12563,x12562,x12564,x12565,x12566,x12567,x12568)) % 174.01/173.91 [1257]~E(x12571,x12572)+E(f580(x12573,x12574,x12571,x12575,x12576,x12577,x12578),f580(x12573,x12574,x12572,x12575,x12576,x12577,x12578)) % 174.01/173.91 [1258]~E(x12581,x12582)+E(f580(x12583,x12584,x12585,x12581,x12586,x12587,x12588),f580(x12583,x12584,x12585,x12582,x12586,x12587,x12588)) % 174.01/173.91 [1259]~E(x12591,x12592)+E(f580(x12593,x12594,x12595,x12596,x12591,x12597,x12598),f580(x12593,x12594,x12595,x12596,x12592,x12597,x12598)) % 174.01/173.91 [1260]~E(x12601,x12602)+E(f580(x12603,x12604,x12605,x12606,x12607,x12601,x12608),f580(x12603,x12604,x12605,x12606,x12607,x12602,x12608)) % 174.01/173.91 [1261]~E(x12611,x12612)+E(f580(x12613,x12614,x12615,x12616,x12617,x12618,x12611),f580(x12613,x12614,x12615,x12616,x12617,x12618,x12612)) % 174.01/173.91 [1262]~E(x12621,x12622)+E(f420(x12621,x12623,x12624),f420(x12622,x12623,x12624)) % 174.01/173.91 [1263]~E(x12631,x12632)+E(f420(x12633,x12631,x12634),f420(x12633,x12632,x12634)) % 174.01/173.91 [1264]~E(x12641,x12642)+E(f420(x12643,x12644,x12641),f420(x12643,x12644,x12642)) % 174.01/173.91 [1265]~E(x12651,x12652)+E(f227(x12651,x12653,x12654,x12655),f227(x12652,x12653,x12654,x12655)) % 174.01/173.91 [1266]~E(x12661,x12662)+E(f227(x12663,x12661,x12664,x12665),f227(x12663,x12662,x12664,x12665)) % 174.01/173.91 [1267]~E(x12671,x12672)+E(f227(x12673,x12674,x12671,x12675),f227(x12673,x12674,x12672,x12675)) % 174.01/173.91 [1268]~E(x12681,x12682)+E(f227(x12683,x12684,x12685,x12681),f227(x12683,x12684,x12685,x12682)) % 174.01/173.91 [1269]~E(x12691,x12692)+E(f274(x12691,x12693,x12694,x12695),f274(x12692,x12693,x12694,x12695)) % 174.01/173.91 [1270]~E(x12701,x12702)+E(f274(x12703,x12701,x12704,x12705),f274(x12703,x12702,x12704,x12705)) % 174.01/173.91 [1271]~E(x12711,x12712)+E(f274(x12713,x12714,x12711,x12715),f274(x12713,x12714,x12712,x12715)) % 174.01/173.91 [1272]~E(x12721,x12722)+E(f274(x12723,x12724,x12725,x12721),f274(x12723,x12724,x12725,x12722)) % 174.01/173.91 [1273]~E(x12731,x12732)+E(f550(x12731,x12733,x12734),f550(x12732,x12733,x12734)) % 174.01/173.91 [1274]~E(x12741,x12742)+E(f550(x12743,x12741,x12744),f550(x12743,x12742,x12744)) % 174.01/173.91 [1275]~E(x12751,x12752)+E(f550(x12753,x12754,x12751),f550(x12753,x12754,x12752)) % 174.01/173.91 [1276]~E(x12761,x12762)+E(f380(x12761,x12763,x12764,x12765),f380(x12762,x12763,x12764,x12765)) % 174.01/173.91 [1277]~E(x12771,x12772)+E(f380(x12773,x12771,x12774,x12775),f380(x12773,x12772,x12774,x12775)) % 174.01/173.91 [1278]~E(x12781,x12782)+E(f380(x12783,x12784,x12781,x12785),f380(x12783,x12784,x12782,x12785)) % 174.01/173.91 [1279]~E(x12791,x12792)+E(f380(x12793,x12794,x12795,x12791),f380(x12793,x12794,x12795,x12792)) % 174.01/173.91 [1280]~E(x12801,x12802)+E(f386(x12801,x12803,x12804,x12805),f386(x12802,x12803,x12804,x12805)) % 174.01/173.91 [1281]~E(x12811,x12812)+E(f386(x12813,x12811,x12814,x12815),f386(x12813,x12812,x12814,x12815)) % 174.01/173.91 [1282]~E(x12821,x12822)+E(f386(x12823,x12824,x12821,x12825),f386(x12823,x12824,x12822,x12825)) % 174.01/173.91 [1283]~E(x12831,x12832)+E(f386(x12833,x12834,x12835,x12831),f386(x12833,x12834,x12835,x12832)) % 174.01/173.91 [1284]~E(x12841,x12842)+E(f561(x12841,x12843),f561(x12842,x12843)) % 174.01/173.91 [1285]~E(x12851,x12852)+E(f561(x12853,x12851),f561(x12853,x12852)) % 174.01/173.91 [1286]~E(x12861,x12862)+E(f463(x12861,x12863,x12864,x12865),f463(x12862,x12863,x12864,x12865)) % 174.01/173.91 [1287]~E(x12871,x12872)+E(f463(x12873,x12871,x12874,x12875),f463(x12873,x12872,x12874,x12875)) % 174.01/173.91 [1288]~E(x12881,x12882)+E(f463(x12883,x12884,x12881,x12885),f463(x12883,x12884,x12882,x12885)) % 174.01/173.91 [1289]~E(x12891,x12892)+E(f463(x12893,x12894,x12895,x12891),f463(x12893,x12894,x12895,x12892)) % 174.01/173.91 [1290]~E(x12901,x12902)+E(f623(x12901,x12903,x12904),f623(x12902,x12903,x12904)) % 174.01/173.91 [1291]~E(x12911,x12912)+E(f623(x12913,x12911,x12914),f623(x12913,x12912,x12914)) % 174.01/173.91 [1292]~E(x12921,x12922)+E(f623(x12923,x12924,x12921),f623(x12923,x12924,x12922)) % 174.01/173.91 [1293]~E(x12931,x12932)+E(f796(x12931,x12933,x12934),f796(x12932,x12933,x12934)) % 174.01/173.91 [1294]~E(x12941,x12942)+E(f796(x12943,x12941,x12944),f796(x12943,x12942,x12944)) % 174.01/173.91 [1295]~E(x12951,x12952)+E(f796(x12953,x12954,x12951),f796(x12953,x12954,x12952)) % 174.01/173.91 [1296]~E(x12961,x12962)+E(f407(x12961,x12963,x12964),f407(x12962,x12963,x12964)) % 174.01/173.91 [1297]~E(x12971,x12972)+E(f407(x12973,x12971,x12974),f407(x12973,x12972,x12974)) % 174.01/173.91 [1298]~E(x12981,x12982)+E(f407(x12983,x12984,x12981),f407(x12983,x12984,x12982)) % 174.01/173.91 [1299]~E(x12991,x12992)+E(f655(x12991,x12993),f655(x12992,x12993)) % 174.01/173.91 [1300]~E(x13001,x13002)+E(f655(x13003,x13001),f655(x13003,x13002)) % 174.01/173.91 [1301]~E(x13011,x13012)+E(f553(x13011,x13013,x13014,x13015,x13016),f553(x13012,x13013,x13014,x13015,x13016)) % 174.01/173.91 [1302]~E(x13021,x13022)+E(f553(x13023,x13021,x13024,x13025,x13026),f553(x13023,x13022,x13024,x13025,x13026)) % 174.01/173.91 [1303]~E(x13031,x13032)+E(f553(x13033,x13034,x13031,x13035,x13036),f553(x13033,x13034,x13032,x13035,x13036)) % 174.01/173.91 [1304]~E(x13041,x13042)+E(f553(x13043,x13044,x13045,x13041,x13046),f553(x13043,x13044,x13045,x13042,x13046)) % 174.01/173.91 [1305]~E(x13051,x13052)+E(f553(x13053,x13054,x13055,x13056,x13051),f553(x13053,x13054,x13055,x13056,x13052)) % 174.01/173.91 [1306]~E(x13061,x13062)+E(f412(x13061,x13063,x13064,x13065),f412(x13062,x13063,x13064,x13065)) % 174.01/173.91 [1307]~E(x13071,x13072)+E(f412(x13073,x13071,x13074,x13075),f412(x13073,x13072,x13074,x13075)) % 174.01/173.91 [1308]~E(x13081,x13082)+E(f412(x13083,x13084,x13081,x13085),f412(x13083,x13084,x13082,x13085)) % 174.01/173.91 [1309]~E(x13091,x13092)+E(f412(x13093,x13094,x13095,x13091),f412(x13093,x13094,x13095,x13092)) % 174.01/173.91 [1310]~E(x13101,x13102)+E(f583(x13101,x13103),f583(x13102,x13103)) % 174.01/173.91 [1311]~E(x13111,x13112)+E(f583(x13113,x13111),f583(x13113,x13112)) % 174.01/173.91 [1312]~E(x13121,x13122)+E(f658(x13121,x13123,x13124,x13125,x13126),f658(x13122,x13123,x13124,x13125,x13126)) % 174.01/173.91 [1313]~E(x13131,x13132)+E(f658(x13133,x13131,x13134,x13135,x13136),f658(x13133,x13132,x13134,x13135,x13136)) % 174.01/173.91 [1314]~E(x13141,x13142)+E(f658(x13143,x13144,x13141,x13145,x13146),f658(x13143,x13144,x13142,x13145,x13146)) % 174.01/173.91 [1315]~E(x13151,x13152)+E(f658(x13153,x13154,x13155,x13151,x13156),f658(x13153,x13154,x13155,x13152,x13156)) % 174.01/173.91 [1316]~E(x13161,x13162)+E(f658(x13163,x13164,x13165,x13166,x13161),f658(x13163,x13164,x13165,x13166,x13162)) % 174.01/173.91 [1317]~E(x13171,x13172)+E(f780(x13171),f780(x13172)) % 174.01/173.91 [1318]~E(x13181,x13182)+E(f413(x13181,x13183,x13184,x13185),f413(x13182,x13183,x13184,x13185)) % 174.01/173.91 [1319]~E(x13191,x13192)+E(f413(x13193,x13191,x13194,x13195),f413(x13193,x13192,x13194,x13195)) % 174.01/173.91 [1320]~E(x13201,x13202)+E(f413(x13203,x13204,x13201,x13205),f413(x13203,x13204,x13202,x13205)) % 174.01/173.91 [1321]~E(x13211,x13212)+E(f413(x13213,x13214,x13215,x13211),f413(x13213,x13214,x13215,x13212)) % 174.01/173.91 [1322]~E(x13221,x13222)+E(f691(x13221,x13223,x13224,x13225),f691(x13222,x13223,x13224,x13225)) % 174.01/173.91 [1323]~E(x13231,x13232)+E(f691(x13233,x13231,x13234,x13235),f691(x13233,x13232,x13234,x13235)) % 174.01/173.91 [1324]~E(x13241,x13242)+E(f691(x13243,x13244,x13241,x13245),f691(x13243,x13244,x13242,x13245)) % 174.01/173.91 [1325]~E(x13251,x13252)+E(f691(x13253,x13254,x13255,x13251),f691(x13253,x13254,x13255,x13252)) % 174.01/173.91 [1326]~E(x13261,x13262)+E(f785(x13261,x13263,x13264),f785(x13262,x13263,x13264)) % 174.01/173.91 [1327]~E(x13271,x13272)+E(f785(x13273,x13271,x13274),f785(x13273,x13272,x13274)) % 174.01/173.91 [1328]~E(x13281,x13282)+E(f785(x13283,x13284,x13281),f785(x13283,x13284,x13282)) % 174.01/173.91 [1329]~E(x13291,x13292)+E(f383(x13291,x13293,x13294,x13295),f383(x13292,x13293,x13294,x13295)) % 174.01/173.91 [1330]~E(x13301,x13302)+E(f383(x13303,x13301,x13304,x13305),f383(x13303,x13302,x13304,x13305)) % 174.01/173.91 [1331]~E(x13311,x13312)+E(f383(x13313,x13314,x13311,x13315),f383(x13313,x13314,x13312,x13315)) % 174.01/173.91 [1332]~E(x13321,x13322)+E(f383(x13323,x13324,x13325,x13321),f383(x13323,x13324,x13325,x13322)) % 174.01/173.91 [1333]~E(x13331,x13332)+E(f138(x13331,x13333),f138(x13332,x13333)) % 174.01/173.91 [1334]~E(x13341,x13342)+E(f138(x13343,x13341),f138(x13343,x13342)) % 174.01/173.91 [1335]~E(x13351,x13352)+E(f699(x13351,x13353,x13354),f699(x13352,x13353,x13354)) % 174.01/173.91 [1336]~E(x13361,x13362)+E(f699(x13363,x13361,x13364),f699(x13363,x13362,x13364)) % 174.01/173.91 [1337]~E(x13371,x13372)+E(f699(x13373,x13374,x13371),f699(x13373,x13374,x13372)) % 174.01/173.91 [1338]~E(x13381,x13382)+E(f329(x13381,x13383,x13384),f329(x13382,x13383,x13384)) % 174.01/173.91 [1339]~E(x13391,x13392)+E(f329(x13393,x13391,x13394),f329(x13393,x13392,x13394)) % 174.01/173.91 [1340]~E(x13401,x13402)+E(f329(x13403,x13404,x13401),f329(x13403,x13404,x13402)) % 174.01/173.91 [1341]~E(x13411,x13412)+E(f703(x13411,x13413,x13414,x13415),f703(x13412,x13413,x13414,x13415)) % 174.01/173.91 [1342]~E(x13421,x13422)+E(f703(x13423,x13421,x13424,x13425),f703(x13423,x13422,x13424,x13425)) % 174.01/173.91 [1343]~E(x13431,x13432)+E(f703(x13433,x13434,x13431,x13435),f703(x13433,x13434,x13432,x13435)) % 174.01/173.91 [1344]~E(x13441,x13442)+E(f703(x13443,x13444,x13445,x13441),f703(x13443,x13444,x13445,x13442)) % 174.01/173.91 [1345]~E(x13451,x13452)+E(f347(x13451,x13453,x13454,x13455),f347(x13452,x13453,x13454,x13455)) % 174.01/173.91 [1346]~E(x13461,x13462)+E(f347(x13463,x13461,x13464,x13465),f347(x13463,x13462,x13464,x13465)) % 174.01/173.91 [1347]~E(x13471,x13472)+E(f347(x13473,x13474,x13471,x13475),f347(x13473,x13474,x13472,x13475)) % 174.01/173.91 [1348]~E(x13481,x13482)+E(f347(x13483,x13484,x13485,x13481),f347(x13483,x13484,x13485,x13482)) % 174.01/173.91 [1349]~E(x13491,x13492)+E(f375(x13491,x13493),f375(x13492,x13493)) % 174.01/173.91 [1350]~E(x13501,x13502)+E(f375(x13503,x13501),f375(x13503,x13502)) % 174.01/173.91 [1351]~E(x13511,x13512)+E(f681(x13511,x13513,x13514),f681(x13512,x13513,x13514)) % 174.01/173.91 [1352]~E(x13521,x13522)+E(f681(x13523,x13521,x13524),f681(x13523,x13522,x13524)) % 174.01/173.91 [1353]~E(x13531,x13532)+E(f681(x13533,x13534,x13531),f681(x13533,x13534,x13532)) % 174.01/173.91 [1354]~E(x13541,x13542)+E(f807(x13541,x13543,x13544),f807(x13542,x13543,x13544)) % 174.01/173.91 [1355]~E(x13551,x13552)+E(f807(x13553,x13551,x13554),f807(x13553,x13552,x13554)) % 174.01/173.91 [1356]~E(x13561,x13562)+E(f807(x13563,x13564,x13561),f807(x13563,x13564,x13562)) % 174.01/173.91 [1357]~E(x13571,x13572)+E(f222(x13571,x13573,x13574,x13575,x13576),f222(x13572,x13573,x13574,x13575,x13576)) % 174.01/173.91 [1358]~E(x13581,x13582)+E(f222(x13583,x13581,x13584,x13585,x13586),f222(x13583,x13582,x13584,x13585,x13586)) % 174.01/173.91 [1359]~E(x13591,x13592)+E(f222(x13593,x13594,x13591,x13595,x13596),f222(x13593,x13594,x13592,x13595,x13596)) % 174.01/173.91 [1360]~E(x13601,x13602)+E(f222(x13603,x13604,x13605,x13601,x13606),f222(x13603,x13604,x13605,x13602,x13606)) % 174.01/173.91 [1361]~E(x13611,x13612)+E(f222(x13613,x13614,x13615,x13616,x13611),f222(x13613,x13614,x13615,x13616,x13612)) % 174.01/173.91 [1362]~E(x13621,x13622)+E(f225(x13621,x13623,x13624,x13625),f225(x13622,x13623,x13624,x13625)) % 174.01/173.91 [1363]~E(x13631,x13632)+E(f225(x13633,x13631,x13634,x13635),f225(x13633,x13632,x13634,x13635)) % 174.01/173.91 [1364]~E(x13641,x13642)+E(f225(x13643,x13644,x13641,x13645),f225(x13643,x13644,x13642,x13645)) % 174.01/173.91 [1365]~E(x13651,x13652)+E(f225(x13653,x13654,x13655,x13651),f225(x13653,x13654,x13655,x13652)) % 174.01/173.91 [1366]~E(x13661,x13662)+E(f748(x13661,x13663,x13664),f748(x13662,x13663,x13664)) % 174.01/173.91 [1367]~E(x13671,x13672)+E(f748(x13673,x13671,x13674),f748(x13673,x13672,x13674)) % 174.01/173.91 [1368]~E(x13681,x13682)+E(f748(x13683,x13684,x13681),f748(x13683,x13684,x13682)) % 174.01/173.91 [1369]~E(x13691,x13692)+E(f770(x13691,x13693,x13694),f770(x13692,x13693,x13694)) % 174.01/173.91 [1370]~E(x13701,x13702)+E(f770(x13703,x13701,x13704),f770(x13703,x13702,x13704)) % 174.01/173.91 [1371]~E(x13711,x13712)+E(f770(x13713,x13714,x13711),f770(x13713,x13714,x13712)) % 174.01/173.91 [1372]~E(x13721,x13722)+E(f840(x13721,x13723),f840(x13722,x13723)) % 174.01/173.91 [1373]~E(x13731,x13732)+E(f840(x13733,x13731),f840(x13733,x13732)) % 174.01/173.91 [1374]~E(x13741,x13742)+E(f501(x13741,x13743,x13744,x13745,x13746,x13747,x13748),f501(x13742,x13743,x13744,x13745,x13746,x13747,x13748)) % 174.01/173.91 [1375]~E(x13751,x13752)+E(f501(x13753,x13751,x13754,x13755,x13756,x13757,x13758),f501(x13753,x13752,x13754,x13755,x13756,x13757,x13758)) % 174.01/173.91 [1376]~E(x13761,x13762)+E(f501(x13763,x13764,x13761,x13765,x13766,x13767,x13768),f501(x13763,x13764,x13762,x13765,x13766,x13767,x13768)) % 174.01/173.91 [1377]~E(x13771,x13772)+E(f501(x13773,x13774,x13775,x13771,x13776,x13777,x13778),f501(x13773,x13774,x13775,x13772,x13776,x13777,x13778)) % 174.01/173.91 [1378]~E(x13781,x13782)+E(f501(x13783,x13784,x13785,x13786,x13781,x13787,x13788),f501(x13783,x13784,x13785,x13786,x13782,x13787,x13788)) % 174.01/173.91 [1379]~E(x13791,x13792)+E(f501(x13793,x13794,x13795,x13796,x13797,x13791,x13798),f501(x13793,x13794,x13795,x13796,x13797,x13792,x13798)) % 174.01/173.91 [1380]~E(x13801,x13802)+E(f501(x13803,x13804,x13805,x13806,x13807,x13808,x13801),f501(x13803,x13804,x13805,x13806,x13807,x13808,x13802)) % 174.01/173.91 [1381]~E(x13811,x13812)+E(f405(x13811,x13813),f405(x13812,x13813)) % 174.01/173.91 [1382]~E(x13821,x13822)+E(f405(x13823,x13821),f405(x13823,x13822)) % 174.01/173.91 [1383]~E(x13831,x13832)+E(f555(x13831,x13833,x13834),f555(x13832,x13833,x13834)) % 174.01/173.91 [1384]~E(x13841,x13842)+E(f555(x13843,x13841,x13844),f555(x13843,x13842,x13844)) % 174.01/173.91 [1385]~E(x13851,x13852)+E(f555(x13853,x13854,x13851),f555(x13853,x13854,x13852)) % 174.01/173.91 [1386]~E(x13861,x13862)+E(f839(x13861,x13863,x13864),f839(x13862,x13863,x13864)) % 174.01/173.91 [1387]~E(x13871,x13872)+E(f839(x13873,x13871,x13874),f839(x13873,x13872,x13874)) % 174.01/173.91 [1388]~E(x13881,x13882)+E(f839(x13883,x13884,x13881),f839(x13883,x13884,x13882)) % 174.01/173.91 [1389]~E(x13891,x13892)+E(f495(x13891,x13893,x13894),f495(x13892,x13893,x13894)) % 174.01/173.91 [1390]~E(x13901,x13902)+E(f495(x13903,x13901,x13904),f495(x13903,x13902,x13904)) % 174.01/173.91 [1391]~E(x13911,x13912)+E(f495(x13913,x13914,x13911),f495(x13913,x13914,x13912)) % 174.01/173.91 [1392]~E(x13921,x13922)+E(f827(x13921,x13923,x13924),f827(x13922,x13923,x13924)) % 174.01/173.91 [1393]~E(x13931,x13932)+E(f827(x13933,x13931,x13934),f827(x13933,x13932,x13934)) % 174.01/173.91 [1394]~E(x13941,x13942)+E(f827(x13943,x13944,x13941),f827(x13943,x13944,x13942)) % 174.01/173.91 [1395]~E(x13951,x13952)+E(f705(x13951,x13953,x13954,x13955,x13956),f705(x13952,x13953,x13954,x13955,x13956)) % 174.01/173.91 [1396]~E(x13961,x13962)+E(f705(x13963,x13961,x13964,x13965,x13966),f705(x13963,x13962,x13964,x13965,x13966)) % 174.01/173.91 [1397]~E(x13971,x13972)+E(f705(x13973,x13974,x13971,x13975,x13976),f705(x13973,x13974,x13972,x13975,x13976)) % 174.01/173.91 [1398]~E(x13981,x13982)+E(f705(x13983,x13984,x13985,x13981,x13986),f705(x13983,x13984,x13985,x13982,x13986)) % 174.01/173.91 [1399]~E(x13991,x13992)+E(f705(x13993,x13994,x13995,x13996,x13991),f705(x13993,x13994,x13995,x13996,x13992)) % 174.01/173.91 [1400]~E(x14001,x14002)+E(f269(x14001,x14003),f269(x14002,x14003)) % 174.01/173.91 [1401]~E(x14011,x14012)+E(f269(x14013,x14011),f269(x14013,x14012)) % 174.01/173.91 [1402]~E(x14021,x14022)+E(f465(x14021,x14023,x14024,x14025,x14026),f465(x14022,x14023,x14024,x14025,x14026)) % 174.01/173.91 [1403]~E(x14031,x14032)+E(f465(x14033,x14031,x14034,x14035,x14036),f465(x14033,x14032,x14034,x14035,x14036)) % 174.01/173.91 [1404]~E(x14041,x14042)+E(f465(x14043,x14044,x14041,x14045,x14046),f465(x14043,x14044,x14042,x14045,x14046)) % 174.01/173.91 [1405]~E(x14051,x14052)+E(f465(x14053,x14054,x14055,x14051,x14056),f465(x14053,x14054,x14055,x14052,x14056)) % 174.01/173.91 [1406]~E(x14061,x14062)+E(f465(x14063,x14064,x14065,x14066,x14061),f465(x14063,x14064,x14065,x14066,x14062)) % 174.01/173.91 [1407]~E(x14071,x14072)+E(f656(x14071,x14073,x14074,x14075),f656(x14072,x14073,x14074,x14075)) % 174.01/173.91 [1408]~E(x14081,x14082)+E(f656(x14083,x14081,x14084,x14085),f656(x14083,x14082,x14084,x14085)) % 174.01/173.91 [1409]~E(x14091,x14092)+E(f656(x14093,x14094,x14091,x14095),f656(x14093,x14094,x14092,x14095)) % 174.01/173.91 [1410]~E(x14101,x14102)+E(f656(x14103,x14104,x14105,x14101),f656(x14103,x14104,x14105,x14102)) % 174.01/173.91 [1411]~E(x14111,x14112)+E(f319(x14111,x14113,x14114,x14115),f319(x14112,x14113,x14114,x14115)) % 174.01/173.91 [1412]~E(x14121,x14122)+E(f319(x14123,x14121,x14124,x14125),f319(x14123,x14122,x14124,x14125)) % 174.01/173.91 [1413]~E(x14131,x14132)+E(f319(x14133,x14134,x14131,x14135),f319(x14133,x14134,x14132,x14135)) % 174.01/173.91 [1414]~E(x14141,x14142)+E(f319(x14143,x14144,x14145,x14141),f319(x14143,x14144,x14145,x14142)) % 174.01/173.91 [1415]~E(x14151,x14152)+E(f230(x14151,x14153,x14154),f230(x14152,x14153,x14154)) % 174.01/173.91 [1416]~E(x14161,x14162)+E(f230(x14163,x14161,x14164),f230(x14163,x14162,x14164)) % 174.01/173.91 [1417]~E(x14171,x14172)+E(f230(x14173,x14174,x14171),f230(x14173,x14174,x14172)) % 174.01/173.91 [1418]~E(x14181,x14182)+E(f825(x14181,x14183,x14184),f825(x14182,x14183,x14184)) % 174.01/173.91 [1419]~E(x14191,x14192)+E(f825(x14193,x14191,x14194),f825(x14193,x14192,x14194)) % 174.01/173.91 [1420]~E(x14201,x14202)+E(f825(x14203,x14204,x14201),f825(x14203,x14204,x14202)) % 174.01/173.91 [1421]~E(x14211,x14212)+E(f499(x14211,x14213,x14214),f499(x14212,x14213,x14214)) % 174.01/173.91 [1422]~E(x14221,x14222)+E(f499(x14223,x14221,x14224),f499(x14223,x14222,x14224)) % 174.01/173.91 [1423]~E(x14231,x14232)+E(f499(x14233,x14234,x14231),f499(x14233,x14234,x14232)) % 174.01/173.91 [1424]~E(x14241,x14242)+E(f363(x14241,x14243,x14244,x14245,x14246),f363(x14242,x14243,x14244,x14245,x14246)) % 174.01/173.91 [1425]~E(x14251,x14252)+E(f363(x14253,x14251,x14254,x14255,x14256),f363(x14253,x14252,x14254,x14255,x14256)) % 174.01/173.91 [1426]~E(x14261,x14262)+E(f363(x14263,x14264,x14261,x14265,x14266),f363(x14263,x14264,x14262,x14265,x14266)) % 174.01/173.91 [1427]~E(x14271,x14272)+E(f363(x14273,x14274,x14275,x14271,x14276),f363(x14273,x14274,x14275,x14272,x14276)) % 174.01/173.91 [1428]~E(x14281,x14282)+E(f363(x14283,x14284,x14285,x14286,x14281),f363(x14283,x14284,x14285,x14286,x14282)) % 174.01/173.91 [1429]~E(x14291,x14292)+E(f378(x14291),f378(x14292)) % 174.01/173.91 [1430]~E(x14301,x14302)+E(f669(x14301,x14303,x14304,x14305,x14306),f669(x14302,x14303,x14304,x14305,x14306)) % 174.01/173.91 [1431]~E(x14311,x14312)+E(f669(x14313,x14311,x14314,x14315,x14316),f669(x14313,x14312,x14314,x14315,x14316)) % 174.01/173.91 [1432]~E(x14321,x14322)+E(f669(x14323,x14324,x14321,x14325,x14326),f669(x14323,x14324,x14322,x14325,x14326)) % 174.01/173.91 [1433]~E(x14331,x14332)+E(f669(x14333,x14334,x14335,x14331,x14336),f669(x14333,x14334,x14335,x14332,x14336)) % 174.01/173.91 [1434]~E(x14341,x14342)+E(f669(x14343,x14344,x14345,x14346,x14341),f669(x14343,x14344,x14345,x14346,x14342)) % 174.01/173.91 [1435]~E(x14351,x14352)+E(f576(x14351,x14353,x14354,x14355,x14356,x14357,x14358,x14359),f576(x14352,x14353,x14354,x14355,x14356,x14357,x14358,x14359)) % 174.01/173.91 [1436]~E(x14361,x14362)+E(f576(x14363,x14361,x14364,x14365,x14366,x14367,x14368,x14369),f576(x14363,x14362,x14364,x14365,x14366,x14367,x14368,x14369)) % 174.01/173.91 [1437]~E(x14371,x14372)+E(f576(x14373,x14374,x14371,x14375,x14376,x14377,x14378,x14379),f576(x14373,x14374,x14372,x14375,x14376,x14377,x14378,x14379)) % 174.01/173.91 [1438]~E(x14381,x14382)+E(f576(x14383,x14384,x14385,x14381,x14386,x14387,x14388,x14389),f576(x14383,x14384,x14385,x14382,x14386,x14387,x14388,x14389)) % 174.01/173.91 [1439]~E(x14391,x14392)+E(f576(x14393,x14394,x14395,x14396,x14391,x14397,x14398,x14399),f576(x14393,x14394,x14395,x14396,x14392,x14397,x14398,x14399)) % 174.01/173.91 [1440]~E(x14401,x14402)+E(f576(x14403,x14404,x14405,x14406,x14407,x14401,x14408,x14409),f576(x14403,x14404,x14405,x14406,x14407,x14402,x14408,x14409)) % 174.01/173.91 [1441]~E(x14411,x14412)+E(f576(x14413,x14414,x14415,x14416,x14417,x14418,x14411,x14419),f576(x14413,x14414,x14415,x14416,x14417,x14418,x14412,x14419)) % 174.01/173.91 [1442]~E(x14421,x14422)+E(f576(x14423,x14424,x14425,x14426,x14427,x14428,x14429,x14421),f576(x14423,x14424,x14425,x14426,x14427,x14428,x14429,x14422)) % 174.01/173.91 [1443]~E(x14431,x14432)+E(f799(x14431,x14433,x14434,x14435),f799(x14432,x14433,x14434,x14435)) % 174.01/173.91 [1444]~E(x14441,x14442)+E(f799(x14443,x14441,x14444,x14445),f799(x14443,x14442,x14444,x14445)) % 174.01/173.91 [1445]~E(x14451,x14452)+E(f799(x14453,x14454,x14451,x14455),f799(x14453,x14454,x14452,x14455)) % 174.01/173.91 [1446]~E(x14461,x14462)+E(f799(x14463,x14464,x14465,x14461),f799(x14463,x14464,x14465,x14462)) % 174.01/173.91 [1447]~E(x14471,x14472)+E(f664(x14471,x14473,x14474,x14475),f664(x14472,x14473,x14474,x14475)) % 174.01/173.91 [1448]~E(x14481,x14482)+E(f664(x14483,x14481,x14484,x14485),f664(x14483,x14482,x14484,x14485)) % 174.01/173.91 [1449]~E(x14491,x14492)+E(f664(x14493,x14494,x14491,x14495),f664(x14493,x14494,x14492,x14495)) % 174.01/173.91 [1450]~E(x14501,x14502)+E(f664(x14503,x14504,x14505,x14501),f664(x14503,x14504,x14505,x14502)) % 174.01/173.91 [1451]~E(x14511,x14512)+E(f700(x14511,x14513),f700(x14512,x14513)) % 174.01/173.91 [1452]~E(x14521,x14522)+E(f700(x14523,x14521),f700(x14523,x14522)) % 174.01/173.91 [1453]~E(x14531,x14532)+E(f508(x14531,x14533,x14534),f508(x14532,x14533,x14534)) % 174.01/173.91 [1454]~E(x14541,x14542)+E(f508(x14543,x14541,x14544),f508(x14543,x14542,x14544)) % 174.01/173.91 [1455]~E(x14551,x14552)+E(f508(x14553,x14554,x14551),f508(x14553,x14554,x14552)) % 174.01/173.91 [1456]~E(x14561,x14562)+E(f605(x14561,x14563),f605(x14562,x14563)) % 174.01/173.91 [1457]~E(x14571,x14572)+E(f605(x14573,x14571),f605(x14573,x14572)) % 174.01/173.91 [1458]~E(x14581,x14582)+E(f364(x14581,x14583,x14584,x14585,x14586),f364(x14582,x14583,x14584,x14585,x14586)) % 174.01/173.91 [1459]~E(x14591,x14592)+E(f364(x14593,x14591,x14594,x14595,x14596),f364(x14593,x14592,x14594,x14595,x14596)) % 174.01/173.91 [1460]~E(x14601,x14602)+E(f364(x14603,x14604,x14601,x14605,x14606),f364(x14603,x14604,x14602,x14605,x14606)) % 174.01/173.91 [1461]~E(x14611,x14612)+E(f364(x14613,x14614,x14615,x14611,x14616),f364(x14613,x14614,x14615,x14612,x14616)) % 174.01/173.91 [1462]~E(x14621,x14622)+E(f364(x14623,x14624,x14625,x14626,x14621),f364(x14623,x14624,x14625,x14626,x14622)) % 174.01/173.91 [1463]~E(x14631,x14632)+E(f404(x14631,x14633),f404(x14632,x14633)) % 174.01/173.91 [1464]~E(x14641,x14642)+E(f404(x14643,x14641),f404(x14643,x14642)) % 174.01/173.91 [1465]~E(x14651,x14652)+E(f597(x14651,x14653,x14654,x14655),f597(x14652,x14653,x14654,x14655)) % 174.01/173.91 [1466]~E(x14661,x14662)+E(f597(x14663,x14661,x14664,x14665),f597(x14663,x14662,x14664,x14665)) % 174.01/173.91 [1467]~E(x14671,x14672)+E(f597(x14673,x14674,x14671,x14675),f597(x14673,x14674,x14672,x14675)) % 174.01/173.91 [1468]~E(x14681,x14682)+E(f597(x14683,x14684,x14685,x14681),f597(x14683,x14684,x14685,x14682)) % 174.01/173.91 [1469]~E(x14691,x14692)+E(f695(x14691,x14693,x14694,x14695),f695(x14692,x14693,x14694,x14695)) % 174.01/173.91 [1470]~E(x14701,x14702)+E(f695(x14703,x14701,x14704,x14705),f695(x14703,x14702,x14704,x14705)) % 174.01/173.91 [1471]~E(x14711,x14712)+E(f695(x14713,x14714,x14711,x14715),f695(x14713,x14714,x14712,x14715)) % 174.01/173.91 [1472]~E(x14721,x14722)+E(f695(x14723,x14724,x14725,x14721),f695(x14723,x14724,x14725,x14722)) % 174.01/173.91 [1473]~E(x14731,x14732)+E(f638(x14731,x14733,x14734,x14735,x14736,x14737,x14738,x14739),f638(x14732,x14733,x14734,x14735,x14736,x14737,x14738,x14739)) % 174.01/173.91 [1474]~E(x14741,x14742)+E(f638(x14743,x14741,x14744,x14745,x14746,x14747,x14748,x14749),f638(x14743,x14742,x14744,x14745,x14746,x14747,x14748,x14749)) % 174.01/173.91 [1475]~E(x14751,x14752)+E(f638(x14753,x14754,x14751,x14755,x14756,x14757,x14758,x14759),f638(x14753,x14754,x14752,x14755,x14756,x14757,x14758,x14759)) % 174.01/173.91 [1476]~E(x14761,x14762)+E(f638(x14763,x14764,x14765,x14761,x14766,x14767,x14768,x14769),f638(x14763,x14764,x14765,x14762,x14766,x14767,x14768,x14769)) % 174.01/173.91 [1477]~E(x14771,x14772)+E(f638(x14773,x14774,x14775,x14776,x14771,x14777,x14778,x14779),f638(x14773,x14774,x14775,x14776,x14772,x14777,x14778,x14779)) % 174.01/173.91 [1478]~E(x14781,x14782)+E(f638(x14783,x14784,x14785,x14786,x14787,x14781,x14788,x14789),f638(x14783,x14784,x14785,x14786,x14787,x14782,x14788,x14789)) % 174.01/173.91 [1479]~E(x14791,x14792)+E(f638(x14793,x14794,x14795,x14796,x14797,x14798,x14791,x14799),f638(x14793,x14794,x14795,x14796,x14797,x14798,x14792,x14799)) % 174.01/173.91 [1480]~E(x14801,x14802)+E(f638(x14803,x14804,x14805,x14806,x14807,x14808,x14809,x14801),f638(x14803,x14804,x14805,x14806,x14807,x14808,x14809,x14802)) % 174.01/173.91 [1481]~E(x14811,x14812)+E(f470(x14811,x14813,x14814),f470(x14812,x14813,x14814)) % 174.01/173.91 [1482]~E(x14821,x14822)+E(f470(x14823,x14821,x14824),f470(x14823,x14822,x14824)) % 174.01/173.91 [1483]~E(x14831,x14832)+E(f470(x14833,x14834,x14831),f470(x14833,x14834,x14832)) % 174.01/173.91 [1484]~E(x14841,x14842)+E(f816(x14841,x14843,x14844),f816(x14842,x14843,x14844)) % 174.01/173.91 [1485]~E(x14851,x14852)+E(f816(x14853,x14851,x14854),f816(x14853,x14852,x14854)) % 174.01/173.91 [1486]~E(x14861,x14862)+E(f816(x14863,x14864,x14861),f816(x14863,x14864,x14862)) % 174.01/173.91 [1487]~E(x14871,x14872)+E(f451(x14871),f451(x14872)) % 174.01/173.91 [1488]~E(x14881,x14882)+E(f714(x14881,x14883,x14884,x14885,x14886,x14887,x14888),f714(x14882,x14883,x14884,x14885,x14886,x14887,x14888)) % 174.01/173.91 [1489]~E(x14891,x14892)+E(f714(x14893,x14891,x14894,x14895,x14896,x14897,x14898),f714(x14893,x14892,x14894,x14895,x14896,x14897,x14898)) % 174.01/173.91 [1490]~E(x14901,x14902)+E(f714(x14903,x14904,x14901,x14905,x14906,x14907,x14908),f714(x14903,x14904,x14902,x14905,x14906,x14907,x14908)) % 174.01/173.91 [1491]~E(x14911,x14912)+E(f714(x14913,x14914,x14915,x14911,x14916,x14917,x14918),f714(x14913,x14914,x14915,x14912,x14916,x14917,x14918)) % 174.01/173.91 [1492]~E(x14921,x14922)+E(f714(x14923,x14924,x14925,x14926,x14921,x14927,x14928),f714(x14923,x14924,x14925,x14926,x14922,x14927,x14928)) % 174.01/173.91 [1493]~E(x14931,x14932)+E(f714(x14933,x14934,x14935,x14936,x14937,x14931,x14938),f714(x14933,x14934,x14935,x14936,x14937,x14932,x14938)) % 174.01/173.91 [1494]~E(x14941,x14942)+E(f714(x14943,x14944,x14945,x14946,x14947,x14948,x14941),f714(x14943,x14944,x14945,x14946,x14947,x14948,x14942)) % 174.01/173.91 [1495]~E(x14951,x14952)+E(f433(x14951,x14953,x14954,x14955),f433(x14952,x14953,x14954,x14955)) % 174.01/173.91 [1496]~E(x14961,x14962)+E(f433(x14963,x14961,x14964,x14965),f433(x14963,x14962,x14964,x14965)) % 174.01/173.91 [1497]~E(x14971,x14972)+E(f433(x14973,x14974,x14971,x14975),f433(x14973,x14974,x14972,x14975)) % 174.01/173.91 [1498]~E(x14981,x14982)+E(f433(x14983,x14984,x14985,x14981),f433(x14983,x14984,x14985,x14982)) % 174.01/173.91 [1499]~E(x14991,x14992)+E(f273(x14991,x14993,x14994,x14995),f273(x14992,x14993,x14994,x14995)) % 174.01/173.91 [1500]~E(x15001,x15002)+E(f273(x15003,x15001,x15004,x15005),f273(x15003,x15002,x15004,x15005)) % 174.01/173.91 [1501]~E(x15011,x15012)+E(f273(x15013,x15014,x15011,x15015),f273(x15013,x15014,x15012,x15015)) % 174.01/173.91 [1502]~E(x15021,x15022)+E(f273(x15023,x15024,x15025,x15021),f273(x15023,x15024,x15025,x15022)) % 174.01/173.91 [1503]~E(x15031,x15032)+E(f643(x15031,x15033),f643(x15032,x15033)) % 174.01/173.91 [1504]~E(x15041,x15042)+E(f643(x15043,x15041),f643(x15043,x15042)) % 174.01/173.91 [1505]~E(x15051,x15052)+E(f419(x15051,x15053,x15054,x15055,x15056),f419(x15052,x15053,x15054,x15055,x15056)) % 174.01/173.91 [1506]~E(x15061,x15062)+E(f419(x15063,x15061,x15064,x15065,x15066),f419(x15063,x15062,x15064,x15065,x15066)) % 174.01/173.91 [1507]~E(x15071,x15072)+E(f419(x15073,x15074,x15071,x15075,x15076),f419(x15073,x15074,x15072,x15075,x15076)) % 174.01/173.91 [1508]~E(x15081,x15082)+E(f419(x15083,x15084,x15085,x15081,x15086),f419(x15083,x15084,x15085,x15082,x15086)) % 174.01/173.91 [1509]~E(x15091,x15092)+E(f419(x15093,x15094,x15095,x15096,x15091),f419(x15093,x15094,x15095,x15096,x15092)) % 174.01/173.91 [1510]~E(x15101,x15102)+E(f808(x15101,x15103,x15104),f808(x15102,x15103,x15104)) % 174.01/173.91 [1511]~E(x15111,x15112)+E(f808(x15113,x15111,x15114),f808(x15113,x15112,x15114)) % 174.01/173.91 [1512]~E(x15121,x15122)+E(f808(x15123,x15124,x15121),f808(x15123,x15124,x15122)) % 174.01/173.91 [1513]~E(x15131,x15132)+E(f486(x15131,x15133,x15134,x15135,x15136),f486(x15132,x15133,x15134,x15135,x15136)) % 174.01/173.91 [1514]~E(x15141,x15142)+E(f486(x15143,x15141,x15144,x15145,x15146),f486(x15143,x15142,x15144,x15145,x15146)) % 174.01/173.91 [1515]~E(x15151,x15152)+E(f486(x15153,x15154,x15151,x15155,x15156),f486(x15153,x15154,x15152,x15155,x15156)) % 174.01/173.91 [1516]~E(x15161,x15162)+E(f486(x15163,x15164,x15165,x15161,x15166),f486(x15163,x15164,x15165,x15162,x15166)) % 174.01/173.91 [1517]~E(x15171,x15172)+E(f486(x15173,x15174,x15175,x15176,x15171),f486(x15173,x15174,x15175,x15176,x15172)) % 174.01/173.91 [1518]~E(x15181,x15182)+E(f675(x15181,x15183,x15184),f675(x15182,x15183,x15184)) % 174.01/173.91 [1519]~E(x15191,x15192)+E(f675(x15193,x15191,x15194),f675(x15193,x15192,x15194)) % 174.01/173.91 [1520]~E(x15201,x15202)+E(f675(x15203,x15204,x15201),f675(x15203,x15204,x15202)) % 174.01/173.91 [1521]~E(x15211,x15212)+E(f551(x15211,x15213,x15214),f551(x15212,x15213,x15214)) % 174.01/173.91 [1522]~E(x15221,x15222)+E(f551(x15223,x15221,x15224),f551(x15223,x15222,x15224)) % 174.01/173.91 [1523]~E(x15231,x15232)+E(f551(x15233,x15234,x15231),f551(x15233,x15234,x15232)) % 174.01/173.91 [1524]~E(x15241,x15242)+E(f377(x15241,x15243),f377(x15242,x15243)) % 174.01/173.91 [1525]~E(x15251,x15252)+E(f377(x15253,x15251),f377(x15253,x15252)) % 174.01/173.91 [1526]~E(x15261,x15262)+E(f245(x15261,x15263,x15264),f245(x15262,x15263,x15264)) % 174.01/173.91 [1527]~E(x15271,x15272)+E(f245(x15273,x15271,x15274),f245(x15273,x15272,x15274)) % 174.01/173.91 [1528]~E(x15281,x15282)+E(f245(x15283,x15284,x15281),f245(x15283,x15284,x15282)) % 174.01/173.91 [1529]~E(x15291,x15292)+E(f204(x15291,x15293,x15294,x15295,x15296,x15297,x15298),f204(x15292,x15293,x15294,x15295,x15296,x15297,x15298)) % 174.01/173.91 [1530]~E(x15301,x15302)+E(f204(x15303,x15301,x15304,x15305,x15306,x15307,x15308),f204(x15303,x15302,x15304,x15305,x15306,x15307,x15308)) % 174.01/173.91 [1531]~E(x15311,x15312)+E(f204(x15313,x15314,x15311,x15315,x15316,x15317,x15318),f204(x15313,x15314,x15312,x15315,x15316,x15317,x15318)) % 174.01/173.91 [1532]~E(x15321,x15322)+E(f204(x15323,x15324,x15325,x15321,x15326,x15327,x15328),f204(x15323,x15324,x15325,x15322,x15326,x15327,x15328)) % 174.01/173.91 [1533]~E(x15331,x15332)+E(f204(x15333,x15334,x15335,x15336,x15331,x15337,x15338),f204(x15333,x15334,x15335,x15336,x15332,x15337,x15338)) % 174.01/173.91 [1534]~E(x15341,x15342)+E(f204(x15343,x15344,x15345,x15346,x15347,x15341,x15348),f204(x15343,x15344,x15345,x15346,x15347,x15342,x15348)) % 174.01/173.91 [1535]~E(x15351,x15352)+E(f204(x15353,x15354,x15355,x15356,x15357,x15358,x15351),f204(x15353,x15354,x15355,x15356,x15357,x15358,x15352)) % 174.01/173.91 [1536]~E(x15361,x15362)+E(f614(x15361,x15363,x15364,x15365,x15366,x15367),f614(x15362,x15363,x15364,x15365,x15366,x15367)) % 174.01/173.91 [1537]~E(x15371,x15372)+E(f614(x15373,x15371,x15374,x15375,x15376,x15377),f614(x15373,x15372,x15374,x15375,x15376,x15377)) % 174.01/173.91 [1538]~E(x15381,x15382)+E(f614(x15383,x15384,x15381,x15385,x15386,x15387),f614(x15383,x15384,x15382,x15385,x15386,x15387)) % 174.01/173.91 [1539]~E(x15391,x15392)+E(f614(x15393,x15394,x15395,x15391,x15396,x15397),f614(x15393,x15394,x15395,x15392,x15396,x15397)) % 174.01/173.91 [1540]~E(x15401,x15402)+E(f614(x15403,x15404,x15405,x15406,x15401,x15407),f614(x15403,x15404,x15405,x15406,x15402,x15407)) % 174.01/173.91 [1541]~E(x15411,x15412)+E(f614(x15413,x15414,x15415,x15416,x15417,x15411),f614(x15413,x15414,x15415,x15416,x15417,x15412)) % 174.01/173.91 [1542]~E(x15421,x15422)+E(f50(x15421),f50(x15422)) % 174.01/173.91 [1543]~E(x15431,x15432)+E(f346(x15431,x15433),f346(x15432,x15433)) % 174.01/173.91 [1544]~E(x15441,x15442)+E(f346(x15443,x15441),f346(x15443,x15442)) % 174.01/173.91 [1545]~E(x15451,x15452)+E(f679(x15451,x15453,x15454),f679(x15452,x15453,x15454)) % 174.01/173.91 [1546]~E(x15461,x15462)+E(f679(x15463,x15461,x15464),f679(x15463,x15462,x15464)) % 174.01/173.91 [1547]~E(x15471,x15472)+E(f679(x15473,x15474,x15471),f679(x15473,x15474,x15472)) % 174.01/173.91 [1548]~E(x15481,x15482)+E(f262(x15481,x15483),f262(x15482,x15483)) % 174.01/173.91 [1549]~E(x15491,x15492)+E(f262(x15493,x15491),f262(x15493,x15492)) % 174.01/173.91 [1550]~E(x15501,x15502)+E(f818(x15501,x15503,x15504),f818(x15502,x15503,x15504)) % 174.01/173.91 [1551]~E(x15511,x15512)+E(f818(x15513,x15511,x15514),f818(x15513,x15512,x15514)) % 174.01/173.91 [1552]~E(x15521,x15522)+E(f818(x15523,x15524,x15521),f818(x15523,x15524,x15522)) % 174.01/173.91 [1553]~E(x15531,x15532)+E(f772(x15531,x15533),f772(x15532,x15533)) % 174.01/173.91 [1554]~E(x15541,x15542)+E(f772(x15543,x15541),f772(x15543,x15542)) % 174.01/173.91 [1555]~E(x15551,x15552)+E(f617(x15551,x15553,x15554,x15555,x15556,x15557),f617(x15552,x15553,x15554,x15555,x15556,x15557)) % 174.01/173.91 [1556]~E(x15561,x15562)+E(f617(x15563,x15561,x15564,x15565,x15566,x15567),f617(x15563,x15562,x15564,x15565,x15566,x15567)) % 174.01/173.91 [1557]~E(x15571,x15572)+E(f617(x15573,x15574,x15571,x15575,x15576,x15577),f617(x15573,x15574,x15572,x15575,x15576,x15577)) % 174.01/173.91 [1558]~E(x15581,x15582)+E(f617(x15583,x15584,x15585,x15581,x15586,x15587),f617(x15583,x15584,x15585,x15582,x15586,x15587)) % 174.01/173.91 [1559]~E(x15591,x15592)+E(f617(x15593,x15594,x15595,x15596,x15591,x15597),f617(x15593,x15594,x15595,x15596,x15592,x15597)) % 174.01/173.91 [1560]~E(x15601,x15602)+E(f617(x15603,x15604,x15605,x15606,x15607,x15601),f617(x15603,x15604,x15605,x15606,x15607,x15602)) % 174.01/173.91 [1561]~E(x15611,x15612)+E(f641(x15611,x15613,x15614),f641(x15612,x15613,x15614)) % 174.01/173.91 [1562]~E(x15621,x15622)+E(f641(x15623,x15621,x15624),f641(x15623,x15622,x15624)) % 174.01/173.91 [1563]~E(x15631,x15632)+E(f641(x15633,x15634,x15631),f641(x15633,x15634,x15632)) % 174.01/173.91 [1564]~E(x15641,x15642)+E(f737(x15641,x15643,x15644,x15645,x15646),f737(x15642,x15643,x15644,x15645,x15646)) % 174.01/173.91 [1565]~E(x15651,x15652)+E(f737(x15653,x15651,x15654,x15655,x15656),f737(x15653,x15652,x15654,x15655,x15656)) % 174.01/173.91 [1566]~E(x15661,x15662)+E(f737(x15663,x15664,x15661,x15665,x15666),f737(x15663,x15664,x15662,x15665,x15666)) % 174.01/173.91 [1567]~E(x15671,x15672)+E(f737(x15673,x15674,x15675,x15671,x15676),f737(x15673,x15674,x15675,x15672,x15676)) % 174.01/173.91 [1568]~E(x15681,x15682)+E(f737(x15683,x15684,x15685,x15686,x15681),f737(x15683,x15684,x15685,x15686,x15682)) % 174.01/173.91 [1569]~E(x15691,x15692)+E(f713(x15691,x15693,x15694,x15695),f713(x15692,x15693,x15694,x15695)) % 174.01/173.91 [1570]~E(x15701,x15702)+E(f713(x15703,x15701,x15704,x15705),f713(x15703,x15702,x15704,x15705)) % 174.01/173.91 [1571]~E(x15711,x15712)+E(f713(x15713,x15714,x15711,x15715),f713(x15713,x15714,x15712,x15715)) % 174.01/173.91 [1572]~E(x15721,x15722)+E(f713(x15723,x15724,x15725,x15721),f713(x15723,x15724,x15725,x15722)) % 174.01/173.91 [1573]~E(x15731,x15732)+E(f426(x15731,x15733,x15734,x15735),f426(x15732,x15733,x15734,x15735)) % 174.01/173.91 [1574]~E(x15741,x15742)+E(f426(x15743,x15741,x15744,x15745),f426(x15743,x15742,x15744,x15745)) % 174.01/173.91 [1575]~E(x15751,x15752)+E(f426(x15753,x15754,x15751,x15755),f426(x15753,x15754,x15752,x15755)) % 174.01/173.91 [1576]~E(x15761,x15762)+E(f426(x15763,x15764,x15765,x15761),f426(x15763,x15764,x15765,x15762)) % 174.01/173.91 [1577]~E(x15771,x15772)+E(f167(x15771),f167(x15772)) % 174.01/173.91 [1578]~E(x15781,x15782)+E(f751(x15781,x15783,x15784),f751(x15782,x15783,x15784)) % 174.01/173.91 [1579]~E(x15791,x15792)+E(f751(x15793,x15791,x15794),f751(x15793,x15792,x15794)) % 174.01/173.91 [1580]~E(x15801,x15802)+E(f751(x15803,x15804,x15801),f751(x15803,x15804,x15802)) % 174.01/173.91 [1581]~E(x15811,x15812)+E(f544(x15811,x15813,x15814,x15815,x15816,x15817),f544(x15812,x15813,x15814,x15815,x15816,x15817)) % 174.01/173.91 [1582]~E(x15821,x15822)+E(f544(x15823,x15821,x15824,x15825,x15826,x15827),f544(x15823,x15822,x15824,x15825,x15826,x15827)) % 174.01/173.91 [1583]~E(x15831,x15832)+E(f544(x15833,x15834,x15831,x15835,x15836,x15837),f544(x15833,x15834,x15832,x15835,x15836,x15837)) % 174.01/173.91 [1584]~E(x15841,x15842)+E(f544(x15843,x15844,x15845,x15841,x15846,x15847),f544(x15843,x15844,x15845,x15842,x15846,x15847)) % 174.01/173.91 [1585]~E(x15851,x15852)+E(f544(x15853,x15854,x15855,x15856,x15851,x15857),f544(x15853,x15854,x15855,x15856,x15852,x15857)) % 174.01/173.91 [1586]~E(x15861,x15862)+E(f544(x15863,x15864,x15865,x15866,x15867,x15861),f544(x15863,x15864,x15865,x15866,x15867,x15862)) % 174.01/173.91 [1587]~E(x15871,x15872)+E(f352(x15871,x15873),f352(x15872,x15873)) % 174.01/173.91 [1588]~E(x15881,x15882)+E(f352(x15883,x15881),f352(x15883,x15882)) % 174.01/173.91 [1589]~E(x15891,x15892)+E(f646(x15891,x15893,x15894,x15895,x15896),f646(x15892,x15893,x15894,x15895,x15896)) % 174.01/173.91 [1590]~E(x15901,x15902)+E(f646(x15903,x15901,x15904,x15905,x15906),f646(x15903,x15902,x15904,x15905,x15906)) % 174.01/173.91 [1591]~E(x15911,x15912)+E(f646(x15913,x15914,x15911,x15915,x15916),f646(x15913,x15914,x15912,x15915,x15916)) % 174.01/173.91 [1592]~E(x15921,x15922)+E(f646(x15923,x15924,x15925,x15921,x15926),f646(x15923,x15924,x15925,x15922,x15926)) % 174.01/173.91 [1593]~E(x15931,x15932)+E(f646(x15933,x15934,x15935,x15936,x15931),f646(x15933,x15934,x15935,x15936,x15932)) % 174.01/173.91 [1594]~E(x15941,x15942)+E(f769(x15941,x15943,x15944),f769(x15942,x15943,x15944)) % 174.01/173.91 [1595]~E(x15951,x15952)+E(f769(x15953,x15951,x15954),f769(x15953,x15952,x15954)) % 174.01/173.91 [1596]~E(x15961,x15962)+E(f769(x15963,x15964,x15961),f769(x15963,x15964,x15962)) % 174.01/173.91 [1597]~E(x15971,x15972)+E(f526(x15971,x15973,x15974,x15975,x15976),f526(x15972,x15973,x15974,x15975,x15976)) % 174.01/173.91 [1598]~E(x15981,x15982)+E(f526(x15983,x15981,x15984,x15985,x15986),f526(x15983,x15982,x15984,x15985,x15986)) % 174.01/173.91 [1599]~E(x15991,x15992)+E(f526(x15993,x15994,x15991,x15995,x15996),f526(x15993,x15994,x15992,x15995,x15996)) % 174.01/173.91 [1600]~E(x16001,x16002)+E(f526(x16003,x16004,x16005,x16001,x16006),f526(x16003,x16004,x16005,x16002,x16006)) % 174.01/173.91 [1601]~E(x16011,x16012)+E(f526(x16013,x16014,x16015,x16016,x16011),f526(x16013,x16014,x16015,x16016,x16012)) % 174.01/173.91 [1602]~E(x16021,x16022)+E(f438(x16021,x16023,x16024,x16025),f438(x16022,x16023,x16024,x16025)) % 174.01/173.91 [1603]~E(x16031,x16032)+E(f438(x16033,x16031,x16034,x16035),f438(x16033,x16032,x16034,x16035)) % 174.01/173.91 [1604]~E(x16041,x16042)+E(f438(x16043,x16044,x16041,x16045),f438(x16043,x16044,x16042,x16045)) % 174.01/173.91 [1605]~E(x16051,x16052)+E(f438(x16053,x16054,x16055,x16051),f438(x16053,x16054,x16055,x16052)) % 174.01/173.91 [1606]~E(x16061,x16062)+E(f589(x16061,x16063,x16064,x16065,x16066,x16067),f589(x16062,x16063,x16064,x16065,x16066,x16067)) % 174.01/173.91 [1607]~E(x16071,x16072)+E(f589(x16073,x16071,x16074,x16075,x16076,x16077),f589(x16073,x16072,x16074,x16075,x16076,x16077)) % 174.01/173.91 [1608]~E(x16081,x16082)+E(f589(x16083,x16084,x16081,x16085,x16086,x16087),f589(x16083,x16084,x16082,x16085,x16086,x16087)) % 174.01/173.91 [1609]~E(x16091,x16092)+E(f589(x16093,x16094,x16095,x16091,x16096,x16097),f589(x16093,x16094,x16095,x16092,x16096,x16097)) % 174.01/173.91 [1610]~E(x16101,x16102)+E(f589(x16103,x16104,x16105,x16106,x16101,x16107),f589(x16103,x16104,x16105,x16106,x16102,x16107)) % 174.01/173.91 [1611]~E(x16111,x16112)+E(f589(x16113,x16114,x16115,x16116,x16117,x16111),f589(x16113,x16114,x16115,x16116,x16117,x16112)) % 174.01/173.91 [1612]~E(x16121,x16122)+E(f409(x16121,x16123,x16124),f409(x16122,x16123,x16124)) % 174.01/173.91 [1613]~E(x16131,x16132)+E(f409(x16133,x16131,x16134),f409(x16133,x16132,x16134)) % 174.01/173.91 [1614]~E(x16141,x16142)+E(f409(x16143,x16144,x16141),f409(x16143,x16144,x16142)) % 174.01/173.91 [1615]~E(x16151,x16152)+E(f367(x16151,x16153,x16154,x16155,x16156),f367(x16152,x16153,x16154,x16155,x16156)) % 174.01/173.91 [1616]~E(x16161,x16162)+E(f367(x16163,x16161,x16164,x16165,x16166),f367(x16163,x16162,x16164,x16165,x16166)) % 174.01/173.91 [1617]~E(x16171,x16172)+E(f367(x16173,x16174,x16171,x16175,x16176),f367(x16173,x16174,x16172,x16175,x16176)) % 174.01/173.91 [1618]~E(x16181,x16182)+E(f367(x16183,x16184,x16185,x16181,x16186),f367(x16183,x16184,x16185,x16182,x16186)) % 174.01/173.91 [1619]~E(x16191,x16192)+E(f367(x16193,x16194,x16195,x16196,x16191),f367(x16193,x16194,x16195,x16196,x16192)) % 174.01/173.91 [1620]~E(x16201,x16202)+E(f236(x16201,x16203),f236(x16202,x16203)) % 174.01/173.91 [1621]~E(x16211,x16212)+E(f236(x16213,x16211),f236(x16213,x16212)) % 174.01/173.91 [1622]~E(x16221,x16222)+E(f686(x16221,x16223,x16224),f686(x16222,x16223,x16224)) % 174.01/173.91 [1623]~E(x16231,x16232)+E(f686(x16233,x16231,x16234),f686(x16233,x16232,x16234)) % 174.01/173.91 [1624]~E(x16241,x16242)+E(f686(x16243,x16244,x16241),f686(x16243,x16244,x16242)) % 174.01/173.91 [1625]~E(x16251,x16252)+E(f672(x16251,x16253),f672(x16252,x16253)) % 174.01/173.91 [1626]~E(x16261,x16262)+E(f672(x16263,x16261),f672(x16263,x16262)) % 174.01/173.91 [1627]~E(x16271,x16272)+E(f685(x16271),f685(x16272)) % 174.01/173.91 [1628]~E(x16281,x16282)+E(f797(x16281,x16283,x16284),f797(x16282,x16283,x16284)) % 174.01/173.91 [1629]~E(x16291,x16292)+E(f797(x16293,x16291,x16294),f797(x16293,x16292,x16294)) % 174.01/173.91 [1630]~E(x16301,x16302)+E(f797(x16303,x16304,x16301),f797(x16303,x16304,x16302)) % 174.01/173.91 [1631]~E(x16311,x16312)+E(f80(x16311,x16313,x16314,x16315,x16316),f80(x16312,x16313,x16314,x16315,x16316)) % 174.01/173.91 [1632]~E(x16321,x16322)+E(f80(x16323,x16321,x16324,x16325,x16326),f80(x16323,x16322,x16324,x16325,x16326)) % 174.01/173.91 [1633]~E(x16331,x16332)+E(f80(x16333,x16334,x16331,x16335,x16336),f80(x16333,x16334,x16332,x16335,x16336)) % 174.01/173.91 [1634]~E(x16341,x16342)+E(f80(x16343,x16344,x16345,x16341,x16346),f80(x16343,x16344,x16345,x16342,x16346)) % 174.01/173.91 [1635]~E(x16351,x16352)+E(f80(x16353,x16354,x16355,x16356,x16351),f80(x16353,x16354,x16355,x16356,x16352)) % 174.01/173.91 [1636]~E(x16361,x16362)+E(f817(x16361,x16363,x16364),f817(x16362,x16363,x16364)) % 174.01/173.91 [1637]~E(x16371,x16372)+E(f817(x16373,x16371,x16374),f817(x16373,x16372,x16374)) % 174.01/173.91 [1638]~E(x16381,x16382)+E(f817(x16383,x16384,x16381),f817(x16383,x16384,x16382)) % 174.01/173.91 [1639]~E(x16391,x16392)+E(f518(x16391,x16393),f518(x16392,x16393)) % 174.01/173.91 [1640]~E(x16401,x16402)+E(f518(x16403,x16401),f518(x16403,x16402)) % 174.01/173.91 [1641]~E(x16411,x16412)+E(f730(x16411),f730(x16412)) % 174.01/173.91 [1642]~E(x16421,x16422)+E(f612(x16421,x16423,x16424),f612(x16422,x16423,x16424)) % 174.01/173.91 [1643]~E(x16431,x16432)+E(f612(x16433,x16431,x16434),f612(x16433,x16432,x16434)) % 174.01/173.91 [1644]~E(x16441,x16442)+E(f612(x16443,x16444,x16441),f612(x16443,x16444,x16442)) % 174.01/173.91 [1645]~E(x16451,x16452)+E(f344(x16451,x16453),f344(x16452,x16453)) % 174.01/173.91 [1646]~E(x16461,x16462)+E(f344(x16463,x16461),f344(x16463,x16462)) % 174.01/173.91 [1647]~E(x16471,x16472)+E(f718(x16471,x16473,x16474,x16475),f718(x16472,x16473,x16474,x16475)) % 174.01/173.91 [1648]~E(x16481,x16482)+E(f718(x16483,x16481,x16484,x16485),f718(x16483,x16482,x16484,x16485)) % 174.01/173.91 [1649]~E(x16491,x16492)+E(f718(x16493,x16494,x16491,x16495),f718(x16493,x16494,x16492,x16495)) % 174.01/173.91 [1650]~E(x16501,x16502)+E(f718(x16503,x16504,x16505,x16501),f718(x16503,x16504,x16505,x16502)) % 174.01/173.91 [1651]~E(x16511,x16512)+E(f677(x16511,x16513,x16514),f677(x16512,x16513,x16514)) % 174.01/173.91 [1652]~E(x16521,x16522)+E(f677(x16523,x16521,x16524),f677(x16523,x16522,x16524)) % 174.01/173.91 [1653]~E(x16531,x16532)+E(f677(x16533,x16534,x16531),f677(x16533,x16534,x16532)) % 174.01/173.91 [1654]~E(x16541,x16542)+E(f572(x16541,x16543,x16544,x16545,x16546),f572(x16542,x16543,x16544,x16545,x16546)) % 174.01/173.91 [1655]~E(x16551,x16552)+E(f572(x16553,x16551,x16554,x16555,x16556),f572(x16553,x16552,x16554,x16555,x16556)) % 174.01/173.91 [1656]~E(x16561,x16562)+E(f572(x16563,x16564,x16561,x16565,x16566),f572(x16563,x16564,x16562,x16565,x16566)) % 174.01/173.91 [1657]~E(x16571,x16572)+E(f572(x16573,x16574,x16575,x16571,x16576),f572(x16573,x16574,x16575,x16572,x16576)) % 174.01/173.91 [1658]~E(x16581,x16582)+E(f572(x16583,x16584,x16585,x16586,x16581),f572(x16583,x16584,x16585,x16586,x16582)) % 174.01/173.91 [1659]~E(x16591,x16592)+E(f683(x16591,x16593),f683(x16592,x16593)) % 174.01/173.91 [1660]~E(x16601,x16602)+E(f683(x16603,x16601),f683(x16603,x16602)) % 174.01/173.91 [1661]~E(x16611,x16612)+E(f554(x16611,x16613,x16614),f554(x16612,x16613,x16614)) % 174.01/173.91 [1662]~E(x16621,x16622)+E(f554(x16623,x16621,x16624),f554(x16623,x16622,x16624)) % 174.01/173.91 [1663]~E(x16631,x16632)+E(f554(x16633,x16634,x16631),f554(x16633,x16634,x16632)) % 174.01/173.91 [1664]~E(x16641,x16642)+E(f562(x16641,x16643,x16644,x16645),f562(x16642,x16643,x16644,x16645)) % 174.01/173.91 [1665]~E(x16651,x16652)+E(f562(x16653,x16651,x16654,x16655),f562(x16653,x16652,x16654,x16655)) % 174.01/173.91 [1666]~E(x16661,x16662)+E(f562(x16663,x16664,x16661,x16665),f562(x16663,x16664,x16662,x16665)) % 174.01/173.91 [1667]~E(x16671,x16672)+E(f562(x16673,x16674,x16675,x16671),f562(x16673,x16674,x16675,x16672)) % 174.01/173.91 [1668]~E(x16681,x16682)+E(f624(x16681,x16683,x16684,x16685),f624(x16682,x16683,x16684,x16685)) % 174.01/173.91 [1669]~E(x16691,x16692)+E(f624(x16693,x16691,x16694,x16695),f624(x16693,x16692,x16694,x16695)) % 174.01/173.91 [1670]~E(x16701,x16702)+E(f624(x16703,x16704,x16701,x16705),f624(x16703,x16704,x16702,x16705)) % 174.01/173.91 [1671]~E(x16711,x16712)+E(f624(x16713,x16714,x16715,x16711),f624(x16713,x16714,x16715,x16712)) % 174.01/173.91 [1672]~E(x16721,x16722)+E(f532(x16721,x16723,x16724),f532(x16722,x16723,x16724)) % 174.01/173.91 [1673]~E(x16731,x16732)+E(f532(x16733,x16731,x16734),f532(x16733,x16732,x16734)) % 174.01/173.91 [1674]~E(x16741,x16742)+E(f532(x16743,x16744,x16741),f532(x16743,x16744,x16742)) % 174.01/173.91 [1675]~E(x16751,x16752)+E(f444(x16751,x16753,x16754,x16755),f444(x16752,x16753,x16754,x16755)) % 174.01/173.91 [1676]~E(x16761,x16762)+E(f444(x16763,x16761,x16764,x16765),f444(x16763,x16762,x16764,x16765)) % 174.01/173.91 [1677]~E(x16771,x16772)+E(f444(x16773,x16774,x16771,x16775),f444(x16773,x16774,x16772,x16775)) % 174.01/173.91 [1678]~E(x16781,x16782)+E(f444(x16783,x16784,x16785,x16781),f444(x16783,x16784,x16785,x16782)) % 174.01/173.91 [1679]~E(x16791,x16792)+E(f500(x16791,x16793,x16794,x16795),f500(x16792,x16793,x16794,x16795)) % 174.01/173.91 [1680]~E(x16801,x16802)+E(f500(x16803,x16801,x16804,x16805),f500(x16803,x16802,x16804,x16805)) % 174.01/173.91 [1681]~E(x16811,x16812)+E(f500(x16813,x16814,x16811,x16815),f500(x16813,x16814,x16812,x16815)) % 174.01/173.91 [1682]~E(x16821,x16822)+E(f500(x16823,x16824,x16825,x16821),f500(x16823,x16824,x16825,x16822)) % 174.01/173.91 [1683]~E(x16831,x16832)+E(f766(x16831,x16833,x16834),f766(x16832,x16833,x16834)) % 174.01/173.91 [1684]~E(x16841,x16842)+E(f766(x16843,x16841,x16844),f766(x16843,x16842,x16844)) % 174.01/173.91 [1685]~E(x16851,x16852)+E(f766(x16853,x16854,x16851),f766(x16853,x16854,x16852)) % 174.01/173.91 [1686]~E(x16861,x16862)+E(f154(x16861,x16863),f154(x16862,x16863)) % 174.01/173.91 [1687]~E(x16871,x16872)+E(f154(x16873,x16871),f154(x16873,x16872)) % 174.01/173.91 [1688]~E(x16881,x16882)+E(f660(x16881,x16883,x16884,x16885,x16886),f660(x16882,x16883,x16884,x16885,x16886)) % 174.01/173.91 [1689]~E(x16891,x16892)+E(f660(x16893,x16891,x16894,x16895,x16896),f660(x16893,x16892,x16894,x16895,x16896)) % 174.01/173.91 [1690]~E(x16901,x16902)+E(f660(x16903,x16904,x16901,x16905,x16906),f660(x16903,x16904,x16902,x16905,x16906)) % 174.01/173.91 [1691]~E(x16911,x16912)+E(f660(x16913,x16914,x16915,x16911,x16916),f660(x16913,x16914,x16915,x16912,x16916)) % 174.01/173.91 [1692]~E(x16921,x16922)+E(f660(x16923,x16924,x16925,x16926,x16921),f660(x16923,x16924,x16925,x16926,x16922)) % 174.01/173.91 [1693]~E(x16931,x16932)+E(f790(x16931,x16933),f790(x16932,x16933)) % 174.01/173.91 [1694]~E(x16941,x16942)+E(f790(x16943,x16941),f790(x16943,x16942)) % 174.01/173.91 [1695]~E(x16951,x16952)+E(f759(x16951,x16953,x16954,x16955),f759(x16952,x16953,x16954,x16955)) % 174.01/173.91 [1696]~E(x16961,x16962)+E(f759(x16963,x16961,x16964,x16965),f759(x16963,x16962,x16964,x16965)) % 174.01/173.91 [1697]~E(x16971,x16972)+E(f759(x16973,x16974,x16971,x16975),f759(x16973,x16974,x16972,x16975)) % 174.01/173.91 [1698]~E(x16981,x16982)+E(f759(x16983,x16984,x16985,x16981),f759(x16983,x16984,x16985,x16982)) % 174.01/173.91 [1699]~E(x16991,x16992)+E(f205(x16991),f205(x16992)) % 174.01/173.91 [1700]~E(x17001,x17002)+E(f663(x17001,x17003,x17004,x17005,x17006),f663(x17002,x17003,x17004,x17005,x17006)) % 174.01/173.91 [1701]~E(x17011,x17012)+E(f663(x17013,x17011,x17014,x17015,x17016),f663(x17013,x17012,x17014,x17015,x17016)) % 174.01/173.91 [1702]~E(x17021,x17022)+E(f663(x17023,x17024,x17021,x17025,x17026),f663(x17023,x17024,x17022,x17025,x17026)) % 174.01/173.91 [1703]~E(x17031,x17032)+E(f663(x17033,x17034,x17035,x17031,x17036),f663(x17033,x17034,x17035,x17032,x17036)) % 174.01/173.91 [1704]~E(x17041,x17042)+E(f663(x17043,x17044,x17045,x17046,x17041),f663(x17043,x17044,x17045,x17046,x17042)) % 174.01/173.91 [1705]~E(x17051,x17052)+E(f565(x17051,x17053,x17054,x17055,x17056,x17057),f565(x17052,x17053,x17054,x17055,x17056,x17057)) % 174.01/173.91 [1706]~E(x17061,x17062)+E(f565(x17063,x17061,x17064,x17065,x17066,x17067),f565(x17063,x17062,x17064,x17065,x17066,x17067)) % 174.01/173.91 [1707]~E(x17071,x17072)+E(f565(x17073,x17074,x17071,x17075,x17076,x17077),f565(x17073,x17074,x17072,x17075,x17076,x17077)) % 174.01/173.91 [1708]~E(x17081,x17082)+E(f565(x17083,x17084,x17085,x17081,x17086,x17087),f565(x17083,x17084,x17085,x17082,x17086,x17087)) % 174.01/173.91 [1709]~E(x17091,x17092)+E(f565(x17093,x17094,x17095,x17096,x17091,x17097),f565(x17093,x17094,x17095,x17096,x17092,x17097)) % 174.01/173.91 [1710]~E(x17101,x17102)+E(f565(x17103,x17104,x17105,x17106,x17107,x17101),f565(x17103,x17104,x17105,x17106,x17107,x17102)) % 174.01/173.91 [1711]~E(x17111,x17112)+E(f722(x17111,x17113,x17114,x17115,x17116),f722(x17112,x17113,x17114,x17115,x17116)) % 174.01/173.91 [1712]~E(x17121,x17122)+E(f722(x17123,x17121,x17124,x17125,x17126),f722(x17123,x17122,x17124,x17125,x17126)) % 174.01/173.91 [1713]~E(x17131,x17132)+E(f722(x17133,x17134,x17131,x17135,x17136),f722(x17133,x17134,x17132,x17135,x17136)) % 174.01/173.91 [1714]~E(x17141,x17142)+E(f722(x17143,x17144,x17145,x17141,x17146),f722(x17143,x17144,x17145,x17142,x17146)) % 174.01/173.91 [1715]~E(x17151,x17152)+E(f722(x17153,x17154,x17155,x17156,x17151),f722(x17153,x17154,x17155,x17156,x17152)) % 174.01/173.91 [1716]~E(x17161,x17162)+E(f595(x17161,x17163,x17164,x17165),f595(x17162,x17163,x17164,x17165)) % 174.01/173.91 [1717]~E(x17171,x17172)+E(f595(x17173,x17171,x17174,x17175),f595(x17173,x17172,x17174,x17175)) % 174.01/173.91 [1718]~E(x17181,x17182)+E(f595(x17183,x17184,x17181,x17185),f595(x17183,x17184,x17182,x17185)) % 174.01/173.91 [1719]~E(x17191,x17192)+E(f595(x17193,x17194,x17195,x17191),f595(x17193,x17194,x17195,x17192)) % 174.01/173.91 [1720]~E(x17201,x17202)+E(f492(x17201),f492(x17202)) % 174.01/173.91 [1721]~E(x17211,x17212)+E(f768(x17211,x17213,x17214),f768(x17212,x17213,x17214)) % 174.01/173.91 [1722]~E(x17221,x17222)+E(f768(x17223,x17221,x17224),f768(x17223,x17222,x17224)) % 174.01/173.91 [1723]~E(x17231,x17232)+E(f768(x17233,x17234,x17231),f768(x17233,x17234,x17232)) % 174.01/173.91 [1724]~E(x17241,x17242)+E(f358(x17241,x17243,x17244,x17245),f358(x17242,x17243,x17244,x17245)) % 174.01/173.91 [1725]~E(x17251,x17252)+E(f358(x17253,x17251,x17254,x17255),f358(x17253,x17252,x17254,x17255)) % 174.01/173.91 [1726]~E(x17261,x17262)+E(f358(x17263,x17264,x17261,x17265),f358(x17263,x17264,x17262,x17265)) % 174.01/173.91 [1727]~E(x17271,x17272)+E(f358(x17273,x17274,x17275,x17271),f358(x17273,x17274,x17275,x17272)) % 174.01/173.91 [1728]~E(x17281,x17282)+E(f348(x17281,x17283,x17284,x17285),f348(x17282,x17283,x17284,x17285)) % 174.01/173.91 [1729]~E(x17291,x17292)+E(f348(x17293,x17291,x17294,x17295),f348(x17293,x17292,x17294,x17295)) % 174.01/173.91 [1730]~E(x17301,x17302)+E(f348(x17303,x17304,x17301,x17305),f348(x17303,x17304,x17302,x17305)) % 174.01/173.91 [1731]~E(x17311,x17312)+E(f348(x17313,x17314,x17315,x17311),f348(x17313,x17314,x17315,x17312)) % 174.01/173.91 [1732]~E(x17321,x17322)+E(f653(x17321,x17323,x17324,x17325),f653(x17322,x17323,x17324,x17325)) % 174.01/173.91 [1733]~E(x17331,x17332)+E(f653(x17333,x17331,x17334,x17335),f653(x17333,x17332,x17334,x17335)) % 174.01/173.91 [1734]~E(x17341,x17342)+E(f653(x17343,x17344,x17341,x17345),f653(x17343,x17344,x17342,x17345)) % 174.01/173.91 [1735]~E(x17351,x17352)+E(f653(x17353,x17354,x17355,x17351),f653(x17353,x17354,x17355,x17352)) % 174.01/173.91 [1736]~E(x17361,x17362)+E(f425(x17361,x17363,x17364,x17365),f425(x17362,x17363,x17364,x17365)) % 174.01/173.91 [1737]~E(x17371,x17372)+E(f425(x17373,x17371,x17374,x17375),f425(x17373,x17372,x17374,x17375)) % 174.01/173.91 [1738]~E(x17381,x17382)+E(f425(x17383,x17384,x17381,x17385),f425(x17383,x17384,x17382,x17385)) % 174.01/173.91 [1739]~E(x17391,x17392)+E(f425(x17393,x17394,x17395,x17391),f425(x17393,x17394,x17395,x17392)) % 174.01/173.91 [1740]~E(x17401,x17402)+E(f698(x17401,x17403,x17404),f698(x17402,x17403,x17404)) % 174.01/173.91 [1741]~E(x17411,x17412)+E(f698(x17413,x17411,x17414),f698(x17413,x17412,x17414)) % 174.01/173.91 [1742]~E(x17421,x17422)+E(f698(x17423,x17424,x17421),f698(x17423,x17424,x17422)) % 174.01/173.91 [1743]~E(x17431,x17432)+E(f608(x17431,x17433,x17434),f608(x17432,x17433,x17434)) % 174.01/173.91 [1744]~E(x17441,x17442)+E(f608(x17443,x17441,x17444),f608(x17443,x17442,x17444)) % 174.01/173.91 [1745]~E(x17451,x17452)+E(f608(x17453,x17454,x17451),f608(x17453,x17454,x17452)) % 174.01/173.91 [1746]~E(x17461,x17462)+E(f813(x17461,x17463,x17464),f813(x17462,x17463,x17464)) % 174.01/173.91 [1747]~E(x17471,x17472)+E(f813(x17473,x17471,x17474),f813(x17473,x17472,x17474)) % 174.01/173.91 [1748]~E(x17481,x17482)+E(f813(x17483,x17484,x17481),f813(x17483,x17484,x17482)) % 174.01/173.91 [1749]~E(x17491,x17492)+E(f471(x17491,x17493,x17494),f471(x17492,x17493,x17494)) % 174.01/173.91 [1750]~E(x17501,x17502)+E(f471(x17503,x17501,x17504),f471(x17503,x17502,x17504)) % 174.01/173.91 [1751]~E(x17511,x17512)+E(f471(x17513,x17514,x17511),f471(x17513,x17514,x17512)) % 174.01/173.91 [1752]~E(x17521,x17522)+E(f237(x17521,x17523),f237(x17522,x17523)) % 174.01/173.91 [1753]~E(x17531,x17532)+E(f237(x17533,x17531),f237(x17533,x17532)) % 174.01/173.91 [1754]~E(x17541,x17542)+E(f717(x17541,x17543,x17544,x17545,x17546),f717(x17542,x17543,x17544,x17545,x17546)) % 174.01/173.91 [1755]~E(x17551,x17552)+E(f717(x17553,x17551,x17554,x17555,x17556),f717(x17553,x17552,x17554,x17555,x17556)) % 174.01/173.91 [1756]~E(x17561,x17562)+E(f717(x17563,x17564,x17561,x17565,x17566),f717(x17563,x17564,x17562,x17565,x17566)) % 174.01/173.91 [1757]~E(x17571,x17572)+E(f717(x17573,x17574,x17575,x17571,x17576),f717(x17573,x17574,x17575,x17572,x17576)) % 174.01/173.91 [1758]~E(x17581,x17582)+E(f717(x17583,x17584,x17585,x17586,x17581),f717(x17583,x17584,x17585,x17586,x17582)) % 174.01/173.91 [1759]~E(x17591,x17592)+E(f528(x17591,x17593,x17594),f528(x17592,x17593,x17594)) % 174.01/173.91 [1760]~E(x17601,x17602)+E(f528(x17603,x17601,x17604),f528(x17603,x17602,x17604)) % 174.01/173.91 [1761]~E(x17611,x17612)+E(f528(x17613,x17614,x17611),f528(x17613,x17614,x17612)) % 174.01/173.91 [1762]~E(x17621,x17622)+E(f342(x17621,x17623),f342(x17622,x17623)) % 174.01/173.91 [1763]~E(x17631,x17632)+E(f342(x17633,x17631),f342(x17633,x17632)) % 174.01/173.91 [1764]~E(x17641,x17642)+E(f439(x17641,x17643,x17644,x17645),f439(x17642,x17643,x17644,x17645)) % 174.01/173.91 [1765]~E(x17651,x17652)+E(f439(x17653,x17651,x17654,x17655),f439(x17653,x17652,x17654,x17655)) % 174.01/173.91 [1766]~E(x17661,x17662)+E(f439(x17663,x17664,x17661,x17665),f439(x17663,x17664,x17662,x17665)) % 174.01/173.91 [1767]~E(x17671,x17672)+E(f439(x17673,x17674,x17675,x17671),f439(x17673,x17674,x17675,x17672)) % 174.01/173.91 [1768]~E(x17681,x17682)+E(f674(x17681,x17683,x17684),f674(x17682,x17683,x17684)) % 174.01/173.91 [1769]~E(x17691,x17692)+E(f674(x17693,x17691,x17694),f674(x17693,x17692,x17694)) % 174.01/173.91 [1770]~E(x17701,x17702)+E(f674(x17703,x17704,x17701),f674(x17703,x17704,x17702)) % 174.01/173.91 [1771]~E(x17711,x17712)+E(f781(x17711,x17713,x17714),f781(x17712,x17713,x17714)) % 174.01/173.91 [1772]~E(x17721,x17722)+E(f781(x17723,x17721,x17724),f781(x17723,x17722,x17724)) % 174.01/173.91 [1773]~E(x17731,x17732)+E(f781(x17733,x17734,x17731),f781(x17733,x17734,x17732)) % 174.01/173.91 [1774]~E(x17741,x17742)+E(f690(x17741,x17743,x17744,x17745),f690(x17742,x17743,x17744,x17745)) % 174.01/173.91 [1775]~E(x17751,x17752)+E(f690(x17753,x17751,x17754,x17755),f690(x17753,x17752,x17754,x17755)) % 174.01/173.91 [1776]~E(x17761,x17762)+E(f690(x17763,x17764,x17761,x17765),f690(x17763,x17764,x17762,x17765)) % 174.01/173.91 [1777]~E(x17771,x17772)+E(f690(x17773,x17774,x17775,x17771),f690(x17773,x17774,x17775,x17772)) % 174.01/173.91 [1778]~E(x17781,x17782)+E(f322(x17781,x17783,x17784,x17785,x17786,x17787),f322(x17782,x17783,x17784,x17785,x17786,x17787)) % 174.01/173.91 [1779]~E(x17791,x17792)+E(f322(x17793,x17791,x17794,x17795,x17796,x17797),f322(x17793,x17792,x17794,x17795,x17796,x17797)) % 174.01/173.91 [1780]~E(x17801,x17802)+E(f322(x17803,x17804,x17801,x17805,x17806,x17807),f322(x17803,x17804,x17802,x17805,x17806,x17807)) % 174.01/173.91 [1781]~E(x17811,x17812)+E(f322(x17813,x17814,x17815,x17811,x17816,x17817),f322(x17813,x17814,x17815,x17812,x17816,x17817)) % 174.01/173.91 [1782]~E(x17821,x17822)+E(f322(x17823,x17824,x17825,x17826,x17821,x17827),f322(x17823,x17824,x17825,x17826,x17822,x17827)) % 174.01/173.91 [1783]~E(x17831,x17832)+E(f322(x17833,x17834,x17835,x17836,x17837,x17831),f322(x17833,x17834,x17835,x17836,x17837,x17832)) % 174.01/173.91 [1784]~E(x17841,x17842)+E(f141(x17841,x17843,x17844,x17845,x17846),f141(x17842,x17843,x17844,x17845,x17846)) % 174.01/173.91 [1785]~E(x17851,x17852)+E(f141(x17853,x17851,x17854,x17855,x17856),f141(x17853,x17852,x17854,x17855,x17856)) % 174.01/173.91 [1786]~E(x17861,x17862)+E(f141(x17863,x17864,x17861,x17865,x17866),f141(x17863,x17864,x17862,x17865,x17866)) % 174.01/173.91 [1787]~E(x17871,x17872)+E(f141(x17873,x17874,x17875,x17871,x17876),f141(x17873,x17874,x17875,x17872,x17876)) % 174.01/173.91 [1788]~E(x17881,x17882)+E(f141(x17883,x17884,x17885,x17886,x17881),f141(x17883,x17884,x17885,x17886,x17882)) % 174.01/173.91 [1789]~E(x17891,x17892)+E(f464(x17891,x17893,x17894),f464(x17892,x17893,x17894)) % 174.01/173.91 [1790]~E(x17901,x17902)+E(f464(x17903,x17901,x17904),f464(x17903,x17902,x17904)) % 174.01/173.91 [1791]~E(x17911,x17912)+E(f464(x17913,x17914,x17911),f464(x17913,x17914,x17912)) % 174.01/173.91 [1792]~E(x17921,x17922)+E(f437(x17921,x17923,x17924,x17925),f437(x17922,x17923,x17924,x17925)) % 174.01/173.91 [1793]~E(x17931,x17932)+E(f437(x17933,x17931,x17934,x17935),f437(x17933,x17932,x17934,x17935)) % 174.01/173.91 [1794]~E(x17941,x17942)+E(f437(x17943,x17944,x17941,x17945),f437(x17943,x17944,x17942,x17945)) % 174.01/173.91 [1795]~E(x17951,x17952)+E(f437(x17953,x17954,x17955,x17951),f437(x17953,x17954,x17955,x17952)) % 174.01/173.91 [1796]~E(x17961,x17962)+E(f459(x17961,x17963),f459(x17962,x17963)) % 174.01/173.91 [1797]~E(x17971,x17972)+E(f459(x17973,x17971),f459(x17973,x17972)) % 174.01/173.91 [1798]~E(x17981,x17982)+E(f745(x17981,x17983,x17984,x17985),f745(x17982,x17983,x17984,x17985)) % 174.01/173.91 [1799]~E(x17991,x17992)+E(f745(x17993,x17991,x17994,x17995),f745(x17993,x17992,x17994,x17995)) % 174.01/173.91 [1800]~E(x18001,x18002)+E(f745(x18003,x18004,x18001,x18005),f745(x18003,x18004,x18002,x18005)) % 174.01/173.91 [1801]~E(x18011,x18012)+E(f745(x18013,x18014,x18015,x18011),f745(x18013,x18014,x18015,x18012)) % 174.01/173.91 [1802]~E(x18021,x18022)+E(f676(x18021,x18023,x18024),f676(x18022,x18023,x18024)) % 174.01/173.91 [1803]~E(x18031,x18032)+E(f676(x18033,x18031,x18034),f676(x18033,x18032,x18034)) % 174.01/173.91 [1804]~E(x18041,x18042)+E(f676(x18043,x18044,x18041),f676(x18043,x18044,x18042)) % 174.01/173.91 [1805]~E(x18051,x18052)+E(f441(x18051,x18053,x18054,x18055),f441(x18052,x18053,x18054,x18055)) % 174.01/173.91 [1806]~E(x18061,x18062)+E(f441(x18063,x18061,x18064,x18065),f441(x18063,x18062,x18064,x18065)) % 174.01/173.91 [1807]~E(x18071,x18072)+E(f441(x18073,x18074,x18071,x18075),f441(x18073,x18074,x18072,x18075)) % 174.01/173.91 [1808]~E(x18081,x18082)+E(f441(x18083,x18084,x18085,x18081),f441(x18083,x18084,x18085,x18082)) % 174.01/173.91 [1809]~E(x18091,x18092)+E(f246(x18091,x18093,x18094),f246(x18092,x18093,x18094)) % 174.01/173.91 [1810]~E(x18101,x18102)+E(f246(x18103,x18101,x18104),f246(x18103,x18102,x18104)) % 174.01/173.91 [1811]~E(x18111,x18112)+E(f246(x18113,x18114,x18111),f246(x18113,x18114,x18112)) % 174.01/173.91 [1812]~E(x18121,x18122)+E(f277(x18121,x18123,x18124,x18125),f277(x18122,x18123,x18124,x18125)) % 174.01/173.91 [1813]~E(x18131,x18132)+E(f277(x18133,x18131,x18134,x18135),f277(x18133,x18132,x18134,x18135)) % 174.01/173.91 [1814]~E(x18141,x18142)+E(f277(x18143,x18144,x18141,x18145),f277(x18143,x18144,x18142,x18145)) % 174.01/173.91 [1815]~E(x18151,x18152)+E(f277(x18153,x18154,x18155,x18151),f277(x18153,x18154,x18155,x18152)) % 174.01/173.91 [1816]~E(x18161,x18162)+E(f195(x18161,x18163,x18164,x18165),f195(x18162,x18163,x18164,x18165)) % 174.01/173.91 [1817]~E(x18171,x18172)+E(f195(x18173,x18171,x18174,x18175),f195(x18173,x18172,x18174,x18175)) % 174.01/173.91 [1818]~E(x18181,x18182)+E(f195(x18183,x18184,x18181,x18185),f195(x18183,x18184,x18182,x18185)) % 174.01/173.91 [1819]~E(x18191,x18192)+E(f195(x18193,x18194,x18195,x18191),f195(x18193,x18194,x18195,x18192)) % 174.01/173.91 [1820]~E(x18201,x18202)+E(f734(x18201,x18203,x18204,x18205),f734(x18202,x18203,x18204,x18205)) % 174.01/173.91 [1821]~E(x18211,x18212)+E(f734(x18213,x18211,x18214,x18215),f734(x18213,x18212,x18214,x18215)) % 174.01/173.91 [1822]~E(x18221,x18222)+E(f734(x18223,x18224,x18221,x18225),f734(x18223,x18224,x18222,x18225)) % 174.01/173.91 [1823]~E(x18231,x18232)+E(f734(x18233,x18234,x18235,x18231),f734(x18233,x18234,x18235,x18232)) % 174.01/173.91 [1824]~E(x18241,x18242)+E(f762(x18241),f762(x18242)) % 174.01/173.91 [1825]~E(x18251,x18252)+E(f684(x18251,x18253),f684(x18252,x18253)) % 174.01/173.91 [1826]~E(x18261,x18262)+E(f684(x18263,x18261),f684(x18263,x18262)) % 174.01/173.91 [1827]~E(x18271,x18272)+E(f833(x18271,x18273,x18274),f833(x18272,x18273,x18274)) % 174.01/173.91 [1828]~E(x18281,x18282)+E(f833(x18283,x18281,x18284),f833(x18283,x18282,x18284)) % 174.01/173.91 [1829]~E(x18291,x18292)+E(f833(x18293,x18294,x18291),f833(x18293,x18294,x18292)) % 174.01/173.91 [1830]~E(x18301,x18302)+E(f376(x18301,x18303,x18304),f376(x18302,x18303,x18304)) % 174.01/173.91 [1831]~E(x18311,x18312)+E(f376(x18313,x18311,x18314),f376(x18313,x18312,x18314)) % 174.01/173.91 [1832]~E(x18321,x18322)+E(f376(x18323,x18324,x18321),f376(x18323,x18324,x18322)) % 174.01/173.91 [1833]~E(x18331,x18332)+E(f152(x18331,x18333),f152(x18332,x18333)) % 174.01/173.91 [1834]~E(x18341,x18342)+E(f152(x18343,x18341),f152(x18343,x18342)) % 174.01/173.91 [1835]~E(x18351,x18352)+E(f519(x18351,x18353,x18354,x18355),f519(x18352,x18353,x18354,x18355)) % 174.01/173.91 [1836]~E(x18361,x18362)+E(f519(x18363,x18361,x18364,x18365),f519(x18363,x18362,x18364,x18365)) % 174.01/173.91 [1837]~E(x18371,x18372)+E(f519(x18373,x18374,x18371,x18375),f519(x18373,x18374,x18372,x18375)) % 174.01/173.91 [1838]~E(x18381,x18382)+E(f519(x18383,x18384,x18385,x18381),f519(x18383,x18384,x18385,x18382)) % 174.01/173.91 [1839]~E(x18391,x18392)+E(f543(x18391,x18393,x18394,x18395,x18396,x18397),f543(x18392,x18393,x18394,x18395,x18396,x18397)) % 174.01/173.91 [1840]~E(x18401,x18402)+E(f543(x18403,x18401,x18404,x18405,x18406,x18407),f543(x18403,x18402,x18404,x18405,x18406,x18407)) % 174.01/173.91 [1841]~E(x18411,x18412)+E(f543(x18413,x18414,x18411,x18415,x18416,x18417),f543(x18413,x18414,x18412,x18415,x18416,x18417)) % 174.01/173.91 [1842]~E(x18421,x18422)+E(f543(x18423,x18424,x18425,x18421,x18426,x18427),f543(x18423,x18424,x18425,x18422,x18426,x18427)) % 174.01/173.91 [1843]~E(x18431,x18432)+E(f543(x18433,x18434,x18435,x18436,x18431,x18437),f543(x18433,x18434,x18435,x18436,x18432,x18437)) % 174.01/173.91 [1844]~E(x18441,x18442)+E(f543(x18443,x18444,x18445,x18446,x18447,x18441),f543(x18443,x18444,x18445,x18446,x18447,x18442)) % 174.01/173.91 [1845]~E(x18451,x18452)+E(f601(x18451,x18453,x18454,x18455),f601(x18452,x18453,x18454,x18455)) % 174.01/173.91 [1846]~E(x18461,x18462)+E(f601(x18463,x18461,x18464,x18465),f601(x18463,x18462,x18464,x18465)) % 174.01/173.91 [1847]~E(x18471,x18472)+E(f601(x18473,x18474,x18471,x18475),f601(x18473,x18474,x18472,x18475)) % 174.01/173.91 [1848]~E(x18481,x18482)+E(f601(x18483,x18484,x18485,x18481),f601(x18483,x18484,x18485,x18482)) % 174.01/173.91 [1849]~E(x18491,x18492)+E(f193(x18491,x18493,x18494,x18495),f193(x18492,x18493,x18494,x18495)) % 174.01/173.91 [1850]~E(x18501,x18502)+E(f193(x18503,x18501,x18504,x18505),f193(x18503,x18502,x18504,x18505)) % 174.01/173.91 [1851]~E(x18511,x18512)+E(f193(x18513,x18514,x18511,x18515),f193(x18513,x18514,x18512,x18515)) % 174.01/173.91 [1852]~E(x18521,x18522)+E(f193(x18523,x18524,x18525,x18521),f193(x18523,x18524,x18525,x18522)) % 174.01/173.91 [1853]~E(x18531,x18532)+E(f368(x18531,x18533,x18534,x18535,x18536),f368(x18532,x18533,x18534,x18535,x18536)) % 174.01/173.91 [1854]~E(x18541,x18542)+E(f368(x18543,x18541,x18544,x18545,x18546),f368(x18543,x18542,x18544,x18545,x18546)) % 174.01/173.91 [1855]~E(x18551,x18552)+E(f368(x18553,x18554,x18551,x18555,x18556),f368(x18553,x18554,x18552,x18555,x18556)) % 174.01/173.91 [1856]~E(x18561,x18562)+E(f368(x18563,x18564,x18565,x18561,x18566),f368(x18563,x18564,x18565,x18562,x18566)) % 174.01/173.91 [1857]~E(x18571,x18572)+E(f368(x18573,x18574,x18575,x18576,x18571),f368(x18573,x18574,x18575,x18576,x18572)) % 174.01/173.91 [1858]~E(x18581,x18582)+E(f582(x18581,x18583),f582(x18582,x18583)) % 174.01/173.91 [1859]~E(x18591,x18592)+E(f582(x18593,x18591),f582(x18593,x18592)) % 174.01/173.91 [1860]~E(x18601,x18602)+E(f432(x18601,x18603,x18604,x18605,x18606,x18607,x18608),f432(x18602,x18603,x18604,x18605,x18606,x18607,x18608)) % 174.01/173.91 [1861]~E(x18611,x18612)+E(f432(x18613,x18611,x18614,x18615,x18616,x18617,x18618),f432(x18613,x18612,x18614,x18615,x18616,x18617,x18618)) % 174.01/173.91 [1862]~E(x18621,x18622)+E(f432(x18623,x18624,x18621,x18625,x18626,x18627,x18628),f432(x18623,x18624,x18622,x18625,x18626,x18627,x18628)) % 174.01/173.91 [1863]~E(x18631,x18632)+E(f432(x18633,x18634,x18635,x18631,x18636,x18637,x18638),f432(x18633,x18634,x18635,x18632,x18636,x18637,x18638)) % 174.01/173.91 [1864]~E(x18641,x18642)+E(f432(x18643,x18644,x18645,x18646,x18641,x18647,x18648),f432(x18643,x18644,x18645,x18646,x18642,x18647,x18648)) % 174.01/173.91 [1865]~E(x18651,x18652)+E(f432(x18653,x18654,x18655,x18656,x18657,x18651,x18658),f432(x18653,x18654,x18655,x18656,x18657,x18652,x18658)) % 174.01/173.91 [1866]~E(x18661,x18662)+E(f432(x18663,x18664,x18665,x18666,x18667,x18668,x18661),f432(x18663,x18664,x18665,x18666,x18667,x18668,x18662)) % 174.01/173.91 [1867]~E(x18671,x18672)+E(f721(x18671,x18673,x18674,x18675,x18676),f721(x18672,x18673,x18674,x18675,x18676)) % 174.01/173.91 [1868]~E(x18681,x18682)+E(f721(x18683,x18681,x18684,x18685,x18686),f721(x18683,x18682,x18684,x18685,x18686)) % 174.01/173.91 [1869]~E(x18691,x18692)+E(f721(x18693,x18694,x18691,x18695,x18696),f721(x18693,x18694,x18692,x18695,x18696)) % 174.01/173.91 [1870]~E(x18701,x18702)+E(f721(x18703,x18704,x18705,x18701,x18706),f721(x18703,x18704,x18705,x18702,x18706)) % 174.01/173.91 [1871]~E(x18711,x18712)+E(f721(x18713,x18714,x18715,x18716,x18711),f721(x18713,x18714,x18715,x18716,x18712)) % 174.01/173.91 [1872]~E(x18721,x18722)+E(f809(x18721,x18723,x18724),f809(x18722,x18723,x18724)) % 174.01/173.91 [1873]~E(x18731,x18732)+E(f809(x18733,x18731,x18734),f809(x18733,x18732,x18734)) % 174.01/173.91 [1874]~E(x18741,x18742)+E(f809(x18743,x18744,x18741),f809(x18743,x18744,x18742)) % 174.01/173.91 [1875]~E(x18751,x18752)+E(f430(x18751,x18753,x18754,x18755),f430(x18752,x18753,x18754,x18755)) % 174.01/173.91 [1876]~E(x18761,x18762)+E(f430(x18763,x18761,x18764,x18765),f430(x18763,x18762,x18764,x18765)) % 174.01/173.91 [1877]~E(x18771,x18772)+E(f430(x18773,x18774,x18771,x18775),f430(x18773,x18774,x18772,x18775)) % 174.01/173.91 [1878]~E(x18781,x18782)+E(f430(x18783,x18784,x18785,x18781),f430(x18783,x18784,x18785,x18782)) % 174.01/173.91 [1879]~E(x18791,x18792)+E(f598(x18791,x18793),f598(x18792,x18793)) % 174.01/173.91 [1880]~E(x18801,x18802)+E(f598(x18803,x18801),f598(x18803,x18802)) % 174.01/173.91 [1881]~E(x18811,x18812)+E(f350(x18811,x18813,x18814,x18815),f350(x18812,x18813,x18814,x18815)) % 174.01/173.91 [1882]~E(x18821,x18822)+E(f350(x18823,x18821,x18824,x18825),f350(x18823,x18822,x18824,x18825)) % 174.01/173.91 [1883]~E(x18831,x18832)+E(f350(x18833,x18834,x18831,x18835),f350(x18833,x18834,x18832,x18835)) % 174.01/173.91 [1884]~E(x18841,x18842)+E(f350(x18843,x18844,x18845,x18841),f350(x18843,x18844,x18845,x18842)) % 174.01/173.91 [1885]~E(x18851,x18852)+E(f421(x18851,x18853,x18854),f421(x18852,x18853,x18854)) % 174.01/173.91 [1886]~E(x18861,x18862)+E(f421(x18863,x18861,x18864),f421(x18863,x18862,x18864)) % 174.01/173.91 [1887]~E(x18871,x18872)+E(f421(x18873,x18874,x18871),f421(x18873,x18874,x18872)) % 174.01/173.91 [1888]~E(x18881,x18882)+E(f632(x18881,x18883,x18884,x18885,x18886,x18887),f632(x18882,x18883,x18884,x18885,x18886,x18887)) % 174.01/173.91 [1889]~E(x18891,x18892)+E(f632(x18893,x18891,x18894,x18895,x18896,x18897),f632(x18893,x18892,x18894,x18895,x18896,x18897)) % 174.01/173.91 [1890]~E(x18901,x18902)+E(f632(x18903,x18904,x18901,x18905,x18906,x18907),f632(x18903,x18904,x18902,x18905,x18906,x18907)) % 174.01/173.91 [1891]~E(x18911,x18912)+E(f632(x18913,x18914,x18915,x18911,x18916,x18917),f632(x18913,x18914,x18915,x18912,x18916,x18917)) % 174.01/173.91 [1892]~E(x18921,x18922)+E(f632(x18923,x18924,x18925,x18926,x18921,x18927),f632(x18923,x18924,x18925,x18926,x18922,x18927)) % 174.01/173.91 [1893]~E(x18931,x18932)+E(f632(x18933,x18934,x18935,x18936,x18937,x18931),f632(x18933,x18934,x18935,x18936,x18937,x18932)) % 174.01/173.91 [1894]~E(x18941,x18942)+E(f607(x18941,x18943),f607(x18942,x18943)) % 174.01/173.91 [1895]~E(x18951,x18952)+E(f607(x18953,x18951),f607(x18953,x18952)) % 174.01/173.91 [1896]~E(x18961,x18962)+E(f592(x18961,x18963,x18964),f592(x18962,x18963,x18964)) % 174.01/173.91 [1897]~E(x18971,x18972)+E(f592(x18973,x18971,x18974),f592(x18973,x18972,x18974)) % 174.01/173.91 [1898]~E(x18981,x18982)+E(f592(x18983,x18984,x18981),f592(x18983,x18984,x18982)) % 174.01/173.91 [1899]~E(x18991,x18992)+E(f838(x18991,x18993,x18994,x18995,x18996,x18997,x18998),f838(x18992,x18993,x18994,x18995,x18996,x18997,x18998)) % 174.01/173.91 [1900]~E(x19001,x19002)+E(f838(x19003,x19001,x19004,x19005,x19006,x19007,x19008),f838(x19003,x19002,x19004,x19005,x19006,x19007,x19008)) % 174.01/173.91 [1901]~E(x19011,x19012)+E(f838(x19013,x19014,x19011,x19015,x19016,x19017,x19018),f838(x19013,x19014,x19012,x19015,x19016,x19017,x19018)) % 174.01/173.91 [1902]~E(x19021,x19022)+E(f838(x19023,x19024,x19025,x19021,x19026,x19027,x19028),f838(x19023,x19024,x19025,x19022,x19026,x19027,x19028)) % 174.01/173.91 [1903]~E(x19031,x19032)+E(f838(x19033,x19034,x19035,x19036,x19031,x19037,x19038),f838(x19033,x19034,x19035,x19036,x19032,x19037,x19038)) % 174.01/173.91 [1904]~E(x19041,x19042)+E(f838(x19043,x19044,x19045,x19046,x19047,x19041,x19048),f838(x19043,x19044,x19045,x19046,x19047,x19042,x19048)) % 174.01/173.91 [1905]~E(x19051,x19052)+E(f838(x19053,x19054,x19055,x19056,x19057,x19058,x19051),f838(x19053,x19054,x19055,x19056,x19057,x19058,x19052)) % 174.01/173.91 [1906]~E(x19061,x19062)+E(f749(x19061),f749(x19062)) % 174.01/173.91 [1907]~E(x19071,x19072)+E(f670(x19071,x19073,x19074,x19075,x19076,x19077,x19078),f670(x19072,x19073,x19074,x19075,x19076,x19077,x19078)) % 174.01/173.91 [1908]~E(x19081,x19082)+E(f670(x19083,x19081,x19084,x19085,x19086,x19087,x19088),f670(x19083,x19082,x19084,x19085,x19086,x19087,x19088)) % 174.01/173.91 [1909]~E(x19091,x19092)+E(f670(x19093,x19094,x19091,x19095,x19096,x19097,x19098),f670(x19093,x19094,x19092,x19095,x19096,x19097,x19098)) % 174.01/173.91 [1910]~E(x19101,x19102)+E(f670(x19103,x19104,x19105,x19101,x19106,x19107,x19108),f670(x19103,x19104,x19105,x19102,x19106,x19107,x19108)) % 174.01/173.91 [1911]~E(x19111,x19112)+E(f670(x19113,x19114,x19115,x19116,x19111,x19117,x19118),f670(x19113,x19114,x19115,x19116,x19112,x19117,x19118)) % 174.01/173.91 [1912]~E(x19121,x19122)+E(f670(x19123,x19124,x19125,x19126,x19127,x19121,x19128),f670(x19123,x19124,x19125,x19126,x19127,x19122,x19128)) % 174.01/173.91 [1913]~E(x19131,x19132)+E(f670(x19133,x19134,x19135,x19136,x19137,x19138,x19131),f670(x19133,x19134,x19135,x19136,x19137,x19138,x19132)) % 174.01/173.91 [1914]~E(x19141,x19142)+E(f709(x19141,x19143,x19144,x19145),f709(x19142,x19143,x19144,x19145)) % 174.01/173.91 [1915]~E(x19151,x19152)+E(f709(x19153,x19151,x19154,x19155),f709(x19153,x19152,x19154,x19155)) % 174.01/173.91 [1916]~E(x19161,x19162)+E(f709(x19163,x19164,x19161,x19165),f709(x19163,x19164,x19162,x19165)) % 174.01/173.91 [1917]~E(x19171,x19172)+E(f709(x19173,x19174,x19175,x19171),f709(x19173,x19174,x19175,x19172)) % 174.01/173.91 [1918]~E(x19181,x19182)+E(f431(x19181,x19183,x19184,x19185),f431(x19182,x19183,x19184,x19185)) % 174.01/173.91 [1919]~E(x19191,x19192)+E(f431(x19193,x19191,x19194,x19195),f431(x19193,x19192,x19194,x19195)) % 174.01/173.91 [1920]~E(x19201,x19202)+E(f431(x19203,x19204,x19201,x19205),f431(x19203,x19204,x19202,x19205)) % 174.01/173.91 [1921]~E(x19211,x19212)+E(f431(x19213,x19214,x19215,x19211),f431(x19213,x19214,x19215,x19212)) % 174.01/173.91 [1922]~E(x19221,x19222)+E(f288(x19221,x19223,x19224),f288(x19222,x19223,x19224)) % 174.01/173.91 [1923]~E(x19231,x19232)+E(f288(x19233,x19231,x19234),f288(x19233,x19232,x19234)) % 174.01/173.91 [1924]~E(x19241,x19242)+E(f288(x19243,x19244,x19241),f288(x19243,x19244,x19242)) % 174.01/173.91 [1925]~E(x19251,x19252)+E(f733(x19251,x19253,x19254,x19255,x19256),f733(x19252,x19253,x19254,x19255,x19256)) % 174.01/173.91 [1926]~E(x19261,x19262)+E(f733(x19263,x19261,x19264,x19265,x19266),f733(x19263,x19262,x19264,x19265,x19266)) % 174.01/173.91 [1927]~E(x19271,x19272)+E(f733(x19273,x19274,x19271,x19275,x19276),f733(x19273,x19274,x19272,x19275,x19276)) % 174.01/173.91 [1928]~E(x19281,x19282)+E(f733(x19283,x19284,x19285,x19281,x19286),f733(x19283,x19284,x19285,x19282,x19286)) % 174.01/173.91 [1929]~E(x19291,x19292)+E(f733(x19293,x19294,x19295,x19296,x19291),f733(x19293,x19294,x19295,x19296,x19292)) % 174.01/173.91 [1930]~E(x19301,x19302)+E(f765(x19301,x19303,x19304),f765(x19302,x19303,x19304)) % 174.01/173.91 [1931]~E(x19311,x19312)+E(f765(x19313,x19311,x19314),f765(x19313,x19312,x19314)) % 174.01/173.91 [1932]~E(x19321,x19322)+E(f765(x19323,x19324,x19321),f765(x19323,x19324,x19322)) % 174.01/173.91 [1933]~E(x19331,x19332)+E(f476(x19331,x19333,x19334),f476(x19332,x19333,x19334)) % 174.01/173.91 [1934]~E(x19341,x19342)+E(f476(x19343,x19341,x19344),f476(x19343,x19342,x19344)) % 174.01/173.91 [1935]~E(x19351,x19352)+E(f476(x19353,x19354,x19351),f476(x19353,x19354,x19352)) % 174.01/173.91 [1936]~E(x19361,x19362)+E(f199(x19361),f199(x19362)) % 174.01/173.91 [1937]~E(x19371,x19372)+E(f411(x19371,x19373,x19374,x19375),f411(x19372,x19373,x19374,x19375)) % 174.01/173.91 [1938]~E(x19381,x19382)+E(f411(x19383,x19381,x19384,x19385),f411(x19383,x19382,x19384,x19385)) % 174.01/173.91 [1939]~E(x19391,x19392)+E(f411(x19393,x19394,x19391,x19395),f411(x19393,x19394,x19392,x19395)) % 174.01/173.91 [1940]~E(x19401,x19402)+E(f411(x19403,x19404,x19405,x19401),f411(x19403,x19404,x19405,x19402)) % 174.01/173.91 [1941]~E(x19411,x19412)+E(f385(x19411,x19413,x19414,x19415,x19416),f385(x19412,x19413,x19414,x19415,x19416)) % 174.01/173.91 [1942]~E(x19421,x19422)+E(f385(x19423,x19421,x19424,x19425,x19426),f385(x19423,x19422,x19424,x19425,x19426)) % 174.01/173.91 [1943]~E(x19431,x19432)+E(f385(x19433,x19434,x19431,x19435,x19436),f385(x19433,x19434,x19432,x19435,x19436)) % 174.01/173.91 [1944]~E(x19441,x19442)+E(f385(x19443,x19444,x19445,x19441,x19446),f385(x19443,x19444,x19445,x19442,x19446)) % 174.01/173.91 [1945]~E(x19451,x19452)+E(f385(x19453,x19454,x19455,x19456,x19451),f385(x19453,x19454,x19455,x19456,x19452)) % 174.01/173.91 [1946]~E(x19461,x19462)+E(f549(x19461,x19463,x19464),f549(x19462,x19463,x19464)) % 174.01/173.91 [1947]~E(x19471,x19472)+E(f549(x19473,x19471,x19474),f549(x19473,x19472,x19474)) % 174.01/173.91 [1948]~E(x19481,x19482)+E(f549(x19483,x19484,x19481),f549(x19483,x19484,x19482)) % 174.01/173.91 [1949]~E(x19491,x19492)+E(f743(x19491,x19493,x19494,x19495),f743(x19492,x19493,x19494,x19495)) % 174.01/173.91 [1950]~E(x19501,x19502)+E(f743(x19503,x19501,x19504,x19505),f743(x19503,x19502,x19504,x19505)) % 174.01/173.91 [1951]~E(x19511,x19512)+E(f743(x19513,x19514,x19511,x19515),f743(x19513,x19514,x19512,x19515)) % 174.01/173.91 [1952]~E(x19521,x19522)+E(f743(x19523,x19524,x19525,x19521),f743(x19523,x19524,x19525,x19522)) % 174.01/173.91 [1953]~E(x19531,x19532)+E(f775(x19531),f775(x19532)) % 174.01/173.91 [1954]~E(x19541,x19542)+E(f613(x19541,x19543,x19544),f613(x19542,x19543,x19544)) % 174.01/173.91 [1955]~E(x19551,x19552)+E(f613(x19553,x19551,x19554),f613(x19553,x19552,x19554)) % 174.01/173.91 [1956]~E(x19561,x19562)+E(f613(x19563,x19564,x19561),f613(x19563,x19564,x19562)) % 174.01/173.91 [1957]~E(x19571,x19572)+E(f564(x19571,x19573,x19574,x19575),f564(x19572,x19573,x19574,x19575)) % 174.01/173.91 [1958]~E(x19581,x19582)+E(f564(x19583,x19581,x19584,x19585),f564(x19583,x19582,x19584,x19585)) % 174.01/173.91 [1959]~E(x19591,x19592)+E(f564(x19593,x19594,x19591,x19595),f564(x19593,x19594,x19592,x19595)) % 174.01/173.91 [1960]~E(x19601,x19602)+E(f564(x19603,x19604,x19605,x19601),f564(x19603,x19604,x19605,x19602)) % 174.01/173.91 [1961]~E(x19611,x19612)+E(f312(x19611),f312(x19612)) % 174.01/173.91 [1962]~E(x19621,x19622)+E(f615(x19621,x19623,x19624,x19625,x19626,x19627),f615(x19622,x19623,x19624,x19625,x19626,x19627)) % 174.01/173.91 [1963]~E(x19631,x19632)+E(f615(x19633,x19631,x19634,x19635,x19636,x19637),f615(x19633,x19632,x19634,x19635,x19636,x19637)) % 174.01/173.91 [1964]~E(x19641,x19642)+E(f615(x19643,x19644,x19641,x19645,x19646,x19647),f615(x19643,x19644,x19642,x19645,x19646,x19647)) % 174.01/173.91 [1965]~E(x19651,x19652)+E(f615(x19653,x19654,x19655,x19651,x19656,x19657),f615(x19653,x19654,x19655,x19652,x19656,x19657)) % 174.01/173.91 [1966]~E(x19661,x19662)+E(f615(x19663,x19664,x19665,x19666,x19661,x19667),f615(x19663,x19664,x19665,x19666,x19662,x19667)) % 174.01/173.91 [1967]~E(x19671,x19672)+E(f615(x19673,x19674,x19675,x19676,x19677,x19671),f615(x19673,x19674,x19675,x19676,x19677,x19672)) % 174.01/173.91 [1968]~E(x19681,x19682)+E(f197(x19681),f197(x19682)) % 174.01/173.91 [1969]~E(x19691,x19692)+E(f823(x19691,x19693,x19694),f823(x19692,x19693,x19694)) % 174.01/173.91 [1970]~E(x19701,x19702)+E(f823(x19703,x19701,x19704),f823(x19703,x19702,x19704)) % 174.01/173.91 [1971]~E(x19711,x19712)+E(f823(x19713,x19714,x19711),f823(x19713,x19714,x19712)) % 174.01/173.91 [1972]~E(x19721,x19722)+E(f511(x19721,x19723,x19724,x19725,x19726,x19727,x19728),f511(x19722,x19723,x19724,x19725,x19726,x19727,x19728)) % 174.01/173.91 [1973]~E(x19731,x19732)+E(f511(x19733,x19731,x19734,x19735,x19736,x19737,x19738),f511(x19733,x19732,x19734,x19735,x19736,x19737,x19738)) % 174.01/173.91 [1974]~E(x19741,x19742)+E(f511(x19743,x19744,x19741,x19745,x19746,x19747,x19748),f511(x19743,x19744,x19742,x19745,x19746,x19747,x19748)) % 174.01/173.91 [1975]~E(x19751,x19752)+E(f511(x19753,x19754,x19755,x19751,x19756,x19757,x19758),f511(x19753,x19754,x19755,x19752,x19756,x19757,x19758)) % 174.01/173.91 [1976]~E(x19761,x19762)+E(f511(x19763,x19764,x19765,x19766,x19761,x19767,x19768),f511(x19763,x19764,x19765,x19766,x19762,x19767,x19768)) % 174.01/173.91 [1977]~E(x19771,x19772)+E(f511(x19773,x19774,x19775,x19776,x19777,x19771,x19778),f511(x19773,x19774,x19775,x19776,x19777,x19772,x19778)) % 174.01/173.91 [1978]~E(x19781,x19782)+E(f511(x19783,x19784,x19785,x19786,x19787,x19788,x19781),f511(x19783,x19784,x19785,x19786,x19787,x19788,x19782)) % 174.01/173.91 [1979]~E(x19791,x19792)+E(f631(x19791,x19793,x19794),f631(x19792,x19793,x19794)) % 174.01/173.91 [1980]~E(x19801,x19802)+E(f631(x19803,x19801,x19804),f631(x19803,x19802,x19804)) % 174.01/173.91 [1981]~E(x19811,x19812)+E(f631(x19813,x19814,x19811),f631(x19813,x19814,x19812)) % 174.01/173.91 [1982]~E(x19821,x19822)+E(f310(x19821,x19823,x19824),f310(x19822,x19823,x19824)) % 174.01/173.91 [1983]~E(x19831,x19832)+E(f310(x19833,x19831,x19834),f310(x19833,x19832,x19834)) % 174.01/173.91 [1984]~E(x19841,x19842)+E(f310(x19843,x19844,x19841),f310(x19843,x19844,x19842)) % 174.01/173.91 [1985]~E(x19851,x19852)+E(f488(x19851,x19853,x19854,x19855),f488(x19852,x19853,x19854,x19855)) % 174.01/173.91 [1986]~E(x19861,x19862)+E(f488(x19863,x19861,x19864,x19865),f488(x19863,x19862,x19864,x19865)) % 174.01/173.91 [1987]~E(x19871,x19872)+E(f488(x19873,x19874,x19871,x19875),f488(x19873,x19874,x19872,x19875)) % 174.01/173.91 [1988]~E(x19881,x19882)+E(f488(x19883,x19884,x19885,x19881),f488(x19883,x19884,x19885,x19882)) % 174.01/173.91 [1989]~E(x19891,x19892)+E(f289(x19891,x19893,x19894),f289(x19892,x19893,x19894)) % 174.01/173.91 [1990]~E(x19901,x19902)+E(f289(x19903,x19901,x19904),f289(x19903,x19902,x19904)) % 174.01/173.91 [1991]~E(x19911,x19912)+E(f289(x19913,x19914,x19911),f289(x19913,x19914,x19912)) % 174.01/173.91 [1992]~E(x19921,x19922)+E(f211(x19921,x19923),f211(x19922,x19923)) % 174.01/173.91 [1993]~E(x19931,x19932)+E(f211(x19933,x19931),f211(x19933,x19932)) % 174.01/173.91 [1994]~E(x19941,x19942)+E(f355(x19941,x19943),f355(x19942,x19943)) % 174.01/173.91 [1995]~E(x19951,x19952)+E(f355(x19953,x19951),f355(x19953,x19952)) % 174.01/173.91 [1996]~E(x19961,x19962)+E(f215(x19961,x19963),f215(x19962,x19963)) % 174.01/173.91 [1997]~E(x19971,x19972)+E(f215(x19973,x19971),f215(x19973,x19972)) % 174.01/173.91 [1998]~E(x19981,x19982)+E(f292(x19981,x19983,x19984),f292(x19982,x19983,x19984)) % 174.01/173.91 [1999]~E(x19991,x19992)+E(f292(x19993,x19991,x19994),f292(x19993,x19992,x19994)) % 174.01/173.91 [2000]~E(x20001,x20002)+E(f292(x20003,x20004,x20001),f292(x20003,x20004,x20002)) % 174.01/173.91 [2001]~E(x20011,x20012)+E(f740(x20011,x20013,x20014,x20015),f740(x20012,x20013,x20014,x20015)) % 174.01/173.91 [2002]~E(x20021,x20022)+E(f740(x20023,x20021,x20024,x20025),f740(x20023,x20022,x20024,x20025)) % 174.01/173.91 [2003]~E(x20031,x20032)+E(f740(x20033,x20034,x20031,x20035),f740(x20033,x20034,x20032,x20035)) % 174.01/173.91 [2004]~E(x20041,x20042)+E(f740(x20043,x20044,x20045,x20041),f740(x20043,x20044,x20045,x20042)) % 174.01/173.91 [2005]~E(x20051,x20052)+E(f746(x20051,x20053,x20054,x20055),f746(x20052,x20053,x20054,x20055)) % 174.01/173.91 [2006]~E(x20061,x20062)+E(f746(x20063,x20061,x20064,x20065),f746(x20063,x20062,x20064,x20065)) % 174.01/173.91 [2007]~E(x20071,x20072)+E(f746(x20073,x20074,x20071,x20075),f746(x20073,x20074,x20072,x20075)) % 174.01/173.91 [2008]~E(x20081,x20082)+E(f746(x20083,x20084,x20085,x20081),f746(x20083,x20084,x20085,x20082)) % 174.01/173.91 [2009]~E(x20091,x20092)+E(f635(x20091,x20093,x20094),f635(x20092,x20093,x20094)) % 174.01/173.91 [2010]~E(x20101,x20102)+E(f635(x20103,x20101,x20104),f635(x20103,x20102,x20104)) % 174.01/173.91 [2011]~E(x20111,x20112)+E(f635(x20113,x20114,x20111),f635(x20113,x20114,x20112)) % 174.01/173.91 [2012]~E(x20121,x20122)+E(f668(x20121,x20123,x20124,x20125,x20126),f668(x20122,x20123,x20124,x20125,x20126)) % 174.01/173.91 [2013]~E(x20131,x20132)+E(f668(x20133,x20131,x20134,x20135,x20136),f668(x20133,x20132,x20134,x20135,x20136)) % 174.01/173.91 [2014]~E(x20141,x20142)+E(f668(x20143,x20144,x20141,x20145,x20146),f668(x20143,x20144,x20142,x20145,x20146)) % 174.01/173.91 [2015]~E(x20151,x20152)+E(f668(x20153,x20154,x20155,x20151,x20156),f668(x20153,x20154,x20155,x20152,x20156)) % 174.01/173.91 [2016]~E(x20161,x20162)+E(f668(x20163,x20164,x20165,x20166,x20161),f668(x20163,x20164,x20165,x20166,x20162)) % 174.01/173.91 [2017]~E(x20171,x20172)+E(f427(x20171,x20173,x20174),f427(x20172,x20173,x20174)) % 174.01/173.91 [2018]~E(x20181,x20182)+E(f427(x20183,x20181,x20184),f427(x20183,x20182,x20184)) % 174.01/173.91 [2019]~E(x20191,x20192)+E(f427(x20193,x20194,x20191),f427(x20193,x20194,x20192)) % 174.01/173.91 [2020]~E(x20201,x20202)+E(f824(x20201,x20203,x20204),f824(x20202,x20203,x20204)) % 174.01/173.91 [2021]~E(x20211,x20212)+E(f824(x20213,x20211,x20214),f824(x20213,x20212,x20214)) % 174.01/173.91 [2022]~E(x20221,x20222)+E(f824(x20223,x20224,x20221),f824(x20223,x20224,x20222)) % 174.01/173.91 [2023]~E(x20231,x20232)+E(f837(x20231,x20233,x20234,x20235,x20236,x20237,x20238),f837(x20232,x20233,x20234,x20235,x20236,x20237,x20238)) % 174.01/173.91 [2024]~E(x20241,x20242)+E(f837(x20243,x20241,x20244,x20245,x20246,x20247,x20248),f837(x20243,x20242,x20244,x20245,x20246,x20247,x20248)) % 174.01/173.91 [2025]~E(x20251,x20252)+E(f837(x20253,x20254,x20251,x20255,x20256,x20257,x20258),f837(x20253,x20254,x20252,x20255,x20256,x20257,x20258)) % 174.01/173.91 [2026]~E(x20261,x20262)+E(f837(x20263,x20264,x20265,x20261,x20266,x20267,x20268),f837(x20263,x20264,x20265,x20262,x20266,x20267,x20268)) % 174.01/173.91 [2027]~E(x20271,x20272)+E(f837(x20273,x20274,x20275,x20276,x20271,x20277,x20278),f837(x20273,x20274,x20275,x20276,x20272,x20277,x20278)) % 174.01/173.91 [2028]~E(x20281,x20282)+E(f837(x20283,x20284,x20285,x20286,x20287,x20281,x20288),f837(x20283,x20284,x20285,x20286,x20287,x20282,x20288)) % 174.01/173.91 [2029]~E(x20291,x20292)+E(f837(x20293,x20294,x20295,x20296,x20297,x20298,x20291),f837(x20293,x20294,x20295,x20296,x20297,x20298,x20292)) % 174.01/173.91 [2030]~E(x20301,x20302)+E(f574(x20301,x20303,x20304),f574(x20302,x20303,x20304)) % 174.01/173.91 [2031]~E(x20311,x20312)+E(f574(x20313,x20311,x20314),f574(x20313,x20312,x20314)) % 174.01/173.91 [2032]~E(x20321,x20322)+E(f574(x20323,x20324,x20321),f574(x20323,x20324,x20322)) % 174.01/173.91 [2033]~E(x20331,x20332)+E(f360(x20331,x20333,x20334,x20335),f360(x20332,x20333,x20334,x20335)) % 174.01/173.91 [2034]~E(x20341,x20342)+E(f360(x20343,x20341,x20344,x20345),f360(x20343,x20342,x20344,x20345)) % 174.01/173.91 [2035]~E(x20351,x20352)+E(f360(x20353,x20354,x20351,x20355),f360(x20353,x20354,x20352,x20355)) % 174.01/173.91 [2036]~E(x20361,x20362)+E(f360(x20363,x20364,x20365,x20361),f360(x20363,x20364,x20365,x20362)) % 174.01/173.91 [2037]~E(x20371,x20372)+E(f826(x20371,x20373,x20374),f826(x20372,x20373,x20374)) % 174.01/173.91 [2038]~E(x20381,x20382)+E(f826(x20383,x20381,x20384),f826(x20383,x20382,x20384)) % 174.01/173.91 [2039]~E(x20391,x20392)+E(f826(x20393,x20394,x20391),f826(x20393,x20394,x20392)) % 174.01/173.91 [2040]~E(x20401,x20402)+E(f275(x20401),f275(x20402)) % 174.01/173.91 [2041]~E(x20411,x20412)+E(f520(x20411,x20413),f520(x20412,x20413)) % 174.01/173.91 [2042]~E(x20421,x20422)+E(f520(x20423,x20421),f520(x20423,x20422)) % 174.01/173.91 [2043]~E(x20431,x20432)+E(f452(x20431,x20433,x20434),f452(x20432,x20433,x20434)) % 174.01/173.91 [2044]~E(x20441,x20442)+E(f452(x20443,x20441,x20444),f452(x20443,x20442,x20444)) % 174.01/173.91 [2045]~E(x20451,x20452)+E(f452(x20453,x20454,x20451),f452(x20453,x20454,x20452)) % 174.01/173.91 [2046]~E(x20461,x20462)+E(f719(x20461,x20463,x20464,x20465,x20466),f719(x20462,x20463,x20464,x20465,x20466)) % 174.01/173.91 [2047]~E(x20471,x20472)+E(f719(x20473,x20471,x20474,x20475,x20476),f719(x20473,x20472,x20474,x20475,x20476)) % 174.01/173.91 [2048]~E(x20481,x20482)+E(f719(x20483,x20484,x20481,x20485,x20486),f719(x20483,x20484,x20482,x20485,x20486)) % 174.01/173.91 [2049]~E(x20491,x20492)+E(f719(x20493,x20494,x20495,x20491,x20496),f719(x20493,x20494,x20495,x20492,x20496)) % 174.01/173.91 [2050]~E(x20501,x20502)+E(f719(x20503,x20504,x20505,x20506,x20501),f719(x20503,x20504,x20505,x20506,x20502)) % 174.01/173.91 [2051]~E(x20511,x20512)+E(f473(x20511),f473(x20512)) % 174.01/173.91 [2052]~E(x20521,x20522)+E(f640(x20521,x20523,x20524),f640(x20522,x20523,x20524)) % 174.01/173.91 [2053]~E(x20531,x20532)+E(f640(x20533,x20531,x20534),f640(x20533,x20532,x20534)) % 174.01/173.91 [2054]~E(x20541,x20542)+E(f640(x20543,x20544,x20541),f640(x20543,x20544,x20542)) % 174.01/173.91 [2055]~E(x20551,x20552)+E(f480(x20551,x20553,x20554,x20555,x20556),f480(x20552,x20553,x20554,x20555,x20556)) % 174.01/173.91 [2056]~E(x20561,x20562)+E(f480(x20563,x20561,x20564,x20565,x20566),f480(x20563,x20562,x20564,x20565,x20566)) % 174.01/173.91 [2057]~E(x20571,x20572)+E(f480(x20573,x20574,x20571,x20575,x20576),f480(x20573,x20574,x20572,x20575,x20576)) % 174.01/173.91 [2058]~E(x20581,x20582)+E(f480(x20583,x20584,x20585,x20581,x20586),f480(x20583,x20584,x20585,x20582,x20586)) % 174.01/173.91 [2059]~E(x20591,x20592)+E(f480(x20593,x20594,x20595,x20596,x20591),f480(x20593,x20594,x20595,x20596,x20592)) % 174.01/173.91 [2060]~E(x20601,x20602)+E(f529(x20601,x20603,x20604,x20605),f529(x20602,x20603,x20604,x20605)) % 174.01/173.91 [2061]~E(x20611,x20612)+E(f529(x20613,x20611,x20614,x20615),f529(x20613,x20612,x20614,x20615)) % 174.01/173.91 [2062]~E(x20621,x20622)+E(f529(x20623,x20624,x20621,x20625),f529(x20623,x20624,x20622,x20625)) % 174.01/173.91 [2063]~E(x20631,x20632)+E(f529(x20633,x20634,x20635,x20631),f529(x20633,x20634,x20635,x20632)) % 174.01/173.91 [2064]~E(x20641,x20642)+E(f716(x20641,x20643,x20644,x20645,x20646),f716(x20642,x20643,x20644,x20645,x20646)) % 174.01/173.91 [2065]~E(x20651,x20652)+E(f716(x20653,x20651,x20654,x20655,x20656),f716(x20653,x20652,x20654,x20655,x20656)) % 174.01/173.91 [2066]~E(x20661,x20662)+E(f716(x20663,x20664,x20661,x20665,x20666),f716(x20663,x20664,x20662,x20665,x20666)) % 174.01/173.91 [2067]~E(x20671,x20672)+E(f716(x20673,x20674,x20675,x20671,x20676),f716(x20673,x20674,x20675,x20672,x20676)) % 174.01/173.91 [2068]~E(x20681,x20682)+E(f716(x20683,x20684,x20685,x20686,x20681),f716(x20683,x20684,x20685,x20686,x20682)) % 174.01/173.91 [2069]~E(x20691,x20692)+E(f389(x20691,x20693,x20694,x20695,x20696),f389(x20692,x20693,x20694,x20695,x20696)) % 174.01/173.91 [2070]~E(x20701,x20702)+E(f389(x20703,x20701,x20704,x20705,x20706),f389(x20703,x20702,x20704,x20705,x20706)) % 174.01/173.91 [2071]~E(x20711,x20712)+E(f389(x20713,x20714,x20711,x20715,x20716),f389(x20713,x20714,x20712,x20715,x20716)) % 174.01/173.91 [2072]~E(x20721,x20722)+E(f389(x20723,x20724,x20725,x20721,x20726),f389(x20723,x20724,x20725,x20722,x20726)) % 174.01/173.91 [2073]~E(x20731,x20732)+E(f389(x20733,x20734,x20735,x20736,x20731),f389(x20733,x20734,x20735,x20736,x20732)) % 174.01/173.91 [2074]~E(x20741,x20742)+E(f399(x20741,x20743,x20744),f399(x20742,x20743,x20744)) % 174.01/173.91 [2075]~E(x20751,x20752)+E(f399(x20753,x20751,x20754),f399(x20753,x20752,x20754)) % 174.01/173.91 [2076]~E(x20761,x20762)+E(f399(x20763,x20764,x20761),f399(x20763,x20764,x20762)) % 174.01/173.91 [2077]~E(x20771,x20772)+E(f537(x20771,x20773,x20774,x20775,x20776,x20777,x20778,x20779),f537(x20772,x20773,x20774,x20775,x20776,x20777,x20778,x20779)) % 174.01/173.91 [2078]~E(x20781,x20782)+E(f537(x20783,x20781,x20784,x20785,x20786,x20787,x20788,x20789),f537(x20783,x20782,x20784,x20785,x20786,x20787,x20788,x20789)) % 174.01/173.91 [2079]~E(x20791,x20792)+E(f537(x20793,x20794,x20791,x20795,x20796,x20797,x20798,x20799),f537(x20793,x20794,x20792,x20795,x20796,x20797,x20798,x20799)) % 174.01/173.91 [2080]~E(x20801,x20802)+E(f537(x20803,x20804,x20805,x20801,x20806,x20807,x20808,x20809),f537(x20803,x20804,x20805,x20802,x20806,x20807,x20808,x20809)) % 174.01/173.91 [2081]~E(x20811,x20812)+E(f537(x20813,x20814,x20815,x20816,x20811,x20817,x20818,x20819),f537(x20813,x20814,x20815,x20816,x20812,x20817,x20818,x20819)) % 174.01/173.91 [2082]~E(x20821,x20822)+E(f537(x20823,x20824,x20825,x20826,x20827,x20821,x20828,x20829),f537(x20823,x20824,x20825,x20826,x20827,x20822,x20828,x20829)) % 174.01/173.91 [2083]~E(x20831,x20832)+E(f537(x20833,x20834,x20835,x20836,x20837,x20838,x20831,x20839),f537(x20833,x20834,x20835,x20836,x20837,x20838,x20832,x20839)) % 174.01/173.91 [2084]~E(x20841,x20842)+E(f537(x20843,x20844,x20845,x20846,x20847,x20848,x20849,x20841),f537(x20843,x20844,x20845,x20846,x20847,x20848,x20849,x20842)) % 174.01/173.91 [2085]~E(x20851,x20852)+E(f131(x20851),f131(x20852)) % 174.01/173.91 [2086]~E(x20861,x20862)+E(f642(x20861,x20863,x20864),f642(x20862,x20863,x20864)) % 174.01/173.91 [2087]~E(x20871,x20872)+E(f642(x20873,x20871,x20874),f642(x20873,x20872,x20874)) % 174.01/173.91 [2088]~E(x20881,x20882)+E(f642(x20883,x20884,x20881),f642(x20883,x20884,x20882)) % 174.01/173.91 [2089]~E(x20891,x20892)+E(f593(x20891,x20893,x20894,x20895),f593(x20892,x20893,x20894,x20895)) % 174.01/173.91 [2090]~E(x20901,x20902)+E(f593(x20903,x20901,x20904,x20905),f593(x20903,x20902,x20904,x20905)) % 174.01/173.91 [2091]~E(x20911,x20912)+E(f593(x20913,x20914,x20911,x20915),f593(x20913,x20914,x20912,x20915)) % 174.01/173.91 [2092]~E(x20921,x20922)+E(f593(x20923,x20924,x20925,x20921),f593(x20923,x20924,x20925,x20922)) % 174.01/173.91 [2093]~E(x20931,x20932)+E(f440(x20931,x20933,x20934,x20935),f440(x20932,x20933,x20934,x20935)) % 174.01/173.91 [2094]~E(x20941,x20942)+E(f440(x20943,x20941,x20944,x20945),f440(x20943,x20942,x20944,x20945)) % 174.01/173.91 [2095]~E(x20951,x20952)+E(f440(x20953,x20954,x20951,x20955),f440(x20953,x20954,x20952,x20955)) % 174.01/173.91 [2096]~E(x20961,x20962)+E(f440(x20963,x20964,x20965,x20961),f440(x20963,x20964,x20965,x20962)) % 174.01/173.91 [2097]~E(x20971,x20972)+E(f636(x20971,x20973),f636(x20972,x20973)) % 174.01/173.91 [2098]~E(x20981,x20982)+E(f636(x20983,x20981),f636(x20983,x20982)) % 174.01/173.91 [2099]~E(x20991,x20992)+E(f814(x20991,x20993,x20994,x20995,x20996),f814(x20992,x20993,x20994,x20995,x20996)) % 174.01/173.91 [2100]~E(x21001,x21002)+E(f814(x21003,x21001,x21004,x21005,x21006),f814(x21003,x21002,x21004,x21005,x21006)) % 174.01/173.91 [2101]~E(x21011,x21012)+E(f814(x21013,x21014,x21011,x21015,x21016),f814(x21013,x21014,x21012,x21015,x21016)) % 174.01/173.91 [2102]~E(x21021,x21022)+E(f814(x21023,x21024,x21025,x21021,x21026),f814(x21023,x21024,x21025,x21022,x21026)) % 174.01/173.91 [2103]~E(x21031,x21032)+E(f814(x21033,x21034,x21035,x21036,x21031),f814(x21033,x21034,x21035,x21036,x21032)) % 174.01/173.91 [2104]~E(x21041,x21042)+E(f556(x21041),f556(x21042)) % 174.01/173.91 [2105]~E(x21051,x21052)+E(f401(x21051,x21053,x21054,x21055),f401(x21052,x21053,x21054,x21055)) % 174.01/173.91 [2106]~E(x21061,x21062)+E(f401(x21063,x21061,x21064,x21065),f401(x21063,x21062,x21064,x21065)) % 174.01/173.91 [2107]~E(x21071,x21072)+E(f401(x21073,x21074,x21071,x21075),f401(x21073,x21074,x21072,x21075)) % 174.01/173.91 [2108]~E(x21081,x21082)+E(f401(x21083,x21084,x21085,x21081),f401(x21083,x21084,x21085,x21082)) % 174.01/173.91 [2109]~E(x21091,x21092)+E(f449(x21091,x21093),f449(x21092,x21093)) % 174.01/173.91 [2110]~E(x21101,x21102)+E(f449(x21103,x21101),f449(x21103,x21102)) % 174.01/173.91 [2111]~E(x21111,x21112)+E(f21(x21111,x21113,x21114,x21115),f21(x21112,x21113,x21114,x21115)) % 174.01/173.91 [2112]~E(x21121,x21122)+E(f21(x21123,x21121,x21124,x21125),f21(x21123,x21122,x21124,x21125)) % 174.01/173.91 [2113]~E(x21131,x21132)+E(f21(x21133,x21134,x21131,x21135),f21(x21133,x21134,x21132,x21135)) % 174.01/173.91 [2114]~E(x21141,x21142)+E(f21(x21143,x21144,x21145,x21141),f21(x21143,x21144,x21145,x21142)) % 174.01/173.91 [2115]~E(x21151,x21152)+E(f795(x21151,x21153,x21154),f795(x21152,x21153,x21154)) % 174.01/173.91 [2116]~E(x21161,x21162)+E(f795(x21163,x21161,x21164),f795(x21163,x21162,x21164)) % 174.01/173.91 [2117]~E(x21171,x21172)+E(f795(x21173,x21174,x21171),f795(x21173,x21174,x21172)) % 174.01/173.91 [2118]~E(x21181,x21182)+E(f314(x21181,x21183,x21184),f314(x21182,x21183,x21184)) % 174.01/173.91 [2119]~E(x21191,x21192)+E(f314(x21193,x21191,x21194),f314(x21193,x21192,x21194)) % 174.01/173.91 [2120]~E(x21201,x21202)+E(f314(x21203,x21204,x21201),f314(x21203,x21204,x21202)) % 174.01/173.91 [2121]~E(x21211,x21212)+E(f804(x21211,x21213,x21214),f804(x21212,x21213,x21214)) % 174.01/173.91 [2122]~E(x21221,x21222)+E(f804(x21223,x21221,x21224),f804(x21223,x21222,x21224)) % 174.01/173.91 [2123]~E(x21231,x21232)+E(f804(x21233,x21234,x21231),f804(x21233,x21234,x21232)) % 174.01/173.91 [2124]~E(x21241,x21242)+E(f396(x21241,x21243,x21244),f396(x21242,x21243,x21244)) % 174.01/173.91 [2125]~E(x21251,x21252)+E(f396(x21253,x21251,x21254),f396(x21253,x21252,x21254)) % 174.01/173.91 [2126]~E(x21261,x21262)+E(f396(x21263,x21264,x21261),f396(x21263,x21264,x21262)) % 174.01/173.91 [2127]~E(x21271,x21272)+E(f801(x21271,x21273),f801(x21272,x21273)) % 174.01/173.91 [2128]~E(x21281,x21282)+E(f801(x21283,x21281),f801(x21283,x21282)) % 174.01/173.91 [2129]~E(x21291,x21292)+E(f510(x21291,x21293,x21294),f510(x21292,x21293,x21294)) % 174.01/173.91 [2130]~E(x21301,x21302)+E(f510(x21303,x21301,x21304),f510(x21303,x21302,x21304)) % 174.01/173.91 [2131]~E(x21311,x21312)+E(f510(x21313,x21314,x21311),f510(x21313,x21314,x21312)) % 174.01/173.91 [2132]~E(x21321,x21322)+E(f767(x21321,x21323,x21324),f767(x21322,x21323,x21324)) % 174.01/173.91 [2133]~E(x21331,x21332)+E(f767(x21333,x21331,x21334),f767(x21333,x21332,x21334)) % 174.01/173.91 [2134]~E(x21341,x21342)+E(f767(x21343,x21344,x21341),f767(x21343,x21344,x21342)) % 174.01/173.91 [2135]~E(x21351,x21352)+E(f805(x21351,x21353,x21354),f805(x21352,x21353,x21354)) % 174.01/173.91 [2136]~E(x21361,x21362)+E(f805(x21363,x21361,x21364),f805(x21363,x21362,x21364)) % 174.01/173.91 [2137]~E(x21371,x21372)+E(f805(x21373,x21374,x21371),f805(x21373,x21374,x21372)) % 174.01/173.91 [2138]~E(x21381,x21382)+E(f398(x21381,x21383,x21384,x21385,x21386),f398(x21382,x21383,x21384,x21385,x21386)) % 174.01/173.91 [2139]~E(x21391,x21392)+E(f398(x21393,x21391,x21394,x21395,x21396),f398(x21393,x21392,x21394,x21395,x21396)) % 174.01/173.91 [2140]~E(x21401,x21402)+E(f398(x21403,x21404,x21401,x21405,x21406),f398(x21403,x21404,x21402,x21405,x21406)) % 174.01/173.91 [2141]~E(x21411,x21412)+E(f398(x21413,x21414,x21415,x21411,x21416),f398(x21413,x21414,x21415,x21412,x21416)) % 174.01/173.91 [2142]~E(x21421,x21422)+E(f398(x21423,x21424,x21425,x21426,x21421),f398(x21423,x21424,x21425,x21426,x21422)) % 174.01/173.91 [2143]~E(x21431,x21432)+E(f667(x21431,x21433,x21434,x21435,x21436),f667(x21432,x21433,x21434,x21435,x21436)) % 174.01/173.91 [2144]~E(x21441,x21442)+E(f667(x21443,x21441,x21444,x21445,x21446),f667(x21443,x21442,x21444,x21445,x21446)) % 174.01/173.91 [2145]~E(x21451,x21452)+E(f667(x21453,x21454,x21451,x21455,x21456),f667(x21453,x21454,x21452,x21455,x21456)) % 174.01/173.91 [2146]~E(x21461,x21462)+E(f667(x21463,x21464,x21465,x21461,x21466),f667(x21463,x21464,x21465,x21462,x21466)) % 174.01/173.91 [2147]~E(x21471,x21472)+E(f667(x21473,x21474,x21475,x21476,x21471),f667(x21473,x21474,x21475,x21476,x21472)) % 174.01/173.91 [2148]~E(x21481,x21482)+E(f351(x21481,x21483,x21484,x21485),f351(x21482,x21483,x21484,x21485)) % 174.01/173.91 [2149]~E(x21491,x21492)+E(f351(x21493,x21491,x21494,x21495),f351(x21493,x21492,x21494,x21495)) % 174.01/173.91 [2150]~E(x21501,x21502)+E(f351(x21503,x21504,x21501,x21505),f351(x21503,x21504,x21502,x21505)) % 174.01/173.91 [2151]~E(x21511,x21512)+E(f351(x21513,x21514,x21515,x21511),f351(x21513,x21514,x21515,x21512)) % 174.01/173.91 [2152]~E(x21521,x21522)+E(f194(x21521,x21523,x21524,x21525),f194(x21522,x21523,x21524,x21525)) % 174.01/173.91 [2153]~E(x21531,x21532)+E(f194(x21533,x21531,x21534,x21535),f194(x21533,x21532,x21534,x21535)) % 174.01/173.91 [2154]~E(x21541,x21542)+E(f194(x21543,x21544,x21541,x21545),f194(x21543,x21544,x21542,x21545)) % 174.01/173.91 [2155]~E(x21551,x21552)+E(f194(x21553,x21554,x21555,x21551),f194(x21553,x21554,x21555,x21552)) % 174.01/173.91 [2156]~E(x21561,x21562)+E(f694(x21561,x21563,x21564,x21565),f694(x21562,x21563,x21564,x21565)) % 174.01/173.91 [2157]~E(x21571,x21572)+E(f694(x21573,x21571,x21574,x21575),f694(x21573,x21572,x21574,x21575)) % 174.01/173.91 [2158]~E(x21581,x21582)+E(f694(x21583,x21584,x21581,x21585),f694(x21583,x21584,x21582,x21585)) % 174.01/173.91 [2159]~E(x21591,x21592)+E(f694(x21593,x21594,x21595,x21591),f694(x21593,x21594,x21595,x21592)) % 174.01/173.91 [2160]~E(x21601,x21602)+E(f370(x21601,x21603,x21604,x21605,x21606),f370(x21602,x21603,x21604,x21605,x21606)) % 174.01/173.91 [2161]~E(x21611,x21612)+E(f370(x21613,x21611,x21614,x21615,x21616),f370(x21613,x21612,x21614,x21615,x21616)) % 174.01/173.91 [2162]~E(x21621,x21622)+E(f370(x21623,x21624,x21621,x21625,x21626),f370(x21623,x21624,x21622,x21625,x21626)) % 174.01/173.91 [2163]~E(x21631,x21632)+E(f370(x21633,x21634,x21635,x21631,x21636),f370(x21633,x21634,x21635,x21632,x21636)) % 174.01/173.91 [2164]~E(x21641,x21642)+E(f370(x21643,x21644,x21645,x21646,x21641),f370(x21643,x21644,x21645,x21646,x21642)) % 174.01/173.91 [2165]~E(x21651,x21652)+E(f482(x21651,x21653,x21654,x21655,x21656),f482(x21652,x21653,x21654,x21655,x21656)) % 174.01/173.91 [2166]~E(x21661,x21662)+E(f482(x21663,x21661,x21664,x21665,x21666),f482(x21663,x21662,x21664,x21665,x21666)) % 174.01/173.91 [2167]~E(x21671,x21672)+E(f482(x21673,x21674,x21671,x21675,x21676),f482(x21673,x21674,x21672,x21675,x21676)) % 174.01/173.91 [2168]~E(x21681,x21682)+E(f482(x21683,x21684,x21685,x21681,x21686),f482(x21683,x21684,x21685,x21682,x21686)) % 174.01/173.91 [2169]~E(x21691,x21692)+E(f482(x21693,x21694,x21695,x21696,x21691),f482(x21693,x21694,x21695,x21696,x21692)) % 174.01/173.91 [2170]~E(x21701,x21702)+E(f366(x21701,x21703,x21704,x21705,x21706),f366(x21702,x21703,x21704,x21705,x21706)) % 174.01/173.91 [2171]~E(x21711,x21712)+E(f366(x21713,x21711,x21714,x21715,x21716),f366(x21713,x21712,x21714,x21715,x21716)) % 174.01/173.91 [2172]~E(x21721,x21722)+E(f366(x21723,x21724,x21721,x21725,x21726),f366(x21723,x21724,x21722,x21725,x21726)) % 174.01/173.91 [2173]~E(x21731,x21732)+E(f366(x21733,x21734,x21735,x21731,x21736),f366(x21733,x21734,x21735,x21732,x21736)) % 174.01/173.91 [2174]~E(x21741,x21742)+E(f366(x21743,x21744,x21745,x21746,x21741),f366(x21743,x21744,x21745,x21746,x21742)) % 174.01/173.91 [2175]~E(x21751,x21752)+E(f443(x21751,x21753,x21754,x21755,x21756),f443(x21752,x21753,x21754,x21755,x21756)) % 174.01/173.91 [2176]~E(x21761,x21762)+E(f443(x21763,x21761,x21764,x21765,x21766),f443(x21763,x21762,x21764,x21765,x21766)) % 174.01/173.91 [2177]~E(x21771,x21772)+E(f443(x21773,x21774,x21771,x21775,x21776),f443(x21773,x21774,x21772,x21775,x21776)) % 174.01/173.91 [2178]~E(x21781,x21782)+E(f443(x21783,x21784,x21785,x21781,x21786),f443(x21783,x21784,x21785,x21782,x21786)) % 174.01/173.91 [2179]~E(x21791,x21792)+E(f443(x21793,x21794,x21795,x21796,x21791),f443(x21793,x21794,x21795,x21796,x21792)) % 174.01/173.91 [2180]~E(x21801,x21802)+E(f391(x21801,x21803,x21804,x21805,x21806),f391(x21802,x21803,x21804,x21805,x21806)) % 174.01/173.91 [2181]~E(x21811,x21812)+E(f391(x21813,x21811,x21814,x21815,x21816),f391(x21813,x21812,x21814,x21815,x21816)) % 174.01/173.91 [2182]~E(x21821,x21822)+E(f391(x21823,x21824,x21821,x21825,x21826),f391(x21823,x21824,x21822,x21825,x21826)) % 174.01/173.91 [2183]~E(x21831,x21832)+E(f391(x21833,x21834,x21835,x21831,x21836),f391(x21833,x21834,x21835,x21832,x21836)) % 174.01/173.91 [2184]~E(x21841,x21842)+E(f391(x21843,x21844,x21845,x21846,x21841),f391(x21843,x21844,x21845,x21846,x21842)) % 174.01/173.91 [2185]~E(x21851,x21852)+E(f232(x21851,x21853,x21854,x21855,x21856),f232(x21852,x21853,x21854,x21855,x21856)) % 174.01/173.91 [2186]~E(x21861,x21862)+E(f232(x21863,x21861,x21864,x21865,x21866),f232(x21863,x21862,x21864,x21865,x21866)) % 174.01/173.91 [2187]~E(x21871,x21872)+E(f232(x21873,x21874,x21871,x21875,x21876),f232(x21873,x21874,x21872,x21875,x21876)) % 174.01/173.91 [2188]~E(x21881,x21882)+E(f232(x21883,x21884,x21885,x21881,x21886),f232(x21883,x21884,x21885,x21882,x21886)) % 174.01/173.91 [2189]~E(x21891,x21892)+E(f232(x21893,x21894,x21895,x21896,x21891),f232(x21893,x21894,x21895,x21896,x21892)) % 174.01/173.91 [2190]~E(x21901,x21902)+E(f726(x21901,x21903,x21904),f726(x21902,x21903,x21904)) % 174.01/173.91 [2191]~E(x21911,x21912)+E(f726(x21913,x21911,x21914),f726(x21913,x21912,x21914)) % 174.01/173.91 [2192]~E(x21921,x21922)+E(f726(x21923,x21924,x21921),f726(x21923,x21924,x21922)) % 174.01/173.91 [2193]~E(x21931,x21932)+E(f345(x21931,x21933),f345(x21932,x21933)) % 174.01/173.91 [2194]~E(x21941,x21942)+E(f345(x21943,x21941),f345(x21943,x21942)) % 174.01/173.91 [2195]~E(x21951,x21952)+E(f201(x21951),f201(x21952)) % 174.01/173.91 [2196]~E(x21961,x21962)+E(f450(x21961,x21963),f450(x21962,x21963)) % 174.01/173.91 [2197]~E(x21971,x21972)+E(f450(x21973,x21971),f450(x21973,x21972)) % 174.01/173.91 [2198]~E(x21981,x21982)+E(f392(x21981,x21983,x21984,x21985,x21986),f392(x21982,x21983,x21984,x21985,x21986)) % 174.01/173.91 [2199]~E(x21991,x21992)+E(f392(x21993,x21991,x21994,x21995,x21996),f392(x21993,x21992,x21994,x21995,x21996)) % 174.01/173.91 [2200]~E(x22001,x22002)+E(f392(x22003,x22004,x22001,x22005,x22006),f392(x22003,x22004,x22002,x22005,x22006)) % 174.01/173.91 [2201]~E(x22011,x22012)+E(f392(x22013,x22014,x22015,x22011,x22016),f392(x22013,x22014,x22015,x22012,x22016)) % 174.01/173.91 [2202]~E(x22021,x22022)+E(f392(x22023,x22024,x22025,x22026,x22021),f392(x22023,x22024,x22025,x22026,x22022)) % 174.01/173.91 [2203]~E(x22031,x22032)+E(f720(x22031,x22033,x22034,x22035,x22036),f720(x22032,x22033,x22034,x22035,x22036)) % 174.01/173.91 [2204]~E(x22041,x22042)+E(f720(x22043,x22041,x22044,x22045,x22046),f720(x22043,x22042,x22044,x22045,x22046)) % 174.01/173.91 [2205]~E(x22051,x22052)+E(f720(x22053,x22054,x22051,x22055,x22056),f720(x22053,x22054,x22052,x22055,x22056)) % 174.01/173.91 [2206]~E(x22061,x22062)+E(f720(x22063,x22064,x22065,x22061,x22066),f720(x22063,x22064,x22065,x22062,x22066)) % 174.01/173.91 [2207]~E(x22071,x22072)+E(f720(x22073,x22074,x22075,x22076,x22071),f720(x22073,x22074,x22075,x22076,x22072)) % 174.01/173.91 [2208]~E(x22081,x22082)+E(f483(x22081,x22083,x22084,x22085,x22086),f483(x22082,x22083,x22084,x22085,x22086)) % 174.01/173.91 [2209]~E(x22091,x22092)+E(f483(x22093,x22091,x22094,x22095,x22096),f483(x22093,x22092,x22094,x22095,x22096)) % 174.01/173.91 [2210]~E(x22101,x22102)+E(f483(x22103,x22104,x22101,x22105,x22106),f483(x22103,x22104,x22102,x22105,x22106)) % 174.01/173.91 [2211]~E(x22111,x22112)+E(f483(x22113,x22114,x22115,x22111,x22116),f483(x22113,x22114,x22115,x22112,x22116)) % 174.01/173.91 [2212]~E(x22121,x22122)+E(f483(x22123,x22124,x22125,x22126,x22121),f483(x22123,x22124,x22125,x22126,x22122)) % 174.01/173.91 [2213]~E(x22131,x22132)+E(f596(x22131,x22133,x22134,x22135),f596(x22132,x22133,x22134,x22135)) % 174.01/173.91 [2214]~E(x22141,x22142)+E(f596(x22143,x22141,x22144,x22145),f596(x22143,x22142,x22144,x22145)) % 174.01/173.91 [2215]~E(x22151,x22152)+E(f596(x22153,x22154,x22151,x22155),f596(x22153,x22154,x22152,x22155)) % 174.01/173.91 [2216]~E(x22161,x22162)+E(f596(x22163,x22164,x22165,x22161),f596(x22163,x22164,x22165,x22162)) % 174.01/173.91 [2217]~E(x22171,x22172)+E(f453(x22171,x22173,x22174,x22175),f453(x22172,x22173,x22174,x22175)) % 174.01/173.91 [2218]~E(x22181,x22182)+E(f453(x22183,x22181,x22184,x22185),f453(x22183,x22182,x22184,x22185)) % 174.01/173.91 [2219]~E(x22191,x22192)+E(f453(x22193,x22194,x22191,x22195),f453(x22193,x22194,x22192,x22195)) % 174.01/173.91 [2220]~E(x22201,x22202)+E(f453(x22203,x22204,x22205,x22201),f453(x22203,x22204,x22205,x22202)) % 174.01/173.91 [2221]~E(x22211,x22212)+E(f359(x22211,x22213,x22214,x22215),f359(x22212,x22213,x22214,x22215)) % 174.01/173.91 [2222]~E(x22221,x22222)+E(f359(x22223,x22221,x22224,x22225),f359(x22223,x22222,x22224,x22225)) % 174.01/173.91 [2223]~E(x22231,x22232)+E(f359(x22233,x22234,x22231,x22235),f359(x22233,x22234,x22232,x22235)) % 174.01/173.91 [2224]~E(x22241,x22242)+E(f359(x22243,x22244,x22245,x22241),f359(x22243,x22244,x22245,x22242)) % 174.01/173.91 [2225]~E(x22251,x22252)+E(f514(x22251,x22253,x22254,x22255,x22256),f514(x22252,x22253,x22254,x22255,x22256)) % 174.01/173.91 [2226]~E(x22261,x22262)+E(f514(x22263,x22261,x22264,x22265,x22266),f514(x22263,x22262,x22264,x22265,x22266)) % 174.01/173.91 [2227]~E(x22271,x22272)+E(f514(x22273,x22274,x22271,x22275,x22276),f514(x22273,x22274,x22272,x22275,x22276)) % 174.01/173.91 [2228]~E(x22281,x22282)+E(f514(x22283,x22284,x22285,x22281,x22286),f514(x22283,x22284,x22285,x22282,x22286)) % 174.01/173.91 [2229]~E(x22291,x22292)+E(f514(x22293,x22294,x22295,x22296,x22291),f514(x22293,x22294,x22295,x22296,x22292)) % 174.01/173.91 [2230]~E(x22301,x22302)+E(f221(x22301,x22303,x22304,x22305,x22306),f221(x22302,x22303,x22304,x22305,x22306)) % 174.01/173.91 [2231]~E(x22311,x22312)+E(f221(x22313,x22311,x22314,x22315,x22316),f221(x22313,x22312,x22314,x22315,x22316)) % 174.01/173.91 [2232]~E(x22321,x22322)+E(f221(x22323,x22324,x22321,x22325,x22326),f221(x22323,x22324,x22322,x22325,x22326)) % 174.01/173.91 [2233]~E(x22331,x22332)+E(f221(x22333,x22334,x22335,x22331,x22336),f221(x22333,x22334,x22335,x22332,x22336)) % 174.01/173.91 [2234]~E(x22341,x22342)+E(f221(x22343,x22344,x22345,x22346,x22341),f221(x22343,x22344,x22345,x22346,x22342)) % 174.01/173.91 [2235]~E(x22351,x22352)+E(f773(x22351,x22353,x22354),f773(x22352,x22353,x22354)) % 174.01/173.91 [2236]~E(x22361,x22362)+E(f773(x22363,x22361,x22364),f773(x22363,x22362,x22364)) % 174.01/173.91 [2237]~E(x22371,x22372)+E(f773(x22373,x22374,x22371),f773(x22373,x22374,x22372)) % 174.01/173.91 [2238]~E(x22381,x22382)+E(f841(x22381,x22383,x22384),f841(x22382,x22383,x22384)) % 174.01/173.91 [2239]~E(x22391,x22392)+E(f841(x22393,x22391,x22394),f841(x22393,x22392,x22394)) % 174.01/173.91 [2240]~E(x22401,x22402)+E(f841(x22403,x22404,x22401),f841(x22403,x22404,x22402)) % 174.01/173.91 [2241]~E(x22411,x22412)+E(f842(x22411,x22413,x22414,x22415),f842(x22412,x22413,x22414,x22415)) % 174.01/173.91 [2242]~E(x22421,x22422)+E(f842(x22423,x22421,x22424,x22425),f842(x22423,x22422,x22424,x22425)) % 174.01/173.91 [2243]~E(x22431,x22432)+E(f842(x22433,x22434,x22431,x22435),f842(x22433,x22434,x22432,x22435)) % 174.01/173.91 [2244]~E(x22441,x22442)+E(f842(x22443,x22444,x22445,x22441),f842(x22443,x22444,x22445,x22442)) % 174.01/173.91 [2245]~E(x22451,x22452)+E(f415(x22451,x22453,x22454,x22455,x22456),f415(x22452,x22453,x22454,x22455,x22456)) % 174.01/173.91 [2246]~E(x22461,x22462)+E(f415(x22463,x22461,x22464,x22465,x22466),f415(x22463,x22462,x22464,x22465,x22466)) % 174.01/173.91 [2247]~E(x22471,x22472)+E(f415(x22473,x22474,x22471,x22475,x22476),f415(x22473,x22474,x22472,x22475,x22476)) % 174.01/173.91 [2248]~E(x22481,x22482)+E(f415(x22483,x22484,x22485,x22481,x22486),f415(x22483,x22484,x22485,x22482,x22486)) % 174.01/173.91 [2249]~E(x22491,x22492)+E(f415(x22493,x22494,x22495,x22496,x22491),f415(x22493,x22494,x22495,x22496,x22492)) % 174.01/173.91 [2250]~E(x22501,x22502)+E(f490(x22501,x22503,x22504,x22505,x22506),f490(x22502,x22503,x22504,x22505,x22506)) % 174.01/173.91 [2251]~E(x22511,x22512)+E(f490(x22513,x22511,x22514,x22515,x22516),f490(x22513,x22512,x22514,x22515,x22516)) % 174.01/173.91 [2252]~E(x22521,x22522)+E(f490(x22523,x22524,x22521,x22525,x22526),f490(x22523,x22524,x22522,x22525,x22526)) % 174.01/173.91 [2253]~E(x22531,x22532)+E(f490(x22533,x22534,x22535,x22531,x22536),f490(x22533,x22534,x22535,x22532,x22536)) % 174.01/173.91 [2254]~E(x22541,x22542)+E(f490(x22543,x22544,x22545,x22546,x22541),f490(x22543,x22544,x22545,x22546,x22542)) % 174.01/173.91 [2255]~E(x22551,x22552)+E(f458(x22551,x22553),f458(x22552,x22553)) % 174.01/173.91 [2256]~E(x22561,x22562)+E(f458(x22563,x22561),f458(x22563,x22562)) % 174.01/173.91 [2257]~E(x22571,x22572)+E(f778(x22571),f778(x22572)) % 174.01/173.91 [2258]~E(x22581,x22582)+E(f633(x22581,x22583,x22584,x22585,x22586,x22587),f633(x22582,x22583,x22584,x22585,x22586,x22587)) % 174.01/173.91 [2259]~E(x22591,x22592)+E(f633(x22593,x22591,x22594,x22595,x22596,x22597),f633(x22593,x22592,x22594,x22595,x22596,x22597)) % 174.01/173.91 [2260]~E(x22601,x22602)+E(f633(x22603,x22604,x22601,x22605,x22606,x22607),f633(x22603,x22604,x22602,x22605,x22606,x22607)) % 174.01/173.91 [2261]~E(x22611,x22612)+E(f633(x22613,x22614,x22615,x22611,x22616,x22617),f633(x22613,x22614,x22615,x22612,x22616,x22617)) % 174.01/173.91 [2262]~E(x22621,x22622)+E(f633(x22623,x22624,x22625,x22626,x22621,x22627),f633(x22623,x22624,x22625,x22626,x22622,x22627)) % 174.01/173.91 [2263]~E(x22631,x22632)+E(f633(x22633,x22634,x22635,x22636,x22637,x22631),f633(x22633,x22634,x22635,x22636,x22637,x22632)) % 174.01/173.91 [2264]~E(x22641,x22642)+E(f774(x22641,x22643,x22644),f774(x22642,x22643,x22644)) % 174.01/173.91 [2265]~E(x22651,x22652)+E(f774(x22653,x22651,x22654),f774(x22653,x22652,x22654)) % 174.01/173.91 [2266]~E(x22661,x22662)+E(f774(x22663,x22664,x22661),f774(x22663,x22664,x22662)) % 174.01/173.91 [2267]~E(x22671,x22672)+E(f540(x22671,x22673,x22674,x22675,x22676),f540(x22672,x22673,x22674,x22675,x22676)) % 174.01/173.91 [2268]~E(x22681,x22682)+E(f540(x22683,x22681,x22684,x22685,x22686),f540(x22683,x22682,x22684,x22685,x22686)) % 174.01/173.91 [2269]~E(x22691,x22692)+E(f540(x22693,x22694,x22691,x22695,x22696),f540(x22693,x22694,x22692,x22695,x22696)) % 174.01/173.91 [2270]~E(x22701,x22702)+E(f540(x22703,x22704,x22705,x22701,x22706),f540(x22703,x22704,x22705,x22702,x22706)) % 174.01/173.91 [2271]~E(x22711,x22712)+E(f540(x22713,x22714,x22715,x22716,x22711),f540(x22713,x22714,x22715,x22716,x22712)) % 174.01/173.91 [2272]~E(x22721,x22722)+E(f629(x22721,x22723,x22724),f629(x22722,x22723,x22724)) % 174.01/173.91 [2273]~E(x22731,x22732)+E(f629(x22733,x22731,x22734),f629(x22733,x22732,x22734)) % 174.01/173.91 [2274]~E(x22741,x22742)+E(f629(x22743,x22744,x22741),f629(x22743,x22744,x22742)) % 174.01/173.91 [2275]~E(x22751,x22752)+E(f462(x22751,x22753,x22754),f462(x22752,x22753,x22754)) % 174.01/173.91 [2276]~E(x22761,x22762)+E(f462(x22763,x22761,x22764),f462(x22763,x22762,x22764)) % 174.01/173.91 [2277]~E(x22771,x22772)+E(f462(x22773,x22774,x22771),f462(x22773,x22774,x22772)) % 174.01/173.91 [2278]~E(x22781,x22782)+E(f661(x22781,x22783,x22784,x22785,x22786),f661(x22782,x22783,x22784,x22785,x22786)) % 174.01/173.91 [2279]~E(x22791,x22792)+E(f661(x22793,x22791,x22794,x22795,x22796),f661(x22793,x22792,x22794,x22795,x22796)) % 174.01/173.91 [2280]~E(x22801,x22802)+E(f661(x22803,x22804,x22801,x22805,x22806),f661(x22803,x22804,x22802,x22805,x22806)) % 174.01/173.91 [2281]~E(x22811,x22812)+E(f661(x22813,x22814,x22815,x22811,x22816),f661(x22813,x22814,x22815,x22812,x22816)) % 174.01/173.91 [2282]~E(x22821,x22822)+E(f661(x22823,x22824,x22825,x22826,x22821),f661(x22823,x22824,x22825,x22826,x22822)) % 174.01/173.91 [2283]~E(x22831,x22832)+E(f469(x22831,x22833,x22834),f469(x22832,x22833,x22834)) % 174.01/173.91 [2284]~E(x22841,x22842)+E(f469(x22843,x22841,x22844),f469(x22843,x22842,x22844)) % 174.01/173.91 [2285]~E(x22851,x22852)+E(f469(x22853,x22854,x22851),f469(x22853,x22854,x22852)) % 174.01/173.91 [2286]~E(x22861,x22862)+E(f771(x22861,x22863),f771(x22862,x22863)) % 174.01/173.91 [2287]~E(x22871,x22872)+E(f771(x22873,x22871),f771(x22873,x22872)) % 174.01/173.91 [2288]~E(x22881,x22882)+E(f783(x22881,x22883,x22884),f783(x22882,x22883,x22884)) % 174.01/173.91 [2289]~E(x22891,x22892)+E(f783(x22893,x22891,x22894),f783(x22893,x22892,x22894)) % 174.01/173.91 [2290]~E(x22901,x22902)+E(f783(x22903,x22904,x22901),f783(x22903,x22904,x22902)) % 174.01/173.91 [2291]~E(x22911,x22912)+E(f505(x22911,x22913),f505(x22912,x22913)) % 174.01/173.91 [2292]~E(x22921,x22922)+E(f505(x22923,x22921),f505(x22923,x22922)) % 174.01/173.91 [2293]~E(x22931,x22932)+E(f585(x22931,x22933),f585(x22932,x22933)) % 174.01/173.91 [2294]~E(x22941,x22942)+E(f585(x22943,x22941),f585(x22943,x22942)) % 174.01/173.91 [2295]~E(x22951,x22952)+E(f521(x22951,x22953,x22954,x22955),f521(x22952,x22953,x22954,x22955)) % 174.01/173.91 [2296]~E(x22961,x22962)+E(f521(x22963,x22961,x22964,x22965),f521(x22963,x22962,x22964,x22965)) % 174.01/173.91 [2297]~E(x22971,x22972)+E(f521(x22973,x22974,x22971,x22975),f521(x22973,x22974,x22972,x22975)) % 174.01/173.91 [2298]~E(x22981,x22982)+E(f521(x22983,x22984,x22985,x22981),f521(x22983,x22984,x22985,x22982)) % 174.01/173.91 [2299]~E(x22991,x22992)+E(f567(x22991,x22993),f567(x22992,x22993)) % 174.01/173.91 [2300]~E(x23001,x23002)+E(f567(x23003,x23001),f567(x23003,x23002)) % 174.01/173.91 [2301]~E(x23011,x23012)+E(f525(x23011,x23013,x23014,x23015),f525(x23012,x23013,x23014,x23015)) % 174.01/173.91 [2302]~E(x23021,x23022)+E(f525(x23023,x23021,x23024,x23025),f525(x23023,x23022,x23024,x23025)) % 174.01/173.91 [2303]~E(x23031,x23032)+E(f525(x23033,x23034,x23031,x23035),f525(x23033,x23034,x23032,x23035)) % 174.01/173.91 [2304]~E(x23041,x23042)+E(f525(x23043,x23044,x23045,x23041),f525(x23043,x23044,x23045,x23042)) % 174.01/173.91 [2305]~E(x23051,x23052)+E(f830(x23051,x23053,x23054),f830(x23052,x23053,x23054)) % 174.01/173.91 [2306]~E(x23061,x23062)+E(f830(x23063,x23061,x23064),f830(x23063,x23062,x23064)) % 174.01/173.91 [2307]~E(x23071,x23072)+E(f830(x23073,x23074,x23071),f830(x23073,x23074,x23072)) % 174.01/173.91 [2308]~E(x23081,x23082)+E(f586(x23081,x23083),f586(x23082,x23083)) % 174.01/173.91 [2309]~E(x23091,x23092)+E(f586(x23093,x23091),f586(x23093,x23092)) % 174.01/173.91 [2310]~E(x23101,x23102)+E(f831(x23101,x23103,x23104),f831(x23102,x23103,x23104)) % 174.01/173.91 [2311]~E(x23111,x23112)+E(f831(x23113,x23111,x23114),f831(x23113,x23112,x23114)) % 174.01/173.91 [2312]~E(x23121,x23122)+E(f831(x23123,x23124,x23121),f831(x23123,x23124,x23122)) % 174.01/173.91 [2313]~E(x23131,x23132)+E(f731(x23131,x23133,x23134),f731(x23132,x23133,x23134)) % 174.01/173.91 [2314]~E(x23141,x23142)+E(f731(x23143,x23141,x23144),f731(x23143,x23142,x23144)) % 174.01/173.91 [2315]~E(x23151,x23152)+E(f731(x23153,x23154,x23151),f731(x23153,x23154,x23152)) % 174.01/173.91 [2316]~E(x23161,x23162)+E(f206(x23161,x23163,x23164,x23165),f206(x23162,x23163,x23164,x23165)) % 174.01/173.91 [2317]~E(x23171,x23172)+E(f206(x23173,x23171,x23174,x23175),f206(x23173,x23172,x23174,x23175)) % 174.01/173.91 [2318]~E(x23181,x23182)+E(f206(x23183,x23184,x23181,x23185),f206(x23183,x23184,x23182,x23185)) % 174.01/173.91 [2319]~E(x23191,x23192)+E(f206(x23193,x23194,x23195,x23191),f206(x23193,x23194,x23195,x23192)) % 174.01/173.91 [2320]~E(x23201,x23202)+E(f447(x23201,x23203),f447(x23202,x23203)) % 174.01/173.91 [2321]~E(x23211,x23212)+E(f447(x23213,x23211),f447(x23213,x23212)) % 174.01/173.91 [2322]~E(x23221,x23222)+E(f388(x23221,x23223,x23224,x23225,x23226),f388(x23222,x23223,x23224,x23225,x23226)) % 174.01/173.91 [2323]~E(x23231,x23232)+E(f388(x23233,x23231,x23234,x23235,x23236),f388(x23233,x23232,x23234,x23235,x23236)) % 174.01/173.91 [2324]~E(x23241,x23242)+E(f388(x23243,x23244,x23241,x23245,x23246),f388(x23243,x23244,x23242,x23245,x23246)) % 174.01/173.91 [2325]~E(x23251,x23252)+E(f388(x23253,x23254,x23255,x23251,x23256),f388(x23253,x23254,x23255,x23252,x23256)) % 174.01/173.91 [2326]~E(x23261,x23262)+E(f388(x23263,x23264,x23265,x23266,x23261),f388(x23263,x23264,x23265,x23266,x23262)) % 174.01/173.91 [2327]~E(x23271,x23272)+E(f689(x23271,x23273,x23274,x23275),f689(x23272,x23273,x23274,x23275)) % 174.01/173.91 [2328]~E(x23281,x23282)+E(f689(x23283,x23281,x23284,x23285),f689(x23283,x23282,x23284,x23285)) % 174.01/173.91 [2329]~E(x23291,x23292)+E(f689(x23293,x23294,x23291,x23295),f689(x23293,x23294,x23292,x23295)) % 174.01/173.91 [2330]~E(x23301,x23302)+E(f689(x23303,x23304,x23305,x23301),f689(x23303,x23304,x23305,x23302)) % 174.01/173.91 [2331]~E(x23311,x23312)+E(f573(x23311),f573(x23312)) % 174.01/173.91 [2332]~E(x23321,x23322)+E(f120(x23321,x23323,x23324,x23325),f120(x23322,x23323,x23324,x23325)) % 174.01/173.91 [2333]~E(x23331,x23332)+E(f120(x23333,x23331,x23334,x23335),f120(x23333,x23332,x23334,x23335)) % 174.01/173.91 [2334]~E(x23341,x23342)+E(f120(x23343,x23344,x23341,x23345),f120(x23343,x23344,x23342,x23345)) % 174.01/173.91 [2335]~E(x23351,x23352)+E(f120(x23353,x23354,x23355,x23351),f120(x23353,x23354,x23355,x23352)) % 174.01/173.91 [2336]~E(x23361,x23362)+E(f257(x23361,x23363,x23364,x23365,x23366),f257(x23362,x23363,x23364,x23365,x23366)) % 174.01/173.91 [2337]~E(x23371,x23372)+E(f257(x23373,x23371,x23374,x23375,x23376),f257(x23373,x23372,x23374,x23375,x23376)) % 174.01/173.91 [2338]~E(x23381,x23382)+E(f257(x23383,x23384,x23381,x23385,x23386),f257(x23383,x23384,x23382,x23385,x23386)) % 174.01/173.91 [2339]~E(x23391,x23392)+E(f257(x23393,x23394,x23395,x23391,x23396),f257(x23393,x23394,x23395,x23392,x23396)) % 174.01/173.91 [2340]~E(x23401,x23402)+E(f257(x23403,x23404,x23405,x23406,x23401),f257(x23403,x23404,x23405,x23406,x23402)) % 174.01/173.91 [2341]~E(x23411,x23412)+E(f317(x23411,x23413,x23414),f317(x23412,x23413,x23414)) % 174.01/173.91 [2342]~E(x23421,x23422)+E(f317(x23423,x23421,x23424),f317(x23423,x23422,x23424)) % 174.01/173.91 [2343]~E(x23431,x23432)+E(f317(x23433,x23434,x23431),f317(x23433,x23434,x23432)) % 174.01/173.91 [2344]~E(x23441,x23442)+E(f192(x23441,x23443,x23444,x23445),f192(x23442,x23443,x23444,x23445)) % 174.01/173.91 [2345]~E(x23451,x23452)+E(f192(x23453,x23451,x23454,x23455),f192(x23453,x23452,x23454,x23455)) % 174.01/173.91 [2346]~E(x23461,x23462)+E(f192(x23463,x23464,x23461,x23465),f192(x23463,x23464,x23462,x23465)) % 174.01/173.91 [2347]~E(x23471,x23472)+E(f192(x23473,x23474,x23475,x23471),f192(x23473,x23474,x23475,x23472)) % 174.01/173.91 [2348]~E(x23481,x23482)+E(f417(x23481,x23483,x23484),f417(x23482,x23483,x23484)) % 174.01/173.91 [2349]~E(x23491,x23492)+E(f417(x23493,x23491,x23494),f417(x23493,x23492,x23494)) % 174.01/173.91 [2350]~E(x23501,x23502)+E(f417(x23503,x23504,x23501),f417(x23503,x23504,x23502)) % 174.01/173.91 [2351]~E(x23511,x23512)+E(f599(x23511,x23513,x23514,x23515),f599(x23512,x23513,x23514,x23515)) % 174.01/173.91 [2352]~E(x23521,x23522)+E(f599(x23523,x23521,x23524,x23525),f599(x23523,x23522,x23524,x23525)) % 174.01/173.91 [2353]~E(x23531,x23532)+E(f599(x23533,x23534,x23531,x23535),f599(x23533,x23534,x23532,x23535)) % 174.01/173.91 [2354]~E(x23541,x23542)+E(f599(x23543,x23544,x23545,x23541),f599(x23543,x23544,x23545,x23542)) % 174.01/173.91 [2355]~E(x23551,x23552)+E(f448(x23551,x23553),f448(x23552,x23553)) % 174.01/173.91 [2356]~E(x23561,x23562)+E(f448(x23563,x23561),f448(x23563,x23562)) % 174.01/173.91 [2357]~E(x23571,x23572)+E(f821(x23571,x23573,x23574),f821(x23572,x23573,x23574)) % 174.01/173.91 [2358]~E(x23581,x23582)+E(f821(x23583,x23581,x23584),f821(x23583,x23582,x23584)) % 174.01/173.91 [2359]~E(x23591,x23592)+E(f821(x23593,x23594,x23591),f821(x23593,x23594,x23592)) % 174.01/173.91 [2360]~E(x23601,x23602)+E(f673(x23601,x23603,x23604),f673(x23602,x23603,x23604)) % 174.01/173.91 [2361]~E(x23611,x23612)+E(f673(x23613,x23611,x23614),f673(x23613,x23612,x23614)) % 174.01/173.91 [2362]~E(x23621,x23622)+E(f673(x23623,x23624,x23621),f673(x23623,x23624,x23622)) % 174.01/173.91 [2363]~E(x23631,x23632)+E(f311(x23631,x23633,x23634),f311(x23632,x23633,x23634)) % 174.01/173.91 [2364]~E(x23641,x23642)+E(f311(x23643,x23641,x23644),f311(x23643,x23642,x23644)) % 174.01/173.91 [2365]~E(x23651,x23652)+E(f311(x23653,x23654,x23651),f311(x23653,x23654,x23652)) % 174.01/173.91 [2366]~E(x23661,x23662)+E(f856(x23661,x23663),f856(x23662,x23663)) % 174.01/173.91 [2367]~E(x23671,x23672)+E(f856(x23673,x23671),f856(x23673,x23672)) % 174.01/173.91 [2368]~E(x23681,x23682)+E(f203(x23681,x23683,x23684,x23685),f203(x23682,x23683,x23684,x23685)) % 174.01/173.91 [2369]~E(x23691,x23692)+E(f203(x23693,x23691,x23694,x23695),f203(x23693,x23692,x23694,x23695)) % 174.01/173.91 [2370]~E(x23701,x23702)+E(f203(x23703,x23704,x23701,x23705),f203(x23703,x23704,x23702,x23705)) % 174.01/173.91 [2371]~E(x23711,x23712)+E(f203(x23713,x23714,x23715,x23711),f203(x23713,x23714,x23715,x23712)) % 174.01/173.91 [2372]~E(x23721,x23722)+E(f268(x23721,x23723),f268(x23722,x23723)) % 174.01/173.91 [2373]~E(x23731,x23732)+E(f268(x23733,x23731),f268(x23733,x23732)) % 174.01/173.91 [2374]~E(x23741,x23742)+E(f602(x23741),f602(x23742)) % 174.01/173.91 [2375]~E(x23751,x23752)+E(f478(x23751,x23753,x23754),f478(x23752,x23753,x23754)) % 174.01/173.91 [2376]~E(x23761,x23762)+E(f478(x23763,x23761,x23764),f478(x23763,x23762,x23764)) % 174.01/173.91 [2377]~E(x23771,x23772)+E(f478(x23773,x23774,x23771),f478(x23773,x23774,x23772)) % 174.01/173.91 [2378]~E(x23781,x23782)+E(f619(x23781),f619(x23782)) % 174.01/173.91 [2379]~E(x23791,x23792)+E(f202(x23791,x23793,x23794,x23795),f202(x23792,x23793,x23794,x23795)) % 174.01/173.91 [2380]~E(x23801,x23802)+E(f202(x23803,x23801,x23804,x23805),f202(x23803,x23802,x23804,x23805)) % 174.01/173.91 [2381]~E(x23811,x23812)+E(f202(x23813,x23814,x23811,x23815),f202(x23813,x23814,x23812,x23815)) % 174.01/173.91 [2382]~E(x23821,x23822)+E(f202(x23823,x23824,x23825,x23821),f202(x23823,x23824,x23825,x23822)) % 174.01/173.91 [2383]~E(x23831,x23832)+E(f637(x23831,x23833,x23834),f637(x23832,x23833,x23834)) % 174.01/173.91 [2384]~E(x23841,x23842)+E(f637(x23843,x23841,x23844),f637(x23843,x23842,x23844)) % 174.01/173.91 [2385]~E(x23851,x23852)+E(f637(x23853,x23854,x23851),f637(x23853,x23854,x23852)) % 174.01/173.91 [2386]~E(x23861,x23862)+E(f513(x23861,x23863,x23864,x23865,x23866),f513(x23862,x23863,x23864,x23865,x23866)) % 174.01/173.91 [2387]~E(x23871,x23872)+E(f513(x23873,x23871,x23874,x23875,x23876),f513(x23873,x23872,x23874,x23875,x23876)) % 174.01/173.91 [2388]~E(x23881,x23882)+E(f513(x23883,x23884,x23881,x23885,x23886),f513(x23883,x23884,x23882,x23885,x23886)) % 174.01/173.91 [2389]~E(x23891,x23892)+E(f513(x23893,x23894,x23895,x23891,x23896),f513(x23893,x23894,x23895,x23892,x23896)) % 174.01/173.91 [2390]~E(x23901,x23902)+E(f513(x23903,x23904,x23905,x23906,x23901),f513(x23903,x23904,x23905,x23906,x23902)) % 174.01/173.91 [2391]~E(x23911,x23912)+E(f271(x23911,x23913,x23914),f271(x23912,x23913,x23914)) % 174.01/173.91 [2392]~E(x23921,x23922)+E(f271(x23923,x23921,x23924),f271(x23923,x23922,x23924)) % 174.01/173.91 [2393]~E(x23931,x23932)+E(f271(x23933,x23934,x23931),f271(x23933,x23934,x23932)) % 174.01/173.91 [2394]~E(x23941,x23942)+E(f220(x23941,x23943,x23944,x23945,x23946),f220(x23942,x23943,x23944,x23945,x23946)) % 174.01/173.91 [2395]~E(x23951,x23952)+E(f220(x23953,x23951,x23954,x23955,x23956),f220(x23953,x23952,x23954,x23955,x23956)) % 174.01/173.91 [2396]~E(x23961,x23962)+E(f220(x23963,x23964,x23961,x23965,x23966),f220(x23963,x23964,x23962,x23965,x23966)) % 174.01/173.91 [2397]~E(x23971,x23972)+E(f220(x23973,x23974,x23975,x23971,x23976),f220(x23973,x23974,x23975,x23972,x23976)) % 174.01/173.91 [2398]~E(x23981,x23982)+E(f220(x23983,x23984,x23985,x23986,x23981),f220(x23983,x23984,x23985,x23986,x23982)) % 174.01/173.91 [2399]~E(x23991,x23992)+E(f97(x23991,x23993,x23994),f97(x23992,x23993,x23994)) % 174.01/173.91 [2400]~E(x24001,x24002)+E(f97(x24003,x24001,x24004),f97(x24003,x24002,x24004)) % 174.01/173.91 [2401]~E(x24011,x24012)+E(f97(x24013,x24014,x24011),f97(x24013,x24014,x24012)) % 174.01/173.91 [2402]~E(x24021,x24022)+E(f527(x24021,x24023,x24024,x24025),f527(x24022,x24023,x24024,x24025)) % 174.01/173.91 [2403]~E(x24031,x24032)+E(f527(x24033,x24031,x24034,x24035),f527(x24033,x24032,x24034,x24035)) % 174.01/173.91 [2404]~E(x24041,x24042)+E(f527(x24043,x24044,x24041,x24045),f527(x24043,x24044,x24042,x24045)) % 174.01/173.91 [2405]~E(x24051,x24052)+E(f527(x24053,x24054,x24055,x24051),f527(x24053,x24054,x24055,x24052)) % 174.01/173.91 [2406]~E(x24061,x24062)+E(f124(x24061),f124(x24062)) % 174.01/173.91 [2407]~E(x24071,x24072)+E(f523(x24071,x24073,x24074),f523(x24072,x24073,x24074)) % 174.01/173.91 [2408]~E(x24081,x24082)+E(f523(x24083,x24081,x24084),f523(x24083,x24082,x24084)) % 174.01/173.91 [2409]~E(x24091,x24092)+E(f523(x24093,x24094,x24091),f523(x24093,x24094,x24092)) % 174.01/173.91 [2410]~E(x24101,x24102)+E(f442(x24101,x24103,x24104,x24105,x24106),f442(x24102,x24103,x24104,x24105,x24106)) % 174.01/173.91 [2411]~E(x24111,x24112)+E(f442(x24113,x24111,x24114,x24115,x24116),f442(x24113,x24112,x24114,x24115,x24116)) % 174.01/173.91 [2412]~E(x24121,x24122)+E(f442(x24123,x24124,x24121,x24125,x24126),f442(x24123,x24124,x24122,x24125,x24126)) % 174.01/173.91 [2413]~E(x24131,x24132)+E(f442(x24133,x24134,x24135,x24131,x24136),f442(x24133,x24134,x24135,x24132,x24136)) % 174.01/173.91 [2414]~E(x24141,x24142)+E(f442(x24143,x24144,x24145,x24146,x24141),f442(x24143,x24144,x24145,x24146,x24142)) % 174.01/173.91 [2415]~E(x24151,x24152)+E(f416(x24151,x24153,x24154),f416(x24152,x24153,x24154)) % 174.01/173.91 [2416]~E(x24161,x24162)+E(f416(x24163,x24161,x24164),f416(x24163,x24162,x24164)) % 174.01/173.91 [2417]~E(x24171,x24172)+E(f416(x24173,x24174,x24171),f416(x24173,x24174,x24172)) % 174.01/173.91 [2418]~E(x24181,x24182)+E(f320(x24181,x24183,x24184,x24185,x24186),f320(x24182,x24183,x24184,x24185,x24186)) % 174.01/173.91 [2419]~E(x24191,x24192)+E(f320(x24193,x24191,x24194,x24195,x24196),f320(x24193,x24192,x24194,x24195,x24196)) % 174.01/173.91 [2420]~E(x24201,x24202)+E(f320(x24203,x24204,x24201,x24205,x24206),f320(x24203,x24204,x24202,x24205,x24206)) % 174.01/173.91 [2421]~E(x24211,x24212)+E(f320(x24213,x24214,x24215,x24211,x24216),f320(x24213,x24214,x24215,x24212,x24216)) % 174.01/173.91 [2422]~E(x24221,x24222)+E(f320(x24223,x24224,x24225,x24226,x24221),f320(x24223,x24224,x24225,x24226,x24222)) % 174.01/173.91 [2423]~E(x24231,x24232)+E(f559(x24231),f559(x24232)) % 174.01/173.91 [2424]~E(x24241,x24242)+E(f654(x24241,x24243,x24244,x24245),f654(x24242,x24243,x24244,x24245)) % 174.01/173.91 [2425]~E(x24251,x24252)+E(f654(x24253,x24251,x24254,x24255),f654(x24253,x24252,x24254,x24255)) % 174.01/173.91 [2426]~E(x24261,x24262)+E(f654(x24263,x24264,x24261,x24265),f654(x24263,x24264,x24262,x24265)) % 174.01/173.91 [2427]~E(x24271,x24272)+E(f654(x24273,x24274,x24275,x24271),f654(x24273,x24274,x24275,x24272)) % 174.01/173.91 [2428]~E(x24281,x24282)+E(f538(x24281,x24283,x24284,x24285,x24286),f538(x24282,x24283,x24284,x24285,x24286)) % 174.01/173.91 [2429]~E(x24291,x24292)+E(f538(x24293,x24291,x24294,x24295,x24296),f538(x24293,x24292,x24294,x24295,x24296)) % 174.01/173.91 [2430]~E(x24301,x24302)+E(f538(x24303,x24304,x24301,x24305,x24306),f538(x24303,x24304,x24302,x24305,x24306)) % 174.01/173.91 [2431]~E(x24311,x24312)+E(f538(x24313,x24314,x24315,x24311,x24316),f538(x24313,x24314,x24315,x24312,x24316)) % 174.01/173.91 [2432]~E(x24321,x24322)+E(f538(x24323,x24324,x24325,x24326,x24321),f538(x24323,x24324,x24325,x24326,x24322)) % 174.01/173.91 [2433]~E(x24331,x24332)+E(f763(x24331,x24333),f763(x24332,x24333)) % 174.01/173.91 [2434]~E(x24341,x24342)+E(f763(x24343,x24341),f763(x24343,x24342)) % 174.01/173.91 [2435]~E(x24351,x24352)+E(f810(x24351,x24353,x24354),f810(x24352,x24353,x24354)) % 174.01/173.91 [2436]~E(x24361,x24362)+E(f810(x24363,x24361,x24364),f810(x24363,x24362,x24364)) % 174.01/173.91 [2437]~E(x24371,x24372)+E(f810(x24373,x24374,x24371),f810(x24373,x24374,x24372)) % 174.01/173.91 [2438]~E(x24381,x24382)+E(f563(x24381,x24383,x24384,x24385),f563(x24382,x24383,x24384,x24385)) % 174.01/173.91 [2439]~E(x24391,x24392)+E(f563(x24393,x24391,x24394,x24395),f563(x24393,x24392,x24394,x24395)) % 174.01/173.91 [2440]~E(x24401,x24402)+E(f563(x24403,x24404,x24401,x24405),f563(x24403,x24404,x24402,x24405)) % 174.01/173.91 [2441]~E(x24411,x24412)+E(f563(x24413,x24414,x24415,x24411),f563(x24413,x24414,x24415,x24412)) % 174.01/173.91 [2442]~E(x24421,x24422)+E(f264(x24421,x24423,x24424),f264(x24422,x24423,x24424)) % 174.01/173.91 [2443]~E(x24431,x24432)+E(f264(x24433,x24431,x24434),f264(x24433,x24432,x24434)) % 174.01/173.91 [2444]~E(x24441,x24442)+E(f264(x24443,x24444,x24441),f264(x24443,x24444,x24442)) % 174.01/173.91 [2445]~E(x24451,x24452)+E(f625(x24451,x24453,x24454,x24455),f625(x24452,x24453,x24454,x24455)) % 174.01/173.91 [2446]~E(x24461,x24462)+E(f625(x24463,x24461,x24464,x24465),f625(x24463,x24462,x24464,x24465)) % 174.01/173.91 [2447]~E(x24471,x24472)+E(f625(x24473,x24474,x24471,x24475),f625(x24473,x24474,x24472,x24475)) % 174.01/173.91 [2448]~E(x24481,x24482)+E(f625(x24483,x24484,x24485,x24481),f625(x24483,x24484,x24485,x24482)) % 174.01/173.91 [2449]~E(x24491,x24492)+E(f725(x24491),f725(x24492)) % 174.01/173.91 [2450]~E(x24501,x24502)+E(f835(x24501,x24503,x24504,x24505),f835(x24502,x24503,x24504,x24505)) % 174.01/173.91 [2451]~E(x24511,x24512)+E(f835(x24513,x24511,x24514,x24515),f835(x24513,x24512,x24514,x24515)) % 174.01/173.91 [2452]~E(x24521,x24522)+E(f835(x24523,x24524,x24521,x24525),f835(x24523,x24524,x24522,x24525)) % 174.01/173.91 [2453]~E(x24531,x24532)+E(f835(x24533,x24534,x24535,x24531),f835(x24533,x24534,x24535,x24532)) % 174.01/173.91 [2454]~E(x24541,x24542)+E(f649(x24541,x24543,x24544,x24545,x24546),f649(x24542,x24543,x24544,x24545,x24546)) % 174.01/173.91 [2455]~E(x24551,x24552)+E(f649(x24553,x24551,x24554,x24555,x24556),f649(x24553,x24552,x24554,x24555,x24556)) % 174.01/173.91 [2456]~E(x24561,x24562)+E(f649(x24563,x24564,x24561,x24565,x24566),f649(x24563,x24564,x24562,x24565,x24566)) % 174.01/173.91 [2457]~E(x24571,x24572)+E(f649(x24573,x24574,x24575,x24571,x24576),f649(x24573,x24574,x24575,x24572,x24576)) % 174.01/173.91 [2458]~E(x24581,x24582)+E(f649(x24583,x24584,x24585,x24586,x24581),f649(x24583,x24584,x24585,x24586,x24582)) % 174.01/173.91 [2459]~E(x24591,x24592)+E(f53(x24591),f53(x24592)) % 174.01/173.91 [2460]~E(x24601,x24602)+E(f402(x24601,x24603),f402(x24602,x24603)) % 174.01/173.91 [2461]~E(x24611,x24612)+E(f402(x24613,x24611),f402(x24613,x24612)) % 174.01/173.91 [2462]~E(x24621,x24622)+E(f620(x24621,x24623),f620(x24622,x24623)) % 174.01/173.91 [2463]~E(x24631,x24632)+E(f620(x24633,x24631),f620(x24633,x24632)) % 174.01/173.91 [2464]~E(x24641,x24642)+E(f587(x24641,x24643,x24644,x24645),f587(x24642,x24643,x24644,x24645)) % 174.01/173.91 [2465]~E(x24651,x24652)+E(f587(x24653,x24651,x24654,x24655),f587(x24653,x24652,x24654,x24655)) % 174.01/173.91 [2466]~E(x24661,x24662)+E(f587(x24663,x24664,x24661,x24665),f587(x24663,x24664,x24662,x24665)) % 174.01/173.91 [2467]~E(x24671,x24672)+E(f587(x24673,x24674,x24675,x24671),f587(x24673,x24674,x24675,x24672)) % 174.01/173.91 [2468]~E(x24681,x24682)+E(f687(x24681,x24683,x24684),f687(x24682,x24683,x24684)) % 174.01/173.91 [2469]~E(x24691,x24692)+E(f687(x24693,x24691,x24694),f687(x24693,x24692,x24694)) % 174.01/173.91 [2470]~E(x24701,x24702)+E(f687(x24703,x24704,x24701),f687(x24703,x24704,x24702)) % 174.01/173.91 [2471]~E(x24711,x24712)+E(f479(x24711,x24713,x24714),f479(x24712,x24713,x24714)) % 174.01/173.91 [2472]~E(x24721,x24722)+E(f479(x24723,x24721,x24724),f479(x24723,x24722,x24724)) % 174.01/173.91 [2473]~E(x24731,x24732)+E(f479(x24733,x24734,x24731),f479(x24733,x24734,x24732)) % 174.01/173.91 [2474]~E(x24741,x24742)+E(f604(x24741,x24743),f604(x24742,x24743)) % 174.01/173.91 [2475]~E(x24751,x24752)+E(f604(x24753,x24751),f604(x24753,x24752)) % 174.01/173.91 [2476]~E(x24761,x24762)+E(f99(x24761,x24763,x24764,x24765),f99(x24762,x24763,x24764,x24765)) % 174.01/173.91 [2477]~E(x24771,x24772)+E(f99(x24773,x24771,x24774,x24775),f99(x24773,x24772,x24774,x24775)) % 174.01/173.91 [2478]~E(x24781,x24782)+E(f99(x24783,x24784,x24781,x24785),f99(x24783,x24784,x24782,x24785)) % 174.01/173.91 [2479]~E(x24791,x24792)+E(f99(x24793,x24794,x24795,x24791),f99(x24793,x24794,x24795,x24792)) % 174.01/173.91 [2480]~E(x24801,x24802)+E(f594(x24801,x24803),f594(x24802,x24803)) % 174.01/173.91 [2481]~E(x24811,x24812)+E(f594(x24813,x24811),f594(x24813,x24812)) % 174.01/173.91 [2482]~E(x24821,x24822)+E(f256(x24821,x24823,x24824,x24825,x24826),f256(x24822,x24823,x24824,x24825,x24826)) % 174.01/173.91 [2483]~E(x24831,x24832)+E(f256(x24833,x24831,x24834,x24835,x24836),f256(x24833,x24832,x24834,x24835,x24836)) % 174.01/173.91 [2484]~E(x24841,x24842)+E(f256(x24843,x24844,x24841,x24845,x24846),f256(x24843,x24844,x24842,x24845,x24846)) % 174.01/173.91 [2485]~E(x24851,x24852)+E(f256(x24853,x24854,x24855,x24851,x24856),f256(x24853,x24854,x24855,x24852,x24856)) % 174.01/173.91 [2486]~E(x24861,x24862)+E(f256(x24863,x24864,x24865,x24866,x24861),f256(x24863,x24864,x24865,x24866,x24862)) % 174.01/173.91 [2487]~E(x24871,x24872)+E(f308(x24871,x24873),f308(x24872,x24873)) % 174.01/173.91 [2488]~E(x24881,x24882)+E(f308(x24883,x24881),f308(x24883,x24882)) % 174.01/173.91 [2489]~E(x24891,x24892)+E(f224(x24891,x24893,x24894),f224(x24892,x24893,x24894)) % 174.01/173.91 [2490]~E(x24901,x24902)+E(f224(x24903,x24901,x24904),f224(x24903,x24902,x24904)) % 174.01/173.91 [2491]~E(x24911,x24912)+E(f224(x24913,x24914,x24911),f224(x24913,x24914,x24912)) % 174.01/173.91 [2492]~E(x24921,x24922)+E(f98(x24921,x24923,x24924,x24925),f98(x24922,x24923,x24924,x24925)) % 174.01/173.91 [2493]~E(x24931,x24932)+E(f98(x24933,x24931,x24934,x24935),f98(x24933,x24932,x24934,x24935)) % 174.01/173.91 [2494]~E(x24941,x24942)+E(f98(x24943,x24944,x24941,x24945),f98(x24943,x24944,x24942,x24945)) % 174.01/173.91 [2495]~E(x24951,x24952)+E(f98(x24953,x24954,x24955,x24951),f98(x24953,x24954,x24955,x24952)) % 174.01/173.91 [2496]~E(x24961,x24962)+E(f340(x24961),f340(x24962)) % 174.01/173.91 [2497]~E(x24971,x24972)+E(f682(x24971,x24973),f682(x24972,x24973)) % 174.01/173.91 [2498]~E(x24981,x24982)+E(f682(x24983,x24981),f682(x24983,x24982)) % 174.01/173.91 [2499]~E(x24991,x24992)+E(f487(x24991,x24993,x24994,x24995,x24996),f487(x24992,x24993,x24994,x24995,x24996)) % 174.01/173.91 [2500]~E(x25001,x25002)+E(f487(x25003,x25001,x25004,x25005,x25006),f487(x25003,x25002,x25004,x25005,x25006)) % 174.01/173.91 [2501]~E(x25011,x25012)+E(f487(x25013,x25014,x25011,x25015,x25016),f487(x25013,x25014,x25012,x25015,x25016)) % 174.01/173.91 [2502]~E(x25021,x25022)+E(f487(x25023,x25024,x25025,x25021,x25026),f487(x25023,x25024,x25025,x25022,x25026)) % 174.01/173.91 [2503]~E(x25031,x25032)+E(f487(x25033,x25034,x25035,x25036,x25031),f487(x25033,x25034,x25035,x25036,x25032)) % 174.01/173.91 [2504]~E(x25041,x25042)+E(f611(x25041,x25043,x25044),f611(x25042,x25043,x25044)) % 174.01/173.91 [2505]~E(x25051,x25052)+E(f611(x25053,x25051,x25054),f611(x25053,x25052,x25054)) % 174.01/173.91 [2506]~E(x25061,x25062)+E(f611(x25063,x25064,x25061),f611(x25063,x25064,x25062)) % 174.01/173.91 [2507]~E(x25071,x25072)+E(f634(x25071,x25073,x25074),f634(x25072,x25073,x25074)) % 174.01/173.91 [2508]~E(x25081,x25082)+E(f634(x25083,x25081,x25084),f634(x25083,x25082,x25084)) % 174.01/173.91 [2509]~E(x25091,x25092)+E(f634(x25093,x25094,x25091),f634(x25093,x25094,x25092)) % 174.01/173.91 [2510]~E(x25101,x25102)+E(f590(x25101,x25103,x25104,x25105),f590(x25102,x25103,x25104,x25105)) % 174.01/173.91 [2511]~E(x25111,x25112)+E(f590(x25113,x25111,x25114,x25115),f590(x25113,x25112,x25114,x25115)) % 174.01/173.91 [2512]~E(x25121,x25122)+E(f590(x25123,x25124,x25121,x25125),f590(x25123,x25124,x25122,x25125)) % 174.01/173.91 [2513]~E(x25131,x25132)+E(f590(x25133,x25134,x25135,x25131),f590(x25133,x25134,x25135,x25132)) % 174.01/173.91 [2514]~E(x25141,x25142)+E(f621(x25141,x25143,x25144),f621(x25142,x25143,x25144)) % 174.01/173.91 [2515]~E(x25151,x25152)+E(f621(x25153,x25151,x25154),f621(x25153,x25152,x25154)) % 174.01/173.91 [2516]~E(x25161,x25162)+E(f621(x25163,x25164,x25161),f621(x25163,x25164,x25162)) % 174.01/173.91 [2517]~E(x25171,x25172)+E(f569(x25171,x25173,x25174),f569(x25172,x25173,x25174)) % 174.01/173.91 [2518]~E(x25181,x25182)+E(f569(x25183,x25181,x25184),f569(x25183,x25182,x25184)) % 174.01/173.91 [2519]~E(x25191,x25192)+E(f569(x25193,x25194,x25191),f569(x25193,x25194,x25192)) % 174.01/173.91 [2520]~E(x25201,x25202)+E(f493(x25201,x25203),f493(x25202,x25203)) % 174.01/173.91 [2521]~E(x25211,x25212)+E(f493(x25213,x25211),f493(x25213,x25212)) % 174.01/173.91 [2522]~E(x25221,x25222)+E(f208(x25221,x25223,x25224,x25225,x25226,x25227,x25228),f208(x25222,x25223,x25224,x25225,x25226,x25227,x25228)) % 174.01/173.91 [2523]~E(x25231,x25232)+E(f208(x25233,x25231,x25234,x25235,x25236,x25237,x25238),f208(x25233,x25232,x25234,x25235,x25236,x25237,x25238)) % 174.01/173.91 [2524]~E(x25241,x25242)+E(f208(x25243,x25244,x25241,x25245,x25246,x25247,x25248),f208(x25243,x25244,x25242,x25245,x25246,x25247,x25248)) % 174.01/173.91 [2525]~E(x25251,x25252)+E(f208(x25253,x25254,x25255,x25251,x25256,x25257,x25258),f208(x25253,x25254,x25255,x25252,x25256,x25257,x25258)) % 174.01/173.91 [2526]~E(x25261,x25262)+E(f208(x25263,x25264,x25265,x25266,x25261,x25267,x25268),f208(x25263,x25264,x25265,x25266,x25262,x25267,x25268)) % 174.01/173.91 [2527]~E(x25271,x25272)+E(f208(x25273,x25274,x25275,x25276,x25277,x25271,x25278),f208(x25273,x25274,x25275,x25276,x25277,x25272,x25278)) % 174.01/173.91 [2528]~E(x25281,x25282)+E(f208(x25283,x25284,x25285,x25286,x25287,x25288,x25281),f208(x25283,x25284,x25285,x25286,x25287,x25288,x25282)) % 174.01/173.91 [2529]~E(x25291,x25292)+E(f791(x25291,x25293),f791(x25292,x25293)) % 174.01/173.91 [2530]~E(x25301,x25302)+E(f791(x25303,x25301),f791(x25303,x25302)) % 174.01/173.91 [2531]~E(x25311,x25312)+E(f219(x25311,x25313,x25314),f219(x25312,x25313,x25314)) % 174.01/173.91 [2532]~E(x25321,x25322)+E(f219(x25323,x25321,x25324),f219(x25323,x25322,x25324)) % 174.01/173.91 [2533]~E(x25331,x25332)+E(f219(x25333,x25334,x25331),f219(x25333,x25334,x25332)) % 174.01/173.91 [2534]~E(x25341,x25342)+E(f339(x25341),f339(x25342)) % 174.01/173.91 [2535]~E(x25351,x25352)+E(f747(x25351,x25353,x25354),f747(x25352,x25353,x25354)) % 174.01/173.91 [2536]~E(x25361,x25362)+E(f747(x25363,x25361,x25364),f747(x25363,x25362,x25364)) % 174.01/173.91 [2537]~E(x25371,x25372)+E(f747(x25373,x25374,x25371),f747(x25373,x25374,x25372)) % 174.01/173.91 [2538]~E(x25381,x25382)+E(f207(x25381,x25383,x25384,x25385),f207(x25382,x25383,x25384,x25385)) % 174.01/173.91 [2539]~E(x25391,x25392)+E(f207(x25393,x25391,x25394,x25395),f207(x25393,x25392,x25394,x25395)) % 174.01/173.91 [2540]~E(x25401,x25402)+E(f207(x25403,x25404,x25401,x25405),f207(x25403,x25404,x25402,x25405)) % 174.01/173.91 [2541]~E(x25411,x25412)+E(f207(x25413,x25414,x25415,x25411),f207(x25413,x25414,x25415,x25412)) % 174.01/173.91 [2542]~E(x25421,x25422)+E(f600(x25421,x25423,x25424,x25425),f600(x25422,x25423,x25424,x25425)) % 174.01/173.91 [2543]~E(x25431,x25432)+E(f600(x25433,x25431,x25434,x25435),f600(x25433,x25432,x25434,x25435)) % 174.01/173.91 [2544]~E(x25441,x25442)+E(f600(x25443,x25444,x25441,x25445),f600(x25443,x25444,x25442,x25445)) % 174.01/173.91 [2545]~E(x25451,x25452)+E(f600(x25453,x25454,x25455,x25451),f600(x25453,x25454,x25455,x25452)) % 174.01/173.91 [2546]~E(x25461,x25462)+E(f752(x25461,x25463,x25464),f752(x25462,x25463,x25464)) % 174.01/173.91 [2547]~E(x25471,x25472)+E(f752(x25473,x25471,x25474),f752(x25473,x25472,x25474)) % 174.01/173.91 [2548]~E(x25481,x25482)+E(f752(x25483,x25484,x25481),f752(x25483,x25484,x25482)) % 174.01/173.91 [2549]~P1(x25491)+P1(x25492)+~E(x25491,x25492) % 174.01/173.91 [2550]~P2(x25501)+P2(x25502)+~E(x25501,x25502) % 174.01/173.91 [2551]~P67(x25511)+P67(x25512)+~E(x25511,x25512) % 174.01/173.91 [2552]~P93(x25521)+P93(x25522)+~E(x25521,x25522) % 174.01/173.91 [2553]~P3(x25531)+P3(x25532)+~E(x25531,x25532) % 174.01/173.91 [2554]~P100(x25541)+P100(x25542)+~E(x25541,x25542) % 174.01/173.91 [2555]~P68(x25551)+P68(x25552)+~E(x25551,x25552) % 174.01/173.91 [2556]~P4(x25561)+P4(x25562)+~E(x25561,x25562) % 174.01/173.91 [2557]~P62(x25571)+P62(x25572)+~E(x25571,x25572) % 174.01/173.91 [2558]~P119(x25581)+P119(x25582)+~E(x25581,x25582) % 174.01/173.91 [2559]~P5(x25591)+P5(x25592)+~E(x25591,x25592) % 174.01/173.91 [2560]~P7(x25601)+P7(x25602)+~E(x25601,x25602) % 174.01/173.91 [2561]P39(x25612,x25613,x25614,x25615)+~E(x25611,x25612)+~P39(x25611,x25613,x25614,x25615) % 174.01/173.91 [2562]P39(x25623,x25622,x25624,x25625)+~E(x25621,x25622)+~P39(x25623,x25621,x25624,x25625) % 174.01/173.91 [2563]P39(x25633,x25634,x25632,x25635)+~E(x25631,x25632)+~P39(x25633,x25634,x25631,x25635) % 174.01/173.91 [2564]P39(x25643,x25644,x25645,x25642)+~E(x25641,x25642)+~P39(x25643,x25644,x25645,x25641) % 174.01/173.91 [2565]~P66(x25651)+P66(x25652)+~E(x25651,x25652) % 174.01/173.91 [2566]P141(x25662,x25663,x25664)+~E(x25661,x25662)+~P141(x25661,x25663,x25664) % 174.01/173.91 [2567]P141(x25673,x25672,x25674)+~E(x25671,x25672)+~P141(x25673,x25671,x25674) % 174.01/173.91 [2568]P141(x25683,x25684,x25682)+~E(x25681,x25682)+~P141(x25683,x25684,x25681) % 174.01/173.91 [2569]P24(x25692,x25693,x25694,x25695)+~E(x25691,x25692)+~P24(x25691,x25693,x25694,x25695) % 174.01/173.91 [2570]P24(x25703,x25702,x25704,x25705)+~E(x25701,x25702)+~P24(x25703,x25701,x25704,x25705) % 174.01/173.91 [2571]P24(x25713,x25714,x25712,x25715)+~E(x25711,x25712)+~P24(x25713,x25714,x25711,x25715) % 174.01/173.91 [2572]P24(x25723,x25724,x25725,x25722)+~E(x25721,x25722)+~P24(x25723,x25724,x25725,x25721) % 174.01/173.91 [2573]P31(x25732,x25733,x25734)+~E(x25731,x25732)+~P31(x25731,x25733,x25734) % 174.01/173.91 [2574]P31(x25743,x25742,x25744)+~E(x25741,x25742)+~P31(x25743,x25741,x25744) % 174.01/173.91 [2575]P31(x25753,x25754,x25752)+~E(x25751,x25752)+~P31(x25753,x25754,x25751) % 174.01/173.91 [2576]~P89(x25761)+P89(x25762)+~E(x25761,x25762) % 174.01/173.91 [2577]~P117(x25771)+P117(x25772)+~E(x25771,x25772) % 174.01/173.91 [2578]P18(x25782,x25783)+~E(x25781,x25782)+~P18(x25781,x25783) % 174.01/173.91 [2579]P18(x25793,x25792)+~E(x25791,x25792)+~P18(x25793,x25791) % 174.01/173.91 [2580]~P73(x25801)+P73(x25802)+~E(x25801,x25802) % 174.01/173.91 [2581]P53(x25812,x25813,x25814)+~E(x25811,x25812)+~P53(x25811,x25813,x25814) % 174.01/173.91 [2582]P53(x25823,x25822,x25824)+~E(x25821,x25822)+~P53(x25823,x25821,x25824) % 174.01/173.91 [2583]P53(x25833,x25834,x25832)+~E(x25831,x25832)+~P53(x25833,x25834,x25831) % 174.01/173.91 [2584]P22(x25842,x25843,x25844)+~E(x25841,x25842)+~P22(x25841,x25843,x25844) % 174.01/173.91 [2585]P22(x25853,x25852,x25854)+~E(x25851,x25852)+~P22(x25853,x25851,x25854) % 174.01/173.91 [2586]P22(x25863,x25864,x25862)+~E(x25861,x25862)+~P22(x25863,x25864,x25861) % 174.01/173.91 [2587]~P137(x25871)+P137(x25872)+~E(x25871,x25872) % 174.01/173.91 [2588]~P92(x25881)+P92(x25882)+~E(x25881,x25882) % 174.01/173.91 [2589]~P85(x25891)+P85(x25892)+~E(x25891,x25892) % 174.01/173.91 [2590]~P81(x25901)+P81(x25902)+~E(x25901,x25902) % 174.01/173.91 [2591]~P8(x25911)+P8(x25912)+~E(x25911,x25912) % 174.01/173.91 [2592]~P74(x25921)+P74(x25922)+~E(x25921,x25922) % 174.01/173.91 [2593]~P79(x25931)+P79(x25932)+~E(x25931,x25932) % 174.01/173.91 [2594]~P110(x25941)+P110(x25942)+~E(x25941,x25942) % 174.01/173.91 [2595]~P80(x25951)+P80(x25952)+~E(x25951,x25952) % 174.01/173.91 [2596]P140(x25962,x25963,x25964)+~E(x25961,x25962)+~P140(x25961,x25963,x25964) % 174.01/173.91 [2597]P140(x25973,x25972,x25974)+~E(x25971,x25972)+~P140(x25973,x25971,x25974) % 174.01/173.91 [2598]P140(x25983,x25984,x25982)+~E(x25981,x25982)+~P140(x25983,x25984,x25981) % 174.01/173.91 [2599]~P63(x25991)+P63(x25992)+~E(x25991,x25992) % 174.01/173.91 [2600]~P88(x26001)+P88(x26002)+~E(x26001,x26002) % 174.01/173.91 [2601]~P118(x26011)+P118(x26012)+~E(x26011,x26012) % 174.01/173.91 [2602]P29(x26022,x26023,x26024,x26025)+~E(x26021,x26022)+~P29(x26021,x26023,x26024,x26025) % 174.01/173.91 [2603]P29(x26033,x26032,x26034,x26035)+~E(x26031,x26032)+~P29(x26033,x26031,x26034,x26035) % 174.01/173.91 [2604]P29(x26043,x26044,x26042,x26045)+~E(x26041,x26042)+~P29(x26043,x26044,x26041,x26045) % 174.01/173.91 [2605]P29(x26053,x26054,x26055,x26052)+~E(x26051,x26052)+~P29(x26053,x26054,x26055,x26051) % 174.01/173.91 [2606]~P99(x26061)+P99(x26062)+~E(x26061,x26062) % 174.01/173.91 [2607]P47(x26072,x26073,x26074)+~E(x26071,x26072)+~P47(x26071,x26073,x26074) % 174.01/173.91 [2608]P47(x26083,x26082,x26084)+~E(x26081,x26082)+~P47(x26083,x26081,x26084) % 174.01/173.91 [2609]P47(x26093,x26094,x26092)+~E(x26091,x26092)+~P47(x26093,x26094,x26091) % 174.01/173.91 [2610]~P111(x26101)+P111(x26102)+~E(x26101,x26102) % 174.01/173.91 [2611]~P65(x26111)+P65(x26112)+~E(x26111,x26112) % 174.01/173.91 [2612]~P86(x26121)+P86(x26122)+~E(x26121,x26122) % 174.01/173.91 [2613]P28(x26132,x26133,x26134)+~E(x26131,x26132)+~P28(x26131,x26133,x26134) % 174.01/173.91 [2614]P28(x26143,x26142,x26144)+~E(x26141,x26142)+~P28(x26143,x26141,x26144) % 174.01/173.91 [2615]P28(x26153,x26154,x26152)+~E(x26151,x26152)+~P28(x26153,x26154,x26151) % 174.01/173.91 [2616]P36(x26162,x26163)+~E(x26161,x26162)+~P36(x26161,x26163) % 174.01/173.91 [2617]P36(x26173,x26172)+~E(x26171,x26172)+~P36(x26173,x26171) % 174.01/173.91 [2618]P49(x26182,x26183)+~E(x26181,x26182)+~P49(x26181,x26183) % 174.01/173.91 [2619]P49(x26193,x26192)+~E(x26191,x26192)+~P49(x26193,x26191) % 174.01/173.91 [2620]~P60(x26201)+P60(x26202)+~E(x26201,x26202) % 174.01/173.91 [2621]~P102(x26211)+P102(x26212)+~E(x26211,x26212) % 174.01/173.91 [2622]~P38(x26221)+P38(x26222)+~E(x26221,x26222) % 174.01/173.91 [2623]~P103(x26231)+P103(x26232)+~E(x26231,x26232) % 174.01/173.91 [2624]~P82(x26241)+P82(x26242)+~E(x26241,x26242) % 174.01/173.91 [2625]~P77(x26251)+P77(x26252)+~E(x26251,x26252) % 174.01/173.91 [2626]~P6(x26261)+P6(x26262)+~E(x26261,x26262) % 174.01/173.91 [2627]~P112(x26271)+P112(x26272)+~E(x26271,x26272) % 174.01/173.91 [2628]~P61(x26281)+P61(x26282)+~E(x26281,x26282) % 174.01/173.91 [2629]~P113(x26291)+P113(x26292)+~E(x26291,x26292) % 174.01/173.91 [2630]~P98(x26301)+P98(x26302)+~E(x26301,x26302) % 174.01/173.91 [2631]P33(x26312,x26313)+~E(x26311,x26312)+~P33(x26311,x26313) % 174.01/173.91 [2632]P33(x26323,x26322)+~E(x26321,x26322)+~P33(x26323,x26321) % 174.01/173.91 [2633]~P70(x26331)+P70(x26332)+~E(x26331,x26332) % 174.01/173.91 [2634]P30(x26342,x26343)+~E(x26341,x26342)+~P30(x26341,x26343) % 174.01/173.91 [2635]P30(x26353,x26352)+~E(x26351,x26352)+~P30(x26353,x26351) % 174.01/173.91 [2636]~P9(x26361)+P9(x26362)+~E(x26361,x26362) % 174.01/173.91 [2637]~P120(x26371)+P120(x26372)+~E(x26371,x26372) % 174.01/173.91 [2638]~P121(x26381)+P121(x26382)+~E(x26381,x26382) % 174.01/173.91 [2639]~P64(x26391)+P64(x26392)+~E(x26391,x26392) % 174.01/173.91 [2640]P54(x26402,x26403,x26404)+~E(x26401,x26402)+~P54(x26401,x26403,x26404) % 174.01/173.91 [2641]P54(x26413,x26412,x26414)+~E(x26411,x26412)+~P54(x26413,x26411,x26414) % 174.01/173.91 [2642]P54(x26423,x26424,x26422)+~E(x26421,x26422)+~P54(x26423,x26424,x26421) % 174.01/173.91 [2643]~P10(x26431)+P10(x26432)+~E(x26431,x26432) % 174.01/173.91 [2644]~P69(x26441)+P69(x26442)+~E(x26441,x26442) % 174.01/173.91 [2645]~P90(x26451)+P90(x26452)+~E(x26451,x26452) % 174.01/173.91 [2646]~P104(x26461)+P104(x26462)+~E(x26461,x26462) % 174.01/173.91 [2647]P58(x26472,x26473)+~E(x26471,x26472)+~P58(x26471,x26473) % 174.01/173.91 [2648]P58(x26483,x26482)+~E(x26481,x26482)+~P58(x26483,x26481) % 174.01/173.91 [2649]~P75(x26491)+P75(x26492)+~E(x26491,x26492) % 174.01/173.91 [2650]~P101(x26501)+P101(x26502)+~E(x26501,x26502) % 174.01/173.91 [2651]~P106(x26511)+P106(x26512)+~E(x26511,x26512) % 174.01/173.91 [2652]~P76(x26521)+P76(x26522)+~E(x26521,x26522) % 174.01/173.91 [2653]P16(x26532,x26533,x26534,x26535)+~E(x26531,x26532)+~P16(x26531,x26533,x26534,x26535) % 174.01/173.91 [2654]P16(x26543,x26542,x26544,x26545)+~E(x26541,x26542)+~P16(x26543,x26541,x26544,x26545) % 174.01/173.91 [2655]P16(x26553,x26554,x26552,x26555)+~E(x26551,x26552)+~P16(x26553,x26554,x26551,x26555) % 174.01/173.91 [2656]P16(x26563,x26564,x26565,x26562)+~E(x26561,x26562)+~P16(x26563,x26564,x26565,x26561) % 174.01/173.91 [2657]P11(x26572,x26573)+~E(x26571,x26572)+~P11(x26571,x26573) % 174.01/173.91 [2658]P11(x26583,x26582)+~E(x26581,x26582)+~P11(x26583,x26581) % 174.01/173.91 [2659]~P87(x26591)+P87(x26592)+~E(x26591,x26592) % 174.01/173.91 [2660]~P133(x26601)+P133(x26602)+~E(x26601,x26602) % 174.01/173.91 [2661]~P105(x26611)+P105(x26612)+~E(x26611,x26612) % 174.01/173.91 [2662]~P84(x26621)+P84(x26622)+~E(x26621,x26622) % 174.01/173.91 [2663]~P91(x26631)+P91(x26632)+~E(x26631,x26632) % 174.01/173.91 [2664]~P122(x26641)+P122(x26642)+~E(x26641,x26642) % 174.01/173.91 [2665]~P95(x26651)+P95(x26652)+~E(x26651,x26652) % 174.01/173.91 [2666]P142(x26662,x26663)+~E(x26661,x26662)+~P142(x26661,x26663) % 174.01/173.91 [2667]P142(x26673,x26672)+~E(x26671,x26672)+~P142(x26673,x26671) % 174.01/173.91 [2668]~P134(x26681)+P134(x26682)+~E(x26681,x26682) % 174.01/173.91 [2669]~P127(x26691)+P127(x26692)+~E(x26691,x26692) % 174.01/173.91 [2670]P32(x26702,x26703,x26704)+~E(x26701,x26702)+~P32(x26701,x26703,x26704) % 174.01/173.91 [2671]P32(x26713,x26712,x26714)+~E(x26711,x26712)+~P32(x26713,x26711,x26714) % 174.01/173.91 [2672]P32(x26723,x26724,x26722)+~E(x26721,x26722)+~P32(x26723,x26724,x26721) % 174.01/173.91 [2673]P57(x26732,x26733,x26734,x26735)+~E(x26731,x26732)+~P57(x26731,x26733,x26734,x26735) % 174.01/173.91 [2674]P57(x26743,x26742,x26744,x26745)+~E(x26741,x26742)+~P57(x26743,x26741,x26744,x26745) % 174.01/173.91 [2675]P57(x26753,x26754,x26752,x26755)+~E(x26751,x26752)+~P57(x26753,x26754,x26751,x26755) % 174.01/173.91 [2676]P57(x26763,x26764,x26765,x26762)+~E(x26761,x26762)+~P57(x26763,x26764,x26765,x26761) % 174.01/173.91 [2677]~P138(x26771)+P138(x26772)+~E(x26771,x26772) % 174.01/173.91 [2678]~P43(x26781)+P43(x26782)+~E(x26781,x26782) % 174.01/173.91 [2679]P42(x26792,x26793)+~E(x26791,x26792)+~P42(x26791,x26793) % 174.01/173.91 [2680]P42(x26803,x26802)+~E(x26801,x26802)+~P42(x26803,x26801) % 174.01/173.91 [2681]~P109(x26811)+P109(x26812)+~E(x26811,x26812) % 174.01/173.91 [2682]P26(x26822,x26823,x26824,x26825,x26826,x26827)+~E(x26821,x26822)+~P26(x26821,x26823,x26824,x26825,x26826,x26827) % 174.01/173.91 [2683]P26(x26833,x26832,x26834,x26835,x26836,x26837)+~E(x26831,x26832)+~P26(x26833,x26831,x26834,x26835,x26836,x26837) % 174.01/173.91 [2684]P26(x26843,x26844,x26842,x26845,x26846,x26847)+~E(x26841,x26842)+~P26(x26843,x26844,x26841,x26845,x26846,x26847) % 174.01/173.91 [2685]P26(x26853,x26854,x26855,x26852,x26856,x26857)+~E(x26851,x26852)+~P26(x26853,x26854,x26855,x26851,x26856,x26857) % 174.01/173.91 [2686]P26(x26863,x26864,x26865,x26866,x26862,x26867)+~E(x26861,x26862)+~P26(x26863,x26864,x26865,x26866,x26861,x26867) % 174.01/173.91 [2687]P26(x26873,x26874,x26875,x26876,x26877,x26872)+~E(x26871,x26872)+~P26(x26873,x26874,x26875,x26876,x26877,x26871) % 174.01/173.91 [2688]~P13(x26881)+P13(x26882)+~E(x26881,x26882) % 174.01/173.91 [2689]~P135(x26891)+P135(x26892)+~E(x26891,x26892) % 174.01/173.91 [2690]P15(x26902,x26903,x26904,x26905,x26906)+~E(x26901,x26902)+~P15(x26901,x26903,x26904,x26905,x26906) % 174.01/173.91 [2691]P15(x26913,x26912,x26914,x26915,x26916)+~E(x26911,x26912)+~P15(x26913,x26911,x26914,x26915,x26916) % 174.01/173.91 [2692]P15(x26923,x26924,x26922,x26925,x26926)+~E(x26921,x26922)+~P15(x26923,x26924,x26921,x26925,x26926) % 174.01/173.91 [2693]P15(x26933,x26934,x26935,x26932,x26936)+~E(x26931,x26932)+~P15(x26933,x26934,x26935,x26931,x26936) % 174.01/173.91 [2694]P15(x26943,x26944,x26945,x26946,x26942)+~E(x26941,x26942)+~P15(x26943,x26944,x26945,x26946,x26941) % 174.01/173.91 [2695]P56(x26952,x26953)+~E(x26951,x26952)+~P56(x26951,x26953) % 174.01/173.91 [2696]P56(x26963,x26962)+~E(x26961,x26962)+~P56(x26963,x26961) % 174.01/173.91 [2697]P25(x26972,x26973,x26974,x26975,x26976)+~E(x26971,x26972)+~P25(x26971,x26973,x26974,x26975,x26976) % 174.01/173.91 [2698]P25(x26983,x26982,x26984,x26985,x26986)+~E(x26981,x26982)+~P25(x26983,x26981,x26984,x26985,x26986) % 174.01/173.91 [2699]P25(x26993,x26994,x26992,x26995,x26996)+~E(x26991,x26992)+~P25(x26993,x26994,x26991,x26995,x26996) % 174.01/173.91 [2700]P25(x27003,x27004,x27005,x27002,x27006)+~E(x27001,x27002)+~P25(x27003,x27004,x27005,x27001,x27006) % 174.01/173.91 [2701]P25(x27013,x27014,x27015,x27016,x27012)+~E(x27011,x27012)+~P25(x27013,x27014,x27015,x27016,x27011) % 174.01/173.91 [2702]~P71(x27021)+P71(x27022)+~E(x27021,x27022) % 174.01/173.91 [2703]~P123(x27031)+P123(x27032)+~E(x27031,x27032) % 174.01/173.91 [2704]P19(x27042,x27043,x27044)+~E(x27041,x27042)+~P19(x27041,x27043,x27044) % 174.01/173.91 [2705]P19(x27053,x27052,x27054)+~E(x27051,x27052)+~P19(x27053,x27051,x27054) % 174.01/173.91 [2706]P19(x27063,x27064,x27062)+~E(x27061,x27062)+~P19(x27063,x27064,x27061) % 174.01/173.91 [2707]~P59(x27071)+P59(x27072)+~E(x27071,x27072) % 174.01/173.91 [2708]~P115(x27081)+P115(x27082)+~E(x27081,x27082) % 174.01/173.91 [2709]P12(x27092,x27093,x27094)+~E(x27091,x27092)+~P12(x27091,x27093,x27094) % 174.01/173.91 [2710]P12(x27103,x27102,x27104)+~E(x27101,x27102)+~P12(x27103,x27101,x27104) % 174.01/173.91 [2711]P12(x27113,x27114,x27112)+~E(x27111,x27112)+~P12(x27113,x27114,x27111) % 174.01/173.91 [2712]~P136(x27121)+P136(x27122)+~E(x27121,x27122) % 174.01/173.91 [2713]P27(x27132,x27133,x27134,x27135,x27136,x27137)+~E(x27131,x27132)+~P27(x27131,x27133,x27134,x27135,x27136,x27137) % 174.01/173.91 [2714]P27(x27143,x27142,x27144,x27145,x27146,x27147)+~E(x27141,x27142)+~P27(x27143,x27141,x27144,x27145,x27146,x27147) % 174.01/173.91 [2715]P27(x27153,x27154,x27152,x27155,x27156,x27157)+~E(x27151,x27152)+~P27(x27153,x27154,x27151,x27155,x27156,x27157) % 174.01/173.91 [2716]P27(x27163,x27164,x27165,x27162,x27166,x27167)+~E(x27161,x27162)+~P27(x27163,x27164,x27165,x27161,x27166,x27167) % 174.01/173.91 [2717]P27(x27173,x27174,x27175,x27176,x27172,x27177)+~E(x27171,x27172)+~P27(x27173,x27174,x27175,x27176,x27171,x27177) % 174.01/173.91 [2718]P27(x27183,x27184,x27185,x27186,x27187,x27182)+~E(x27181,x27182)+~P27(x27183,x27184,x27185,x27186,x27187,x27181) % 174.01/173.91 [2719]~P124(x27191)+P124(x27192)+~E(x27191,x27192) % 174.01/173.91 [2720]~P78(x27201)+P78(x27202)+~E(x27201,x27202) % 174.01/173.91 [2721]~P129(x27211)+P129(x27212)+~E(x27211,x27212) % 174.01/173.91 [2722]P50(x27222,x27223,x27224,x27225)+~E(x27221,x27222)+~P50(x27221,x27223,x27224,x27225) % 174.01/173.91 [2723]P50(x27233,x27232,x27234,x27235)+~E(x27231,x27232)+~P50(x27233,x27231,x27234,x27235) % 174.01/173.91 [2724]P50(x27243,x27244,x27242,x27245)+~E(x27241,x27242)+~P50(x27243,x27244,x27241,x27245) % 174.01/173.91 [2725]P50(x27253,x27254,x27255,x27252)+~E(x27251,x27252)+~P50(x27253,x27254,x27255,x27251) % 174.01/173.91 [2726]~P128(x27261)+P128(x27262)+~E(x27261,x27262) % 174.01/173.91 [2727]P55(x27272,x27273,x27274,x27275,x27276)+~E(x27271,x27272)+~P55(x27271,x27273,x27274,x27275,x27276) % 174.01/173.91 [2728]P55(x27283,x27282,x27284,x27285,x27286)+~E(x27281,x27282)+~P55(x27283,x27281,x27284,x27285,x27286) % 174.01/173.91 [2729]P55(x27293,x27294,x27292,x27295,x27296)+~E(x27291,x27292)+~P55(x27293,x27294,x27291,x27295,x27296) % 174.01/173.91 [2730]P55(x27303,x27304,x27305,x27302,x27306)+~E(x27301,x27302)+~P55(x27303,x27304,x27305,x27301,x27306) % 174.01/173.91 [2731]P55(x27313,x27314,x27315,x27316,x27312)+~E(x27311,x27312)+~P55(x27313,x27314,x27315,x27316,x27311) % 174.01/173.91 [2732]P23(x27322,x27323,x27324,x27325)+~E(x27321,x27322)+~P23(x27321,x27323,x27324,x27325) % 174.01/173.91 [2733]P23(x27333,x27332,x27334,x27335)+~E(x27331,x27332)+~P23(x27333,x27331,x27334,x27335) % 174.01/173.91 [2734]P23(x27343,x27344,x27342,x27345)+~E(x27341,x27342)+~P23(x27343,x27344,x27341,x27345) % 174.01/173.91 [2735]P23(x27353,x27354,x27355,x27352)+~E(x27351,x27352)+~P23(x27353,x27354,x27355,x27351) % 174.01/173.91 [2736]P20(x27362,x27363,x27364)+~E(x27361,x27362)+~P20(x27361,x27363,x27364) % 174.01/173.91 [2737]P20(x27373,x27372,x27374)+~E(x27371,x27372)+~P20(x27373,x27371,x27374) % 174.01/173.91 [2738]P20(x27383,x27384,x27382)+~E(x27381,x27382)+~P20(x27383,x27384,x27381) % 174.01/173.91 [2739]~P131(x27391)+P131(x27392)+~E(x27391,x27392) % 174.01/173.91 [2740]P44(x27402,x27403)+~E(x27401,x27402)+~P44(x27401,x27403) % 174.01/173.91 [2741]P44(x27413,x27412)+~E(x27411,x27412)+~P44(x27413,x27411) % 174.01/173.91 [2742]P40(x27422,x27423,x27424,x27425)+~E(x27421,x27422)+~P40(x27421,x27423,x27424,x27425) % 174.01/173.91 [2743]P40(x27433,x27432,x27434,x27435)+~E(x27431,x27432)+~P40(x27433,x27431,x27434,x27435) % 174.01/173.91 [2744]P40(x27443,x27444,x27442,x27445)+~E(x27441,x27442)+~P40(x27443,x27444,x27441,x27445) % 174.01/173.91 [2745]P40(x27453,x27454,x27455,x27452)+~E(x27451,x27452)+~P40(x27453,x27454,x27455,x27451) % 174.01/173.91 [2746]~P130(x27461)+P130(x27462)+~E(x27461,x27462) % 174.01/173.91 [2747]P41(x27472,x27473,x27474,x27475,x27476,x27477)+~E(x27471,x27472)+~P41(x27471,x27473,x27474,x27475,x27476,x27477) % 174.01/173.91 [2748]P41(x27483,x27482,x27484,x27485,x27486,x27487)+~E(x27481,x27482)+~P41(x27483,x27481,x27484,x27485,x27486,x27487) % 174.01/173.91 [2749]P41(x27493,x27494,x27492,x27495,x27496,x27497)+~E(x27491,x27492)+~P41(x27493,x27494,x27491,x27495,x27496,x27497) % 174.01/173.91 [2750]P41(x27503,x27504,x27505,x27502,x27506,x27507)+~E(x27501,x27502)+~P41(x27503,x27504,x27505,x27501,x27506,x27507) % 174.01/173.91 [2751]P41(x27513,x27514,x27515,x27516,x27512,x27517)+~E(x27511,x27512)+~P41(x27513,x27514,x27515,x27516,x27511,x27517) % 174.01/173.91 [2752]P41(x27523,x27524,x27525,x27526,x27527,x27522)+~E(x27521,x27522)+~P41(x27523,x27524,x27525,x27526,x27527,x27521) % 174.01/173.91 [2753]P34(x27532,x27533,x27534,x27535)+~E(x27531,x27532)+~P34(x27531,x27533,x27534,x27535) % 174.01/173.91 [2754]P34(x27543,x27542,x27544,x27545)+~E(x27541,x27542)+~P34(x27543,x27541,x27544,x27545) % 174.01/173.91 [2755]P34(x27553,x27554,x27552,x27555)+~E(x27551,x27552)+~P34(x27553,x27554,x27551,x27555) % 174.01/173.91 [2756]P34(x27563,x27564,x27565,x27562)+~E(x27561,x27562)+~P34(x27563,x27564,x27565,x27561) % 174.01/173.91 [2757]~P125(x27571)+P125(x27572)+~E(x27571,x27572) % 174.01/173.91 [2758]~P114(x27581)+P114(x27582)+~E(x27581,x27582) % 174.01/173.91 [2759]~P132(x27591)+P132(x27592)+~E(x27591,x27592) % 174.01/173.91 [2760]~P126(x27601)+P126(x27602)+~E(x27601,x27602) % 174.01/173.91 [2761]~P83(x27611)+P83(x27612)+~E(x27611,x27612) % 174.01/173.91 [2762]~P94(x27621)+P94(x27622)+~E(x27621,x27622) % 174.01/173.91 [2763]P17(x27632,x27633,x27634,x27635,x27636,x27637)+~E(x27631,x27632)+~P17(x27631,x27633,x27634,x27635,x27636,x27637) % 174.01/173.91 [2764]P17(x27643,x27642,x27644,x27645,x27646,x27647)+~E(x27641,x27642)+~P17(x27643,x27641,x27644,x27645,x27646,x27647) % 174.01/173.91 [2765]P17(x27653,x27654,x27652,x27655,x27656,x27657)+~E(x27651,x27652)+~P17(x27653,x27654,x27651,x27655,x27656,x27657) % 174.01/173.91 [2766]P17(x27663,x27664,x27665,x27662,x27666,x27667)+~E(x27661,x27662)+~P17(x27663,x27664,x27665,x27661,x27666,x27667) % 174.01/173.91 [2767]P17(x27673,x27674,x27675,x27676,x27672,x27677)+~E(x27671,x27672)+~P17(x27673,x27674,x27675,x27676,x27671,x27677) % 174.01/173.91 [2768]P17(x27683,x27684,x27685,x27686,x27687,x27682)+~E(x27681,x27682)+~P17(x27683,x27684,x27685,x27686,x27687,x27681) % 174.01/173.91 [2769]P51(x27692,x27693,x27694,x27695,x27696,x27697,x27698)+~E(x27691,x27692)+~P51(x27691,x27693,x27694,x27695,x27696,x27697,x27698) % 174.01/173.91 [2770]P51(x27703,x27702,x27704,x27705,x27706,x27707,x27708)+~E(x27701,x27702)+~P51(x27703,x27701,x27704,x27705,x27706,x27707,x27708) % 174.01/173.91 [2771]P51(x27713,x27714,x27712,x27715,x27716,x27717,x27718)+~E(x27711,x27712)+~P51(x27713,x27714,x27711,x27715,x27716,x27717,x27718) % 174.01/173.91 [2772]P51(x27723,x27724,x27725,x27722,x27726,x27727,x27728)+~E(x27721,x27722)+~P51(x27723,x27724,x27725,x27721,x27726,x27727,x27728) % 174.01/173.91 [2773]P51(x27733,x27734,x27735,x27736,x27732,x27737,x27738)+~E(x27731,x27732)+~P51(x27733,x27734,x27735,x27736,x27731,x27737,x27738) % 174.01/173.91 [2774]P51(x27743,x27744,x27745,x27746,x27747,x27742,x27748)+~E(x27741,x27742)+~P51(x27743,x27744,x27745,x27746,x27747,x27741,x27748) % 174.01/173.91 [2775]P51(x27753,x27754,x27755,x27756,x27757,x27758,x27752)+~E(x27751,x27752)+~P51(x27753,x27754,x27755,x27756,x27757,x27758,x27751) % 174.01/173.91 [2776]~P96(x27761)+P96(x27762)+~E(x27761,x27762) % 174.01/173.91 [2777]~P97(x27771)+P97(x27772)+~E(x27771,x27772) % 174.01/173.91 [2778]~P139(x27781)+P139(x27782)+~E(x27781,x27782) % 174.01/173.91 [2779]~P116(x27791)+P116(x27792)+~E(x27791,x27792) % 174.01/173.91 [2780]P21(x27802,x27803,x27804)+~E(x27801,x27802)+~P21(x27801,x27803,x27804) % 174.01/173.91 [2781]P21(x27813,x27812,x27814)+~E(x27811,x27812)+~P21(x27813,x27811,x27814) % 174.01/173.91 [2782]P21(x27823,x27824,x27822)+~E(x27821,x27822)+~P21(x27823,x27824,x27821) % 174.01/173.91 [2783]P46(x27832,x27833,x27834)+~E(x27831,x27832)+~P46(x27831,x27833,x27834) % 174.01/173.91 [2784]P46(x27843,x27842,x27844)+~E(x27841,x27842)+~P46(x27843,x27841,x27844) % 174.01/173.91 [2785]P46(x27853,x27854,x27852)+~E(x27851,x27852)+~P46(x27853,x27854,x27851) % 174.01/173.91 [2786]~P72(x27861)+P72(x27862)+~E(x27861,x27862) % 174.01/173.91 [2787]~P107(x27871)+P107(x27872)+~E(x27871,x27872) % 174.01/173.91 [2788]~P35(x27881)+P35(x27882)+~E(x27881,x27882) % 174.01/173.91 [2789]~P108(x27891)+P108(x27892)+~E(x27891,x27892) % 174.01/173.91 [2790]P48(x27902,x27903)+~E(x27901,x27902)+~P48(x27901,x27903) % 174.01/173.91 [2791]P48(x27913,x27912)+~E(x27911,x27912)+~P48(x27913,x27911) % 174.01/173.91 [2792]P52(x27922,x27923,x27924,x27925)+~E(x27921,x27922)+~P52(x27921,x27923,x27924,x27925) % 174.01/173.91 [2793]P52(x27933,x27932,x27934,x27935)+~E(x27931,x27932)+~P52(x27933,x27931,x27934,x27935) % 174.01/173.91 [2794]P52(x27943,x27944,x27942,x27945)+~E(x27941,x27942)+~P52(x27943,x27944,x27941,x27945) % 174.01/173.91 [2795]P52(x27953,x27954,x27955,x27952)+~E(x27951,x27952)+~P52(x27953,x27954,x27955,x27951) % 174.01/173.91 [2796]P45(x27962,x27963,x27964)+~E(x27961,x27962)+~P45(x27961,x27963,x27964) % 174.01/173.91 [2797]P45(x27973,x27972,x27974)+~E(x27971,x27972)+~P45(x27973,x27971,x27974) % 174.01/173.91 [2798]P45(x27983,x27984,x27982)+~E(x27981,x27982)+~P45(x27983,x27984,x27981) % 174.01/173.91 [2799]P37(x27992,x27993)+~E(x27991,x27992)+~P37(x27991,x27993) % 174.01/173.91 [2800]P37(x28003,x28002)+~E(x28001,x28002)+~P37(x28003,x28001) % 174.01/173.91 [2801]P14(x28012,x28013,x28014)+~E(x28011,x28012)+~P14(x28011,x28013,x28014) % 174.01/173.91 [2802]P14(x28023,x28022,x28024)+~E(x28021,x28022)+~P14(x28023,x28021,x28024) % 174.01/173.91 [2803]P14(x28033,x28034,x28032)+~E(x28031,x28032)+~P14(x28033,x28034,x28031) % 174.01/173.91 % 174.01/173.91 %------------------------------------------- % 174.01/173.94 cnf(10049,plain, % 174.01/173.94 (E(f39(x100491,x100492,x100493,x100494,x100495,x100496,x100497,x100498,x100499,a27),x100492)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(10052,plain, % 174.01/173.94 (E(f39(x100521,x100522,x100523,x100524,x100525,x100526,x100527,x100528,x100529,a27),x100522)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(10055,plain, % 174.01/173.94 (~E(f777(a116,x100551),x100551)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(10058,plain, % 174.01/173.94 (E(f39(x100581,x100582,x100583,x100584,x100585,x100586,x100587,x100588,x100589,a27),x100582)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(10065,plain, % 174.01/173.94 (~E(f777(a116,x100651),x100651)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(10076,plain, % 174.01/173.94 (~E(f777(a116,x100761),x100761)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(10079,plain, % 174.01/173.94 (~P1(f777(f66(x100791,x100792,f182(f858(x100791,a845))),x100793))), % 174.01/173.94 inference(rename_variables,[],[4478])). % 174.01/173.94 cnf(10082,plain, % 174.01/173.94 (~P1(f777(f66(x100821,x100822,f182(f858(x100821,a845))),x100823))), % 174.01/173.94 inference(rename_variables,[],[4478])). % 174.01/173.94 cnf(10085,plain, % 174.01/173.94 (~E(f777(a116,x100851),x100851)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(10088,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x100881),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(10091,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x100911),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(10108,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x101081)),x101081))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(10111,plain, % 174.01/173.94 (~E(f777(f777(f142(x101111),x101112),x101113),x101113)), % 174.01/173.94 inference(rename_variables,[],[4401])). % 174.01/173.94 cnf(10117,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x101171),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(10120,plain, % 174.01/173.94 (E(f39(x101201,x101202,x101203,x101204,x101205,x101206,x101207,x101208,x101209,a27),x101202)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(10123,plain, % 174.01/173.94 (E(f39(x101231,x101232,x101233,x101234,x101235,x101236,x101237,x101238,x101239,a27),x101232)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(10130,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),f777(f777(f84(a851),x101301),x101302)),x101302))), % 174.01/173.94 inference(rename_variables,[],[4479])). % 174.01/173.94 cnf(10133,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),f777(f777(f84(a851),x101331),x101332)),x101332))), % 174.01/173.94 inference(rename_variables,[],[4479])). % 174.01/173.94 cnf(10154,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x101541),x101541))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(10157,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f54(a851,x101571,x101572)),x101571))), % 174.01/173.94 inference(rename_variables,[],[3639])). % 174.01/173.94 cnf(10176,plain, % 174.01/173.94 (E(f777(f44(a851),f777(f259(a851),x101761)),x101761)), % 174.01/173.94 inference(rename_variables,[],[3084])). % 174.01/173.94 cnf(10184,plain, % 174.01/173.94 (~E(f777(a116,x101841),x101841)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(10187,plain, % 174.01/173.94 (~E(f777(a116,x101871),x101871)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(10190,plain, % 174.01/173.94 (~E(f777(a116,x101901),x101901)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(10195,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x101951),f777(a116,x101951)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(10198,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x101981),f777(a116,x101981)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(10200,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x102001),f777(a116,x102001)))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,4367,10055,10065,10076,10085,10184,10187,3028,3087,3052,3035,3120,4401,3084,4483,3103,3255,10195,4455,10088,10091,3772,3189,4452,4395,4451,10154,3281,3703,3639,4464,10108,4009,4462,4443,3163,4447,4478,10079,4481,4479,10130,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220])). % 174.01/173.94 cnf(10207,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x102071),x102071))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(10214,plain, % 174.01/173.94 (E(f39(x102141,x102142,x102143,x102144,x102145,x102146,x102147,x102148,x102149,a27),x102142)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(10217,plain, % 174.01/173.94 (E(f39(x102171,x102172,x102173,x102174,x102175,x102176,x102177,x102178,x102179,a27),x102172)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(10242,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x102421),x102421))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(10247,plain, % 174.01/173.94 (~E(f777(f777(f777(f76(x102471,f855(x102472)),x102473),x102474),f777(f229(x102472),x102475)),f777(f20(f855(x102472),x102471),f185(x102472)))), % 174.01/173.94 inference(rename_variables,[],[4475])). % 174.01/173.94 cnf(10251,plain, % 174.01/173.94 (E(f777(f777(f84(a851),x102511),f682(x102511,x102511)),x102511)), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,4367,10055,10065,10076,10085,10184,10187,3028,3087,3052,3035,3120,4475,4401,3084,3964,4483,3103,3255,10195,10198,4455,10088,10091,3619,3772,3214,3216,3189,4452,4395,3914,3185,3186,4451,10154,3281,3703,3639,10157,4464,10108,4009,4462,4443,3163,4447,4478,10079,4481,3662,4479,10130,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352])). % 174.01/173.94 cnf(10276,plain, % 174.01/173.94 (~E(f777(f777(f142(x102761),x102762),x102763),x102763)), % 174.01/173.94 inference(rename_variables,[],[4401])). % 174.01/173.94 cnf(10279,plain, % 174.01/173.94 (~E(f777(a29,x102791),f37(x102792,x102793))), % 174.01/173.94 inference(rename_variables,[],[4385])). % 174.01/173.94 cnf(10292,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x102921),x102921))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(10295,plain, % 174.01/173.94 (~E(f777(a116,x102951),x102951)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(10302,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x103021),x103021))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(10311,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x103111),f777(a116,x103111)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(10316,plain, % 174.01/173.94 (E(f777(f777(f127(x103161),f117(x103161)),x103162),x103162)), % 174.01/173.94 inference(rename_variables,[],[3140])). % 174.01/173.94 cnf(10334,plain, % 174.01/173.94 (~P1(f777(f66(x103341,x103342,f182(f858(x103341,a845))),x103343))), % 174.01/173.94 inference(rename_variables,[],[4478])). % 174.01/173.94 cnf(10353,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x103531),x103531))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(10374,plain, % 174.01/173.94 (~E(f777(a29,x103741),f37(x103742,x103743))), % 174.01/173.94 inference(rename_variables,[],[4385])). % 174.01/173.94 cnf(10383,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x103831),x103831))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(10388,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x103881),f777(a116,x103881)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(10400,plain, % 174.01/173.94 (~E(f777(f144(x104001),f777(a116,f777(f777(f127(x104001),f777(f144(x104001),x104002)),f777(f777(f142(x104001),x104003),f117(x104001))))),f777(f777(f142(x104001),x104003),x104002))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,4367,10055,10065,10076,10085,10184,10187,10190,10295,4385,10279,3028,3087,3052,3035,3120,3140,10316,4475,4401,10111,3084,3964,4483,3103,3545,3255,10195,10198,10311,10388,4455,10088,10091,10117,4471,3619,3772,3214,3216,3189,4452,4395,3914,3185,10207,3186,3187,4451,10154,10242,10353,3281,3703,3639,10157,4464,10108,4009,4462,4443,4446,3163,3164,4447,4478,10079,10082,4481,3662,4479,10130,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890])). % 174.01/173.94 cnf(10401,plain, % 174.01/173.94 (~E(f777(a116,x104011),x104011)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(10415,plain, % 174.01/173.94 (P1(f777(f777(f235(a103),f777(a7,x104151)),f777(a7,f777(a116,x104151))))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,4367,10055,10065,10076,10085,10184,10187,10190,10295,4385,10279,3028,3087,3052,3035,3120,3140,10316,4475,4401,10111,3084,3964,4483,3103,3545,3255,10195,10198,10311,10388,3634,4455,10088,10091,10117,4471,3619,3772,3214,3216,3189,4452,4395,3914,3185,10207,3186,3187,4451,10154,10242,10353,3281,3703,3639,10157,4464,10108,4009,4462,4443,4446,3163,3164,4447,4478,10079,10082,4481,3662,4479,10130,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972])). % 174.01/173.94 cnf(10426,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x104261),x104261))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(10429,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x104291),f777(a116,f777(f777(f84(a851),x104292),x104291))))), % 174.01/173.94 inference(rename_variables,[],[3632])). % 174.01/173.94 cnf(10432,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x104321),f777(f777(f85(a851),x104321),x104321)))), % 174.01/173.94 inference(rename_variables,[],[3456])). % 174.01/173.94 cnf(10434,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x104341),f777(f777(f85(a851),f777(a116,x104341)),f777(a116,x104341))))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,4367,10055,10065,10076,10085,10184,10187,10190,10295,4385,10279,3028,3087,3052,3035,3120,3140,10316,4475,4401,10111,3084,3964,4483,3103,3545,3255,10195,10198,10311,10388,3634,4455,10088,10091,10117,4471,3619,3772,3214,3216,3189,4452,4395,3914,3185,10207,10302,3186,3187,4451,10154,10242,10353,3281,3703,3639,10157,4464,10108,4009,4462,4443,4446,3163,3164,4447,4478,10079,10082,3456,10432,4481,3662,4479,10130,3632,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998])). % 174.01/173.94 cnf(10435,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x104351),f777(f777(f85(a851),x104351),x104351)))), % 174.01/173.94 inference(rename_variables,[],[3456])). % 174.01/173.94 cnf(10440,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x104401),f777(a116,x104401)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(10443,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x104431),f777(a116,x104431)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(10446,plain, % 174.01/173.94 (P1(f777(f777(f336(x104461),x104462),f241(f858(x104461,a845))))), % 174.01/173.94 inference(rename_variables,[],[3342])). % 174.01/173.94 cnf(10459,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),f777(f777(f84(a851),x104591),x104592)),x104592))), % 174.01/173.94 inference(rename_variables,[],[4479])). % 174.01/173.94 cnf(10462,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),f777(f777(f84(a851),x104621),x104622)),x104622))), % 174.01/173.94 inference(rename_variables,[],[4479])). % 174.01/173.94 cnf(10465,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x104651)),x104651))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(10468,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x104681)),x104681))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(10471,plain, % 174.01/173.94 (P1(f777(f241(f858(x104711,a845)),x104712))), % 174.01/173.94 inference(rename_variables,[],[3249])). % 174.01/173.94 cnf(10474,plain, % 174.01/173.94 (E(f777(f44(a851),f777(f259(a851),x104741)),x104741)), % 174.01/173.94 inference(rename_variables,[],[3084])). % 174.01/173.94 cnf(10477,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x104771),f777(a116,x104771)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(10484,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x104841),x104841))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(10489,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x104891),x104891))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(10498,plain, % 174.01/173.94 (E(f39(x104981,x104982,x104983,x104984,x104985,x104986,x104987,x104988,x104989,a27),x104982)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(10501,plain, % 174.01/173.94 (P1(f777(f241(f858(x105011,a845)),x105012))), % 174.01/173.94 inference(rename_variables,[],[3249])). % 174.01/173.94 cnf(10503,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(f777(f85(a851),f777(a116,x105031)),f777(a116,x105031))),x105031))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,10217,4367,10055,10065,10076,10085,10184,10187,10190,10295,4385,10279,3028,3087,3052,3035,3120,3140,10316,4475,4401,10111,3084,10176,3964,4483,3103,3545,3491,3255,10195,10198,10311,10388,10440,10443,3634,4455,10088,10091,10117,4471,3619,3395,3772,3214,3216,3189,4452,4395,3914,3185,10207,10302,10426,3186,3187,10292,4451,10154,10242,10353,3342,3249,10471,3281,3703,3639,10157,4464,10108,10465,4009,4462,4443,4446,3163,3164,4447,4478,10079,10082,3456,10432,10435,4481,3662,4479,10130,10133,10459,3632,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213])). % 174.01/173.94 cnf(10504,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x105041),f777(f777(f85(a851),x105041),x105041)))), % 174.01/173.94 inference(rename_variables,[],[3456])). % 174.01/173.94 cnf(10508,plain, % 174.01/173.94 (E(f777(f144(x105081),f39(x105082,f777(f777(f127(x105081),f777(f144(x105081),x105083)),f777(f777(f142(x105081),x105084),f117(x105081))),x105085,x105086,x105087,x105088,x105089,x1050810,x1050811,a27)),f777(f777(f142(x105081),x105084),x105083))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,4385,10279,3028,3087,3052,3035,3120,3140,10316,4475,4401,10111,3084,10176,3964,4483,3103,3545,3491,3255,10195,10198,10311,10388,10440,10443,3634,4455,10088,10091,10117,4471,3619,3395,3772,3214,3216,3189,4452,4395,3914,3185,10207,10302,10426,3186,3187,10292,4451,10154,10242,10353,3342,3249,10471,3281,3703,3639,10157,4464,10108,10465,4009,4462,4443,4446,3163,3164,4447,4478,10079,10082,3456,10432,10435,4481,3662,4479,10130,10133,10459,3632,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256])). % 174.01/173.94 cnf(10509,plain, % 174.01/173.94 (E(f39(x105091,x105092,x105093,x105094,x105095,x105096,x105097,x105098,x105099,a27),x105092)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(10515,plain, % 174.01/173.94 (~P1(f777(f777(f235(a103),f777(a7,x105151)),f777(a7,f4(a851))))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,4385,10279,3028,3087,3052,3035,3120,3140,10316,4475,4401,10111,3084,10176,3964,4483,3103,3545,3491,3255,10195,10198,10311,10388,10440,10443,10477,3634,4455,10088,10091,10117,4471,3619,3395,3772,3214,3216,3189,4452,4395,3914,3185,10207,10302,10426,3186,3187,10292,4451,10154,10242,10353,3342,3249,10471,3281,3703,3639,10157,4464,10108,10465,4009,4462,4443,4446,3163,3164,4447,4478,10079,10082,3456,10432,10435,4481,3662,4479,10130,10133,10459,3632,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262])). % 174.01/173.94 cnf(10517,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),f777(a109,a87)),f777(a109,a101)))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,4385,10279,3028,3087,3052,3035,3120,3140,10316,4475,4401,10111,3084,10176,3964,4483,3103,3545,3491,3255,10195,10198,10311,10388,10440,10443,10477,3634,4455,10088,10091,10117,4471,3619,3395,3772,3214,3216,3189,4452,4395,3914,3185,10207,10302,10426,3186,3187,10292,4451,10154,10242,10353,3342,3249,10471,3281,3703,3639,10157,4464,10108,10465,4009,4462,4443,4446,3163,3164,4445,4447,4478,10079,10082,3456,10432,10435,4481,3662,4479,10130,10133,10459,3632,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263])). % 174.01/173.94 cnf(10521,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,f777(a116,f777(f777(f84(a851),x105211),x105212)))),f777(a116,x105212)))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,4385,10279,3028,3087,3052,3035,3120,3140,10316,4475,4401,10111,3084,10176,3964,4483,3103,3545,3491,3255,10195,10198,10311,10388,10440,10443,10477,3634,4455,10088,10091,10117,4471,3619,3395,3772,3214,3216,3189,4452,4395,3914,3185,10207,10302,10426,3186,3187,10292,4451,10154,10242,10353,3342,3249,10471,3281,3703,3639,10157,4464,10108,10465,4009,4462,4443,4446,3163,3164,4445,4447,4478,10079,10082,3456,10432,10435,4481,3662,4479,10130,10133,10459,3632,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265])). % 174.01/173.94 cnf(10544,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x105441),x105441))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(10555,plain, % 174.01/173.94 (~P1(f777(f777(f182(f858(x105551,f858(x105552,a845))),x105553),x105554))), % 174.01/173.94 inference(rename_variables,[],[4482])). % 174.01/173.94 cnf(10566,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x105661),f777(a116,x105661)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(10569,plain, % 174.01/173.94 (~E(f777(a116,x105691),x105691)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(10571,plain, % 174.01/173.94 (P1(f777(f777(f235(a3),f777(f777(f5(a3),x105711),f82(a3))),x105711))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,4385,10279,3028,3087,3052,3035,3120,3140,10316,4475,4401,10111,3084,10176,3964,3818,4483,3103,3545,3491,3255,10195,10198,10311,10388,10440,10443,10477,3634,4455,10088,10091,10117,4471,3619,3395,3772,3214,3216,3189,4452,4395,3914,3185,10207,10302,10426,3186,10544,3187,10292,10489,4451,10154,10242,10353,3342,4467,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,4009,4462,4443,4446,3163,3164,4445,4447,4478,10079,10082,3456,10432,10435,4481,4482,3662,4479,10130,10133,10459,3632,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538])). % 174.01/173.94 cnf(10572,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x105721),x105721))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(10577,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x105771),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(10592,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x105921),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(10595,plain, % 174.01/173.94 (~P1(f777(f777(f235(f858(x105951,a845)),x105952),f182(f858(x105951,a845))))), % 174.01/173.94 inference(rename_variables,[],[4476])). % 174.01/173.94 cnf(10598,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x105981),x105981))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(10601,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x106011),x106011))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(10615,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x106151),f777(f777(f5(a851),x106151),x106152)))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,4385,10279,3028,3087,3052,3035,3120,3140,10316,4475,4401,10111,3084,10176,3964,3818,4483,3103,3545,3491,3255,10195,10198,10311,10388,10440,10443,10477,3634,4455,10088,10091,10117,10577,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3914,4476,3185,10207,10302,10426,3186,10544,10598,10601,3187,10292,10489,3188,4451,10154,10242,10353,10383,3342,4467,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,4009,4462,4443,4446,3163,3164,4445,4447,4478,10079,10082,3456,10432,10435,4481,4482,3662,4479,10130,10133,10459,3632,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708])). % 174.01/173.94 cnf(10616,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x106161),x106161))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(10625,plain, % 174.01/173.94 (~P1(f777(f777(f336(x106251),x106252),f182(f858(x106251,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(10634,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x106341),x106341))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(10637,plain, % 174.01/173.94 (~P1(f777(f777(f336(x106371),x106372),f182(f858(x106371,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(10640,plain, % 174.01/173.94 (P1(f777(f777(f281(a851),x106401),x106401))), % 174.01/173.94 inference(rename_variables,[],[3188])). % 174.01/173.94 cnf(10643,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x106431,a845)),f777(f305(x106432,x106431,x106433),f777(f307(x106432,x106431,x106433),x106434))),x106434))), % 174.01/173.94 inference(rename_variables,[],[4069])). % 174.01/173.94 cnf(10650,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x106501,a845)),f777(f160(x106501),f777(f128(x106501,x106502),x106503))),f777(f160(x106501),x106503)))), % 174.01/173.94 inference(rename_variables,[],[3828])). % 174.01/173.94 cnf(10653,plain, % 174.01/173.94 (E(f777(f305(x106531,x106531,f9(x106531)),x106532),x106532)), % 174.01/173.94 inference(rename_variables,[],[3245])). % 174.01/173.94 cnf(10658,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f4(a851)),x106581))), % 174.01/173.94 inference(rename_variables,[],[3208])). % 174.01/173.94 cnf(10661,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x106611),x106611))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(10664,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x106641),x106641))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(10671,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x106711),x106711))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(10682,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x106821),f777(a116,f777(f777(f84(a851),x106822),x106821))))), % 174.01/173.94 inference(rename_variables,[],[3632])). % 174.01/173.94 cnf(10685,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x106851),f777(f777(f85(a851),x106851),x106851)))), % 174.01/173.94 inference(rename_variables,[],[3456])). % 174.01/173.94 cnf(10695,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x106951),x106951))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(10698,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x106981),x106981))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(10701,plain, % 174.01/173.94 (~E(f777(a116,x107011),x107011)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(10706,plain, % 174.01/173.94 (P1(f777(f777(f281(a851),x107061),x107061))), % 174.01/173.94 inference(rename_variables,[],[3188])). % 174.01/173.94 cnf(10709,plain, % 174.01/173.94 (P1(f777(f777(f336(x107091),x107092),f241(f858(x107091,a845))))), % 174.01/173.94 inference(rename_variables,[],[3342])). % 174.01/173.94 cnf(10714,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x107141),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(10716,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x107161,a845)),x107162),f46(f858(x107161,a845),f777(f303(x107161),x107162))))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,4385,10279,3028,3087,3052,3035,3245,3120,3140,10316,4475,4401,10111,3084,10176,3964,3818,4483,3103,3384,3545,3491,3255,10195,10198,10311,10388,10440,10443,10477,10566,3634,4455,10088,10091,10117,10577,10592,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3546,3914,4476,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,3342,10446,4467,10625,10637,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,3208,4009,4462,4443,4446,3163,3164,4445,4447,4478,10079,10082,3456,10432,10435,10504,10685,4481,4482,4069,3662,4479,10130,10133,10459,3632,10429,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447])). % 174.01/173.94 cnf(10725,plain, % 174.01/173.94 (~E(f777(a116,x107251),f4(a851))), % 174.01/173.94 inference(rename_variables,[],[4379])). % 174.01/173.94 cnf(10732,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f4(a851)),x107321))), % 174.01/173.94 inference(rename_variables,[],[3208])). % 174.01/173.94 cnf(10739,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x107391),x107391))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(10746,plain, % 174.01/173.94 (~P1(f777(f777(f336(x107461),x107462),f182(f858(x107461,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(10750,plain, % 174.01/173.94 (E(f777(f777(f106(f858(x107501,a845)),f777(f777(f106(f858(x107501,a845)),x107502),f777(f83(f858(x107501,a845)),x107503))),x107503),f182(f858(x107501,a845)))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,4385,10279,4379,3028,3087,3052,3035,3245,3120,3140,10316,4475,4401,10111,3084,10176,3964,3818,4483,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,3634,4455,10088,10091,10117,10577,10592,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3546,3914,4476,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,3342,10446,10709,4467,10625,10637,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,3208,10658,4009,4462,3711,4443,4446,3163,3164,4445,4447,4478,10079,10082,3456,10432,10435,10504,10685,4481,4482,4069,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728])). % 174.01/173.94 cnf(10754,plain, % 174.01/173.94 (P1(f777(f777(f336(x107541),x107542),f241(f858(x107541,a845))))), % 174.01/173.94 inference(rename_variables,[],[3342])). % 174.01/173.94 cnf(10757,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x107571),f852(x107571))),f777(f777(f243(f852(x107571),f852(x107571)),x107572),f117(x107571))),f137(x107571,x107573)))), % 174.01/173.94 inference(rename_variables,[],[4483])). % 174.01/173.94 cnf(10763,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(x107631,x107631)),x107632),f262(x107631,f182(f858(x107631,a845)))))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,4385,10279,4379,3028,3087,3052,3035,3245,3120,3140,10316,4475,4401,10111,3084,10176,3964,3818,4483,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,3634,4455,10088,10091,10117,10577,10592,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3546,3914,4476,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,3342,10446,10709,4467,10625,10637,10746,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,3208,10658,4009,4462,3711,4443,4446,3163,3164,4445,4447,4478,10079,10082,3456,10432,10435,10504,10685,4481,4482,4069,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873])). % 174.01/173.94 cnf(10764,plain, % 174.01/173.94 (~P1(f777(f777(f336(x107641),x107642),f182(f858(x107641,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(10766,plain, % 174.01/173.94 (~P1(f777(f777(f336(x107661),x107662),f777(f307(x107661,x107663,x107664),f182(f858(x107663,a845)))))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,4385,10279,4379,3028,3087,3052,3035,3245,3120,3140,10316,4475,4401,10111,3084,10176,3964,3818,4483,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,3634,4455,10088,10091,10117,10577,10592,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3546,3914,4476,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,3342,10446,10709,4467,10625,10637,10746,10764,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,3208,10658,4009,4462,3711,4443,4446,3163,3164,4445,4447,4478,10079,10082,3456,10432,10435,10504,10685,4481,4482,4069,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905])). % 174.01/173.94 cnf(10767,plain, % 174.01/173.94 (~P1(f777(f777(f336(x107671),x107672),f182(f858(x107671,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(10770,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x107701,a845)),x107702),f777(f777(f304(x107701),x107703),x107702)))), % 174.01/173.94 inference(rename_variables,[],[3627])). % 174.01/173.94 cnf(10773,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x107731),x107731))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(10776,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x107761,a845)),x107762),f777(f777(f304(x107761),x107763),x107762)))), % 174.01/173.94 inference(rename_variables,[],[3627])). % 174.01/173.94 cnf(10787,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x107871,a845)),x107872),f777(f777(f304(x107871),x107873),x107872)))), % 174.01/173.94 inference(rename_variables,[],[3627])). % 174.01/173.94 cnf(10792,plain, % 174.01/173.94 (~P1(f777(f66(x107921,x107922,f182(f858(x107921,a845))),x107923))), % 174.01/173.94 inference(rename_variables,[],[4478])). % 174.01/173.94 cnf(10805,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x108051),f777(a116,x108051)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(10815,plain, % 174.01/173.94 (~E(f777(f315(x108151,x108152),x108153),f777(f306(x108152,x108151),x108154))), % 174.01/173.94 inference(rename_variables,[],[4440])). % 174.01/173.94 cnf(10818,plain, % 174.01/173.94 (~P1(f777(f777(f336(x108181),x108182),f182(f858(x108181,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(10821,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(x108211,x108211)),f777(f777(f243(x108211,x108211),x108212),x108212)),f302(x108211,x108213)))), % 174.01/173.94 inference(rename_variables,[],[3818])). % 174.01/173.94 cnf(10824,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x108241,a845)),f777(f160(x108241),f153(x108241,x108242,x108243))),f777(f160(x108241),x108243)))), % 174.01/173.94 inference(rename_variables,[],[3876])). % 174.01/173.94 cnf(10827,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x108271,a845)),x108272),f241(f858(x108271,a845))))), % 174.01/173.94 inference(rename_variables,[],[3563])). % 174.01/173.94 cnf(10834,plain, % 174.01/173.94 (~E(f777(a116,x108341),x108341)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(10850,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x108501,a845)),f182(f858(x108501,a845))),x108502))), % 174.01/173.94 inference(rename_variables,[],[3631])). % 174.01/173.94 cnf(10861,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x108611),f852(x108611))),f777(f777(f243(f852(x108611),f852(x108611)),x108612),f117(x108611))),f139(x108611,x108613)))), % 174.01/173.94 inference(rename_variables,[],[4484])). % 174.01/173.94 cnf(10869,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(f852(x108691),f852(x108691))),f777(f777(f243(f852(x108691),f852(x108691)),f117(x108691)),f117(x108691))),f777(f777(f283(f852(x108691),f852(x108691),f852(x108691)),f149(x108691,x108692)),f302(f852(x108691),f149(x108691,x108692)))))), % 174.01/173.94 inference(scs_inference,[],[4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,4385,10279,4379,3642,3028,4440,3087,3052,3035,3245,3120,3140,10316,4475,3817,4401,10111,3084,10176,3964,3818,10821,4483,10757,4484,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,3634,4455,10088,10091,10117,10577,10592,10714,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3876,3546,3914,3563,4476,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,3342,10446,10709,10754,4467,10625,10637,10746,10764,10767,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,3208,10658,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,4478,10079,10082,10334,3789,3627,10770,10776,3631,3456,10432,10435,10504,10685,4481,4482,4069,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553])). % 174.01/173.94 cnf(10879,plain, % 174.01/173.94 (P29(x108791,x108791,f9(x108791),x108792)), % 174.01/173.94 inference(rename_variables,[],[3428])). % 174.01/173.94 cnf(10884,plain, % 174.01/173.94 (~E(f777(f305(x108841,f858(x108841,a845),x108842),x108843),f777(f303(x108841),x108843))), % 174.01/173.94 inference(rename_variables,[],[4465])). % 174.01/173.94 cnf(10889,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x108891,a845)),x108892),f241(f858(x108891,a845))))), % 174.01/173.94 inference(rename_variables,[],[3563])). % 174.01/173.94 cnf(10896,plain, % 174.01/173.94 (P36(x108961,f777(f777(f282(a851,x108961),a239),x108962))), % 174.01/173.94 inference(rename_variables,[],[3291])). % 174.01/173.94 cnf(10903,plain, % 174.01/173.94 (~P1(f777(f777(f336(x109031),x109032),f182(f858(x109031,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(10906,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x109061)),x109061))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(10908,plain, % 174.01/173.94 (~E(f777(f777(f10(x109081,a851),f777(f5(a851),f4(a851))),x109082),f777(a116,x109083))), % 174.01/173.94 inference(scs_inference,[],[3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,4385,10279,10374,4379,3642,3028,4440,3087,3052,3035,3245,3120,3140,10316,4475,3817,4401,10111,4465,3291,3084,10176,3964,3818,10821,4483,10757,4484,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,4455,10088,10091,10117,10577,10592,10714,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3876,3546,3914,3563,10827,4476,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,3342,10446,10709,10754,4467,10625,10637,10746,10764,10767,10818,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,3208,10658,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,4478,10079,10082,10334,3789,3627,10770,10776,3631,3456,10432,10435,10504,10685,4481,4482,4069,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718])). % 174.01/173.94 cnf(10913,plain, % 174.01/173.94 (~P1(f777(f777(f336(x109131),x109132),f182(f858(x109131,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(10921,plain, % 174.01/173.94 (~P1(f777(f777(f336(a851),f777(a116,f777(f134(a851,a851,f84(a851),f4(a851)),x109211))),f777(f160(a851),x109211)))), % 174.01/173.94 inference(scs_inference,[],[3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,4385,10279,10374,4379,3642,3028,4440,3087,3052,3035,3245,3120,3140,10316,4475,3817,4401,10111,4465,3291,3084,10176,3964,3818,10821,4483,10757,4484,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,4455,10088,10091,10117,10577,10592,10714,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3876,3546,3914,3563,10827,4476,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,3342,10446,10709,10754,4467,10625,10637,10746,10764,10767,10818,10903,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,10906,3208,10658,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,4478,10079,10082,10334,3789,3627,10770,10776,3631,3456,10432,10435,10504,10685,4481,4482,4069,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756])). % 174.01/173.94 cnf(10922,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x109221)),x109221))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(10925,plain, % 174.01/173.94 (~P1(f777(f777(f336(x109251),x109252),f182(f858(x109251,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(10933,plain, % 174.01/173.94 (E(f777(x109331,f704(f777(x109331,x109332),f777(f229(x109333),x109332),x109331,x109334,x109333)),f777(x109331,x109332))), % 174.01/173.94 inference(scs_inference,[],[3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,4385,10279,10374,4379,3642,3028,4440,3087,3052,3035,3245,3120,3140,10316,3290,4475,3817,4401,10111,4465,3291,3084,10176,3964,3818,10821,4483,10757,4484,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,4455,10088,10091,10117,10577,10592,10714,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3876,3546,3914,3563,10827,4476,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,3342,10446,10709,10754,4467,10625,10637,10746,10764,10767,10818,10903,10913,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,10906,3208,10658,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,4478,10079,10082,10334,3789,3627,10770,10776,3631,3456,10432,10435,10504,10685,4481,4482,4069,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818])). % 174.01/173.94 cnf(10940,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(x109401,x109401)),f777(f777(f243(x109401,x109401),x109402),x109402)),f302(x109401,x109403)))), % 174.01/173.94 inference(rename_variables,[],[3818])). % 174.01/173.94 cnf(10947,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x109471),f852(x109471))),f777(f777(f243(f852(x109471),f852(x109471)),x109472),f117(x109471))),f137(x109471,x109473)))), % 174.01/173.94 inference(rename_variables,[],[4483])). % 174.01/173.94 cnf(10950,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x109501),f852(x109501))),f777(f777(f243(f852(x109501),f852(x109501)),x109502),f117(x109501))),f139(x109501,x109503)))), % 174.01/173.94 inference(rename_variables,[],[4484])). % 174.01/173.94 cnf(10953,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x109531),f852(x109531))),f777(f777(f243(f852(x109531),f852(x109531)),x109532),f117(x109531))),f148(x109531,x109533)))), % 174.01/173.94 inference(rename_variables,[],[4485])). % 174.01/173.94 cnf(10958,plain, % 174.01/173.94 (~P1(f777(f777(f235(f858(x109581,a845)),x109582),f182(f858(x109581,a845))))), % 174.01/173.94 inference(rename_variables,[],[4476])). % 174.01/173.94 cnf(10961,plain, % 174.01/173.94 (~P1(f777(f777(f336(x109611),x109612),f182(f858(x109611,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(10965,plain, % 174.01/173.94 (~P39(f38(f777(a29,x109651),x109652),x109653,f4(a851),x109654)), % 174.01/173.94 inference(scs_inference,[],[3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,4385,10279,10374,4379,3642,3028,4440,3087,3052,3035,3245,3120,3140,10316,3290,4475,3817,4401,10111,4465,3291,3084,10176,3964,3818,10821,4483,10757,10947,4484,10861,4485,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,4455,10088,10091,10117,10577,10592,10714,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3876,3546,3914,3563,10827,4476,10595,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,3342,10446,10709,10754,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,10906,3208,10658,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,4478,10079,10082,10334,3789,3627,10770,10776,3631,3456,10432,10435,10504,10685,4481,4482,4069,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995])). % 174.01/173.94 cnf(10971,plain, % 174.01/173.94 (~P39(f38(x109711,f38(x109712,f38(f38(f777(a29,x109713),x109714),x109715))),x109716,f4(a851),x109717)), % 174.01/173.94 inference(scs_inference,[],[3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,4385,10279,10374,4379,3642,3028,4440,3087,3052,3035,3245,3120,3140,10316,3290,4475,3817,4401,10111,4465,3291,3084,10176,3964,3818,10821,4483,10757,10947,4484,10861,4485,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,4455,10088,10091,10117,10577,10592,10714,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3876,3546,3914,3563,10827,4476,10595,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,3342,10446,10709,10754,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,10906,3208,10658,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,4478,10079,10082,10334,3789,3627,10770,10776,3631,3456,10432,10435,10504,10685,4481,4482,4069,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998])). % 174.01/173.94 cnf(10973,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x109731,a845)),x109732),f777(f777(f105(f858(x109731,a845)),x109733),f241(f858(x109731,a845)))))), % 174.01/173.94 inference(scs_inference,[],[3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,4385,10279,10374,4379,3642,3028,4440,3087,3052,3035,3245,3120,3140,10316,3290,4475,3817,4401,10111,4465,3291,3084,10176,3964,3818,10821,4483,10757,10947,4484,10861,4485,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,4455,10088,10091,10117,10577,10592,10714,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3876,3546,3914,3563,10827,10889,4476,10595,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,3342,10446,10709,10754,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,10906,3208,10658,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,4478,10079,10082,10334,3789,3627,10770,10776,3631,3456,10432,10435,10504,10685,4481,4482,4069,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001])). % 174.01/173.94 cnf(10974,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x109741,a845)),x109742),f241(f858(x109741,a845))))), % 174.01/173.94 inference(rename_variables,[],[3563])). % 174.01/173.94 cnf(10977,plain, % 174.01/173.94 (~P1(f777(f777(f182(f858(x109771,f858(x109772,a845))),x109773),x109774))), % 174.01/173.94 inference(rename_variables,[],[4482])). % 174.01/173.94 cnf(10984,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x109841),x109841))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(10989,plain, % 174.01/173.94 (~P1(f777(f777(f336(x109891),x109892),f182(f858(x109891,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(10992,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x109921,a845)),x109922),x109922))), % 174.01/173.94 inference(rename_variables,[],[3485])). % 174.01/173.94 cnf(10995,plain, % 174.01/173.94 (E(f321(x109951,x109952,x109953,f777(f777(f12(f859(x109951,x109953),x109952,x109951),x109954),f306(x109951,x109953)),f777(f777(f12(f859(x109951,x109953),x109952,x109953),x109954),f315(x109953,x109951))),x109954)), % 174.01/173.94 inference(rename_variables,[],[4049])). % 174.01/173.94 cnf(11001,plain, % 174.01/173.94 (~P1(f777(f777(f336(x110011),x110012),f182(f858(x110011,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11004,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x110041,a845)),f182(f858(x110041,a845))),x110042))), % 174.01/173.94 inference(rename_variables,[],[3631])). % 174.01/173.94 cnf(11007,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(x110071,x110071)),f777(f777(f243(x110071,x110071),x110072),x110072)),f302(x110071,x110073)))), % 174.01/173.94 inference(rename_variables,[],[3818])). % 174.01/173.94 cnf(11009,plain, % 174.01/173.94 (~E(f777(f777(f106(f858(f857(f852(x110091),f852(x110091)),a845)),f777(f280(f852(x110091),f852(x110091)),f149(x110091,x110092))),f302(f852(x110091),f149(x110091,x110092))),f182(f858(f857(f852(x110091),f852(x110091)),a845)))), % 174.01/173.94 inference(scs_inference,[],[3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,4385,10279,10374,4379,3642,3028,4440,3087,3052,3035,4049,10995,3245,3120,3140,10316,3290,4475,3817,4401,10111,4465,3291,3084,10176,3964,3818,10821,10940,4483,10757,10947,4484,10861,4485,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,4455,10088,10091,10117,10577,10592,10714,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3876,3546,3914,3563,10827,10889,4476,10595,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,10671,3342,10446,10709,10754,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,10906,3208,10658,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,4478,10079,10082,10334,3789,3627,10770,10776,3485,3631,10850,3456,10432,10435,10504,10685,4481,4482,10555,4069,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176])). % 174.01/173.94 cnf(11014,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x110141),f852(x110141))),f777(f777(f243(f852(x110141),f852(x110141)),x110142),f117(x110141))),f148(x110141,x110143)))), % 174.01/173.94 inference(rename_variables,[],[4485])). % 174.01/173.94 cnf(11017,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x110171),f852(x110171))),f777(f777(f243(f852(x110171),f852(x110171)),f117(x110171)),x110172)),f137(x110171,x110173)))), % 174.01/173.94 inference(rename_variables,[],[4486])). % 174.01/173.94 cnf(11022,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f858(x110221,a845),f858(x110221,a845))),f777(f777(f243(f858(x110221,a845),f858(x110221,a845)),x110222),f182(f858(x110221,a845)))),f301(x110221)))), % 174.01/173.94 inference(scs_inference,[],[3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,4385,10279,10374,4379,3642,3028,4440,3087,3052,3035,4049,10995,3245,3120,3140,10316,3290,4475,3817,4401,10111,4465,3291,3084,10176,3964,3818,10821,10940,4483,10757,10947,4484,10861,4485,10953,4486,4487,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,4455,10088,10091,10117,10577,10592,10714,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3876,3546,3914,3563,10827,10889,4476,10595,10958,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,10671,3342,10446,10709,10754,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,10906,3208,10658,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,4478,10079,10082,10334,3789,3627,10770,10776,3485,3631,10850,3456,10432,10435,10504,10685,4481,4482,10555,4069,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299])). % 174.01/173.94 cnf(11025,plain, % 174.01/173.94 (P1(f777(f777(f336(x110251),x110252),f241(f858(x110251,a845))))), % 174.01/173.94 inference(rename_variables,[],[3342])). % 174.01/173.94 cnf(11030,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x110301,a845)),f182(f858(x110301,a845))),x110302))), % 174.01/173.94 inference(rename_variables,[],[3631])). % 174.01/173.94 cnf(11033,plain, % 174.01/173.94 (~P1(f777(f777(f336(x110331),x110332),f182(f858(x110331,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11036,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x110361,a845)),x110362),f241(f858(x110361,a845))))), % 174.01/173.94 inference(rename_variables,[],[3563])). % 174.01/173.94 cnf(11040,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x110401,a845)),f777(f279(x110402,x110401,x110403),f182(f858(x110402,a845)))),x110404))), % 174.01/173.94 inference(scs_inference,[],[3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,4385,10279,10374,4379,3642,3028,4440,3087,3052,3035,4049,10995,3245,3120,3140,10316,3290,4475,3817,4401,10111,4465,3291,3084,10176,3964,3818,10821,10940,4483,10757,10947,4484,10861,4485,10953,4486,4487,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,4455,10088,10091,10117,10577,10592,10714,4471,3619,3395,3772,3214,3216,3189,4452,4395,3925,3828,10650,3876,3546,3914,3563,10827,10889,10974,4476,10595,10958,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,3188,10640,4451,10154,10242,10353,10383,10616,10664,10671,3342,10446,10709,10754,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,10906,3208,10658,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,4478,10079,10082,10334,3789,3627,10770,10776,3485,3631,10850,11004,11030,3456,10432,10435,10504,10685,4481,4482,10555,4069,3969,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401])). % 174.01/173.94 cnf(11041,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x110411,a845)),f182(f858(x110411,a845))),x110412))), % 174.01/173.94 inference(rename_variables,[],[3631])). % 174.01/173.94 cnf(11061,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x110611),f852(x110611))),f777(f777(f243(f852(x110611),f852(x110611)),x110612),f117(x110611))),f137(x110611,x110613)))), % 174.01/173.94 inference(rename_variables,[],[4483])). % 174.01/173.94 cnf(11064,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x110641),f852(x110641))),f777(f777(f243(f852(x110641),f852(x110641)),x110642),f117(x110641))),f139(x110641,x110643)))), % 174.01/173.94 inference(rename_variables,[],[4484])). % 174.01/173.94 cnf(11067,plain, % 174.01/173.94 (~E(f777(f777(f142(x110671),x110672),x110673),x110673)), % 174.01/173.94 inference(rename_variables,[],[4401])). % 174.01/173.94 cnf(11070,plain, % 174.01/173.94 (~E(f777(a116,x110701),x110701)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11073,plain, % 174.01/173.94 (~P1(f777(f777(f336(x110731),x110732),f182(f858(x110731,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11078,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(f852(x110781),f852(x110781))),f777(f777(f243(f852(x110781),f852(x110781)),x110782),x110782)),f149(x110781,f302(x110781,x110783))))), % 174.01/173.94 inference(rename_variables,[],[3958])). % 174.01/173.94 cnf(11081,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x110811),f852(x110811))),f777(f777(f243(f852(x110811),f852(x110811)),x110812),f117(x110811))),f137(x110811,x110813)))), % 174.01/173.94 inference(rename_variables,[],[4483])). % 174.01/173.94 cnf(11089,plain, % 174.01/173.94 (~P1(f777(f777(f336(x110891),x110892),f182(f858(x110891,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11092,plain, % 174.01/173.94 (~P1(f777(f777(f336(x110921),x110922),f182(f858(x110921,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11095,plain, % 174.01/173.94 (~P1(f777(f777(f336(x110951),x110952),f182(f858(x110951,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11098,plain, % 174.01/173.94 (P1(f777(f777(f336(x110981),x110982),f241(f858(x110981,a845))))), % 174.01/173.94 inference(rename_variables,[],[3342])). % 174.01/173.94 cnf(11109,plain, % 174.01/173.94 (~E(f777(f315(x111091,x111092),x111093),f777(f306(x111092,x111091),x111094))), % 174.01/173.94 inference(rename_variables,[],[4440])). % 174.01/173.94 cnf(11112,plain, % 174.01/173.94 (~E(f777(f315(x111121,x111122),x111123),f777(f306(x111122,x111121),x111124))), % 174.01/173.94 inference(rename_variables,[],[4440])). % 174.01/173.94 cnf(11117,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x111171),f852(x111171))),f777(f777(f243(f852(x111171),f852(x111171)),x111172),f117(x111171))),f137(x111171,x111173)))), % 174.01/173.94 inference(rename_variables,[],[4483])). % 174.01/173.94 cnf(11120,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x111201),f852(x111201))),f777(f777(f243(f852(x111201),f852(x111201)),x111202),f117(x111201))),f139(x111201,x111203)))), % 174.01/173.94 inference(rename_variables,[],[4484])). % 174.01/173.94 cnf(11123,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x111231),f852(x111231))),f777(f777(f243(f852(x111231),f852(x111231)),x111232),f117(x111231))),f137(x111231,x111233)))), % 174.01/173.94 inference(rename_variables,[],[4483])). % 174.01/173.94 cnf(11126,plain, % 174.01/173.94 (~P1(f777(f777(f336(x111261),x111262),f182(f858(x111261,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11129,plain, % 174.01/173.94 (~P1(f777(f777(f182(f858(x111291,f858(x111292,a845))),x111293),x111294))), % 174.01/173.94 inference(rename_variables,[],[4482])). % 174.01/173.94 cnf(11132,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x111321),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(11134,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(x111341,x111342)),f777(f777(f243(x111341,x111342),f777(x111343,x111344)),f777(x111345,x111344))),f777(f305(f857(x111346,x111346),f857(x111341,x111342),f254(x111346,x111341,x111346,x111342,x111343,x111345)),f302(x111346,x111347))))), % 174.01/173.94 inference(scs_inference,[],[3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,4385,10279,10374,4379,3642,3028,4440,10815,11109,3087,3052,3035,4049,10995,3245,3120,3140,10316,3290,4475,3817,4401,10111,10276,4465,3291,3084,10176,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,4484,10861,10950,11064,4485,10953,4486,11017,4487,3103,3384,3545,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,4455,10088,10091,10117,10577,10592,10714,4471,3619,3395,3772,3214,3216,3189,4452,4395,3958,11078,3925,3828,10650,3876,3546,3914,3563,10827,10889,10974,4476,10595,10958,3185,10207,10302,10426,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,3188,10640,10706,4451,10154,10242,10353,10383,10616,10664,10671,3342,10446,10709,10754,11025,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,3249,10471,3281,3703,3639,10157,4464,10108,10465,10468,10906,3208,10658,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,4478,10079,10082,10334,3789,3627,10770,10776,3485,3631,10850,11004,11030,3456,10432,10435,10504,10685,4481,4482,10555,10977,4069,3969,3662,4479,10130,10133,10459,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897])). % 174.01/173.94 cnf(11137,plain, % 174.01/173.94 (~P1(f777(f777(f336(x111371),x111372),f182(f858(x111371,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11140,plain, % 174.01/173.94 (~P1(f777(f777(f336(x111401),x111402),f182(f858(x111401,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11143,plain, % 174.01/173.94 (P1(f777(f777(f336(x111431),f777(x111432,x111433)),f777(f305(x111434,x111431,x111432),f241(f858(x111434,a845)))))), % 174.01/173.94 inference(rename_variables,[],[3789])). % 174.01/173.94 cnf(11150,plain, % 174.01/173.94 (E(f39(x111501,x111502,x111503,x111504,x111505,x111506,x111507,x111508,x111509,a27),x111502)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11153,plain, % 174.01/173.94 (~E(f777(a116,x111531),x111531)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11160,plain, % 174.01/173.94 (~E(f777(a116,x111601),x111601)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11165,plain, % 174.01/173.94 (E(f39(x111651,x111652,x111653,x111654,x111655,x111656,x111657,x111658,x111659,a27),x111652)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11166,plain, % 174.01/173.94 (E(f40(x111661,x111662,x111663,x111664,x111665,x111666,x111667,x111668,x111669,a27),x111662)), % 174.01/173.94 inference(rename_variables,[],[4342])). % 174.01/173.94 cnf(11169,plain, % 174.01/173.94 (E(f39(x111691,x111692,x111693,x111694,x111695,x111696,x111697,x111698,x111699,a27),x111692)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11176,plain, % 174.01/173.94 (~E(f777(a116,x111761),x111761)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11181,plain, % 174.01/173.94 (~E(f777(f777(f84(a3),x111811),x111811),a101)), % 174.01/173.94 inference(rename_variables,[],[4398])). % 174.01/173.94 cnf(11190,plain, % 174.01/173.94 (E(f777(f777(f5(a851),f4(a851)),x111901),f4(a851))), % 174.01/173.94 inference(rename_variables,[],[3106])). % 174.01/173.94 cnf(11193,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x111931),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(11198,plain, % 174.01/173.94 (E(f777(f777(f84(a3),f777(f777(f85(a3),x111981),f777(f777(f45(a3),x111982),x111981))),f54(a3,x111982,x111981)),x111982)), % 174.01/173.94 inference(rename_variables,[],[3735])). % 174.01/173.94 cnf(11210,plain, % 174.01/173.94 (E(f39(x112101,x112102,x112103,x112104,x112105,x112106,x112107,x112108,x112109,a27),x112102)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11213,plain, % 174.01/173.94 (E(f39(x112131,x112132,x112133,x112134,x112135,x112136,x112137,x112138,x112139,a27),x112132)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11216,plain, % 174.01/173.94 (E(f39(x112161,x112162,x112163,x112164,x112165,x112166,x112167,x112168,x112169,a27),x112162)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11219,plain, % 174.01/173.94 (E(f39(x112191,x112192,x112193,x112194,x112195,x112196,x112197,x112198,x112199,a27),x112192)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11224,plain, % 174.01/173.94 (~E(f777(a116,x112241),x112241)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11227,plain, % 174.01/173.94 (~E(f777(a116,x112271),x112271)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11231,plain, % 174.01/173.94 (E(f39(x112311,x112312,x112313,x112314,x112315,x112316,x112317,x112318,x112319,a27),x112312)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11254,plain, % 174.01/173.94 (P1(f777(f777(f336(x112541),x112542),f241(f858(x112541,a845))))), % 174.01/173.94 inference(rename_variables,[],[3342])). % 174.01/173.94 cnf(11262,plain, % 174.01/173.94 (E(f39(x112621,x112622,x112623,x112624,x112625,x112626,x112627,x112628,x112629,a27),x112622)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11267,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x112671),x112671))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(11274,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x112741),x112741))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(11275,plain, % 174.01/173.94 (E(f39(x112751,x112752,x112753,x112754,x112755,x112756,x112757,x112758,x112759,a27),x112752)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11288,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),f777(f777(f84(a851),x112881),x112882)),x112882))), % 174.01/173.94 inference(rename_variables,[],[4479])). % 174.01/173.94 cnf(11291,plain, % 174.01/173.94 (~P1(f777(f777(f235(a3),f777(f104(a3),x112911)),f4(a3)))), % 174.01/173.94 inference(rename_variables,[],[4471])). % 174.01/173.94 cnf(11302,plain, % 174.01/173.94 (E(f39(x113021,x113022,x113023,x113024,x113025,x113026,x113027,x113028,x113029,a27),x113022)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11305,plain, % 174.01/173.94 (E(f39(x113051,x113052,x113053,x113054,x113055,x113056,x113057,x113058,x113059,a27),x113052)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11316,plain, % 174.01/173.94 (E(f39(x113161,x113162,x113163,x113164,x113165,x113166,x113167,x113168,x113169,a27),x113162)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11321,plain, % 174.01/173.94 (E(f39(x113211,x113212,x113213,x113214,x113215,x113216,x113217,x113218,x113219,a27),x113212)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11324,plain, % 174.01/173.94 (~P1(f777(f777(f235(a3),f777(f104(a3),x113241)),f4(a3)))), % 174.01/173.94 inference(rename_variables,[],[4471])). % 174.01/173.94 cnf(11327,plain, % 174.01/173.94 (E(f39(x113271,x113272,x113273,x113274,x113275,x113276,x113277,x113278,x113279,a27),x113272)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11330,plain, % 174.01/173.94 (~E(f777(a116,x113301),x113301)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11336,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),f4(a3)),a87))), % 174.01/173.94 inference(scs_inference,[],[2804,3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,4342,11166,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,4385,10279,10374,4379,2810,2813,2822,2828,2832,2833,2835,2843,2850,2853,2855,2859,2861,2862,2874,2875,2885,2949,2960,2963,2977,4363,3642,3028,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,4049,10995,3245,3120,3140,10316,3290,4475,3817,4401,10111,10276,4465,3291,3083,3084,10176,10474,3005,3106,11190,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,11123,4484,10861,10950,11064,4485,10953,4486,11017,4487,3103,3384,3545,4398,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,4455,10088,10091,10117,10577,10592,10714,11132,11193,4471,11291,11324,3619,3395,3772,3214,3216,3189,4452,4395,3376,4472,3958,11078,3510,3925,3828,10650,3876,3546,3914,3563,10827,10889,10974,4476,10595,10958,3185,10207,10302,10426,10484,11267,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,3188,10640,10706,4451,10154,10242,10353,10383,10616,10664,10671,3342,10446,10709,10754,11025,11098,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,3249,10471,3286,3281,3703,3639,10157,4464,10108,10465,10468,10906,10922,3208,10658,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,4478,10079,10082,10334,3789,3627,10770,10776,3485,3631,10850,11004,11030,3456,10432,10435,10504,10685,4481,4482,10555,10977,4069,3969,3662,4479,10130,10133,10459,10462,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346])). % 174.01/173.94 cnf(11341,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x113411),x113411))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11364,plain, % 174.01/173.94 (~P1(f777(f777(f235(a3),f777(f104(a3),x113641)),f4(a3)))), % 174.01/173.94 inference(rename_variables,[],[4471])). % 174.01/173.94 cnf(11377,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x113771),x113771))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(11380,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x113801)),x113801))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(11381,plain, % 174.01/173.94 (~E(f777(a116,x113811),x113811)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11391,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),f777(f777(f84(a851),x113911),x113912)),x113911))), % 174.01/173.94 inference(rename_variables,[],[4480])). % 174.01/173.94 cnf(11394,plain, % 174.01/173.94 (~P1(f777(f777(f235(a3),f777(f104(a3),x113941)),f4(a3)))), % 174.01/173.94 inference(rename_variables,[],[4471])). % 174.01/173.94 cnf(11397,plain, % 174.01/173.94 (~E(f777(a116,x113971),x113971)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11410,plain, % 174.01/173.94 (P1(f777(f777(f336(x114101),x114102),f777(f777(f304(x114101),x114102),x114103)))), % 174.01/173.94 inference(rename_variables,[],[3500])). % 174.01/173.94 cnf(11411,plain, % 174.01/173.94 (~P1(f777(f777(f234(a3),f4(a3)),f777(f83(a3),f777(f104(a3),f777(a116,x114111)))))), % 174.01/173.94 inference(rename_variables,[],[4481])). % 174.01/173.94 cnf(11414,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),f777(f777(f5(a851),x114141),x114142)),f777(a116,x114141)))), % 174.01/173.94 inference(rename_variables,[],[3634])). % 174.01/173.94 cnf(11417,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f54(a851,x114171,x114172)),x114171))), % 174.01/173.94 inference(rename_variables,[],[3639])). % 174.01/173.94 cnf(11423,plain, % 174.01/173.94 (E(f777(f777(f127(x114231),x114232),f117(x114231)),x114232)), % 174.01/173.94 inference(rename_variables,[],[3121])). % 174.01/173.94 cnf(11426,plain, % 174.01/173.94 (E(f39(x114261,x114262,x114263,x114264,x114265,x114266,x114267,x114268,x114269,a27),x114262)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11429,plain, % 174.01/173.94 (E(f39(x114291,x114292,x114293,x114294,x114295,x114296,x114297,x114298,x114299,a27),x114292)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11433,plain, % 174.01/173.94 (E(f39(x114331,x114332,x114333,x114334,x114335,x114336,x114337,x114338,x114339,a27),x114332)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11436,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x114361)),x114361))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(11437,plain, % 174.01/173.94 (E(f39(x114371,x114372,x114373,x114374,x114375,x114376,x114377,x114378,x114379,a27),x114372)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11446,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x114461),x114461))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11447,plain, % 174.01/173.94 (E(f39(x114471,x114472,x114473,x114474,x114475,x114476,x114477,x114478,x114479,a27),x114472)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11450,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f54(a851,x114501,x114502)),x114501))), % 174.01/173.94 inference(rename_variables,[],[3639])). % 174.01/173.94 cnf(11451,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f4(a851)),x114511))), % 174.01/173.94 inference(rename_variables,[],[3208])). % 174.01/173.94 cnf(11468,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x114681),x114681))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11471,plain, % 174.01/173.94 (E(f39(x114711,x114712,x114713,x114714,x114715,x114716,x114717,x114718,x114719,a27),x114712)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11474,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x114741),x114741))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11477,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x114771),x114771))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11480,plain, % 174.01/173.94 (P1(f777(f777(f336(x114801),f777(x114802,x114803)),f777(f305(x114804,x114801,x114802),f241(f858(x114804,a845)))))), % 174.01/173.94 inference(rename_variables,[],[3789])). % 174.01/173.94 cnf(11481,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),f777(f777(f84(a851),x114811),x114812)),x114812))), % 174.01/173.94 inference(rename_variables,[],[4479])). % 174.01/173.94 cnf(11484,plain, % 174.01/173.94 (P1(f777(f777(f336(x114841),f777(x114842,x114843)),f777(f305(x114844,x114841,x114842),f241(f858(x114844,a845)))))), % 174.01/173.94 inference(rename_variables,[],[3789])). % 174.01/173.94 cnf(11485,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x114851)),x114851))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(11490,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),f777(f777(f84(a851),x114901),x114902)),x114901))), % 174.01/173.94 inference(rename_variables,[],[4480])). % 174.01/173.94 cnf(11493,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x114931),x114931))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11496,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x114961),x114961))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(11503,plain, % 174.01/173.94 (P1(f777(f777(f336(x115031),x115032),f241(f858(x115031,a845))))), % 174.01/173.94 inference(rename_variables,[],[3342])). % 174.01/173.94 cnf(11504,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x115041)),x115041))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(11507,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x115071),x115071))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(11520,plain, % 174.01/173.94 (~P1(f777(f777(f336(x115201),x115202),f182(f858(x115201,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11523,plain, % 174.01/173.94 (E(f777(f777(f20(x115231,x115232),x115233),x115234),x115233)), % 174.01/173.94 inference(rename_variables,[],[3177])). % 174.01/173.94 cnf(11526,plain, % 174.01/173.94 (E(f777(f777(f20(x115261,x115262),x115263),x115264),x115263)), % 174.01/173.94 inference(rename_variables,[],[3177])). % 174.01/173.94 cnf(11537,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f777(f777(f45(a851),x115371),x115372)),x115371))), % 174.01/173.94 inference(rename_variables,[],[3606])). % 174.01/173.94 cnf(11538,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),f4(a851)),f777(a116,x115381)))), % 174.01/173.94 inference(rename_variables,[],[3269])). % 174.01/173.94 cnf(11540,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),f777(f777(f45(a851),x115401),f39(x115402,f4(a851),x115403,x115404,x115405,x115406,x115407,x115408,x115409,a27))),f4(a851)))), % 174.01/173.94 inference(scs_inference,[],[2804,3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,4342,11166,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,4385,10279,10374,4379,2810,2813,2822,2828,2832,2833,2835,2843,2850,2853,2855,2857,2859,2861,2862,2874,2875,2885,2933,2944,2949,2960,2962,2963,2977,2979,4363,3121,11423,3642,3028,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,4049,10995,3245,3120,3140,10316,3290,4475,3817,4401,10111,10276,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,11123,4484,10861,10950,11064,4485,10953,4486,11017,4487,3103,3384,3545,4244,4245,4398,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,11414,3269,4455,10088,10091,10117,10577,10592,10714,11132,11193,4471,11291,11324,11364,3619,3395,3772,3214,3216,3189,4452,4395,3376,4472,3958,11078,3510,3925,3828,10650,3876,3546,3914,3563,10827,10889,10974,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,10698,3188,10640,10706,3263,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,3342,10446,10709,10754,11025,11098,11254,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,3249,10471,3286,3281,3703,3639,10157,11417,4464,10108,10465,10468,10906,10922,11380,11436,11485,3208,10658,10732,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,3789,11143,11480,3627,10770,10776,3485,3631,10850,11004,11030,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,4069,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941])). % 174.01/173.94 cnf(11541,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x115411),x115411))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(11542,plain, % 174.01/173.94 (E(f39(x115421,x115422,x115423,x115424,x115425,x115426,x115427,x115428,x115429,a27),x115422)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11545,plain, % 174.01/173.94 (P1(f777(f777(f336(x115451),f777(x115452,x115453)),f777(f305(x115454,x115451,x115452),f241(f858(x115454,a845)))))), % 174.01/173.94 inference(rename_variables,[],[3789])). % 174.01/173.94 cnf(11548,plain, % 174.01/173.94 (P1(f777(f65(x115481),f171(x115481,x115482,f168(x115481,x115482,x115483))))), % 174.01/173.94 inference(rename_variables,[],[3732])). % 174.01/173.94 cnf(11551,plain, % 174.01/173.94 (P1(f777(f65(x115511),f171(x115511,x115512,f168(x115511,x115512,x115513))))), % 174.01/173.94 inference(rename_variables,[],[3732])). % 174.01/173.94 cnf(11554,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),f777(f83(a3),f777(f104(a3),x115541))),f777(f104(a3),x115542)))), % 174.01/173.94 inference(rename_variables,[],[3663])). % 174.01/173.94 cnf(11557,plain, % 174.01/173.94 (~P1(f777(f777(f336(x115571),x115572),f182(f858(x115571,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11569,plain, % 174.01/173.94 (~P1(f777(f777(f336(a851),f4(a851)),f777(f298(a851),x115691)))), % 174.01/173.94 inference(scs_inference,[],[2804,3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,4342,11166,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,4385,10279,10374,4379,2810,2813,2822,2828,2832,2833,2835,2843,2850,2853,2855,2857,2859,2861,2862,2864,2874,2875,2885,2933,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,3642,3028,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,4049,10995,3245,3120,3140,10316,3290,4475,3817,4401,10111,10276,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,11123,4484,10861,10950,11064,4485,10953,4486,11017,4487,3103,3384,3545,4244,4245,4398,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,11414,3269,4455,10088,10091,10117,10577,10592,10714,11132,11193,4471,11291,11324,11364,3619,3395,3772,3214,3216,3189,4452,4395,3376,4472,3958,11078,3510,3732,11548,3925,3828,10650,3876,3546,3914,3563,10827,10889,10974,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,10698,3188,10640,10706,3263,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,3342,10446,10709,10754,11025,11098,11254,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,3249,10471,3286,3281,3703,3639,10157,11417,4464,10108,10465,10468,10906,10922,11380,11436,11485,3208,10658,10732,3663,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,3938,3789,11143,11480,11484,3627,10770,10776,3485,3631,10850,11004,11030,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,4069,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029])). % 174.01/173.94 cnf(11571,plain, % 174.01/173.94 (~P1(f777(f777(f336(a851),x115711),f777(f259(a851),f4(a851))))), % 174.01/173.94 inference(scs_inference,[],[2804,3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,4342,11166,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,4385,10279,10374,4379,2810,2813,2822,2828,2832,2833,2835,2843,2850,2853,2855,2857,2859,2861,2862,2864,2874,2875,2885,2933,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,3642,3028,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,4049,10995,3245,3120,3140,10316,3290,4475,3817,4401,10111,10276,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,11123,4484,10861,10950,11064,4485,10953,4486,11017,4487,3103,3384,3545,4244,4245,4398,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,3634,11414,3269,4455,10088,10091,10117,10577,10592,10714,11132,11193,4471,11291,11324,11364,3619,3395,3772,3214,3216,3189,4452,4395,3376,4472,3958,11078,3510,3732,11548,3925,3828,10650,3876,3546,3914,3563,10827,10889,10974,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,10698,3188,10640,10706,3263,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,3342,10446,10709,10754,11025,11098,11254,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,3249,10471,3286,3281,3703,3639,10157,11417,4464,10108,10465,10468,10906,10922,11380,11436,11485,3208,10658,10732,3663,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,3938,3789,11143,11480,11484,3627,10770,10776,3485,3631,10850,11004,11030,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,4069,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030])). % 174.01/173.94 cnf(11578,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x115781),x115781))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(11579,plain, % 174.01/173.94 (E(f39(x115791,x115792,x115793,x115794,x115795,x115796,x115797,x115798,x115799,a27),x115792)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(11582,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x115821),f777(a116,x115821)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(11585,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x115851),x115851))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(11596,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x115961),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(11599,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x115991),x115991))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(11604,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x116041),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(11613,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f4(a851)),x116131))), % 174.01/173.94 inference(rename_variables,[],[3208])). % 174.01/173.94 cnf(11614,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x116141)),x116141))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(11617,plain, % 174.01/173.94 (~P1(f777(f66(x116171,x116172,f182(f858(x116171,a845))),x116173))), % 174.01/173.94 inference(rename_variables,[],[4478])). % 174.01/173.94 cnf(11628,plain, % 174.01/173.94 (~P1(f777(f777(f281(a851),f777(a116,f777(f777(f84(a851),f777(a116,f4(a851))),x116281))),f777(a116,f4(a851))))), % 174.01/173.94 inference(scs_inference,[],[2804,3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,4342,11166,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,4385,10279,10374,4379,2810,2813,2822,2828,2832,2833,2835,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2874,2875,2885,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,3642,3028,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,4049,10995,3245,3120,3140,10316,3290,4475,3817,4401,10111,10276,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,11123,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,3545,4244,4245,4398,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,3634,11414,3269,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,4471,11291,11324,11364,3619,3395,3772,3214,3216,3189,4452,4395,3376,4472,3958,11078,3510,3732,11548,3925,3828,10650,3876,3546,3914,3563,10827,10889,10974,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,10698,11377,11585,3188,10640,10706,3263,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,3342,10446,10709,10754,11025,11098,11254,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,3208,10658,10732,11451,3663,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,3627,10770,10776,3485,3631,10850,11004,11030,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,4069,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291])). % 174.01/173.94 cnf(11630,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x116301),f777(a116,x116301)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(11640,plain, % 174.01/173.94 (P1(f777(f777(f235(a3),f777(f83(a3),f82(a3))),f4(a3)))), % 174.01/173.94 inference(scs_inference,[],[2804,3428,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,4342,11166,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,4385,10279,10374,4379,2810,2813,2822,2828,2832,2833,2835,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2874,2875,2885,2887,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,3642,3028,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,4049,10995,3245,3120,3140,10316,3290,4475,3817,4401,10111,10276,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,11123,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,3545,4244,4245,4398,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,3634,11414,3269,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,4471,11291,11324,11364,11394,3619,3395,3772,3214,3216,3189,4452,4395,3376,4472,3958,11078,3510,3732,11548,3925,3828,10650,3876,3546,3914,3563,10827,10889,10974,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,10698,11377,11585,3188,10640,10706,3263,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,3342,10446,10709,10754,11025,11098,11254,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,3208,10658,10732,11451,3663,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,3627,10770,10776,3485,3631,10850,11004,11030,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,4069,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346])). % 174.01/173.94 cnf(11645,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x116451),x116451))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11648,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x116481),x116481))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11651,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x116511),x116511))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11654,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x116541),x116541))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11657,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x116571)),x116571))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(11660,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x116601)),x116601))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(11663,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x116631)),x116631))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(11666,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x116661)),x116661))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(11684,plain, % 174.01/173.94 (E(f777(f183(f852(x116841)),f777(f143(x116841),x116842)),f777(f183(f852(x116841)),x116842))), % 174.01/173.94 inference(rename_variables,[],[3199])). % 174.01/173.94 cnf(11687,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x116871),x116871))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(11692,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x116921),f777(f79(a3),x116921)))), % 174.01/173.94 inference(scs_inference,[],[2804,3428,3488,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,4342,11166,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,4385,10279,10374,4379,2810,2813,2822,2828,2832,2833,2835,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2874,2875,2885,2887,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,3238,3642,3028,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,4049,10995,3199,3245,3120,3140,10316,3290,4475,3817,4401,10111,10276,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,11123,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,3545,4244,4245,4398,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,3634,11414,3269,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,4471,11291,11324,11364,11394,3619,3395,3772,3214,3216,3189,4452,4395,3376,4472,3958,11078,3510,3732,11548,3925,3828,10650,3876,3546,3914,3563,10827,10889,10974,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,3186,10544,10598,10601,10634,10661,10695,10739,3187,10292,10489,10572,10698,11377,11585,11599,3188,10640,10706,3263,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,3342,10446,10709,10754,11025,11098,11254,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,3208,10658,10732,11451,3663,4009,4462,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,3627,10770,10776,3485,3631,10850,11004,11030,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,4069,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452])). % 174.01/173.94 cnf(11693,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x116931),x116931))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(11704,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x117041),x117041))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(11707,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(f857(f852(x117071),f852(x117071)),a845)),f149(x117071,x117072)),f302(f852(x117071),f148(x117071,x117072))))), % 174.01/173.94 inference(rename_variables,[],[3881])). % 174.01/173.94 cnf(11714,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x117141),f777(a116,x117141)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(11717,plain, % 174.01/173.94 (P1(f777(f777(f336(f858(x117171,a845)),x117172),f777(f303(x117171),x117172)))), % 174.01/173.94 inference(rename_variables,[],[3546])). % 174.01/173.94 cnf(11718,plain, % 174.01/173.94 (~E(f777(a116,x117181),x117181)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11725,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x117251),x117251))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(11730,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x117301),x117301))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(11739,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x117391,a845)),x117392),f777(f777(f304(x117391),x117393),x117392)))), % 174.01/173.94 inference(rename_variables,[],[3627])). % 174.01/173.94 cnf(11742,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x117421),x117421))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(11743,plain, % 174.01/173.94 (~E(f777(a116,x117431),x117431)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11756,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x117561),x117561))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11757,plain, % 174.01/173.94 (~E(f777(a116,x117571),x117571)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11760,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x117601),x117601))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(11763,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x117631),x117631))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(11766,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x117661),x117661))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(11769,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x117691),x117691))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(11772,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x117721),x117721))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(11775,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x117751),x117751))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(11778,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x117781),x117781))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11781,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x117811),x117811))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11782,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x117821),f777(a116,x117821)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(11791,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x117911),x117911))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11792,plain, % 174.01/173.94 (~E(f777(a116,x117921),x117921)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11797,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x117971),x117971))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(11812,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x118121),x118121))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(11817,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f4(a851)),x118171))), % 174.01/173.94 inference(rename_variables,[],[3208])). % 174.01/173.94 cnf(11836,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x118361),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(11839,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x118391),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(11842,plain, % 174.01/173.94 (~P1(f777(f777(f336(x118421),x118422),f182(f858(x118421,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11845,plain, % 174.01/173.94 (~P1(f777(f777(f336(x118451),x118452),f182(f858(x118451,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11848,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x118481),x118481))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11851,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x118511),x118511))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11854,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x118541),x118541))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11856,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x118561),f777(f777(f106(a851),x118561),x118562)))), % 174.01/173.94 inference(scs_inference,[],[2804,3428,3488,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,4342,11166,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,4385,10279,10374,4379,2810,2813,2822,2828,2832,2833,2835,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2874,2875,2885,2887,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,3130,3238,3642,3951,3028,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,4049,10995,3199,3245,3120,3140,10316,3290,4475,3817,4401,10111,10276,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,11123,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,3545,4244,4245,4398,3491,3697,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,3634,11414,3269,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,4471,11291,11324,11364,11394,3619,3395,3772,3214,3216,3189,4452,4395,3376,4472,3958,11078,3510,3732,11548,11551,3925,3881,3828,10650,3876,3546,3914,3563,10827,10889,10974,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,3188,10640,10706,3263,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,3342,10446,10709,10754,11025,11098,11254,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,3663,4009,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,3627,10770,10776,10787,3485,3631,10850,11004,11030,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,4069,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957])). % 174.01/173.94 cnf(11857,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x118571),x118571))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11860,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x118601),f777(a116,x118601)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(11867,plain, % 174.01/173.94 (P1(f777(f777(f336(f858(x118671,a845)),x118672),f777(f303(x118671),x118672)))), % 174.01/173.94 inference(rename_variables,[],[3546])). % 174.01/173.94 cnf(11872,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x118721,a845)),f777(f160(x118721),f777(f128(x118721,x118722),x118723))),f777(f160(x118721),x118723)))), % 174.01/173.94 inference(rename_variables,[],[3828])). % 174.01/173.94 cnf(11879,plain, % 174.01/173.94 (~P1(f777(f777(f336(x118791),x118792),f182(f858(x118791,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11888,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x118881,a845)),x118882),f241(f858(x118881,a845))))), % 174.01/173.94 inference(rename_variables,[],[3563])). % 174.01/173.94 cnf(11889,plain, % 174.01/173.94 (~E(f777(a116,x118891),x118891)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(11892,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x118921,a845)),f777(f160(x118921),f777(f128(x118921,x118922),x118923))),f777(f160(x118921),x118923)))), % 174.01/173.94 inference(rename_variables,[],[3828])). % 174.01/173.94 cnf(11898,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x118981),f777(a116,x118981)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(11907,plain, % 174.01/173.94 (E(f777(f183(f852(x119071)),f777(f143(x119071),x119072)),f777(f183(f852(x119071)),x119072))), % 174.01/173.94 inference(rename_variables,[],[3199])). % 174.01/173.94 cnf(11910,plain, % 174.01/173.94 (P39(a27,x119101,x119102,x119101)), % 174.01/173.94 inference(rename_variables,[],[3404])). % 174.01/173.94 cnf(11923,plain, % 174.01/173.94 (P1(f777(f65(x119231),f182(f858(x119231,a845))))), % 174.01/173.94 inference(rename_variables,[],[3263])). % 174.01/173.94 cnf(11924,plain, % 174.01/173.94 (~P1(f777(f777(f336(x119241),x119242),f182(f858(x119241,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11927,plain, % 174.01/173.94 (P39(a27,x119271,x119272,x119271)), % 174.01/173.94 inference(rename_variables,[],[3404])). % 174.01/173.94 cnf(11932,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x119321),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(11933,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x119331),x119331))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(11940,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x119401,a845)),f777(f160(x119401),f153(x119401,x119402,x119403))),f777(f160(x119401),x119403)))), % 174.01/173.94 inference(rename_variables,[],[3876])). % 174.01/173.94 cnf(11945,plain, % 174.01/173.94 (P29(x119451,x119451,f9(x119451),x119452)), % 174.01/173.94 inference(rename_variables,[],[3428])). % 174.01/173.94 cnf(11950,plain, % 174.01/173.94 (P1(f777(f777(f336(f858(x119501,a845)),x119502),f777(f303(x119501),x119502)))), % 174.01/173.94 inference(rename_variables,[],[3546])). % 174.01/173.94 cnf(11957,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x119571),x119571))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(11960,plain, % 174.01/173.94 (~P1(f777(f777(f336(x119601),x119602),f182(f858(x119601,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(11963,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x119631,a845)),x119632),f777(f777(f304(x119631),x119633),x119632)))), % 174.01/173.94 inference(rename_variables,[],[3627])). % 174.01/173.94 cnf(11964,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x119641,a845)),x119642),f241(f858(x119641,a845))))), % 174.01/173.94 inference(rename_variables,[],[3563])). % 174.01/173.94 cnf(11971,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x119711),f777(a116,x119711)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(11974,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x119741),f777(a116,x119741)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(11977,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x119771),x119771))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(11980,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x119801),x119801))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(11983,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x119831),x119831))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(11986,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x119861),x119861))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(11989,plain, % 174.01/173.94 (P1(f777(f777(f281(a851),x119891),x119891))), % 174.01/173.94 inference(rename_variables,[],[3188])). % 174.01/173.94 cnf(11992,plain, % 174.01/173.94 (P1(f777(f777(f281(a851),x119921),x119921))), % 174.01/173.94 inference(rename_variables,[],[3188])). % 174.01/173.94 cnf(11996,plain, % 174.01/173.94 (~P1(f777(f777(f234(a3),f777(f777(f5(a3),a87),a101)),f4(a3)))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,3428,10879,3488,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,4342,11166,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,4385,10279,10374,4379,2810,2813,2822,2828,2832,2833,2834,2835,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2874,2875,2885,2887,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,3130,3238,3642,3951,3028,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,3041,3042,4049,10995,3199,11684,3245,3120,3140,10316,3290,4475,3817,4401,10111,10276,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,11123,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,3545,4244,4245,4398,3491,3697,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,4471,11291,11324,11364,11394,3619,3395,3772,3214,3216,3189,4452,4395,3376,4472,3958,11078,3510,3732,11548,11551,3227,3925,3881,3828,10650,11872,3876,10824,3546,11717,11867,3914,3563,10827,10889,10974,11036,11888,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,3188,10640,10706,11989,3263,11923,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,3342,10446,10709,10754,11025,11098,11254,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,3663,4009,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,3627,10770,10776,10787,11739,3485,3631,10850,11004,11030,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,4069,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592])). % 174.01/173.94 cnf(11999,plain, % 174.01/173.94 (P1(f777(f777(f336(f858(x119991,a845)),x119992),f777(f303(x119991),x119992)))), % 174.01/173.94 inference(rename_variables,[],[3546])). % 174.01/173.94 cnf(12003,plain, % 174.01/173.94 (~P1(f777(f777(f235(a3),f777(f777(f84(a3),a87),a87)),f4(a3)))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,3428,10879,3488,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,4342,11166,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,4385,10279,10374,4379,2810,2813,2822,2828,2832,2833,2834,2835,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2874,2875,2885,2887,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,3130,3238,3642,3951,3028,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,3041,3042,4049,10995,3199,11684,3245,3120,3140,10316,3290,4475,3817,4401,10111,10276,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,11123,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,3545,4244,4245,4398,3491,3697,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,4471,11291,11324,11364,11394,3619,3395,3772,3214,3216,3189,4452,4395,3376,4472,3958,11078,3510,3732,11548,11551,3227,3925,3881,3828,10650,11872,3876,10824,3546,11717,11867,11950,3914,3563,10827,10889,10974,11036,11888,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,3188,10640,10706,11989,3263,11923,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,3342,10446,10709,10754,11025,11098,11254,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,3663,4009,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,3627,10770,10776,10787,11739,3485,3631,10850,11004,11030,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,4069,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628])). % 174.01/173.94 cnf(12008,plain, % 174.01/173.94 (~E(f777(a116,x120081),x120081)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(12009,plain, % 174.01/173.94 (E(f777(f305(x120091,x120091,f9(x120091)),x120092),x120092)), % 174.01/173.94 inference(rename_variables,[],[3245])). % 174.01/173.94 cnf(12012,plain, % 174.01/173.94 (P34(x120121,x120122,f117(x120121),f117(x120121))), % 174.01/173.94 inference(rename_variables,[],[3436])). % 174.01/173.94 cnf(12015,plain, % 174.01/173.94 (~E(f777(a116,x120151),x120151)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(12018,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x120181,a845)),f777(f160(x120181),f153(x120181,x120182,x120183))),f777(f160(x120181),x120183)))), % 174.01/173.94 inference(rename_variables,[],[3876])). % 174.01/173.94 cnf(12019,plain, % 174.01/173.94 (P1(f777(f65(x120191),f777(f160(x120191),x120192)))), % 174.01/173.94 inference(rename_variables,[],[3227])). % 174.01/173.94 cnf(12030,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x120301),x120301))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(12033,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x120331),x120331))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(12042,plain, % 174.01/173.94 (E(f777(f183(f852(x120421)),f777(f143(x120421),x120422)),f777(f183(f852(x120421)),x120422))), % 174.01/173.94 inference(rename_variables,[],[3199])). % 174.01/173.94 cnf(12045,plain, % 174.01/173.94 (P18(a851,f777(f144(a851),f777(f777(f145(f852(x120451),a851),f183(f852(x120451))),f166(x120451,x120452))))), % 174.01/173.94 inference(rename_variables,[],[3745])). % 174.01/173.94 cnf(12048,plain, % 174.01/173.94 (P29(x120481,x120481,f9(x120481),x120482)), % 174.01/173.94 inference(rename_variables,[],[3428])). % 174.01/173.94 cnf(12051,plain, % 174.01/173.94 (P1(f777(f777(f336(f852(x120511)),f117(x120511)),f151(x120511,x120512)))), % 174.01/173.94 inference(rename_variables,[],[3384])). % 174.01/173.94 cnf(12054,plain, % 174.01/173.94 (~P1(f777(f777(f182(f858(x120541,f858(x120542,a845))),x120543),x120544))), % 174.01/173.94 inference(rename_variables,[],[4482])). % 174.01/173.94 cnf(12059,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x120591),x120591))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12060,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f4(a851)),x120601))), % 174.01/173.94 inference(rename_variables,[],[3208])). % 174.01/173.94 cnf(12062,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),f4(a3)),f796(x120621,f182(f858(x120622,f858(x120623,a845))),f82(a3))))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,3428,10879,11945,3436,3488,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,4342,11166,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,4385,10279,10374,4379,2810,2813,2822,2828,2832,2833,2834,2835,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2874,2875,2885,2887,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,3130,3238,3642,3951,3028,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,3041,3042,4049,10995,3066,3199,11684,11907,3245,10653,3120,3140,10316,3290,4475,3817,4401,10111,10276,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,11123,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,3545,4244,4245,4398,3491,3697,3745,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,4471,11291,11324,11364,11394,3619,3395,3772,3214,3216,3189,4452,4395,3376,4472,3958,11078,3510,3732,11548,11551,3227,3925,3881,3828,10650,11872,3876,10824,11940,3546,11717,11867,11950,11999,3914,3563,10827,10889,10974,11036,11888,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,3188,10640,10706,11989,3263,11923,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,3342,10446,10709,10754,11025,11098,11254,11503,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,11817,3663,4009,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,3627,10770,10776,10787,11739,3485,3631,10850,11004,11030,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,11129,12054,4069,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907])). % 174.01/173.94 cnf(12063,plain, % 174.01/173.94 (~P1(f777(f777(f182(f858(x120631,f858(x120632,a845))),x120633),x120634))), % 174.01/173.94 inference(rename_variables,[],[4482])). % 174.01/173.94 cnf(12066,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(f857(f852(x120661),f852(x120661)),a845)),f149(x120661,x120662)),f302(f852(x120661),f148(x120661,x120662))))), % 174.01/173.94 inference(rename_variables,[],[3881])). % 174.01/173.94 cnf(12071,plain, % 174.01/173.94 (P1(f777(f777(f235(f858(x120711,a845)),f182(f858(x120711,a845))),f241(f858(x120711,a845))))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,3428,10879,11945,3436,3488,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,4342,11166,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,4385,10279,10374,4379,2810,2813,2822,2828,2832,2833,2834,2835,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2874,2875,2885,2887,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,3130,3238,3642,3951,3028,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,3041,3042,4049,10995,3066,3199,11684,11907,3245,10653,3120,3140,10316,3290,4475,3817,4401,10111,10276,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,11123,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,3545,4244,4245,4398,3491,3697,3745,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,4471,11291,11324,11364,11394,3619,3395,3772,3214,3216,3189,4452,4395,3376,4472,3958,11078,3510,3732,11548,11551,3227,3925,3881,11707,12066,3828,10650,11872,3876,10824,11940,3546,11717,11867,11950,11999,3914,3563,10827,10889,10974,11036,11888,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,3188,10640,10706,11989,3263,11923,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,3342,10446,10709,10754,11025,11098,11254,11503,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,11817,3663,4009,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,3627,10770,10776,10787,11739,3485,3631,10850,11004,11030,11041,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,11129,12054,4069,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992])). % 174.01/173.94 cnf(12072,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x120721,a845)),f182(f858(x120721,a845))),x120722))), % 174.01/173.94 inference(rename_variables,[],[3631])). % 174.01/173.94 cnf(12075,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x120751,a845)),f777(f305(x120752,x120751,x120753),f777(f307(x120752,x120751,x120753),x120754))),x120754))), % 174.01/173.94 inference(rename_variables,[],[4069])). % 174.01/173.94 cnf(12078,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x120781,a845)),f777(f160(x120781),f153(x120781,x120782,x120783))),f777(f160(x120781),x120783)))), % 174.01/173.94 inference(rename_variables,[],[3876])). % 174.01/173.94 cnf(12079,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x120791,a845)),f777(f160(x120791),f777(f128(x120791,x120792),x120793))),f777(f160(x120791),x120793)))), % 174.01/173.94 inference(rename_variables,[],[3828])). % 174.01/173.94 cnf(12084,plain, % 174.01/173.94 (P29(x120841,f855(x120841),f229(x120841),x120842)), % 174.01/173.94 inference(rename_variables,[],[3437])). % 174.01/173.94 cnf(12089,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x120891,a845)),f777(f305(x120892,x120891,x120893),f777(f307(x120892,x120891,x120893),x120894))),x120894))), % 174.01/173.94 inference(rename_variables,[],[4069])). % 174.01/173.94 cnf(12092,plain, % 174.01/173.94 (P1(f777(f65(f855(x120921)),f777(f305(x120922,f855(x120921),f168(x120922,x120921,x120923)),f241(f858(x120922,a845)))))), % 174.01/173.94 inference(rename_variables,[],[3938])). % 174.01/173.94 cnf(12097,plain, % 174.01/173.94 (P1(f777(f777(f336(f858(x120971,a845)),x120972),f777(f303(x120971),x120972)))), % 174.01/173.94 inference(rename_variables,[],[3546])). % 174.01/173.94 cnf(12100,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x121001),f852(x121001))),f777(f777(f243(f852(x121001),f852(x121001)),x121002),f117(x121001))),f137(x121001,x121003)))), % 174.01/173.94 inference(rename_variables,[],[4483])). % 174.01/173.94 cnf(12103,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x121031),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(12105,plain, % 174.01/173.94 (~P1(f777(f65(x121051),f241(f858(x121051,a845))))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,3428,10879,11945,3436,3437,3488,3157,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,4342,11166,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,4385,10279,10374,4379,2810,2813,2822,2828,2832,2833,2834,2835,2837,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2874,2875,2885,2887,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,3130,3238,3642,3951,3028,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,3041,3042,4049,10995,3066,3199,11684,11907,3245,10653,3120,3140,10316,3290,4475,3817,4401,10111,10276,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,3818,10821,10940,11007,4483,10757,10947,11061,11081,11117,11123,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,12051,3545,4244,4245,4398,3491,3697,3745,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,4471,11291,11324,11364,11394,3619,3395,3772,3214,3216,3189,4452,4395,3376,4472,3958,11078,3510,3732,11548,11551,3227,3925,3881,11707,12066,3828,10650,11872,11892,3876,10824,11940,12018,3546,11717,11867,11950,11999,3914,3563,10827,10889,10974,11036,11888,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,3188,10640,10706,11989,3263,11923,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,3342,10446,10709,10754,11025,11098,11254,11503,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,11817,3663,4009,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,3627,10770,10776,10787,11739,3485,10992,3631,10850,11004,11030,11041,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,11129,12054,4069,10643,12075,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992,7993,7994,8014,8015,8049,8053,8057,8066,8080,8107,8111,8117])). % 174.01/173.94 cnf(12106,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x121061,a845)),x121062),x121062))), % 174.01/173.94 inference(rename_variables,[],[3485])). % 174.01/173.94 cnf(12109,plain, % 174.01/173.94 (~P1(f777(f777(f336(x121091),x121092),f182(f858(x121091,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12112,plain, % 174.01/173.94 (~P1(f777(f777(f182(f858(x121121,f858(x121122,a845))),x121123),x121124))), % 174.01/173.94 inference(rename_variables,[],[4482])). % 174.01/173.94 cnf(12115,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x121151,a845)),f777(f305(x121152,x121151,x121153),f777(f307(x121152,x121151,x121153),x121154))),x121154))), % 174.01/173.94 inference(rename_variables,[],[4069])). % 174.01/173.94 cnf(12116,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x121161,a845)),x121162),x121162))), % 174.01/173.94 inference(rename_variables,[],[3485])). % 174.01/173.94 cnf(12121,plain, % 174.01/173.94 (E(f39(x121211,x121212,x121213,x121214,x121215,x121216,x121217,x121218,x121219,a27),x121212)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(12124,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x121241,a845)),f777(f160(x121241),f153(x121241,x121242,x121243))),f777(f160(x121241),x121243)))), % 174.01/173.94 inference(rename_variables,[],[3876])). % 174.01/173.94 cnf(12125,plain, % 174.01/173.94 (P1(f777(f65(x121251),f777(f160(x121251),x121252)))), % 174.01/173.94 inference(rename_variables,[],[3227])). % 174.01/173.94 cnf(12128,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x121281),x121281))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(12131,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x121311),x121311))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(12134,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x121341),x121341))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(12145,plain, % 174.01/173.94 (P29(x121451,x121451,f9(x121451),x121452)), % 174.01/173.94 inference(rename_variables,[],[3428])). % 174.01/173.94 cnf(12152,plain, % 174.01/173.94 (~P1(f777(f777(f336(x121521),x121522),f182(f858(x121521,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12155,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(x121551,x121551)),f777(f777(f243(x121551,x121551),x121552),x121552)),f302(x121551,x121553)))), % 174.01/173.94 inference(rename_variables,[],[3818])). % 174.01/173.94 cnf(12158,plain, % 174.01/173.94 (~P1(f777(f777(f336(x121581),x121582),f182(f858(x121581,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12161,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(x121611,x121611)),f777(f777(f243(x121611,x121611),x121612),x121612)),f302(x121611,x121613)))), % 174.01/173.94 inference(rename_variables,[],[3818])). % 174.01/173.94 cnf(12171,plain, % 174.01/173.94 (~E(f777(f777(f142(x121711),x121712),x121713),x121713)), % 174.01/173.94 inference(rename_variables,[],[4401])). % 174.01/173.94 cnf(12174,plain, % 174.01/173.94 (P1(f777(f777(f336(x121741),x121742),f241(f858(x121741,a845))))), % 174.01/173.94 inference(rename_variables,[],[3342])). % 174.01/173.94 cnf(12175,plain, % 174.01/173.94 (~E(f777(a116,x121751),x121751)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(12178,plain, % 174.01/173.94 (P1(f777(f777(f336(f852(x121781)),f117(x121781)),f151(x121781,x121782)))), % 174.01/173.94 inference(rename_variables,[],[3384])). % 174.01/173.94 cnf(12179,plain, % 174.01/173.94 (~E(f777(f777(f142(x121791),x121792),x121793),f117(x121791))), % 174.01/173.94 inference(rename_variables,[],[4410])). % 174.01/173.94 cnf(12182,plain, % 174.01/173.94 (P1(f777(f777(f336(x121821),f777(x121822,x121823)),f777(f305(x121824,x121821,x121822),f241(f858(x121824,a845)))))), % 174.01/173.94 inference(rename_variables,[],[3789])). % 174.01/173.94 cnf(12183,plain, % 174.01/173.94 (P29(x121831,x121831,f9(x121831),x121832)), % 174.01/173.94 inference(rename_variables,[],[3428])). % 174.01/173.94 cnf(12186,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x121861,a845)),f182(f858(x121861,a845))),x121862))), % 174.01/173.94 inference(rename_variables,[],[3631])). % 174.01/173.94 cnf(12187,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x121871,a845)),x121872),x121872))), % 174.01/173.94 inference(rename_variables,[],[3485])). % 174.01/173.94 cnf(12190,plain, % 174.01/173.94 (P1(f777(f777(f336(x121901),f777(x121902,x121903)),f777(f305(x121904,x121901,x121902),f241(f858(x121904,a845)))))), % 174.01/173.94 inference(rename_variables,[],[3789])). % 174.01/173.94 cnf(12191,plain, % 174.01/173.94 (P29(x121911,x121911,f9(x121911),x121912)), % 174.01/173.94 inference(rename_variables,[],[3428])). % 174.01/173.94 cnf(12194,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(f852(x121941),f852(x121941))),f777(f777(f243(f852(x121941),f852(x121941)),f117(x121941)),f117(x121941))),f149(x121941,x121942)))), % 174.01/173.94 inference(rename_variables,[],[3964])). % 174.01/173.94 cnf(12200,plain, % 174.01/173.94 (P29(x122001,x122001,f9(x122001),x122002)), % 174.01/173.94 inference(rename_variables,[],[3428])). % 174.01/173.94 cnf(12203,plain, % 174.01/173.94 (E(f777(f777(f127(x122031),x122032),f117(x122031)),x122032)), % 174.01/173.94 inference(rename_variables,[],[3121])). % 174.01/173.94 cnf(12204,plain, % 174.01/173.94 (~E(f777(f777(f142(x122041),x122042),x122043),x122043)), % 174.01/173.94 inference(rename_variables,[],[4401])). % 174.01/173.94 cnf(12207,plain, % 174.01/173.94 (E(f777(f777(f127(x122071),x122072),f117(x122071)),x122072)), % 174.01/173.94 inference(rename_variables,[],[3121])). % 174.01/173.94 cnf(12208,plain, % 174.01/173.94 (~E(f777(f777(f142(x122081),x122082),x122083),x122083)), % 174.01/173.94 inference(rename_variables,[],[4401])). % 174.01/173.94 cnf(12211,plain, % 174.01/173.94 (E(f777(f777(f127(x122111),x122112),f117(x122111)),x122112)), % 174.01/173.94 inference(rename_variables,[],[3121])). % 174.01/173.94 cnf(12220,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x122201,a845)),x122202),f241(f858(x122201,a845))))), % 174.01/173.94 inference(rename_variables,[],[3563])). % 174.01/173.94 cnf(12224,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x122241),x122241))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(12225,plain, % 174.01/173.94 (~E(f777(a116,x122251),x122251)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(12228,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x122281,a845)),f182(f858(x122281,a845))),x122282))), % 174.01/173.94 inference(rename_variables,[],[3631])). % 174.01/173.94 cnf(12231,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x122311),x122311))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12234,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x122341,a845)),x122342),x122342))), % 174.01/173.94 inference(rename_variables,[],[3485])). % 174.01/173.94 cnf(12239,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x122391,a845)),x122392),f777(f777(f304(x122391),x122393),x122392)))), % 174.01/173.94 inference(rename_variables,[],[3627])). % 174.01/173.94 cnf(12242,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x122421,a845)),x122422),x122422))), % 174.01/173.94 inference(rename_variables,[],[3485])). % 174.01/173.94 cnf(12243,plain, % 174.01/173.94 (~P1(f777(f777(f336(x122431),x122432),f182(f858(x122431,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12246,plain, % 174.01/173.94 (~P1(f777(f777(f336(x122461),x122462),f182(f858(x122461,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12252,plain, % 174.01/173.94 (~P1(f777(f777(f234(f858(f857(x122521,x122521),a845)),f777(f305(f857(x122521,x122521),f857(x122521,x122521),f9(f857(x122521,x122521))),f241(f858(f857(x122521,x122521),a845)))),f777(f305(f857(x122521,x122521),f857(x122521,x122521),f9(f857(x122521,x122521))),f777(a116,f241(f858(f857(x122521,x122521),a845))))))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,3428,10879,11945,12048,12145,12183,12191,12200,3436,3437,3488,3157,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,4342,11166,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,4385,10279,10374,3242,4379,2810,2813,2822,2828,2832,2833,2834,2835,2837,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2874,2875,2885,2887,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,12203,12207,3130,3238,3642,3951,3028,4381,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,3041,3042,4049,10995,3066,3199,11684,11907,3245,10653,12009,3119,3120,3140,10316,3290,4475,3817,4401,10111,10276,11067,12171,12204,4410,12179,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,12194,3818,10821,10940,11007,12155,12161,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,4398,11181,3491,3697,3745,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,4471,11291,11324,11364,11394,3619,3395,3772,3214,3216,3189,4452,4395,3572,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,3925,3881,11707,12066,3828,10650,11872,11892,3876,10824,11940,12018,12078,12124,3546,11717,11867,11950,11999,3914,3563,10827,10889,10974,11036,11888,11964,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,3188,10640,10706,11989,3263,11923,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,3342,10446,10709,10754,11025,11098,11254,11503,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,11817,3663,4009,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,11545,12182,3627,10770,10776,10787,11739,11963,3485,10992,12106,12116,12187,12234,3631,10850,11004,11030,11041,12072,12186,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,11129,12054,12063,4069,10643,12075,12089,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,88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% 174.01/173.94 cnf(12253,plain, % 174.01/173.94 (P29(x122531,x122531,f9(x122531),x122532)), % 174.01/173.94 inference(rename_variables,[],[3428])). % 174.01/173.94 cnf(12256,plain, % 174.01/173.94 (~P1(f777(f777(f336(x122561),x122562),f182(f858(x122561,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12259,plain, % 174.01/173.94 (P1(f777(f777(f336(x122591),f777(x122592,x122593)),f777(f305(x122594,x122591,x122592),f241(f858(x122594,a845)))))), % 174.01/173.94 inference(rename_variables,[],[3789])). % 174.01/173.94 cnf(12260,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(x122601,x122601)),f777(f777(f243(x122601,x122601),x122602),x122602)),f302(x122601,x122603)))), % 174.01/173.94 inference(rename_variables,[],[3818])). % 174.01/173.94 cnf(12263,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(x122631,x122631)),f777(f777(f243(x122631,x122631),x122632),x122632)),f302(x122631,x122633)))), % 174.01/173.94 inference(rename_variables,[],[3818])). % 174.01/173.94 cnf(12266,plain, % 174.01/173.94 (P1(f777(f65(x122661),f777(f160(x122661),x122662)))), % 174.01/173.94 inference(rename_variables,[],[3227])). % 174.01/173.94 cnf(12271,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(f852(x122711),f852(x122711))),f777(f777(f243(f852(x122711),f852(x122711)),f117(x122711)),f117(x122711))),f777(f777(f283(f852(x122711),f852(x122711),f852(x122711)),f149(x122711,x122712)),f149(x122711,x122712))))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,3428,10879,11945,12048,12145,12183,12191,12200,3436,3437,3488,3157,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,4342,11166,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,4385,10279,10374,3242,4379,2810,2813,2822,2828,2832,2833,2834,2835,2837,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2874,2875,2885,2887,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,12203,12207,12211,3130,3238,3642,3951,3028,4381,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,3041,3042,4049,10995,3066,3199,11684,11907,3245,10653,12009,3119,3120,3140,10316,3290,4475,3817,4401,10111,10276,11067,12171,12204,4410,12179,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,12194,3818,10821,10940,11007,12155,12161,12260,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,4398,11181,3491,3697,3745,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,4471,11291,11324,11364,11394,3619,3395,3772,3214,3216,3189,4452,4395,3572,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,3925,3881,11707,12066,3828,10650,11872,11892,3876,10824,11940,12018,12078,12124,3546,11717,11867,11950,11999,3914,3563,10827,10889,10974,11036,11888,11964,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,3188,10640,10706,11989,3263,11923,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,3342,10446,10709,10754,11025,11098,11254,11503,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,11817,3663,4009,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,11545,12182,12190,3627,10770,10776,10787,11739,11963,3485,10992,12106,12116,12187,12234,3631,10850,11004,11030,11041,12072,12186,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,11129,12054,12063,4069,10643,12075,12089,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992,7993,7994,8014,8015,8049,8053,8057,8066,8080,8107,8111,8117,8130,8149,8155,8177,8217,8247,8259,8276,8279,8308,8335,8399,8400,8403,8404,8421,8511,8512,8513,8514,8537,8561,8583,8625,8643,8696,8737,8740,8753,8790,8808,8824,8825,8840,8841,8969,8974,8992,9008,9028,9030,9033,9036,9039,9040,9052,9053,9076,9149,9184,9185,9250,9256,9290])). % 174.01/173.94 cnf(12273,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(x122731,x122731)),f777(f777(f243(x122731,x122731),x122732),x122732)),f777(f777(f283(x122731,x122731,x122731),f302(x122731,x122733)),f302(x122731,f302(x122731,x122733)))))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,3428,10879,11945,12048,12145,12183,12191,12200,3436,3437,3488,3157,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,4342,11166,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,4385,10279,10374,3242,4379,2810,2813,2822,2828,2832,2833,2834,2835,2837,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2874,2875,2885,2887,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3121,11423,12203,12207,12211,3130,3238,3642,3951,3028,4381,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,3041,3042,4049,10995,3066,3199,11684,11907,3245,10653,12009,3119,3120,3140,10316,3290,4475,3817,4401,10111,10276,11067,12171,12204,4410,12179,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,12194,3818,10821,10940,11007,12155,12161,12260,12263,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,4398,11181,3491,3697,3745,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,4471,11291,11324,11364,11394,3619,3395,3772,3214,3216,3189,4452,4395,3572,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,3925,3881,11707,12066,3828,10650,11872,11892,3876,10824,11940,12018,12078,12124,3546,11717,11867,11950,11999,3914,3563,10827,10889,10974,11036,11888,11964,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,3188,10640,10706,11989,3263,11923,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,3342,10446,10709,10754,11025,11098,11254,11503,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,11817,3663,4009,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,11545,12182,12190,3627,10770,10776,10787,11739,11963,3485,10992,12106,12116,12187,12234,3631,10850,11004,11030,11041,12072,12186,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,11129,12054,12063,4069,10643,12075,12089,3969,3662,3606,4479,10130,10133,10459,10462,11288,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992,7993,7994,8014,8015,8049,8053,8057,8066,8080,8107,8111,8117,8130,8149,8155,8177,8217,8247,8259,8276,8279,8308,8335,8399,8400,8403,8404,8421,8511,8512,8513,8514,8537,8561,8583,8625,8643,8696,8737,8740,8753,8790,8808,8824,8825,8840,8841,8969,8974,8992,9008,9028,9030,9033,9036,9039,9040,9052,9053,9076,9149,9184,9185,9250,9256,9290,9301])). % 174.01/173.94 cnf(12276,plain, % 174.01/173.94 (~P1(f777(f777(f182(f858(x122761,f858(x122762,a845))),x122763),x122764))), % 174.01/173.94 inference(rename_variables,[],[4482])). % 174.01/173.94 cnf(12279,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x122791,a845)),x122792),f241(f858(x122791,a845))))), % 174.01/173.94 inference(rename_variables,[],[3563])). % 174.01/173.94 cnf(12282,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(x122821,x122821)),f777(f777(f243(x122821,x122821),x122822),x122822)),f302(x122821,x122823)))), % 174.01/173.94 inference(rename_variables,[],[3818])). % 174.01/173.94 cnf(12285,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),f777(f777(f84(a851),x122851),x122852)),x122852))), % 174.01/173.94 inference(rename_variables,[],[4479])). % 174.01/173.94 cnf(12286,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x122861),f777(a116,x122861)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(12289,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x122891,a845)),x122892),f241(f858(x122891,a845))))), % 174.01/173.94 inference(rename_variables,[],[3563])). % 174.01/173.94 cnf(12292,plain, % 174.01/173.94 (E(f39(x122921,x122922,x122923,x122924,x122925,x122926,x122927,x122928,x122929,a27),x122922)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(12303,plain, % 174.01/173.94 (~P1(f777(f777(f336(x123031),x123032),f182(f858(x123031,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12304,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(f852(x123041),f852(x123041))),f777(f777(f243(f852(x123041),f852(x123041)),f117(x123041)),f117(x123041))),f149(x123041,x123042)))), % 174.01/173.94 inference(rename_variables,[],[3964])). % 174.01/173.94 cnf(12306,plain, % 174.01/173.94 (P1(f777(f777(f336(f857(a851,a851)),f777(f777(f243(a851,a851),f4(a851)),f777(a116,f4(a851)))),f777(f777(f283(a851,a851,a851),f302(a851,a325)),f302(a851,f302(a851,a325)))))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,3428,10879,11945,12048,12145,12183,12191,12200,3436,3437,3488,3157,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,12121,4342,11166,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,4385,10279,10374,3242,4379,2810,2813,2822,2828,2832,2833,2834,2835,2837,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2874,2875,2885,2887,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3522,3121,11423,12203,12207,12211,3130,3238,3642,3951,3028,4381,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,3041,3042,4049,10995,3066,3199,11684,11907,3245,10653,12009,3119,3120,3140,10316,3290,4475,3817,4401,10111,10276,11067,12171,12204,4410,12179,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,12194,3818,10821,10940,11007,12155,12161,12260,12263,12282,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,4398,11181,3491,3697,3745,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,4471,11291,11324,11364,11394,3619,3395,3772,3214,3216,3189,4452,4395,3572,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,3925,3881,11707,12066,3828,10650,11872,11892,3876,10824,11940,12018,12078,12124,3546,11717,11867,11950,11999,3914,3563,10827,10889,10974,11036,11888,11964,12220,12279,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,3188,10640,10706,11989,3263,11923,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,3342,10446,10709,10754,11025,11098,11254,11503,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,12256,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,11817,3663,4009,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,11545,12182,12190,3627,10770,10776,10787,11739,11963,3485,10992,12106,12116,12187,12234,3962,3631,10850,11004,11030,11041,12072,12186,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,11129,12054,12063,12112,4069,10643,12075,12089,3969,3662,3606,4479,10130,10133,10459,10462,11288,11481,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992,7993,7994,8014,8015,8049,8053,8057,8066,8080,8107,8111,8117,8130,8149,8155,8177,8217,8247,8259,8276,8279,8308,8335,8399,8400,8403,8404,8421,8511,8512,8513,8514,8537,8561,8583,8625,8643,8696,8737,8740,8753,8790,8808,8824,8825,8840,8841,8969,8974,8992,9008,9028,9030,9033,9036,9039,9040,9052,9053,9076,9149,9184,9185,9250,9256,9290,9301,9305,9309,9310,9324,9348,9359,9368,9369,9371,9373,9400])). % 174.01/173.94 cnf(12309,plain, % 174.01/173.94 (~P1(f777(f777(f336(x123091),x123092),f182(f858(x123091,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12312,plain, % 174.01/173.94 (~P1(f777(f777(f336(x123121),x123122),f182(f858(x123121,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12315,plain, % 174.01/173.94 (P1(f777(f777(f189(a27),x123151),x123151))), % 174.01/173.94 inference(rename_variables,[],[3185])). % 174.01/173.94 cnf(12317,plain, % 174.01/173.94 (~P1(f777(f777(f336(f857(f852(x123171),f852(x123171))),f777(f777(f243(f852(x123171),f852(x123171)),x123172),x123172)),f139(x123171,f777(f777(f283(x123171,x123173,x123171),x123174),f182(f858(f857(x123173,x123171),a845))))))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,3428,10879,11945,12048,12145,12183,12191,12200,3436,3437,3488,3157,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,12121,4342,11166,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,4385,10279,10374,3242,4379,2810,2813,2822,2828,2832,2833,2834,2835,2837,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2874,2875,2885,2887,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4363,3522,3121,11423,12203,12207,12211,3130,3238,3642,3951,3028,4381,4440,10815,11109,11112,3735,11198,3087,3052,3047,3035,3041,3042,4049,10995,3066,3199,11684,11907,3245,10653,12009,3119,3120,3140,10316,3290,4475,3817,4401,10111,10276,11067,12171,12204,4410,12179,3177,11523,4465,3581,3291,3083,3084,10176,10474,3346,3005,3106,11190,3964,12194,12304,3818,10821,10940,11007,12155,12161,12260,12263,12282,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,4398,11181,3491,3697,3745,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,4471,11291,11324,11364,11394,3619,3395,3772,3214,3216,3189,4452,4395,3572,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,3925,3881,11707,12066,3828,10650,11872,11892,3876,10824,11940,12018,12078,12124,3546,11717,11867,11950,11999,3914,3563,10827,10889,10974,11036,11888,11964,12220,12279,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,12128,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,3188,10640,10706,11989,3263,11923,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,12224,3342,10446,10709,10754,11025,11098,11254,11503,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,12256,12303,12309,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,11817,3663,4009,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4105,4478,10079,10082,10334,10792,11617,3938,3789,11143,11480,11484,11545,12182,12190,3627,10770,10776,10787,11739,11963,3485,10992,12106,12116,12187,12234,3962,3631,10850,11004,11030,11041,12072,12186,3456,10432,10435,10504,10685,4481,11411,4482,10555,10977,11129,12054,12063,12112,4069,10643,12075,12089,3969,3662,3606,4479,10130,10133,10459,10462,11288,11481,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992,7993,7994,8014,8015,8049,8053,8057,8066,8080,8107,8111,8117,8130,8149,8155,8177,8217,8247,8259,8276,8279,8308,8335,8399,8400,8403,8404,8421,8511,8512,8513,8514,8537,8561,8583,8625,8643,8696,8737,8740,8753,8790,8808,8824,8825,8840,8841,8969,8974,8992,9008,9028,9030,9033,9036,9039,9040,9052,9053,9076,9149,9184,9185,9250,9256,9290,9301,9305,9309,9310,9324,9348,9359,9368,9369,9371,9373,9400,9516,9595,9733,9734])). % 174.01/173.94 cnf(12318,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x123181),x123181))), % 174.01/173.94 inference(rename_variables,[],[4451])). % 174.01/173.94 cnf(12321,plain, % 174.01/173.94 (P1(f777(f777(f336(x123211),x123212),f241(f858(x123211,a845))))), % 174.01/173.94 inference(rename_variables,[],[3342])). % 174.01/173.94 cnf(12328,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x123281,a845)),x123282),x123282))), % 174.01/173.94 inference(rename_variables,[],[3485])). % 174.01/173.94 cnf(12331,plain, % 174.01/173.94 (~P1(f777(f777(f336(x123311),x123312),f182(f858(x123311,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12334,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),f4(a3)),f777(f777(f244(a3),f777(f79(a3),x123341)),x123342)))), % 174.01/173.94 inference(rename_variables,[],[3662])). % 174.01/173.94 cnf(12337,plain, % 174.01/173.94 (~E(f777(a116,x123371),x123371)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(12339,plain, % 174.01/173.94 (E(f39(x123391,x123392,x123393,x123394,x123395,x123396,x123397,x123398,x123399,a27),x123392)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(12341,plain, % 174.01/173.94 (P39(a27,x123411,x123412,x123411)), % 174.01/173.94 inference(rename_variables,[],[3404])). % 174.01/173.94 cnf(12343,plain, % 174.01/173.94 (P39(a27,x123431,x123432,x123431)), % 174.01/173.94 inference(rename_variables,[],[3404])). % 174.01/173.94 cnf(12350,plain, % 174.01/173.94 (P31(x123501,f4(a851),f777(f777(f777(f95(x123501),x123502),f777(a29,x123503)),x123504))), % 174.01/173.94 inference(rename_variables,[],[3556])). % 174.01/173.94 cnf(12358,plain, % 174.01/173.94 (P53(x123581,x123581,f262(x123581,x123582))), % 174.01/173.94 inference(rename_variables,[],[3157])). % 174.01/173.94 cnf(12364,plain, % 174.01/173.94 (E(f39(x123641,x123642,x123643,x123644,x123645,x123646,x123647,x123648,x123649,a27),x123642)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(12369,plain, % 174.01/173.94 (P29(x123691,x123691,f9(x123691),x123692)), % 174.01/173.94 inference(rename_variables,[],[3428])). % 174.01/173.94 cnf(12371,plain, % 174.01/173.94 (P29(x123711,x123711,f9(x123711),x123712)), % 174.01/173.94 inference(rename_variables,[],[3428])). % 174.01/173.94 cnf(12377,plain, % 174.01/173.94 (P47(x123771,x123772,f262(x123771,x123772))), % 174.01/173.94 inference(rename_variables,[],[3156])). % 174.01/173.94 cnf(12379,plain, % 174.01/173.94 (P47(x123791,x123792,f262(x123791,x123792))), % 174.01/173.94 inference(rename_variables,[],[3156])). % 174.01/173.94 cnf(12383,plain, % 174.01/173.94 (P28(x123831,x123832,f182(f858(f850(x123831),a845)))), % 174.01/173.94 inference(rename_variables,[],[3241])). % 174.01/173.94 cnf(12391,plain, % 174.01/173.94 (E(f39(x123911,x123912,x123913,x123914,x123915,x123916,x123917,x123918,x123919,a27),x123912)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(12393,plain, % 174.01/173.94 (E(f39(x123931,x123932,x123933,x123934,x123935,x123936,x123937,x123938,x123939,a27),x123932)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(12395,plain, % 174.01/173.94 (E(f39(x123951,x123952,x123953,x123954,x123955,x123956,x123957,x123958,x123959,a27),x123952)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(12398,plain, % 174.01/173.94 (E(f39(x123981,x123982,x123983,x123984,x123985,x123986,x123987,x123988,x123989,a27),x123982)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(12400,plain, % 174.01/173.94 (P54(x124001,f182(f858(x124001,a845)),x124002)), % 174.01/173.94 inference(rename_variables,[],[3206])). % 174.01/173.94 cnf(12404,plain, % 174.01/173.94 (E(f39(x124041,x124042,x124043,x124044,x124045,x124046,x124047,x124048,x124049,a27),x124042)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(12406,plain, % 174.01/173.94 (E(f39(x124061,x124062,x124063,x124064,x124065,x124066,x124067,x124068,x124069,a27),x124062)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(12410,plain, % 174.01/173.94 (E(f39(x124101,x124102,x124103,x124104,x124105,x124106,x124107,x124108,x124109,a27),x124102)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(12418,plain, % 174.01/173.94 (P19(x124181,f858(x124181,a845),f304(x124181))), % 174.01/173.94 inference(rename_variables,[],[3160])). % 174.01/173.94 cnf(12422,plain, % 174.01/173.94 (E(f39(x124221,x124222,x124223,x124224,x124225,x124226,x124227,x124228,x124229,a27),x124222)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(12425,plain, % 174.01/173.94 (E(f182(f858(f857(x124251,x124251),a845)),f262(x124251,f182(f858(x124251,a845))))), % 174.01/173.94 inference(rename_variables,[],[3258])). % 174.01/173.94 cnf(12430,plain, % 174.01/173.94 (P41(x124301,x124302,x124303,x124304,f182(f858(x124301,a845)),x124304)), % 174.01/173.94 inference(rename_variables,[],[4131])). % 174.01/173.94 cnf(12433,plain, % 174.01/173.94 (P41(x124331,x124332,x124333,x124334,f182(f858(x124331,a845)),x124334)), % 174.01/173.94 inference(rename_variables,[],[4131])). % 174.01/173.94 cnf(12443,plain, % 174.01/173.94 (P37(x124431,f185(x124431))), % 174.01/173.94 inference(rename_variables,[],[3025])). % 174.01/173.94 cnf(12452,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x124521),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(12461,plain, % 174.01/173.94 (~P1(f777(f777(f235(a3),f777(f104(a3),x124611)),f777(f83(a3),f777(f104(a3),x124612))))), % 174.01/173.94 inference(rename_variables,[],[4477])). % 174.01/173.94 cnf(12467,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f777(f44(x124671),f777(f160(x124671),x124672))),f777(f183(f852(x124671)),x124672)))), % 174.01/173.94 inference(rename_variables,[],[3728])). % 174.01/173.94 cnf(12471,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x124711),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(12474,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x124741),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(12477,plain, % 174.01/173.94 (P1(f777(f65(a851),f299(a851,x124771,x124772)))), % 174.01/173.94 inference(rename_variables,[],[3396])). % 174.01/173.94 cnf(12480,plain, % 174.01/173.94 (P1(f777(f65(a851),f299(a851,x124801,x124802)))), % 174.01/173.94 inference(rename_variables,[],[3396])). % 174.01/173.94 cnf(12483,plain, % 174.01/173.94 (P1(f777(f65(a851),f299(a851,x124831,x124832)))), % 174.01/173.94 inference(rename_variables,[],[3396])). % 174.01/173.94 cnf(12486,plain, % 174.01/173.94 (P1(f777(f65(a851),f299(a851,x124861,x124862)))), % 174.01/173.94 inference(rename_variables,[],[3396])). % 174.01/173.94 cnf(12493,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),f777(f83(a3),f777(f104(a3),x124931))),f777(f104(a3),x124932)))), % 174.01/173.94 inference(rename_variables,[],[3663])). % 174.01/173.94 cnf(12496,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x124961),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(12497,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x124971),x124971))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12504,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x125041),f777(a116,x125041)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(12510,plain, % 174.01/173.94 (P1(f777(f777(f336(x125101),f777(x125102,x125103)),f777(f305(x125104,x125101,x125102),f241(f858(x125104,a845)))))), % 174.01/173.94 inference(rename_variables,[],[3789])). % 174.01/173.94 cnf(12511,plain, % 174.01/173.94 (~E(f777(a116,x125111),f4(a851))), % 174.01/173.94 inference(rename_variables,[],[4379])). % 174.01/173.94 cnf(12513,plain, % 174.01/173.94 (~P1(f777(f777(f235(a3),f4(a3)),f777(f108(a3),f4(a3))))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,11927,12341,12343,3428,10879,11945,12048,12145,12183,12191,12200,12253,12369,3436,12012,3437,12084,3488,3156,12377,12379,3157,12358,4131,12430,12433,3160,12418,3004,3025,12443,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,12121,12292,12339,12364,12391,12393,12395,12398,12404,12406,12410,4342,11166,3487,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,12225,4385,10279,10374,3242,3206,12400,4379,10725,2810,2813,2822,2828,2832,2833,2834,2835,2837,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2874,2875,2885,2887,2888,2913,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4362,3060,4363,3522,3168,4354,3121,11423,12203,12207,12211,3130,3238,3642,3951,3028,4381,4399,4440,10815,11109,11112,3735,11198,3241,12383,3099,3087,3052,3556,12350,3047,3848,3561,4327,3035,3014,3041,3042,4049,10995,3066,3199,11684,11907,12042,3245,10653,12009,3119,3120,3140,10316,3290,4475,10247,3817,4401,10111,10276,11067,12171,12204,4410,12179,3177,11523,4465,3581,3291,10896,3511,3258,12425,3083,3084,10176,10474,3346,3075,3005,3106,11190,3964,12194,12304,3818,10821,10940,11007,12155,12161,12260,12263,12282,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,4398,11181,3491,3525,3697,3745,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,12286,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,12452,12471,12474,4471,11291,11324,11364,11394,3619,3395,3396,12477,12480,12483,3772,3214,3216,3189,4452,3082,4395,3572,3883,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,3925,3881,11707,12066,3828,10650,11872,11892,3876,10824,11940,12018,12078,12124,3546,11717,11867,11950,11999,3914,3563,10827,10889,10974,11036,11888,11964,12220,12279,12289,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,12128,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,12231,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,3188,10640,10706,11989,3263,11923,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,12224,3342,10446,10709,10754,11025,11098,11254,11503,12174,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,12256,12303,12309,12312,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,11817,3663,11554,4009,3401,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4105,4478,10079,10082,10334,10792,11617,3938,12092,3789,11143,11480,11484,11545,12182,12190,12259,3627,10770,10776,10787,11739,11963,3485,10992,12106,12116,12187,12234,12242,3962,3631,10850,11004,11030,11041,12072,12186,3728,12467,3456,10432,10435,10504,10685,4481,11411,4477,12461,4482,10555,10977,11129,12054,12063,12112,12276,4069,10643,12075,12089,3969,3662,3606,11537,4479,10130,10133,10459,10462,11288,11481,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992,7993,7994,8014,8015,8049,8053,8057,8066,8080,8107,8111,8117,8130,8149,8155,8177,8217,8247,8259,8276,8279,8308,8335,8399,8400,8403,8404,8421,8511,8512,8513,8514,8537,8561,8583,8625,8643,8696,8737,8740,8753,8790,8808,8824,8825,8840,8841,8969,8974,8992,9008,9028,9030,9033,9036,9039,9040,9052,9053,9076,9149,9184,9185,9250,9256,9290,9301,9305,9309,9310,9324,9348,9359,9368,9369,9371,9373,9400,9516,9595,9733,9734,9804,9874,9954,9965,9970,3,2549,2561,2562,2564,2566,2567,2568,2573,2574,2575,2579,2581,2582,2583,2594,2596,2597,2598,2602,2603,2604,2605,2607,2608,2609,2613,2614,2615,2616,2617,2622,2625,2626,2632,2636,2640,2641,2643,2644,2647,2651,2653,2655,2658,2670,2672,2704,2706,2707,2709,2711,2729,2730,2740,2747,2750,2751,2752,2753,2772,2790,2791,2799,2800,5179,5355,5361,5362,5439,5531,5560,5592,5608,5614,5616,5677,5678,5679,5680,5696,5731,5860,5906,5931,5967,6002,6006,6155])). % 174.01/173.94 cnf(12515,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),f777(f108(a3),a87)),f4(a3)))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,11927,12341,12343,3428,10879,11945,12048,12145,12183,12191,12200,12253,12369,3436,12012,3437,12084,3488,3156,12377,12379,3157,12358,4131,12430,12433,3160,12418,3004,3025,12443,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,12121,12292,12339,12364,12391,12393,12395,12398,12404,12406,12410,4342,11166,3487,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,12225,4385,10279,10374,3242,3206,12400,4379,10725,2810,2813,2822,2828,2832,2833,2834,2835,2837,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2874,2875,2885,2887,2888,2913,2933,2943,2944,2949,2960,2962,2963,2966,2977,2979,4362,3060,4363,3522,3168,4354,3121,11423,12203,12207,12211,3130,3238,3642,3951,3028,4381,4399,4440,10815,11109,11112,3735,11198,3241,12383,3099,3087,3052,3556,12350,3047,3848,3561,4327,3035,3014,3041,3042,4049,10995,3066,3199,11684,11907,12042,3245,10653,12009,3119,3120,3140,10316,3290,4475,10247,3817,4401,10111,10276,11067,12171,12204,4410,12179,3177,11523,4465,3581,3291,10896,3511,3258,12425,3083,3084,10176,10474,3346,3075,3005,3106,11190,3964,12194,12304,3818,10821,10940,11007,12155,12161,12260,12263,12282,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,4398,11181,3491,3525,3697,3745,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,12286,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,12452,12471,12474,4471,11291,11324,11364,11394,3619,3395,3396,12477,12480,12483,3772,3214,3216,3189,4452,3082,4395,3572,3883,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,3925,3881,11707,12066,3828,10650,11872,11892,3876,10824,11940,12018,12078,12124,3546,11717,11867,11950,11999,3914,3563,10827,10889,10974,11036,11888,11964,12220,12279,12289,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,12128,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,12231,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,11812,3188,10640,10706,11989,3263,11923,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,12224,3342,10446,10709,10754,11025,11098,11254,11503,12174,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,12256,12303,12309,12312,3249,10471,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,11817,3663,11554,4009,3401,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4105,4478,10079,10082,10334,10792,11617,3938,12092,3789,11143,11480,11484,11545,12182,12190,12259,3627,10770,10776,10787,11739,11963,3485,10992,12106,12116,12187,12234,12242,3962,3631,10850,11004,11030,11041,12072,12186,3728,12467,3456,10432,10435,10504,10685,4481,11411,4477,12461,4482,10555,10977,11129,12054,12063,12112,12276,4069,10643,12075,12089,3969,3662,3606,11537,4479,10130,10133,10459,10462,11288,11481,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992,7993,7994,8014,8015,8049,8053,8057,8066,8080,8107,8111,8117,8130,8149,8155,8177,8217,8247,8259,8276,8279,8308,8335,8399,8400,8403,8404,8421,8511,8512,8513,8514,8537,8561,8583,8625,8643,8696,8737,8740,8753,8790,8808,8824,8825,8840,8841,8969,8974,8992,9008,9028,9030,9033,9036,9039,9040,9052,9053,9076,9149,9184,9185,9250,9256,9290,9301,9305,9309,9310,9324,9348,9359,9368,9369,9371,9373,9400,9516,9595,9733,9734,9804,9874,9954,9965,9970,3,2549,2561,2562,2564,2566,2567,2568,2573,2574,2575,2579,2581,2582,2583,2594,2596,2597,2598,2602,2603,2604,2605,2607,2608,2609,2613,2614,2615,2616,2617,2622,2625,2626,2632,2636,2640,2641,2643,2644,2647,2651,2653,2655,2658,2670,2672,2704,2706,2707,2709,2711,2729,2730,2740,2747,2750,2751,2752,2753,2772,2790,2791,2799,2800,5179,5355,5361,5362,5439,5531,5560,5592,5608,5614,5616,5677,5678,5679,5680,5696,5731,5860,5906,5931,5967,6002,6006,6155,6162])). % 174.01/173.94 cnf(12516,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x125161),x125161))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(12519,plain, % 174.01/173.94 (P1(f777(f65(a851),f299(a851,x125191,x125192)))), % 174.01/173.94 inference(rename_variables,[],[3396])). % 174.01/173.94 cnf(12522,plain, % 174.01/173.94 (P1(f777(f65(a851),f299(a851,x125221,x125222)))), % 174.01/173.94 inference(rename_variables,[],[3396])). % 174.01/173.94 cnf(12525,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x125251),x125251))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12538,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x125381),f777(a116,x125381)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(12543,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f54(a851,x125431,x125432)),x125431))), % 174.01/173.94 inference(rename_variables,[],[3639])). % 174.01/173.94 cnf(12552,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x125521),f777(a116,x125521)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(12553,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x125531),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(12562,plain, % 174.01/173.94 (~P1(f777(f777(f235(a3),f777(f104(a3),x125621)),f4(a3)))), % 174.01/173.94 inference(rename_variables,[],[4471])). % 174.01/173.94 cnf(12563,plain, % 174.01/173.94 (P1(f777(f241(f858(x125631,a845)),x125632))), % 174.01/173.94 inference(rename_variables,[],[3249])). % 174.01/173.94 cnf(12566,plain, % 174.01/173.94 (~P1(f777(f777(f235(a3),f777(f104(a3),x125661)),f4(a3)))), % 174.01/173.94 inference(rename_variables,[],[4471])). % 174.01/173.94 cnf(12567,plain, % 174.01/173.94 (P1(f777(f241(f858(x125671,a845)),x125672))), % 174.01/173.94 inference(rename_variables,[],[3249])). % 174.01/173.94 cnf(12570,plain, % 174.01/173.94 (P1(f777(f241(f858(x125701,a845)),x125702))), % 174.01/173.94 inference(rename_variables,[],[3249])). % 174.01/173.94 cnf(12573,plain, % 174.01/173.94 (P1(f777(f241(f858(x125731,a845)),x125732))), % 174.01/173.94 inference(rename_variables,[],[3249])). % 174.01/173.94 cnf(12581,plain, % 174.01/173.94 (~P1(f777(f777(f336(x125811),x125812),f182(f858(x125811,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12582,plain, % 174.01/173.94 (P1(f777(f65(x125821),f182(f858(x125821,a845))))), % 174.01/173.94 inference(rename_variables,[],[3263])). % 174.01/173.94 cnf(12594,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f4(a851)),x125941))), % 174.01/173.94 inference(rename_variables,[],[3208])). % 174.01/173.94 cnf(12597,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x125971),f777(a116,x125971)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(12598,plain, % 174.01/173.94 (~E(f777(a116,x125981),x125981)), % 174.01/173.94 inference(rename_variables,[],[4367])). % 174.01/173.94 cnf(12601,plain, % 174.01/173.94 (~P1(f777(f777(f336(x126011),x126012),f182(f858(x126011,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12604,plain, % 174.01/173.94 (~P1(f777(f777(f336(x126041),x126042),f182(f858(x126041,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12606,plain, % 174.01/173.94 (P1(f777(f777(f281(a851),x126061),f54(a851,x126061,x126061)))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,11927,12341,12343,3428,10879,11945,12048,12145,12183,12191,12200,12253,12369,3436,12012,3437,12084,3488,3156,12377,12379,3157,12358,4131,12430,12433,3160,12418,3004,3025,12443,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,12121,12292,12339,12364,12391,12393,12395,12398,12404,12406,12410,4342,11166,3487,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,12225,12337,4385,10279,10374,3242,3206,12400,4379,10725,2810,2813,2822,2828,2832,2833,2834,2835,2837,2843,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2871,2874,2875,2885,2887,2888,2913,2933,2943,2944,2949,2953,2956,2960,2962,2963,2966,2977,2979,4362,3060,4363,3522,3168,3512,4354,3121,11423,12203,12207,12211,3130,3238,3642,3951,3028,4381,4399,4440,10815,11109,11112,3735,11198,3241,12383,3099,3087,3052,3556,12350,3047,3848,3561,4327,3035,3014,3041,3042,4049,10995,3066,3199,11684,11907,12042,3245,10653,12009,3119,3120,3140,10316,3290,4475,10247,3817,4401,10111,10276,11067,12171,12204,4410,12179,3177,11523,4465,3581,3291,10896,3511,3258,12425,3083,3084,10176,10474,3346,3075,3005,3106,11190,3964,12194,12304,3818,10821,10940,11007,12155,12161,12260,12263,12282,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,4398,11181,3491,3525,3697,3745,12045,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,12286,12504,12538,12552,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,12452,12471,12474,12496,4471,11291,11324,11364,11394,12562,12566,3619,3395,3396,12477,12480,12483,12486,12519,3772,3214,3216,3189,4452,3082,4395,3572,3883,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,3925,3881,11707,12066,3828,10650,11872,11892,3876,10824,11940,12018,12078,12124,3546,11717,11867,11950,11999,12097,3914,3563,10827,10889,10974,11036,11888,11964,12220,12279,12289,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,12128,12315,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,12231,12497,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,11812,3188,10640,10706,11989,11992,3263,11923,12582,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,12224,3342,10446,10709,10754,11025,11098,11254,11503,12174,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,12256,12303,12309,12312,12331,12581,12601,3249,10471,10501,12563,12567,12570,3286,3281,3703,3639,10157,11417,11450,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,3208,10658,10732,11451,11613,11817,12060,3663,11554,4009,3401,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4105,4478,10079,10082,10334,10792,11617,3938,12092,3789,11143,11480,11484,11545,12182,12190,12259,3627,10770,10776,10787,11739,11963,3485,10992,12106,12116,12187,12234,12242,3962,3631,10850,11004,11030,11041,12072,12186,3728,12467,3456,10432,10435,10504,10685,4481,11411,4477,12461,4482,10555,10977,11129,12054,12063,12112,12276,4069,10643,12075,12089,3969,3662,12334,3606,11537,4479,10130,10133,10459,10462,11288,11481,4480,11391,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,65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% 174.01/173.94 cnf(12609,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x126091),x126091))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12616,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x126161),x126161))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12620,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x126201),f777(a116,x126201)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(12623,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x126231),x126231))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12628,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x126281),x126281))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12631,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x126311),x126311))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12634,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x126341),x126341))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12637,plain, % 174.01/173.94 (E(f777(f777(f5(f858(x126371,a845)),f182(f858(x126371,a845))),x126372),f182(f858(x126371,a845)))), % 174.01/173.94 inference(rename_variables,[],[3458])). % 174.01/173.94 cnf(12638,plain, % 174.01/173.94 (P1(f777(f65(x126381),f182(f858(x126381,a845))))), % 174.01/173.94 inference(rename_variables,[],[3263])). % 174.01/173.94 cnf(12641,plain, % 174.01/173.94 (E(f777(f777(f5(f858(x126411,a845)),f182(f858(x126411,a845))),x126412),f182(f858(x126411,a845)))), % 174.01/173.94 inference(rename_variables,[],[3458])). % 174.01/173.94 cnf(12642,plain, % 174.01/173.94 (P1(f777(f65(x126421),f182(f858(x126421,a845))))), % 174.01/173.94 inference(rename_variables,[],[3263])). % 174.01/173.94 cnf(12645,plain, % 174.01/173.94 (E(f777(f777(f5(f858(x126451,a845)),f182(f858(x126451,a845))),x126452),f182(f858(x126451,a845)))), % 174.01/173.94 inference(rename_variables,[],[3458])). % 174.01/173.94 cnf(12646,plain, % 174.01/173.94 (P1(f777(f65(x126461),f182(f858(x126461,a845))))), % 174.01/173.94 inference(rename_variables,[],[3263])). % 174.01/173.94 cnf(12649,plain, % 174.01/173.94 (E(f777(f777(f5(f858(x126491,a845)),f182(f858(x126491,a845))),x126492),f182(f858(x126491,a845)))), % 174.01/173.94 inference(rename_variables,[],[3458])). % 174.01/173.94 cnf(12650,plain, % 174.01/173.94 (P1(f777(f65(x126501),f182(f858(x126501,a845))))), % 174.01/173.94 inference(rename_variables,[],[3263])). % 174.01/173.94 cnf(12654,plain, % 174.01/173.94 (E(f39(x126541,x126542,x126543,x126544,x126545,x126546,x126547,x126548,x126549,a27),x126542)), % 174.01/173.94 inference(rename_variables,[],[4341])). % 174.01/173.94 cnf(12659,plain, % 174.01/173.94 (P1(f777(f777(f281(a851),f777(a116,f4(a851))),x126591))), % 174.01/173.94 inference(rename_variables,[],[3343])). % 174.01/173.94 cnf(12660,plain, % 174.01/173.94 (~P1(f777(f777(f234(a851),f777(a116,x126601)),x126601))), % 174.01/173.94 inference(rename_variables,[],[4464])). % 174.01/173.94 cnf(12663,plain, % 174.01/173.94 (E(f777(f777(f5(f858(x126631,a845)),f182(f858(x126631,a845))),x126632),f182(f858(x126631,a845)))), % 174.01/173.94 inference(rename_variables,[],[3458])). % 174.01/173.94 cnf(12664,plain, % 174.01/173.94 (P1(f777(f65(x126641),f182(f858(x126641,a845))))), % 174.01/173.94 inference(rename_variables,[],[3263])). % 174.01/173.94 cnf(12668,plain, % 174.01/173.94 (P1(f777(f65(x126681),f182(f858(x126681,a845))))), % 174.01/173.94 inference(rename_variables,[],[3263])). % 174.01/173.94 cnf(12671,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x126711),x126711))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12677,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x126771),x126771))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(12680,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x126801),f777(a116,x126801)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(12687,plain, % 174.01/173.94 (P1(f777(f777(f235(a851),x126871),f777(a116,x126871)))), % 174.01/173.94 inference(rename_variables,[],[3255])). % 174.01/173.94 cnf(12690,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x126901),x126901))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12701,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x127011),x127011))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12704,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x127041),x127041))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(12711,plain, % 174.01/173.94 (~P1(f777(f777(f336(x127111),x127112),f182(f858(x127111,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12722,plain, % 174.01/173.94 (P1(f777(f777(f336(x127221),x127222),f241(f858(x127221,a845))))), % 174.01/173.94 inference(rename_variables,[],[3342])). % 174.01/173.94 cnf(12728,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x127281,a845)),f777(f160(x127281),f777(f128(x127281,x127282),x127283))),f777(f160(x127281),x127283)))), % 174.01/173.94 inference(rename_variables,[],[3828])). % 174.01/173.94 cnf(12734,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x127341),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(12735,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x127351),x127351))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(12739,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x127391),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(12740,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x127401),x127401))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(12745,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x127451),x127451))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12752,plain, % 174.01/173.94 (E(f777(f777(f20(x127521,x127522),x127523),x127524),x127523)), % 174.01/173.94 inference(rename_variables,[],[3177])). % 174.01/173.94 cnf(12755,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x127551,a845)),f777(f160(x127551),f153(x127551,x127552,x127553))),f777(f160(x127551),x127553)))), % 174.01/173.94 inference(rename_variables,[],[3876])). % 174.01/173.94 cnf(12758,plain, % 174.01/173.94 (P1(f777(f777(f234(f858(x127581,a845)),f182(f858(x127581,a845))),x127582))), % 174.01/173.94 inference(rename_variables,[],[3631])). % 174.01/173.94 cnf(12759,plain, % 174.01/173.94 (~P1(f777(f777(f336(x127591),x127592),f182(f858(x127591,a845))))), % 174.01/173.94 inference(rename_variables,[],[4467])). % 174.01/173.94 cnf(12764,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),f815(f777(x127641,f4(a851)),x127641,f4(a851))),f4(a851)))), % 174.01/173.94 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% 174.01/173.94 cnf(12766,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x127661),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(12767,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x127671),x127671))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(12771,plain, % 174.01/173.94 (~P1(f777(f777(f235(a851),x127711),f4(a851)))), % 174.01/173.94 inference(rename_variables,[],[4455])). % 174.01/173.94 cnf(12772,plain, % 174.01/173.94 (P1(f777(f777(f234(a3),x127721),x127721))), % 174.01/173.94 inference(rename_variables,[],[3187])). % 174.01/173.94 cnf(12775,plain, % 174.01/173.94 (P1(f777(f777(f234(a851),x127751),x127751))), % 174.01/173.94 inference(rename_variables,[],[3186])). % 174.01/173.94 cnf(12777,plain, % 174.01/173.94 (~P1(f777(f777(f234(f858(a851,a845)),f297(a851,f777(a116,x127771),f777(a116,x127771))),f297(a851,x127772,x127771)))), % 174.01/173.94 inference(scs_inference,[],[2804,3404,11910,11927,12341,12343,3428,10879,11945,12048,12145,12183,12191,12200,12253,12369,3436,12012,3437,12084,3488,3156,12377,12379,3157,12358,4131,12430,12433,3160,12418,3004,3025,12443,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,12121,12292,12339,12364,12391,12393,12395,12398,12404,12406,12410,12422,4342,11166,3487,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,12225,12337,4385,10279,10374,3242,3206,12400,4379,10725,2810,2813,2822,2828,2832,2833,2834,2835,2837,2840,2843,2844,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2871,2874,2875,2885,2887,2888,2906,2908,2913,2918,2919,2933,2943,2944,2945,2948,2949,2953,2956,2960,2962,2963,2966,2977,2979,4362,3060,4363,3522,3168,3512,3762,4354,3121,11423,12203,12207,12211,3130,3238,3642,3951,3028,4381,4399,4440,10815,11109,11112,3735,11198,3241,12383,3099,3087,3052,3556,12350,3047,3848,3561,4327,3035,3014,3041,3042,4049,10995,3066,3199,11684,11907,12042,3245,10653,12009,3119,3120,3140,10316,3290,4475,10247,3817,4401,10111,10276,11067,12171,12204,4410,12179,3177,11523,11526,4465,3581,3291,10896,3511,3258,12425,3083,3084,10176,10474,3346,3075,3005,3106,11190,3964,12194,12304,3818,10821,10940,11007,12155,12161,12260,12263,12282,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,4398,11181,3491,3525,3697,3458,12637,12641,12645,12649,12663,3745,12045,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,12286,12504,12538,12552,12597,12620,12680,12687,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,12452,12471,12474,12496,12553,12734,12739,12766,4471,11291,11324,11364,11394,12562,12566,3619,3395,3396,12477,12480,12483,12486,12519,3772,3214,3216,3189,4452,3082,4395,3572,3883,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,12266,3925,3881,11707,12066,3828,10650,11872,11892,12079,3876,10824,11940,12018,12078,12124,3546,11717,11867,11950,11999,12097,3914,3563,10827,10889,10974,11036,11888,11964,12220,12279,12289,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,12128,12315,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,12231,12497,12525,12609,12616,12623,12628,12631,12634,12671,12690,12701,12745,12775,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,11812,12516,12677,12704,12735,12740,12767,3188,10640,10706,11989,11992,3263,11923,12582,12638,12642,12646,12650,12664,12668,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,12224,12318,3342,10446,10709,10754,11025,11098,11254,11503,12174,12321,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,12256,12303,12309,12312,12331,12581,12601,12604,12711,3249,10471,10501,12563,12567,12570,12573,3286,3281,3703,3639,10157,11417,11450,12543,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,12660,3208,10658,10732,11451,11613,11817,12060,3663,11554,12493,4009,3401,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4105,4478,10079,10082,10334,10792,11617,3938,12092,3789,11143,11480,11484,11545,12182,12190,12259,3627,10770,10776,10787,11739,11963,3485,10992,12106,12116,12187,12234,12242,3962,3631,10850,11004,11030,11041,12072,12186,12228,3728,12467,3343,3456,10432,10435,10504,10685,4481,11411,4477,12461,4482,10555,10977,11129,12054,12063,12112,12276,4069,10643,12075,12089,3969,3662,12334,3606,11537,4479,10130,10133,10459,10462,11288,11481,12285,4480,11391,11490,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,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% 174.01/173.95 cnf(12778,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),x127781),x127781))), % 174.01/173.95 inference(rename_variables,[],[3186])). % 174.01/173.95 cnf(12781,plain, % 174.01/173.95 (~P1(f777(f777(f234(a851),f777(a116,x127811)),x127811))), % 174.01/173.95 inference(rename_variables,[],[4464])). % 174.01/173.95 cnf(12786,plain, % 174.01/173.95 (E(x127861,f525(f777(f9(x127862),f777(f9(x127862),x127861)),f9(x127862),x127862,x127862))), % 174.01/173.95 inference(scs_inference,[],[2804,3404,11910,11927,12341,12343,3428,10879,11945,12048,12145,12183,12191,12200,12253,12369,12371,3436,12012,3437,12084,3488,3156,12377,12379,3157,12358,4131,12430,12433,3160,12418,3004,3025,12443,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,12121,12292,12339,12364,12391,12393,12395,12398,12404,12406,12410,12422,4342,11166,3487,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,12225,12337,4385,10279,10374,3242,3206,12400,4379,10725,2810,2813,2822,2828,2832,2833,2834,2835,2837,2840,2843,2844,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2871,2874,2875,2885,2887,2888,2906,2908,2913,2918,2919,2933,2943,2944,2945,2948,2949,2953,2956,2960,2962,2963,2966,2977,2979,4362,3060,4363,3522,3168,3512,3762,4354,3121,11423,12203,12207,12211,3130,3238,3642,3951,3027,3028,4381,4399,4440,10815,11109,11112,3735,11198,3241,12383,3099,3087,3052,3556,12350,3047,3848,3561,4327,3035,3014,3041,3042,4049,10995,3066,3199,11684,11907,12042,3245,10653,12009,3119,3120,3140,10316,3290,4475,10247,3817,4401,10111,10276,11067,12171,12204,4410,12179,3177,11523,11526,4465,3581,3291,10896,3511,3258,12425,3083,3084,10176,10474,3346,3075,3005,3106,11190,3964,12194,12304,3818,10821,10940,11007,12155,12161,12260,12263,12282,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,4398,11181,3491,3525,3697,3458,12637,12641,12645,12649,12663,3745,12045,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,12286,12504,12538,12552,12597,12620,12680,12687,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,12452,12471,12474,12496,12553,12734,12739,12766,4471,11291,11324,11364,11394,12562,12566,3619,3395,3396,12477,12480,12483,12486,12519,3772,3214,3216,3189,4452,3082,4395,3572,3883,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,12266,3925,3881,11707,12066,3828,10650,11872,11892,12079,3876,10824,11940,12018,12078,12124,3546,11717,11867,11950,11999,12097,3914,3563,10827,10889,10974,11036,11888,11964,12220,12279,12289,4476,10595,10958,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,12128,12315,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,12231,12497,12525,12609,12616,12623,12628,12631,12634,12671,12690,12701,12745,12775,12778,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,11812,12516,12677,12704,12735,12740,12767,3188,10640,10706,11989,11992,3263,11923,12582,12638,12642,12646,12650,12664,12668,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,12224,12318,3342,10446,10709,10754,11025,11098,11254,11503,12174,12321,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,12256,12303,12309,12312,12331,12581,12601,12604,12711,3249,10471,10501,12563,12567,12570,12573,3286,3281,3703,3639,10157,11417,11450,12543,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,12660,12781,3208,10658,10732,11451,11613,11817,12060,3663,11554,12493,4009,3401,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,4105,4478,10079,10082,10334,10792,11617,3938,12092,3789,11143,11480,11484,11545,12182,12190,12259,12510,3627,10770,10776,10787,11739,11963,3485,10992,12106,12116,12187,12234,12242,3962,3631,10850,11004,11030,11041,12072,12186,12228,3728,12467,3343,3456,10432,10435,10504,10685,4481,11411,4477,12461,4482,10555,10977,11129,12054,12063,12112,12276,4069,10643,12075,12089,3969,3662,12334,3606,11537,4479,10130,10133,10459,10462,11288,11481,12285,4480,11391,11490,3632,10429,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992,7993,7994,8014,8015,8049,8053,8057,8066,8080,8107,8111,8117,8130,8149,8155,8177,8217,8247,8259,8276,8279,8308,8335,8399,8400,8403,8404,8421,8511,8512,8513,8514,8537,8561,8583,8625,8643,8696,8737,8740,8753,8790,8808,8824,8825,8840,8841,8969,8974,8992,9008,9028,9030,9033,9036,9039,9040,9052,9053,9076,9149,9184,9185,9250,9256,9290,9301,9305,9309,9310,9324,9348,9359,9368,9369,9371,9373,9400,9516,9595,9733,9734,9804,9874,9954,9965,9970,3,2549,2561,2562,2564,2566,2567,2568,2573,2574,2575,2579,2581,2582,2583,2594,2596,2597,2598,2602,2603,2604,2605,2607,2608,2609,2613,2614,2615,2616,2617,2622,2625,2626,2632,2636,2640,2641,2643,2644,2647,2651,2653,2655,2658,2670,2672,2704,2706,2707,2709,2711,2729,2730,2740,2747,2750,2751,2752,2753,2772,2790,2791,2799,2800,5179,5355,5361,5362,5439,5531,5560,5592,5608,5614,5616,5677,5678,5679,5680,5696,5731,5860,5906,5931,5967,6002,6006,6155,6162,6200,6201,6222,6224,6226,6232,6233,6234,6235,6236,6237,6238,6239,6240,6327,6401,6402,6493,6528,6529,6570,6571,6718,6731,6792,6813,6814,6818,6843,6867,6876,6878,6882,6925,6948,6949,6965,6966,6968,6999,7046,7047,7143,7212,7213,7214,7215,7231,7271,7285,7329,7330,7339,7348,7350,7362,7397,7398,7399,7400,7545,7546,7552,7553,7555,7557,7633,7767,7770,7772,7773,7788,7826,7903,7947,8001,8020,8021,8093,8190,8257,8258,8260,8292,8296,8331,8360,8361,8452,8453,8454,8455,8587])). % 174.01/173.95 cnf(12787,plain, % 174.01/173.95 (P1(f777(f777(f336(x127871),f777(x127872,x127873)),f777(f305(x127874,x127871,x127872),f241(f858(x127874,a845)))))), % 174.01/173.95 inference(rename_variables,[],[3789])). % 174.01/173.95 cnf(12788,plain, % 174.01/173.95 (P29(x127881,x127881,f9(x127881),x127882)), % 174.01/173.95 inference(rename_variables,[],[3428])). % 174.01/173.95 cnf(12793,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x127931,a845)),x127932),f241(f858(x127931,a845))))), % 174.01/173.95 inference(rename_variables,[],[3563])). % 174.01/173.95 cnf(12794,plain, % 174.01/173.95 (P29(x127941,x127941,f9(x127941),x127942)), % 174.01/173.95 inference(rename_variables,[],[3428])). % 174.01/173.95 cnf(12798,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x127981,a845)),x127982),f241(f858(x127981,a845))))), % 174.01/173.95 inference(rename_variables,[],[3563])). % 174.01/173.95 cnf(12799,plain, % 174.01/173.95 (P29(x127991,x127991,f9(x127991),x127992)), % 174.01/173.95 inference(rename_variables,[],[3428])). % 174.01/173.95 cnf(12803,plain, % 174.01/173.95 (P29(x128031,x128031,f9(x128031),x128032)), % 174.01/173.95 inference(rename_variables,[],[3428])). % 174.01/173.95 cnf(12806,plain, % 174.01/173.95 (~P1(f777(f777(f235(f858(x128061,a845)),x128062),f182(f858(x128061,a845))))), % 174.01/173.95 inference(rename_variables,[],[4476])). % 174.01/173.95 cnf(12809,plain, % 174.01/173.95 (P29(x128091,x128091,f9(x128091),x128092)), % 174.01/173.95 inference(rename_variables,[],[3428])). % 174.01/173.95 cnf(12812,plain, % 174.01/173.95 (P29(x128121,x128121,f9(x128121),x128122)), % 174.01/173.95 inference(rename_variables,[],[3428])). % 174.01/173.95 cnf(12823,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x128231,a845)),f182(f858(x128231,a845))),x128232))), % 174.01/173.95 inference(rename_variables,[],[3631])). % 174.01/173.95 cnf(12827,plain, % 174.01/173.95 (E(f39(x128271,x128272,x128273,x128274,x128275,x128276,x128277,x128278,x128279,a27),x128272)), % 174.01/173.95 inference(rename_variables,[],[4341])). % 174.01/173.95 cnf(12831,plain, % 174.01/173.95 (~P1(f777(f777(f336(x128311),x128312),f182(f858(x128311,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(12835,plain, % 174.01/173.95 (P1(f777(f777(f336(x128351),f777(x128352,x128353)),f777(f305(x128354,x128351,x128352),f241(f858(x128354,a845)))))), % 174.01/173.95 inference(rename_variables,[],[3789])). % 174.01/173.95 cnf(12836,plain, % 174.01/173.95 (P29(x128361,x128361,f9(x128361),x128362)), % 174.01/173.95 inference(rename_variables,[],[3428])). % 174.01/173.95 cnf(12846,plain, % 174.01/173.95 (~P1(f777(f777(f336(x128461),x128462),f182(f858(x128461,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(12849,plain, % 174.01/173.95 (~P1(f777(f777(f336(x128491),x128492),f182(f858(x128491,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(12852,plain, % 174.01/173.95 (E(f39(x128521,x128522,x128523,x128524,x128525,x128526,x128527,x128528,x128529,a27),x128522)), % 174.01/173.95 inference(rename_variables,[],[4341])). % 174.01/173.95 cnf(12854,plain, % 174.01/173.95 (~E(f777(a116,x128541),x128541)), % 174.01/173.95 inference(rename_variables,[],[4367])). % 174.01/173.95 cnf(12857,plain, % 174.01/173.95 (P1(f777(f777(f281(a851),x128571),x128571))), % 174.01/173.95 inference(rename_variables,[],[3188])). % 174.01/173.95 cnf(12859,plain, % 174.01/173.95 (~E(f777(a116,x128591),x128591)), % 174.01/173.95 inference(rename_variables,[],[4367])). % 174.01/173.95 cnf(12863,plain, % 174.01/173.95 (E(f39(x128631,x128632,x128633,x128634,x128635,x128636,x128637,x128638,x128639,a27),x128632)), % 174.01/173.95 inference(rename_variables,[],[4341])). % 174.01/173.95 cnf(12864,plain, % 174.01/173.95 (~E(f777(a116,x128641),x128641)), % 174.01/173.95 inference(rename_variables,[],[4367])). % 174.01/173.95 cnf(12868,plain, % 174.01/173.95 (E(f777(f777(f20(x128681,x128682),x128683),x128684),x128683)), % 174.01/173.95 inference(rename_variables,[],[3177])). % 174.01/173.95 cnf(12871,plain, % 174.01/173.95 (P1(f777(f777(f235(a851),x128711),f777(a116,x128711)))), % 174.01/173.95 inference(rename_variables,[],[3255])). % 174.01/173.95 cnf(12872,plain, % 174.01/173.95 (~E(f777(a116,x128721),x128721)), % 174.01/173.95 inference(rename_variables,[],[4367])). % 174.01/173.95 cnf(12875,plain, % 174.01/173.95 (P1(f777(f777(f235(a851),x128751),f777(a116,f777(f777(f84(a851),x128752),x128751))))), % 174.01/173.95 inference(rename_variables,[],[3632])). % 174.01/173.95 cnf(12876,plain, % 174.01/173.95 (P1(f777(f777(f235(a851),x128761),f777(a116,x128761)))), % 174.01/173.95 inference(rename_variables,[],[3255])). % 174.01/173.95 cnf(12878,plain, % 174.01/173.95 (~E(f777(f777(f85(a851),f777(a116,f4(a851))),f37(x128781,x128782)),f777(f777(f85(a851),f777(a116,f4(a851))),f38(x128783,x128784)))), % 174.01/173.95 inference(scs_inference,[],[2804,3404,11910,11927,12341,12343,3428,10879,11945,12048,12145,12183,12191,12200,12253,12369,12371,12788,12794,12799,12803,12809,12812,3436,12012,3437,12084,3488,3156,12377,12379,3157,12358,4131,12430,12433,3160,12418,3004,3025,12443,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,12121,12292,12339,12364,12391,12393,12395,12398,12404,12406,12410,12422,12654,12827,12852,4342,11166,3487,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,12225,12337,12598,12854,12859,12864,12872,4385,10279,10374,3242,3206,12400,4379,10725,2810,2813,2822,2828,2832,2833,2834,2835,2837,2840,2843,2844,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2871,2874,2875,2885,2887,2888,2906,2908,2913,2918,2919,2933,2943,2944,2945,2948,2949,2953,2956,2960,2962,2963,2966,2977,2979,4362,3060,4363,3522,3168,3512,3762,4354,3121,11423,12203,12207,12211,3130,3238,3642,3951,3027,3028,4381,4399,4440,10815,11109,11112,3735,11198,3241,12383,3099,3087,3052,3556,12350,3047,3848,3067,3561,4327,3035,3014,3041,3042,4049,10995,3066,3199,11684,11907,12042,3245,10653,12009,3119,3120,3140,10316,3290,4475,10247,3817,4401,10111,10276,11067,12171,12204,12208,4410,12179,3177,11523,11526,12752,4465,10884,3150,3581,3172,3291,10896,3511,3258,12425,3083,3084,10176,10474,4449,3346,3075,3005,3129,3106,11190,3964,12194,12304,3818,10821,10940,11007,12155,12161,12260,12263,12282,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,11014,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,4398,11181,3491,3525,3697,3458,12637,12641,12645,12649,12663,3745,12045,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,12286,12504,12538,12552,12597,12620,12680,12687,12871,3634,11414,3269,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,12452,12471,12474,12496,12553,12734,12739,12766,4471,11291,11324,11364,11394,12562,12566,3619,3395,3396,12477,12480,12483,12486,12519,3772,3214,3216,3189,4452,3082,4395,3572,3883,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,12266,3925,3881,11707,12066,3828,10650,11872,11892,12079,3876,10824,11940,12018,12078,12124,3546,11717,11867,11950,11999,12097,3914,3563,10827,10889,10974,11036,11888,11964,12220,12279,12289,12793,12798,4476,10595,10958,12806,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,12128,12315,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,12231,12497,12525,12609,12616,12623,12628,12631,12634,12671,12690,12701,12745,12775,12778,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,11812,12516,12677,12704,12735,12740,12767,3188,10640,10706,11989,11992,3263,11923,12582,12638,12642,12646,12650,12664,12668,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,12224,12318,3342,10446,10709,10754,11025,11098,11254,11503,12174,12321,12722,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,12256,12303,12309,12312,12331,12581,12601,12604,12711,12759,12831,12846,3249,10471,10501,12563,12567,12570,12573,3286,3281,3703,3639,10157,11417,11450,12543,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,12660,12781,3208,10658,10732,11451,11613,11817,12060,3663,11554,12493,4009,3401,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,3500,11410,4105,4478,10079,10082,10334,10792,11617,3938,12092,3789,11143,11480,11484,11545,12182,12190,12259,12510,12787,12835,3627,10770,10776,10787,11739,11963,12239,3485,10992,12106,12116,12187,12234,12242,3962,3631,10850,11004,11030,11041,12072,12186,12228,12758,3728,12467,3343,12659,3456,10432,10435,10504,10685,4481,11411,4477,12461,4482,10555,10977,11129,12054,12063,12112,12276,4069,10643,12075,12089,12115,3969,3662,12334,3606,11537,4479,10130,10133,10459,10462,11288,11481,12285,4480,11391,11490,3632,10429,10682,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,54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9,9832,5502,5763,5764,5924,6309,6310,6404])). % 174.01/173.95 cnf(12880,plain, % 174.01/173.95 (~E(f777(a116,x128801),x128801)), % 174.01/173.95 inference(rename_variables,[],[4367])). % 174.01/173.95 cnf(12885,plain, % 174.01/173.95 (P1(f777(f777(f234(a3),f4(a3)),f777(f104(a3),x128851)))), % 174.01/173.95 inference(rename_variables,[],[3286])). % 174.01/173.95 cnf(12888,plain, % 174.01/173.95 (P1(f777(f777(f234(a3),f4(a3)),f777(f104(a3),x128881)))), % 174.01/173.95 inference(rename_variables,[],[3286])). % 174.01/173.95 cnf(12889,plain, % 174.01/173.95 (P1(f777(f777(f234(a3),x128891),x128891))), % 174.01/173.95 inference(rename_variables,[],[3187])). % 174.01/173.95 cnf(12892,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),f4(a851)),x128921))), % 174.01/173.95 inference(rename_variables,[],[3208])). % 174.01/173.95 cnf(12893,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),x128931),x128931))), % 174.01/173.95 inference(rename_variables,[],[3186])). % 174.01/173.95 cnf(12896,plain, % 174.01/173.95 (~E(f777(a116,x128961),f4(a851))), % 174.01/173.95 inference(rename_variables,[],[4379])). % 174.01/173.95 cnf(12899,plain, % 174.01/173.95 (P1(f777(f777(f234(a3),x128991),x128991))), % 174.01/173.95 inference(rename_variables,[],[3187])). % 174.01/173.95 cnf(12903,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x129031,a845)),f777(f160(x129031),f153(x129031,x129032,x129033))),f777(f160(x129031),x129033)))), % 174.01/173.95 inference(rename_variables,[],[3876])). % 174.01/173.95 cnf(12908,plain, % 174.01/173.95 (~P1(f777(f777(f336(x129081),x129082),f182(f858(x129081,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(12911,plain, % 174.01/173.95 (P1(f777(f65(a851),f299(a851,x129111,x129112)))), % 174.01/173.95 inference(rename_variables,[],[3396])). % 174.01/173.95 cnf(12912,plain, % 174.01/173.95 (E(f777(f777(f181(a851),f777(a116,x129121)),f777(a116,x129122)),f777(a116,f777(f777(f181(a851),x129121),x129122)))), % 174.01/173.95 inference(rename_variables,[],[3357])). % 174.01/173.95 cnf(12915,plain, % 174.01/173.95 (P1(f777(f65(a851),f299(a851,x129151,x129152)))), % 174.01/173.95 inference(rename_variables,[],[3396])). % 174.01/173.95 cnf(12916,plain, % 174.01/173.95 (E(f777(f777(f238(a851),f777(a116,x129161)),f777(a116,x129162)),f777(a116,f777(f777(f238(a851),x129161),x129162)))), % 174.01/173.95 inference(rename_variables,[],[3356])). % 174.01/173.95 cnf(12919,plain, % 174.01/173.95 (P1(f777(f65(a851),f299(a851,x129191,x129192)))), % 174.01/173.95 inference(rename_variables,[],[3396])). % 174.01/173.95 cnf(12923,plain, % 174.01/173.95 (P1(f777(f65(a851),f299(a851,x129231,x129232)))), % 174.01/173.95 inference(rename_variables,[],[3396])). % 174.01/173.95 cnf(12927,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x129271,a845)),f777(f160(x129271),f777(f128(x129271,x129272),x129273))),f777(f160(x129271),x129273)))), % 174.01/173.95 inference(rename_variables,[],[3828])). % 174.01/173.95 cnf(12928,plain, % 174.01/173.95 (E(f777(f777(f20(x129281,x129282),x129283),x129284),x129283)), % 174.01/173.95 inference(rename_variables,[],[3177])). % 174.01/173.95 cnf(12931,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x129311,a845)),f777(f160(x129311),f777(f777(f161(x129311),x129312),x129313))),f777(f160(x129311),x129313)))), % 174.01/173.95 inference(rename_variables,[],[3871])). % 174.01/173.95 cnf(12932,plain, % 174.01/173.95 (E(f777(f777(f20(x129321,x129322),x129323),x129324),x129323)), % 174.01/173.95 inference(rename_variables,[],[3177])). % 174.01/173.95 cnf(12936,plain, % 174.01/173.95 (E(f777(f777(f20(x129361,x129362),x129363),x129364),x129363)), % 174.01/173.95 inference(rename_variables,[],[3177])). % 174.01/173.95 cnf(12943,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x129431,a845)),x129432),x129432))), % 174.01/173.95 inference(rename_variables,[],[3485])). % 174.01/173.95 cnf(12949,plain, % 174.01/173.95 (P1(f777(f777(f234(a3),f4(a3)),f777(f104(a3),x129491)))), % 174.01/173.95 inference(rename_variables,[],[3286])). % 174.01/173.95 cnf(12953,plain, % 174.01/173.95 (~P1(f777(f777(f336(x129531),x129532),f182(f858(x129531,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(12956,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x129561,a845)),f777(f160(x129561),f162(x129561,x129562,x129563))),f777(f160(x129561),x129562)))), % 174.01/173.95 inference(rename_variables,[],[3877])). % 174.01/173.95 cnf(12960,plain, % 174.01/173.95 (~P1(f777(f777(f336(x129601),x129602),f182(f858(x129601,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(12963,plain, % 174.01/173.95 (~P1(f777(f777(f336(x129631),x129632),f182(f858(x129631,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(12964,plain, % 174.01/173.95 (E(f39(x129641,x129642,x129643,x129644,x129645,x129646,x129647,x129648,x129649,a27),x129642)), % 174.01/173.95 inference(rename_variables,[],[4341])). % 174.01/173.95 cnf(12965,plain, % 174.01/173.95 (P29(x129651,x129651,f9(x129651),x129652)), % 174.01/173.95 inference(rename_variables,[],[3428])). % 174.01/173.95 cnf(12969,plain, % 174.01/173.95 (E(f39(x129691,x129692,x129693,x129694,x129695,x129696,x129697,x129698,x129699,a27),x129692)), % 174.01/173.95 inference(rename_variables,[],[4341])). % 174.01/173.95 cnf(12975,plain, % 174.01/173.95 (E(f39(x129751,x129752,x129753,x129754,x129755,x129756,x129757,x129758,x129759,a27),x129752)), % 174.01/173.95 inference(rename_variables,[],[4341])). % 174.01/173.95 cnf(12976,plain, % 174.01/173.95 (P1(f777(f777(f234(a3),x129761),x129761))), % 174.01/173.95 inference(rename_variables,[],[3187])). % 174.01/173.95 cnf(12979,plain, % 174.01/173.95 (E(f39(x129791,x129792,x129793,x129794,x129795,x129796,x129797,x129798,x129799,a27),x129792)), % 174.01/173.95 inference(rename_variables,[],[4341])). % 174.01/173.95 cnf(12980,plain, % 174.01/173.95 (P1(f777(f777(f234(a3),x129801),x129801))), % 174.01/173.95 inference(rename_variables,[],[3187])). % 174.01/173.95 cnf(12983,plain, % 174.01/173.95 (E(f39(x129831,x129832,x129833,x129834,x129835,x129836,x129837,x129838,x129839,a27),x129832)), % 174.01/173.95 inference(rename_variables,[],[4341])). % 174.01/173.95 cnf(12987,plain, % 174.01/173.95 (P1(f777(f777(f235(a851),x129871),f777(a116,x129871)))), % 174.01/173.95 inference(rename_variables,[],[3255])). % 174.01/173.95 cnf(12989,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),x129891),x129891))), % 174.01/173.95 inference(rename_variables,[],[3186])). % 174.01/173.95 cnf(12990,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),f4(a851)),x129901))), % 174.01/173.95 inference(rename_variables,[],[3208])). % 174.01/173.95 cnf(12993,plain, % 174.01/173.95 (P1(f777(f777(f235(a851),x129931),f777(a116,x129931)))), % 174.01/173.95 inference(rename_variables,[],[3255])). % 174.01/173.95 cnf(12996,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),f4(a851)),x129961))), % 174.01/173.95 inference(rename_variables,[],[3208])). % 174.01/173.95 cnf(13000,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),f4(a851)),x130001))), % 174.01/173.95 inference(rename_variables,[],[3208])). % 174.01/173.95 cnf(13001,plain, % 174.01/173.95 (P1(f777(f777(f235(a851),f4(a851)),f777(a116,x130011)))), % 174.01/173.95 inference(rename_variables,[],[3269])). % 174.01/173.95 cnf(13002,plain, % 174.01/173.95 (E(f39(x130021,x130022,x130023,x130024,x130025,x130026,x130027,x130028,x130029,a27),x130022)), % 174.01/173.95 inference(rename_variables,[],[4341])). % 174.01/173.95 cnf(13005,plain, % 174.01/173.95 (P1(f777(f57(f39(x130051,f777(f777(f84(a851),f777(f777(f85(a851),f777(f242(a851,a851),f777(f777(f243(a851,a851),f4(a851)),x130052))),f777(a116,f777(f777(f84(a851),x130053),f777(f252(a851,a851),f777(f777(f243(a851,a851),f4(a851)),x130052)))))),f777(f252(a851,a851),f777(f777(f243(a851,a851),f4(a851)),x130052))),x130054,x130055,x130056,x130057,x130058,x130059,x1300510,a27),f777(a116,f777(f777(f84(a851),x130053),f777(f252(a851,a851),f777(f777(f243(a851,a851),f4(a851)),x130052))))),f777(f777(f243(a851,a851),f4(a851)),x130052)))), % 174.01/173.95 inference(scs_inference,[],[2804,3404,11910,11927,12341,12343,3428,10879,11945,12048,12145,12183,12191,12200,12253,12369,12371,12788,12794,12799,12803,12809,12812,12836,12965,3436,12012,3437,12084,3488,3156,12377,12379,3157,12358,4131,12430,12433,3160,12418,3004,3025,12443,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,12121,12292,12339,12364,12391,12393,12395,12398,12404,12406,12410,12422,12654,12827,12852,12863,12964,12969,12975,12979,12983,13002,4342,11166,3487,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,12225,12337,12598,12854,12859,12864,12872,4385,10279,10374,3242,3206,12400,4379,10725,12511,12896,2810,2813,2822,2828,2832,2833,2834,2835,2837,2840,2843,2844,2845,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2871,2874,2875,2885,2887,2888,2893,2906,2908,2913,2918,2919,2933,2943,2944,2945,2948,2949,2953,2956,2960,2962,2963,2966,2977,2979,4362,3060,4363,3522,3168,3512,3762,4354,3121,11423,12203,12207,12211,3130,3238,3642,3951,3027,3028,4381,4399,4440,10815,11109,11112,3735,11198,3241,12383,3099,3087,3052,3556,12350,3047,3848,3067,3561,4327,3035,3014,3041,3042,4049,10995,3066,3199,11684,11907,12042,3245,10653,12009,3119,3120,3140,10316,3290,4475,10247,3817,4401,10111,10276,11067,12171,12204,12208,4410,12179,3177,11523,11526,12752,12868,12928,12932,12936,4465,10884,3150,3581,3172,3291,10896,3511,3283,3258,12425,3083,3084,10176,10474,4449,3346,3075,3005,3129,3106,11190,3964,12194,12304,3818,10821,10940,11007,12155,12161,12260,12263,12282,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,11014,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,3367,4398,11181,3491,3525,3697,3458,12637,12641,12645,12649,12663,3745,12045,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,12286,12504,12538,12552,12597,12620,12680,12687,12871,12876,12987,12993,3634,11414,3269,11538,13001,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,12452,12471,12474,12496,12553,12734,12739,12766,4471,11291,11324,11364,11394,12562,12566,3619,3395,3396,12477,12480,12483,12486,12519,12522,12911,12915,12919,3398,3772,3356,12916,3357,12912,3214,3216,3189,4452,3082,4395,3572,3883,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,12266,3925,3881,11707,12066,3828,10650,11872,11892,12079,12728,12927,3871,12931,3876,10824,11940,12018,12078,12124,12755,12903,3877,3546,11717,11867,11950,11999,12097,3914,3563,10827,10889,10974,11036,11888,11964,12220,12279,12289,12793,12798,4476,10595,10958,12806,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,12128,12315,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,12231,12497,12525,12609,12616,12623,12628,12631,12634,12671,12690,12701,12745,12775,12778,12893,12989,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,11812,12516,12677,12704,12735,12740,12767,12772,12889,12899,12976,12980,3188,10640,10706,11989,11992,12857,3263,11923,12582,12638,12642,12646,12650,12664,12668,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,12224,12318,3342,10446,10709,10754,11025,11098,11254,11503,12174,12321,12722,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,12256,12303,12309,12312,12331,12581,12601,12604,12711,12759,12831,12846,12849,12908,12953,12960,12963,3249,10471,10501,12563,12567,12570,12573,3286,12885,12888,3281,3703,3639,10157,11417,11450,12543,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,12660,12781,3208,10658,10732,11451,11613,11817,12060,12594,12892,12990,12996,13000,3663,11554,12493,4009,3401,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,4185,3500,11410,4105,4478,10079,10082,10334,10792,11617,3938,12092,3789,11143,11480,11484,11545,12182,12190,12259,12510,12787,12835,3627,10770,10776,10787,11739,11963,12239,3485,10992,12106,12116,12187,12234,12242,12328,12943,3962,3631,10850,11004,11030,11041,12072,12186,12228,12758,12823,3728,12467,3343,12659,3456,10432,10435,10504,10685,4481,11411,4477,12461,4482,10555,10977,11129,12054,12063,12112,12276,4069,10643,12075,12089,12115,3969,3662,12334,3606,11537,4479,10130,10133,10459,10462,11288,11481,12285,4480,11391,11490,3632,10429,10682,12875,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992,7993,7994,8014,8015,8049,8053,8057,8066,8080,8107,8111,8117,8130,8149,8155,8177,8217,8247,8259,8276,8279,8308,8335,8399,8400,8403,8404,8421,8511,8512,8513,8514,8537,8561,8583,8625,8643,8696,8737,8740,8753,8790,8808,8824,8825,8840,8841,8969,8974,8992,9008,9028,9030,9033,9036,9039,9040,9052,9053,9076,9149,9184,9185,9250,9256,9290,9301,9305,9309,9310,9324,9348,9359,9368,9369,9371,9373,9400,9516,9595,9733,9734,9804,9874,9954,9965,9970,3,2549,2561,2562,2564,2566,2567,2568,2573,2574,2575,2579,2581,2582,2583,2594,2596,2597,2598,2602,2603,2604,2605,2607,2608,2609,2613,2614,2615,2616,2617,2622,2625,2626,2632,2636,2640,2641,2643,2644,2647,2651,2653,2655,2658,2670,2672,2704,2706,2707,2709,2711,2729,2730,2740,2747,2750,2751,2752,2753,2772,2790,2791,2799,2800,5179,5355,5361,5362,5439,5531,5560,5592,5608,5614,5616,5677,5678,5679,5680,5696,5731,5860,5906,5931,5967,6002,6006,6155,6162,6200,6201,6222,6224,6226,6232,6233,6234,6235,6236,6237,6238,6239,6240,6327,6401,6402,6493,6528,6529,6570,6571,6718,6731,6792,6813,6814,6818,6843,6867,6876,6878,6882,6925,6948,6949,6965,6966,6968,6999,7046,7047,7143,7212,7213,7214,7215,7231,7271,7285,7329,7330,7339,7348,7350,7362,7397,7398,7399,7400,7545,7546,7552,7553,7555,7557,7633,7767,7770,7772,7773,7788,7826,7903,7947,8001,8020,8021,8093,8190,8257,8258,8260,8292,8296,8331,8360,8361,8452,8453,8454,8455,8587,8804,8805,8865,8880,8934,8935,9049,9080,9103,9133,9164,9346,9590,9772,9829,9832,5502,5763,5764,5924,6309,6310,6404,6424,6425,6812,6866,7084,8245,8447,8524,8730,8891,8892,8957,8958,9200,9201,9202,9203,9402,9653,9830,9953,9961,10014,10015,6384,7325,7587,7588,8352,8353,8777,8791])). % 174.01/173.95 cnf(13075,plain, % 174.01/173.95 (P1(f777(f777(f235(a3),f4(a3)),f777(f79(a3),f82(a3))))), % 174.01/173.95 inference(scs_inference,[],[2804,3404,11910,11927,12341,12343,3428,10879,11945,12048,12145,12183,12191,12200,12253,12369,12371,12788,12794,12799,12803,12809,12812,12836,12965,3436,12012,3437,12084,3488,3156,12377,12379,3157,12358,4131,12430,12433,3160,12418,3004,3025,12443,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,12121,12292,12339,12364,12391,12393,12395,12398,12404,12406,12410,12422,12654,12827,12852,12863,12964,12969,12975,12979,12983,13002,4342,11166,3487,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,12225,12337,12598,12854,12859,12864,12872,4385,10279,10374,3242,3206,12400,4379,10725,12511,12896,2810,2813,2822,2823,2828,2832,2833,2834,2835,2837,2840,2843,2844,2845,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2871,2874,2875,2885,2887,2888,2893,2906,2908,2913,2916,2918,2919,2933,2943,2944,2945,2948,2949,2953,2956,2960,2962,2963,2966,2977,2979,4362,3060,4363,3522,3168,3512,3762,4354,3121,11423,12203,12207,12211,3130,3238,3642,3951,3027,3028,4381,4399,4440,10815,11109,11112,3735,11198,3241,12383,3099,3087,3052,3556,12350,3047,3848,3067,3561,4327,3035,3014,3041,3042,4049,10995,3066,3199,11684,11907,12042,3245,10653,12009,3119,3120,3140,10316,3290,4475,10247,3817,4401,10111,10276,11067,12171,12204,12208,4410,12179,3177,11523,11526,12752,12868,12928,12932,12936,4465,10884,3150,3581,3172,3291,10896,3511,3283,3258,12425,3083,3084,10176,10474,4449,3346,3075,3005,3129,3106,11190,3964,12194,12304,3818,10821,10940,11007,12155,12161,12260,12263,12282,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,11014,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,3367,4398,11181,3491,3525,3697,3458,12637,12641,12645,12649,12663,3745,12045,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,12286,12504,12538,12552,12597,12620,12680,12687,12871,12876,12987,12993,3634,11414,3269,11538,13001,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,12452,12471,12474,12496,12553,12734,12739,12766,12771,4471,11291,11324,11364,11394,12562,12566,3619,3395,3396,12477,12480,12483,12486,12519,12522,12911,12915,12919,3398,3772,3356,12916,3357,12912,3214,3216,3189,4452,3082,4395,3572,3883,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,12266,3925,3881,11707,12066,3828,10650,11872,11892,12079,12728,12927,3871,12931,3876,10824,11940,12018,12078,12124,12755,12903,3877,12956,3546,11717,11867,11950,11999,12097,3914,3563,10827,10889,10974,11036,11888,11964,12220,12279,12289,12793,12798,4476,10595,10958,12806,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,12128,12315,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,12231,12497,12525,12609,12616,12623,12628,12631,12634,12671,12690,12701,12745,12775,12778,12893,12989,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,11812,12516,12677,12704,12735,12740,12767,12772,12889,12899,12976,12980,3188,10640,10706,11989,11992,12857,3263,11923,12582,12638,12642,12646,12650,12664,12668,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,12224,12318,3342,10446,10709,10754,11025,11098,11254,11503,12174,12321,12722,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,12256,12303,12309,12312,12331,12581,12601,12604,12711,12759,12831,12846,12849,12908,12953,12960,12963,3249,10471,10501,12563,12567,12570,12573,3286,12885,12888,12949,3281,3703,3639,10157,11417,11450,12543,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,12660,12781,3208,10658,10732,11451,11613,11817,12060,12594,12892,12990,12996,13000,3663,11554,12493,4009,3401,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,4185,3500,11410,4105,4478,10079,10082,10334,10792,11617,3938,12092,3789,11143,11480,11484,11545,12182,12190,12259,12510,12787,12835,3627,10770,10776,10787,11739,11963,12239,3485,10992,12106,12116,12187,12234,12242,12328,12943,3962,3631,10850,11004,11030,11041,12072,12186,12228,12758,12823,3728,12467,3343,12659,3456,10432,10435,10504,10685,4481,11411,4477,12461,4482,10555,10977,11129,12054,12063,12112,12276,4069,10643,12075,12089,12115,3969,3662,12334,3606,11537,4479,10130,10133,10459,10462,11288,11481,12285,4480,11391,11490,3632,10429,10682,12875,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992,7993,7994,8014,8015,8049,8053,8057,8066,8080,8107,8111,8117,8130,8149,8155,8177,8217,8247,8259,8276,8279,8308,8335,8399,8400,8403,8404,8421,8511,8512,8513,8514,8537,8561,8583,8625,8643,8696,8737,8740,8753,8790,8808,8824,8825,8840,8841,8969,8974,8992,9008,9028,9030,9033,9036,9039,9040,9052,9053,9076,9149,9184,9185,9250,9256,9290,9301,9305,9309,9310,9324,9348,9359,9368,9369,9371,9373,9400,9516,9595,9733,9734,9804,9874,9954,9965,9970,3,2549,2561,2562,2564,2566,2567,2568,2573,2574,2575,2579,2581,2582,2583,2594,2596,2597,2598,2602,2603,2604,2605,2607,2608,2609,2613,2614,2615,2616,2617,2622,2625,2626,2632,2636,2640,2641,2643,2644,2647,2651,2653,2655,2658,2670,2672,2704,2706,2707,2709,2711,2729,2730,2740,2747,2750,2751,2752,2753,2772,2790,2791,2799,2800,5179,5355,5361,5362,5439,5531,5560,5592,5608,5614,5616,5677,5678,5679,5680,5696,5731,5860,5906,5931,5967,6002,6006,6155,6162,6200,6201,6222,6224,6226,6232,6233,6234,6235,6236,6237,6238,6239,6240,6327,6401,6402,6493,6528,6529,6570,6571,6718,6731,6792,6813,6814,6818,6843,6867,6876,6878,6882,6925,6948,6949,6965,6966,6968,6999,7046,7047,7143,7212,7213,7214,7215,7231,7271,7285,7329,7330,7339,7348,7350,7362,7397,7398,7399,7400,7545,7546,7552,7553,7555,7557,7633,7767,7770,7772,7773,7788,7826,7903,7947,8001,8020,8021,8093,8190,8257,8258,8260,8292,8296,8331,8360,8361,8452,8453,8454,8455,8587,8804,8805,8865,8880,8934,8935,9049,9080,9103,9133,9164,9346,9590,9772,9829,9832,5502,5763,5764,5924,6309,6310,6404,6424,6425,6812,6866,7084,8245,8447,8524,8730,8891,8892,8957,8958,9200,9201,9202,9203,9402,9653,9830,9953,9961,10014,10015,6384,7325,7587,7588,8352,8353,8777,8791,9654,10013,4521,4558,4559,4560,4615,4623,4752,4766,4767,4795,4796,4823,4881,4883,4941,5055,5083,5117,5118,5120,5125,5127,5128,5153,5221,5243,5376,5444,5556])). % 174.01/173.95 cnf(13111,plain, % 174.01/173.95 (~P1(f777(f65(x131111),f46(f858(x131111,a845),f241(f858(f858(x131111,a845),a845)))))), % 174.01/173.95 inference(scs_inference,[],[2804,3404,11910,11927,12341,12343,3428,10879,11945,12048,12145,12183,12191,12200,12253,12369,12371,12788,12794,12799,12803,12809,12812,12836,12965,3436,12012,3437,12084,3488,3156,12377,12379,3157,12358,4131,12430,12433,3160,12418,3004,3025,12443,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,12121,12292,12339,12364,12391,12393,12395,12398,12404,12406,12410,12422,12654,12827,12852,12863,12964,12969,12975,12979,12983,13002,4342,11166,3487,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,12225,12337,12598,12854,12859,12864,12872,4385,10279,10374,3242,3206,12400,4379,10725,12511,12896,2810,2813,2822,2823,2828,2832,2833,2834,2835,2837,2840,2843,2844,2845,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2871,2874,2875,2885,2887,2888,2893,2906,2908,2913,2916,2918,2919,2933,2943,2944,2945,2948,2949,2953,2956,2960,2962,2963,2966,2977,2979,4362,3060,4363,3522,3168,3512,3762,4354,3121,11423,12203,12207,12211,3130,3238,3642,3951,3027,3028,4381,4399,4440,10815,11109,11112,3735,11198,3241,12383,3099,3087,3052,3556,12350,3047,3848,3067,3561,4327,3035,3014,3041,3042,4049,10995,3066,3199,11684,11907,12042,3245,10653,12009,3119,3120,3140,10316,3290,4475,10247,3817,4401,10111,10276,11067,12171,12204,12208,4410,12179,3177,11523,11526,12752,12868,12928,12932,12936,4465,10884,3150,3581,3172,3291,10896,3511,3283,3258,12425,3083,3084,10176,10474,4449,3346,3075,3005,3129,3106,11190,3964,12194,12304,3818,10821,10940,11007,12155,12161,12260,12263,12282,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,11014,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,3367,4398,11181,3491,3525,3697,3458,12637,12641,12645,12649,12663,3745,12045,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,12286,12504,12538,12552,12597,12620,12680,12687,12871,12876,12987,12993,3634,11414,3269,11538,13001,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,12452,12471,12474,12496,12553,12734,12739,12766,12771,4471,11291,11324,11364,11394,12562,12566,3619,3395,3396,12477,12480,12483,12486,12519,12522,12911,12915,12919,3398,3772,3356,12916,3357,12912,3214,3216,3189,4452,3082,4395,3572,3883,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,12266,3925,3881,11707,12066,3828,10650,11872,11892,12079,12728,12927,3871,12931,3876,10824,11940,12018,12078,12124,12755,12903,3877,12956,3546,11717,11867,11950,11999,12097,3914,3563,10827,10889,10974,11036,11888,11964,12220,12279,12289,12793,12798,4476,10595,10958,12806,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,12128,12315,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,12231,12497,12525,12609,12616,12623,12628,12631,12634,12671,12690,12701,12745,12775,12778,12893,12989,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,11812,12516,12677,12704,12735,12740,12767,12772,12889,12899,12976,12980,3188,10640,10706,11989,11992,12857,3263,11923,12582,12638,12642,12646,12650,12664,12668,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,12224,12318,3342,10446,10709,10754,11025,11098,11254,11503,12174,12321,12722,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,12256,12303,12309,12312,12331,12581,12601,12604,12711,12759,12831,12846,12849,12908,12953,12960,12963,3249,10471,10501,12563,12567,12570,12573,3286,12885,12888,12949,3281,3703,3639,10157,11417,11450,12543,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,12660,12781,3208,10658,10732,11451,11613,11817,12060,12594,12892,12990,12996,13000,3663,11554,12493,4009,3401,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,4185,3500,11410,4105,4478,10079,10082,10334,10792,11617,3938,12092,3789,11143,11480,11484,11545,12182,12190,12259,12510,12787,12835,3627,10770,10776,10787,11739,11963,12239,3485,10992,12106,12116,12187,12234,12242,12328,12943,3962,3631,10850,11004,11030,11041,12072,12186,12228,12758,12823,3728,12467,3343,12659,3456,10432,10435,10504,10685,4481,11411,4477,12461,4482,10555,10977,11129,12054,12063,12112,12276,4069,10643,12075,12089,12115,3969,3662,12334,3606,11537,4479,10130,10133,10459,10462,11288,11481,12285,4480,11391,11490,3632,10429,10682,12875,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992,7993,7994,8014,8015,8049,8053,8057,8066,8080,8107,8111,8117,8130,8149,8155,8177,8217,8247,8259,8276,8279,8308,8335,8399,8400,8403,8404,8421,8511,8512,8513,8514,8537,8561,8583,8625,8643,8696,8737,8740,8753,8790,8808,8824,8825,8840,8841,8969,8974,8992,9008,9028,9030,9033,9036,9039,9040,9052,9053,9076,9149,9184,9185,9250,9256,9290,9301,9305,9309,9310,9324,9348,9359,9368,9369,9371,9373,9400,9516,9595,9733,9734,9804,9874,9954,9965,9970,3,2549,2561,2562,2564,2566,2567,2568,2573,2574,2575,2579,2581,2582,2583,2594,2596,2597,2598,2602,2603,2604,2605,2607,2608,2609,2613,2614,2615,2616,2617,2622,2625,2626,2632,2636,2640,2641,2643,2644,2647,2651,2653,2655,2658,2670,2672,2704,2706,2707,2709,2711,2729,2730,2740,2747,2750,2751,2752,2753,2772,2790,2791,2799,2800,5179,5355,5361,5362,5439,5531,5560,5592,5608,5614,5616,5677,5678,5679,5680,5696,5731,5860,5906,5931,5967,6002,6006,6155,6162,6200,6201,6222,6224,6226,6232,6233,6234,6235,6236,6237,6238,6239,6240,6327,6401,6402,6493,6528,6529,6570,6571,6718,6731,6792,6813,6814,6818,6843,6867,6876,6878,6882,6925,6948,6949,6965,6966,6968,6999,7046,7047,7143,7212,7213,7214,7215,7231,7271,7285,7329,7330,7339,7348,7350,7362,7397,7398,7399,7400,7545,7546,7552,7553,7555,7557,7633,7767,7770,7772,7773,7788,7826,7903,7947,8001,8020,8021,8093,8190,8257,8258,8260,8292,8296,8331,8360,8361,8452,8453,8454,8455,8587,8804,8805,8865,8880,8934,8935,9049,9080,9103,9133,9164,9346,9590,9772,9829,9832,5502,5763,5764,5924,6309,6310,6404,6424,6425,6812,6866,7084,8245,8447,8524,8730,8891,8892,8957,8958,9200,9201,9202,9203,9402,9653,9830,9953,9961,10014,10015,6384,7325,7587,7588,8352,8353,8777,8791,9654,10013,4521,4558,4559,4560,4615,4623,4752,4766,4767,4795,4796,4823,4881,4883,4941,5055,5083,5117,5118,5120,5125,5127,5128,5153,5221,5243,5376,5444,5556,5557,5581,5582,5586,5621,5644,5646,5654,5660,5744,5823,5882,5926,5949,5971,6022,6068,6144])). % 174.01/173.95 cnf(13127,plain, % 174.01/173.95 (~P1(f777(f777(f235(a851),f4(a851)),f39(x131271,f4(a851),x131272,x131273,x131274,x131275,x131276,x131277,x131278,a27)))), % 174.01/173.95 inference(scs_inference,[],[2804,3404,11910,11927,12341,12343,3428,10879,11945,12048,12145,12183,12191,12200,12253,12369,12371,12788,12794,12799,12803,12809,12812,12836,12965,3436,12012,3437,12084,3488,3156,12377,12379,3157,12358,4131,12430,12433,3160,12418,3004,3025,12443,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,12121,12292,12339,12364,12391,12393,12395,12398,12404,12406,12410,12422,12654,12827,12852,12863,12964,12969,12975,12979,12983,13002,4342,11166,3487,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,12225,12337,12598,12854,12859,12864,12872,4385,10279,10374,3242,3206,12400,4379,10725,12511,12896,2810,2813,2822,2823,2828,2832,2833,2834,2835,2837,2840,2843,2844,2845,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2871,2874,2875,2885,2887,2888,2893,2906,2908,2913,2916,2918,2919,2933,2943,2944,2945,2948,2949,2953,2956,2960,2962,2963,2966,2977,2979,4362,3060,4363,3522,3168,3512,3762,4354,3121,11423,12203,12207,12211,3130,3238,3642,3951,3027,3028,4381,4399,4440,10815,11109,11112,3735,11198,3241,12383,3099,3087,3052,3556,12350,3047,3848,3067,3561,4327,3035,3014,3041,3042,4049,10995,3066,3199,11684,11907,12042,3245,10653,12009,3119,3120,3140,10316,3290,4475,10247,3817,4401,10111,10276,11067,12171,12204,12208,4410,12179,3177,11523,11526,12752,12868,12928,12932,12936,4465,10884,3150,3581,3172,3291,10896,3511,3283,3258,12425,3083,3084,10176,10474,4449,3346,3075,3005,3129,3106,11190,3964,12194,12304,3818,10821,10940,11007,12155,12161,12260,12263,12282,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,11014,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,3367,4398,11181,3491,3525,3697,3458,12637,12641,12645,12649,12663,3745,12045,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,12286,12504,12538,12552,12597,12620,12680,12687,12871,12876,12987,12993,3634,11414,3269,11538,13001,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,12452,12471,12474,12496,12553,12734,12739,12766,12771,4471,11291,11324,11364,11394,12562,12566,3619,3395,3396,12477,12480,12483,12486,12519,12522,12911,12915,12919,3398,3772,3356,12916,3357,12912,3214,3216,3189,4452,3082,4395,3572,3883,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,12266,3925,3881,11707,12066,3828,10650,11872,11892,12079,12728,12927,3871,12931,3876,10824,11940,12018,12078,12124,12755,12903,3877,12956,3546,11717,11867,11950,11999,12097,3914,3563,10827,10889,10974,11036,11888,11964,12220,12279,12289,12793,12798,4476,10595,10958,12806,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,12128,12315,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,12231,12497,12525,12609,12616,12623,12628,12631,12634,12671,12690,12701,12745,12775,12778,12893,12989,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,11812,12516,12677,12704,12735,12740,12767,12772,12889,12899,12976,12980,3188,10640,10706,11989,11992,12857,3263,11923,12582,12638,12642,12646,12650,12664,12668,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,12224,12318,3342,10446,10709,10754,11025,11098,11254,11503,12174,12321,12722,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,12256,12303,12309,12312,12331,12581,12601,12604,12711,12759,12831,12846,12849,12908,12953,12960,12963,3249,10471,10501,12563,12567,12570,12573,3286,12885,12888,12949,3281,3703,3639,10157,11417,11450,12543,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,12660,12781,3208,10658,10732,11451,11613,11817,12060,12594,12892,12990,12996,13000,3663,11554,12493,4009,3401,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,4185,3500,11410,4105,4478,10079,10082,10334,10792,11617,3938,12092,3789,11143,11480,11484,11545,12182,12190,12259,12510,12787,12835,3627,10770,10776,10787,11739,11963,12239,3485,10992,12106,12116,12187,12234,12242,12328,12943,3962,3631,10850,11004,11030,11041,12072,12186,12228,12758,12823,3728,12467,3343,12659,3456,10432,10435,10504,10685,4481,11411,4477,12461,4482,10555,10977,11129,12054,12063,12112,12276,4069,10643,12075,12089,12115,3969,3662,12334,3606,11537,4479,10130,10133,10459,10462,11288,11481,12285,4480,11391,11490,3632,10429,10682,12875,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992,7993,7994,8014,8015,8049,8053,8057,8066,8080,8107,8111,8117,8130,8149,8155,8177,8217,8247,8259,8276,8279,8308,8335,8399,8400,8403,8404,8421,8511,8512,8513,8514,8537,8561,8583,8625,8643,8696,8737,8740,8753,8790,8808,8824,8825,8840,8841,8969,8974,8992,9008,9028,9030,9033,9036,9039,9040,9052,9053,9076,9149,9184,9185,9250,9256,9290,9301,9305,9309,9310,9324,9348,9359,9368,9369,9371,9373,9400,9516,9595,9733,9734,9804,9874,9954,9965,9970,3,2549,2561,2562,2564,2566,2567,2568,2573,2574,2575,2579,2581,2582,2583,2594,2596,2597,2598,2602,2603,2604,2605,2607,2608,2609,2613,2614,2615,2616,2617,2622,2625,2626,2632,2636,2640,2641,2643,2644,2647,2651,2653,2655,2658,2670,2672,2704,2706,2707,2709,2711,2729,2730,2740,2747,2750,2751,2752,2753,2772,2790,2791,2799,2800,5179,5355,5361,5362,5439,5531,5560,5592,5608,5614,5616,5677,5678,5679,5680,5696,5731,5860,5906,5931,5967,6002,6006,6155,6162,6200,6201,6222,6224,6226,6232,6233,6234,6235,6236,6237,6238,6239,6240,6327,6401,6402,6493,6528,6529,6570,6571,6718,6731,6792,6813,6814,6818,6843,6867,6876,6878,6882,6925,6948,6949,6965,6966,6968,6999,7046,7047,7143,7212,7213,7214,7215,7231,7271,7285,7329,7330,7339,7348,7350,7362,7397,7398,7399,7400,7545,7546,7552,7553,7555,7557,7633,7767,7770,7772,7773,7788,7826,7903,7947,8001,8020,8021,8093,8190,8257,8258,8260,8292,8296,8331,8360,8361,8452,8453,8454,8455,8587,8804,8805,8865,8880,8934,8935,9049,9080,9103,9133,9164,9346,9590,9772,9829,9832,5502,5763,5764,5924,6309,6310,6404,6424,6425,6812,6866,7084,8245,8447,8524,8730,8891,8892,8957,8958,9200,9201,9202,9203,9402,9653,9830,9953,9961,10014,10015,6384,7325,7587,7588,8352,8353,8777,8791,9654,10013,4521,4558,4559,4560,4615,4623,4752,4766,4767,4795,4796,4823,4881,4883,4941,5055,5083,5117,5118,5120,5125,5127,5128,5153,5221,5243,5376,5444,5556,5557,5581,5582,5586,5621,5644,5646,5654,5660,5744,5823,5882,5926,5949,5971,6022,6068,6144,6268,6435,6474,6650,6651,6809,6879,6918])). % 174.01/173.95 cnf(13182,plain, % 174.01/173.95 (P1(f777(f777(f281(a3),f4(a3)),f54(a3,f4(a3),f4(a3))))), % 174.01/173.95 inference(scs_inference,[],[2804,3404,11910,11927,12341,12343,3428,10879,11945,12048,12145,12183,12191,12200,12253,12369,12371,12788,12794,12799,12803,12809,12812,12836,12965,3436,12012,3437,12084,3488,3156,12377,12379,3157,12358,4131,12430,12433,3160,12418,3004,3025,12443,4389,4341,10049,10052,10058,10120,10123,10214,10217,10498,10509,11150,11165,11169,11210,11213,11216,11219,11231,11262,11275,11302,11305,11316,11321,11327,11426,11429,11433,11437,11447,11471,11542,11579,12121,12292,12339,12364,12391,12393,12395,12398,12404,12406,12410,12422,12654,12827,12852,12863,12964,12969,12975,12979,12983,13002,4342,11166,3487,3068,4367,10055,10065,10076,10085,10184,10187,10190,10295,10401,10569,10701,10834,11070,11153,11160,11176,11224,11227,11330,11381,11397,11718,11743,11757,11792,11889,12008,12015,12175,12225,12337,12598,12854,12859,12864,12872,12880,4385,10279,10374,3242,3206,12400,4379,10725,12511,12896,2810,2813,2822,2823,2828,2832,2833,2834,2835,2837,2840,2843,2844,2845,2847,2850,2853,2855,2857,2859,2861,2862,2864,2865,2870,2871,2874,2875,2885,2887,2888,2893,2906,2908,2913,2916,2918,2919,2933,2936,2943,2944,2945,2948,2949,2953,2956,2960,2962,2963,2966,2977,2979,4362,3060,4363,3522,3168,3512,3762,4354,3121,11423,12203,12207,12211,3130,3238,3642,3951,3027,3028,4381,4399,4440,10815,11109,11112,3735,11198,3241,12383,3099,3085,3087,3052,3556,12350,3047,3848,3067,3561,4327,3035,3014,3041,3042,4049,10995,3066,3199,11684,11907,12042,3245,10653,12009,3119,3120,3140,10316,3290,4475,10247,3817,4401,10111,10276,11067,12171,12204,12208,4410,12179,3177,11523,11526,12752,12868,12928,12932,12936,4465,10884,3150,3581,3172,3291,10896,3511,3283,3258,12425,3083,3084,10176,10474,4449,3346,3075,3005,3129,3106,11190,3964,12194,12304,3818,10821,10940,11007,12155,12161,12260,12263,12282,4483,10757,10947,11061,11081,11117,11123,12100,4484,10861,10950,11064,11120,4485,10953,11014,4486,11017,4487,3103,3384,12051,12178,3545,4244,4245,3367,4398,11181,3491,3525,3697,3458,12637,12641,12645,12649,12663,3745,12045,3370,3622,3255,10195,10198,10311,10388,10440,10443,10477,10566,10805,11582,11630,11714,11782,11860,11898,11971,11974,12286,12504,12538,12552,12597,12620,12680,12687,12871,12876,12987,12993,3634,11414,3269,11538,13001,3453,4455,10088,10091,10117,10577,10592,10714,11132,11193,11596,11604,11836,11839,11932,12103,12452,12471,12474,12496,12553,12734,12739,12766,12771,4471,11291,11324,11364,11394,12562,12566,3619,3395,3396,12477,12480,12483,12486,12519,12522,12911,12915,12919,12923,3398,3772,3356,12916,3357,12912,3214,3216,3189,4452,3082,4395,3572,3883,3376,4472,3958,11078,3510,3732,11548,11551,3227,12019,12125,12266,3925,3881,11707,12066,3828,10650,11872,11892,12079,12728,12927,3871,12931,3876,10824,11940,12018,12078,12124,12755,12903,3877,12956,3546,11717,11867,11950,11999,12097,3914,3563,10827,10889,10974,11036,11888,11964,12220,12279,12289,12793,12798,4476,10595,10958,12806,3185,10207,10302,10426,10484,11267,11274,11496,11507,11541,11578,11687,11742,11957,12128,12315,3186,10544,10598,10601,10634,10661,10695,10739,10773,11760,11763,11766,11769,11977,11980,11983,11986,12059,12231,12497,12525,12609,12616,12623,12628,12631,12634,12671,12690,12701,12745,12775,12778,12893,12989,3187,10292,10489,10572,10698,11377,11585,11599,11693,11704,11725,11730,11772,11775,11797,11812,12516,12677,12704,12735,12740,12767,12772,12889,12899,12976,12980,3188,10640,10706,11989,11992,12857,3263,11923,12582,12638,12642,12646,12650,12664,12668,4451,10154,10242,10353,10383,10616,10664,10671,10984,11341,11446,11468,11474,11477,11493,11645,11648,11651,11654,11756,11778,11781,11791,11848,11851,11854,11857,11933,12030,12033,12131,12134,12224,12318,3342,10446,10709,10754,11025,11098,11254,11503,12174,12321,12722,4467,10625,10637,10746,10764,10767,10818,10903,10913,10925,10961,10989,11001,11033,11073,11089,11092,11095,11126,11137,11140,11520,11557,11842,11845,11879,11924,11960,12109,12152,12158,12243,12246,12256,12303,12309,12312,12331,12581,12601,12604,12711,12759,12831,12846,12849,12908,12953,12960,12963,3249,10471,10501,12563,12567,12570,12573,3286,12885,12888,12949,3281,3703,3639,10157,11417,11450,12543,4464,10108,10465,10468,10906,10922,11380,11436,11485,11504,11614,11657,11660,11663,11666,12660,12781,3208,10658,10732,11451,11613,11817,12060,12594,12892,12990,12996,13000,3663,11554,12493,4009,3401,4462,3674,3711,4443,4444,4446,3163,3164,4445,4447,4185,3500,11410,4105,4478,10079,10082,10334,10792,11617,3938,12092,3789,11143,11480,11484,11545,12182,12190,12259,12510,12787,12835,3627,10770,10776,10787,11739,11963,12239,3485,10992,12106,12116,12187,12234,12242,12328,12943,3962,3631,10850,11004,11030,11041,12072,12186,12228,12758,12823,3728,12467,3343,12659,3456,10432,10435,10504,10685,4481,11411,4477,12461,4482,10555,10977,11129,12054,12063,12112,12276,4069,10643,12075,12089,12115,3969,3662,12334,3606,11537,4479,10130,10133,10459,10462,11288,11481,12285,4480,11391,11490,3632,10429,10682,12875,3633,3898,4492,4497,4503,4565,4568,4596,4614,4621,4622,4658,4687,4693,4797,4798,4835,4858,4859,4882,4884,4897,4901,4921,4927,4944,4948,4949,4954,4959,4960,4983,5007,5008,5018,5024,5030,5075,5076,5084,5094,5096,5097,5106,5108,5116,5121,5134,5140,5143,5144,5148,5183,5193,5200,5202,5203,5206,5207,5208,5216,5217,5220,5225,5226,5227,5234,5238,5239,5240,5248,5251,5253,5259,5271,5278,5291,5293,5301,5302,5306,5309,5335,5341,5351,5352,5353,5368,5380,5402,5408,5426,5427,5430,5449,5457,5458,5460,5461,5470,5471,5485,5489,5498,5499,5501,5516,5519,5530,5541,5548,5561,5567,5573,5574,5575,5578,5583,5620,5622,5625,5627,5630,5631,5632,5634,5636,5638,5641,5648,5662,5676,5682,5683,5702,5703,5708,5709,5711,5714,5717,5718,5723,5767,5781,5789,5793,5805,5815,5832,5850,5853,5863,5890,5905,5932,5952,5953,5956,5970,5972,5973,5975,5988,5989,5992,5994,5997,5998,6012,6018,6019,6020,6023,6025,6067,6077,6086,6121,6123,6125,6127,6137,6139,6142,6148,6150,6154,6157,6165,6172,6173,6174,6180,6206,6213,6220,6256,6257,6261,6262,6263,6264,6265,6266,6267,6274,6311,6312,6321,6341,6342,6367,6371,6382,6383,6391,6422,6423,6438,6460,6461,6480,6483,6484,6530,6538,6563,6604,6620,6629,6638,6639,6640,6641,6663,6664,6670,6682,6685,6688,6690,6691,6692,6694,6708,6721,6723,6724,6735,6738,6795,6808,6810,6816,6830,6833,6834,6871,6886,6914,6947,6997,7028,7085,7113,7116,7174,7186,7253,7255,7270,7280,7283,7284,7302,7308,7310,7363,7373,7379,7382,7395,7440,7443,7447,7494,7495,7513,7576,7583,7602,7626,7648,7662,7678,7687,7695,7724,7726,7728,7736,7780,7790,7815,7873,7905,7939,7984,7999,8087,8135,8154,8178,8197,8219,8318,8320,8326,8346,8350,8364,8385,8396,8398,8410,8416,8420,8444,8459,8460,8471,8472,8473,8479,8480,8485,8486,8487,8488,8489,8507,8508,8509,8517,8529,8531,8545,8547,8553,8558,8579,8580,8609,8622,8626,8644,8665,8666,8668,8669,8679,8680,8702,8711,8718,8719,8720,8721,8744,8745,8756,8792,8798,8802,8815,8818,8820,8821,8828,8837,8902,8931,8932,8933,8947,8961,8967,8994,8995,8996,8997,8998,9001,9038,9041,9065,9099,9109,9110,9120,9130,9131,9145,9155,9157,9176,9198,9259,9297,9298,9299,9325,9326,9343,9360,9367,9378,9401,9419,9429,9430,9431,9432,9433,9448,9453,9488,9489,9495,9496,9532,9533,9558,9582,9584,9585,9600,9606,9630,9659,9706,9743,9756,9758,9762,9763,9765,9774,9775,9795,9800,9821,9826,9897,9973,9974,10025,2,8,9,4506,4522,4553,4554,4556,4580,4588,4589,4600,4647,4649,4692,4720,4812,4813,4829,4848,4904,4907,4908,4911,4912,4924,4934,4946,4947,4957,4967,4978,4979,4997,5002,5003,5004,5005,5006,5014,5017,5025,5089,5100,5131,5141,5146,5164,5182,5189,5190,5192,5197,5212,5214,5215,5222,5230,5231,5244,5245,5246,5247,5249,5250,5255,5256,5257,5258,5287,5288,5289,5297,5298,5299,5300,5330,5346,5348,5350,5387,5389,5390,5392,5393,5395,5396,5398,5407,5412,5414,5416,5417,5418,5419,5420,5421,5428,5438,5441,5452,5464,5465,5468,5478,5481,5482,5483,5508,5518,5532,5533,5542,5543,5545,5547,5551,5585,5589,5591,5649,5684,5685,5698,5701,5704,5705,5706,5707,5715,5719,5729,5730,5732,5733,5741,5762,5797,5810,5811,5812,5816,5826,5840,5844,5845,5846,5849,5865,5876,5877,5907,5908,5912,5934,5938,5941,5959,5964,5965,5990,5993,6001,6008,6010,6017,6021,6029,6030,6031,6032,6070,6071,6087,6141,6175,6177,6178,6202,6203,6205,6209,6210,6216,6230,6249,6269,6270,6275,6287,6288,6291,6304,6325,6330,6332,6346,6347,6351,6353,6354,6355,6357,6359,6360,6361,6369,6376,6377,6378,6379,6385,6387,6394,6431,6437,6452,6455,6456,6457,6495,6497,6499,6504,6505,6516,6519,6534,6559,6560,6561,6562,6573,6577,6594,6598,6621,6642,6658,6659,6660,6665,6678,6700,6702,6704,6706,6709,6710,6717,6719,6732,6740,6780,6783,6784,6800,6801,6802,6803,6823,6824,6842,6869,6891,6901,6903,6904,6906,6908,6909,6943,6944,6945,6950,6951,6953,6955,6956,6957,6979,6987,6988,7000,7010,7052,7061,7067,7075,7086,7091,7093,7099,7107,7120,7137,7154,7156,7166,7172,7233,7235,7236,7237,7245,7246,7252,7254,7279,7324,7343,7360,7376,7377,7394,7422,7426,7451,7478,7496,7499,7500,7510,7528,7529,7531,7533,7535,7537,7538,7539,7591,7592,7625,7627,7628,7629,7635,7654,7663,7674,7679,7685,7686,7692,7702,7703,7705,7734,7761,7791,7828,7829,7876,7883,7884,7906,7907,7926,7927,7992,7993,7994,8014,8015,8049,8053,8057,8066,8080,8107,8111,8117,8130,8149,8155,8177,8217,8247,8259,8276,8279,8308,8335,8399,8400,8403,8404,8421,8511,8512,8513,8514,8537,8561,8583,8625,8643,8696,8737,8740,8753,8790,8808,8824,8825,8840,8841,8969,8974,8992,9008,9028,9030,9033,9036,9039,9040,9052,9053,9076,9149,9184,9185,9250,9256,9290,9301,9305,9309,9310,9324,9348,9359,9368,9369,9371,9373,9400,9516,9595,9733,9734,9804,9874,9954,9965,9970,3,2549,2561,2562,2564,2566,2567,2568,2573,2574,2575,2579,2581,2582,2583,2594,2596,2597,2598,2602,2603,2604,2605,2607,2608,2609,2613,2614,2615,2616,2617,2622,2625,2626,2632,2636,2640,2641,2643,2644,2647,2651,2653,2655,2658,2670,2672,2704,2706,2707,2709,2711,2729,2730,2740,2747,2750,2751,2752,2753,2772,2790,2791,2799,2800,5179,5355,5361,5362,5439,5531,5560,5592,5608,5614,5616,5677,5678,5679,5680,5696,5731,5860,5906,5931,5967,6002,6006,6155,6162,6200,6201,6222,6224,6226,6232,6233,6234,6235,6236,6237,6238,6239,6240,6327,6401,6402,6493,6528,6529,6570,6571,6718,6731,6792,6813,6814,6818,6843,6867,6876,6878,6882,6925,6948,6949,6965,6966,6968,6999,7046,7047,7143,7212,7213,7214,7215,7231,7271,7285,7329,7330,7339,7348,7350,7362,7397,7398,7399,7400,7545,7546,7552,7553,7555,7557,7633,7767,7770,7772,7773,7788,7826,7903,7947,8001,8020,8021,8093,8190,8257,8258,8260,8292,8296,8331,8360,8361,8452,8453,8454,8455,8587,8804,8805,8865,8880,8934,8935,9049,9080,9103,9133,9164,9346,9590,9772,9829,9832,5502,5763,5764,5924,6309,6310,6404,6424,6425,6812,6866,7084,8245,8447,8524,8730,8891,8892,8957,8958,9200,9201,9202,9203,9402,9653,9830,9953,9961,10014,10015,6384,7325,7587,7588,8352,8353,8777,8791,9654,10013,4521,4558,4559,4560,4615,4623,4752,4766,4767,4795,4796,4823,4881,4883,4941,5055,5083,5117,5118,5120,5125,5127,5128,5153,5221,5243,5376,5444,5556,5557,5581,5582,5586,5621,5644,5646,5654,5660,5744,5823,5882,5926,5949,5971,6022,6068,6144,6268,6435,6474,6650,6651,6809,6879,6918,7089,7331,7405,7740,7743,7917,7919,7920,8962,9111,9174,9751,9752,4772,4780,4971,5282,5886,5899,5920,5936,6000,6039,6140,6199,6687])). % 174.01/173.95 cnf(13317,plain, % 174.01/173.95 (~P1(f777(f777(f182(f858(x133171,f858(x133172,a845))),x133173),x133174))), % 174.01/173.95 inference(rename_variables,[],[4482])). % 174.01/173.95 cnf(13322,plain, % 174.01/173.95 (~E(f777(f777(f142(x133221),x133222),x133223),x133223)), % 174.01/173.95 inference(rename_variables,[],[4401])). % 174.01/173.95 cnf(13325,plain, % 174.01/173.95 (E(f40(x133251,x133252,x133253,x133254,x133255,x133256,x133257,x133258,x133259,a27),x133252)), % 174.01/173.95 inference(rename_variables,[],[4342])). % 174.01/173.95 cnf(13330,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),x133301),f777(f777(f85(a851),x133301),x133301)))), % 174.01/173.95 inference(rename_variables,[],[3456])). % 174.01/173.95 cnf(13333,plain, % 174.01/173.95 (~P1(f777(f777(f336(f857(x133331,x133331)),x133332),f262(x133331,f182(f858(x133331,a845)))))), % 174.01/173.95 inference(rename_variables,[],[10763])). % 174.01/173.95 cnf(13344,plain, % 174.01/173.95 (P1(f777(f777(f235(a851),x133441),f777(a116,f777(f777(f84(a851),x133442),x133441))))), % 174.01/173.95 inference(rename_variables,[],[3632])). % 174.01/173.95 cnf(13351,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),x133511),x133511))), % 174.01/173.95 inference(rename_variables,[],[3186])). % 174.01/173.95 cnf(13356,plain, % 174.01/173.95 (~P1(f777(f777(f336(x133561),x133562),f182(f858(x133561,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(13359,plain, % 174.01/173.95 (~E(f777(f777(f142(x133591),x133592),x133593),x133593)), % 174.01/173.95 inference(rename_variables,[],[4401])). % 174.01/173.95 cnf(13379,plain, % 174.01/173.95 (E(f777(x133791,f704(f777(x133791,x133792),f777(f229(x133793),x133792),x133791,x133794,x133793)),f777(x133791,x133792))), % 174.01/173.95 inference(rename_variables,[],[10933])). % 174.01/173.95 cnf(13384,plain, % 174.01/173.95 (~E(f777(f777(f142(x133841),x133842),x133843),x133843)), % 174.01/173.95 inference(rename_variables,[],[4401])). % 174.01/173.95 cnf(13387,plain, % 174.01/173.95 (~P1(f777(f777(f336(x133871),x133872),f182(f858(x133871,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(13398,plain, % 174.01/173.95 (~P1(f777(f777(f336(x133981),x133982),f182(f858(x133981,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(13405,plain, % 174.01/173.95 (P1(f777(f777(f336(x134051),f777(x134052,x134053)),f777(f305(x134054,x134051,x134052),f241(f858(x134054,a845)))))), % 174.01/173.95 inference(rename_variables,[],[3789])). % 174.01/173.95 cnf(13409,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x134091,a845)),x134092),f777(f777(f304(x134091),x134093),x134092)))), % 174.01/173.95 inference(rename_variables,[],[3627])). % 174.01/173.95 cnf(13425,plain, % 174.01/173.95 (P1(f777(f777(f234(a3),x134251),x134251))), % 174.01/173.95 inference(rename_variables,[],[3187])). % 174.01/173.95 cnf(13428,plain, % 174.01/173.95 (~P1(f777(f777(f336(f857(x134281,x134281)),x134282),f262(x134281,f182(f858(x134281,a845)))))), % 174.01/173.95 inference(rename_variables,[],[10763])). % 174.01/173.95 cnf(13436,plain, % 174.01/173.95 (~E(f777(a116,x134361),f4(a851))), % 174.01/173.95 inference(rename_variables,[],[4379])). % 174.01/173.95 cnf(13439,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x134391,a845)),x134392),x134392))), % 174.01/173.95 inference(rename_variables,[],[3485])). % 174.01/173.95 cnf(13447,plain, % 174.01/173.95 (~P1(f777(f777(f234(a851),f777(a116,x134471)),x134471))), % 174.01/173.95 inference(rename_variables,[],[4464])). % 174.01/173.95 cnf(13450,plain, % 174.01/173.95 (~P1(f777(f777(f235(a851),f777(f777(f84(a851),x134501),x134502)),x134502))), % 174.01/173.95 inference(rename_variables,[],[4479])). % 174.01/173.95 cnf(13453,plain, % 174.01/173.95 (~P1(f777(f777(f336(x134531),x134532),f777(f307(x134531,x134533,x134534),f182(f858(x134533,a845)))))), % 174.01/173.95 inference(rename_variables,[],[10766])). % 174.01/173.95 cnf(13458,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),x134581),f777(f777(f85(a851),x134581),x134581)))), % 174.01/173.95 inference(rename_variables,[],[3456])). % 174.01/173.95 cnf(13465,plain, % 174.01/173.95 (~P1(f777(f777(f336(x134651),x134652),f182(f858(x134651,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(13470,plain, % 174.01/173.95 (~E(f777(f777(f142(x134701),x134702),x134703),x134703)), % 174.01/173.95 inference(rename_variables,[],[4401])). % 174.01/173.95 cnf(13480,plain, % 174.01/173.95 (~P1(f777(f777(f336(a851),x134801),f777(f259(a851),f4(a851))))), % 174.01/173.95 inference(rename_variables,[],[11571])). % 174.01/173.95 cnf(13483,plain, % 174.01/173.95 (P1(f777(f777(f235(a3),f777(f777(f5(a3),x134831),f82(a3))),x134831))), % 174.01/173.95 inference(rename_variables,[],[10571])). % 174.01/173.95 cnf(13488,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),x134881),f777(f777(f85(a851),x134881),x134881)))), % 174.01/173.95 inference(rename_variables,[],[3456])). % 174.01/173.95 cnf(13494,plain, % 174.01/173.95 (~E(f777(f777(f142(x134941),x134942),x134943),x134943)), % 174.01/173.95 inference(rename_variables,[],[4401])). % 174.01/173.95 cnf(13500,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),f4(a851)),x135001))), % 174.01/173.95 inference(rename_variables,[],[3208])). % 174.01/173.95 cnf(13505,plain, % 174.01/173.95 (E(f777(x135051,f704(f777(x135051,x135052),f777(f229(x135053),x135052),x135051,x135054,x135053)),f777(x135051,x135052))), % 174.01/173.95 inference(rename_variables,[],[10933])). % 174.01/173.95 cnf(13515,plain, % 174.01/173.95 (~E(f777(a29,x135151),f37(x135152,x135153))), % 174.01/173.95 inference(rename_variables,[],[4385])). % 174.01/173.95 cnf(13523,plain, % 174.01/173.95 (~E(f777(a116,x135231),f4(a851))), % 174.01/173.95 inference(rename_variables,[],[4379])). % 174.01/173.95 cnf(13526,plain, % 174.01/173.95 (~P1(f777(f777(f336(x135261),x135262),f182(f858(x135261,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(13536,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),x135361),x135361))), % 174.01/173.95 inference(rename_variables,[],[3186])). % 174.01/173.95 cnf(13539,plain, % 174.01/173.95 (~E(f777(f777(f142(x135391),x135392),x135393),x135393)), % 174.01/173.95 inference(rename_variables,[],[4401])). % 174.01/173.95 cnf(13544,plain, % 174.01/173.95 (P1(f777(f777(f235(a3),f777(f777(f5(a3),x135441),f82(a3))),x135441))), % 174.01/173.95 inference(rename_variables,[],[10571])). % 174.01/173.95 cnf(13563,plain, % 174.01/173.95 (~P1(f777(f777(f336(f857(x135631,x135631)),x135632),f262(x135631,f182(f858(x135631,a845)))))), % 174.01/173.95 inference(rename_variables,[],[10763])). % 174.01/173.95 cnf(13570,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),x135701),f777(a116,x135701)))), % 174.01/173.95 inference(rename_variables,[],[10200])). % 174.01/173.95 cnf(13580,plain, % 174.01/173.95 (~P1(f777(f777(f336(x135801),x135802),f182(f858(x135801,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(13594,plain, % 174.01/173.95 (E(f40(x135941,x135942,x135943,x135944,x135945,x135946,x135947,x135948,x135949,a27),x135942)), % 174.01/173.95 inference(rename_variables,[],[4342])). % 174.01/173.95 cnf(13618,plain, % 174.01/173.95 (P1(f777(f777(f336(x136181),f777(x136182,x136183)),f777(f305(x136184,x136181,x136182),f241(f858(x136184,a845)))))), % 174.01/173.95 inference(rename_variables,[],[3789])). % 174.01/173.95 cnf(13621,plain, % 174.01/173.95 (~E(f777(f777(f142(x136211),x136212),x136213),x136213)), % 174.01/173.95 inference(rename_variables,[],[4401])). % 174.01/173.95 cnf(13650,plain, % 174.01/173.95 (P1(f777(f777(f235(a3),f777(f777(f5(a3),x136501),f82(a3))),x136501))), % 174.01/173.95 inference(rename_variables,[],[10571])). % 174.01/173.95 cnf(13655,plain, % 174.01/173.95 (E(f40(x136551,x136552,x136553,x136554,x136555,x136556,x136557,x136558,x136559,a27),x136552)), % 174.01/173.95 inference(rename_variables,[],[4342])). % 174.01/173.95 cnf(13658,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x136581,a845)),x136582),x136582))), % 174.01/173.95 inference(rename_variables,[],[3485])). % 174.01/173.95 cnf(13668,plain, % 174.01/173.95 (E(f777(x136681,f704(f777(x136681,x136682),f777(f229(x136683),x136682),x136681,x136684,x136683)),f777(x136681,x136682))), % 174.01/173.95 inference(rename_variables,[],[10933])). % 174.01/173.95 cnf(13673,plain, % 174.01/173.95 (~P1(f777(f777(f336(a851),x136731),f777(f259(a851),f4(a851))))), % 174.01/173.95 inference(rename_variables,[],[11571])). % 174.01/173.95 cnf(13678,plain, % 174.01/173.95 (~P39(f38(x136781,f38(x136782,f38(f38(f777(a29,x136783),x136784),x136785))),x136786,f4(a851),x136787)), % 174.01/173.95 inference(rename_variables,[],[10971])). % 174.01/173.95 cnf(13709,plain, % 174.01/173.95 (P1(f777(f777(f234(a851),f54(a851,x137091,x137092)),x137091))), % 174.01/173.95 inference(rename_variables,[],[3639])). % 174.01/173.95 cnf(13712,plain, % 174.01/173.95 (~P1(f777(f777(f234(a851),f777(a116,x137121)),x137121))), % 174.01/173.95 inference(rename_variables,[],[4464])). % 174.01/173.95 cnf(13746,plain, % 174.01/173.95 (E(f40(x137461,x137462,x137463,x137464,x137465,x137466,x137467,x137468,x137469,a27),x137462)), % 174.01/173.95 inference(rename_variables,[],[4342])). % 174.01/173.95 cnf(13749,plain, % 174.01/173.95 (~P1(f777(f777(f182(f858(x137491,f858(x137492,a845))),x137493),x137494))), % 174.01/173.95 inference(rename_variables,[],[4482])). % 174.01/173.95 cnf(13779,plain, % 174.01/173.95 (~P1(f777(f777(f336(a851),x137791),f777(f259(a851),f4(a851))))), % 174.01/173.95 inference(rename_variables,[],[11571])). % 174.01/173.95 cnf(13784,plain, % 174.01/173.95 (~P1(f777(f777(f336(x137841),x137842),f182(f858(x137841,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(13808,plain, % 174.01/173.95 (~P1(f777(f777(f336(a851),x138081),f777(f259(a851),f4(a851))))), % 174.01/173.95 inference(rename_variables,[],[11571])). % 174.01/173.95 cnf(13816,plain, % 174.01/173.95 (~P1(f777(f777(f234(a851),f777(a116,x138161)),x138161))), % 174.01/173.95 inference(rename_variables,[],[4464])). % 174.01/173.95 cnf(13836,plain, % 174.01/173.95 (~P1(f777(f777(f336(f857(x138361,x138361)),x138362),f262(x138361,f182(f858(x138361,a845)))))), % 174.01/173.95 inference(rename_variables,[],[10763])). % 174.01/173.95 cnf(13845,plain, % 174.01/173.95 (E(f40(x138451,x138452,x138453,x138454,x138455,x138456,x138457,x138458,x138459,a27),x138452)), % 174.01/173.95 inference(rename_variables,[],[4342])). % 174.01/173.95 cnf(13850,plain, % 174.01/173.95 (~P1(f777(f777(f336(a851),x138501),f777(f259(a851),f4(a851))))), % 174.01/173.95 inference(rename_variables,[],[11571])). % 174.01/173.95 cnf(13857,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x138571,a845)),f777(f160(x138571),f153(x138571,x138572,x138573))),f777(f160(x138571),x138573)))), % 174.01/173.95 inference(rename_variables,[],[3876])). % 174.01/173.95 cnf(13869,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x138691,a845)),f777(f160(x138691),f153(x138691,x138692,x138693))),f777(f160(x138691),x138693)))), % 174.01/173.95 inference(rename_variables,[],[3876])). % 174.01/173.95 cnf(13884,plain, % 174.01/173.95 (~P1(f777(f777(f336(f857(x138841,x138841)),x138842),f262(x138841,f182(f858(x138841,a845)))))), % 174.01/173.95 inference(rename_variables,[],[10763])). % 174.01/173.95 cnf(13887,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x138871,a845)),f777(f160(x138871),f153(x138871,x138872,x138873))),f777(f160(x138871),x138873)))), % 174.01/173.95 inference(rename_variables,[],[3876])). % 174.01/173.95 cnf(13905,plain, % 174.01/173.95 (~P1(f777(f777(f336(x139051),x139052),f182(f858(x139051,a845))))), % 174.01/173.95 inference(rename_variables,[],[4467])). % 174.01/173.95 cnf(13911,plain, % 174.01/173.95 (P1(f777(f777(f235(a3),f777(f777(f5(a3),x139111),f82(a3))),x139111))), % 174.01/173.95 inference(rename_variables,[],[10571])). % 174.01/173.95 cnf(13948,plain, % 174.01/173.95 (P1(f777(f777(f234(f858(x139481,a845)),x139482),f777(f777(f105(f858(x139481,a845)),x139483),f241(f858(x139481,a845)))))), % 174.01/173.95 inference(rename_variables,[],[10973])). % 174.01/173.95 cnf(13988,plain, % 174.01/173.95 ($false), % 174.01/173.95 inference(scs_inference,[],[3216,3214,3772,3964,4481,3186,13351,13536,4452,3164,3818,3263,4483,3281,3634,4467,13356,13387,13398,13465,13526,13580,13784,13905,3269,3876,13857,13869,13887,3789,13405,13618,3014,3290,4385,13515,4379,13436,13523,4440,4401,13322,13359,13384,13470,13494,13539,13621,4465,4398,3828,3187,13425,3639,13709,3208,13500,3500,3627,13409,3485,13439,13658,3631,3728,3343,3456,13330,13458,13488,4069,3632,13344,3633,4341,4342,13325,13594,13655,13746,13845,3129,3545,4484,4485,4487,4451,4464,13447,13712,13816,4477,4482,13317,13749,4479,13450,4480,3437,10908,12878,10400,11009,12606,10200,13570,12515,11640,11540,12764,3183,12271,11134,13075,12071,12062,13182,10434,11692,10415,11336,10869,12273,12306,10973,13948,13005,10716,10571,13483,13544,13650,13911,11040,10933,13379,13505,13668,12786,10750,10251,10508,3246,3221,11022,10517,12777,10521,12003,11996,13127,12105,11569,11571,13480,13673,13779,13808,13850,11628,10515,12513,10921,10763,13333,13428,13563,13836,13884,10766,13453,10503,10615,11856,13111,12317,12252,10971,13678,10965,2969,3729,3736,9,6685,10025,4798,6263,4614,4959,5084,6682,9974,9584,6834,8486,5625,8385,5581,5648,6997,6220,8931,4835,6018,8902,5485,6265,5143,5153,7310,9433,8410,5216,5890,9488,9752,8472,7494,8154,9774,5271,5368,8398,2,9001,5882,6808,8479,5097,5499,5793,6025,8420,9582,4565,5718,9155,6125,9419,5106,7085,9111,6563,6810,8350,8820,9297,6077,5207,5622,6422,9495,9532,5402,6620,7984,5541,4503,5489,6137,6639,4560,8459,4883,9325,9496,8,5120,6947,8558,9826,6830,5975,5470,8837,4693,5220,6321,7331,9775,6121,5335,6020,5227,9706,5682,5970,7284,5461,5561,4921,6664,8471,5708,7270,7583,6708,4492,4927,5805,5221,5144,6144,9176,5121,7648,7724,9157,5203,5430,5932,7602,5193,6871,8815,5352,6483,6914,8473,9041,5108,5703,6157,6180,7939,9821,8668,4881,4568,8508,8720,8798,8997,9751,5075,5234,5293,5444,6086,5582,8609,5380,5573,7726,5815,9453,6382,5309,5501,5202,5641,8998,5076,5306,5850,5863,8996,6638,8933,8485,9429,4497,4797,5638,5118,5291,5744,7280,5426,5953,7373,8326,7815,9431,5998,6651,8545,4858,4954,5471,5575,6019,7728,8994,5972,5781,7405,7919,6735,9198,4559,5789,6268,9120,8679,7363,6139,7174,7255,8792,5007,8802,5302,4960,8962,9600,9765,7917,8531,9378,5458,5134,5621,6886,9897,9367,7382,6724,7379,9973,8744,7283,5853,6694,6068,5620,6795,8488,8644,5630,5702,6723,9259,6341,9360,9174,5225,5239,5926,6604,5971,8197,5973,7116,8719,7999,5055,5989,6670,6641,5498,6435,8665,4766,5457,9762,6206,7495,8489,7695,8460,4596]), % 174.01/173.95 ['proof']). % 174.01/173.95 % SZS output end Proof % 174.01/173.95 % Total time :158.910000s %------------------------------------------------------------------------------