%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW362+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n020.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 18:08:25 EDT 2024 % Result : Theorem 112.26s 112.08s % Output : CNFRefutation 112.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SWW362+1 : TPTP v8.2.0. Released v5.2.0. % 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.14/0.36 % Computer : n020.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Wed Jun 19 05:32:24 EDT 2024 % 0.14/0.36 % CPUTime : % 0.57/0.61 start to proof:theBenchmark % 111.86/111.92 %------------------------------------------- % 111.86/111.92 % File :CSE---1.7 % 111.86/111.92 % Problem :theBenchmark % 111.86/111.92 % Transform :cnf % 111.86/111.92 % Format :tptp:raw % 111.86/111.92 % Command :java -jar mcs_scs.jar %d %s % 111.86/111.92 % 111.86/111.92 % Result :Theorem 82.930000s % 111.86/111.92 % Output :CNFRefutation 82.930000s % 111.86/111.92 %------------------------------------------- % 111.86/111.93 %------------------------------------------------------------------------------ % 111.86/111.93 % File : SWW362+1 : TPTP v8.2.0. Released v5.2.0. % 111.86/111.93 % Domain : Software Verification % 111.86/111.93 % Problem : Hoare's Logic with Procedures 435429, 5000 axioms selected % 111.86/111.93 % Version : Especial. % 111.86/111.93 % English : % 111.86/111.93 % 111.86/111.93 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 111.86/111.93 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 111.86/111.93 % Source : [Bla11] % 111.86/111.93 % Names : hoare_435429.5000.p [Bla11] % 111.86/111.93 % 111.86/111.93 % Status : ContradictoryAxioms % 111.86/111.93 % Rating : 0.61 v8.1.0, 0.64 v7.5.0, 0.72 v7.4.0, 0.83 v7.3.0, 0.72 v7.1.0, 0.74 v7.0.0, 0.77 v6.4.0, 0.73 v6.3.0, 0.71 v6.2.0, 0.84 v6.1.0, 0.87 v6.0.0, 0.83 v5.5.0, 0.89 v5.4.0, 0.93 v5.3.0, 0.96 v5.2.0 % 111.86/111.93 % Syntax : Number of formulae : 5227 (1637 unt; 0 def) % 111.86/111.93 % Number of atoms : 12826 (4422 equ) % 111.86/111.93 % Maximal formula atoms : 13 ( 2 avg) % 111.86/111.93 % Number of connectives : 8606 (1007 ~; 154 |; 739 &) % 111.86/111.93 % ( 911 <=>;5795 =>; 0 <=; 0 <~>) % 111.86/111.93 % Maximal formula depth : 22 ( 6 avg) % 111.86/111.93 % Maximal term depth : 19 ( 2 avg) % 111.86/111.93 % Number of predicates : 150 ( 149 usr; 0 prp; 1-6 aty) % 111.86/111.93 % Number of functors : 377 ( 377 usr; 50 con; 0-7 aty) % 111.86/111.93 % Number of variables : 16551 (16397 !; 154 ?) % 111.86/111.93 % SPC : FOF_CAX_RFO_SEQ % 111.86/111.93 % 111.86/111.93 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 111.86/111.93 % 2011-03-01 12:33:51 % 111.86/111.93 %------------------------------------------------------------------------------ % 111.86/111.93 %----Relevant facts (4983) % 111.86/111.93 fof(fact_ext,axiom, % 111.86/111.93 ! [V_g_2,V_f_2] : % 111.86/111.93 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 111.86/111.93 => V_f_2 = V_g_2 ) ). % 111.86/111.93 % 111.86/111.93 fof(fact_assms_I1_J,axiom, % 111.86/111.93 ! [V_G_2,V_ts_2] : % 111.86/111.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),V_ts_2),V_G_2)) % 111.86/111.93 => v_P(V_G_2,V_ts_2) ) ). % 111.86/111.93 % 111.86/111.93 fof(fact_finite__imageI,axiom, % 111.86/111.93 ! [V_h_2,T_c,V_F_2,T_b] : % 111.86/111.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 111.86/111.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ). % 111.86/111.93 % 111.86/111.93 fof(fact_empty__subsetI,axiom, % 111.86/111.93 ! [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)) ). % 111.86/111.93 % 111.86/111.93 fof(fact_finite_OinsertI,axiom, % 111.86/111.93 ! [V_a_2,V_A_2,T_b] : % 111.86/111.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ). % 111.86/111.93 % 111.86/111.93 fof(fact_finite_OemptyI,axiom, % 111.86/111.93 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 111.86/111.93 % 111.86/111.93 fof(fact_image__eqI,axiom, % 111.86/111.93 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] : % 111.86/111.93 ( V_b_2 = hAPP(V_f_2,V_x_2) % 111.86/111.93 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 111.86/111.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_subsetD,axiom, % 111.86/111.94 ! [V_c_2,V_B_2,V_A_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 111.86/111.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_insertE,axiom, % 111.86/111.94 ! [V_A_2,V_b_2,V_a_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) % 111.86/111.94 => ( V_a_2 != V_b_2 % 111.86/111.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_insertCI,axiom, % 111.86/111.94 ! [V_b_2,V_B_2,V_a_2,T_b] : % 111.86/111.94 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 111.86/111.94 => V_a_2 = V_b_2 ) % 111.86/111.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_emptyE,axiom, % 111.86/111.94 ! [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)))) ). % 111.86/111.94 % 111.86/111.94 fof(fact_finite__surj,axiom, % 111.86/111.94 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.94 => ( 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))) % 111.86/111.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_subset__singletonD,axiom, % 111.86/111.94 ! [V_x_2,V_A_2,T_b] : % 111.86/111.94 ( 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))))) % 111.86/111.94 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.86/111.94 | 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))) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_equalityCE,axiom, % 111.86/111.94 ! [V_c_2,T_b,V_B_2,V_A_2] : % 111.86/111.94 ( V_A_2 = V_B_2 % 111.86/111.94 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 111.86/111.94 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) % 111.86/111.94 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 111.86/111.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_equalityI,axiom, % 111.86/111.94 ! [V_B_2,V_A_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 111.86/111.94 => V_A_2 = V_B_2 ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_eq__mem__trans,axiom, % 111.86/111.94 ! [V_A_2,T_b,V_b_2,V_a_2] : % 111.86/111.94 ( V_a_2 = V_b_2 % 111.86/111.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 111.86/111.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_eqelem__imp__iff,axiom, % 111.86/111.94 ! [V_A_2,T_b,V_y_2,V_x_2] : % 111.86/111.94 ( V_x_2 = V_y_2 % 111.86/111.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.94 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_eqset__imp__iff,axiom, % 111.86/111.94 ! [V_x_2,T_b,V_B_2,V_A_2] : % 111.86/111.94 ( V_A_2 = V_B_2 % 111.86/111.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.94 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_mem__def,axiom, % 111.86/111.94 ! [V_A_2,V_x_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.94 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_finite__code,axiom, % 111.86/111.94 ! [V_A_2,T_b] : % 111.86/111.94 ( class_Finite__Set_Ofinite(T_b) % 111.86/111.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_finite,axiom, % 111.86/111.94 ! [V_A_2,T_b] : % 111.86/111.94 ( class_Finite__Set_Ofinite(T_b) % 111.86/111.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_insert__code,axiom, % 111.86/111.94 ! [V_x_2,V_A_2,V_y_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) % 111.86/111.94 <=> ( V_y_2 = V_x_2 % 111.86/111.94 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_insert__commute,axiom, % 111.86/111.94 ! [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)) ). % 111.86/111.94 % 111.86/111.94 fof(fact_insert__absorb2,axiom, % 111.86/111.94 ! [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) ). % 111.86/111.94 % 111.86/111.94 fof(fact_equalityE,axiom, % 111.86/111.94 ! [T_b,V_B_2,V_A_2] : % 111.86/111.94 ( V_A_2 = V_B_2 % 111.86/111.94 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_subset__trans,axiom, % 111.86/111.94 ! [V_C_2,V_B_2,V_A_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 111.86/111.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_equalityD2,axiom, % 111.86/111.94 ! [T_b,V_B_2,V_A_2] : % 111.86/111.94 ( V_A_2 = V_B_2 % 111.86/111.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_equalityD1,axiom, % 111.86/111.94 ! [T_b,V_B_2,V_A_2] : % 111.86/111.94 ( V_A_2 = V_B_2 % 111.86/111.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_set__eq__subset,axiom, % 111.86/111.94 ! [T_b,V_B_2,V_A_2] : % 111.86/111.94 ( V_A_2 = V_B_2 % 111.86/111.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.94 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_subset__refl,axiom, % 111.86/111.94 ! [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)) ). % 111.86/111.94 % 111.86/111.94 fof(fact_equals0D,axiom, % 111.86/111.94 ! [V_a_2,T_b,V_A_2] : % 111.86/111.94 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.86/111.94 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_empty__iff,axiom, % 111.86/111.94 ! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 111.86/111.94 % 111.86/111.94 fof(fact_ex__in__conv,axiom, % 111.86/111.94 ! [V_A_2,T_b] : % 111.86/111.94 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.86/111.94 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_all__not__in__conv,axiom, % 111.86/111.94 ! [V_A_2,T_b] : % 111.86/111.94 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.86/111.94 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_insert__absorb,axiom, % 111.86/111.94 ! [V_A_2,V_a_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.86/111.94 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_insertI2,axiom, % 111.86/111.94 ! [V_b_2,V_B_2,V_a_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 111.86/111.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_insert__ident,axiom, % 111.86/111.94 ! [V_B_2,V_A_2,V_x_2,T_b] : % 111.86/111.94 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 111.86/111.94 => ( 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) % 111.86/111.94 <=> V_A_2 = V_B_2 ) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_insert__iff,axiom, % 111.86/111.94 ! [V_A_2,V_b_2,V_a_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) % 111.86/111.94 <=> ( V_a_2 = V_b_2 % 111.86/111.94 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_insertI1,axiom, % 111.86/111.94 ! [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))) ). % 111.86/111.94 % 111.86/111.94 fof(fact_set__mp,axiom, % 111.86/111.94 ! [V_x_2,V_B_2,V_A_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_set__rev__mp,axiom, % 111.86/111.94 ! [V_B_2,V_A_2,V_x_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_in__mono,axiom, % 111.86/111.94 ! [V_x_2,V_B_2,V_A_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_rev__image__eqI,axiom, % 111.86/111.94 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.94 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 111.86/111.94 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_imageI,axiom, % 111.86/111.94 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.94 => 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))) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_image__iff,axiom, % 111.86/111.94 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 111.86/111.94 <=> ? [B_x] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 111.86/111.94 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_finite_Oequations_I1_J,axiom, % 111.86/111.94 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 111.86/111.94 % 111.86/111.94 fof(fact_singleton__inject,axiom, % 111.86/111.94 ! [V_b_2,V_a_2,T_b] : % 111.86/111.94 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) % 111.86/111.94 => V_a_2 = V_b_2 ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_doubleton__eq__iff,axiom, % 111.86/111.94 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 111.86/111.94 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 111.86/111.94 <=> ( ( V_a_2 = V_c_2 % 111.86/111.94 & V_b_2 = V_d_2 ) % 111.86/111.94 | ( V_a_2 = V_d_2 % 111.86/111.94 & V_b_2 = V_c_2 ) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_insert__not__empty,axiom, % 111.86/111.94 ! [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)) ). % 111.86/111.94 % 111.86/111.94 fof(fact_empty__not__insert,axiom, % 111.86/111.94 ! [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) ). % 111.86/111.94 % 111.86/111.94 fof(fact_finite__insert,axiom, % 111.86/111.94 ! [V_A_2,V_a_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) % 111.86/111.94 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_subset__empty,axiom, % 111.86/111.94 ! [V_A_2,T_b] : % 111.86/111.94 ( 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)))) % 111.86/111.94 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_image__is__empty,axiom, % 111.86/111.94 ! [V_A_2,V_f_2,T_b,T_c] : % 111.86/111.94 ( 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)) % 111.86/111.94 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_image__empty,axiom, % 111.86/111.94 ! [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)) ). % 111.86/111.94 % 111.86/111.94 fof(fact_empty__is__image,axiom, % 111.86/111.94 ! [V_A_2,V_f_2,T_c,T_b] : % 111.86/111.94 ( 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) % 111.86/111.94 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_finite__subset,axiom, % 111.86/111.94 ! [V_B_2,V_A_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 111.86/111.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_rev__finite__subset,axiom, % 111.86/111.94 ! [V_A_2,V_B_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 111.86/111.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 111.86/111.94 % 111.86/111.94 fof(fact_insert__mono,axiom, % 111.86/111.94 ! [V_a_2,V_D_2,V_C_2,T_b] : % 111.86/111.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) % 111.86/111.94 => 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))) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_subset__insertI2,axiom, % 111.86/111.95 ! [V_b_2,V_B_2,V_A_2,T_b] : % 111.86/111.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_subset__insertI,axiom, % 111.86/111.95 ! [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))) ). % 111.86/111.95 % 111.86/111.95 fof(fact_image__insert,axiom, % 111.86/111.95 ! [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)) ). % 111.86/111.95 % 111.86/111.95 fof(fact_image__mono,axiom, % 111.86/111.95 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 111.86/111.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.95 => 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))) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_subset__image__iff,axiom, % 111.86/111.95 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 111.86/111.95 ( 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))) % 111.86/111.95 <=> ? [B_AA] : % 111.86/111.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) % 111.86/111.95 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_singletonE,axiom, % 111.86/111.95 ! [V_a_2,V_b_2,T_b] : % 111.86/111.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 111.86/111.95 => V_b_2 = V_a_2 ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_singleton__iff,axiom, % 111.86/111.95 ! [V_a_2,V_b_2,T_b] : % 111.86/111.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 111.86/111.95 <=> V_b_2 = V_a_2 ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_subset__insert,axiom, % 111.86/111.95 ! [V_B_2,V_A_2,V_x_2,T_b] : % 111.86/111.95 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.95 => ( 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))) % 111.86/111.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_insert__subset,axiom, % 111.86/111.95 ! [V_B_2,V_A_2,V_x_2,T_b] : % 111.86/111.95 ( 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)) % 111.86/111.95 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 111.86/111.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_insert__image,axiom, % 111.86/111.95 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] : % 111.86/111.95 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.95 => 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) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_assms_I3_J,axiom, % 111.86/111.95 ! [V_G_2,V_c_2] : % 111.86/111.95 ( v_wt(V_c_2) % 111.86/111.95 => ( ! [B_x] : % 111.86/111.95 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_U)) % 111.86/111.95 => v_P(V_G_2,hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,B_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ) % 111.86/111.95 => v_P(V_G_2,hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_the__elem__eq,axiom, % 111.86/111.95 ! [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 ). % 111.86/111.95 % 111.86/111.95 fof(fact_order__refl,axiom, % 111.86/111.95 ! [V_x,T_a] : % 111.86/111.95 ( class_Orderings_Opreorder(T_a) % 111.86/111.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__one_Oinsert,axiom, % 111.86/111.95 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 111.86/111.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.95 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.86/111.95 => 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)) ) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_bot__apply,axiom, % 111.86/111.95 ! [V_x_2,T_c,T_b] : % 111.86/111.95 ( class_Orderings_Obot(T_b) % 111.86/111.95 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_le__funE,axiom, % 111.86/111.95 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 111.86/111.95 ( class_Orderings_Oord(T_c) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 111.86/111.95 => 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))) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_le__funD,axiom, % 111.86/111.95 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] : % 111.86/111.95 ( class_Orderings_Oord(T_c) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 111.86/111.95 => 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))) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_le__fun__def,axiom, % 111.86/111.95 ! [V_g_2,V_f_2,T_b,T_c] : % 111.86/111.95 ( class_Orderings_Oord(T_c) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 111.86/111.95 <=> ! [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))) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_bot__least,axiom, % 111.86/111.95 ! [V_x,T_a] : % 111.86/111.95 ( class_Orderings_Obot(T_a) % 111.86/111.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_assms_I2_J,axiom, % 111.86/111.95 ! [V_G_2,V_pn_2] : % 111.86/111.95 ( v_P(hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,V_pn_2)),V_G_2),hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(V_pn_2)))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) % 111.86/111.95 => v_P(V_G_2,hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,V_pn_2)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__one__idem_Osubset__idem,axiom, % 111.86/111.95 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 111.86/111.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.95 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 111.86/111.95 => 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) ) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_finite__subset__induct,axiom, % 111.86/111.95 ! [V_Pa_2,V_A_2,V_F_2,T_b] : % 111.86/111.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2)) % 111.86/111.95 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 111.86/111.95 => ( ! [B_a,B_F] : % 111.86/111.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 111.86/111.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F)) % 111.86/111.95 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 111.86/111.95 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) ) % 111.86/111.95 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_assms_I4_J,axiom, % 111.86/111.95 ! [V_pn_2] : % 111.86/111.95 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),v_U)) % 111.86/111.95 => v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(V_pn_2))) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__one__idem_Oidem,axiom, % 111.86/111.95 ! [V_x_2,V_F_2,V_f_2,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 111.86/111.95 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_linorder__linear,axiom, % 111.86/111.95 ! [V_y,V_x,T_a] : % 111.86/111.95 ( class_Orderings_Olinorder(T_a) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 111.86/111.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_order__eq__iff,axiom, % 111.86/111.95 ! [V_y_2,V_x_2,T_b] : % 111.86/111.95 ( class_Orderings_Oorder(T_b) % 111.86/111.95 => ( V_x_2 = V_y_2 % 111.86/111.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 111.86/111.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_order__eq__refl,axiom, % 111.86/111.95 ! [V_y,V_x,T_a] : % 111.86/111.95 ( class_Orderings_Opreorder(T_a) % 111.86/111.95 => ( V_x = V_y % 111.86/111.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_order__antisym__conv,axiom, % 111.86/111.95 ! [V_x_2,V_y_2,T_b] : % 111.86/111.95 ( class_Orderings_Oorder(T_b) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 111.86/111.95 <=> V_x_2 = V_y_2 ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_ord__eq__le__trans,axiom, % 111.86/111.95 ! [V_c,V_b,V_a,T_a] : % 111.86/111.95 ( class_Orderings_Oord(T_a) % 111.86/111.95 => ( V_a = V_b % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 111.86/111.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_xt1_I3_J,axiom, % 111.86/111.95 ! [V_c,V_b,V_a,T_a] : % 111.86/111.95 ( class_Orderings_Oorder(T_a) % 111.86/111.95 => ( V_a = V_b % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 111.86/111.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_ord__le__eq__trans,axiom, % 111.86/111.95 ! [V_c,V_b,V_a,T_a] : % 111.86/111.95 ( class_Orderings_Oord(T_a) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.86/111.95 => ( V_b = V_c % 111.86/111.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_xt1_I4_J,axiom, % 111.86/111.95 ! [V_c,V_a,V_b,T_a] : % 111.86/111.95 ( class_Orderings_Oorder(T_a) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 111.86/111.95 => ( V_b = V_c % 111.86/111.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_order__antisym,axiom, % 111.86/111.95 ! [V_y,V_x,T_a] : % 111.86/111.95 ( class_Orderings_Oorder(T_a) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 111.86/111.95 => V_x = V_y ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_order__trans,axiom, % 111.86/111.95 ! [V_z,V_y,V_x,T_a] : % 111.86/111.95 ( class_Orderings_Opreorder(T_a) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 111.86/111.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_xt1_I5_J,axiom, % 111.86/111.95 ! [V_x,V_y,T_a] : % 111.86/111.95 ( class_Orderings_Oorder(T_a) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 111.86/111.95 => V_x = V_y ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_xt1_I6_J,axiom, % 111.86/111.95 ! [V_z,V_x,V_y,T_a] : % 111.86/111.95 ( class_Orderings_Oorder(T_a) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 111.86/111.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_linorder__le__cases,axiom, % 111.86/111.95 ! [V_y,V_x,T_a] : % 111.86/111.95 ( class_Orderings_Olinorder(T_a) % 111.86/111.95 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 111.86/111.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__one_Osingleton,axiom, % 111.86/111.95 ! [V_x_2,V_F_2,V_f_2,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 111.86/111.95 => 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 ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__one__idem_Oin__idem,axiom, % 111.86/111.95 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 111.86/111.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.95 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 111.86/111.95 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 111.86/111.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.95 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.86/111.95 => 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)) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__one_Oclosed,axiom, % 111.86/111.95 ! [V_A_2,V_F_2,V_f_2,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 111.86/111.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.95 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.86/111.95 => ( ! [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)))))) % 111.86/111.95 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__one__idem_Ohom__commute,axiom, % 111.86/111.95 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 111.86/111.95 => ( ! [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)) % 111.86/111.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 111.86/111.95 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.86/111.95 => 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)) ) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__image__simple_Oinsert,axiom, % 111.86/111.95 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 111.86/111.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 111.86/111.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 111.86/111.95 => 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)) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__one_Oremove,axiom, % 111.86/111.95 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 111.86/111.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.95 => ( ( hAPP(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)) % 111.86/111.95 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 111.86/111.95 & ( hAPP(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)) % 111.86/111.95 => 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)))))) ) ) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 111.86/111.95 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 111.86/111.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) % 111.86/111.95 => 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) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 111.86/111.95 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 111.86/111.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 111.86/111.95 => 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)) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_finite__induct,axiom, % 111.86/111.95 ! [V_Pa_2,V_F_2,T_b] : % 111.86/111.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 111.86/111.95 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 111.86/111.95 => ( ! [B_x,B_F] : % 111.86/111.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) % 111.86/111.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F)) % 111.86/111.95 => ( hBOOL(hAPP(V_Pa_2,B_F)) % 111.86/111.95 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) ) % 111.86/111.95 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 111.86/111.95 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 111.86/111.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 111.86/111.95 => 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) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__one_Oinsert__remove,axiom, % 111.86/111.95 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 111.86/111.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.95 => ( ( hAPP(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)) % 111.86/111.95 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 111.86/111.95 & ( hAPP(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)) % 111.86/111.95 => 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)))))) ) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_folding__one_Oeq__fold_H,axiom, % 111.86/111.95 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] : % 111.86/111.95 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 111.86/111.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.95 => 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) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_subset__insert__iff,axiom, % 111.86/111.95 ! [V_B_2,V_x_2,V_A_2,T_b] : % 111.86/111.95 ( 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))) % 111.86/111.95 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.95 => 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)) ) % 111.86/111.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 111.86/111.95 % 111.86/111.95 fof(fact_diff__single__insert,axiom, % 111.86/111.95 ! [V_B_2,V_x_2,V_A_2,T_b] : % 111.86/111.95 ( 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)) % 111.86/111.95 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_DiffE,axiom, % 111.86/111.96 ! [V_B_2,V_A_2,V_c_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 111.86/111.96 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_DiffI,axiom, % 111.86/111.96 ! [V_B_2,V_A_2,V_c_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_finite__Diff,axiom, % 111.86/111.96 ! [V_B_2,V_A_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => 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))) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_Diff__idemp,axiom, % 111.86/111.96 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ). % 111.86/111.96 % 111.86/111.96 fof(fact_folding__image__simple__idem_Oidem,axiom, % 111.86/111.96 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 111.86/111.96 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_DiffD2,axiom, % 111.86/111.96 ! [V_B_2,V_A_2,V_c_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 111.86/111.96 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_DiffD1,axiom, % 111.86/111.96 ! [V_B_2,V_A_2,V_c_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_Diff__iff,axiom, % 111.86/111.96 ! [V_B_2,V_A_2,V_c_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 111.86/111.96 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 111.86/111.96 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fold__empty,axiom, % 111.86/111.96 ! [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 ). % 111.86/111.96 % 111.86/111.96 fof(fact_Diff__cancel,axiom, % 111.86/111.96 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 111.86/111.96 % 111.86/111.96 fof(fact_Diff__empty,axiom, % 111.86/111.96 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ). % 111.86/111.96 % 111.86/111.96 fof(fact_empty__Diff,axiom, % 111.86/111.96 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ). % 111.86/111.96 % 111.86/111.96 fof(fact_finite__Diff2,axiom, % 111.86/111.96 ! [V_A_2,V_B_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 111.86/111.96 => ( 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))) % 111.86/111.96 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_double__diff,axiom, % 111.86/111.96 ! [V_C_2,V_B_2,V_A_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 111.86/111.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_Diff__mono,axiom, % 111.86/111.96 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_Diff__subset,axiom, % 111.86/111.96 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 111.86/111.96 % 111.86/111.96 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 111.86/111.96 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 111.86/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 111.86/111.96 => 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)))))) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_insert__Diff1,axiom, % 111.86/111.96 ! [V_A_2,V_B_2,V_x_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 111.86/111.96 => 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) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_insert__Diff__if,axiom, % 111.86/111.96 ! [V_A_2,V_B_2,V_x_2,T_b] : % 111.86/111.96 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 111.86/111.96 => 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) ) % 111.86/111.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 111.86/111.96 => 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)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_insert__Diff__single,axiom, % 111.86/111.96 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ). % 111.86/111.96 % 111.86/111.96 fof(fact_Diff__insert2,axiom, % 111.86/111.96 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2) ). % 111.86/111.96 % 111.86/111.96 fof(fact_Diff__insert,axiom, % 111.86/111.96 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 111.86/111.96 % 111.86/111.96 fof(fact_finite__Diff__insert,axiom, % 111.86/111.96 ! [V_B_2,V_a_2,V_A_2,T_b] : % 111.86/111.96 ( 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)))) % 111.86/111.96 <=> 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))) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_image__diff__subset,axiom, % 111.86/111.96 ! [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)))) ). % 111.86/111.96 % 111.86/111.96 fof(fact_folding__image__simple_Oempty,axiom, % 111.86/111.96 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 111.86/111.96 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_folding__image__simple_Oremove,axiom, % 111.86/111.96 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 111.86/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 111.86/111.96 => 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)))))) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_insert__Diff,axiom, % 111.86/111.96 ! [V_A_2,V_a_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.86/111.96 => 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 ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_Diff__insert__absorb,axiom, % 111.86/111.96 ! [V_A_2,V_x_2,T_b] : % 111.86/111.96 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.96 => 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 ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 111.86/111.96 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 111.86/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => 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) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__left__comm_Ofold__rec,axiom, % 111.86/111.96 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 111.86/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.96 => 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)))))) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 111.86/111.96 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 111.86/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => 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)))))) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_minus__apply,axiom, % 111.86/111.96 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 111.86/111.96 ( class_Groups_Ominus(T_b) % 111.86/111.96 => 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)) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_diff__eq__diff__less__eq,axiom, % 111.86/111.96 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 111.86/111.96 ( class_Groups_Oordered__ab__group__add(T_b) % 111.86/111.96 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 111.86/111.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 111.86/111.96 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 111.86/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.96 => 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) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__left__comm_Ofold__insert,axiom, % 111.86/111.96 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 111.86/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.96 => 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)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_finite__empty__induct,axiom, % 111.86/111.96 ! [V_Pa_2,V_A_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => ( hBOOL(hAPP(V_Pa_2,V_A_2)) % 111.86/111.96 => ( ! [B_a,B_A] : % 111.86/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) % 111.86/111.96 => ( hBOOL(hAPP(V_Pa_2,B_A)) % 111.86/111.96 => 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)))))) ) ) ) % 111.86/111.96 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 111.86/111.96 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 111.86/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => 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) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 111.86/111.96 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 111.86/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => 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)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_psubset__insert__iff,axiom, % 111.86/111.96 ! [V_B_2,V_x_2,V_A_2,T_b] : % 111.86/111.96 ( 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))) % 111.86/111.96 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 111.86/111.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) % 111.86/111.96 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.96 => 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)) ) % 111.86/111.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 111.86/111.96 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.96 => ( 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) % 111.86/111.96 => 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)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 111.86/111.96 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 111.86/111.96 => 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)) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_psubset__trans,axiom, % 111.86/111.96 ! [V_C_2,V_B_2,V_A_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__less__irrefl,axiom, % 111.86/111.96 ! [V_x,T_a] : % 111.86/111.96 ( class_Orderings_Opreorder(T_a) % 111.86/111.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_linorder__neq__iff,axiom, % 111.86/111.96 ! [V_y_2,V_x_2,T_b] : % 111.86/111.96 ( class_Orderings_Olinorder(T_b) % 111.86/111.96 => ( V_x_2 != V_y_2 % 111.86/111.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 111.86/111.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_not__less__iff__gr__or__eq,axiom, % 111.86/111.96 ! [V_y_2,V_x_2,T_b] : % 111.86/111.96 ( class_Orderings_Olinorder(T_b) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 111.86/111.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 111.86/111.96 | V_x_2 = V_y_2 ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_linorder__less__linear,axiom, % 111.86/111.96 ! [V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Olinorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 | V_x = V_y % 111.86/111.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_linorder__antisym__conv3,axiom, % 111.86/111.96 ! [V_x_2,V_y_2,T_b] : % 111.86/111.96 ( class_Orderings_Olinorder(T_b) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 111.86/111.96 <=> V_x_2 = V_y_2 ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_linorder__neqE,axiom, % 111.86/111.96 ! [V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Olinorder(T_a) % 111.86/111.96 => ( V_x != V_y % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_less__imp__neq,axiom, % 111.86/111.96 ! [V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 => V_x != V_y ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__less__not__sym,axiom, % 111.86/111.96 ! [V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Opreorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__less__imp__not__less,axiom, % 111.86/111.96 ! [V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Opreorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__less__imp__not__eq,axiom, % 111.86/111.96 ! [V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 => V_x != V_y ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__less__imp__not__eq2,axiom, % 111.86/111.96 ! [V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 => V_y != V_x ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__less__asym_H,axiom, % 111.86/111.96 ! [V_b,V_a,T_a] : % 111.86/111.96 ( class_Orderings_Opreorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.86/111.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_xt1_I9_J,axiom, % 111.86/111.96 ! [V_a,V_b,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 111.86/111.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_ord__eq__less__trans,axiom, % 111.86/111.96 ! [V_c,V_b,V_a,T_a] : % 111.86/111.96 ( class_Orderings_Oord(T_a) % 111.86/111.96 => ( V_a = V_b % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_xt1_I1_J,axiom, % 111.86/111.96 ! [V_c,V_b,V_a,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( V_a = V_b % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_ord__less__eq__trans,axiom, % 111.86/111.96 ! [V_c,V_b,V_a,T_a] : % 111.86/111.96 ( class_Orderings_Oord(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.86/111.96 => ( V_b = V_c % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_xt1_I2_J,axiom, % 111.86/111.96 ! [V_c,V_a,V_b,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 111.86/111.96 => ( V_b = V_c % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__less__trans,axiom, % 111.86/111.96 ! [V_z,V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Opreorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_xt1_I10_J,axiom, % 111.86/111.96 ! [V_z,V_x,V_y,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__less__asym,axiom, % 111.86/111.96 ! [V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Opreorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_linorder__cases,axiom, % 111.86/111.96 ! [V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Olinorder(T_a) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 => ( V_x != V_y % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 111.86/111.96 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 111.86/111.96 => 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) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_diff__eq__diff__less,axiom, % 111.86/111.96 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 111.86/111.96 ( class_Groups_Oordered__ab__group__add(T_b) % 111.86/111.96 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 111.86/111.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 111.86/111.96 ! [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) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 111.86/111.96 ! [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) ). % 111.86/111.96 % 111.86/111.96 fof(fact_less__fun__def,axiom, % 111.86/111.96 ! [V_g_2,V_f_2,T_b,T_c] : % 111.86/111.96 ( class_Orderings_Oord(T_c) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 111.86/111.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 111.86/111.96 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_linorder__not__less,axiom, % 111.86/111.96 ! [V_y_2,V_x_2,T_b] : % 111.86/111.96 ( class_Orderings_Olinorder(T_b) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 111.86/111.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_linorder__not__le,axiom, % 111.86/111.96 ! [V_y_2,V_x_2,T_b] : % 111.86/111.96 ( class_Orderings_Olinorder(T_b) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 111.86/111.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_linorder__le__less__linear,axiom, % 111.86/111.96 ! [V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Olinorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 111.86/111.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__less__le,axiom, % 111.86/111.96 ! [V_y_2,V_x_2,T_b] : % 111.86/111.96 ( class_Orderings_Oorder(T_b) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 111.86/111.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 111.86/111.96 & V_x_2 != V_y_2 ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_less__le__not__le,axiom, % 111.86/111.96 ! [V_y_2,V_x_2,T_b] : % 111.86/111.96 ( class_Orderings_Opreorder(T_b) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 111.86/111.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 111.86/111.96 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__le__less,axiom, % 111.86/111.96 ! [V_y_2,V_x_2,T_b] : % 111.86/111.96 ( class_Orderings_Oorder(T_b) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 111.86/111.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 111.86/111.96 | V_x_2 = V_y_2 ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_leI,axiom, % 111.86/111.96 ! [V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Olinorder(T_a) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_not__leE,axiom, % 111.86/111.96 ! [V_x,V_y,T_a] : % 111.86/111.96 ( class_Orderings_Olinorder(T_a) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_linorder__antisym__conv1,axiom, % 111.86/111.96 ! [V_y_2,V_x_2,T_b] : % 111.86/111.96 ( class_Orderings_Olinorder(T_b) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 111.86/111.96 <=> V_x_2 = V_y_2 ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__neq__le__trans,axiom, % 111.86/111.96 ! [V_b,V_a,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( V_a != V_b % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_xt1_I12_J,axiom, % 111.86/111.96 ! [V_b,V_a,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( V_a != V_b % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_leD,axiom, % 111.86/111.96 ! [V_x,V_y,T_a] : % 111.86/111.96 ( class_Orderings_Olinorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 111.86/111.96 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__less__imp__le,axiom, % 111.86/111.96 ! [V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Opreorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_linorder__antisym__conv2,axiom, % 111.86/111.96 ! [V_y_2,V_x_2,T_b] : % 111.86/111.96 ( class_Orderings_Olinorder(T_b) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) % 111.86/111.96 <=> V_x_2 = V_y_2 ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__le__imp__less__or__eq,axiom, % 111.86/111.96 ! [V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 | V_x = V_y ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__le__neq__trans,axiom, % 111.86/111.96 ! [V_b,V_a,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.86/111.96 => ( V_a != V_b % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_xt1_I11_J,axiom, % 111.86/111.96 ! [V_a,V_b,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 111.86/111.96 => ( V_a != V_b % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__less__le__trans,axiom, % 111.86/111.96 ! [V_z,V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Opreorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_xt1_I7_J,axiom, % 111.86/111.96 ! [V_z,V_x,V_y,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_order__le__less__trans,axiom, % 111.86/111.96 ! [V_z,V_y,V_x,T_a] : % 111.86/111.96 ( class_Orderings_Opreorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_xt1_I8_J,axiom, % 111.86/111.96 ! [V_z,V_x,V_y,T_a] : % 111.86/111.96 ( class_Orderings_Oorder(T_a) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_psubsetD,axiom, % 111.86/111.96 ! [V_c_2,V_B_2,V_A_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_not__psubset__empty,axiom, % 111.86/111.96 ! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ). % 111.86/111.96 % 111.86/111.96 fof(fact_psubset__eq,axiom, % 111.86/111.96 ! [V_B_2,V_A_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.96 & V_A_2 != V_B_2 ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_subset__iff__psubset__eq,axiom, % 111.86/111.96 ! [V_B_2,V_A_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.96 | V_A_2 = V_B_2 ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_psubset__imp__subset,axiom, % 111.86/111.96 ! [V_B_2,V_A_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_psubset__subset__trans,axiom, % 111.86/111.96 ! [V_C_2,V_B_2,V_A_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_subset__psubset__trans,axiom, % 111.86/111.96 ! [V_C_2,V_B_2,V_A_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__left__comm__idem__insert,axiom, % 111.86/111.96 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ). % 111.86/111.96 % 111.86/111.96 fof(fact_diff__eq__diff__eq,axiom, % 111.86/111.96 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 111.86/111.96 ( class_Groups_Oab__group__add(T_b) % 111.86/111.96 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2) % 111.86/111.96 => ( V_a_2 = V_b_2 % 111.86/111.96 <=> V_c_2 = V_d_2 ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 111.86/111.96 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 111.86/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => 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) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 111.86/111.96 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] : % 111.86/111.96 ( 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)) % 111.86/111.96 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.86/111.96 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 111.86/111.96 | ? [B_x,B_y] : % 111.86/111.96 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 111.86/111.96 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2)) % 111.86/111.96 & 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) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_Diff1__fold__graph,axiom, % 111.86/111.96 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( 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)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.96 => 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))) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__upd__image,axiom, % 111.86/111.96 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 111.86/111.96 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.96 => hAPP(c_Set_Oimage(T_b,T_c,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)))))) ) % 111.86/111.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.86/111.96 => hAPP(c_Set_Oimage(T_b,T_c,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) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 111.86/111.96 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 111.86/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => 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))) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_psubset__imp__ex__mem,axiom, % 111.86/111.96 ! [V_B_2,V_A_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.96 => ? [B_b] : 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))) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_setsum__diff1,axiom, % 111.86/111.96 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 111.86/111.96 ( class_Groups_Oab__group__add(T_c) % 111.86/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.86/111.96 => 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)) ) % 111.86/111.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.86/111.96 => 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) ) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_setsum__diff1__ring,axiom, % 111.86/111.96 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 111.86/111.96 ( class_Rings_Oring(T_c) % 111.86/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.86/111.96 => 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)) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_finite__subset__image,axiom, % 111.86/111.96 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 111.86/111.96 => ( 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))) % 111.86/111.96 => ? [B_C] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_C),V_A_2)) % 111.86/111.96 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_C)) % 111.86/111.96 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_C) ) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fold1Set__sing,axiom, % 111.86/111.96 ! [V_b_2,V_a_2,V_f_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2)) % 111.86/111.96 <=> V_a_2 = V_b_2 ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_image__subsetI,axiom, % 111.86/111.96 ! [V_B_2,V_f_2,T_c,V_A_2,T_b] : % 111.86/111.96 ( ! [B_x] : % 111.86/111.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.86/111.96 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,B_x)),V_B_2)) ) % 111.86/111.96 => 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)) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_card__Diff1__le,axiom, % 111.86/111.96 ! [V_x_2,V_A_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.86/111.96 => 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))) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__upd__triv,axiom, % 111.86/111.96 ! [V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2 ). % 111.86/111.96 % 111.86/111.96 fof(fact_fold1Set_Ointros,axiom, % 111.86/111.96 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2)) % 111.86/111.96 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.86/111.96 => 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)) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__upd__idem__iff,axiom, % 111.86/111.96 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 111.86/111.96 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2 % 111.86/111.96 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__upd__upd,axiom, % 111.86/111.96 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__upd__same,axiom, % 111.86/111.96 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2 ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__upd__apply,axiom, % 111.86/111.96 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 111.86/111.96 ( ( V_z_2 = V_x_2 % 111.86/111.96 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 ) % 111.86/111.96 & ( V_z_2 != V_x_2 % 111.86/111.96 => 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) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__upd__twist,axiom, % 111.86/111.96 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] : % 111.86/111.96 ( V_a_2 != V_c_2 % 111.86/111.96 => c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_c_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_c_2,V_d_2),V_a_2,V_b_2) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__upd__other,axiom, % 111.86/111.96 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] : % 111.86/111.96 ( V_z_2 != V_x_2 % 111.86/111.96 => 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) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_fun__upd__idem,axiom, % 111.86/111.96 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] : % 111.86/111.96 ( hAPP(V_f_2,V_x_2) = V_y_2 % 111.86/111.96 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_psubset__card__mono,axiom, % 111.86/111.96 ! [V_A_2,V_B_2,T_b] : % 111.86/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 111.86/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.86/111.96 => 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))) ) ) ). % 111.86/111.96 % 111.86/111.96 fof(fact_empty__fold__graphE,axiom, % 111.86/111.96 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] : % 111.99/111.96 ( 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)) % 111.99/111.96 => V_x_2 = V_z_2 ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_fold__graph_OemptyI,axiom, % 111.99/111.96 ! [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)) ). % 111.99/111.96 % 111.99/111.96 fof(fact_fold__graph_Oequations_I1_J,axiom, % 111.99/111.96 ! [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)) ). % 111.99/111.96 % 111.99/111.96 fof(fact_fold__graph__imp__finite,axiom, % 111.99/111.96 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 111.99/111.96 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_card__psubset,axiom, % 111.99/111.96 ! [V_A_2,V_B_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.99/111.96 => ( 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))) % 111.99/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 111.99/111.96 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 111.99/111.96 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 111.99/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) % 111.99/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 111.99/111.96 => V_y_2 = V_x_2 ) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_setsum__diff__nat,axiom, % 111.99/111.96 ! [V_f_2,V_A_2,V_B_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 111.99/111.96 => 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)) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_card__insert__le,axiom, % 111.99/111.96 ! [V_x_2,V_A_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.96 => 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)))) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_card__seteq,axiom, % 111.99/111.96 ! [V_A_2,V_B_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.99/111.96 => ( 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))) % 111.99/111.96 => V_A_2 = V_B_2 ) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_card__mono,axiom, % 111.99/111.96 ! [V_A_2,V_B_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.99/111.96 => 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))) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_card__image__le,axiom, % 111.99/111.96 ! [V_f_2,T_c,V_A_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.96 => 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))) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_diff__card__le__card__Diff,axiom, % 111.99/111.96 ! [V_A_2,V_B_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 111.99/111.96 => 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)))) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_fold1Set__nonempty,axiom, % 111.99/111.96 ! [V_x_2,V_A_2,V_f_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2)) % 111.99/111.96 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_empty__fold1SetE,axiom, % 111.99/111.96 ! [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)) ). % 111.99/111.96 % 111.99/111.96 fof(fact_card__Diff2__less,axiom, % 111.99/111.96 ! [V_y_2,V_x_2,V_A_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 111.99/111.96 => 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))) ) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_card__Diff1__less,axiom, % 111.99/111.96 ! [V_x_2,V_A_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.96 => 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))) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_fold__graph_OinsertI,axiom, % 111.99/111.96 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] : % 111.99/111.96 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 111.99/111.96 => 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))) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_setsum__diff1__nat,axiom, % 111.99/111.96 ! [V_f_2,V_A_2,V_a_2,T_b] : % 111.99/111.96 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.99/111.96 => 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)) ) % 111.99/111.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.99/111.96 => 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) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_setsum__diff,axiom, % 111.99/111.96 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 111.99/111.96 ( class_Groups_Oab__group__add(T_c) % 111.99/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 111.99/111.96 => 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)) ) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_card__Diff__subset,axiom, % 111.99/111.96 ! [V_A_2,V_B_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 111.99/111.96 => 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)) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_fun__left__comm_Ofold__equality,axiom, % 111.99/111.96 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 111.99/111.96 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 111.99/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 111.99/111.96 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 111.99/111.96 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] : % 111.99/111.96 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 111.99/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.99/111.96 => ? [B_y_H] : % 111.99/111.96 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 111.99/111.96 & 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)) ) ) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_card__Diff__singleton,axiom, % 111.99/111.96 ! [V_x_2,V_A_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.96 => 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)) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_card__Diff__singleton__if,axiom, % 111.99/111.96 ! [V_x_2,V_A_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.96 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.96 => 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)) ) % 111.99/111.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.96 => 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) ) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_setsum__strict__mono,axiom, % 111.99/111.96 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 111.99/111.96 ( ( class_Groups_Ocomm__monoid__add(T_c) % 111.99/111.96 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) ) % 111.99/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.96 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.96 => ( ! [B_x] : % 111.99/111.96 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.99/111.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 111.99/111.96 => 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))) ) ) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_card__Suc__Diff1,axiom, % 111.99/111.96 ! [V_x_2,V_A_2,T_b] : % 111.99/111.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.96 => 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) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_setsum_Oremove,axiom, % 111.99/111.96 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 111.99/111.96 ( class_Groups_Ocomm__monoid__add(T_c) % 111.99/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.96 => 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)))))) ) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_setsum__diff1_H,axiom, % 111.99/111.96 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 111.99/111.96 ( class_Groups_Ocomm__monoid__add(T_c) % 111.99/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.96 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.99/111.96 => 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)))))) ) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_insert__fold1SetE,axiom, % 111.99/111.96 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] : % 111.99/111.96 ( 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)) % 111.99/111.96 => ~ ! [B_a,B_A] : % 111.99/111.96 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 111.99/111.96 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2)) % 111.99/111.96 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_fold1Set_Oequations,axiom, % 111.99/111.96 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] : % 111.99/111.96 ( 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)) % 111.99/111.96 <=> ? [B_a,B_A] : % 111.99/111.96 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) % 111.99/111.96 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2)) % 111.99/111.96 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ). % 111.99/111.96 % 111.99/111.96 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 111.99/111.97 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] : % 111.99/111.97 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 111.99/111.97 => ( 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)) % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.97 => ~ ! [B_y] : % 111.99/111.97 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 111.99/111.97 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_fold__graph__permute__diff,axiom, % 111.99/111.97 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] : % 111.99/111.97 ( class_Groups_Oab__semigroup__mult(T_b) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 111.99/111.97 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_mult__1__left,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Groups_Omonoid__mult(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_mult__1,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Groups_Ocomm__monoid__mult(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_one__reorient,axiom, % 111.99/111.97 ! [V_x_2,T_b] : % 111.99/111.97 ( class_Groups_Oone(T_b) % 111.99/111.97 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2 % 111.99/111.97 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_mult__1__right,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Groups_Omonoid__mult(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_mult_Ocomm__neutral,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Groups_Ocomm__monoid__mult(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_times_Oidem,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_mult__idem,axiom, % 111.99/111.97 ! [V_x,T_a] : % 111.99/111.97 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_mult__left__idem,axiom, % 111.99/111.97 ! [V_b,V_a,T_a] : % 111.99/111.97 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 111.99/111.97 ! [V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Oab__semigroup__add(T_a) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 111.99/111.97 ! [V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Oab__semigroup__mult(T_a) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__left__cancel,axiom, % 111.99/111.97 ! [V_c_2,V_b_2,V_a_2,T_b] : % 111.99/111.97 ( class_Groups_Ocancel__semigroup__add(T_b) % 111.99/111.97 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2) % 111.99/111.97 <=> V_b_2 = V_c_2 ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__right__cancel,axiom, % 111.99/111.97 ! [V_c_2,V_a_2,V_b_2,T_b] : % 111.99/111.97 ( class_Groups_Ocancel__semigroup__add(T_b) % 111.99/111.97 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2) % 111.99/111.97 <=> V_b_2 = V_c_2 ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__left__imp__eq,axiom, % 111.99/111.97 ! [V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Ocancel__semigroup__add(T_a) % 111.99/111.97 => ( 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) % 111.99/111.97 => V_b = V_c ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__imp__eq,axiom, % 111.99/111.97 ! [V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 111.99/111.97 => ( 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) % 111.99/111.97 => V_b = V_c ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__right__imp__eq,axiom, % 111.99/111.97 ! [V_c,V_a,V_b,T_a] : % 111.99/111.97 ( class_Groups_Ocancel__semigroup__add(T_a) % 111.99/111.97 => ( 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) % 111.99/111.97 => V_b = V_c ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__le__cancel__right,axiom, % 111.99/111.97 ! [V_b_2,V_c_2,V_a_2,T_b] : % 111.99/111.97 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__le__cancel__left,axiom, % 111.99/111.97 ! [V_b_2,V_a_2,V_c_2,T_b] : % 111.99/111.97 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__right__mono,axiom, % 111.99/111.97 ! [V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.99/111.97 => 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))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__left__mono,axiom, % 111.99/111.97 ! [V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.99/111.97 => 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))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__mono,axiom, % 111.99/111.97 ! [V_d,V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 111.99/111.97 => 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))) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__le__imp__le__right,axiom, % 111.99/111.97 ! [V_b,V_c,V_a,T_a] : % 111.99/111.97 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 111.99/111.97 => ( 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))) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__le__imp__le__left,axiom, % 111.99/111.97 ! [V_b,V_a,V_c,T_a] : % 111.99/111.97 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 111.99/111.97 => ( 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))) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__less__imp__less__left,axiom, % 111.99/111.97 ! [V_b,V_a,V_c,T_a] : % 111.99/111.97 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 111.99/111.97 => ( 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))) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__less__imp__less__right,axiom, % 111.99/111.97 ! [V_b,V_c,V_a,T_a] : % 111.99/111.97 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 111.99/111.97 => ( 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))) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__strict__mono,axiom, % 111.99/111.97 ! [V_d,V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 111.99/111.97 => 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))) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__strict__left__mono,axiom, % 111.99/111.97 ! [V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.97 => 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))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__strict__right__mono,axiom, % 111.99/111.97 ! [V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.97 => 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))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__less__cancel__left,axiom, % 111.99/111.97 ! [V_b_2,V_a_2,V_c_2,T_b] : % 111.99/111.97 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__less__cancel__right,axiom, % 111.99/111.97 ! [V_b_2,V_c_2,V_a_2,T_b] : % 111.99/111.97 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__diff__cancel,axiom, % 111.99/111.97 ! [V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Ogroup__add(T_a) % 111.99/111.97 => 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 ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__add__cancel,axiom, % 111.99/111.97 ! [V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Ogroup__add(T_a) % 111.99/111.97 => 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 ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_fun__left__comm,axiom, % 111.99/111.97 ! [T_b] : % 111.99/111.97 ( class_Groups_Oab__semigroup__mult(T_b) % 111.99/111.97 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_fun__left__comm__idem,axiom, % 111.99/111.97 ! [T_b] : % 111.99/111.97 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 111.99/111.97 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_card_Oinsert,axiom, % 111.99/111.97 ! [V_x_2,V_A_2,T_b] : % 111.99/111.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.97 => 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)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__le__less__mono,axiom, % 111.99/111.97 ! [V_d,V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 111.99/111.97 => 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))) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__less__le__mono,axiom, % 111.99/111.97 ! [V_d,V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 111.99/111.97 => 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))) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_card_Oinsert__remove,axiom, % 111.99/111.97 ! [V_x_2,V_A_2,T_b] : % 111.99/111.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => 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)))))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_card_Oremove,axiom, % 111.99/111.97 ! [V_x_2,V_A_2,T_b] : % 111.99/111.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.97 => 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)))))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_fold__graph__insert__swap,axiom, % 111.99/111.97 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] : % 111.99/111.97 ( class_Groups_Oab__semigroup__mult(T_b) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2)) % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 111.99/111.97 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_setsum_Oinsert,axiom, % 111.99/111.97 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 111.99/111.97 ( class_Groups_Ocomm__monoid__add(T_c) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.97 => 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)) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_setsum__insert,axiom, % 111.99/111.97 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] : % 111.99/111.97 ( class_Groups_Ocomm__monoid__add(T_c) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2)) % 111.99/111.97 => 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)) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_card__insert__if,axiom, % 111.99/111.97 ! [V_x_2,V_A_2,T_b] : % 111.99/111.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.97 => 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) ) % 111.99/111.97 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.97 => 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)) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_card__insert__disjoint,axiom, % 111.99/111.97 ! [V_x_2,V_A_2,T_b] : % 111.99/111.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.97 => 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)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_setsum_Oinsert__remove,axiom, % 111.99/111.97 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 111.99/111.97 ( class_Groups_Ocomm__monoid__add(T_c) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => 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)))))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_card__insert,axiom, % 111.99/111.97 ! [V_x_2,V_A_2,T_b] : % 111.99/111.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => 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)))))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_card__Diff__insert,axiom, % 111.99/111.97 ! [V_B_2,V_a_2,V_A_2,T_b] : % 111.99/111.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) % 111.99/111.97 => 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)) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__mono,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_lessI,axiom, % 111.99/111.97 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__add__iff2,axiom, % 111.99/111.97 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 111.99/111.97 ( class_Rings_Oordered__ring(T_b) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__add__iff1,axiom, % 111.99/111.97 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 111.99/111.97 ( class_Rings_Oordered__ring(T_b) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__add__iff1,axiom, % 111.99/111.97 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 111.99/111.97 ( class_Rings_Oordered__ring(T_b) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__add__iff2,axiom, % 111.99/111.97 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 111.99/111.97 ( class_Rings_Oordered__ring(T_b) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__Suc__1,axiom, % 111.99/111.97 ! [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 ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__Suc__eq__diff__pred,axiom, % 111.99/111.97 ! [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) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__less__add__iff2,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 111.99/111.97 => ( 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_na_2))) % 111.99/111.97 <=> 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_na_2))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__less__add__iff1,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 111.99/111.97 => ( 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_na_2))) % 111.99/111.97 <=> 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_na_2)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__diff__iff,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_na_2)) % 111.99/111.97 => ( 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_na_2),V_k_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_left__add__mult__distrib,axiom, % 111.99/111.97 ! [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) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__add__right__cancel,axiom, % 111.99/111.97 ! [V_na_2,V_k_2,V_m_2] : % 111.99/111.97 ( 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_na_2),V_k_2) % 111.99/111.97 <=> V_m_2 = V_na_2 ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__add__left__cancel,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.97 ( 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_na_2) % 111.99/111.97 <=> V_m_2 = V_na_2 ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__mult__distrib,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__mult__assoc,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__add__assoc,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__mult__distrib2,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__add__left__commute,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__mult__commute,axiom, % 111.99/111.97 ! [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) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__add__commute,axiom, % 111.99/111.97 ! [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) ). % 111.99/111.97 % 111.99/111.97 fof(fact_linorder__neqE__linordered__idom,axiom, % 111.99/111.97 ! [V_y,V_x,T_a] : % 111.99/111.97 ( class_Rings_Olinordered__idom(T_a) % 111.99/111.97 => ( V_x != V_y % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_n__not__Suc__n,axiom, % 111.99/111.97 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__n__not__n,axiom, % 111.99/111.97 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__Suc__right,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_mult__Suc__right,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__Suc,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__Suc__shift,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_mult__Suc,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat_Oinject,axiom, % 111.99/111.97 ! [V_nat_H_2,V_nat_2] : % 111.99/111.97 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 111.99/111.97 <=> V_nat_2 = V_nat_H_2 ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__mult__cancel1,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.97 ( 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_na_2) % 111.99/111.97 <=> V_m_2 = V_na_2 ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__inject,axiom, % 111.99/111.97 ! [V_y,V_x] : % 111.99/111.97 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 111.99/111.97 => V_x = V_y ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__not__refl,axiom, % 111.99/111.97 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_not__add__less1,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_not__add__less2,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__neq__iff,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( V_m_2 != V_na_2 % 111.99/111.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 111.99/111.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__add__left__cancel__less,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.97 ( 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_na_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_linorder__neqE__nat,axiom, % 111.99/111.97 ! [V_y,V_x] : % 111.99/111.97 ( V_x != V_y % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__irrefl__nat,axiom, % 111.99/111.97 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__not__refl2,axiom, % 111.99/111.97 ! [V_m,V_n] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 111.99/111.97 => V_m != V_n ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__not__refl3,axiom, % 111.99/111.97 ! [V_t,V_s] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 111.99/111.97 => V_s != V_t ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_trans__less__add1,axiom, % 111.99/111.97 ! [V_m,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_trans__less__add2,axiom, % 111.99/111.97 ! [V_m,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__less__mono1,axiom, % 111.99/111.97 ! [V_k,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__less__mono,axiom, % 111.99/111.97 ! [V_l,V_k,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 111.99/111.97 => 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))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__add__eq__less,axiom, % 111.99/111.97 ! [V_n,V_m,V_l,V_k] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 111.99/111.97 => ( 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) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__lessD1,axiom, % 111.99/111.97 ! [V_k,V_j,V_i] : % 111.99/111.97 ( 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)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__less__cases,axiom, % 111.99/111.97 ! [V_Pa_2,V_na_2,V_m_2] : % 111.99/111.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 111.99/111.97 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) % 111.99/111.97 => ( ( V_m_2 = V_na_2 % 111.99/111.97 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) % 111.99/111.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 111.99/111.97 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) % 111.99/111.97 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__refl,axiom, % 111.99/111.97 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__le__linear,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_eq__imp__le,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( V_m = V_n % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__trans,axiom, % 111.99/111.97 ! [V_k,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__antisym,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 111.99/111.97 => V_m = V_n ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__square,axiom, % 111.99/111.97 ! [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))) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__cube,axiom, % 111.99/111.97 ! [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)))) ). % 111.99/111.97 % 111.99/111.97 fof(fact_mult__le__mono1,axiom, % 111.99/111.97 ! [V_k,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_mult__le__mono2,axiom, % 111.99/111.97 ! [V_k,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_mult__le__mono,axiom, % 111.99/111.97 ! [V_l,V_k,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 111.99/111.97 => 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))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__add2,axiom, % 111.99/111.97 ! [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))) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__add1,axiom, % 111.99/111.97 ! [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))) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__iff__add,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 111.99/111.97 <=> ? [B_k] : V_na_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__add__left__cancel__le,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.97 ( 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_na_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_trans__le__add1,axiom, % 111.99/111.97 ! [V_m,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_trans__le__add2,axiom, % 111.99/111.97 ! [V_m,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__le__mono1,axiom, % 111.99/111.97 ! [V_k,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__le__mono,axiom, % 111.99/111.97 ! [V_l,V_k,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 111.99/111.97 => 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))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__leD2,axiom, % 111.99/111.97 ! [V_n,V_k,V_m] : % 111.99/111.97 ( 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)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__leD1,axiom, % 111.99/111.97 ! [V_n,V_k,V_m] : % 111.99/111.97 ( 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)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__leE,axiom, % 111.99/111.97 ! [V_n,V_k,V_m] : % 111.99/111.97 ( 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)) % 111.99/111.97 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__mult__distrib2,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__add__inverse2,axiom, % 111.99/111.97 ! [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 ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__add__inverse,axiom, % 111.99/111.97 ! [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 ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__diff__left,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__commute,axiom, % 111.99/111.97 ! [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) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__mult__distrib,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__cancel,axiom, % 111.99/111.97 ! [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) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__cancel2,axiom, % 111.99/111.97 ! [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) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__mult__1,axiom, % 111.99/111.97 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__1__eq__mult__iff,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2) % 111.99/111.97 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 111.99/111.97 & V_na_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__mult__1__right,axiom, % 111.99/111.97 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__mult__eq__1__iff,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 111.99/111.97 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 111.99/111.97 & V_na_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__class_Odistrib,axiom, % 111.99/111.97 ! [V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring(T_a) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_combine__common__factor,axiom, % 111.99/111.97 ! [V_c,V_b,V_e,V_a,T_a] : % 111.99/111.97 ( class_Rings_Osemiring(T_a) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__add__Suc1,axiom, % 111.99/111.97 ! [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)))) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__add__Suc2,axiom, % 111.99/111.97 ! [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)))) ). % 111.99/111.97 % 111.99/111.97 fof(fact_not__less__eq,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__iff__Suc__add,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 111.99/111.97 <=> ? [B_k] : V_na_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__Suc__eq,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 111.99/111.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 111.99/111.97 | V_m_2 = V_na_2 ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__less__eq,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_na_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__mult__less__cancel1,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.97 ( 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_na_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_not__less__less__Suc__eq,axiom, % 111.99/111.97 ! [V_m_2,V_na_2] : % 111.99/111.97 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) % 111.99/111.97 <=> V_na_2 = V_m_2 ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__antisym,axiom, % 111.99/111.97 ! [V_m,V_n] : % 111.99/111.97 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 111.99/111.97 => V_m = V_n ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__SucI,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__lessI,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__trans__Suc,axiom, % 111.99/111.97 ! [V_k,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__SucE,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => V_m = V_n ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__lessD,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__less__SucD,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__n__not__le__n,axiom, % 111.99/111.97 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_not__less__eq__eq,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__Suc__eq,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 111.99/111.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 111.99/111.97 | V_m_2 = hAPP(c_Nat_OSuc,V_na_2) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__le__mono,axiom, % 111.99/111.97 ! [V_m_2,V_na_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),hAPP(c_Nat_OSuc,V_m_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_m_2)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__SucI,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__SucE,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__leD,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__mult__le__cancel1,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.97 ( 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_na_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__or__eq__imp__le,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 | V_m = V_n ) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__neq__implies__less,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => ( V_m != V_n % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__imp__le__nat,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__eq__less__or__eq,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 111.99/111.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 111.99/111.97 | V_m_2 = V_na_2 ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__less__le,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 111.99/111.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 111.99/111.97 & V_m_2 != V_na_2 ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__Suc__Suc,axiom, % 111.99/111.97 ! [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) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__diff__diff,axiom, % 111.99/111.97 ! [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) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__less__mono2,axiom, % 111.99/111.97 ! [V_l,V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 111.99/111.97 => 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))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__imp__diff__less,axiom, % 111.99/111.97 ! [V_n,V_k,V_j] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__diff__inverse,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => 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 ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__diff__conv,axiom, % 111.99/111.97 ! [V_k_2,V_j_2,V_i_2] : % 111.99/111.97 ( 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))) % 111.99/111.97 <=> 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__le__self,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__le__mono2,axiom, % 111.99/111.97 ! [V_l,V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__le__mono,axiom, % 111.99/111.97 ! [V_l,V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__diff__cancel,axiom, % 111.99/111.97 ! [V_n,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 111.99/111.97 => 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 ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_eq__diff__iff,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_na_2)) % 111.99/111.97 => ( 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_na_2),V_k_2) % 111.99/111.97 <=> V_m_2 = V_na_2 ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Nat_Odiff__diff__eq,axiom, % 111.99/111.97 ! [V_n,V_m,V_k] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 111.99/111.97 => 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) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__diff__iff,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_na_2)) % 111.99/111.97 => ( 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_na_2),V_k_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__diff__right,axiom, % 111.99/111.97 ! [V_i,V_j,V_k] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__diff__conv,axiom, % 111.99/111.97 ! [V_i_2,V_k_2,V_j_2] : % 111.99/111.97 ( 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)) % 111.99/111.97 <=> 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__add__diff,axiom, % 111.99/111.97 ! [V_m,V_n,V_k] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__add__diff__inverse,axiom, % 111.99/111.97 ! [V_m,V_n] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 111.99/111.97 => 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 ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__diff__assoc,axiom, % 111.99/111.97 ! [V_i,V_j,V_k] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__diff__conv2,axiom, % 111.99/111.97 ! [V_i_2,V_j_2,V_k_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 111.99/111.97 => ( 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))) % 111.99/111.97 <=> 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)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__add__diff__inverse2,axiom, % 111.99/111.97 ! [V_m,V_n] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 111.99/111.97 => 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 ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__imp__diff__is__add,axiom, % 111.99/111.97 ! [V_k_2,V_j_2,V_i_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 111.99/111.97 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 111.99/111.97 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__add__assoc,axiom, % 111.99/111.97 ! [V_i,V_j,V_k] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__diff__assoc2,axiom, % 111.99/111.97 ! [V_i,V_j,V_k] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__add__assoc2,axiom, % 111.99/111.97 ! [V_i,V_j,V_k] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__le__add__iff1,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 111.99/111.97 => ( 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_na_2))) % 111.99/111.97 <=> 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_na_2)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__diff__add__eq1,axiom, % 111.99/111.97 ! [V_n,V_m,V_u,V_i,V_j] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__eq__add__iff1,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 111.99/111.97 => ( 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_na_2) % 111.99/111.97 <=> 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_na_2 ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__le__add__iff2,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 111.99/111.97 => ( 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_na_2))) % 111.99/111.97 <=> 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_na_2))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__diff__add__eq2,axiom, % 111.99/111.97 ! [V_n,V_m,V_u,V_j,V_i] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_nat__eq__add__iff2,axiom, % 111.99/111.97 ! [V_na_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 111.99/111.97 => ( 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_na_2) % 111.99/111.97 <=> 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_na_2) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__eq__plus1__left,axiom, % 111.99/111.97 ! [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) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__eq__plus1,axiom, % 111.99/111.97 ! [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)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__add__one,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Rings_Olinordered__semidom(T_a) % 111.99/111.97 => 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)))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__1__mult,axiom, % 111.99/111.97 ! [V_n,V_m,T_a] : % 111.99/111.97 ( class_Rings_Olinordered__semidom(T_a) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_eq__add__iff2,axiom, % 111.99/111.97 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 111.99/111.97 ( class_Rings_Oring(T_b) % 111.99/111.97 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) % 111.99/111.97 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_eq__add__iff1,axiom, % 111.99/111.97 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] : % 111.99/111.97 ( class_Rings_Oring(T_b) % 111.99/111.97 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) % 111.99/111.97 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__le__lessD,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__less__Suc__eq,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) % 111.99/111.97 <=> V_na_2 = V_m_2 ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__leI,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le__imp__less__Suc,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__le__eq,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_na_2)) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__Suc__eq__le,axiom, % 111.99/111.97 ! [V_na_2,V_m_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__eq__Suc__le,axiom, % 111.99/111.97 ! [V_m_2,V_na_2] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 111.99/111.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__less__Suc,axiom, % 111.99/111.97 ! [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))) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Suc__diff__le,axiom, % 111.99/111.97 ! [V_m,V_n] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__Suc__diff__eq2,axiom, % 111.99/111.97 ! [V_m,V_j,V_k] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__Suc__diff__eq1,axiom, % 111.99/111.97 ! [V_m,V_j,V_k] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_diff__less__mono,axiom, % 111.99/111.97 ! [V_c,V_b,V_a] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 111.99/111.97 => 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))) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 111.99/111.97 ! [V_m,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 111.99/111.97 ! [V_a,V_m,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 111.99/111.97 ! [V_m,V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_termination__basic__simps_I3_J,axiom, % 111.99/111.97 ! [V_z,V_y,V_x] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_termination__basic__simps_I4_J,axiom, % 111.99/111.97 ! [V_y,V_z,V_x] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_termination__basic__simps_I5_J,axiom, % 111.99/111.97 ! [V_y,V_x] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 111.99/111.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_termination__basic__simps_I1_J,axiom, % 111.99/111.97 ! [V_z,V_y,V_x] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_termination__basic__simps_I2_J,axiom, % 111.99/111.97 ! [V_y,V_z,V_x] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 111.99/111.97 ! [V_d,V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 111.99/111.97 ! [V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 111.99/111.97 ! [V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 111.99/111.97 ! [V_d,V_c,V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 111.99/111.97 ! [V_d,V_c,V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 111.99/111.97 ! [V_c,V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 111.99/111.97 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 111.99/111.97 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 111.99/111.97 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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))) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 111.99/111.97 ! [V_rx,V_ly,V_lx,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 111.99/111.97 ! [V_rx,V_ly,V_lx,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 111.99/111.97 ! [V_ry,V_rx,V_lx,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 111.99/111.97 ! [V_ry,V_rx,V_lx,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 111.99/111.97 ! [V_b,V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_crossproduct__eq,axiom, % 111.99/111.97 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] : % 111.99/111.97 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 111.99/111.97 => ( 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)) % 111.99/111.97 <=> ( V_w_2 = V_x_2 % 111.99/111.97 | V_y_2 = V_z_2 ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 111.99/111.97 ! [V_b,V_m,V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 111.99/111.97 ! [V_c,V_b,V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_crossproduct__noteq,axiom, % 111.99/111.97 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 111.99/111.97 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 111.99/111.97 => ( ( V_a_2 != V_b_2 % 111.99/111.97 & V_c_2 != V_d_2 ) % 111.99/111.97 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 111.99/111.97 ! [V_z,V_y,V_x,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => 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)) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_fold1__eq__fold,axiom, % 111.99/111.97 ! [V_a_2,V_A_2,T_b] : % 111.99/111.97 ( class_Groups_Oab__semigroup__mult(T_b) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.99/111.97 => 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) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_fold1__insert,axiom, % 111.99/111.97 ! [V_x_2,V_A_2,T_b] : % 111.99/111.97 ( class_Groups_Oab__semigroup__mult(T_b) % 111.99/111.97 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.97 => 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)) ) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_setprod_Oremove,axiom, % 111.99/111.97 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 111.99/111.97 ( class_Groups_Ocomm__monoid__mult(T_c) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.97 => 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)))))) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_convex__bound__lt,axiom, % 111.99/111.97 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 111.99/111.97 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 111.99/111.97 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 111.99/111.97 => 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)) ) ) ) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_card__Plus,axiom, % 111.99/111.97 ! [V_B_2,T_c,V_A_2,T_b] : % 111.99/111.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 111.99/111.97 => 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)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__monoid__big_Oinfinite,axiom, % 111.99/111.97 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 111.99/111.97 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 111.99/111.97 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 111.99/111.97 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_fold1__eq__fold__idem,axiom, % 111.99/111.97 ! [V_a_2,V_A_2,T_b] : % 111.99/111.97 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => 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) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Max__mono,axiom, % 111.99/111.97 ! [V_N_2,V_M_2,T_b] : % 111.99/111.97 ( class_Orderings_Olinorder(T_b) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 111.99/111.97 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 111.99/111.97 => 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))) ) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_Min__antimono,axiom, % 111.99/111.97 ! [V_N_2,V_M_2,T_b] : % 111.99/111.97 ( class_Orderings_Olinorder(T_b) % 111.99/111.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) % 111.99/111.97 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 111.99/111.97 => 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))) ) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_mult__eq__if,axiom, % 111.99/111.97 ! [V_n,V_m] : % 111.99/111.97 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 111.99/111.97 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.97 => 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)) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_less__zeroE,axiom, % 111.99/111.97 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 111.99/111.97 % 111.99/111.97 fof(fact_le0,axiom, % 111.99/111.97 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 111.99/111.97 % 111.99/111.97 fof(fact_zero__less__Suc,axiom, % 111.99/111.97 ! [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))) ). % 111.99/111.97 % 111.99/111.97 fof(fact_setprod__zero__iff,axiom, % 111.99/111.97 ! [V_f_2,V_A_2,T_b,T_c] : % 111.99/111.97 ( ( class_Rings_Ocomm__semiring__1(T_c) % 111.99/111.97 & class_Rings_Ono__zero__divisors(T_c) ) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => ( 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) % 111.99/111.97 <=> ? [B_x] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.99/111.97 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_setprod__zero,axiom, % 111.99/111.97 ! [V_f_2,V_A_2,T_b,T_c] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_c) % 111.99/111.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.97 => ( ? [B_x] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.99/111.97 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 111.99/111.97 => 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) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_zero__reorient,axiom, % 111.99/111.97 ! [V_x_2,T_b] : % 111.99/111.97 ( class_Groups_Ozero(T_b) % 111.99/111.97 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2 % 111.99/111.97 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_bot__nat__def,axiom, % 111.99/111.97 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 111.99/111.97 % 111.99/111.97 fof(fact_setprod__pos__nat__iff,axiom, % 111.99/111.97 ! [V_f_2,V_S_2,T_b] : % 111.99/111.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 111.99/111.97 => ( 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))) % 111.99/111.97 <=> ! [B_x] : % 111.99/111.97 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 111.99/111.97 => 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))) ) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add_Ocomm__neutral,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Groups_Ocomm__monoid__add(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__0__right,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Groups_Omonoid__add(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_double__zero__sym,axiom, % 111.99/111.97 ! [V_a_2,T_b] : % 111.99/111.97 ( class_Groups_Olinordered__ab__group__add(T_b) % 111.99/111.97 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) % 111.99/111.97 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__0,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Groups_Ocomm__monoid__add(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__0__left,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Groups_Omonoid__add(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_add__0__iff,axiom, % 111.99/111.97 ! [V_a_2,V_b_2,T_b] : % 111.99/111.97 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) % 111.99/111.97 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) % 111.99/111.97 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 111.99/111.97 % 111.99/111.97 fof(fact_mult__zero__left,axiom, % 111.99/111.97 ! [V_a,T_a] : % 111.99/111.97 ( class_Rings_Omult__zero(T_a) % 111.99/111.97 => 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) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__zero__right,axiom, % 111.99/111.98 ! [V_a,T_a] : % 111.99/111.98 ( class_Rings_Omult__zero(T_a) % 111.99/111.98 => 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) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__eq__0__iff,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,T_b] : % 111.99/111.98 ( class_Rings_Oring__no__zero__divisors(T_b) % 111.99/111.98 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_no__zero__divisors,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Ono__zero__divisors(T_a) % 111.99/111.98 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divisors__zero,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Ono__zero__divisors(T_a) % 111.99/111.98 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 111.99/111.98 ! [V_a,T_a] : % 111.99/111.98 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.98 => 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) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 111.99/111.98 ! [V_a,T_a] : % 111.99/111.98 ( class_Rings_Ocomm__semiring__1(T_a) % 111.99/111.98 => 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) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_diff__0__right,axiom, % 111.99/111.98 ! [V_a,T_a] : % 111.99/111.98 ( class_Groups_Ogroup__add(T_a) % 111.99/111.98 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_diff__self,axiom, % 111.99/111.98 ! [V_a,T_a] : % 111.99/111.98 ( class_Groups_Ogroup__add(T_a) % 111.99/111.98 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_eq__iff__diff__eq__0,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,T_b] : % 111.99/111.98 ( class_Groups_Oab__group__add(T_b) % 111.99/111.98 => ( V_a_2 = V_b_2 % 111.99/111.98 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_right__minus__eq,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,T_b] : % 111.99/111.98 ( class_Groups_Ogroup__add(T_b) % 111.99/111.98 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 <=> V_a_2 = V_b_2 ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_one__neq__zero,axiom, % 111.99/111.98 ! [T_a] : % 111.99/111.98 ( class_Rings_Ozero__neq__one(T_a) % 111.99/111.98 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_zero__neq__one,axiom, % 111.99/111.98 ! [T_a] : % 111.99/111.98 ( class_Rings_Ozero__neq__one(T_a) % 111.99/111.98 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Zero__not__Suc,axiom, % 111.99/111.98 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 111.99/111.98 % 111.99/111.98 fof(fact_nat_Osimps_I2_J,axiom, % 111.99/111.98 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Suc__not__Zero,axiom, % 111.99/111.98 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 111.99/111.98 % 111.99/111.98 fof(fact_nat_Osimps_I3_J,axiom, % 111.99/111.98 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Zero__neq__Suc,axiom, % 111.99/111.98 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Suc__neq__Zero,axiom, % 111.99/111.98 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 111.99/111.98 % 111.99/111.98 fof(fact_not__less0,axiom, % 111.99/111.98 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 111.99/111.98 % 111.99/111.98 fof(fact_neq0__conv,axiom, % 111.99/111.98 ! [V_na_2] : % 111.99/111.98 ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_less__nat__zero__code,axiom, % 111.99/111.98 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 111.99/111.98 % 111.99/111.98 fof(fact_gr__implies__not0,axiom, % 111.99/111.98 ! [V_n,V_m] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 111.99/111.98 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_gr0I,axiom, % 111.99/111.98 ! [V_n] : % 111.99/111.98 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__eq__self__zero,axiom, % 111.99/111.98 ! [V_n,V_m] : % 111.99/111.98 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 111.99/111.98 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__is__0,axiom, % 111.99/111.98 ! [V_na_2,V_m_2] : % 111.99/111.98 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Nat_Oadd__0__right,axiom, % 111.99/111.98 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 111.99/111.98 % 111.99/111.98 fof(fact_plus__nat_Oadd__0,axiom, % 111.99/111.98 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 111.99/111.98 % 111.99/111.98 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 111.99/111.98 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 111.99/111.98 % 111.99/111.98 fof(fact_le__0__eq,axiom, % 111.99/111.98 ! [V_na_2] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 111.99/111.98 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_diff__0__eq__0,axiom, % 111.99/111.98 ! [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) ). % 111.99/111.98 % 111.99/111.98 fof(fact_minus__nat_Odiff__0,axiom, % 111.99/111.98 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 111.99/111.98 % 111.99/111.98 fof(fact_diff__self__eq__0,axiom, % 111.99/111.98 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 111.99/111.98 % 111.99/111.98 fof(fact_diffs0__imp__equal,axiom, % 111.99/111.98 ! [V_n,V_m] : % 111.99/111.98 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 => V_m = V_n ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__cancel2,axiom, % 111.99/111.98 ! [V_na_2,V_k_2,V_m_2] : % 111.99/111.98 ( 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_na_2),V_k_2) % 111.99/111.98 <=> ( V_m_2 = V_na_2 % 111.99/111.98 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__cancel1,axiom, % 111.99/111.98 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.98 ( 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_na_2) % 111.99/111.98 <=> ( V_m_2 = V_na_2 % 111.99/111.98 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_nat__mult__eq__cancel__disj,axiom, % 111.99/111.98 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.98 ( 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_na_2) % 111.99/111.98 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 | V_m_2 = V_na_2 ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__is__0,axiom, % 111.99/111.98 ! [V_na_2,V_m_2] : % 111.99/111.98 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 | V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__0__right,axiom, % 111.99/111.98 ! [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) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__0,axiom, % 111.99/111.98 ! [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) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setprod_Oempty,axiom, % 111.99/111.98 ! [V_g_2,T_c,T_b] : % 111.99/111.98 ( class_Groups_Ocomm__monoid__mult(T_b) % 111.99/111.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setprod__empty,axiom, % 111.99/111.98 ! [V_f_2,T_c,T_b] : % 111.99/111.98 ( class_Groups_Ocomm__monoid__mult(T_b) % 111.99/111.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setprod__infinite,axiom, % 111.99/111.98 ! [V_f_2,V_A_2,T_b,T_c] : % 111.99/111.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 111.99/111.98 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setprod_Oinfinite,axiom, % 111.99/111.98 ! [V_g_2,V_A_2,T_b,T_c] : % 111.99/111.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 111.99/111.98 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setprod__eq__1__iff,axiom, % 111.99/111.98 ! [V_f_2,V_F_2,T_b] : % 111.99/111.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 111.99/111.98 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 111.99/111.98 <=> ! [B_x] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 111.99/111.98 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_finite__PlusD_I2_J,axiom, % 111.99/111.98 ! [V_B_2,V_A_2,T_c,T_b] : % 111.99/111.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) % 111.99/111.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_finite__PlusD_I1_J,axiom, % 111.99/111.98 ! [V_B_2,V_A_2,T_c,T_b] : % 111.99/111.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) % 111.99/111.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_finite__Plus,axiom, % 111.99/111.98 ! [V_B_2,T_c,V_A_2,T_b] : % 111.99/111.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 111.99/111.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_finite__Plus__iff,axiom, % 111.99/111.98 ! [V_B_2,V_A_2,T_c,T_b] : % 111.99/111.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) % 111.99/111.98 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_card__Plus__conv__if,axiom, % 111.99/111.98 ! [V_B_2,T_c,V_A_2,T_b] : % 111.99/111.98 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 111.99/111.98 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) % 111.99/111.98 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) % 111.99/111.98 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 111.99/111.98 ! [V_a_2,T_b] : % 111.99/111.98 ( class_Groups_Olinordered__ab__group__add(T_b) % 111.99/111.98 => ( 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))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 111.99/111.98 ! [V_a_2,T_b] : % 111.99/111.98 ( class_Groups_Olinordered__ab__group__add(T_b) % 111.99/111.98 => ( 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))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__nonneg__nonneg,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__nonneg__eq__0__iff,axiom, % 111.99/111.98 ! [V_y_2,V_x_2,T_b] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2)) % 111.99/111.98 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__increasing,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__increasing2,axiom, % 111.99/111.98 ! [V_a,V_b,V_c,T_a] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__nonpos__nonpos,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_split__mult__neg__le,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Oordered__cancel__semiring(T_a) % 111.99/111.98 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 111.99/111.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 111.99/111.98 => 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))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_split__mult__pos__le,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Oordered__ring(T_a) % 111.99/111.98 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 111.99/111.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 111.99/111.98 => 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))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__mono,axiom, % 111.99/111.98 ! [V_d,V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Oordered__semiring(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__mono_H,axiom, % 111.99/111.98 ! [V_d,V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Oordered__semiring(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__left__mono__neg,axiom, % 111.99/111.98 ! [V_c,V_a,V_b,T_a] : % 111.99/111.98 ( class_Rings_Oordered__ring(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__right__mono__neg,axiom, % 111.99/111.98 ! [V_c,V_a,V_b,T_a] : % 111.99/111.98 ( class_Rings_Oordered__ring(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_comm__mult__left__mono,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Oordered__comm__semiring(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__left__mono,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Oordered__semiring(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__right__mono,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Oordered__semiring(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__nonpos__nonpos,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Oordered__ring(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__nonpos__nonneg,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Oordered__cancel__semiring(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__nonneg__nonpos2,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Oordered__cancel__semiring(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__nonneg__nonpos,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Oordered__cancel__semiring(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__nonneg__nonneg,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Oordered__cancel__semiring(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__le__0__iff,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,T_b] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 111.99/111.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_zero__le__mult__iff,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,T_b] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2))) % 111.99/111.98 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) % 111.99/111.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_zero__le__square,axiom, % 111.99/111.98 ! [V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__ring(T_a) % 111.99/111.98 => 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))) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_pos__add__strict,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semidom(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 111.99/111.98 ! [V_a_2,T_b] : % 111.99/111.98 ( class_Groups_Olinordered__ab__group__add(T_b) % 111.99/111.98 => ( 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))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 111.99/111.98 ! [V_a_2,T_b] : % 111.99/111.98 ( class_Groups_Olinordered__ab__group__add(T_b) % 111.99/111.98 => ( 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))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__pos__pos,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__neg__neg,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_not__square__less__zero,axiom, % 111.99/111.98 ! [V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__ring(T_a) % 111.99/111.98 => ~ 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))) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__less__cancel__right__disj,axiom, % 111.99/111.98 ! [V_b_2,V_c_2,V_a_2,T_b] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))) % 111.99/111.98 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) % 111.99/111.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__less__cancel__left__disj,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,V_c_2,T_b] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 111.99/111.98 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) % 111.99/111.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__less__cancel__left__pos,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,V_c_2,T_b] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__pos__pos,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__pos__neg,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__pos__neg2,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_zero__less__mult__pos,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( 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))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_zero__less__mult__pos2,axiom, % 111.99/111.98 ! [V_a,V_b,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( 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))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__less__cancel__left__neg,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,V_c_2,T_b] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__neg__pos,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__neg__neg,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__strict__right__mono,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__strict__left__mono,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_comm__mult__strict__left__mono,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__strict__right__mono__neg,axiom, % 111.99/111.98 ! [V_c,V_a,V_b,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__strict__left__mono__neg,axiom, % 111.99/111.98 ! [V_c,V_a,V_b,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_le__iff__diff__le__0,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,T_b] : % 111.99/111.98 ( class_Groups_Oordered__ab__group__add(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_less__iff__diff__less__0,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,T_b] : % 111.99/111.98 ( class_Groups_Oordered__ab__group__add(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_sum__squares__eq__zero__iff,axiom, % 111.99/111.98 ! [V_y_2,V_x_2,T_b] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_b) % 111.99/111.98 => ( 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) % 111.99/111.98 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__scale__eq__noteq,axiom, % 111.99/111.98 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 111.99/111.98 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 111.99/111.98 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => ( ( V_a = V_b % 111.99/111.98 & V_c != V_d ) % 111.99/111.98 => 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)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_zero__le__one,axiom, % 111.99/111.98 ! [T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semidom(T_a) % 111.99/111.98 => 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))) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_not__one__le__zero,axiom, % 111.99/111.98 ! [T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semidom(T_a) % 111.99/111.98 => ~ 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))) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_not__one__less__zero,axiom, % 111.99/111.98 ! [T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semidom(T_a) % 111.99/111.98 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_zero__less__one,axiom, % 111.99/111.98 ! [T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semidom(T_a) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setsum__empty,axiom, % 111.99/111.98 ! [V_f_2,T_c,T_b] : % 111.99/111.98 ( class_Groups_Ocomm__monoid__add(T_b) % 111.99/111.98 => 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) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setsum_Oempty,axiom, % 111.99/111.98 ! [V_g_2,T_c,T_b] : % 111.99/111.98 ( class_Groups_Ocomm__monoid__add(T_b) % 111.99/111.98 => 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) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setsum_Oinfinite,axiom, % 111.99/111.98 ! [V_g_2,V_A_2,T_b,T_c] : % 111.99/111.98 ( class_Groups_Ocomm__monoid__add(T_c) % 111.99/111.98 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => 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) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setsum__infinite,axiom, % 111.99/111.98 ! [V_f_2,V_A_2,T_b,T_c] : % 111.99/111.98 ( class_Groups_Ocomm__monoid__add(T_c) % 111.99/111.98 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => 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) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_gr0__conv__Suc,axiom, % 111.99/111.98 ! [V_na_2] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) % 111.99/111.98 <=> ? [B_m] : V_na_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_less__Suc0,axiom, % 111.99/111.98 ! [V_na_2] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) % 111.99/111.98 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_less__Suc__eq__0__disj,axiom, % 111.99/111.98 ! [V_na_2,V_m_2] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 111.99/111.98 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 | ? [B_j] : % 111.99/111.98 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_na_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_one__is__add,axiom, % 111.99/111.98 ! [V_na_2,V_m_2] : % 111.99/111.98 ( 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_na_2) % 111.99/111.98 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 111.99/111.98 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 111.99/111.98 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__is__1,axiom, % 111.99/111.98 ! [V_na_2,V_m_2] : % 111.99/111.98 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 111.99/111.98 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 111.99/111.98 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 111.99/111.98 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__gr__0,axiom, % 111.99/111.98 ! [V_na_2,V_m_2] : % 111.99/111.98 ( 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_na_2))) % 111.99/111.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 111.99/111.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_card_Oempty,axiom, % 111.99/111.98 ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 111.99/111.98 % 111.99/111.98 fof(fact_card__infinite,axiom, % 111.99/111.98 ! [V_A_2,T_b] : % 111.99/111.98 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__eq__1__iff,axiom, % 111.99/111.98 ! [V_na_2,V_m_2] : % 111.99/111.98 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 111.99/111.98 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 111.99/111.98 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_diff__less,axiom, % 111.99/111.98 ! [V_m,V_n] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 111.99/111.98 => 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)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_zero__less__diff,axiom, % 111.99/111.98 ! [V_m_2,V_na_2] : % 111.99/111.98 ( 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_na_2),V_m_2))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_nat__0__less__mult__iff,axiom, % 111.99/111.98 ! [V_na_2,V_m_2] : % 111.99/111.98 ( 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_na_2))) % 111.99/111.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__less__cancel1,axiom, % 111.99/111.98 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.98 ( 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_na_2))) % 111.99/111.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__less__cancel2,axiom, % 111.99/111.98 ! [V_na_2,V_k_2,V_m_2] : % 111.99/111.98 ( 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_na_2),V_k_2))) % 111.99/111.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_nat__mult__eq__cancel1,axiom, % 111.99/111.98 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 111.99/111.98 => ( 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_na_2) % 111.99/111.98 <=> V_m_2 = V_na_2 ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_nat__mult__less__cancel1,axiom, % 111.99/111.98 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 111.99/111.98 => ( 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_na_2))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__less__mono1,axiom, % 111.99/111.98 ! [V_k,V_j,V_i] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 111.99/111.98 => 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))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__less__mono2,axiom, % 111.99/111.98 ! [V_k,V_j,V_i] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 111.99/111.98 => 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))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_diff__add__0,axiom, % 111.99/111.98 ! [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) ). % 111.99/111.98 % 111.99/111.98 fof(fact_fold1__singleton__def,axiom, % 111.99/111.98 ! [V_a_2,V_f_2,T_b,V_g_2] : % 111.99/111.98 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2) % 111.99/111.98 => 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 ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_fold1__singleton,axiom, % 111.99/111.98 ! [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 ). % 111.99/111.98 % 111.99/111.98 fof(fact_diff__is__0__eq,axiom, % 111.99/111.98 ! [V_na_2,V_m_2] : % 111.99/111.98 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_diff__is__0__eq_H,axiom, % 111.99/111.98 ! [V_n,V_m] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 111.99/111.98 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_One__nat__def,axiom, % 111.99/111.98 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Min_Osingleton,axiom, % 111.99/111.98 ! [V_x_2,T_b] : % 111.99/111.98 ( class_Orderings_Olinorder(T_b) % 111.99/111.98 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Max_Osingleton,axiom, % 111.99/111.98 ! [V_x_2,T_b] : % 111.99/111.98 ( class_Orderings_Olinorder(T_b) % 111.99/111.98 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__eq__self__implies__10,axiom, % 111.99/111.98 ! [V_n,V_m] : % 111.99/111.98 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 111.99/111.98 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 111.99/111.98 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setsum__eq__0__iff,axiom, % 111.99/111.98 ! [V_f_2,V_F_2,T_b] : % 111.99/111.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 111.99/111.98 => ( 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) % 111.99/111.98 <=> ! [B_x] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) % 111.99/111.98 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_folding__one_Oeq__fold,axiom, % 111.99/111.98 ! [V_A_2,V_F_2,V_f_2,T_b] : % 111.99/111.98 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__pos__nonneg,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__nonneg__pos,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__strict__increasing,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__strict__increasing2,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__neg__nonpos,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__nonpos__neg,axiom, % 111.99/111.98 ! [V_b,V_a,T_a] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__le__cancel__left__pos,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,V_c_2,T_b] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__le__cancel__left__neg,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,V_c_2,T_b] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__strict__mono,axiom, % 111.99/111.98 ! [V_d,V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__strict__mono_H,axiom, % 111.99/111.98 ! [V_d,V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__less__le__imp__less,axiom, % 111.99/111.98 ! [V_d,V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__le__less__imp__less,axiom, % 111.99/111.98 ! [V_d,V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__right__less__imp__less,axiom, % 111.99/111.98 ! [V_b,V_c,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring(T_a) % 111.99/111.98 => ( 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))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__less__imp__less__right,axiom, % 111.99/111.98 ! [V_b,V_c,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( 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))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__left__less__imp__less,axiom, % 111.99/111.98 ! [V_b,V_a,V_c,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring(T_a) % 111.99/111.98 => ( 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))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__less__imp__less__left,axiom, % 111.99/111.98 ! [V_b,V_a,V_c,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( 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))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__right__le__imp__le,axiom, % 111.99/111.98 ! [V_b,V_c,V_a,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( 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))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__left__le__imp__le,axiom, % 111.99/111.98 ! [V_b,V_a,V_c,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__strict(T_a) % 111.99/111.98 => ( 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))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_sum__squares__le__zero__iff,axiom, % 111.99/111.98 ! [V_y_2,V_x_2,T_b] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_b) % 111.99/111.98 => ( 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))) % 111.99/111.98 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_sum__squares__ge__zero,axiom, % 111.99/111.98 ! [V_y,V_x,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__ring(T_a) % 111.99/111.98 => 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)))) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_not__sum__squares__lt__zero,axiom, % 111.99/111.98 ! [V_y,V_x,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__ring(T_a) % 111.99/111.98 => ~ 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))) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_sum__squares__gt__zero__iff,axiom, % 111.99/111.98 ! [V_y_2,V_x_2,T_b] : % 111.99/111.98 ( class_Rings_Olinordered__ring__strict(T_b) % 111.99/111.98 => ( 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)))) % 111.99/111.98 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__left__le__one__le,axiom, % 111.99/111.98 ! [V_y,V_x,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__idom(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 111.99/111.98 => 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)) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__right__le__one__le,axiom, % 111.99/111.98 ! [V_y,V_x,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__idom(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 111.99/111.98 => 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)) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_zero__less__two,axiom, % 111.99/111.98 ! [T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semidom(T_a) % 111.99/111.98 => 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)))) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_card__eq__0__iff,axiom, % 111.99/111.98 ! [V_A_2,T_b] : % 111.99/111.98 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.98 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_card__ge__0__finite,axiom, % 111.99/111.98 ! [V_A_2,T_b] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) % 111.99/111.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_diff__Suc__less,axiom, % 111.99/111.98 ! [V_i,V_n] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 111.99/111.98 => 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)) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Suc__pred,axiom, % 111.99/111.98 ! [V_n] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 111.99/111.98 => 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 ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_n__less__m__mult__n,axiom, % 111.99/111.98 ! [V_m,V_n] : % 111.99/111.98 ( 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)) % 111.99/111.98 => ( 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)) % 111.99/111.98 => 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))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_n__less__n__mult__m,axiom, % 111.99/111.98 ! [V_m,V_n] : % 111.99/111.98 ( 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)) % 111.99/111.98 => ( 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)) % 111.99/111.98 => 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))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_one__less__mult,axiom, % 111.99/111.98 ! [V_m,V_n] : % 111.99/111.98 ( 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)) % 111.99/111.98 => ( 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)) % 111.99/111.98 => 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))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_nat__diff__split,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,V_Pa_2] : % 111.99/111.98 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 111.99/111.98 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 111.99/111.98 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 111.99/111.98 & ! [B_d] : % 111.99/111.98 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 111.99/111.98 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_nat__diff__split__asm,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,V_Pa_2] : % 111.99/111.98 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 111.99/111.98 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 111.99/111.98 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 111.99/111.98 | ? [B_d] : % 111.99/111.98 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 111.99/111.98 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_one__le__mult__iff,axiom, % 111.99/111.98 ! [V_na_2,V_m_2] : % 111.99/111.98 ( 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_na_2))) % 111.99/111.98 <=> ( 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)) % 111.99/111.98 & 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_na_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__le__cancel1,axiom, % 111.99/111.98 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.98 ( 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_na_2))) % 111.99/111.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__le__cancel2,axiom, % 111.99/111.98 ! [V_na_2,V_k_2,V_m_2] : % 111.99/111.98 ( 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_na_2),V_k_2))) % 111.99/111.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_nat__mult__le__cancel1,axiom, % 111.99/111.98 ! [V_na_2,V_m_2,V_k_2] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 111.99/111.98 => ( 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_na_2))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Min__le,axiom, % 111.99/111.98 ! [V_x_2,V_A_2,T_b] : % 111.99/111.98 ( class_Orderings_Olinorder(T_b) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Max__ge,axiom, % 111.99/111.98 ! [V_x_2,V_A_2,T_b] : % 111.99/111.98 ( class_Orderings_Olinorder(T_b) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Min__in,axiom, % 111.99/111.98 ! [V_A_2,T_b] : % 111.99/111.98 ( class_Orderings_Olinorder(T_b) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Max__in,axiom, % 111.99/111.98 ! [V_A_2,T_b] : % 111.99/111.98 ( class_Orderings_Olinorder(T_b) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setprod_Oinsert,axiom, % 111.99/111.98 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] : % 111.99/111.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setprod__insert,axiom, % 111.99/111.98 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] : % 111.99/111.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.99/111.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setsum__eq__Suc0__iff,axiom, % 111.99/111.98 ! [V_f_2,V_A_2,T_b] : % 111.99/111.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => ( 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)) % 111.99/111.98 <=> ? [B_x] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.99/111.98 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 111.99/111.98 & ! [B_xa] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 111.99/111.98 => ( B_x != B_xa % 111.99/111.98 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setsum__eq__1__iff,axiom, % 111.99/111.98 ! [V_f_2,V_A_2,T_b] : % 111.99/111.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => ( 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) % 111.99/111.98 <=> ? [B_x] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.99/111.98 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 111.99/111.98 & ! [B_xa] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 111.99/111.98 => ( B_x != B_xa % 111.99/111.98 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_convex__bound__le,axiom, % 111.99/111.98 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 111.99/111.98 ( class_Rings_Olinordered__semiring__1(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 111.99/111.98 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 111.99/111.98 => 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)) ) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setprod_Oinsert__remove,axiom, % 111.99/111.98 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] : % 111.99/111.98 ( class_Groups_Ocomm__monoid__mult(T_c) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_card__gt__0__iff,axiom, % 111.99/111.98 ! [V_A_2,T_b] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) % 111.99/111.98 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_fold1__insert__idem,axiom, % 111.99/111.98 ! [V_x_2,V_A_2,T_b] : % 111.99/111.98 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 111.99/111.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => 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)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Suc__diff__1,axiom, % 111.99/111.98 ! [V_n] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 111.99/111.98 => 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 ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Suc__pred_H,axiom, % 111.99/111.98 ! [V_n] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 111.99/111.98 => 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))) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__eq__if,axiom, % 111.99/111.98 ! [V_n,V_m] : % 111.99/111.98 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 111.99/111.98 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 => 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)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_semilattice__big_OF__eq,axiom, % 111.99/111.98 ! [V_A_2,V_F_2,V_f_2,T_b] : % 111.99/111.98 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_even__less__0__iff,axiom, % 111.99/111.98 ! [V_a_2,T_b] : % 111.99/111.98 ( class_Rings_Olinordered__idom(T_b) % 111.99/111.98 => ( 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))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setsum__mono2,axiom, % 111.99/111.98 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 111.99/111.98 ( class_Groups_Oordered__comm__monoid__add(T_c) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.99/111.98 => ( ! [B_b] : % 111.99/111.98 ( 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))) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) ) % 111.99/111.98 => 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))) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_Plus__eq__empty__conv,axiom, % 111.99/111.98 ! [V_B_2,V_A_2,T_c,T_b] : % 111.99/111.98 ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) % 111.99/111.98 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.98 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_fold1__in,axiom, % 111.99/111.98 ! [V_A_2,T_b] : % 111.99/111.98 ( class_Groups_Oab__semigroup__mult(T_b) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.98 => ( ! [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)))))) % 111.99/111.98 => 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)) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_card__Suc__eq,axiom, % 111.99/111.98 ! [V_k_2,V_A_2,T_b] : % 111.99/111.98 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 111.99/111.98 <=> ? [B_b,B_B] : % 111.99/111.98 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) % 111.99/111.98 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B)) % 111.99/111.98 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2 % 111.99/111.98 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 111.99/111.98 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setsum__mono3,axiom, % 111.99/111.98 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 111.99/111.98 ( ( class_Groups_Ocomm__monoid__add(T_c) % 111.99/111.98 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 111.99/111.98 => ( ! [B_x] : % 111.99/111.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 111.99/111.98 => 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))) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_double__eq__0__iff,axiom, % 111.99/111.98 ! [V_a_2,T_b] : % 111.99/111.98 ( class_Groups_Olinordered__ab__group__add(T_b) % 111.99/111.98 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_setprod__diff1,axiom, % 111.99/111.98 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] : % 111.99/111.98 ( class_Fields_Ofield(T_c) % 111.99/111.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.98 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c) % 111.99/111.98 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.99/111.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 111.99/111.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.99/111.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__zero__left,axiom, % 111.99/111.98 ! [V_a,T_a] : % 111.99/111.98 ( class_Rings_Odivision__ring(T_a) % 111.99/111.98 => 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) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__zero,axiom, % 111.99/111.98 ! [V_a,T_a] : % 111.99/111.98 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 111.99/111.98 => 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) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__divide__distrib,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Odivision__ring(T_a) % 111.99/111.98 => 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)) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_times__divide__eq__right,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Odivision__ring(T_a) % 111.99/111.98 => 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) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_diff__divide__distrib,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Rings_Odivision__ring(T_a) % 111.99/111.98 => 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)) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__1,axiom, % 111.99/111.98 ! [V_a,T_a] : % 111.99/111.98 ( class_Rings_Odivision__ring(T_a) % 111.99/111.98 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_eq__divide__imp,axiom, % 111.99/111.98 ! [V_b,V_a,V_c,T_a] : % 111.99/111.98 ( class_Rings_Odivision__ring(T_a) % 111.99/111.98 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 111.99/111.98 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__eq__imp,axiom, % 111.99/111.98 ! [V_a,V_b,V_c,T_a] : % 111.99/111.98 ( class_Rings_Odivision__ring(T_a) % 111.99/111.98 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 111.99/111.98 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_nonzero__divide__eq__eq,axiom, % 111.99/111.98 ! [V_a_2,V_b_2,V_c_2,T_b] : % 111.99/111.98 ( class_Rings_Odivision__ring(T_b) % 111.99/111.98 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2 % 111.99/111.98 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_nonzero__eq__divide__eq,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,V_c_2,T_b] : % 111.99/111.98 ( class_Rings_Odivision__ring(T_b) % 111.99/111.98 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) % 111.99/111.98 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_right__inverse__eq,axiom, % 111.99/111.98 ! [V_a_2,V_b_2,T_b] : % 111.99/111.98 ( class_Rings_Odivision__ring(T_b) % 111.99/111.98 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b) % 111.99/111.98 <=> V_a_2 = V_b_2 ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__self,axiom, % 111.99/111.98 ! [V_a,T_a] : % 111.99/111.98 ( class_Rings_Odivision__ring(T_a) % 111.99/111.98 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__self__if,axiom, % 111.99/111.98 ! [V_a,T_a] : % 111.99/111.98 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 111.99/111.98 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 111.99/111.98 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__left__mono__neg,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( 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))) % 111.99/111.98 => 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))) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__left__mono,axiom, % 111.99/111.98 ! [V_c,V_a,V_b,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => ( 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))) % 111.99/111.98 => 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))) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_neg__divide__le__eq,axiom, % 111.99/111.98 ! [V_a_2,V_b_2,V_c_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_neg__le__divide__eq,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,V_c_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__imp__le__div__pos,axiom, % 111.99/111.98 ! [V_x,V_z,V_y,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 111.99/111.98 => ( 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)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__imp__div__pos__le,axiom, % 111.99/111.98 ! [V_z,V_x,V_y,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 111.99/111.98 => ( 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))) % 111.99/111.98 => 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)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_pos__divide__le__eq,axiom, % 111.99/111.98 ! [V_a_2,V_b_2,V_c_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_pos__le__divide__eq,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,V_c_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__le__eq,axiom, % 111.99/111.98 ! [V_a_2,V_c_2,V_b_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 111.99/111.98 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) % 111.99/111.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) % 111.99/111.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_times__divide__times__eq,axiom, % 111.99/111.98 ! [V_w,V_z,V_y,V_x,T_a] : % 111.99/111.98 ( class_Fields_Ofield__inverse__zero(T_a) % 111.99/111.98 => 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)) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__right__mono__neg,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__right__mono,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__le__0__iff,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 111.99/111.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_zero__le__divide__iff,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) % 111.99/111.98 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) % 111.99/111.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__strict__right__mono__neg,axiom, % 111.99/111.98 ! [V_c,V_a,V_b,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__strict__right__mono,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__neg__neg,axiom, % 111.99/111.98 ! [V_y,V_x,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__neg__pos,axiom, % 111.99/111.98 ! [V_y,V_x,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__pos__neg,axiom, % 111.99/111.98 ! [V_y,V_x,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__pos__pos,axiom, % 111.99/111.98 ! [V_y,V_x,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__less__0__iff,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) % 111.99/111.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_zero__less__divide__iff,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) % 111.99/111.98 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) % 111.99/111.98 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_eq__divide__eq,axiom, % 111.99/111.98 ! [V_c_2,V_b_2,V_a_2,T_b] : % 111.99/111.98 ( class_Fields_Ofield__inverse__zero(T_b) % 111.99/111.98 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) % 111.99/111.98 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) % 111.99/111.98 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__eq__eq,axiom, % 111.99/111.98 ! [V_a_2,V_c_2,V_b_2,T_b] : % 111.99/111.98 ( class_Fields_Ofield__inverse__zero(T_b) % 111.99/111.98 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2 % 111.99/111.98 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) % 111.99/111.98 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__divide__mult__cancel__right,axiom, % 111.99/111.98 ! [V_b,V_a,V_c,T_a] : % 111.99/111.98 ( class_Fields_Ofield__inverse__zero(T_a) % 111.99/111.98 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => 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) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__divide__mult__cancel__left,axiom, % 111.99/111.98 ! [V_b,V_a,V_c,T_a] : % 111.99/111.98 ( class_Fields_Ofield__inverse__zero(T_a) % 111.99/111.98 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => 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) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_frac__eq__eq,axiom, % 111.99/111.98 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] : % 111.99/111.98 ( class_Fields_Ofield(T_b) % 111.99/111.98 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.98 => ( 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) % 111.99/111.98 <=> 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) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__nonneg__pos,axiom, % 111.99/111.98 ! [V_y,V_x,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__nonneg__neg,axiom, % 111.99/111.98 ! [V_y,V_x,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_frac__less2,axiom, % 111.99/111.98 ! [V_z,V_w,V_y,V_x,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 111.99/111.98 => 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))) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_frac__less,axiom, % 111.99/111.98 ! [V_z,V_w,V_y,V_x,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 111.99/111.98 => 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))) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_frac__le,axiom, % 111.99/111.98 ! [V_z,V_w,V_y,V_x,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 111.99/111.98 => 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))) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__nonpos__pos,axiom, % 111.99/111.98 ! [V_y,V_x,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__nonpos__neg,axiom, % 111.99/111.98 ! [V_y,V_x,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_less__divide__eq,axiom, % 111.99/111.98 ! [V_c_2,V_b_2,V_a_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 111.99/111.98 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) % 111.99/111.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) % 111.99/111.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__less__eq,axiom, % 111.99/111.98 ! [V_a_2,V_c_2,V_b_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 111.99/111.98 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) % 111.99/111.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) % 111.99/111.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_pos__less__divide__eq,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,V_c_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_pos__divide__less__eq,axiom, % 111.99/111.98 ! [V_a_2,V_b_2,V_c_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__imp__div__pos__less,axiom, % 111.99/111.98 ! [V_z,V_x,V_y,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 111.99/111.98 => ( 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))) % 111.99/111.98 => 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)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_mult__imp__less__div__pos,axiom, % 111.99/111.98 ! [V_x,V_z,V_y,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 111.99/111.98 => ( 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)) % 111.99/111.98 => 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))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_neg__less__divide__eq,axiom, % 111.99/111.98 ! [V_b_2,V_a_2,V_c_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_neg__divide__less__eq,axiom, % 111.99/111.98 ! [V_a_2,V_b_2,V_c_2,T_b] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_b) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) % 111.99/111.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__strict__left__mono,axiom, % 111.99/111.98 ! [V_c,V_a,V_b,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 111.99/111.98 => ( 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))) % 111.99/111.98 => 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))) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__strict__left__mono__neg,axiom, % 111.99/111.98 ! [V_c,V_b,V_a,T_a] : % 111.99/111.98 ( class_Fields_Olinordered__field(T_a) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 111.99/111.98 => ( 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))) % 111.99/111.98 => 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))) ) ) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__num__frac,axiom, % 111.99/111.98 ! [V_x,V_z,V_y,T_a] : % 111.99/111.98 ( class_Fields_Ofield__inverse__zero(T_a) % 111.99/111.98 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => 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) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__divide__eq__iff,axiom, % 111.99/111.98 ! [V_y,V_x,V_z,T_a] : % 111.99/111.98 ( class_Fields_Ofield(T_a) % 111.99/111.98 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => 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) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_add__frac__num,axiom, % 111.99/111.98 ! [V_z,V_x,V_y,T_a] : % 111.99/111.98 ( class_Fields_Ofield__inverse__zero(T_a) % 111.99/111.98 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.98 => 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) ) ) ). % 111.99/111.98 % 111.99/111.98 fof(fact_divide__add__eq__iff,axiom, % 111.99/111.98 ! [V_y,V_x,V_z,T_a] : % 111.99/111.98 ( class_Fields_Ofield(T_a) % 111.99/111.98 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.99 => 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) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_add__frac__eq,axiom, % 111.99/111.99 ! [V_w,V_x,V_z,V_y,T_a] : % 111.99/111.99 ( class_Fields_Ofield(T_a) % 111.99/111.99 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.99 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.99 => 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)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_diff__divide__eq__iff,axiom, % 111.99/111.99 ! [V_y,V_x,V_z,T_a] : % 111.99/111.99 ( class_Fields_Ofield(T_a) % 111.99/111.99 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.99 => 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) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_divide__diff__eq__iff,axiom, % 111.99/111.99 ! [V_y,V_x,V_z,T_a] : % 111.99/111.99 ( class_Fields_Ofield(T_a) % 111.99/111.99 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.99 => 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) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_diff__frac__eq,axiom, % 111.99/111.99 ! [V_w,V_x,V_z,V_y,T_a] : % 111.99/111.99 ( class_Fields_Ofield(T_a) % 111.99/111.99 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.99 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 111.99/111.99 => 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)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_less__half__sum,axiom, % 111.99/111.99 ! [V_b,V_a,T_a] : % 111.99/111.99 ( class_Fields_Olinordered__field(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.99 => 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))))) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_gt__half__sum,axiom, % 111.99/111.99 ! [V_b,V_a,T_a] : % 111.99/111.99 ( class_Fields_Olinordered__field(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 111.99/111.99 => 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)) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_le__divide__eq,axiom, % 111.99/111.99 ! [V_c_2,V_b_2,V_a_2,T_b] : % 111.99/111.99 ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 111.99/111.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) % 111.99/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) % 111.99/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Ints__odd__less__0,axiom, % 111.99/111.99 ! [V_a_2,T_b] : % 111.99/111.99 ( class_Rings_Olinordered__idom(T_b) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 111.99/111.99 => ( 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))) % 111.99/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_hom__fold1__commute,axiom, % 111.99/111.99 ! [V_N_2,V_h_2,T_b] : % 111.99/111.99 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 111.99/111.99 => ( ! [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)) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 111.99/111.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.99 => 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)) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_ex__least__nat__less,axiom, % 111.99/111.99 ! [V_na_2,V_Pa_2] : % 111.99/111.99 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 111.99/111.99 => ( hBOOL(hAPP(V_Pa_2,V_na_2)) % 111.99/111.99 => ? [B_k] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_na_2)) % 111.99/111.99 & ! [B_i] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 111.99/111.99 => ~ hBOOL(hAPP(V_Pa_2,B_i)) ) % 111.99/111.99 & 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)))) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_setprod__mono__one__left,axiom, % 111.99/111.99 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 111.99/111.99 ( class_Groups_Ocomm__monoid__mult(T_c) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 111.99/111.99 => ( ! [B_x] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 111.99/111.99 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 111.99/111.99 => 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) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_setprod__mono__one__right,axiom, % 111.99/111.99 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 111.99/111.99 ( class_Groups_Ocomm__monoid__mult(T_c) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 111.99/111.99 => ( ! [B_x] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 111.99/111.99 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 111.99/111.99 => 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) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_setsum__mono__zero__left,axiom, % 111.99/111.99 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 111.99/111.99 ( class_Groups_Ocomm__monoid__add(T_c) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 111.99/111.99 => ( ! [B_x] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 111.99/111.99 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 111.99/111.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_setsum__mono__zero__right,axiom, % 111.99/111.99 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] : % 111.99/111.99 ( class_Groups_Ocomm__monoid__add(T_c) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) % 111.99/111.99 => ( ! [B_x] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) % 111.99/111.99 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 111.99/111.99 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_field__le__mult__one__interval,axiom, % 111.99/111.99 ! [V_y,V_x,T_a] : % 111.99/111.99 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 111.99/111.99 => ( ! [B_z] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 111.99/111.99 => 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)) ) ) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Ints__0,axiom, % 111.99/111.99 ! [T_b] : % 111.99/111.99 ( class_Rings_Oring__1(T_b) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Ints__add,axiom, % 111.99/111.99 ! [V_b_2,V_a_2,T_b] : % 111.99/111.99 ( class_Rings_Oring__1(T_b) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Ints__mult,axiom, % 111.99/111.99 ! [V_b_2,V_a_2,T_b] : % 111.99/111.99 ( class_Rings_Oring__1(T_b) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Ints__diff,axiom, % 111.99/111.99 ! [V_b_2,V_a_2,T_b] : % 111.99/111.99 ( class_Rings_Oring__1(T_b) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Ints__1,axiom, % 111.99/111.99 ! [T_b] : % 111.99/111.99 ( class_Rings_Oring__1(T_b) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Ints__double__eq__0__iff,axiom, % 111.99/111.99 ! [V_a_2,T_b] : % 111.99/111.99 ( class_Int_Oring__char__0(T_b) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 111.99/111.99 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.99 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Ints__odd__nonzero,axiom, % 111.99/111.99 ! [V_a_2,T_b] : % 111.99/111.99 ( class_Int_Oring__char__0(T_b) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 111.99/111.99 => 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) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Min_Oremove,axiom, % 111.99/111.99 ! [V_x_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.99 => ( ( hAPP(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)) % 111.99/111.99 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) % 111.99/111.99 & ( hAPP(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)) % 111.99/111.99 => 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)))))) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Max_Oremove,axiom, % 111.99/111.99 ! [V_x_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.99 => ( ( hAPP(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)) % 111.99/111.99 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) % 111.99/111.99 & ( hAPP(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)) % 111.99/111.99 => 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)))))) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_setprod__pos__nat,axiom, % 111.99/111.99 ! [V_f_2,V_S_2,T_b] : % 111.99/111.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 111.99/111.99 => ( ! [B_x] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_setsum__SucD,axiom, % 111.99/111.99 ! [V_na_2,V_A_2,V_f_2,T_b] : % 111.99/111.99 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_na_2) % 111.99/111.99 => ? [B_x] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.99/111.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_card_Oneutral,axiom, % 111.99/111.99 ! [V_A_2,T_b] : % 111.99/111.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.99/111.99 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 111.99/111.99 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Min__eqI,axiom, % 111.99/111.99 ! [V_x_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( ! [B_y] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) ) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.99 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Max__eqI,axiom, % 111.99/111.99 ! [V_x_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( ! [B_y] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) ) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.99 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_expand__Suc,axiom, % 111.99/111.99 ! [V_v] : % 111.99/111.99 ( 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))) % 111.99/111.99 => 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))) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_max__number__of,axiom, % 111.99/111.99 ! [V_v,V_u,T_b] : % 111.99/111.99 ( ( class_Int_Onumber(T_b) % 111.99/111.99 & class_Orderings_Oord(T_b) ) % 111.99/111.99 => ( ( 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))) % 111.99/111.99 => 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) ) % 111.99/111.99 & ( ~ 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))) % 111.99/111.99 => 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) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__number__of,axiom, % 111.99/111.99 ! [V_v,V_u,T_b] : % 111.99/111.99 ( ( class_Int_Onumber(T_b) % 111.99/111.99 & class_Orderings_Oord(T_b) ) % 111.99/111.99 => ( ( 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))) % 111.99/111.99 => 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) ) % 111.99/111.99 & ( ~ 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))) % 111.99/111.99 => 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) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_eq__number__of,axiom, % 111.99/111.99 ! [V_y_2,V_x_2,T_b] : % 111.99/111.99 ( ( class_Int_Onumber__ring(T_b) % 111.99/111.99 & class_Int_Oring__char__0(T_b) ) % 111.99/111.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 111.99/111.99 <=> V_x_2 = V_y_2 ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_number__of__reorient,axiom, % 111.99/111.99 ! [V_x_2,V_w_2,T_b] : % 111.99/111.99 ( class_Int_Onumber(T_b) % 111.99/111.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2 % 111.99/111.99 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 111.99/111.99 ! [V_x,V_z,V_y,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup__inf__distrib2,axiom, % 111.99/111.99 ! [V_x,V_z,V_y,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf__assoc,axiom, % 111.99/111.99 ! [V_z,V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf_Oassoc,axiom, % 111.99/111.99 ! [V_c,V_b,V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup__assoc,axiom, % 111.99/111.99 ! [V_z,V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup_Oassoc,axiom, % 111.99/111.99 ! [V_c,V_b,V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 111.99/111.99 ! [V_z,V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup__inf__distrib1,axiom, % 111.99/111.99 ! [V_z,V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf__left__commute,axiom, % 111.99/111.99 ! [V_z,V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 111.99/111.99 ! [V_c,V_a,V_b,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup__left__commute,axiom, % 111.99/111.99 ! [V_z,V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup_Oleft__commute,axiom, % 111.99/111.99 ! [V_c,V_a,V_b,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf__left__idem,axiom, % 111.99/111.99 ! [V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 111.99/111.99 ! [V_b,V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup__left__idem,axiom, % 111.99/111.99 ! [V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup_Oleft__idem,axiom, % 111.99/111.99 ! [V_b,V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf__sup__absorb,axiom, % 111.99/111.99 ! [V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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 ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup__inf__absorb,axiom, % 111.99/111.99 ! [V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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 ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf__commute,axiom, % 111.99/111.99 ! [V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf_Ocommute,axiom, % 111.99/111.99 ! [V_b,V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup__commute,axiom, % 111.99/111.99 ! [V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup_Ocommute,axiom, % 111.99/111.99 ! [V_b,V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf_Oidem,axiom, % 111.99/111.99 ! [V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup_Oidem,axiom, % 111.99/111.99 ! [V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Odistrib__inf__le,axiom, % 111.99/111.99 ! [V_z,V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)))) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Odistrib__sup__le,axiom, % 111.99/111.99 ! [V_z,V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)))) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Min_Oidem,axiom, % 111.99/111.99 ! [V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Max_Oidem,axiom, % 111.99/111.99 ! [V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_le__max__iff__disj,axiom, % 111.99/111.99 ! [V_y_2,V_x_2,V_z_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( 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))) % 111.99/111.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) % 111.99/111.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ole__supE,axiom, % 111.99/111.99 ! [V_x,V_b,V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( 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)) % 111.99/111.99 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 111.99/111.99 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup__mono,axiom, % 111.99/111.99 ! [V_d,V_b,V_c,V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 111.99/111.99 => 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))) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup__least,axiom, % 111.99/111.99 ! [V_z,V_x,V_y,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 111.99/111.99 => 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)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ole__supI,axiom, % 111.99/111.99 ! [V_b,V_x,V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 111.99/111.99 => 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)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup__absorb1,axiom, % 111.99/111.99 ! [V_x,V_y,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 111.99/111.99 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup__absorb2,axiom, % 111.99/111.99 ! [V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 111.99/111.99 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ole__supI2,axiom, % 111.99/111.99 ! [V_a,V_b,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 111.99/111.99 => 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))) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ole__supI1,axiom, % 111.99/111.99 ! [V_b,V_a,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 111.99/111.99 => 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))) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ole__sup__iff,axiom, % 111.99/111.99 ! [V_z_2,V_y_2,V_x_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( 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)) % 111.99/111.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 111.99/111.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ole__iff__sup,axiom, % 111.99/111.99 ! [V_y_2,V_x_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 111.99/111.99 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_le__maxI2,axiom, % 111.99/111.99 ! [V_x,V_y,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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))) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_le__maxI1,axiom, % 111.99/111.99 ! [V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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))) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__le__iff__disj,axiom, % 111.99/111.99 ! [V_z_2,V_y_2,V_x_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( 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)) % 111.99/111.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 111.99/111.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ole__infE,axiom, % 111.99/111.99 ! [V_b,V_a,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( 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))) % 111.99/111.99 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 111.99/111.99 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf__mono,axiom, % 111.99/111.99 ! [V_d,V_b,V_c,V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 111.99/111.99 => 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))) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf__greatest,axiom, % 111.99/111.99 ! [V_z,V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 111.99/111.99 => 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))) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ole__infI,axiom, % 111.99/111.99 ! [V_b,V_a,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 111.99/111.99 => 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))) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf__absorb2,axiom, % 111.99/111.99 ! [V_x,V_y,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 111.99/111.99 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf__absorb1,axiom, % 111.99/111.99 ! [V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 111.99/111.99 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ole__infI2,axiom, % 111.99/111.99 ! [V_a,V_x,V_b,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 111.99/111.99 => 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)) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ole__infI1,axiom, % 111.99/111.99 ! [V_b,V_x,V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 111.99/111.99 => 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)) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ole__inf__iff,axiom, % 111.99/111.99 ! [V_z_2,V_y_2,V_x_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( 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))) % 111.99/111.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 111.99/111.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ole__iff__inf,axiom, % 111.99/111.99 ! [V_y_2,V_x_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 111.99/111.99 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf__le2,axiom, % 111.99/111.99 ! [V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oinf__le1,axiom, % 111.99/111.99 ! [V_y,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_max__less__iff__conj,axiom, % 111.99/111.99 ! [V_z_2,V_y_2,V_x_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( 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)) % 111.99/111.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 111.99/111.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_less__max__iff__disj,axiom, % 111.99/111.99 ! [V_y_2,V_x_2,V_z_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( 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))) % 111.99/111.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 111.99/111.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oless__supI1,axiom, % 111.99/111.99 ! [V_b,V_a,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 111.99/111.99 => 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))) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oless__supI2,axiom, % 111.99/111.99 ! [V_a,V_b,V_x,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 111.99/111.99 => 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))) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__less__iff__disj,axiom, % 111.99/111.99 ! [V_z_2,V_y_2,V_x_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( 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)) % 111.99/111.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) % 111.99/111.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__less__iff__conj,axiom, % 111.99/111.99 ! [V_y_2,V_x_2,V_z_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( 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))) % 111.99/111.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) % 111.99/111.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oless__infI1,axiom, % 111.99/111.99 ! [V_b,V_x,V_a,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 111.99/111.99 => 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)) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Oless__infI2,axiom, % 111.99/111.99 ! [V_a,V_x,V_b,T_a] : % 111.99/111.99 ( class_Orderings_Olinorder(T_a) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 111.99/111.99 => 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)) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_le__number__of,axiom, % 111.99/111.99 ! [V_y_2,V_x_2,T_b] : % 111.99/111.99 ( ( class_Int_Onumber__ring(T_b) % 111.99/111.99 & class_Rings_Olinordered__idom(T_b) ) % 111.99/111.99 => ( 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))) % 111.99/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_max__add__distrib__left,axiom, % 111.99/111.99 ! [V_z,V_y,V_x,T_a] : % 111.99/111.99 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_less__number__of,axiom, % 111.99/111.99 ! [V_y_2,V_x_2,T_b] : % 111.99/111.99 ( ( class_Int_Onumber__ring(T_b) % 111.99/111.99 & class_Rings_Olinordered__idom(T_b) ) % 111.99/111.99 => ( 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))) % 111.99/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__add__distrib__left,axiom, % 111.99/111.99 ! [V_z,V_y,V_x,T_a] : % 111.99/111.99 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_max__diff__distrib__left,axiom, % 111.99/111.99 ! [V_z,V_y,V_x,T_a] : % 111.99/111.99 ( class_Groups_Oordered__ab__group__add(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__diff__distrib__left,axiom, % 111.99/111.99 ! [V_z,V_y,V_x,T_a] : % 111.99/111.99 ( class_Groups_Oordered__ab__group__add(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_add__number__of__left,axiom, % 111.99/111.99 ! [V_z,V_w,V_v,T_a] : % 111.99/111.99 ( class_Int_Onumber__ring(T_a) % 111.99/111.99 => 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) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_add__number__of__eq,axiom, % 111.99/111.99 ! [V_w,V_v,T_a] : % 111.99/111.99 ( class_Int_Onumber__ring(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_number__of__add,axiom, % 111.99/111.99 ! [V_w,V_v,T_a] : % 111.99/111.99 ( class_Int_Onumber__ring(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_mult__number__of__left,axiom, % 111.99/111.99 ! [V_z,V_w,V_v,T_a] : % 111.99/111.99 ( class_Int_Onumber__ring(T_a) % 111.99/111.99 => 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) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_arith__simps_I32_J,axiom, % 111.99/111.99 ! [V_w,V_v,T_a] : % 111.99/111.99 ( class_Int_Onumber__ring(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_number__of__mult,axiom, % 111.99/111.99 ! [V_w,V_v,T_a] : % 111.99/111.99 ( class_Int_Onumber__ring(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_max__0R,axiom, % 111.99/111.99 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 111.99/111.99 % 111.99/111.99 fof(fact_max__0L,axiom, % 111.99/111.99 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 111.99/111.99 % 111.99/111.99 fof(fact_number__of__diff,axiom, % 111.99/111.99 ! [V_w,V_v,T_a] : % 111.99/111.99 ( class_Int_Onumber__ring(T_a) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__0R,axiom, % 111.99/111.99 ! [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) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__0L,axiom, % 111.99/111.99 ! [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) ). % 111.99/111.99 % 111.99/111.99 fof(fact_max__Suc__Suc,axiom, % 111.99/111.99 ! [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)) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__Suc__Suc,axiom, % 111.99/111.99 ! [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)) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__diff,axiom, % 111.99/111.99 ! [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) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 111.99/111.99 ! [T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 111.99/111.99 ! [T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_le__number__of__eq__not__less,axiom, % 111.99/111.99 ! [V_w_2,V_v_2,T_b] : % 111.99/111.99 ( ( class_Int_Onumber(T_b) % 111.99/111.99 & class_Orderings_Olinorder(T_b) ) % 111.99/111.99 => ( 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))) % 111.99/111.99 <=> ~ 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))) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_right__distrib__number__of,axiom, % 111.99/111.99 ! [V_c,V_b,V_v,T_b] : % 111.99/111.99 ( ( class_Int_Onumber(T_b) % 111.99/111.99 & class_Rings_Osemiring(T_b) ) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_left__distrib__number__of,axiom, % 111.99/111.99 ! [V_v,V_b,V_a,T_b] : % 111.99/111.99 ( ( class_Int_Onumber(T_b) % 111.99/111.99 & class_Rings_Osemiring(T_b) ) % 111.99/111.99 => 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))) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_add__number__of__diff1,axiom, % 111.99/111.99 ! [V_c,V_w,V_v,T_a] : % 111.99/111.99 ( class_Int_Onumber__ring(T_a) % 111.99/111.99 => 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) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_right__diff__distrib__number__of,axiom, % 111.99/111.99 ! [V_c,V_b,V_v,T_b] : % 111.99/111.99 ( ( class_Int_Onumber(T_b) % 111.99/111.99 & class_Rings_Oring(T_b) ) % 111.99/111.99 => 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)) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_left__diff__distrib__number__of,axiom, % 111.99/111.99 ! [V_v,V_b,V_a,T_b] : % 111.99/111.99 ( ( class_Int_Onumber(T_b) % 111.99/111.99 & class_Rings_Oring(T_b) ) % 111.99/111.99 => 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))) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_nat__minus__add__max,axiom, % 111.99/111.99 ! [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) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Ints__number__of,axiom, % 111.99/111.99 ! [V_w_2,T_b] : % 111.99/111.99 ( class_Int_Onumber__ring(T_b) % 111.99/111.99 => 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))) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_eq__divide__eq__number__of1,axiom, % 111.99/111.99 ! [V_w_2,V_b_2,V_a_2,T_b] : % 111.99/111.99 ( ( class_Fields_Ofield__inverse__zero(T_b) % 111.99/111.99 & class_Int_Onumber(T_b) ) % 111.99/111.99 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) % 111.99/111.99 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2 ) % 111.99/111.99 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.99 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_eq__divide__eq__number__of,axiom, % 111.99/111.99 ! [V_c_2,V_b_2,V_w_2,T_b] : % 111.99/111.99 ( ( class_Fields_Ofield__inverse__zero(T_b) % 111.99/111.99 & class_Int_Onumber(T_b) ) % 111.99/111.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) % 111.99/111.99 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2 ) % 111.99/111.99 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_divide__eq__eq__number__of,axiom, % 111.99/111.99 ! [V_w_2,V_c_2,V_b_2,T_b] : % 111.99/111.99 ( ( class_Fields_Ofield__inverse__zero(T_b) % 111.99/111.99 & class_Int_Onumber(T_b) ) % 111.99/111.99 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) % 111.99/111.99 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.99 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) ) % 111.99/111.99 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_divide__eq__eq__number__of1,axiom, % 111.99/111.99 ! [V_a_2,V_w_2,V_b_2,T_b] : % 111.99/111.99 ( ( class_Fields_Ofield__inverse__zero(T_b) % 111.99/111.99 & class_Int_Onumber(T_b) ) % 111.99/111.99 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2 % 111.99/111.99 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.99 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) % 111.99/111.99 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) % 111.99/111.99 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ofold__sup__insert,axiom, % 111.99/111.99 ! [V_a_2,V_b_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ofold__inf__insert,axiom, % 111.99/111.99 ! [V_a_2,V_b_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Max_Oin__idem,axiom, % 111.99/111.99 ! [V_x_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.99 => 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) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Min_Oin__idem,axiom, % 111.99/111.99 ! [V_x_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 111.99/111.99 => 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) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Max_OF__eq,axiom, % 111.99/111.99 ! [V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => 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) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Min_OF__eq,axiom, % 111.99/111.99 ! [V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => 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) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_less__divide__eq__number__of1,axiom, % 111.99/111.99 ! [V_w_2,V_b_2,V_a_2,T_b] : % 111.99/111.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.99 & class_Int_Onumber(T_b) ) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) % 111.99/111.99 <=> ( ( 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))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) % 111.99/111.99 & ( ~ 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))) % 111.99/111.99 => ( ( 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))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 111.99/111.99 & ( ~ 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))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_less__divide__eq__number__of,axiom, % 111.99/111.99 ! [V_c_2,V_b_2,V_w_2,T_b] : % 111.99/111.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.99 & class_Int_Onumber(T_b) ) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 111.99/111.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) % 111.99/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) % 111.99/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.99 => 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))) ) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_divide__less__eq__number__of,axiom, % 111.99/111.99 ! [V_w_2,V_c_2,V_b_2,T_b] : % 111.99/111.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.99 & class_Int_Onumber(T_b) ) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 111.99/111.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) % 111.99/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) % 111.99/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.99 => 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))) ) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_divide__less__eq__number__of1,axiom, % 111.99/111.99 ! [V_a_2,V_w_2,V_b_2,T_b] : % 111.99/111.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.99 & class_Int_Onumber(T_b) ) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) % 111.99/111.99 <=> ( ( 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))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 111.99/111.99 & ( ~ 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))) % 111.99/111.99 => ( ( 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))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) % 111.99/111.99 & ( ~ 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))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Osup__le__fold__sup,axiom, % 111.99/111.99 ! [V_b_2,V_a_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 111.99/111.99 ! [V_b_2,V_a_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2))) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Ofold1__belowI,axiom, % 111.99/111.99 ! [V_a_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 111.99/111.99 => 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)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_fold1__below__iff,axiom, % 111.99/111.99 ! [V_x_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.99 => ( 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)) % 111.99/111.99 <=> ? [B_x] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.99/111.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_min__max_Obelow__fold1__iff,axiom, % 111.99/111.99 ! [V_x_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.99 => ( 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))) % 111.99/111.99 <=> ! [B_x] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_fold1__strict__below__iff,axiom, % 111.99/111.99 ! [V_x_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.99 => ( 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)) % 111.99/111.99 <=> ? [B_x] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.99/111.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_strict__below__fold1__iff,axiom, % 111.99/111.99 ! [V_x_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.99 => ( 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))) % 111.99/111.99 <=> ! [B_x] : % 111.99/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Max__insert,axiom, % 111.99/111.99 ! [V_x_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.99 => 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)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Min__insert,axiom, % 111.99/111.99 ! [V_x_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.99 => 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)) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Max_Osubset__idem,axiom, % 111.99/111.99 ! [V_B_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 111.99/111.99 => 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) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Min_Osubset__idem,axiom, % 111.99/111.99 ! [V_B_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 111.99/111.99 => 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) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Max_Oeq__fold__idem_H,axiom, % 111.99/111.99 ! [V_a_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => 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) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_Min_Oeq__fold__idem_H,axiom, % 111.99/111.99 ! [V_a_2,V_A_2,T_b] : % 111.99/111.99 ( class_Orderings_Olinorder(T_b) % 111.99/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 111.99/111.99 => 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) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_le__divide__eq__number__of1,axiom, % 111.99/111.99 ! [V_w_2,V_b_2,V_a_2,T_b] : % 111.99/111.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.99 & class_Int_Onumber(T_b) ) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) % 111.99/111.99 <=> ( ( 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))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) % 111.99/111.99 & ( ~ 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))) % 111.99/111.99 => ( ( 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))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 111.99/111.99 & ( ~ 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))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_le__divide__eq__number__of,axiom, % 111.99/111.99 ! [V_c_2,V_b_2,V_w_2,T_b] : % 111.99/111.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.99 & class_Int_Onumber(T_b) ) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) % 111.99/111.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) % 111.99/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) % 111.99/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.99 => 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))) ) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_divide__le__eq__number__of,axiom, % 111.99/111.99 ! [V_w_2,V_c_2,V_b_2,T_b] : % 111.99/111.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 111.99/111.99 & class_Int_Onumber(T_b) ) % 111.99/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) % 111.99/111.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) % 111.99/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) % 111.99/111.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) % 111.99/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) % 111.99/111.99 => 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))) ) ) ) ) ) ) ). % 111.99/111.99 % 111.99/111.99 fof(fact_divide__le__eq__number__of1,axiom, % 111.99/111.99 ! [V_a_2,V_w_2,V_b_2,T_b] : % 111.99/111.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 112.10/111.99 & class_Int_Onumber(T_b) ) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) % 112.10/111.99 <=> ( ( 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))) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) % 112.10/111.99 & ( ~ 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))) % 112.10/111.99 => ( ( 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))) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) % 112.10/111.99 & ( ~ 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))) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Max_Oinsert,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => 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)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Min_Oinsert,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => 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)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_fold1__antimono,axiom, % 112.10/111.99 ! [V_B_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.10/111.99 => 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))) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Max_Oinsert__remove,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ( hAPP(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)) % 112.10/111.99 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 112.10/111.99 & ( hAPP(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)) % 112.10/111.99 => 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)))))) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Min_Oinsert__remove,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ( hAPP(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)) % 112.10/111.99 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) % 112.10/111.99 & ( hAPP(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)) % 112.10/111.99 => 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)))))) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Max_Oeq__fold_H,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/111.99 => 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) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Min_Oeq__fold_H,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/111.99 => 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) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_max__ord__max,axiom, % 112.10/111.99 ! [T_b] : % 112.10/111.99 ( class_Orderings_Oord(T_b) % 112.10/111.99 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__ord__min,axiom, % 112.10/111.99 ! [T_b] : % 112.10/111.99 ( class_Orderings_Oord(T_b) % 112.10/111.99 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Max_Oclosed,axiom, % 112.10/111.99 ! [V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => ( ! [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)))))) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Min_Oclosed,axiom, % 112.10/111.99 ! [V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => ( ! [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)))))) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OSup__fin_Oremove,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/111.99 => ( ( hAPP(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)) % 112.10/111.99 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 ) % 112.10/111.99 & ( hAPP(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)) % 112.10/111.99 => 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)))))) ) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OInf__fin_Oremove,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/111.99 => ( ( hAPP(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)) % 112.10/111.99 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 ) % 112.10/111.99 & ( hAPP(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)) % 112.10/111.99 => 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)))))) ) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Max_Ohom__commute,axiom, % 112.10/111.99 ! [V_N_2,V_h_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( ! [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)) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 112.10/111.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => 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)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Min_Ohom__commute,axiom, % 112.10/111.99 ! [V_N_2,V_h_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( ! [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)) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 112.10/111.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => 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)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_times__numeral__code_I5_J,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_plus__numeral__code_I9_J,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_less__eq__number__of__int__code,axiom, % 112.10/111.99 ! [V_l_2,V_k_2] : % 112.10/111.99 ( 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))) % 112.10/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_less__number__of__int__code,axiom, % 112.10/111.99 ! [V_l_2,V_k_2] : % 112.10/111.99 ( 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))) % 112.10/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zless__linear,axiom, % 112.10/111.99 ! [V_y,V_x] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 112.10/111.99 | V_x = V_y % 112.10/111.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zless__le,axiom, % 112.10/111.99 ! [V_w_2,V_z_2] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 112.10/111.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 112.10/111.99 & V_z_2 != V_w_2 ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zle__antisym,axiom, % 112.10/111.99 ! [V_w,V_z] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 112.10/111.99 => V_z = V_w ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zle__trans,axiom, % 112.10/111.99 ! [V_k,V_j,V_i] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zle__linear,axiom, % 112.10/111.99 ! [V_w,V_z] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 112.10/111.99 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zle__refl,axiom, % 112.10/111.99 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zdiff__zmult__distrib2,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zdiff__zmult__distrib,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zmult__1,axiom, % 112.10/111.99 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 112.10/111.99 % 112.10/111.99 fof(fact_zmult__1__right,axiom, % 112.10/111.99 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 112.10/111.99 % 112.10/111.99 fof(fact_zadd__commute,axiom, % 112.10/111.99 ! [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) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zmult__commute,axiom, % 112.10/111.99 ! [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) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zadd__left__commute,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zadd__zmult__distrib2,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zadd__assoc,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zmult__assoc,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zadd__zmult__distrib,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zadd__left__mono,axiom, % 112.10/111.99 ! [V_k,V_j,V_i] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 112.10/111.99 => 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))) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zle__add1__eq__le,axiom, % 112.10/111.99 ! [V_z_2,V_w_2] : % 112.10/111.99 ( 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)))) % 112.10/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_add1__zle__eq,axiom, % 112.10/111.99 ! [V_z_2,V_w_2] : % 112.10/111.99 ( 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)) % 112.10/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zless__imp__add1__zle,axiom, % 112.10/111.99 ! [V_z,V_w] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 112.10/111.99 => 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)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zadd__zless__mono,axiom, % 112.10/111.99 ! [V_z,V_z_H,V_w,V_w_H] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 112.10/111.99 => 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))) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zless__add1__eq,axiom, % 112.10/111.99 ! [V_z_2,V_w_2] : % 112.10/111.99 ( 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)))) % 112.10/111.99 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 112.10/111.99 | V_w_2 = V_z_2 ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zadd__strict__right__mono,axiom, % 112.10/111.99 ! [V_k,V_j,V_i] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 112.10/111.99 => 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))) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zle__diff1__eq,axiom, % 112.10/111.99 ! [V_z_2,V_w_2] : % 112.10/111.99 ( 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)))) % 112.10/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zmult__zless__mono2,axiom, % 112.10/111.99 ! [V_k,V_j,V_i] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 112.10/111.99 => 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))) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_pos__zmult__eq__1__iff,axiom, % 112.10/111.99 ! [V_na_2,V_m_2] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 112.10/111.99 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_na_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 112.10/111.99 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 112.10/111.99 & V_na_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_odd__less__0,axiom, % 112.10/111.99 ! [V_z_2] : % 112.10/111.99 ( 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))) % 112.10/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_int__0__less__1,axiom, % 112.10/111.99 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))) ). % 112.10/111.99 % 112.10/111.99 fof(fact_le__imp__0__less,axiom, % 112.10/111.99 ! [V_z] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 112.10/111.99 => 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))) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_int__one__le__iff__zero__less,axiom, % 112.10/111.99 ! [V_z_2] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 112.10/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zadd__0__right,axiom, % 112.10/111.99 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 112.10/111.99 % 112.10/111.99 fof(fact_zadd__0,axiom, % 112.10/111.99 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 112.10/111.99 % 112.10/111.99 fof(fact_odd__nonzero,axiom, % 112.10/111.99 ! [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) ). % 112.10/111.99 % 112.10/111.99 fof(fact_less__bin__lemma,axiom, % 112.10/111.99 ! [V_l_2,V_k_2] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 112.10/111.99 <=> 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))) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OInf__le__Sup,axiom, % 112.10/111.99 ! [V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => 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))) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/111.99 => 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) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/111.99 => 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) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 112.10/111.99 ! [V_x_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => 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 ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 112.10/111.99 ! [V_x_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => 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 ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 112.10/111.99 ! [V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => 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) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 112.10/111.99 ! [V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => 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) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => 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)) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => 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)) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 112.10/111.99 ! [V_B_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 112.10/111.99 => 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) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 112.10/111.99 ! [V_B_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 112.10/111.99 => 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) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_Osup__Inf__absorb,axiom, % 112.10/111.99 ! [V_a_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.10/111.99 => 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 ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 112.10/111.99 ! [V_a_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.10/111.99 => 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 ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 112.10/111.99 ! [V_a_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => 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) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 112.10/111.99 ! [V_a_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => 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) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => 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)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => 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)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ( hAPP(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)) % 112.10/111.99 => 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 ) % 112.10/111.99 & ( hAPP(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)) % 112.10/111.99 => 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)))))) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ( hAPP(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)) % 112.10/111.99 => 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 ) % 112.10/111.99 & ( hAPP(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)) % 112.10/111.99 => 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)))))) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/111.99 => 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) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 112.10/111.99 ! [V_x_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/111.99 => 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) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_self__quotient__aux2,axiom, % 112.10/111.99 ! [V_q,V_r,V_a] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.10/111.99 => ( 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)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_self__quotient__aux1,axiom, % 112.10/111.99 ! [V_q,V_r,V_a] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.10/111.99 => ( 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)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_q__pos__lemma,axiom, % 112.10/111.99 ! [V_r_H,V_q_H,V_b_H] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_q__neg__lemma,axiom, % 112.10/111.99 ! [V_r_H,V_q_H,V_b_H] : % 112.10/111.99 ( 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))) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_unique__quotient__lemma,axiom, % 112.10/111.99 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 112.10/111.99 ( 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))) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zdiv__mono2__lemma,axiom, % 112.10/111.99 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 112.10/111.99 ( 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) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_unique__quotient__lemma__neg,axiom, % 112.10/111.99 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 112.10/111.99 ( 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))) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zdiv__mono2__neg__lemma,axiom, % 112.10/111.99 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 112.10/111.99 ( 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) % 112.10/111.99 => ( 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))) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_number__of__is__id,axiom, % 112.10/111.99 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 112.10/111.99 % 112.10/111.99 fof(fact_int__0__neq__1,axiom, % 112.10/111.99 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 112.10/111.99 ! [V_y,V_x] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 112.10/111.99 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))) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 112.10/111.99 ! [V_y,V_x] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/111.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 112.10/111.99 ! [V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => ( ! [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)))))) % 112.10/111.99 => 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)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 112.10/111.99 ! [V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => ( ! [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)))))) % 112.10/111.99 => 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)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 112.10/111.99 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))) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 112.10/111.99 ! [V_N_2,V_h_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( ! [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)) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 112.10/111.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => 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)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_tsub__def,axiom, % 112.10/111.99 ! [V_x,V_y] : % 112.10/111.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 112.10/111.99 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 112.10/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 112.10/111.99 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 112.10/111.99 ! [V_N_2,V_h_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( ! [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)) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 112.10/111.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/111.99 => 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)) ) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_of__nat__number__of__lemma,axiom, % 112.10/111.99 ! [V_v,T_a] : % 112.10/111.99 ( class_Int_Onumber__ring(T_a) % 112.10/111.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/111.99 => 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) ) % 112.10/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/111.99 => 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) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_nat__number__of__mult__left,axiom, % 112.10/111.99 ! [V_k,V_v_H,V_v] : % 112.10/111.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 112.10/111.99 => 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) ) % 112.10/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 112.10/111.99 => 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) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_mult__nat__number__of,axiom, % 112.10/111.99 ! [V_v_H,V_v] : % 112.10/111.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 112.10/111.99 => 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) ) % 112.10/111.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 112.10/111.99 => 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)) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 112.10/111.99 ! [V_c_2,V_b_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ! [B_x] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2))) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 112.10/111.99 ! [V_c_2,V_b_2,V_A_2,T_b] : % 112.10/111.99 ( class_Orderings_Olinorder(T_b) % 112.10/111.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/111.99 => ( ! [B_x] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) % 112.10/111.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2))) ) ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_of__nat__eq__iff,axiom, % 112.10/111.99 ! [V_na_2,V_m_2,T_b] : % 112.10/111.99 ( class_Nat_Osemiring__char__0(T_b) % 112.10/111.99 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2) % 112.10/111.99 <=> V_m_2 = V_na_2 ) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Pls__def,axiom, % 112.10/111.99 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 112.10/111.99 % 112.10/111.99 fof(fact_rel__simps_I19_J,axiom, % 112.10/111.99 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_rel__simps_I2_J,axiom, % 112.10/111.99 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_add__Pls__right,axiom, % 112.10/111.99 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 112.10/111.99 % 112.10/111.99 fof(fact_add__Pls,axiom, % 112.10/111.99 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 112.10/111.99 % 112.10/111.99 fof(fact_mult__Pls,axiom, % 112.10/111.99 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 112.10/111.99 % 112.10/111.99 fof(fact_diff__bin__simps_I1_J,axiom, % 112.10/111.99 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 112.10/111.99 % 112.10/111.99 fof(fact_int__0,axiom, % 112.10/111.99 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) ). % 112.10/111.99 % 112.10/111.99 fof(fact_int__eq__0__conv,axiom, % 112.10/111.99 ! [V_na_2] : % 112.10/111.99 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/111.99 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 112.10/111.99 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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zero__zle__int,axiom, % 112.10/111.99 ! [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))) ). % 112.10/111.99 % 112.10/111.99 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 112.10/111.99 ! [V_Pa_2] : % 112.10/111.99 ( ! [B_x] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 112.10/111.99 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.10/111.99 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 112.10/111.99 ! [V_Pa_2] : % 112.10/111.99 ( ? [B_x] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 112.10/111.99 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.10/111.99 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 112.10/111.99 ! [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))) ). % 112.10/111.99 % 112.10/111.99 fof(fact_int__less__0__conv,axiom, % 112.10/111.99 ! [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))) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zless__int,axiom, % 112.10/111.99 ! [V_na_2,V_m_2] : % 112.10/111.99 ( 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_na_2))) % 112.10/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 112.10/111.99 ! [V_y_2,V_x_2] : % 112.10/111.99 ( 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))) % 112.10/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zle__int,axiom, % 112.10/111.99 ! [V_na_2,V_m_2] : % 112.10/111.99 ( 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_na_2))) % 112.10/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 112.10/111.99 ! [V_y_2,V_x_2] : % 112.10/111.99 ( 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))) % 112.10/111.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zadd__int__left,axiom, % 112.10/111.99 ! [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) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zadd__int,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zle__iff__zadd,axiom, % 112.10/111.99 ! [V_z_2,V_w_2] : % 112.10/111.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 112.10/111.99 <=> ? [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)) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zero__le__imp__of__nat,axiom, % 112.10/111.99 ! [V_m,T_a] : % 112.10/111.99 ( class_Rings_Olinordered__semidom(T_a) % 112.10/111.99 => 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))) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_of__nat__0__le__iff,axiom, % 112.10/111.99 ! [V_n,T_a] : % 112.10/111.99 ( class_Rings_Olinordered__semidom(T_a) % 112.10/111.99 => 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))) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_of__nat__less__0__iff,axiom, % 112.10/111.99 ! [V_m,T_a] : % 112.10/111.99 ( class_Rings_Olinordered__semidom(T_a) % 112.10/111.99 => ~ 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))) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_number__of__Pls,axiom, % 112.10/111.99 ! [T_a] : % 112.10/111.99 ( class_Int_Onumber__ring(T_a) % 112.10/111.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_semiring__norm_I112_J,axiom, % 112.10/111.99 ! [T_a] : % 112.10/111.99 ( class_Int_Onumber__ring(T_a) % 112.10/111.99 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_zmult__int,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_int__mult,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 112.10/111.99 ! [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)) ). % 112.10/111.99 % 112.10/111.99 fof(fact_add__numeral__0,axiom, % 112.10/111.99 ! [V_a,T_a] : % 112.10/111.99 ( class_Int_Onumber__ring(T_a) % 112.10/111.99 => 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 ) ). % 112.10/111.99 % 112.10/111.99 fof(fact_add__numeral__0__right,axiom, % 112.10/111.99 ! [V_a,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_of__nat__0,axiom, % 112.10/112.00 ! [T_a] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_of__nat__less__iff,axiom, % 112.10/112.00 ! [V_na_2,V_m_2,T_b] : % 112.10/112.00 ( class_Rings_Olinordered__semidom(T_b) % 112.10/112.00 => ( 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_na_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__imp__of__nat__less,axiom, % 112.10/112.00 ! [V_n,V_m,T_a] : % 112.10/112.00 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 112.10/112.00 => 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))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_of__nat__less__imp__less,axiom, % 112.10/112.00 ! [V_n,V_m,T_a] : % 112.10/112.00 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.00 => ( 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))) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_int__1,axiom, % 112.10/112.00 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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 112.10/112.00 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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_of__nat__le__iff,axiom, % 112.10/112.00 ! [V_na_2,V_m_2,T_b] : % 112.10/112.00 ( class_Rings_Olinordered__semidom(T_b) % 112.10/112.00 => ( 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_na_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_of__nat__add,axiom, % 112.10/112.00 ! [V_n,V_m,T_a] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_bin__less__0__simps_I1_J,axiom, % 112.10/112.00 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_semiring__norm_I113_J,axiom, % 112.10/112.00 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__number__of__Pls,axiom, % 112.10/112.00 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 112.10/112.00 % 112.10/112.00 fof(fact_of__nat__mult,axiom, % 112.10/112.00 ! [V_n,V_m,T_a] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zero__is__num__zero,axiom, % 112.10/112.00 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 112.10/112.00 % 112.10/112.00 fof(fact_of__nat__1,axiom, % 112.10/112.00 ! [T_a] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Ints__of__nat,axiom, % 112.10/112.00 ! [V_na_2,T_b] : % 112.10/112.00 ( class_Rings_Oring__1(T_b) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),c_Int_Oring__1__class_OInts(T_b))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_int__le__0__conv,axiom, % 112.10/112.00 ! [V_na_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.00 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_int__Suc0__eq__1,axiom, % 112.10/112.00 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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zless__iff__Suc__zadd,axiom, % 112.10/112.00 ! [V_z_2,V_w_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 112.10/112.00 <=> ? [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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_int__Suc,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiff__int,axiom, % 112.10/112.00 ! [V_m,V_n] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_of__nat__Suc,axiom, % 112.10/112.00 ! [V_m,T_a] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_divide__Numeral0,axiom, % 112.10/112.00 ! [V_x,T_a] : % 112.10/112.00 ( ( class_Fields_Ofield__inverse__zero(T_a) % 112.10/112.00 & class_Int_Onumber__ring(T_a) ) % 112.10/112.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_eq__number__of__0,axiom, % 112.10/112.00 ! [V_v_2] : % 112.10/112.00 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_eq__0__number__of,axiom, % 112.10/112.00 ! [V_v_2] : % 112.10/112.00 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__nat__number__of,axiom, % 112.10/112.00 ! [V_v_H_2,V_v_2] : % 112.10/112.00 ( 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))) % 112.10/112.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 112.10/112.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_of__nat__diff,axiom, % 112.10/112.00 ! [V_m,V_n,T_a] : % 112.10/112.00 ( class_Rings_Oring__1(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 112.10/112.00 => 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)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_le__nat__number__of,axiom, % 112.10/112.00 ! [V_v_H_2,V_v_2] : % 112.10/112.00 ( 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))) % 112.10/112.00 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zero__less__int__conv,axiom, % 112.10/112.00 ! [V_na_2] : % 112.10/112.00 ( 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_na_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmult__zless__mono2__lemma,axiom, % 112.10/112.00 ! [V_k,V_j,V_i] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 112.10/112.00 => 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))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_le__special_I3_J,axiom, % 112.10/112.00 ! [V_x_2,T_b] : % 112.10/112.00 ( ( class_Int_Onumber__ring(T_b) % 112.10/112.00 & class_Rings_Olinordered__idom(T_b) ) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_le__special_I1_J,axiom, % 112.10/112.00 ! [V_y_2,T_b] : % 112.10/112.00 ( ( class_Int_Onumber__ring(T_b) % 112.10/112.00 & class_Rings_Olinordered__idom(T_b) ) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__special_I3_J,axiom, % 112.10/112.00 ! [V_x_2,T_b] : % 112.10/112.00 ( ( class_Int_Onumber__ring(T_b) % 112.10/112.00 & class_Rings_Olinordered__idom(T_b) ) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__special_I1_J,axiom, % 112.10/112.00 ! [V_y_2,T_b] : % 112.10/112.00 ( ( class_Int_Onumber__ring(T_b) % 112.10/112.00 & class_Rings_Olinordered__idom(T_b) ) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_of__nat__0__less__iff,axiom, % 112.10/112.00 ! [V_na_2,T_b] : % 112.10/112.00 ( class_Rings_Olinordered__semidom(T_b) % 112.10/112.00 => ( 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_na_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__0__number__of,axiom, % 112.10/112.00 ! [V_v_2] : % 112.10/112.00 ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_add__nat__number__of,axiom, % 112.10/112.00 ! [V_v_H,V_v] : % 112.10/112.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 112.10/112.00 => 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) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 112.10/112.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 112.10/112.00 => 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) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 112.10/112.00 => 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)) ) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 112.10/112.00 ! [V_y,V_x] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 112.10/112.00 => 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))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_tsub__eq,axiom, % 112.10/112.00 ! [V_x,V_y] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 112.10/112.00 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiff__int__split,axiom, % 112.10/112.00 ! [V_y_2,V_x_2,V_Pa_2] : % 112.10/112.00 ( 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)))) % 112.10/112.00 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 112.10/112.00 => 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)))) ) % 112.10/112.00 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 112.10/112.00 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_number__of2,axiom, % 112.10/112.00 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))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__number__of__add__1,axiom, % 112.10/112.00 ! [V_v] : % 112.10/112.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 112.10/112.00 => 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) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 112.10/112.00 => 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)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__1__add__number__of,axiom, % 112.10/112.00 ! [V_v] : % 112.10/112.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 112.10/112.00 => 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) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 112.10/112.00 => 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)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__number__of__diff__1,axiom, % 112.10/112.00 ! [V_v] : % 112.10/112.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 112.10/112.00 => 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) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 112.10/112.00 => 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)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_setsum__bounded,axiom, % 112.10/112.00 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] : % 112.10/112.00 ( ( class_Groups_Oordered__ab__semigroup__add(T_c) % 112.10/112.00 & class_Rings_Osemiring__1(T_c) ) % 112.10/112.00 => ( ! [B_i] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2)) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) ) % 112.10/112.00 => 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))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Nats__number__of,axiom, % 112.10/112.00 ! [V_w_2,T_b] : % 112.10/112.00 ( class_Int_Onumber__ring(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 112.10/112.00 => 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))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 112.10/112.00 ! [V_A_2,V_x_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 112.10/112.00 <=> 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 112.10/112.00 ! [V_B_2,V_A_2] : % 112.10/112.00 ( V_A_2 = V_B_2 % 112.10/112.00 <=> 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 112.10/112.00 ! [V_y_2,V_x_2] : % 112.10/112.00 ( 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) % 112.10/112.00 <=> V_x_2 = V_y_2 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 112.10/112.00 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))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 112.10/112.00 ! [V_A_2] : % 112.10/112.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 112.10/112.00 <=> 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 112.10/112.00 ! [V_B_2,V_A_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.10/112.00 <=> 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 112.10/112.00 ! [V_B_2,V_A_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.10/112.00 <=> 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_int__int__eq,axiom, % 112.10/112.00 ! [V_na_2,V_m_2] : % 112.10/112.00 ( 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_na_2) % 112.10/112.00 <=> V_m_2 = V_na_2 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_succ__pred,axiom, % 112.10/112.00 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 112.10/112.00 % 112.10/112.00 fof(fact_le__iff__pred__less,axiom, % 112.10/112.00 ! [V_l_2,V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_pred__def,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_succ__def,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Nats__0,axiom, % 112.10/112.00 ! [T_b] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_b) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Nats__add,axiom, % 112.10/112.00 ! [V_b_2,V_a_2,T_b] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Nats__mult,axiom, % 112.10/112.00 ! [V_b_2,V_a_2,T_b] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b))) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Nats__1,axiom, % 112.10/112.00 ! [T_b] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_b) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_of__nat__in__Nats,axiom, % 112.10/112.00 ! [V_na_2,T_b] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_b) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_number__of__succ,axiom, % 112.10/112.00 ! [V_k,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Suc__diff__number__of,axiom, % 112.10/112.00 ! [V_m,V_v] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 112.10/112.00 => 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Suc__nat__number__of__add,axiom, % 112.10/112.00 ! [V_n,V_v] : % 112.10/112.00 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.00 => 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) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.00 => 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) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_decr__mult__lemma,axiom, % 112.10/112.00 ! [V_k_2,V_Pa_2,V_d_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 112.10/112.00 => ( ! [B_x] : % 112.10/112.00 ( hBOOL(hAPP(V_Pa_2,B_x)) % 112.10/112.00 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 112.10/112.00 => ! [B_x] : % 112.10/112.00 ( hBOOL(hAPP(V_Pa_2,B_x)) % 112.10/112.00 => 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)))) ) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_incr__mult__lemma,axiom, % 112.10/112.00 ! [V_k_2,V_Pa_2,V_d_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 112.10/112.00 => ( ! [B_x] : % 112.10/112.00 ( hBOOL(hAPP(V_Pa_2,B_x)) % 112.10/112.00 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 112.10/112.00 => ! [B_x] : % 112.10/112.00 ( hBOOL(hAPP(V_Pa_2,B_x)) % 112.10/112.00 => 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)))) ) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Suc__nat__number__of,axiom, % 112.10/112.00 ! [V_v] : % 112.10/112.00 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.00 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.00 => 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)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zero__less__imp__eq__int,axiom, % 112.10/112.00 ! [V_k] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 112.10/112.00 => ? [B_n] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 112.10/112.00 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_of__nat__number__of__eq,axiom, % 112.10/112.00 ! [V_v,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.00 => 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) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.00 => 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) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_decr__lemma,axiom, % 112.10/112.00 ! [V_z,V_x,V_d] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__idempotent,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__le__D1,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__ge__self,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__eq__0,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 112.10/112.00 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 112.10/112.00 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__zero,axiom, % 112.10/112.00 ! [T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__add__abs,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__mult,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__mult__self,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__minus__commute,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__one,axiom, % 112.10/112.00 ! [T_a] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.00 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__of__nat,axiom, % 112.10/112.00 ! [V_n,T_a] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__divide,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 112.10/112.00 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__int__eq,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_not__neg__0,axiom, % 112.10/112.00 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_not__neg__int,axiom, % 112.10/112.00 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_not__neg__1,axiom, % 112.10/112.00 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__of__nonneg,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.00 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__le__zero__iff,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__ge__zero,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__of__pos,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.00 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zero__less__abs__iff,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__not__less__zero,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => ~ 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__triangle__ineq,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => 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)))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__mult__less,axiom, % 112.10/112.00 ! [V_d,V_b,V_c,V_a,T_a] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 112.10/112.00 => 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))) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__triangle__ineq3,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => 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)))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__triangle__ineq2,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => 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)))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__triangle__ineq2__sym,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => 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)))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nonzero__abs__divide,axiom, % 112.10/112.00 ! [V_a,V_b,T_a] : % 112.10/112.00 ( class_Fields_Olinordered__field(T_a) % 112.10/112.00 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.00 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__zmult__eq__1,axiom, % 112.10/112.00 ! [V_n,V_m] : % 112.10/112.00 ( 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) % 112.10/112.00 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_not__neg__eq__ge__0,axiom, % 112.10/112.00 ! [V_x_2] : % 112.10/112.00 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__def,axiom, % 112.10/112.00 ! [V_Z_2] : % 112.10/112.00 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_not__neg__number__of__Pls,axiom, % 112.10/112.00 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__eq__mult,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Rings_Oordered__ring__abs(T_a) % 112.10/112.00 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 112.10/112.00 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 112.10/112.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 112.10/112.00 => 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)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__mult__pos,axiom, % 112.10/112.00 ! [V_y,V_x,T_a] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 112.10/112.00 => 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)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__triangle__ineq4,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => 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)))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__diff__triangle__ineq,axiom, % 112.10/112.00 ! [V_d,V_c,V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => 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))))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__div__pos,axiom, % 112.10/112.00 ! [V_x,V_y,T_a] : % 112.10/112.00 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 112.10/112.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zabs__less__one__iff,axiom, % 112.10/112.00 ! [V_z_2] : % 112.10/112.00 ( 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))) % 112.10/112.00 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__imp__number__of__eq__0,axiom, % 112.10/112.00 ! [V_v] : % 112.10/112.00 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.00 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_eq__nat__number__of,axiom, % 112.10/112.00 ! [V_v_H_2,V_v_2] : % 112.10/112.00 ( 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) % 112.10/112.00 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 112.10/112.00 => 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))) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 112.10/112.00 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 112.10/112.00 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 112.10/112.00 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__number__of__add__left,axiom, % 112.10/112.00 ! [V_k,V_v_H,V_v] : % 112.10/112.00 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.00 => 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) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.00 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 112.10/112.00 => 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) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 112.10/112.00 => 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) ) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_int__nat__number__of,axiom, % 112.10/112.00 ! [V_v] : % 112.10/112.00 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.00 => 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) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.00 => 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) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__number__of__pred__iff__0,axiom, % 112.10/112.00 ! [V_v_2] : % 112.10/112.00 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 112.10/112.00 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_incr__lemma,axiom, % 112.10/112.00 ! [V_x,V_z,V_d] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 112.10/112.00 => 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)))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 112.10/112.00 ! [V_N_2] : % 112.10/112.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 112.10/112.00 <=> ? [B_m] : % 112.10/112.00 ! [B_x] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_finite__nat__set__iff__bounded,axiom, % 112.10/112.00 ! [V_N_2] : % 112.10/112.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 112.10/112.00 <=> ? [B_m] : % 112.10/112.00 ! [B_x] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_int__val__lemma,axiom, % 112.10/112.00 ! [V_k_2,V_f_2,V_na_2] : % 112.10/112.00 ( ! [B_i] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_na_2)) % 112.10/112.00 => 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))) ) % 112.10/112.00 => ( 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)) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_na_2))) % 112.10/112.00 => ? [B_i] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_na_2)) % 112.10/112.00 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat0__intermed__int__val,axiom, % 112.10/112.00 ! [V_k_2,V_f_2,V_na_2] : % 112.10/112.00 ( ! [B_i] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_na_2)) % 112.10/112.00 => 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))) ) % 112.10/112.00 => ( 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)) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_na_2))) % 112.10/112.00 => ? [B_i] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_na_2)) % 112.10/112.00 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__Min__eq__Max,axiom, % 112.10/112.00 ! [V_S_2,T_b] : % 112.10/112.00 ( class_Groups_Olinordered__ab__group__add(T_b) % 112.10/112.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.10/112.00 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.00 => 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)) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__Max__eq__Min,axiom, % 112.10/112.00 ! [V_S_2,T_b] : % 112.10/112.00 ( class_Groups_Olinordered__ab__group__add(T_b) % 112.10/112.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.10/112.00 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.00 => 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)) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__intermed__int__val,axiom, % 112.10/112.00 ! [V_k_2,V_f_2,V_na_2,V_m_2] : % 112.10/112.00 ( ! [B_i] : % 112.10/112.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 112.10/112.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_na_2)) ) % 112.10/112.00 => 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))) ) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_na_2))) % 112.10/112.00 => ? [B_i] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 112.10/112.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_na_2)) % 112.10/112.00 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ComplI,axiom, % 112.10/112.00 ! [V_A_2,V_c_2,T_b] : % 112.10/112.00 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_negative__zle,axiom, % 112.10/112.00 ! [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))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_negative__zless,axiom, % 112.10/112.00 ! [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))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_number__of__minus,axiom, % 112.10/112.00 ! [V_w,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_arith__simps_I30_J,axiom, % 112.10/112.00 ! [V_w,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__minus,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_a) % 112.10/112.00 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_double__compl,axiom, % 112.10/112.00 ! [V_x,T_a] : % 112.10/112.00 ( class_Lattices_Oboolean__algebra(T_a) % 112.10/112.00 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_uminus__apply,axiom, % 112.10/112.00 ! [V_x_2,V_A_2,T_c,T_b] : % 112.10/112.00 ( class_Groups_Ouminus(T_b) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_equation__minus__iff,axiom, % 112.10/112.00 ! [V_b_2,V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_b) % 112.10/112.00 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) % 112.10/112.00 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__equation__iff,axiom, % 112.10/112.00 ! [V_b_2,V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_b) % 112.10/112.00 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2 % 112.10/112.00 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__equal__iff__equal,axiom, % 112.10/112.00 ! [V_b_2,V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_b) % 112.10/112.00 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) % 112.10/112.00 <=> V_a_2 = V_b_2 ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_compl__eq__compl__iff,axiom, % 112.10/112.00 ! [V_y_2,V_x_2,T_b] : % 112.10/112.00 ( class_Lattices_Oboolean__algebra(T_b) % 112.10/112.00 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2) % 112.10/112.00 <=> V_x_2 = V_y_2 ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__number__of__mult,axiom, % 112.10/112.00 ! [V_z,V_w,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_le__minus__iff,axiom, % 112.10/112.00 ! [V_b_2,V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__le__iff,axiom, % 112.10/112.00 ! [V_b_2,V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__le__iff__le,axiom, % 112.10/112.00 ! [V_a_2,V_b_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_compl__le__compl__iff,axiom, % 112.10/112.00 ! [V_y_2,V_x_2,T_b] : % 112.10/112.00 ( class_Lattices_Oboolean__algebra(T_b) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_le__imp__neg__le,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 112.10/112.00 => 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))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_compl__mono,axiom, % 112.10/112.00 ! [V_y,V_x,T_a] : % 112.10/112.00 ( class_Lattices_Oboolean__algebra(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 112.10/112.00 => 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))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__zero,axiom, % 112.10/112.00 ! [T_a] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_a) % 112.10/112.00 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__0__equal__iff__equal,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_b) % 112.10/112.00 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 112.10/112.00 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_equal__neg__zero,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Olinordered__ab__group__add(T_b) % 112.10/112.00 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) % 112.10/112.00 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__equal__0__iff__equal,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_b) % 112.10/112.00 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 112.10/112.00 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__equal__zero,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Olinordered__ab__group__add(T_b) % 112.10/112.00 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2 % 112.10/112.00 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__less__iff__less,axiom, % 112.10/112.00 ! [V_a_2,V_b_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__less__iff,axiom, % 112.10/112.00 ! [V_b_2,V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__minus__iff,axiom, % 112.10/112.00 ! [V_b_2,V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__add__distrib,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oab__group__add(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__add,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_add__minus__cancel,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_a) % 112.10/112.00 => 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 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__add__cancel,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_a) % 112.10/112.00 => 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 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_square__eq__iff,axiom, % 112.10/112.00 ! [V_b_2,V_a_2,T_b] : % 112.10/112.00 ( class_Rings_Oidom(T_b) % 112.10/112.00 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2) % 112.10/112.00 <=> ( V_a_2 = V_b_2 % 112.10/112.00 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__mult__minus,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Rings_Oring(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__mult__commute,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Rings_Oring(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__mult__left,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Rings_Oring(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__mult__right,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Rings_Oring(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Compl__iff,axiom, % 112.10/112.00 ! [V_A_2,V_c_2,T_b] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 112.10/112.00 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ComplD,axiom, % 112.10/112.00 ! [V_A_2,V_c_2,T_b] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 112.10/112.00 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ComplE,axiom, % 112.10/112.00 ! [V_A_2,V_c_2,T_b] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 112.10/112.00 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__diff__eq,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oab__group__add(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Compl__subset__Compl__iff,axiom, % 112.10/112.00 ! [V_B_2,V_A_2,T_b] : % 112.10/112.00 ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Compl__anti__mono,axiom, % 112.10/112.00 ! [V_B_2,V_A_2,T_b] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.10/112.00 => 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zminus__0,axiom, % 112.10/112.00 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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__divide__left,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Rings_Odivision__ring(T_a) % 112.10/112.00 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__divide__right,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Fields_Ofield__inverse__zero(T_a) % 112.10/112.00 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__divide__divide,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Fields_Ofield__inverse__zero(T_a) % 112.10/112.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__minus__cancel,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__Pls,axiom, % 112.10/112.00 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 112.10/112.00 % 112.10/112.00 fof(fact_zminus__zadd__distrib,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__numeral__code_I5_J,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmult__zminus,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__0__le__iff__le,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_le__minus__self__iff,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Olinordered__ab__group__add(T_b) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__le__0__iff__le,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__le__self__iff,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Olinordered__ab__group__add(T_b) % 112.10/112.00 => ( 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)) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__minus__self__iff,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__0__less__iff__less,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__less__0__iff__less,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__less__nonneg,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Olinordered__ab__group__add(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__unique,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_a) % 112.10/112.00 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.00 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ab__left__minus,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Oab__group__add(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_left__minus,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_eq__neg__iff__add__eq__0,axiom, % 112.10/112.00 ! [V_b_2,V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_b) % 112.10/112.00 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) % 112.10/112.00 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_right__minus,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_diff__0,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 112.10/112.00 ! [V_y,V_x,T_a] : % 112.10/112.00 ( class_Rings_Ocomm__ring__1(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_diff__def,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ab__diff__minus,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oab__group__add(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_diff__minus__eq__add,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Ogroup__add(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 112.10/112.00 ! [V_x,T_a] : % 112.10/112.00 ( class_Rings_Ocomm__ring__1(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_square__eq__1__iff,axiom, % 112.10/112.00 ! [V_x_2,T_b] : % 112.10/112.00 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 112.10/112.00 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 112.10/112.00 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b) % 112.10/112.00 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nonzero__minus__divide__divide,axiom, % 112.10/112.00 ! [V_a,V_b,T_a] : % 112.10/112.00 ( class_Rings_Odivision__ring(T_a) % 112.10/112.00 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nonzero__minus__divide__right,axiom, % 112.10/112.00 ! [V_a,V_b,T_a] : % 112.10/112.00 ( class_Rings_Odivision__ring(T_a) % 112.10/112.00 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.00 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__le__D2,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__leI,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__le__iff,axiom, % 112.10/112.00 ! [V_b_2,V_a_2,T_b] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) % 112.10/112.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 112.10/112.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__ge__minus__self,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__less__iff,axiom, % 112.10/112.00 ! [V_b_2,V_a_2,T_b] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) % 112.10/112.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 112.10/112.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_subset__Compl__self__eq,axiom, % 112.10/112.00 ! [V_A_2,T_b] : % 112.10/112.00 ( 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))) % 112.10/112.00 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__max__eq__min,axiom, % 112.10/112.00 ! [V_y,V_x,T_a] : % 112.10/112.00 ( class_Groups_Olinordered__ab__group__add(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__min__eq__max,axiom, % 112.10/112.00 ! [V_y,V_x,T_a] : % 112.10/112.00 ( class_Groups_Olinordered__ab__group__add(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zadd__zminus__inverse2,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_negative__eq__positive,axiom, % 112.10/112.00 ! [V_m_2,V_na_2] : % 112.10/112.00 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) % 112.10/112.00 <=> ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.00 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_not__int__zless__negative,axiom, % 112.10/112.00 ! [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)))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_diff__int__def,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_diff__int__def__symmetric,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Ints__minus,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Rings_Oring__1(T_b) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 112.10/112.00 => 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))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__of__nonpos,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 112.10/112.00 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__minus__le__zero,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__if,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Oabs__if(T_a) % 112.10/112.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 112.10/112.00 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 112.10/112.00 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__of__neg,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 112.10/112.00 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_diff__number__of__eq,axiom, % 112.10/112.00 ! [V_w,V_v,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_int__zle__neg,axiom, % 112.10/112.00 ! [V_m_2,V_na_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))) % 112.10/112.00 <=> ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.00 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_negative__zle__0,axiom, % 112.10/112.00 ! [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))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__numeral__code_I6_J,axiom, % 112.10/112.00 ! [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))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zabs__def,axiom, % 112.10/112.00 ! [V_i] : % 112.10/112.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.00 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.00 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__zminus__int,axiom, % 112.10/112.00 ! [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))))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__number__of,axiom, % 112.10/112.00 ! [V_x,T_a] : % 112.10/112.00 ( ( class_Int_Onumber__ring(T_a) % 112.10/112.00 & class_Rings_Olinordered__idom(T_a) ) % 112.10/112.00 => ( ( 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))) % 112.10/112.00 => 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)) ) % 112.10/112.00 & ( ~ 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))) % 112.10/112.00 => 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) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_add__number__of__diff2,axiom, % 112.10/112.00 ! [V_w,V_c,V_v,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_number__of__pred,axiom, % 112.10/112.00 ! [V_w,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_not__zle__0__negative,axiom, % 112.10/112.00 ! [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))))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_negative__zless__0,axiom, % 112.10/112.00 ! [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))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ord_OatMost__iff,axiom, % 112.10/112.00 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ord_OatLeast__iff,axiom, % 112.10/112.00 ! [V_k_2,V_less__eq_2,V_i_2,T_b] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ord_OlessThan__iff,axiom, % 112.10/112.00 ! [V_k_2,V_less_2,V_i_2,T_b] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ord_OgreaterThan__iff,axiom, % 112.10/112.00 ! [V_k_2,V_less_2,V_i_2,T_b] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ord_OatLeastAtMost__iff,axiom, % 112.10/112.00 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] : % 112.10/112.00 ( 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))) % 112.10/112.00 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 112.10/112.00 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 112.10/112.00 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] : % 112.10/112.00 ( 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))) % 112.10/112.00 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 112.10/112.00 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ord_OatLeastLessThan__iff,axiom, % 112.10/112.00 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 112.10/112.00 ( 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))) % 112.10/112.00 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 112.10/112.00 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_double__complement,axiom, % 112.10/112.00 ! [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 ). % 112.10/112.00 % 112.10/112.00 fof(fact_Compl__eq__Compl__iff,axiom, % 112.10/112.00 ! [V_B_2,V_A_2,T_b] : % 112.10/112.00 ( 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) % 112.10/112.00 <=> V_A_2 = V_B_2 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zminus__zminus,axiom, % 112.10/112.00 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 112.10/112.00 % 112.10/112.00 fof(fact_eq__special_I1_J,axiom, % 112.10/112.00 ! [V_y_2,T_b] : % 112.10/112.00 ( class_Int_Onumber__ring(T_b) % 112.10/112.00 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 112.10/112.00 <=> 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)))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_eq__special_I3_J,axiom, % 112.10/112.00 ! [V_x_2,T_b] : % 112.10/112.00 ( class_Int_Onumber__ring(T_b) % 112.10/112.00 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b) % 112.10/112.00 <=> 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)))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 112.10/112.00 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] : % 112.10/112.00 ( 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))) % 112.10/112.00 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 112.10/112.00 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_negD,axiom, % 112.10/112.00 ! [V_x] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.00 => ? [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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_sgn__1__neg,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.00 => ( 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)) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_sgn__neg,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 112.10/112.00 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_sgn__if,axiom, % 112.10/112.00 ! [V_x,T_a] : % 112.10/112.00 ( class_Groups_Osgn__if(T_a) % 112.10/112.00 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.00 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 112.10/112.00 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 112.10/112.00 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 112.10/112.00 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_sgn__sgn,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_sgn__0__0,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.00 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) % 112.10/112.00 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_sgn0,axiom, % 112.10/112.00 ! [T_a] : % 112.10/112.00 ( class_Groups_Osgn__if(T_a) % 112.10/112.00 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_sgn__times,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_iszero__def,axiom, % 112.10/112.00 ! [V_z_2,T_b] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_b) % 112.10/112.00 => ( c_Int_Oiszero(T_b,V_z_2) % 112.10/112.00 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_iszero__0,axiom, % 112.10/112.00 ! [T_a] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_a) % 112.10/112.00 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_not__iszero__1,axiom, % 112.10/112.00 ! [T_a] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_a) % 112.10/112.00 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_sgn__greater,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_sgn__less,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_abs__sgn,axiom, % 112.10/112.00 ! [V_k,T_a] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mult__sgn__abs,axiom, % 112.10/112.00 ! [V_x,T_a] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.00 => 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 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_iszero__Numeral0,axiom, % 112.10/112.00 ! [T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_sgn__pos,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.00 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_sgn__1__pos,axiom, % 112.10/112.00 ! [V_a_2,T_b] : % 112.10/112.00 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.00 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_eq__number__of__eq,axiom, % 112.10/112.00 ! [V_y_2,V_x_2,T_b] : % 112.10/112.00 ( class_Int_Onumber__ring(T_b) % 112.10/112.00 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 112.10/112.00 <=> 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)))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zsgn__def,axiom, % 112.10/112.00 ! [V_i] : % 112.10/112.00 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.00 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 112.10/112.00 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 112.10/112.00 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 112.10/112.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 112.10/112.00 => 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)) ) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_eq__special_I2_J,axiom, % 112.10/112.00 ! [V_y_2,T_b] : % 112.10/112.00 ( class_Int_Onumber__ring(T_b) % 112.10/112.00 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) % 112.10/112.00 <=> 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)))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_eq__special_I4_J,axiom, % 112.10/112.00 ! [V_x_2,T_b] : % 112.10/112.00 ( class_Int_Onumber__ring(T_b) % 112.10/112.00 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b) % 112.10/112.00 <=> 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))))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_diff__special_I1_J,axiom, % 112.10/112.00 ! [V_w,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_diff__special_I2_J,axiom, % 112.10/112.00 ! [V_v,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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)))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Suc__diff__eq__diff__pred,axiom, % 112.10/112.00 ! [V_m,V_n] : % 112.10/112.00 ( 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)) % 112.10/112.00 => 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)))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_setprod__pos,axiom, % 112.10/112.00 ! [V_f_2,V_A_2,T_b,T_c] : % 112.10/112.00 ( class_Rings_Olinordered__semidom(T_c) % 112.10/112.00 => ( ! [B_x] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_setprod__nonneg,axiom, % 112.10/112.00 ! [V_f_2,V_A_2,T_b,T_c] : % 112.10/112.00 ( class_Rings_Olinordered__semidom(T_c) % 112.10/112.00 => ( ! [B_x] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) ) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I51_J,axiom, % 112.10/112.00 ! [V_l_2,V_k_2] : % 112.10/112.00 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 112.10/112.00 <=> V_k_2 = V_l_2 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I34_J,axiom, % 112.10/112.00 ! [V_l_2,V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__eq__int__code_I16_J,axiom, % 112.10/112.00 ! [V_k2_2,V_k1_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I17_J,axiom, % 112.10/112.00 ! [V_l_2,V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__int__code_I16_J,axiom, % 112.10/112.00 ! [V_k2_2,V_k1_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I46_J,axiom, % 112.10/112.00 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I39_J,axiom, % 112.10/112.00 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 112.10/112.00 % 112.10/112.00 fof(fact_bin__less__0__simps_I4_J,axiom, % 112.10/112.00 ! [V_w_2] : % 112.10/112.00 ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I22_J,axiom, % 112.10/112.00 ! [V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I12_J,axiom, % 112.10/112.00 ! [V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Bit1__def,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__number__of__Bit1,axiom, % 112.10/112.00 ! [V_w_2] : % 112.10/112.00 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 112.10/112.00 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__Bit1,axiom, % 112.10/112.00 ! [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))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_iszero__number__of__Bit1,axiom, % 112.10/112.00 ! [V_w,T_a] : % 112.10/112.00 ( ( class_Int_Onumber__ring(T_a) % 112.10/112.00 & class_Int_Oring__char__0(T_a) ) % 112.10/112.00 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_succ__Pls,axiom, % 112.10/112.00 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 112.10/112.00 % 112.10/112.00 fof(fact_number__of__Bit1,axiom, % 112.10/112.00 ! [V_w,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mult__numeral__1,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mult__numeral__1__right,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_numeral__1__eq__1,axiom, % 112.10/112.00 ! [T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_semiring__norm_I110_J,axiom, % 112.10/112.00 ! [T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I5_J,axiom, % 112.10/112.00 ! [V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I29_J,axiom, % 112.10/112.00 ! [V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_divide__Numeral1,axiom, % 112.10/112.00 ! [V_x,T_a] : % 112.10/112.00 ( ( class_Fields_Ofield(T_a) % 112.10/112.00 & class_Int_Onumber__ring(T_a) ) % 112.10/112.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_divide__numeral__1,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( ( class_Fields_Ofield(T_a) % 112.10/112.00 & class_Int_Onumber__ring(T_a) ) % 112.10/112.00 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_one__is__num__one,axiom, % 112.10/112.00 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Numeral1__eq1__nat,axiom, % 112.10/112.00 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__numeral__1__eq__1,axiom, % 112.10/112.00 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 112.10/112.00 % 112.10/112.00 fof(fact_not__iszero__Numeral1,axiom, % 112.10/112.00 ! [T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_numeral__3__eq__3,axiom, % 112.10/112.00 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)))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_numeral__1__eq__Suc__0,axiom, % 112.10/112.00 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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 112.10/112.00 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))))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Suc3__eq__add__3,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 112.10/112.00 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)))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_le__special_I2_J,axiom, % 112.10/112.00 ! [V_y_2,T_b] : % 112.10/112.00 ( ( class_Int_Onumber__ring(T_b) % 112.10/112.00 & class_Rings_Olinordered__idom(T_b) ) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_le__special_I4_J,axiom, % 112.10/112.00 ! [V_x_2,T_b] : % 112.10/112.00 ( ( class_Int_Onumber__ring(T_b) % 112.10/112.00 & class_Rings_Olinordered__idom(T_b) ) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__special_I4_J,axiom, % 112.10/112.00 ! [V_x_2,T_b] : % 112.10/112.00 ( ( class_Int_Onumber__ring(T_b) % 112.10/112.00 & class_Rings_Olinordered__idom(T_b) ) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__special_I2_J,axiom, % 112.10/112.00 ! [V_y_2,T_b] : % 112.10/112.00 ( ( class_Int_Onumber__ring(T_b) % 112.10/112.00 & class_Rings_Olinordered__idom(T_b) ) % 112.10/112.00 => ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_add__special_I3_J,axiom, % 112.10/112.00 ! [V_v,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_add__special_I2_J,axiom, % 112.10/112.00 ! [V_w,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_one__code__numeral__code,axiom, % 112.10/112.00 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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__2__cases,axiom, % 112.10/112.00 ! [V_n] : % 112.10/112.00 ( 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))))) % 112.10/112.00 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.00 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_half__gt__zero,axiom, % 112.10/112.00 ! [V_r,T_a] : % 112.10/112.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 112.10/112.00 & class_Int_Onumber__ring(T_a) ) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 112.10/112.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_half__gt__zero__iff,axiom, % 112.10/112.00 ! [V_r_2,T_b] : % 112.10/112.00 ( ( class_Fields_Olinordered__field__inverse__zero(T_b) % 112.10/112.00 & class_Int_Onumber__ring(T_b) ) % 112.10/112.00 => ( 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)))))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__1__add__1,axiom, % 112.10/112.00 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))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 112.10/112.00 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)))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_code__numeral__zero__minus__one,axiom, % 112.10/112.00 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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I48_J,axiom, % 112.10/112.00 ! [V_l_2,V_k_2] : % 112.10/112.00 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 112.10/112.00 <=> V_k_2 = V_l_2 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__eq__int__code_I13_J,axiom, % 112.10/112.00 ! [V_k2_2,V_k1_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I31_J,axiom, % 112.10/112.00 ! [V_l_2,V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__int__code_I13_J,axiom, % 112.10/112.00 ! [V_k2_2,V_k1_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I14_J,axiom, % 112.10/112.00 ! [V_l_2,V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Bit0__Pls,axiom, % 112.10/112.00 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I38_J,axiom, % 112.10/112.00 ! [V_l_2] : % 112.10/112.00 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 112.10/112.00 <=> c_Int_OPls = V_l_2 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I44_J,axiom, % 112.10/112.00 ! [V_k_2] : % 112.10/112.00 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 112.10/112.00 <=> V_k_2 = c_Int_OPls ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I49_J,axiom, % 112.10/112.00 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I50_J,axiom, % 112.10/112.00 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Bit0__def,axiom, % 112.10/112.00 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 112.10/112.00 % 112.10/112.00 fof(fact_add__Bit0__Bit0,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mult__Bit0,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_diff__bin__simps_I7_J,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_minus__Bit0,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_bin__less__0__simps_I3_J,axiom, % 112.10/112.00 ! [V_w_2] : % 112.10/112.00 ( 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))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I21_J,axiom, % 112.10/112.00 ! [V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I27_J,axiom, % 112.10/112.00 ! [V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__eq__int__code_I14_J,axiom, % 112.10/112.00 ! [V_k2_2,V_k1_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I32_J,axiom, % 112.10/112.00 ! [V_l_2,V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I4_J,axiom, % 112.10/112.00 ! [V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I10_J,axiom, % 112.10/112.00 ! [V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__int__code_I15_J,axiom, % 112.10/112.00 ! [V_k2_2,V_k1_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I16_J,axiom, % 112.10/112.00 ! [V_l_2,V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_add__Bit1__Bit0,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_add__Bit0__Bit1,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_diff__bin__simps_I3_J,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_diff__bin__simps_I9_J,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_diff__bin__simps_I10_J,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__number__of__Bit0,axiom, % 112.10/112.00 ! [V_w_2] : % 112.10/112.00 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 112.10/112.00 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_pred__Bit0,axiom, % 112.10/112.00 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_pred__Bit1,axiom, % 112.10/112.00 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 112.10/112.00 % 112.10/112.00 fof(fact_iszero__number__of__Bit0,axiom, % 112.10/112.00 ! [V_w_2,T_b] : % 112.10/112.00 ( ( class_Int_Onumber__ring(T_b) % 112.10/112.00 & class_Int_Oring__char__0(T_b) ) % 112.10/112.00 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2))) % 112.10/112.00 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_succ__Bit1,axiom, % 112.10/112.00 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_succ__Bit0,axiom, % 112.10/112.00 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 112.10/112.00 % 112.10/112.00 fof(fact_number__of__Bit0,axiom, % 112.10/112.00 ! [V_w,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__eq__int__code_I15_J,axiom, % 112.10/112.00 ! [V_k2_2,V_k1_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I33_J,axiom, % 112.10/112.00 ! [V_l_2,V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_less__int__code_I14_J,axiom, % 112.10/112.00 ! [V_k2_2,V_k1_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_rel__simps_I15_J,axiom, % 112.10/112.00 ! [V_l_2,V_k_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mult__Bit1,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_diff__bin__simps_I8_J,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_add__Bit1__Bit1,axiom, % 112.10/112.00 ! [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))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zero__code__numeral__code,axiom, % 112.10/112.00 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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_double__number__of__Bit0,axiom, % 112.10/112.00 ! [V_w,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_number__of1,axiom, % 112.10/112.00 ! [V_n] : % 112.10/112.00 ( 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))) % 112.10/112.00 => ( 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)))) % 112.10/112.00 & 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)))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mult__2__right,axiom, % 112.10/112.00 ! [V_z,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mult__2,axiom, % 112.10/112.00 ! [V_z,T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_one__add__one__is__two,axiom, % 112.10/112.00 ! [T_a] : % 112.10/112.00 ( class_Int_Onumber__ring(T_a) % 112.10/112.00 => 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_semiring__norm_I115_J,axiom, % 112.10/112.00 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))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_numeral__2__eq__2,axiom, % 112.10/112.00 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))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 112.10/112.00 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))))) ). % 112.10/112.00 % 112.10/112.00 fof(fact_add__2__eq__Suc,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_add__2__eq__Suc_H,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__mult__2,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__mult__2__right,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__number__of__Bit1,axiom, % 112.10/112.00 ! [V_v,V_w] : % 112.10/112.00 ( ( 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))) % 112.10/112.00 => 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)) ) % 112.10/112.00 & ( ~ 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))) % 112.10/112.00 => 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)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__zmod__mult__2,axiom, % 112.10/112.00 ! [V_b,V_a] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_pos__zmod__mult__2,axiom, % 112.10/112.00 ! [V_b,V_a] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.10/112.00 => 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__zdiv__mult__2,axiom, % 112.10/112.00 ! [V_b,V_a] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_pos__zdiv__mult__2,axiom, % 112.10/112.00 ! [V_b,V_a] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_of__nat__double,axiom, % 112.10/112.00 ! [V_x,T_a] : % 112.10/112.00 ( class_Rings_Osemiring__1(T_a) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.00 => 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))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_DIVISION__BY__ZERO,axiom, % 112.10/112.00 ! [V_a] : % 112.10/112.00 ( 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) % 112.10/112.00 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__div__trivial,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__zdiv__trivial,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__mod__trivial,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiv__zadd1__eq,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__div__equality2,axiom, % 112.10/112.00 ! [V_a,V_b,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__div__equality,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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 ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_div__mod__equality2,axiom, % 112.10/112.00 ! [V_c,V_a,V_b,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_div__mod__equality,axiom, % 112.10/112.00 ! [V_c,V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiv__zmod__equality2,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiv__zmod__equality,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiv__zmult1__eq,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__zdiv__equality,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmult__div__cancel,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__zdiv__equality_H,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__self,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__by__0,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__0,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__add__self2,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__add__self1,axiom, % 112.10/112.00 ! [V_a,V_b,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__add__right__eq,axiom, % 112.10/112.00 ! [V_c,V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__add__left__eq,axiom, % 112.10/112.00 ! [V_c,V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__add__eq,axiom, % 112.10/112.00 ! [V_c,V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__simps_I2_J,axiom, % 112.10/112.00 ! [V_c,V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__simps_I1_J,axiom, % 112.10/112.00 ! [V_b,V_c,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__add__cong,axiom, % 112.10/112.00 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 112.10/112.00 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 112.10/112.00 => 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) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__mult__right__eq,axiom, % 112.10/112.00 ! [V_c,V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__mult__left__eq,axiom, % 112.10/112.00 ! [V_c,V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__mult__eq,axiom, % 112.10/112.00 ! [V_c,V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__mult__mult1,axiom, % 112.10/112.00 ! [V_b,V_a,V_c,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__mult__mult2,axiom, % 112.10/112.00 ! [V_b,V_c,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__simps_I4_J,axiom, % 112.10/112.00 ! [V_b,V_c,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__mult__cong,axiom, % 112.10/112.00 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 112.10/112.00 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 112.10/112.00 => 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) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__diff__right__eq,axiom, % 112.10/112.00 ! [V_c,V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Oring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__diff__left__eq,axiom, % 112.10/112.00 ! [V_c,V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Oring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__diff__eq,axiom, % 112.10/112.00 ! [V_c,V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Oring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__diff__cong,axiom, % 112.10/112.00 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 112.10/112.00 ( class_Divides_Oring__div(T_a) % 112.10/112.00 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 112.10/112.00 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 112.10/112.00 => 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) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__minus__cong,axiom, % 112.10/112.00 ! [V_a_H,V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Oring__div(T_a) % 112.10/112.00 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 112.10/112.00 => 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) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__minus__eq,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Oring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiv__zero,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__self,axiom, % 112.10/112.00 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__zero,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__int,axiom, % 112.10/112.00 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiv__zminus2,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiv__zminus__zminus,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__simps_I3_J,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__zmult1__eq,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiff__zmod__right,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiff__zmod__left,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__zminus2,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__zminus__zminus,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zminus__zmod,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_div__by__0,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_div__0,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_div__by__1,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__mult__self2__is__0,axiom, % 112.10/112.00 ! [V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__mult__self1__is__0,axiom, % 112.10/112.00 ! [V_a,V_b,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__zmult2__eq,axiom, % 112.10/112.00 ! [V_b,V_a,V_c] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__mult__self2,axiom, % 112.10/112.00 ! [V_c,V_b,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__mult__self1,axiom, % 112.10/112.00 ! [V_b,V_c,V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => 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) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_mod__by__1,axiom, % 112.10/112.00 ! [V_a,T_a] : % 112.10/112.00 ( class_Divides_Osemiring__div(T_a) % 112.10/112.00 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiv__zminus2__eq__if,axiom, % 112.10/112.00 ! [V_a,V_b] : % 112.10/112.00 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.00 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.00 => 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)) ) % 112.10/112.00 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.00 => 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)) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiv__zminus1__eq__if,axiom, % 112.10/112.00 ! [V_a,V_b] : % 112.10/112.00 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.00 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.00 => 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)) ) % 112.10/112.00 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.00 => 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)) ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__0,axiom, % 112.10/112.00 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 112.10/112.00 % 112.10/112.00 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 112.10/112.00 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 112.10/112.00 ! [V_y,V_x] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 112.10/112.00 => 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))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_div__neg__pos__less0,axiom, % 112.10/112.00 ! [V_b,V_a] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.10/112.00 => 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))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 112.10/112.00 ! [V_a_2,V_b_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 112.10/112.00 ! [V_a_2,V_b_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_eq__nat__nat__iff,axiom, % 112.10/112.00 ! [V_z_H_2,V_z_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 112.10/112.00 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 112.10/112.00 <=> V_z_2 = V_z_H_2 ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 112.10/112.00 ! [V_y_2,V_x_2] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 112.10/112.00 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 112.10/112.00 <=> V_x_2 = V_y_2 ) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_all__nat,axiom, % 112.10/112.00 ! [V_Pa_2] : % 112.10/112.00 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 112.10/112.00 <=> ! [B_x] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 112.10/112.00 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_ex__nat,axiom, % 112.10/112.00 ! [V_Pa_2] : % 112.10/112.00 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 112.10/112.00 <=> ? [B_x] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 112.10/112.00 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiv__self,axiom, % 112.10/112.00 ! [V_a] : % 112.10/112.00 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.00 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 112.10/112.00 ! [V_y,V_x] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 112.10/112.00 => 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))) ) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__le__nonneg__dividend,axiom, % 112.10/112.00 ! [V_k,V_m] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_neg__mod__bound,axiom, % 112.10/112.00 ! [V_a,V_b] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.00 => 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))) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_pos__mod__bound,axiom, % 112.10/112.00 ! [V_a,V_b] : % 112.10/112.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.10/112.00 => 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)) ) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zdiv__number__of__Bit0,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__number__of__def,axiom, % 112.10/112.00 ! [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)) ). % 112.10/112.00 % 112.10/112.00 fof(fact_nat__number__of,axiom, % 112.10/112.00 ! [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) ). % 112.10/112.00 % 112.10/112.00 fof(fact_zmod__eq__0__iff,axiom, % 112.10/112.00 ! [V_d_2,V_m_2] : % 112.10/112.00 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.00 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zmod__zminus2__not__zero,axiom, % 112.10/112.01 ! [V_l,V_k] : % 112.10/112.01 ( 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) % 112.10/112.01 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zmod__zminus1__not__zero,axiom, % 112.10/112.01 ! [V_l,V_k] : % 112.10/112.01 ( 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) % 112.10/112.01 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 112.10/112.01 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_neg__nat,axiom, % 112.10/112.01 ! [V_z] : % 112.10/112.01 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 112.10/112.01 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_not__neg__nat,axiom, % 112.10/112.01 ! [V_z] : % 112.10/112.01 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 112.10/112.01 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__mult__mult1__if,axiom, % 112.10/112.01 ! [V_b,V_a,V_c,T_a] : % 112.10/112.01 ( class_Divides_Osemiring__div(T_a) % 112.10/112.01 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => 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) ) % 112.10/112.01 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => 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) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__mult__self2__is__id,axiom, % 112.10/112.01 ! [V_a,V_b,T_a] : % 112.10/112.01 ( class_Divides_Osemiring__div(T_a) % 112.10/112.01 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => 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 ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__mult__self1__is__id,axiom, % 112.10/112.01 ! [V_a,V_b,T_a] : % 112.10/112.01 ( class_Divides_Osemiring__div(T_a) % 112.10/112.01 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => 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 ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__mult__mult2,axiom, % 112.10/112.01 ! [V_b,V_a,V_c,T_a] : % 112.10/112.01 ( class_Divides_Osemiring__div(T_a) % 112.10/112.01 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => 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) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__mult__mult1,axiom, % 112.10/112.01 ! [V_b,V_a,V_c,T_a] : % 112.10/112.01 ( class_Divides_Osemiring__div(T_a) % 112.10/112.01 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => 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) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__self,axiom, % 112.10/112.01 ! [V_a,T_a] : % 112.10/112.01 ( class_Divides_Osemiring__div(T_a) % 112.10/112.01 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_transfer__int__nat__set__return__embed,axiom, % 112.10/112.01 ! [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 ). % 112.10/112.01 % 112.10/112.01 fof(fact_split__neg__lemma,axiom, % 112.10/112.01 ! [V_na_2,V_Pa_2,V_k_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_2,V_k_2))) % 112.10/112.01 <=> ! [B_i,B_j] : % 112.10/112.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 & V_na_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) ) % 112.10/112.01 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_split__pos__lemma,axiom, % 112.10/112.01 ! [V_na_2,V_Pa_2,V_k_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_2,V_k_2))) % 112.10/112.01 <=> ! [B_i,B_j] : % 112.10/112.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 112.10/112.01 & V_na_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) ) % 112.10/112.01 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 112.10/112.01 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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__le__0,axiom, % 112.10/112.01 ! [V_z] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__0__iff,axiom, % 112.10/112.01 ! [V_i_2] : % 112.10/112.01 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zdiv__eq__0__iff,axiom, % 112.10/112.01 ! [V_k_2,V_i_2] : % 112.10/112.01 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.01 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.01 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 112.10/112.01 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 112.10/112.01 ! [V_a_2,V_b_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 112.10/112.01 ! [V_i_2,V_k_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 112.10/112.01 => ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 112.10/112.01 ! [V_b_2,V_a_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 112.10/112.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zdiv__mono2,axiom, % 112.10/112.01 ! [V_b,V_b_H,V_a] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 112.10/112.01 => 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__nonneg__neg__le0,axiom, % 112.10/112.01 ! [V_b,V_a] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__pos__pos__trivial,axiom, % 112.10/112.01 ! [V_b,V_a] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 112.10/112.01 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 112.10/112.01 ! [V_a_2,V_b_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__nonpos__pos__le0,axiom, % 112.10/112.01 ! [V_b,V_a] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zdiv__mono2__neg,axiom, % 112.10/112.01 ! [V_b,V_b_H,V_a] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 112.10/112.01 => 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__neg__neg__trivial,axiom, % 112.10/112.01 ! [V_b,V_a] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 112.10/112.01 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zdiv__mono1,axiom, % 112.10/112.01 ! [V_b,V_a_H,V_a] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zdiv__mono1__neg,axiom, % 112.10/112.01 ! [V_b,V_a_H,V_a] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__mono__iff,axiom, % 112.10/112.01 ! [V_w_2,V_z_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 112.10/112.01 => ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zless__nat__conj,axiom, % 112.10/112.01 ! [V_z_2,V_w_2] : % 112.10/112.01 ( 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))) % 112.10/112.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 112.10/112.01 ! [V_y_2,V_x_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 112.10/112.01 => ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__1,axiom, % 112.10/112.01 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_int__div__less__self,axiom, % 112.10/112.01 ! [V_k,V_x] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zdiv__zmult2__eq,axiom, % 112.10/112.01 ! [V_b,V_a,V_c] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_int__nat__eq,axiom, % 112.10/112.01 ! [V_z] : % 112.10/112.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 112.10/112.01 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 112.10/112.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 112.10/112.01 => 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) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_int__eq__iff,axiom, % 112.10/112.01 ! [V_z_2,V_m_2] : % 112.10/112.01 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 112.10/112.01 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__0__le,axiom, % 112.10/112.01 ! [V_z] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 112.10/112.01 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zless__nat__eq__int__zless,axiom, % 112.10/112.01 ! [V_z_2,V_m_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 112.10/112.01 <=> 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_pos__mod__sign,axiom, % 112.10/112.01 ! [V_a,V_b] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.10/112.01 => 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_pos__mod__conj,axiom, % 112.10/112.01 ! [V_a,V_b] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.10/112.01 => ( 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))) % 112.10/112.01 & 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__pos__pos__trivial,axiom, % 112.10/112.01 ! [V_b,V_a] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 112.10/112.01 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_neg__mod__sign,axiom, % 112.10/112.01 ! [V_a,V_b] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_neg__mod__conj,axiom, % 112.10/112.01 ! [V_a,V_b] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => ( 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))) % 112.10/112.01 & 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__neg__neg__trivial,axiom, % 112.10/112.01 ! [V_b,V_a] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 112.10/112.01 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__zminus__int,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zmod__zminus1__eq__if,axiom, % 112.10/112.01 ! [V_b,V_a] : % 112.10/112.01 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.01 => 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) ) % 112.10/112.01 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zmod__zminus2__eq__if,axiom, % 112.10/112.01 ! [V_b,V_a] : % 112.10/112.01 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.01 => 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) ) % 112.10/112.01 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.01 => 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) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__abs__mult__distrib,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__mult__self2,axiom, % 112.10/112.01 ! [V_c,V_a,V_b,T_a] : % 112.10/112.01 ( class_Divides_Osemiring__div(T_a) % 112.10/112.01 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__mult__self1,axiom, % 112.10/112.01 ! [V_c,V_a,V_b,T_a] : % 112.10/112.01 ( class_Divides_Osemiring__div(T_a) % 112.10/112.01 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__add__self2,axiom, % 112.10/112.01 ! [V_a,V_b,T_a] : % 112.10/112.01 ( class_Divides_Osemiring__div(T_a) % 112.10/112.01 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__add__self1,axiom, % 112.10/112.01 ! [V_a,V_b,T_a] : % 112.10/112.01 ( class_Divides_Osemiring__div(T_a) % 112.10/112.01 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zero__less__nat__eq,axiom, % 112.10/112.01 ! [V_z_2] : % 112.10/112.01 ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__less__eq__zless,axiom, % 112.10/112.01 ! [V_z_2,V_w_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 112.10/112.01 => ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 112.10/112.01 ! [V_y_2,V_x_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 112.10/112.01 => ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__eq__iff,axiom, % 112.10/112.01 ! [V_m_2,V_w_2] : % 112.10/112.01 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 112.10/112.01 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 112.10/112.01 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 112.10/112.01 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__eq__iff2,axiom, % 112.10/112.01 ! [V_w_2,V_m_2] : % 112.10/112.01 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 112.10/112.01 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 112.10/112.01 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 112.10/112.01 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__le__eq__zle,axiom, % 112.10/112.01 ! [V_z_2,V_w_2] : % 112.10/112.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 112.10/112.01 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 112.10/112.01 => ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_split__nat,axiom, % 112.10/112.01 ! [V_i_2,V_Pa_2] : % 112.10/112.01 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2))) % 112.10/112.01 <=> ( ! [B_n] : % 112.10/112.01 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 112.10/112.01 => hBOOL(hAPP(V_Pa_2,B_n)) ) % 112.10/112.01 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__add__distrib,axiom, % 112.10/112.01 ! [V_z_H,V_z] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 112.10/112.01 ! [V_y,V_x] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_int__eq__iff__number__of,axiom, % 112.10/112.01 ! [V_v_2,V_m_2] : % 112.10/112.01 ( 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) % 112.10/112.01 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 112.10/112.01 & 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__mult__distrib,axiom, % 112.10/112.01 ! [V_z_H,V_z] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 112.10/112.01 ! [V_y,V_x] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__pos__neg__trivial,axiom, % 112.10/112.01 ! [V_b,V_a] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.10/112.01 => ( 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))) % 112.10/112.01 => 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) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__diff__distrib,axiom, % 112.10/112.01 ! [V_z,V_z_H] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 112.10/112.01 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)))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 112.10/112.01 ! [V_y,V_x] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_one__less__nat__eq,axiom, % 112.10/112.01 ! [V_z_2] : % 112.10/112.01 ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_divmod__int__rel__div__eq,axiom, % 112.10/112.01 ! [V_r_1,V_y,V_b_1,V_a_1] : % 112.10/112.01 ( 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) % 112.10/112.01 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 112.10/112.01 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.01 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_split__zdiv,axiom, % 112.10/112.01 ! [V_k_2,V_na_2,V_Pa_2] : % 112.10/112.01 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2))) % 112.10/112.01 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.01 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 112.10/112.01 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 112.10/112.01 => ! [B_i] : % 112.10/112.01 ( ? [B_j] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 112.10/112.01 & V_na_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) ) % 112.10/112.01 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) % 112.10/112.01 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => ! [B_i] : % 112.10/112.01 ( ? [B_j] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 & V_na_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) ) % 112.10/112.01 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__less__iff,axiom, % 112.10/112.01 ! [V_m_2,V_w_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 112.10/112.01 <=> 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 112.10/112.01 ! [V_z] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 112.10/112.01 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)))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_divmod__int__rel__mod__eq,axiom, % 112.10/112.01 ! [V_y,V_q_1,V_b_1,V_a_1] : % 112.10/112.01 ( 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) % 112.10/112.01 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 112.10/112.01 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.01 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zmult2__lemma__aux2,axiom, % 112.10/112.01 ! [V_q,V_r,V_b,V_c] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zmult2__lemma__aux1,axiom, % 112.10/112.01 ! [V_q,V_r,V_b,V_c] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zmult2__lemma__aux4,axiom, % 112.10/112.01 ! [V_q,V_b,V_r,V_c] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 112.10/112.01 => 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zmult2__lemma__aux3,axiom, % 112.10/112.01 ! [V_q,V_b,V_r,V_c] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 112.10/112.01 => 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_split__zmod,axiom, % 112.10/112.01 ! [V_k_2,V_na_2,V_Pa_2] : % 112.10/112.01 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_2,V_k_2))) % 112.10/112.01 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.01 => hBOOL(hAPP(V_Pa_2,V_na_2)) ) % 112.10/112.01 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 112.10/112.01 => ! [B_i,B_j] : % 112.10/112.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 112.10/112.01 & V_na_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) ) % 112.10/112.01 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) % 112.10/112.01 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => ! [B_i,B_j] : % 112.10/112.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 & V_na_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) ) % 112.10/112.01 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__mult__distrib__neg,axiom, % 112.10/112.01 ! [V_z_H,V_z] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zmod__number__of__Bit0,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__2,axiom, % 112.10/112.01 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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zdiv__number__of__Bit1,axiom, % 112.10/112.01 ! [V_v,V_w] : % 112.10/112.01 ( ( 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))) % 112.10/112.01 => 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)) ) % 112.10/112.01 & ( ~ 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))) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__aux__def,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__of__aux__code,axiom, % 112.10/112.01 ! [V_n,V_i] : % 112.10/112.01 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 112.10/112.01 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 112.10/112.01 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_transfer__morphism__nat__int,axiom, % 112.10/112.01 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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_z3div__def,axiom, % 112.10/112.01 ! [V_k,V_l] : % 112.10/112.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 112.10/112.01 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_z3mod__def,axiom, % 112.10/112.01 ! [V_k,V_l] : % 112.10/112.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 112.10/112.01 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_one__mod__nat__number__of,axiom, % 112.10/112.01 ! [V_v_H] : % 112.10/112.01 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 112.10/112.01 => 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)) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__add1__eq,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__mult1__eq,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__mult2__eq,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Divides_Omod__div__equality_H,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mult__div__cancel,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__mod__equality_H,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__le__mono,axiom, % 112.10/112.01 ! [V_k,V_n,V_m] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 112.10/112.01 => 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__le__dividend,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__mult2__eq,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__less,axiom, % 112.10/112.01 ! [V_n,V_m] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 112.10/112.01 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__less__eq__dividend,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__mult__distrib2,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__mult__distrib,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__1,axiom, % 112.10/112.01 ! [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 ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__less,axiom, % 112.10/112.01 ! [V_n,V_m] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 112.10/112.01 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__mult__div__cancel__disj,axiom, % 112.10/112.01 ! [V_n,V_m,V_k] : % 112.10/112.01 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 => 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) ) % 112.10/112.01 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 => 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) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__1,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__Suc,axiom, % 112.10/112.01 ! [V_n,V_m] : % 112.10/112.01 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 112.10/112.01 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 112.10/112.01 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__less__divisor,axiom, % 112.10/112.01 ! [V_m,V_n] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__eq__0__iff,axiom, % 112.10/112.01 ! [V_d_2,V_m_2] : % 112.10/112.01 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__if,axiom, % 112.10/112.01 ! [V_n,V_m] : % 112.10/112.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 112.10/112.01 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 112.10/112.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 112.10/112.01 => 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) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__geq,axiom, % 112.10/112.01 ! [V_n,V_m] : % 112.10/112.01 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__mult__self3,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_le__mod__geq,axiom, % 112.10/112.01 ! [V_m,V_n] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zdiv__int,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zmod__int,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__le__mono2,axiom, % 112.10/112.01 ! [V_k,V_n,V_m] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__mult__div__cancel1,axiom, % 112.10/112.01 ! [V_n,V_m,V_k] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__mult__self__is__m,axiom, % 112.10/112.01 ! [V_m,V_n] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.10/112.01 => 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 ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__mult__self1__is__m,axiom, % 112.10/112.01 ! [V_m,V_n] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.10/112.01 => 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 ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__less__dividend,axiom, % 112.10/112.01 ! [V_m,V_n] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__le__divisor,axiom, % 112.10/112.01 ! [V_m,V_n] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__mult__self4,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__if,axiom, % 112.10/112.01 ! [V_m,V_n] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.10/112.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 112.10/112.01 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 112.10/112.01 => 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)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__geq,axiom, % 112.10/112.01 ! [V_m,V_n] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.10/112.01 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_split__div,axiom, % 112.10/112.01 ! [V_k_2,V_na_2,V_Pa_2] : % 112.10/112.01 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_na_2),V_k_2))) % 112.10/112.01 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 112.10/112.01 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 => ! [B_i,B_j] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 112.10/112.01 => ( V_na_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) % 112.10/112.01 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__div__distrib,axiom, % 112.10/112.01 ! [V_y,V_x] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 112.10/112.01 ! [V_y,V_x] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_split__mod,axiom, % 112.10/112.01 ! [V_k_2,V_na_2,V_Pa_2] : % 112.10/112.01 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_na_2,V_k_2))) % 112.10/112.01 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 => hBOOL(hAPP(V_Pa_2,V_na_2)) ) % 112.10/112.01 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 => ! [B_i,B_j] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 112.10/112.01 => ( V_na_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) % 112.10/112.01 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__lemma,axiom, % 112.10/112.01 ! [V_q,V_b,V_r,V_c] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Suc__times__mod__eq,axiom, % 112.10/112.01 ! [V_m,V_k] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__mod__distrib,axiom, % 112.10/112.01 ! [V_y,V_x] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 112.10/112.01 ! [V_y,V_x] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_le__div__geq,axiom, % 112.10/112.01 ! [V_m,V_n] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_split__div__lemma,axiom, % 112.10/112.01 ! [V_m_2,V_q_2,V_na_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) % 112.10/112.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),V_q_2)),V_m_2)) % 112.10/112.01 & 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_na_2),hAPP(c_Nat_OSuc,V_q_2)))) ) % 112.10/112.01 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_na_2) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_split__div_H,axiom, % 112.10/112.01 ! [V_na_2,V_m_2,V_Pa_2] : % 112.10/112.01 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_na_2))) % 112.10/112.01 <=> ( ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 112.10/112.01 | ? [B_q] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),B_q)),V_m_2)) % 112.10/112.01 & 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_na_2),hAPP(c_Nat_OSuc,B_q)))) % 112.10/112.01 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__Suc__eq__div__add3,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Suc__div__eq__add3__div,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div2__Suc__Suc,axiom, % 112.10/112.01 ! [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))))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_add__self__div__2,axiom, % 112.10/112.01 ! [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 ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__Suc__eq__mod__add3,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Suc__mod__eq__add3__mod,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod2__Suc__Suc,axiom, % 112.10/112.01 ! [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)))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__nat__number__of,axiom, % 112.10/112.01 ! [V_v_H,V_v] : % 112.10/112.01 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.01 => 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) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod__nat__number__of,axiom, % 112.10/112.01 ! [V_v_H,V_v] : % 112.10/112.01 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.01 => 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) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.01 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 112.10/112.01 => 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) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 112.10/112.01 => 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))) ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__2__gt__zero,axiom, % 112.10/112.01 ! [V_n] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 112.10/112.01 => 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)))))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_one__div__nat__number__of,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mod2__gr__0,axiom, % 112.10/112.01 ! [V_m_2] : % 112.10/112.01 ( 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)))))) % 112.10/112.01 <=> 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Suc__n__div__2__gt__zero,axiom, % 112.10/112.01 ! [V_n] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.10/112.01 => 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)))))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_int__of__code,axiom, % 112.10/112.01 ! [V_k] : % 112.10/112.01 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 112.10/112.01 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 112.10/112.01 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 112.10/112.01 => ( ( 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) % 112.10/112.01 => 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)))))) ) % 112.10/112.01 & ( 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) % 112.10/112.01 => 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)) ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 112.10/112.01 ! [V_B_2,V_A_2] : % 112.10/112.01 ( c_Nat__Transfer_Onat__set(V_A_2) % 112.10/112.01 => ( c_Nat__Transfer_Onat__set(V_B_2) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.10/112.01 <=> 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__minus1__odd,axiom, % 112.10/112.01 ! [V_n,T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_odd__power__less__zero,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_odd__0__le__power__imp__0__le,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.01 => ( 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))))) % 112.10/112.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power2__diff,axiom, % 112.10/112.01 ! [V_y,V_x,T_a] : % 112.10/112.01 ( class_Int_Onumber__ring(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zpower__int,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_int__power,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 112.10/112.01 ! [V_q,V_y,V_x,T_a] : % 112.10/112.01 ( class_Rings_Ocomm__semiring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 112.10/112.01 ! [V_q,V_p,V_x,T_a] : % 112.10/112.01 ( class_Rings_Ocomm__semiring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zpower__zpower,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 112.10/112.01 ! [V_x,T_a] : % 112.10/112.01 ( class_Rings_Ocomm__semiring__1(T_a) % 112.10/112.01 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zpower__zmod,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__power__eq,axiom, % 112.10/112.01 ! [V_n,V_z] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 112.10/112.01 ! [V_n,V_x] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 112.10/112.01 ! [V_q,V_x,T_a] : % 112.10/112.01 ( class_Rings_Ocomm__semiring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 112.10/112.01 ! [V_q,V_x,T_a] : % 112.10/112.01 ( class_Rings_Ocomm__semiring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 112.10/112.01 ! [V_q,V_x,T_a] : % 112.10/112.01 ( class_Rings_Ocomm__semiring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 112.10/112.01 ! [V_x,T_a] : % 112.10/112.01 ( class_Rings_Ocomm__semiring__1(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 112.10/112.01 ! [V_q,V_p,V_x,T_a] : % 112.10/112.01 ( class_Rings_Ocomm__semiring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 112.10/112.01 ! [V_n,V_x] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 112.10/112.01 => 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zpower__zadd__distrib,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Ints__power,axiom, % 112.10/112.01 ! [V_na_2,V_a_2,T_b] : % 112.10/112.01 ( class_Rings_Oring__1(T_b) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) % 112.10/112.01 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_na_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 112.10/112.01 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__nat__number__of__number__of,axiom, % 112.10/112.01 ! [V_w,V_v] : % 112.10/112.01 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.01 => 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)) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__nat__number__of,axiom, % 112.10/112.01 ! [V_n,V_v] : % 112.10/112.01 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.01 => 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) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__set__def,axiom, % 112.10/112.01 ! [V_S_2] : % 112.10/112.01 ( c_Nat__Transfer_Onat__set(V_S_2) % 112.10/112.01 <=> ! [B_x] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 112.10/112.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 112.10/112.01 ! [V_B_2,V_A_2] : % 112.10/112.01 ( c_Nat__Transfer_Onat__set(V_A_2) % 112.10/112.01 => ( c_Nat__Transfer_Onat__set(V_B_2) % 112.10/112.01 => ( V_A_2 = V_B_2 % 112.10/112.01 <=> 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) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zero__le__zpower__abs,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power3__eq__cube,axiom, % 112.10/112.01 ! [V_a,T_a] : % 112.10/112.01 ( class_Groups_Omonoid__mult(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__eq__if,axiom, % 112.10/112.01 ! [V_p,V_m] : % 112.10/112.01 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 112.10/112.01 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 => 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)))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zero__less__zpower__abs__iff,axiom, % 112.10/112.01 ! [V_na_2,V_x_2] : % 112.10/112.01 ( 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_na_2))) % 112.10/112.01 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.10/112.01 | V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 112.10/112.01 ! [V_x_2,V_A_2] : % 112.10/112.01 ( c_Nat__Transfer_Onat__set(V_A_2) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 112.10/112.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zero__eq__power2,axiom, % 112.10/112.01 ! [V_a_2,T_b] : % 112.10/112.01 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 112.10/112.01 => ( 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) % 112.10/112.01 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zero__power2,axiom, % 112.10/112.01 ! [T_a] : % 112.10/112.01 ( class_Rings_Osemiring__1(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power2__eq__square,axiom, % 112.10/112.01 ! [V_a,T_a] : % 112.10/112.01 ( class_Groups_Omonoid__mult(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 112.10/112.01 ! [V_x,T_a] : % 112.10/112.01 ( class_Rings_Ocomm__semiring__1(T_a) % 112.10/112.01 => 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)))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_one__power2,axiom, % 112.10/112.01 ! [T_a] : % 112.10/112.01 ( class_Rings_Osemiring__1(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power2__minus,axiom, % 112.10/112.01 ! [V_a,T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => 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)))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__even__eq,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Groups_Omonoid__mult(T_a) % 112.10/112.01 => 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)))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power2__abs,axiom, % 112.10/112.01 ! [V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.01 => 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)))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_abs__power2,axiom, % 112.10/112.01 ! [V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.01 => 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)))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_transfer__nat__int__set__return__embed,axiom, % 112.10/112.01 ! [V_A_2] : % 112.10/112.01 ( c_Nat__Transfer_Onat__set(V_A_2) % 112.10/112.01 => 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 ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zero__le__power2,axiom, % 112.10/112.01 ! [V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.01 => 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)))))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power2__le__imp__le,axiom, % 112.10/112.01 ! [V_y,V_x,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( 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)))))) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 112.10/112.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power2__eq__imp__eq,axiom, % 112.10/112.01 ! [V_y,V_x,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( 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)))) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 112.10/112.01 => V_x = V_y ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power2__less__0,axiom, % 112.10/112.01 ! [V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.01 => ~ 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zero__less__power2,axiom, % 112.10/112.01 ! [V_a_2,T_b] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.01 => ( 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)))))) % 112.10/112.01 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_sum__power2__eq__zero__iff,axiom, % 112.10/112.01 ! [V_y_2,V_x_2,T_b] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.01 => ( 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) % 112.10/112.01 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 112.10/112.01 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power2__eq__square__number__of,axiom, % 112.10/112.01 ! [V_w,T_b] : % 112.10/112.01 ( ( class_Groups_Omonoid__mult(T_b) % 112.10/112.01 & class_Int_Onumber(T_b) ) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power2__eq__1__iff,axiom, % 112.10/112.01 ! [V_a_2,T_b] : % 112.10/112.01 ( class_Rings_Oring__1__no__zero__divisors(T_b) % 112.10/112.01 => ( 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) % 112.10/112.01 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b) % 112.10/112.01 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 112.10/112.01 ! [V_n,V_x,T_a] : % 112.10/112.01 ( class_Rings_Ocomm__semiring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__minus__even,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 112.10/112.01 ! [V_A_2] : % 112.10/112.01 ( c_Nat__Transfer_Onat__set(V_A_2) % 112.10/112.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 112.10/112.01 <=> 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 112.10/112.01 ! [V_A_2] : % 112.10/112.01 ( c_Nat__Transfer_Onat__set(V_A_2) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power2__less__imp__less,axiom, % 112.10/112.01 ! [V_y,V_x,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( 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)))))) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 112.10/112.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_sum__power2__ge__zero,axiom, % 112.10/112.01 ! [V_y,V_x,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.01 => 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))))))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_sum__power2__le__zero__iff,axiom, % 112.10/112.01 ! [V_y_2,V_x_2,T_b] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.01 => ( 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))) % 112.10/112.01 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b) % 112.10/112.01 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_sum__power2__gt__zero__iff,axiom, % 112.10/112.01 ! [V_y_2,V_x_2,T_b] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.01 => ( 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))))))) % 112.10/112.01 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b) % 112.10/112.01 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_not__sum__power2__lt__zero,axiom, % 112.10/112.01 ! [V_y,V_x,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.01 => ~ 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power2__sum,axiom, % 112.10/112.01 ! [V_y,V_x,T_a] : % 112.10/112.01 ( class_Int_Onumber__ring(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zero__le__even__power_H,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.01 => 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)))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 112.10/112.01 ! [V_n,V_x,T_a] : % 112.10/112.01 ( class_Rings_Ocomm__semiring__1(T_a) % 112.10/112.01 => 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__odd__eq,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Groups_Omonoid__mult(T_a) % 112.10/112.01 => 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))))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__minus1__even,axiom, % 112.10/112.01 ! [V_n,T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_int__power__div__base,axiom, % 112.10/112.01 ! [V_k,V_m] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 112.10/112.01 => 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)))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 112.10/112.01 ! [V_B_2,V_A_2] : % 112.10/112.01 ( c_Nat__Transfer_Onat__set(V_A_2) % 112.10/112.01 => ( c_Nat__Transfer_Onat__set(V_B_2) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.10/112.01 <=> 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__strict__mono,axiom, % 112.10/112.01 ! [V_n,V_b,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.10/112.01 => 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))) ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__diff,axiom, % 112.10/112.01 ! [V_m,V_n,V_a,T_a] : % 112.10/112.01 ( class_Fields_Ofield(T_a) % 112.10/112.01 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 112.10/112.01 => 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)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_one__less__power,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.10/112.01 => 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__increasing__iff,axiom, % 112.10/112.01 ! [V_y_2,V_x_2,V_b_2,T_b] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_b) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__le__imp__le__exp,axiom, % 112.10/112.01 ! [V_n,V_m,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 112.10/112.01 => ( 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))) % 112.10/112.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__decreasing,axiom, % 112.10/112.01 ! [V_a,V_N,V_n,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 112.10/112.01 => 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))) ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_field__power__not__zero,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 112.10/112.01 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__Suc__0,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 112.10/112.01 ! [V_m_2,V_x_2] : % 112.10/112.01 ( 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)) % 112.10/112.01 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__zero__less__power__iff,axiom, % 112.10/112.01 ! [V_na_2,V_x_2] : % 112.10/112.01 ( 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_na_2))) % 112.10/112.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 112.10/112.01 | V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__power__less__imp__less,axiom, % 112.10/112.01 ! [V_n,V_m,V_i] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 112.10/112.01 => ( 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))) % 112.10/112.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__mult__distrib,axiom, % 112.10/112.01 ! [V_n,V_b,V_a,T_a] : % 112.10/112.01 ( class_Groups_Ocomm__monoid__mult(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__commutes,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Groups_Omonoid__mult(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__one,axiom, % 112.10/112.01 ! [V_n,T_a] : % 112.10/112.01 ( class_Groups_Omonoid__mult(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__nat__power,axiom, % 112.10/112.01 ! [V_n,V_m,T_a] : % 112.10/112.01 ( class_Rings_Osemiring__1(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__mult,axiom, % 112.10/112.01 ! [V_n,V_m,V_a,T_a] : % 112.10/112.01 ( class_Groups_Omonoid__mult(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__divide,axiom, % 112.10/112.01 ! [V_n,V_b,V_a,T_a] : % 112.10/112.01 ( class_Fields_Ofield__inverse__zero(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__abs,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__one__right,axiom, % 112.10/112.01 ! [V_a,T_a] : % 112.10/112.01 ( class_Groups_Omonoid__mult(T_a) % 112.10/112.01 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zero__le__power,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__mono,axiom, % 112.10/112.01 ! [V_n,V_b,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.01 => 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zero__less__power,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__eq__0__iff,axiom, % 112.10/112.01 ! [V_na_2,V_a_2,T_b] : % 112.10/112.01 ( ( class_Power_Opower(T_b) % 112.10/112.01 & class_Rings_Omult__zero(T_b) % 112.10/112.01 & class_Rings_Ono__zero__divisors(T_b) % 112.10/112.01 & class_Rings_Ozero__neq__one(T_b) ) % 112.10/112.01 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_na_2) = c_Groups_Ozero__class_Ozero(T_b) % 112.10/112.01 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b) % 112.10/112.01 & V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_one__le__power,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 112.10/112.01 => 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))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__0__Suc,axiom, % 112.10/112.01 ! [V_n,T_a] : % 112.10/112.01 ( ( class_Power_Opower(T_a) % 112.10/112.01 & class_Rings_Osemiring__0(T_a) ) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__inject__exp,axiom, % 112.10/112.01 ! [V_na_2,V_m_2,V_a_2,T_b] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_b) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)) % 112.10/112.01 => ( 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_na_2) % 112.10/112.01 <=> V_m_2 = V_na_2 ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__Suc2,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Groups_Omonoid__mult(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__Suc,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Power_Opower(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__one__le__power,axiom, % 112.10/112.01 ! [V_n,V_i] : % 112.10/112.01 ( 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)) % 112.10/112.01 => 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__0,axiom, % 112.10/112.01 ! [V_a,T_a] : % 112.10/112.01 ( class_Power_Opower(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__add,axiom, % 112.10/112.01 ! [V_n,V_m,V_a,T_a] : % 112.10/112.01 ( class_Groups_Omonoid__mult(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nonzero__power__divide,axiom, % 112.10/112.01 ! [V_n,V_a,V_b,T_a] : % 112.10/112.01 ( class_Fields_Ofield(T_a) % 112.10/112.01 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__one__over,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Fields_Ofield__inverse__zero(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_abs__power__minus,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__less__imp__less__base,axiom, % 112.10/112.01 ! [V_b,V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( 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))) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 112.10/112.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__le__imp__le__base,axiom, % 112.10/112.01 ! [V_b,V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( 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)))) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 112.10/112.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__inject__base,axiom, % 112.10/112.01 ! [V_b,V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( 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)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 112.10/112.01 => V_a = V_b ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__less__power__Suc,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 112.10/112.01 => 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)))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__gt1__lemma,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 112.10/112.01 => 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)))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__0__left,axiom, % 112.10/112.01 ! [V_n,T_a] : % 112.10/112.01 ( ( class_Power_Opower(T_a) % 112.10/112.01 & class_Rings_Osemiring__0(T_a) ) % 112.10/112.01 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 => 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) ) % 112.10/112.01 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 => 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) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__gt1,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 112.10/112.01 => 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)))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__strict__increasing,axiom, % 112.10/112.01 ! [V_a,V_N,V_n,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 112.10/112.01 => 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__less__imp__less__exp,axiom, % 112.10/112.01 ! [V_n,V_m,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 112.10/112.01 => ( 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))) % 112.10/112.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__strict__increasing__iff,axiom, % 112.10/112.01 ! [V_y_2,V_x_2,V_b_2,T_b] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_b) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zero__le__power__abs,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_a) % 112.10/112.01 => 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__increasing,axiom, % 112.10/112.01 ! [V_a,V_N,V_n,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 112.10/112.01 => 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__minus,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__Suc__less,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 112.10/112.01 => 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__eq__imp__eq__base,axiom, % 112.10/112.01 ! [V_b,V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( 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) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.10/112.01 => V_a = V_b ) ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__Suc__less__one,axiom, % 112.10/112.01 ! [V_n,V_a,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 112.10/112.01 => 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__strict__decreasing,axiom, % 112.10/112.01 ! [V_a,V_N,V_n,T_a] : % 112.10/112.01 ( class_Rings_Olinordered__semidom(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 112.10/112.01 => 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))) ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__power__power,axiom, % 112.10/112.01 ! [T_b] : % 112.10/112.01 ( class_Power_Opower(T_b) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__m1__odd,axiom, % 112.10/112.01 ! [V_n,T_a] : % 112.10/112.01 ( class_Int_Onumber__ring(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power__m1__even,axiom, % 112.10/112.01 ! [V_n,T_a] : % 112.10/112.01 ( class_Int_Onumber__ring(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 112.10/112.01 ! [V_A_2,V_x_2] : % 112.10/112.01 ( c_Nat__Transfer_Ois__nat(V_x_2) % 112.10/112.01 => ( c_Nat__Transfer_Onat__set(V_A_2) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 112.10/112.01 <=> 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))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_code__numeral_Osize_I1_J,axiom, % 112.10/112.01 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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I24_J,axiom, % 112.10/112.01 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I7_J,axiom, % 112.10/112.01 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I37_J,axiom, % 112.10/112.01 c_Int_OPls != c_Int_OMin ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I40_J,axiom, % 112.10/112.01 c_Int_OMin != c_Int_OPls ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I47_J,axiom, % 112.10/112.01 ! [V_k_2] : % 112.10/112.01 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 112.10/112.01 <=> V_k_2 = c_Int_OMin ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I43_J,axiom, % 112.10/112.01 ! [V_l_2] : % 112.10/112.01 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 112.10/112.01 <=> c_Int_OMin = V_l_2 ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Bit1__Min,axiom, % 112.10/112.01 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I45_J,axiom, % 112.10/112.01 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I42_J,axiom, % 112.10/112.01 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 112.10/112.01 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 112.10/112.01 ! [V_y,V_x] : % 112.10/112.01 ( c_Nat__Transfer_Ois__nat(V_x) % 112.10/112.01 => ( c_Nat__Transfer_Ois__nat(V_y) % 112.10/112.01 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 112.10/112.01 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 112.10/112.01 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 112.10/112.01 ! [V_y,V_x] : % 112.10/112.01 ( c_Nat__Transfer_Ois__nat(V_x) % 112.10/112.01 => ( c_Nat__Transfer_Ois__nat(V_y) % 112.10/112.01 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 112.10/112.01 ! [V_y,V_x] : % 112.10/112.01 ( c_Nat__Transfer_Ois__nat(V_x) % 112.10/112.01 => ( c_Nat__Transfer_Ois__nat(V_y) % 112.10/112.01 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 112.10/112.01 ! [V_y,V_x] : % 112.10/112.01 ( c_Nat__Transfer_Ois__nat(V_x) % 112.10/112.01 => ( c_Nat__Transfer_Ois__nat(V_y) % 112.10/112.01 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 112.10/112.01 ! [V_n,V_x] : % 112.10/112.01 ( c_Nat__Transfer_Ois__nat(V_x) % 112.10/112.01 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_bin__less__0__simps_I2_J,axiom, % 112.10/112.01 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I20_J,axiom, % 112.10/112.01 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I23_J,axiom, % 112.10/112.01 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I26_J,axiom, % 112.10/112.01 ! [V_k_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I30_J,axiom, % 112.10/112.01 ! [V_k_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I3_J,axiom, % 112.10/112.01 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I6_J,axiom, % 112.10/112.01 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I9_J,axiom, % 112.10/112.01 ! [V_k_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I13_J,axiom, % 112.10/112.01 ! [V_k_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I28_J,axiom, % 112.10/112.01 ! [V_k_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I8_J,axiom, % 112.10/112.01 ! [V_k_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_eq__number__of__Pls__Min,axiom, % 112.10/112.01 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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Int_OMin__def,axiom, % 112.10/112.01 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mult__Min,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 112.10/112.01 ! [V_y,V_x] : % 112.10/112.01 ( c_Nat__Transfer_Ois__nat(V_x) % 112.10/112.01 => ( c_Nat__Transfer_Ois__nat(V_y) % 112.10/112.01 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_neg__number__of__Min,axiom, % 112.10/112.01 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_pred__Pls,axiom, % 112.10/112.01 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 112.10/112.01 % 112.10/112.01 fof(fact_add__Min,axiom, % 112.10/112.01 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 112.10/112.01 % 112.10/112.01 fof(fact_add__Min__right,axiom, % 112.10/112.01 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 112.10/112.01 % 112.10/112.01 fof(fact_pred__Min,axiom, % 112.10/112.01 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nonzero__number__of__Min,axiom, % 112.10/112.01 ! [T_a] : % 112.10/112.01 ( class_Int_Onumber__ring(T_a) % 112.10/112.01 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_succ__Min,axiom, % 112.10/112.01 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 112.10/112.01 % 112.10/112.01 fof(fact_diff__bin__simps_I2_J,axiom, % 112.10/112.01 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 112.10/112.01 % 112.10/112.01 fof(fact_is__nat__def,axiom, % 112.10/112.01 ! [V_x_2] : % 112.10/112.01 ( c_Nat__Transfer_Ois__nat(V_x_2) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mult__minus1,axiom, % 112.10/112.01 ! [V_z,T_a] : % 112.10/112.01 ( class_Int_Onumber__ring(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_mult__minus1__right,axiom, % 112.10/112.01 ! [V_z,T_a] : % 112.10/112.01 ( class_Int_Onumber__ring(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_number__of__Min,axiom, % 112.10/112.01 ! [T_a] : % 112.10/112.01 ( class_Int_Onumber__ring(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_arith__simps_I31_J,axiom, % 112.10/112.01 ! [T_a] : % 112.10/112.01 ( class_Int_Onumber__ring(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_abs__minus__one,axiom, % 112.10/112.01 ! [T_a] : % 112.10/112.01 ( ( class_Int_Onumber__ring(T_a) % 112.10/112.01 & class_Rings_Olinordered__idom(T_a) ) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_divide__minus1,axiom, % 112.10/112.01 ! [V_x,T_a] : % 112.10/112.01 ( ( class_Fields_Ofield__inverse__zero(T_a) % 112.10/112.01 & class_Int_Onumber__ring(T_a) ) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I25_J,axiom, % 112.10/112.01 ! [V_k_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_rel__simps_I11_J,axiom, % 112.10/112.01 ! [V_k_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zmod__minus1__right,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_diff__bin__simps_I4_J,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_minus__Min,axiom, % 112.10/112.01 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zmult__eq__1__iff,axiom, % 112.10/112.01 ! [V_na_2,V_m_2] : % 112.10/112.01 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_na_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 112.10/112.01 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 112.10/112.01 & V_na_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 112.10/112.01 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 112.10/112.01 & V_na_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 112.10/112.01 ! [V_n,V_m] : % 112.10/112.01 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 112.10/112.01 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 112.10/112.01 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_diff__bin__simps_I6_J,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_diff__bin__simps_I5_J,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_power_Opower_Opower__0,axiom, % 112.10/112.01 ! [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 ). % 112.10/112.01 % 112.10/112.01 fof(fact_power_Opower_Opower__Suc,axiom, % 112.10/112.01 ! [V_na_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_na_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_na_2)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zdiv__minus1__right,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 112.10/112.01 ! [V_x_2,V_A_2] : % 112.10/112.01 ( c_Nat__Transfer_Onat__set(V_A_2) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 112.10/112.01 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_minus1__divide,axiom, % 112.10/112.01 ! [V_x,T_a] : % 112.10/112.01 ( ( class_Fields_Ofield__inverse__zero(T_a) % 112.10/112.01 & class_Int_Onumber__ring(T_a) ) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_abs__power__minus__one,axiom, % 112.10/112.01 ! [V_n,T_a] : % 112.10/112.01 ( ( class_Int_Onumber__ring(T_a) % 112.10/112.01 & class_Rings_Olinordered__idom(T_a) ) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__eq__minus1,axiom, % 112.10/112.01 ! [V_b] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 112.10/112.01 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 112.10/112.01 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_div__pos__neg__trivial,axiom, % 112.10/112.01 ! [V_b,V_a] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.10/112.01 => ( 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))) % 112.10/112.01 => 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) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_zmod__minus1,axiom, % 112.10/112.01 ! [V_b] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_code__numeral_Osize_I2_J,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_card__greaterThanLessThan__int,axiom, % 112.10/112.01 ! [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)))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__of__nat,axiom, % 112.10/112.01 ! [V_k,T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => 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)))) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.10/112.01 => 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)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nitpick_Oint__lcm__def,axiom, % 112.10/112.01 ! [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)))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_code__numeral_Osize_I3_J,axiom, % 112.10/112.01 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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_finite__greaterThanLessThan__int,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__eq__iff,axiom, % 112.10/112.01 ! [V_z_2,V_w_2,T_b] : % 112.10/112.01 ( class_Int_Oring__char__0(T_b) % 112.10/112.01 => ( 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) % 112.10/112.01 <=> V_w_2 = V_z_2 ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_code__numeral_Oinject,axiom, % 112.10/112.01 ! [V_code__numeral_H_2,V_code__numeral_2] : % 112.10/112.01 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 112.10/112.01 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_number__of__eq,axiom, % 112.10/112.01 ! [V_k,T_a] : % 112.10/112.01 ( class_Int_Onumber__ring(T_a) % 112.10/112.01 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_int__number__of__def,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__int__eq,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_code__numeral_Osimps_I2_J,axiom, % 112.10/112.01 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 112.10/112.01 % 112.10/112.01 fof(fact_code__numeral_Osimps_I3_J,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__eq__0__iff,axiom, % 112.10/112.01 ! [V_z_2,T_b] : % 112.10/112.01 ( class_Int_Oring__char__0(T_b) % 112.10/112.01 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b) % 112.10/112.01 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__0__eq__iff,axiom, % 112.10/112.01 ! [V_z_2,T_b] : % 112.10/112.01 ( class_Int_Oring__char__0(T_b) % 112.10/112.01 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) % 112.10/112.01 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__0,axiom, % 112.10/112.01 ! [T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__le__iff,axiom, % 112.10/112.01 ! [V_z_2,V_w_2,T_b] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.01 => ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__less__iff,axiom, % 112.10/112.01 ! [V_z_2,V_w_2,T_b] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.01 => ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__add,axiom, % 112.10/112.01 ! [V_z,V_w,T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__number__of__eq,axiom, % 112.10/112.01 ! [V_v,T_a] : % 112.10/112.01 ( class_Int_Onumber__ring(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__mult,axiom, % 112.10/112.01 ! [V_z,V_w,T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__1,axiom, % 112.10/112.01 ! [T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__diff,axiom, % 112.10/112.01 ! [V_z,V_w,T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__of__nat__eq,axiom, % 112.10/112.01 ! [V_n,T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__minus,axiom, % 112.10/112.01 ! [V_z,T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Ints__of__int,axiom, % 112.10/112.01 ! [V_z_2,T_b] : % 112.10/112.01 ( class_Rings_Oring__1(T_b) % 112.10/112.01 => 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__power,axiom, % 112.10/112.01 ! [V_n,V_z,T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_greaterThanLessThan__empty,axiom, % 112.10/112.01 ! [V_k_2,V_l_2,T_b] : % 112.10/112.01 ( class_Orderings_Oorder(T_b) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_image__uminus__greaterThanLessThan,axiom, % 112.10/112.01 ! [V_y_2,V_x_2,T_b] : % 112.10/112.01 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_code__numeral_Osize_I4_J,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__m1,axiom, % 112.10/112.01 ! [T_a] : % 112.10/112.01 ( class_Int_Onumber__ring(T_a) % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Suc__code__numeral__minus__one,axiom, % 112.10/112.01 ! [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 ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__0__le__iff,axiom, % 112.10/112.01 ! [V_z_2,T_b] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.01 => ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__le__0__iff,axiom, % 112.10/112.01 ! [V_z_2,T_b] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.01 => ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__0__less__iff,axiom, % 112.10/112.01 ! [V_z_2,T_b] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.01 => ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__int__less__0__iff,axiom, % 112.10/112.01 ! [V_z_2,T_b] : % 112.10/112.01 ( class_Rings_Olinordered__idom(T_b) % 112.10/112.01 => ( 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))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_of__nat__nat,axiom, % 112.10/112.01 ! [V_z,T_a] : % 112.10/112.01 ( class_Rings_Oring__1(T_a) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 112.10/112.01 => 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) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nitpick_Onat__lcm__def,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_card__Pow,axiom, % 112.10/112.01 ! [V_A_2,T_b] : % 112.10/112.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_code__numeral_Osimps_I5_J,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_code__numeral_Osimps_I4_J,axiom, % 112.10/112.01 ! [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 ). % 112.10/112.01 % 112.10/112.01 fof(fact_card__atLeastAtMost__int,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_finite__greaterThanLessThan,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_PowI,axiom, % 112.10/112.01 ! [V_B_2,V_A_2,T_b] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.10/112.01 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_finite__atLeastAtMost__int,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Cantors__paradox,axiom, % 112.10/112.01 ! [V_A_2,T_b] : % 112.10/112.01 ~ ? [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Pow__top,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Pow__not__empty,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Pow__bottom,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Pow__empty,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_finite__Pow__iff,axiom, % 112.10/112.01 ! [V_A_2,T_b] : % 112.10/112.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2))) % 112.10/112.01 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Pow__iff,axiom, % 112.10/112.01 ! [V_B_2,V_A_2,T_b] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 112.10/112.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_PowD,axiom, % 112.10/112.01 ! [V_B_2,V_A_2,T_b] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) % 112.10/112.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Pow__mono,axiom, % 112.10/112.01 ! [V_B_2,V_A_2,T_b] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.10/112.01 => 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_image__Pow__surj,axiom, % 112.10/112.01 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : % 112.10/112.01 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2 % 112.10/112.01 => 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) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 112.10/112.01 ! [V_y_2,V_x_2] : % 112.10/112.01 ( c_Nat__Transfer_Ois__nat(V_x_2) % 112.10/112.01 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_atLeastatMost__empty__iff,axiom, % 112.10/112.01 ! [V_b_2,V_a_2,T_b] : % 112.10/112.01 ( class_Orderings_Oorder(T_b) % 112.10/112.01 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.01 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_atLeastatMost__empty__iff2,axiom, % 112.10/112.01 ! [V_b_2,V_a_2,T_b] : % 112.10/112.01 ( class_Orderings_Oorder(T_b) % 112.10/112.01 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) % 112.10/112.01 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_atLeastatMost__empty,axiom, % 112.10/112.01 ! [V_a_2,V_b_2,T_b] : % 112.10/112.01 ( class_Orderings_Oorder(T_b) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) % 112.10/112.01 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_atLeastatMost__subset__iff,axiom, % 112.10/112.01 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 112.10/112.01 ( class_Orderings_Oorder(T_b) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2))) % 112.10/112.01 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 112.10/112.01 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_atLeastAtMost__singleton_H,axiom, % 112.10/112.01 ! [V_b_2,V_a_2,T_b] : % 112.10/112.01 ( class_Orderings_Oorder(T_b) % 112.10/112.01 => ( V_a_2 = V_b_2 % 112.10/112.01 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_atLeastAtMost__singleton__iff,axiom, % 112.10/112.01 ! [V_c_2,V_b_2,V_a_2,T_b] : % 112.10/112.01 ( class_Orderings_Oorder(T_b) % 112.10/112.01 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) % 112.10/112.01 <=> ( V_a_2 = V_b_2 % 112.10/112.01 & V_b_2 = V_c_2 ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_atLeastAtMost__singleton,axiom, % 112.10/112.01 ! [V_a_2,T_b] : % 112.10/112.01 ( class_Orderings_Oorder(T_b) % 112.10/112.01 => 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_image__uminus__atLeastAtMost,axiom, % 112.10/112.01 ! [V_y_2,V_x_2,T_b] : % 112.10/112.01 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.01 => 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)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_image__Pow__mono,axiom, % 112.10/112.01 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.10/112.01 ( 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)) % 112.10/112.01 => 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))) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 112.10/112.01 ! [V_y_2,V_x_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 112.10/112.01 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_atLeastatMost__psubset__iff,axiom, % 112.10/112.01 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 112.10/112.01 ( class_Orderings_Oorder(T_b) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2))) % 112.10/112.01 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) % 112.10/112.01 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) % 112.10/112.01 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) % 112.10/112.01 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) ) % 112.10/112.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_card__greaterThanLessThan,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_simp__from__to,axiom, % 112.10/112.01 ! [V_i_2,V_j_2] : % 112.10/112.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 112.10/112.01 => 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)) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_nat__gcd_Osimps,axiom, % 112.10/112.01 ! [V_x,V_y] : % 112.10/112.01 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 112.10/112.01 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 => 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)) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_Nitpick_Oint__gcd__def,axiom, % 112.10/112.01 ! [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)))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_bset_I8_J,axiom, % 112.10/112.01 ! [V_B_2,V_t_2,V_D_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 112.10/112.01 => ( 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)) % 112.10/112.01 => ! [B_x] : % 112.10/112.01 ( ! [B_xa] : % 112.10/112.01 ( 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))) % 112.10/112.01 => ! [B_xb] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 112.10/112.01 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 112.10/112.01 => 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))) ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_aset_I6_J,axiom, % 112.10/112.01 ! [V_A_2,V_t_2,V_D_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 112.10/112.01 => ( 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)) % 112.10/112.01 => ! [B_x] : % 112.10/112.01 ( ! [B_xa] : % 112.10/112.01 ( 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))) % 112.10/112.01 => ! [B_xb] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 112.10/112.01 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 112.10/112.01 => 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)) ) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_bset_I3_J,axiom, % 112.10/112.01 ! [V_B_2,V_t_2,V_D_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 112.10/112.01 => ( 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)) % 112.10/112.01 => ( ! [B_x] : % 112.10/112.01 ( 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))) % 112.10/112.01 => ! [B_xa] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 112.10/112.01 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 112.10/112.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_aset_I3_J,axiom, % 112.10/112.01 ! [V_A_2,V_t_2,V_D_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 112.10/112.01 => ( 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)) % 112.10/112.01 => ( ! [B_x] : % 112.10/112.01 ( 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))) % 112.10/112.01 => ! [B_xa] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 112.10/112.01 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 112.10/112.01 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_finite__atLeastAtMost,axiom, % 112.10/112.01 ! [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))) ). % 112.10/112.01 % 112.10/112.01 fof(fact_image__Suc__atLeastAtMost,axiom, % 112.10/112.01 ! [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)) ). % 112.10/112.01 % 112.10/112.01 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 112.10/112.01 ! [V_k_2,V_f_2] : % 112.10/112.01 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.10/112.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_atLeastAtMostSuc__conv,axiom, % 112.10/112.01 ! [V_na_2,V_m_2] : % 112.10/112.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) % 112.10/112.01 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_na_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2)) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_setsum__head__Suc,axiom, % 112.10/112.01 ! [V_f_2,V_na_2,V_m_2,T_b] : % 112.10/112.01 ( class_Groups_Ocomm__monoid__add(T_b) % 112.10/112.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 112.10/112.01 => 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_na_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_na_2))) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_card__atLeastAtMost,axiom, % 112.10/112.01 ! [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) ). % 112.10/112.01 % 112.10/112.01 fof(fact_setsum__cl__ivl__Suc,axiom, % 112.10/112.01 ! [V_f_2,V_m_2,V_na_2,T_b] : % 112.10/112.01 ( class_Groups_Ocomm__monoid__add(T_b) % 112.10/112.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) % 112.10/112.01 => 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_na_2))) = c_Groups_Ozero__class_Ozero(T_b) ) % 112.10/112.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) % 112.10/112.01 => 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_na_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_na_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_na_2))) ) ) ) ). % 112.10/112.01 % 112.10/112.01 fof(fact_setsum__ub__add__nat,axiom, % 112.10/112.01 ! [V_p_2,V_f_2,V_na_2,V_m_2,T_b] : % 112.10/112.01 ( class_Groups_Ocomm__monoid__add(T_b) % 112.10/112.01 => ( 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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) % 112.10/112.02 => 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_na_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_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_p_2)))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 112.10/112.02 ! [V_na_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_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_na_2))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 112.10/112.02 ! [V_na_2,V_m_2] : % 112.10/112.02 ( c_Nat__Transfer_Ois__nat(V_m_2) % 112.10/112.02 => ( c_Nat__Transfer_Ois__nat(V_na_2) % 112.10/112.02 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_na_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_na_2))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_aset_I4_J,axiom, % 112.10/112.02 ! [V_A_2,V_t_2,V_D_2] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 112.10/112.02 => ! [B_x] : % 112.10/112.02 ( ! [B_xa] : % 112.10/112.02 ( 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))) % 112.10/112.02 => ! [B_xb] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 112.10/112.02 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 112.10/112.02 => ( B_x != V_t_2 % 112.10/112.02 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_bset_I4_J,axiom, % 112.10/112.02 ! [V_B_2,V_t_2,V_D_2] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 112.10/112.02 => ! [B_x] : % 112.10/112.02 ( ! [B_xa] : % 112.10/112.02 ( 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))) % 112.10/112.02 => ! [B_xb] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 112.10/112.02 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 112.10/112.02 => ( B_x != V_t_2 % 112.10/112.02 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_bset_I7_J,axiom, % 112.10/112.02 ! [V_B_2,V_t_2,V_D_2] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 112.10/112.02 => ! [B_x] : % 112.10/112.02 ( ! [B_xa] : % 112.10/112.02 ( 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))) % 112.10/112.02 => ! [B_xb] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 112.10/112.02 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 112.10/112.02 => 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))) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_aset_I5_J,axiom, % 112.10/112.02 ! [V_A_2,V_t_2,V_D_2] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 112.10/112.02 => ! [B_x] : % 112.10/112.02 ( ! [B_xa] : % 112.10/112.02 ( 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))) % 112.10/112.02 => ! [B_xb] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 112.10/112.02 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 112.10/112.02 => 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)) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_bset_I6_J,axiom, % 112.10/112.02 ! [V_t_2,V_B_2,V_D_2] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 112.10/112.02 => ! [B_x] : % 112.10/112.02 ( ! [B_xa] : % 112.10/112.02 ( 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))) % 112.10/112.02 => ! [B_xb] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 112.10/112.02 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 112.10/112.02 => 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)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_all__nat__less,axiom, % 112.10/112.02 ! [V_Pa_2,V_na_2] : % 112.10/112.02 ( ! [B_m] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_na_2)) % 112.10/112.02 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 112.10/112.02 <=> ! [B_x] : % 112.10/112.02 ( 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_na_2))) % 112.10/112.02 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ex__nat__less,axiom, % 112.10/112.02 ! [V_Pa_2,V_na_2] : % 112.10/112.02 ( ? [B_m] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_na_2)) % 112.10/112.02 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 112.10/112.02 <=> ? [B_x] : % 112.10/112.02 ( 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_na_2))) % 112.10/112.02 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_aset_I8_J,axiom, % 112.10/112.02 ! [V_t_2,V_A_2,V_D_2] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 112.10/112.02 => ! [B_x] : % 112.10/112.02 ( ! [B_xa] : % 112.10/112.02 ( 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))) % 112.10/112.02 => ! [B_xb] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 112.10/112.02 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 112.10/112.02 => 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))) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_periodic__finite__ex,axiom, % 112.10/112.02 ! [V_Pa_2,V_d_2] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 112.10/112.02 => ( ! [B_x,B_k] : % 112.10/112.02 ( hBOOL(hAPP(V_Pa_2,B_x)) % 112.10/112.02 <=> 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)))) ) % 112.10/112.02 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 112.10/112.02 <=> ? [B_x] : % 112.10/112.02 ( 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))) % 112.10/112.02 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_aset_I7_J,axiom, % 112.10/112.02 ! [V_t_2,V_A_2,V_D_2] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 112.10/112.02 => ! [B_x] : % 112.10/112.02 ( ! [B_xa] : % 112.10/112.02 ( 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))) % 112.10/112.02 => ! [B_xb] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 112.10/112.02 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 112.10/112.02 => 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))) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_bset_I5_J,axiom, % 112.10/112.02 ! [V_t_2,V_B_2,V_D_2] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 112.10/112.02 => ! [B_x] : % 112.10/112.02 ( ! [B_xa] : % 112.10/112.02 ( 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))) % 112.10/112.02 => ! [B_xb] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 112.10/112.02 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 112.10/112.02 => 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)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 112.10/112.02 ! [V_na_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_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_na_2))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 112.10/112.02 ! [V_na_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_nat__mod__eq__lemma,axiom, % 112.10/112.02 ! [V_y,V_n,V_x] : % 112.10/112.02 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 112.10/112.02 => ? [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)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_mod__induct__0,axiom, % 112.10/112.02 ! [V_i_2,V_Pa_2,V_p_2] : % 112.10/112.02 ( ! [B_i] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 112.10/112.02 => ( hBOOL(hAPP(V_Pa_2,B_i)) % 112.10/112.02 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 112.10/112.02 => ( hBOOL(hAPP(V_Pa_2,V_i_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 112.10/112.02 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__lessThan,axiom, % 112.10/112.02 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__atMost,axiom, % 112.10/112.02 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_lessThan__eq__iff,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2) % 112.10/112.02 <=> V_x_2 = V_y_2 ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atMost__eq__iff,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2) % 112.10/112.02 <=> V_x_2 = V_y_2 ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_lessThan__Suc__atMost,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_card__lessThan,axiom, % 112.10/112.02 ! [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 ). % 112.10/112.02 % 112.10/112.02 fof(fact_lessThan__0,axiom, % 112.10/112.02 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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeast0AtMost,axiom, % 112.10/112.02 ! [V_na_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_2) ). % 112.10/112.02 % 112.10/112.02 fof(fact_lessThan__Suc,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_card__atMost,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atMost__Suc,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atMost__iff,axiom, % 112.10/112.02 ! [V_k_2,V_i_2,T_b] : % 112.10/112.02 ( class_Orderings_Oord(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) % 112.10/112.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_lessThan__iff,axiom, % 112.10/112.02 ! [V_k_2,V_i_2,T_b] : % 112.10/112.02 ( class_Orderings_Oord(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) % 112.10/112.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_lessThan__subset__iff,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( 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))) % 112.10/112.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atMost__subset__iff,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => ( 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))) % 112.10/112.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_lessThan__strict__subset__iff,axiom, % 112.10/112.02 ! [V_na_2,V_m_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( 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_na_2))) % 112.10/112.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_na_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atMost__0,axiom, % 112.10/112.02 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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_single__Diff__lessThan,axiom, % 112.10/112.02 ! [V_k_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => 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))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_image__atLeastZeroLessThan__int,axiom, % 112.10/112.02 ! [V_u_2] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 112.10/112.02 => 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))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_log_Osimps,axiom, % 112.10/112.02 ! [V_i,V_b] : % 112.10/112.02 ( ( ( 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))) % 112.10/112.02 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 112.10/112.02 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 112.10/112.02 & ( ~ ( 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))) % 112.10/112.02 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 112.10/112.02 => 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))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_mod__div__decomp,axiom, % 112.10/112.02 ! [V_b,V_a,T_a] : % 112.10/112.02 ( class_Divides_Osemiring__div(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_greaterThan__Suc,axiom, % 112.10/112.02 ! [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)))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_image__uminus__lessThan,axiom, % 112.10/112.02 ! [V_x_2,T_b] : % 112.10/112.02 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__atLeastLessThan__int,axiom, % 112.10/112.02 ! [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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_greaterThan__eq__iff,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2) % 112.10/112.02 <=> V_x_2 = V_y_2 ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastLessThan__eq__iff,axiom, % 112.10/112.02 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) % 112.10/112.02 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2) % 112.10/112.02 <=> ( V_a_2 = V_c_2 % 112.10/112.02 & V_b_2 = V_d_2 ) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 112.10/112.02 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) % 112.10/112.02 => V_a_2 = V_c_2 ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 112.10/112.02 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) % 112.10/112.02 => V_b_2 = V_d_2 ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastLessThan__empty,axiom, % 112.10/112.02 ! [V_a_2,V_b_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) % 112.10/112.02 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastLessThan__empty__iff,axiom, % 112.10/112.02 ! [V_b_2,V_a_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastLessThan__empty__iff2,axiom, % 112.10/112.02 ! [V_b_2,V_a_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) % 112.10/112.02 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastLessThan__subset__iff,axiom, % 112.10/112.02 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2))) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) % 112.10/112.02 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) % 112.10/112.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__diff,axiom, % 112.10/112.02 ! [V_m_2,V_na_2,V_i_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_na_2)) % 112.10/112.02 => 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_na_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_na_2),V_m_2) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 112.10/112.02 ! [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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_greaterThan__iff,axiom, % 112.10/112.02 ! [V_k_2,V_i_2,T_b] : % 112.10/112.02 ( class_Orderings_Oord(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) % 112.10/112.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_greaterThan__subset__iff,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( 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))) % 112.10/112.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__greaterThan,axiom, % 112.10/112.02 ! [V_k_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__atMost,axiom, % 112.10/112.02 ! [V_k_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_card__atLeastZeroLessThan__int,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_card__atLeastLessThan__int,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_image__uminus__greaterThan,axiom, % 112.10/112.02 ! [V_x_2,T_b] : % 112.10/112.02 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_minus__shift__def,axiom, % 112.10/112.02 ! [V_r,V_l,V_k] : % 112.10/112.02 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 112.10/112.02 => 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) ) % 112.10/112.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inc__shift__def,axiom, % 112.10/112.02 ! [V_k,V_v] : % 112.10/112.02 ( ( V_v = V_k % 112.10/112.02 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 112.10/112.02 & ( V_v != V_k % 112.10/112.02 => 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)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeast__Suc,axiom, % 112.10/112.02 ! [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)))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_greaterThan__0,axiom, % 112.10/112.02 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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I18_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 112.10/112.02 => 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) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__atLeastLessThan,axiom, % 112.10/112.02 ! [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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_UNIV__I,axiom, % 112.10/112.02 ! [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)))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_UnCI,axiom, % 112.10/112.02 ! [V_A_2,V_B_2,V_c_2,T_b] : % 112.10/112.02 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) % 112.10/112.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) % 112.10/112.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_UnE,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_c_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 112.10/112.02 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 112.10/112.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__Pow__subset,axiom, % 112.10/112.02 ! [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)))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_less__supI1,axiom, % 112.10/112.02 ! [V_b,V_a,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 112.10/112.02 => 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))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_less__supI2,axiom, % 112.10/112.02 ! [V_a,V_b,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 112.10/112.02 => 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))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__Diff,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__Diff__cancel2,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__Diff__cancel,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__upper1,axiom, % 112.10/112.02 ! [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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__upper2,axiom, % 112.10/112.02 ! [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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_subset__Un__eq,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.10/112.02 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__absorb1,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__absorb2,axiom, % 112.10/112.02 ! [V_A_2,V_B_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__least,axiom, % 112.10/112.02 ! [V_B_2,V_C_2,V_A_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 112.10/112.02 => 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)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__mono,axiom, % 112.10/112.02 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 112.10/112.02 => 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))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastLessThan__add__Un,axiom, % 112.10/112.02 ! [V_k_2,V_j_2,V_i_2] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 112.10/112.02 => 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))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I14_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__ord_I3_J,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__ge1,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => 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))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__ord_I4_J,axiom, % 112.10/112.02 ! [V_x,V_y,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__ge2,axiom, % 112.10/112.02 ! [V_x,V_y,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => 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))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_le__iff__sup,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 112.10/112.02 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_le__sup__iff,axiom, % 112.10/112.02 ! [V_z_2,V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_b) % 112.10/112.02 => ( 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)) % 112.10/112.02 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) % 112.10/112.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_le__supI1,axiom, % 112.10/112.02 ! [V_b,V_a,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 112.10/112.02 => 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))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_le__supI2,axiom, % 112.10/112.02 ! [V_a,V_b,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 112.10/112.02 => 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))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__absorb2,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__absorb1,axiom, % 112.10/112.02 ! [V_x,V_y,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_le__supI,axiom, % 112.10/112.02 ! [V_b,V_x,V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 112.10/112.02 => 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)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__least,axiom, % 112.10/112.02 ! [V_z,V_x,V_y,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 112.10/112.02 => 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)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__mono,axiom, % 112.10/112.02 ! [V_d,V_b,V_c,V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 112.10/112.02 => 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))) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_le__supE,axiom, % 112.10/112.02 ! [V_x,V_b,V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => ( 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)) % 112.10/112.02 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 112.10/112.02 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_subset__UNIV,axiom, % 112.10/112.02 ! [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)))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_UnI2,axiom, % 112.10/112.02 ! [V_A_2,V_B_2,V_c_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) % 112.10/112.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_UnI1,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_c_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 112.10/112.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__iff,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_c_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 112.10/112.02 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 112.10/112.02 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__Prod__UNIV,axiom, % 112.10/112.02 ! [T_c,T_b] : % 112.10/112.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) % 112.10/112.02 => 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)))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__option__UNIV,axiom, % 112.10/112.02 ! [T_b] : % 112.10/112.02 ( 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)))) % 112.10/112.02 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__fun__UNIVD2,axiom, % 112.10/112.02 ! [T_c,T_b] : % 112.10/112.02 ( 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)))) % 112.10/112.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__eq__bot__iff,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Lattices_Obounded__lattice__bot(T_b) % 112.10/112.02 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b) % 112.10/112.02 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b) % 112.10/112.02 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__bot__right,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Obounded__lattice__bot(T_a) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__bot__left,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Obounded__lattice__bot(T_a) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__UnI,axiom, % 112.10/112.02 ! [V_G_2,V_F_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) % 112.10/112.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__Un,axiom, % 112.10/112.02 ! [V_G_2,V_F_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) % 112.10/112.02 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 112.10/112.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__empty,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( 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)) % 112.10/112.02 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__empty__right,axiom, % 112.10/112.02 ! [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 ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__empty__left,axiom, % 112.10/112.02 ! [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 ). % 112.10/112.02 % 112.10/112.02 fof(fact_UNIV__not__empty,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__UNIV,axiom, % 112.10/112.02 ! [T_b] : % 112.10/112.02 ( class_Finite__Set_Ofinite(T_b) % 112.10/112.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__max,axiom, % 112.10/112.02 ! [T_b] : % 112.10/112.02 ( ( class_Lattices_Osemilattice__sup(T_b) % 112.10/112.02 & class_Orderings_Olinorder(T_b) ) % 112.10/112.02 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeast__eq__iff,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2) % 112.10/112.02 <=> V_x_2 = V_y_2 ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_UNIV__Plus__UNIV,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__apply,axiom, % 112.10/112.02 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__assoc,axiom, % 112.10/112.02 ! [V_z,V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__aci_I6_J,axiom, % 112.10/112.02 ! [V_z,V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup_Oassoc,axiom, % 112.10/112.02 ! [V_c,V_b,V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__left__commute,axiom, % 112.10/112.02 ! [V_z,V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__aci_I7_J,axiom, % 112.10/112.02 ! [V_z,V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup_Oleft__commute,axiom, % 112.10/112.02 ! [V_c,V_a,V_b,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__left__idem,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__aci_I8_J,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup_Oleft__idem,axiom, % 112.10/112.02 ! [V_b,V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__commute,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__aci_I5_J,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup_Ocommute,axiom, % 112.10/112.02 ! [V_b,V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__idem,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup_Oidem,axiom, % 112.10/112.02 ! [V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_a) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__top__right,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Obounded__lattice__top(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__top__left,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Obounded__lattice__top(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_top__apply,axiom, % 112.10/112.02 ! [V_x_2,T_c,T_b] : % 112.10/112.02 ( class_Orderings_Otop(T_b) % 112.10/112.02 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ball__Un,axiom, % 112.10/112.02 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 112.10/112.02 ( ! [B_x] : % 112.10/112.02 ( 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))) % 112.10/112.02 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.10/112.02 <=> ( ! [B_x] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.10/112.02 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.10/112.02 & ! [B_x] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 112.10/112.02 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_bex__Un,axiom, % 112.10/112.02 ! [V_Pa_2,V_B_2,V_A_2,T_b] : % 112.10/112.02 ( ? [B_x] : % 112.10/112.02 ( 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))) % 112.10/112.02 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.10/112.02 <=> ( ? [B_x] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.10/112.02 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.10/112.02 | ? [B_x] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 112.10/112.02 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__assoc,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__left__commute,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__left__absorb,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__commute,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__absorb,axiom, % 112.10/112.02 ! [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 ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__UNIV__right,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__UNIV__left,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_Oidem,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_compl__sup__top,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Oboolean__algebra(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__compl__top,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Oboolean__algebra(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__partition2,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__partition,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeast__0,axiom, % 112.10/112.02 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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Pow__UNIV,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__insert__right,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__insert__left,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_image__Un,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__Plus__UNIV__iff,axiom, % 112.10/112.02 ! [T_c,T_b] : % 112.10/112.02 ( 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)))) % 112.10/112.02 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 112.10/112.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 112.10/112.02 ! [V_B_2,V_A_2] : % 112.10/112.02 ( c_Nat__Transfer_Onat__set(V_A_2) % 112.10/112.02 => ( c_Nat__Transfer_Onat__set(V_B_2) % 112.10/112.02 => 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)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_fun__left__comm__idem__sup,axiom, % 112.10/112.02 ! [T_b] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_b) % 112.10/112.02 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_infinite__UNIV__nat,axiom, % 112.10/112.02 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_top__greatest,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Orderings_Otop(T_a) % 112.10/112.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I1_J,axiom, % 112.10/112.02 ! [V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I13_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I12_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_all__nat__less__eq,axiom, % 112.10/112.02 ! [V_Pa_2,V_na_2] : % 112.10/112.02 ( ! [B_m] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_na_2)) % 112.10/112.02 => hBOOL(hAPP(V_Pa_2,B_m)) ) % 112.10/112.02 <=> ! [B_x] : % 112.10/112.02 ( 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_na_2))) % 112.10/112.02 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ex__nat__less__eq,axiom, % 112.10/112.02 ! [V_Pa_2,V_na_2] : % 112.10/112.02 ( ? [B_m] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_na_2)) % 112.10/112.02 & hBOOL(hAPP(V_Pa_2,B_m)) ) % 112.10/112.02 <=> ? [B_x] : % 112.10/112.02 ( 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_na_2))) % 112.10/112.02 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_insert__is__Un,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_union__fold__insert,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I17_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 112.10/112.02 => 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) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Diff__subset__conv,axiom, % 112.10/112.02 ! [V_C_2,V_B_2,V_A_2,T_b] : % 112.10/112.02 ( 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)) % 112.10/112.02 <=> 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))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Diff__partition,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.10/112.02 => 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 ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_range__eqI,axiom, % 112.10/112.02 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] : % 112.10/112.02 ( V_b_2 = hAPP(V_f_2,V_x_2) % 112.10/112.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_rangeI,axiom, % 112.10/112.02 ! [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))))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastLessThan0,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 112.10/112.02 ! [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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeast0LessThan,axiom, % 112.10/112.02 ! [V_na_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Diff__UNIV,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 112.10/112.02 ! [V_A_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 112.10/112.02 => ( 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))) % 112.10/112.02 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__Diff__eq,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_card__atLeastLessThan,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__UNIV__eq,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__empty__eq,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__compl,axiom, % 112.10/112.02 ! [V_A_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) % 112.10/112.02 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__eq__Diff__UNIV,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_image__Suc__atLeastLessThan,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 112.10/112.02 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 112.10/112.02 => 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)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 112.10/112.02 ! [V_B_2,V_A_2] : % 112.10/112.02 ( c_Nat__Transfer_Onat__set(V_A_2) % 112.10/112.02 => ( c_Nat__Transfer_Onat__set(V_B_2) % 112.10/112.02 => 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))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeast__iff,axiom, % 112.10/112.02 ! [V_k_2,V_i_2,T_b] : % 112.10/112.02 ( class_Orderings_Oord(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) % 112.10/112.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_fold__sup__insert,axiom, % 112.10/112.02 ! [V_a_2,V_b_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeast__subset__iff,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => ( 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))) % 112.10/112.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_setsum__add__nat__ivl,axiom, % 112.10/112.02 ! [V_f_2,V_p_2,V_na_2,V_m_2,T_b] : % 112.10/112.02 ( class_Groups_Ocomm__monoid__add(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_p_2)) % 112.10/112.02 => 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_na_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_na_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)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_setsum__diff__nat__ivl,axiom, % 112.10/112.02 ! [V_f_2,V_p_2,V_na_2,V_m_2,T_b] : % 112.10/112.02 ( class_Groups_Oab__group__add(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_p_2)) % 112.10/112.02 => 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_na_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_na_2),V_p_2)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_compl__bot__eq,axiom, % 112.10/112.02 ! [T_a] : % 112.10/112.02 ( class_Lattices_Oboolean__algebra(T_a) % 112.10/112.02 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_compl__top__eq,axiom, % 112.10/112.02 ! [T_a] : % 112.10/112.02 ( class_Lattices_Oboolean__algebra(T_a) % 112.10/112.02 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I21_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 112.10/112.02 => 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) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I8_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_surj__Compl__image__subset,axiom, % 112.10/112.02 ! [V_A_2,V_f_2,T_b,T_c] : % 112.10/112.02 ( 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)) % 112.10/112.02 => 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)))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastLessThan__singleton,axiom, % 112.10/112.02 ! [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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__atLeast,axiom, % 112.10/112.02 ! [V_k_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__lessThan,axiom, % 112.10/112.02 ! [V_k_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_folding__one__idem_Ounion__idem,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 112.10/112.02 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.10/112.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => 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)) ) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeast__Suc__greaterThan,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Pow__insert,axiom, % 112.10/112.02 ! [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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_subset__card__intvl__is__intvl,axiom, % 112.10/112.02 ! [V_k_2,V_A_2] : % 112.10/112.02 ( 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))))) % 112.10/112.02 => 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))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__le__fold__sup,axiom, % 112.10/112.02 ! [V_b_2,V_a_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Osemilattice__sup(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.10/112.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 112.10/112.02 ! [V_k_2,V_f_2,T_b] : % 112.10/112.02 ( class_Groups_Ocomm__monoid__add(T_b) % 112.10/112.02 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b) % 112.10/112.02 => 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)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_setsum__head__upt__Suc,axiom, % 112.10/112.02 ! [V_f_2,V_na_2,V_m_2,T_b] : % 112.10/112.02 ( class_Groups_Ocomm__monoid__add(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) % 112.10/112.02 => 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_na_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_na_2))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_fold1__Un2,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.10/112.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => 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)) ) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Min__Un,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.10/112.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => 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)) ) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Max__Un,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.10/112.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => 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)) ) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.10/112.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => 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)) ) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.10/112.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => 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)) ) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I15_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 112.10/112.02 => 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) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__UNIV__card__ge__0,axiom, % 112.10/112.02 ! [T_b] : % 112.10/112.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 112.10/112.02 => 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))))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastLessThanSuc,axiom, % 112.10/112.02 ! [V_na_2,V_m_2] : % 112.10/112.02 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 112.10/112.02 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_na_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2)) ) % 112.10/112.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 112.10/112.02 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I2_J,axiom, % 112.10/112.02 ! [V_u_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I10_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I7_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_image__uminus__atMost,axiom, % 112.10/112.02 ! [V_x_2,T_b] : % 112.10/112.02 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_image__uminus__atLeast,axiom, % 112.10/112.02 ! [V_x_2,T_b] : % 112.10/112.02 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_setsum__op__ivl__Suc,axiom, % 112.10/112.02 ! [V_f_2,V_m_2,V_na_2,T_b] : % 112.10/112.02 ( class_Groups_Ocomm__monoid__add(T_b) % 112.10/112.02 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 112.10/112.02 => 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_na_2))) = c_Groups_Ozero__class_Ozero(T_b) ) % 112.10/112.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) % 112.10/112.02 => 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_na_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_na_2))),hAPP(V_f_2,V_na_2)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I6_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I3_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__fun__UNIVD1,axiom, % 112.10/112.02 ! [T_c,T_b] : % 112.10/112.02 ( 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)))) % 112.10/112.02 => ( 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)) % 112.10/112.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup1E,axiom, % 112.10/112.02 ! [V_x_2,V_B_2,V_A_2,T_b] : % 112.10/112.02 ( 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)) % 112.10/112.02 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 112.10/112.02 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup1CI,axiom, % 112.10/112.02 ! [T_b,V_A_2,V_x_2,V_B_2] : % 112.10/112.02 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 112.10/112.02 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_top1I,axiom, % 112.10/112.02 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I19_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 112.10/112.02 => 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) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__greaterThanAtMost,axiom, % 112.10/112.02 ! [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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__greaterThanAtMost__int,axiom, % 112.10/112.02 ! [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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_card__UNIV__unit,axiom, % 112.10/112.02 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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__nat__def,axiom, % 112.10/112.02 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 112.10/112.02 % 112.10/112.02 fof(fact_infinite__UNIV__int,axiom, % 112.10/112.02 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_greaterThanAtMost__empty,axiom, % 112.10/112.02 ! [V_k_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) % 112.10/112.02 => 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)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_greaterThanAtMost__empty__iff,axiom, % 112.10/112.02 ! [V_l_2,V_k_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => ( 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)) % 112.10/112.02 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 112.10/112.02 ! [V_l_2,V_k_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => ( 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) % 112.10/112.02 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I20_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 112.10/112.02 => 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) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_card__greaterThanAtMost,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_eq__mem,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2))) % 112.10/112.02 <=> V_x_2 = V_y_2 ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_rev__predicate1D,axiom, % 112.10/112.02 ! [V_Q_2,T_b,V_x_2,V_Pa_2] : % 112.10/112.02 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) % 112.10/112.02 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_predicate1D,axiom, % 112.10/112.02 ! [V_x_2,V_Q_2,V_Pa_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2)) % 112.10/112.02 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.10/112.02 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup1I2,axiom, % 112.10/112.02 ! [V_A_2,T_b,V_x_2,V_B_2] : % 112.10/112.02 ( hBOOL(hAPP(V_B_2,V_x_2)) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup1I1,axiom, % 112.10/112.02 ! [V_B_2,T_b,V_x_2,V_A_2] : % 112.10/112.02 ( hBOOL(hAPP(V_A_2,V_x_2)) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I22_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) % 112.10/112.02 => 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) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_image__uminus__greaterThanAtMost,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_image__uminus__atLeastLessThan,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Groups_Oordered__ab__group__add(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_card__UNIV__bool,axiom, % 112.10/112.02 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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I9_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I11_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_card__greaterThanAtMost__int,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I16_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) % 112.10/112.02 => 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) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I5_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__un_I4_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_Oremove,axiom, % 112.10/112.02 ! [V_x_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/112.02 => ( ( hAPP(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)) % 112.10/112.02 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 ) % 112.10/112.02 & ( hAPP(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)) % 112.10/112.02 => 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)))))) ) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_iso__tuple__UNIV__I,axiom, % 112.10/112.02 ! [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)))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Powp__mono,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.10/112.02 => 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))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 112.10/112.02 ! [V_x_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/112.02 => 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) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_Osingleton,axiom, % 112.10/112.02 ! [V_x_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => 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 ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_Oin__idem,axiom, % 112.10/112.02 ! [V_x_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/112.02 => 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) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_OF__eq,axiom, % 112.10/112.02 ! [V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_Oinsert__idem,axiom, % 112.10/112.02 ! [V_x_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => 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)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_Osubset__idem,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 112.10/112.02 => 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) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_Ounion__idem,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.10/112.02 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => 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)) ) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 112.10/112.02 ! [V_a_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_Oinsert,axiom, % 112.10/112.02 ! [V_x_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.10/112.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => 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)) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_Oinsert__remove,axiom, % 112.10/112.02 ! [V_x_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( ( hAPP(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)) % 112.10/112.02 => 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 ) % 112.10/112.02 & ( hAPP(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)) % 112.10/112.02 => 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)))))) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_Oclosed,axiom, % 112.10/112.02 ! [V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => ( ! [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)))))) % 112.10/112.02 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fin_Ohom__commute,axiom, % 112.10/112.02 ! [V_N_2,V_h_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => ( ! [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)) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 112.10/112.02 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.10/112.02 => 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)) ) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Sup__fold__sup,axiom, % 112.10/112.02 ! [V_A_2,T_b] : % 112.10/112.02 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_setsum__Un__nat,axiom, % 112.10/112.02 ! [V_f_2,V_B_2,V_A_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.10/112.02 => 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))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf1I,axiom, % 112.10/112.02 ! [T_b,V_B_2,V_x_2,V_A_2] : % 112.10/112.02 ( hBOOL(hAPP(V_A_2,V_x_2)) % 112.10/112.02 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 112.10/112.02 => 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)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf1E,axiom, % 112.10/112.02 ! [V_x_2,V_B_2,V_A_2,T_b] : % 112.10/112.02 ( 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)) % 112.10/112.02 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 112.10/112.02 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_IntI,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_c_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) % 112.10/112.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_IntE,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_c_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 112.10/112.02 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 112.10/112.02 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__Int,axiom, % 112.10/112.02 ! [V_G_2,V_F_2,T_b] : % 112.10/112.02 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 112.10/112.02 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) ) % 112.10/112.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__inf__distrib2,axiom, % 112.10/112.02 ! [V_x,V_z,V_y,T_a] : % 112.10/112.02 ( class_Lattices_Odistrib__lattice(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__distrib2,axiom, % 112.10/112.02 ! [V_x,V_z,V_y,T_a] : % 112.10/112.02 ( class_Lattices_Odistrib__lattice(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__eq__top__iff,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Lattices_Obounded__lattice__top(T_b) % 112.10/112.02 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b) % 112.10/112.02 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b) % 112.10/112.02 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__inf__distrib1,axiom, % 112.10/112.02 ! [V_z,V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Odistrib__lattice(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__distrib1,axiom, % 112.10/112.02 ! [V_z,V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Odistrib__lattice(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_sup__inf__absorb,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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 ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__absorb,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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 ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__top__right,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Obounded__lattice__top(T_a) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__top__left,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Obounded__lattice__top(T_a) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__Int__crazy,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__Int__distrib2,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__Un__distrib2,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__Int__distrib,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__Un__distrib,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__UNIV__right,axiom, % 112.10/112.02 ! [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 ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__UNIV__left,axiom, % 112.10/112.02 ! [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 ). % 112.10/112.02 % 112.10/112.02 fof(fact_insert__inter__insert,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Pow__Int__eq,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Inf__fin_Oidem,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__absorb,axiom, % 112.10/112.02 ! [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 ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__commute,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__left__absorb,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__left__commute,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__assoc,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf_Oidem,axiom, % 112.10/112.02 ! [V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__idem,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf_Ocommute,axiom, % 112.10/112.02 ! [V_b,V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__aci_I1_J,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__commute,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf_Oleft__idem,axiom, % 112.10/112.02 ! [V_b,V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__aci_I4_J,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__left__idem,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf_Oleft__commute,axiom, % 112.10/112.02 ! [V_c,V_a,V_b,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__aci_I3_J,axiom, % 112.10/112.02 ! [V_z,V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__left__commute,axiom, % 112.10/112.02 ! [V_z,V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf_Oassoc,axiom, % 112.10/112.02 ! [V_c,V_b,V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__aci_I2_J,axiom, % 112.10/112.02 ! [V_z,V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__assoc,axiom, % 112.10/112.02 ! [V_z,V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__apply,axiom, % 112.10/112.02 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__min,axiom, % 112.10/112.02 ! [T_b] : % 112.10/112.02 ( ( class_Lattices_Osemilattice__inf(T_b) % 112.10/112.02 & class_Orderings_Olinorder(T_b) ) % 112.10/112.02 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__empty__left,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__empty__right,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_disjoint__iff__not__equal,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( 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)) % 112.10/112.02 <=> ! [B_x] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.10/112.02 => ! [B_xa] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) % 112.10/112.02 => B_x != B_xa ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__bot__left,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Obounded__lattice__bot(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__bot__right,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Obounded__lattice__bot(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__iff,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_c_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 112.10/112.02 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 112.10/112.02 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_IntD1,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_c_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 112.10/112.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_IntD2,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_c_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 112.10/112.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__mono,axiom, % 112.10/112.02 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) % 112.10/112.02 => 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))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__greatest,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_C_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) % 112.10/112.02 => 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))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__absorb1,axiom, % 112.10/112.02 ! [V_A_2,V_B_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__absorb2,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__lower2,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__lower1,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_le__infE,axiom, % 112.10/112.02 ! [V_b,V_a,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => ( 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))) % 112.10/112.02 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 112.10/112.02 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__mono,axiom, % 112.10/112.02 ! [V_d,V_b,V_c,V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 112.10/112.02 => 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))) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__greatest,axiom, % 112.10/112.02 ! [V_z,V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 112.10/112.02 => 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))) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_le__infI,axiom, % 112.10/112.02 ! [V_b,V_a,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 112.10/112.02 => 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))) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__absorb2,axiom, % 112.10/112.02 ! [V_x,V_y,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__absorb1,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_le__infI2,axiom, % 112.10/112.02 ! [V_a,V_x,V_b,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 112.10/112.02 => 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)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_le__infI1,axiom, % 112.10/112.02 ! [V_b,V_x,V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 112.10/112.02 => 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)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_le__inf__iff,axiom, % 112.10/112.02 ! [V_z_2,V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_b) % 112.10/112.02 => ( 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))) % 112.10/112.02 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 112.10/112.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_le__iff__inf,axiom, % 112.10/112.02 ! [V_y_2,V_x_2,T_b] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_b) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 112.10/112.02 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__le2,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__ord_I2_J,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__le1,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__sup__ord_I1_J,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Diff__Int__distrib,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__Diff,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Diff__Int__distrib2,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Diff__Int2,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_less__infI2,axiom, % 112.10/112.02 ! [V_a,V_x,V_b,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 112.10/112.02 => 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)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_less__infI1,axiom, % 112.10/112.02 ! [V_b,V_x,V_a,T_a] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_a) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 112.10/112.02 => 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)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 112.10/112.02 ! [V_B_2,V_A_2] : % 112.10/112.02 ( c_Nat__Transfer_Onat__set(V_A_2) % 112.10/112.02 => ( c_Nat__Transfer_Onat__set(V_B_2) % 112.10/112.02 => 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)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf1D1,axiom, % 112.10/112.02 ! [V_x_2,V_B_2,V_A_2,T_b] : % 112.10/112.02 ( 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)) % 112.10/112.02 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf1D2,axiom, % 112.10/112.02 ! [V_x_2,V_B_2,V_A_2,T_b] : % 112.10/112.02 ( 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)) % 112.10/112.02 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_fun__left__comm__idem__inf,axiom, % 112.10/112.02 ! [T_b] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_b) % 112.10/112.02 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_distrib__sup__le,axiom, % 112.10/112.02 ! [V_z,V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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)))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_distrib__inf__le,axiom, % 112.10/112.02 ! [V_z,V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Olattice(T_a) % 112.10/112.02 => 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)))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__compl__bot,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Oboolean__algebra(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_compl__inf__bot,axiom, % 112.10/112.02 ! [V_x,T_a] : % 112.10/112.02 ( class_Lattices_Oboolean__algebra(T_a) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_diff__eq,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Oboolean__algebra(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_compl__inf,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Oboolean__algebra(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_compl__sup,axiom, % 112.10/112.02 ! [V_y,V_x,T_a] : % 112.10/112.02 ( class_Lattices_Oboolean__algebra(T_a) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__insert__right,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_a_2,T_b] : % 112.10/112.02 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.10/112.02 => 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)) ) % 112.10/112.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__insert__left,axiom, % 112.10/112.02 ! [V_B_2,V_C_2,V_a_2,T_b] : % 112.10/112.02 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 112.10/112.02 => 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)) ) % 112.10/112.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 112.10/112.02 => 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) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__insert__right__if0,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_a_2,T_b] : % 112.10/112.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__insert__left__if0,axiom, % 112.10/112.02 ! [V_B_2,V_C_2,V_a_2,T_b] : % 112.10/112.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 112.10/112.02 => 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) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__insert__right__if1,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,V_a_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__insert__left__if1,axiom, % 112.10/112.02 ! [V_B_2,V_C_2,V_a_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_image__Int__subset,axiom, % 112.10/112.02 ! [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)))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Diff__triv,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( 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)) % 112.10/112.02 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Diff__disjoint,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__Int__assoc__eq,axiom, % 112.10/112.02 ! [V_C_2,V_B_2,V_A_2,T_b] : % 112.10/112.02 ( 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)) % 112.10/112.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Diff__Int,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Diff__Un,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Un__Diff__Int,axiom, % 112.10/112.02 ! [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 ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__int_I11_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 112.10/112.02 ! [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))) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__disjoint,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__disjoint2,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__Int,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Compl__Un,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Diff__eq,axiom, % 112.10/112.02 ! [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)) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Diff__Compl,axiom, % 112.10/112.02 ! [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) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__int_I14_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_finite__UnionD,axiom, % 112.10/112.02 ! [V_A_2,T_b] : % 112.10/112.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) % 112.10/112.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 112.10/112.02 ! [V_B_2,V_A_2] : % 112.10/112.02 ( c_Nat__Transfer_Onat__set(V_A_2) % 112.10/112.02 => ( c_Nat__Transfer_Onat__set(V_B_2) % 112.10/112.02 => 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))) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_fold__inf__insert,axiom, % 112.10/112.02 ! [V_a_2,V_b_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Osemilattice__inf(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_inf__Sup__absorb,axiom, % 112.10/112.02 ! [V_a_2,V_A_2,T_b] : % 112.10/112.02 ( class_Lattices_Olattice(T_b) % 112.10/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.10/112.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.10/112.02 => 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 ) ) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_disjoint__eq__subset__Compl,axiom, % 112.10/112.02 ! [V_B_2,V_A_2,T_b] : % 112.10/112.02 ( 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)) % 112.10/112.02 <=> 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))) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__int_I15_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__atLeastAtMost,axiom, % 112.10/112.02 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__atLeastLessThan,axiom, % 112.10/112.02 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__int_I4_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__int_I2_J,axiom, % 112.10/112.02 ! [V_u_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__int_I16_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__int_I13_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__int_I12_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.10/112.02 => 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)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_Int__greaterThanAtMost,axiom, % 112.10/112.02 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 112.10/112.02 ( class_Orderings_Olinorder(T_b) % 112.10/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 112.10/112.02 % 112.10/112.02 fof(fact_ivl__disj__int_I9_J,axiom, % 112.10/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.10/112.02 ( class_Orderings_Oorder(T_b) % 112.23/112.02 => 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)) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_Int__greaterThanLessThan,axiom, % 112.23/112.02 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] : % 112.23/112.02 ( class_Orderings_Olinorder(T_b) % 112.23/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_Int__atLeastAtMostR1,axiom, % 112.23/112.02 ! [V_d_2,V_c_2,V_b_2,T_b] : % 112.23/112.02 ( class_Orderings_Olinorder(T_b) % 112.23/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_Int__atLeastAtMostL1,axiom, % 112.23/112.02 ! [V_d_2,V_b_2,V_a_2,T_b] : % 112.23/112.02 ( class_Orderings_Olinorder(T_b) % 112.23/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_ivl__disj__int_I8_J,axiom, % 112.23/112.02 ! [V_u_2,V_l_2,T_b] : % 112.23/112.02 ( class_Orderings_Oorder(T_b) % 112.23/112.02 => 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)) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_ivl__disj__int_I7_J,axiom, % 112.23/112.02 ! [V_u_2,V_l_2,T_b] : % 112.23/112.02 ( class_Orderings_Oorder(T_b) % 112.23/112.02 => 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)) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_Int__atLeastAtMostR2,axiom, % 112.23/112.02 ! [V_d_2,V_c_2,V_a_2,T_b] : % 112.23/112.02 ( class_Orderings_Olinorder(T_b) % 112.23/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_Int__atLeastAtMostL2,axiom, % 112.23/112.02 ! [V_c_2,V_b_2,V_a_2,T_b] : % 112.23/112.02 ( class_Orderings_Olinorder(T_b) % 112.23/112.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_ivl__disj__int_I3_J,axiom, % 112.23/112.02 ! [V_u_2,V_l_2,T_b] : % 112.23/112.02 ( class_Orderings_Oorder(T_b) % 112.23/112.02 => 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)) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_ivl__disj__int_I10_J,axiom, % 112.23/112.02 ! [V_u_2,V_m_2,V_l_2,T_b] : % 112.23/112.02 ( class_Orderings_Oorder(T_b) % 112.23/112.02 => 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)) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_ivl__disj__int_I1_J,axiom, % 112.23/112.02 ! [V_u_2,V_l_2,T_b] : % 112.23/112.02 ( class_Orderings_Oorder(T_b) % 112.23/112.02 => 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)) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_ivl__disj__int_I6_J,axiom, % 112.23/112.02 ! [V_u_2,V_l_2,T_b] : % 112.23/112.02 ( class_Orderings_Oorder(T_b) % 112.23/112.02 => 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)) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_ivl__disj__int_I5_J,axiom, % 112.23/112.02 ! [V_u_2,V_l_2,T_b] : % 112.23/112.02 ( class_Orderings_Oorder(T_b) % 112.23/112.02 => 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)) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_folding__image__simple_Ounion__inter,axiom, % 112.23/112.02 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 112.23/112.02 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 112.23/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 112.23/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 112.23/112.02 => 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)) ) ) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_compl__unique,axiom, % 112.23/112.02 ! [V_y,V_x,T_a] : % 112.23/112.02 ( class_Lattices_Oboolean__algebra(T_a) % 112.23/112.02 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 112.23/112.02 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 112.23/112.02 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_fold__inf__le__inf,axiom, % 112.23/112.02 ! [V_b_2,V_a_2,V_A_2,T_b] : % 112.23/112.02 ( class_Lattices_Osemilattice__inf(T_b) % 112.23/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.23/112.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_fold1__belowI,axiom, % 112.23/112.02 ! [V_a_2,V_A_2,T_b] : % 112.23/112.02 ( class_Lattices_Osemilattice__inf(T_b) % 112.23/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.02 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.23/112.02 => 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)) ) ) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_below__fold1__iff,axiom, % 112.23/112.02 ! [V_x_2,V_A_2,T_b] : % 112.23/112.02 ( class_Lattices_Osemilattice__inf(T_b) % 112.23/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.02 => ( 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))) % 112.23/112.02 <=> ! [B_x] : % 112.23/112.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.23/112.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_setsum__Un__Int,axiom, % 112.23/112.02 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 112.23/112.02 ( class_Groups_Ocomm__monoid__add(T_c) % 112.23/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.02 => 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)) ) ) ) ). % 112.23/112.02 % 112.23/112.02 fof(fact_setprod_Ounion__inter,axiom, % 112.23/112.02 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 112.23/112.02 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => 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)) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod__Un__Int,axiom, % 112.23/112.03 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => 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)) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_card__Un__Int,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => 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))) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_card_Ounion__inter,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_card__Diff__subset__Int,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( 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))) % 112.23/112.03 => 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))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_atMost__Int__atLeast,axiom, % 112.23/112.03 ! [V_na_2,T_b] : % 112.23/112.03 ( class_Orderings_Oorder(T_b) % 112.23/112.03 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_na_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_na_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_na_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_folding__one_Ounion__inter,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 112.23/112.03 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_folding__one_Ounion__disjoint,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] : % 112.23/112.03 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_sup__Sup__fold__sup,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Sup__fin__Sup,axiom, % 112.23/112.03 ! [V_A_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__Un__disjoint,axiom, % 112.23/112.03 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__Un,axiom, % 112.23/112.03 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Oab__group__add(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => 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))) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod__Un__disjoint,axiom, % 112.23/112.03 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod_Ounion__disjoint,axiom, % 112.23/112.03 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_card__Un__disjoint,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fold1__Un,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Groups_Oab__semigroup__mult(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Sup__fin_Ounion__inter,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Min_Ounion__inter,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Orderings_Olinorder(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Min_Ounion__disjoint,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Orderings_Olinorder(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Max_Ounion__inter,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Orderings_Olinorder(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Max_Ounion__disjoint,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Orderings_Olinorder(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Orderings_Olinorder(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Orderings_Olinorder(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Orderings_Olinorder(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Orderings_Olinorder(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_UnionI,axiom, % 112.23/112.03 ! [V_A_2,V_C_2,V_X_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) % 112.23/112.03 => 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))) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Sup__binary,axiom, % 112.23/112.03 ! [V_b_2,V_a_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Un__eq__Union,axiom, % 112.23/112.03 ! [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))))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Sup__UNIV,axiom, % 112.23/112.03 ! [T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_inf__nat__def,axiom, % 112.23/112.03 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Union__Pow__eq,axiom, % 112.23/112.03 ! [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 ). % 112.23/112.03 % 112.23/112.03 fof(fact_Union__disjoint,axiom, % 112.23/112.03 ! [V_A_2,V_C_2,T_b] : % 112.23/112.03 ( 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)) % 112.23/112.03 <=> ! [B_x] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Union__Int__subset,axiom, % 112.23/112.03 ! [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)))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Union__upper,axiom, % 112.23/112.03 ! [V_A_2,V_B_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 112.23/112.03 => 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))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Sup__le__iff,axiom, % 112.23/112.03 ! [V_b_2,V_A_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2)) % 112.23/112.03 <=> ! [B_x] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_less__Sup__iff,axiom, % 112.23/112.03 ! [V_S_2,V_a_2,T_b] : % 112.23/112.03 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 & class_Orderings_Olinorder(T_b) ) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2))) % 112.23/112.03 <=> ? [B_x] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 112.23/112.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Union__empty,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Union__mono,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( 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)) % 112.23/112.03 => 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))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Union__insert,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_subset__Pow__Union,axiom, % 112.23/112.03 ! [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)))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Union__UNIV,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Union__Un__distrib,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Sup__upper,axiom, % 112.23/112.03 ! [V_A_2,V_x_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.23/112.03 => 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))) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Sup__empty,axiom, % 112.23/112.03 ! [T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Sup__singleton,axiom, % 112.23/112.03 ! [V_a_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => 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 ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Sup__insert,axiom, % 112.23/112.03 ! [V_A_2,V_a_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_card_Ounion__inter__neutral,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( ( ? [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))) % 112.23/112.03 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 112.23/112.03 => 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)) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod__Un,axiom, % 112.23/112.03 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Fields_Ofield(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( ! [B_x] : % 112.23/112.03 ( 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))) % 112.23/112.03 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) ) % 112.23/112.03 => 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))) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod_Ounion__inter__neutral,axiom, % 112.23/112.03 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( ! [B_x] : % 112.23/112.03 ( 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))) % 112.23/112.03 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod__Un__one,axiom, % 112.23/112.03 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 112.23/112.03 => ( ! [B_x] : % 112.23/112.03 ( 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))) % 112.23/112.03 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__Un__zero,axiom, % 112.23/112.03 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 112.23/112.03 => ( ! [B_x] : % 112.23/112.03 ( 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))) % 112.23/112.03 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum_Ounion__inter__neutral,axiom, % 112.23/112.03 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( ! [B_x] : % 112.23/112.03 ( 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))) % 112.23/112.03 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_finite__Union,axiom, % 112.23/112.03 ! [V_A_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) % 112.23/112.03 => ( ! [B_M] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2)) % 112.23/112.03 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) ) % 112.23/112.03 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Oremove,axiom, % 112.23/112.03 ! [V_x_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.23/112.03 => ( ( hAPP(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)) % 112.23/112.03 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 ) % 112.23/112.03 & ( hAPP(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)) % 112.23/112.03 => 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)))))) ) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Osingleton,axiom, % 112.23/112.03 ! [V_x_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => 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 ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_sup__Inf__absorb,axiom, % 112.23/112.03 ! [V_a_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.23/112.03 => 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 ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Oin__idem,axiom, % 112.23/112.03 ! [V_x_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.23/112.03 => 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) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_OF__eq,axiom, % 112.23/112.03 ! [V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Oinsert__idem,axiom, % 112.23/112.03 ! [V_x_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => 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)) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Osubset__idem,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 112.23/112.03 => 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) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Ounion__idem,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => 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)) ) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__le__Sup,axiom, % 112.23/112.03 ! [V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => 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))) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 112.23/112.03 ! [V_a_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Oinsert,axiom, % 112.23/112.03 ! [V_x_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Oinsert__remove,axiom, % 112.23/112.03 ! [V_x_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( ( hAPP(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)) % 112.23/112.03 => 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 ) % 112.23/112.03 & ( hAPP(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)) % 112.23/112.03 => 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)))))) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Ounion__inter,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 112.23/112.03 ! [V_x_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.23/112.03 => 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) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Oclosed,axiom, % 112.23/112.03 ! [V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => ( ! [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)))))) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_insert__partition,axiom, % 112.23/112.03 ! [V_F_2,V_x_2,T_b] : % 112.23/112.03 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)) % 112.23/112.03 => ( ! [B_x] : % 112.23/112.03 ( 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))) % 112.23/112.03 => ! [B_xa] : % 112.23/112.03 ( 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))) % 112.23/112.03 => ( B_x != B_xa % 112.23/112.03 => 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)) ) ) ) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fold__Un__disjoint,axiom, % 112.23/112.03 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => ( 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)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin_Ohom__commute,axiom, % 112.23/112.03 ! [V_N_2,V_h_2,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => ( ! [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)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 112.23/112.03 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fold__image__empty,axiom, % 112.23/112.03 ! [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 ). % 112.23/112.03 % 112.23/112.03 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 112.23/112.03 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 112.23/112.03 => 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) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_comm__monoid__big_OF__eq,axiom, % 112.23/112.03 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) % 112.23/112.03 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 112.23/112.03 => 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) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 112.23/112.03 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fold__image__insert,axiom, % 112.23/112.03 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Oab__semigroup__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.23/112.03 => 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)) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum_OF__eq,axiom, % 112.23/112.03 ! [V_g_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_c) % 112.23/112.03 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum_Oeq__fold,axiom, % 112.23/112.03 ! [V_g_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod_Oeq__fold,axiom, % 112.23/112.03 ! [V_g_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod_OF__eq,axiom, % 112.23/112.03 ! [V_g_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fold__image__Un__Int,axiom, % 112.23/112.03 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.23/112.03 => 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))) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fold__image__Un__one,axiom, % 112.23/112.03 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 112.23/112.03 => ( ! [B_x] : % 112.23/112.03 ( 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))) % 112.23/112.03 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_card__partition,axiom, % 112.23/112.03 ! [V_k_2,V_C_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) % 112.23/112.03 => ( ! [B_c] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2)) % 112.23/112.03 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 ) % 112.23/112.03 => ( ! [B_c1] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2)) % 112.23/112.03 => ! [B_c2] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2)) % 112.23/112.03 => ( B_c1 != B_c2 % 112.23/112.03 => 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)) ) ) ) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fold__inf,axiom, % 112.23/112.03 ! [V_A_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 112.23/112.03 => ( ! [B_x] : % 112.23/112.03 ( 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))) % 112.23/112.03 => hAPP(V_g_2,B_x) = V_z_2 ) % 112.23/112.03 => 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)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_finite__Inter,axiom, % 112.23/112.03 ! [V_M_2,T_b] : % 112.23/112.03 ( ? [B_x] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) % 112.23/112.03 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) ) % 112.23/112.03 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_InterE,axiom, % 112.23/112.03 ! [V_X_2,V_C_2,V_A_2,T_b] : % 112.23/112.03 ( 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))) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_InterD,axiom, % 112.23/112.03 ! [V_X_2,V_C_2,V_A_2,T_b] : % 112.23/112.03 ( 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))) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_le__Inf__iff,axiom, % 112.23/112.03 ! [V_A_2,V_b_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))) % 112.23/112.03 <=> ! [B_x] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__less__iff,axiom, % 112.23/112.03 ! [V_a_2,V_S_2,T_b] : % 112.23/112.03 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 & class_Orderings_Olinorder(T_b) ) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2)) % 112.23/112.03 <=> ? [B_x] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 112.23/112.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inter__lower,axiom, % 112.23/112.03 ! [V_A_2,V_B_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inter__anti__mono,axiom, % 112.23/112.03 ! [V_A_2,V_B_2,T_b] : % 112.23/112.03 ( 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)) % 112.23/112.03 => 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))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inter__empty,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inter__insert,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inter__UNIV,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__lower,axiom, % 112.23/112.03 ! [V_A_2,V_x_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inter__Un__distrib,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__singleton,axiom, % 112.23/112.03 ! [V_a_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => 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 ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__empty,axiom, % 112.23/112.03 ! [T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__UNIV,axiom, % 112.23/112.03 ! [T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__insert,axiom, % 112.23/112.03 ! [V_A_2,V_a_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Int__eq__Inter,axiom, % 112.23/112.03 ! [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))))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inter__Un__subset,axiom, % 112.23/112.03 ! [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)))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__binary,axiom, % 112.23/112.03 ! [V_b_2,V_a_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_inf__Inf__fold__inf,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inf__fin__Inf,axiom, % 112.23/112.03 ! [V_A_2,T_b] : % 112.23/112.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fold__image__1,axiom, % 112.23/112.03 ! [V_f_2,V_S_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.23/112.03 => ( ! [B_x] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 112.23/112.03 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) ) % 112.23/112.03 => 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) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fold__image__cong,axiom, % 112.23/112.03 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Oab__semigroup__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( ! [B_x] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.23/112.03 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 112.23/112.03 => 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) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_inf__le__fold__inf,axiom, % 112.23/112.03 ! [V_c_2,V_b_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Osemilattice__inf(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( ! [B_x] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2))) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fold__sup__le__sup,axiom, % 112.23/112.03 ! [V_c_2,V_b_2,V_A_2,T_b] : % 112.23/112.03 ( class_Lattices_Osemilattice__sup(T_b) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => ( ! [B_x] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2))) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Inter__subset,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( ! [B_X] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) ) % 112.23/112.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_InterI,axiom, % 112.23/112.03 ! [V_A_2,V_C_2,T_b] : % 112.23/112.03 ( ! [B_X] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) ) % 112.23/112.03 => 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))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__ivl__cong,axiom, % 112.23/112.03 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] : % 112.23/112.03 ( ( class_Groups_Ocomm__monoid__add(T_c) % 112.23/112.03 & class_Orderings_Oord(T_b) ) % 112.23/112.03 => ( V_a_2 = V_c_2 % 112.23/112.03 => ( V_b_2 = V_d_2 % 112.23/112.03 => ( ! [B_x] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x)) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2)) % 112.23/112.03 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 112.23/112.03 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_UnionE,axiom, % 112.23/112.03 ! [V_C_2,V_A_2,T_b] : % 112.23/112.03 ( 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))) % 112.23/112.03 => ~ ! [B_X] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) % 112.23/112.03 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_field__le__epsilon,axiom, % 112.23/112.03 ! [V_y,V_x,T_a] : % 112.23/112.03 ( class_Fields_Olinordered__field(T_a) % 112.23/112.03 => ( ! [B_e] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 112.23/112.03 => 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))) ) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_subtract__code__numeral__def,axiom, % 112.23/112.03 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 112.23/112.03 % 112.23/112.03 fof(fact_minus__code__numeral__code,axiom, % 112.23/112.03 ! [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) ). % 112.23/112.03 % 112.23/112.03 fof(fact_pair__box_Osize_I1_J,axiom, % 112.23/112.03 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_pair__box_Oinject,axiom, % 112.23/112.03 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] : % 112.23/112.03 ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2) % 112.23/112.03 <=> ( V_a_2 = V_a_H_2 % 112.23/112.03 & V_b_2 = V_b_H_2 ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_pair__box_Osize_I2_J,axiom, % 112.23/112.03 ! [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) ). % 112.23/112.03 % 112.23/112.03 fof(fact_pair__box_Orecs,axiom, % 112.23/112.03 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 112.23/112.03 % 112.23/112.03 fof(fact_pair__box_Osimps_I2_J,axiom, % 112.23/112.03 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 112.23/112.03 % 112.23/112.03 fof(fact_arith__series__int,axiom, % 112.23/112.03 ! [V_na_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_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__abs,axiom, % 112.23/112.03 ! [V_A_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 112.23/112.03 => 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))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__abs__ge__zero,axiom, % 112.23/112.03 ! [V_A_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 112.23/112.03 => 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))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fold__image__def,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_card__eq__setsum,axiom, % 112.23/112.03 ! [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) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 112.23/112.03 ! [V_na_2,V_m_2,V_f_2,T_b] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 => 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_na_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_na_2)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 112.23/112.03 ! [V_A_2,V_f_2,T_b] : % 112.23/112.03 ( ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 & class_Groups_Ocomm__monoid__mult(T_b) ) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_inf__fun__def,axiom, % 112.23/112.03 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_inf__Int__eq,axiom, % 112.23/112.03 ! [V_x_2,V_S_2,V_R_2,T_b] : % 112.23/112.03 ( 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)) % 112.23/112.03 <=> 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))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 112.23/112.03 ! [V_na_2,V_m_2,V_f_2,T_b] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 => 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_na_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_na_2)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod_Odistrib,axiom, % 112.23/112.03 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_less__eq__Suc__le__raw,axiom, % 112.23/112.03 ! [V_na_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_pred__equals__eq,axiom, % 112.23/112.03 ! [V_S_2,V_R_2,T_b] : % 112.23/112.03 ( 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) % 112.23/112.03 <=> V_R_2 = V_S_2 ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_bot__empty__eq,axiom, % 112.23/112.03 ! [V_x_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) % 112.23/112.03 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_pred__subset__eq,axiom, % 112.23/112.03 ! [V_S_2,V_R_2,T_b] : % 112.23/112.03 ( 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))) % 112.23/112.03 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__addf,axiom, % 112.23/112.03 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__subtractf,axiom, % 112.23/112.03 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Groups_Oab__group__add(T_b) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fun__diff__def,axiom, % 112.23/112.03 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] : % 112.23/112.03 ( class_Groups_Ominus(T_b) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_bot__fun__def,axiom, % 112.23/112.03 ! [V_x_2,T_c,T_b] : % 112.23/112.03 ( class_Orderings_Obot(T_b) % 112.23/112.03 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_int__setprod,axiom, % 112.23/112.03 ! [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) ). % 112.23/112.03 % 112.23/112.03 fof(fact_abs__setprod,axiom, % 112.23/112.03 ! [V_A_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Fields_Olinordered__field(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fun__Compl__def,axiom, % 112.23/112.03 ! [V_x_2,V_A_2,T_c,T_b] : % 112.23/112.03 ( class_Groups_Ouminus(T_b) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod__timesf,axiom, % 112.23/112.03 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_b) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 112.23/112.03 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 112.23/112.03 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 112.23/112.03 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 112.23/112.03 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fun__upd__def,axiom, % 112.23/112.03 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] : % 112.23/112.03 ( ( V_x_2 = V_a_2 % 112.23/112.03 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 ) % 112.23/112.03 & ( V_x_2 != V_a_2 % 112.23/112.03 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod__1,axiom, % 112.23/112.03 ! [V_A_2,T_c,T_b] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_of__int__setprod,axiom, % 112.23/112.03 ! [V_A_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 112.23/112.03 & class_Rings_Oring__1(T_b) ) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_of__int__setsum,axiom, % 112.23/112.03 ! [V_A_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Rings_Oring__1(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__0,axiom, % 112.23/112.03 ! [V_A_2,T_c,T_b] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__divide__distrib,axiom, % 112.23/112.03 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Fields_Ofield(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_abs__setsum__abs,axiom, % 112.23/112.03 ! [V_A_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__product,axiom, % 112.23/112.03 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Rings_Osemiring__0(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__left__distrib,axiom, % 112.23/112.03 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Rings_Osemiring__0(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__right__distrib,axiom, % 112.23/112.03 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] : % 112.23/112.03 ( class_Rings_Osemiring__0(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__commute,axiom, % 112.23/112.03 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__negf,axiom, % 112.23/112.03 ! [V_A_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Groups_Oab__group__add(T_b) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_int__setsum,axiom, % 112.23/112.03 ! [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) ). % 112.23/112.03 % 112.23/112.03 fof(fact_image__image,axiom, % 112.23/112.03 ! [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) ). % 112.23/112.03 % 112.23/112.03 fof(fact_image__ident,axiom, % 112.23/112.03 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 112.23/112.03 % 112.23/112.03 fof(fact_finite__range__imageI,axiom, % 112.23/112.03 ! [V_f_2,T_d,V_g_2,T_c,T_b] : % 112.23/112.03 ( 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))))) % 112.23/112.03 => 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))))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum_Odistrib,axiom, % 112.23/112.03 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_image__constant__conv,axiom, % 112.23/112.03 ! [V_c_2,T_c,T_b,V_A_2] : % 112.23/112.03 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 112.23/112.03 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.23/112.03 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_range__composition,axiom, % 112.23/112.03 ! [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)))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_sup__fun__def,axiom, % 112.23/112.03 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Lattices_Olattice(T_b) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_sup__Un__eq,axiom, % 112.23/112.03 ! [V_x_2,V_S_2,V_R_2,T_b] : % 112.23/112.03 ( 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)) % 112.23/112.03 <=> 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))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_of__nat__setsum,axiom, % 112.23/112.03 ! [V_A_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( class_Rings_Osemiring__1(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod__dividef,axiom, % 112.23/112.03 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Fields_Ofield__inverse__zero(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_nat__number__of__Bit0,axiom, % 112.23/112.03 ! [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))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 112.23/112.03 ! [V_na_2,V_k_2,V_m_2,V_f_2,T_b] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 => 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_na_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_na_2)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 112.23/112.03 ! [V_na_2,V_k_2,V_m_2,V_f_2,T_b] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 => 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_na_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_na_2)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_of__nat__setprod,axiom, % 112.23/112.03 ! [V_A_2,V_f_2,T_c,T_b] : % 112.23/112.03 ( ( class_Groups_Ocomm__monoid__mult(T_b) % 112.23/112.03 & class_Rings_Osemiring__1(T_b) ) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_image__add__atLeastLessThan,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_image__add__atLeastAtMost,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__delta,axiom, % 112.23/112.03 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.23/112.03 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 112.23/112.03 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 112.23/112.03 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__delta_H,axiom, % 112.23/112.03 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.23/112.03 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 112.23/112.03 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 112.23/112.03 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_image__constant,axiom, % 112.23/112.03 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.23/112.03 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod__delta_H,axiom, % 112.23/112.03 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.23/112.03 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 112.23/112.03 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 112.23/112.03 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod__delta,axiom, % 112.23/112.03 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.23/112.03 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 112.23/112.03 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 112.23/112.03 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__constant,axiom, % 112.23/112.03 ! [V_A_2,V_y_2,T_c,T_b] : % 112.23/112.03 ( class_Rings_Osemiring__1(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_power__number__of__even,axiom, % 112.23/112.03 ! [V_w_2,V_z_2,T_b] : % 112.23/112.03 ( class_Int_Onumber__ring(T_b) % 112.23/112.03 => 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))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fold__image__distrib,axiom, % 112.23/112.03 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_dual__max,axiom, % 112.23/112.03 ! [T_b] : % 112.23/112.03 ( class_Orderings_Olinorder(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_dual__min,axiom, % 112.23/112.03 ! [T_b] : % 112.23/112.03 ( class_Orderings_Olinorder(T_b) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod__constant,axiom, % 112.23/112.03 ! [V_y_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_zpower__number__of__even,axiom, % 112.23/112.03 ! [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))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__lessThan__Suc,axiom, % 112.23/112.03 ! [V_na_2,V_f_2,T_b] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 => 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_na_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_na_2))),hAPP(V_f_2,V_na_2)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__atMost__Suc,axiom, % 112.23/112.03 ! [V_na_2,V_f_2,T_b] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 => 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_na_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_na_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_na_2))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 112.23/112.03 ! [V_A_2,V_f_2,T_b] : % 112.23/112.03 ( ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 & class_Groups_Ocomm__monoid__mult(T_b) ) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_image__add__int__atLeastLessThan,axiom, % 112.23/112.03 ! [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) ). % 112.23/112.03 % 112.23/112.03 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 112.23/112.03 ! [V_f_2,V_A_2,T_b] : % 112.23/112.03 ( ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 & class_Groups_Ocomm__monoid__mult(T_b) ) % 112.23/112.03 => ( c_Nat__Transfer_Onat__set(V_A_2) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Powp__Pow__eq,axiom, % 112.23/112.03 ! [V_x_2,V_A_2,T_b] : % 112.23/112.03 ( 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)) % 112.23/112.03 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__restrict__set,axiom, % 112.23/112.03 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_image__eq__fold__image,axiom, % 112.23/112.03 ! [V_f_2,T_c,V_A_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_power__number__of__even__number__of,axiom, % 112.23/112.03 ! [V_w_2,V_v_2,T_b] : % 112.23/112.03 ( class_Int_Onumber__ring(T_b) % 112.23/112.03 => 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))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_card__def,axiom, % 112.23/112.03 ! [V_A_2,T_b] : % 112.23/112.03 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_card_Oeq__fold__g,axiom, % 112.23/112.03 ! [V_A_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_fun__left__comm__idem__remove,axiom, % 112.23/112.03 ! [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))))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_diff__nat__eq__if,axiom, % 112.23/112.03 ! [V_z_2,V_z_H_2] : % 112.23/112.03 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 112.23/112.03 => 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) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 112.23/112.03 ! [V_f_2,V_A_2,T_b] : % 112.23/112.03 ( ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 & class_Groups_Ocomm__monoid__mult(T_b) ) % 112.23/112.03 => ( c_Nat__Transfer_Onat__set(V_A_2) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__head,axiom, % 112.23/112.03 ! [V_Pa_2,V_na_2,V_m_2,T_b] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__add(T_b) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 112.23/112.03 => 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_na_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_na_2))) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_minus__fold__remove,axiom, % 112.23/112.03 ! [V_B_2,V_A_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.23/112.03 => 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) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_eq__number__of__Suc,axiom, % 112.23/112.03 ! [V_na_2,V_v_2] : % 112.23/112.03 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_na_2) % 112.23/112.03 <=> 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_na_2))))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Suc__eq__number__of,axiom, % 112.23/112.03 ! [V_v_2,V_na_2] : % 112.23/112.03 ( hAPP(c_Nat_OSuc,V_na_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 112.23/112.03 <=> 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_na_2))))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_nat__number__of__Bit1,axiom, % 112.23/112.03 ! [V_w_2] : % 112.23/112.03 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 112.23/112.03 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 112.23/112.03 => 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)))) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_geometric__sum,axiom, % 112.23/112.03 ! [V_na_2,V_x_2,T_b] : % 112.23/112.03 ( class_Fields_Ofield(T_b) % 112.23/112.03 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b) % 112.23/112.03 => 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_na_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_na_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))) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_gauss__sum,axiom, % 112.23/112.03 ! [V_na_2,T_b] : % 112.23/112.03 ( class_Rings_Ocomm__semiring__1(T_b) % 112.23/112.03 => 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_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),c_Groups_Oone__class_Oone(T_b))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setsum__natinterval__difff,axiom, % 112.23/112.03 ! [V_f_2,V_na_2,V_m_2,T_b] : % 112.23/112.03 ( class_Groups_Oab__group__add(T_b) % 112.23/112.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 112.23/112.03 => 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_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 112.23/112.03 => 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_na_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_less__number__of__Suc,axiom, % 112.23/112.03 ! [V_na_2,V_v_2] : % 112.23/112.03 ( 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_na_2))) % 112.23/112.03 <=> 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_na_2)))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_less__Suc__number__of,axiom, % 112.23/112.03 ! [V_v_2,V_na_2] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 112.23/112.03 <=> 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_na_2)),c_Int_Onat))))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_le__Suc__number__of,axiom, % 112.23/112.03 ! [V_v_2,V_na_2] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) % 112.23/112.03 <=> 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_na_2)),c_Int_Onat))))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_le__number__of__Suc,axiom, % 112.23/112.03 ! [V_na_2,V_v_2] : % 112.23/112.03 ( 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_na_2))) % 112.23/112.03 <=> 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_na_2)))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_max__Suc__number__of,axiom, % 112.23/112.03 ! [V_na_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_na_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_na_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_na_2)))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_max__number__of__Suc,axiom, % 112.23/112.03 ! [V_v_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_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_na_2)),c_Int_Onat)))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_power__number__of__odd,axiom, % 112.23/112.03 ! [V_z_2,V_w_2,T_b] : % 112.23/112.03 ( class_Int_Onumber__ring(T_b) % 112.23/112.03 => ( ( 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))) % 112.23/112.03 => 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))) ) % 112.23/112.03 & ( ~ 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))) % 112.23/112.03 => 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) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_setprod__gen__delta,axiom, % 112.23/112.03 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] : % 112.23/112.03 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.23/112.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.23/112.03 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 112.23/112.03 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) % 112.23/112.03 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 112.23/112.03 ! [V_x_2,V_y_2,V_c_2] : % 112.23/112.03 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 112.23/112.03 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 112.23/112.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 112.23/112.03 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 112.23/112.03 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_zpower__number__of__odd,axiom, % 112.23/112.03 ! [V_z_2,V_w_2] : % 112.23/112.03 ( ( 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))) % 112.23/112.03 => 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))) ) % 112.23/112.03 & ( ~ 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))) % 112.23/112.03 => 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) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_arith__series__general,axiom, % 112.23/112.03 ! [V_na_2,V_d_2,V_a_2,T_b] : % 112.23/112.03 ( class_Rings_Ocomm__semiring__1(T_b) % 112.23/112.03 => 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_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_min__number__of__Suc,axiom, % 112.23/112.03 ! [V_v_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2)),c_Int_Onat)))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_min__Suc__number__of,axiom, % 112.23/112.03 ! [V_na_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_na_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_na_2)))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_arith__series__nat,axiom, % 112.23/112.03 ! [V_na_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_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_power__number__of__odd__number__of,axiom, % 112.23/112.03 ! [V_v_2,V_w_2,T_b] : % 112.23/112.03 ( class_Int_Onumber__ring(T_b) % 112.23/112.03 => ( ( 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))) % 112.23/112.03 => 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))) ) % 112.23/112.03 & ( ~ 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))) % 112.23/112.03 => 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) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_diff__nat__number__of,axiom, % 112.23/112.03 ! [V_v_2,V_v_H_2] : % 112.23/112.03 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 112.23/112.03 => 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) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_nat__case__add__eq__if,axiom, % 112.23/112.03 ! [V_na_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_na_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_na_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_na_2)))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_nat__case__number__of,axiom, % 112.23/112.03 ! [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))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_nat__rec__add__eq__if,axiom, % 112.23/112.03 ! [V_na_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_na_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_na_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_na_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_na_2))))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 112.23/112.03 ! [V_na_2,T_b] : % 112.23/112.03 ( class_Rings_Osemiring__1(T_b) % 112.23/112.03 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_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_na_2,c_Groups_Ozero__class_Ozero(T_b)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_nat__rec__0,axiom, % 112.23/112.03 ! [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 ). % 112.23/112.03 % 112.23/112.03 fof(fact_nat__rec__Suc,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_nat__case__0,axiom, % 112.23/112.03 ! [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 ). % 112.23/112.03 % 112.23/112.03 fof(fact_nat__case__Suc,axiom, % 112.23/112.03 ! [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) ). % 112.23/112.03 % 112.23/112.03 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 112.23/112.03 ! [V_i_2,V_inc_2,T_b] : % 112.23/112.03 ( class_Rings_Osemiring__1(T_b) % 112.23/112.03 => 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 ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 112.23/112.03 ! [V_i_2,V_na_2,V_inc_2,T_b] : % 112.23/112.03 ( class_Rings_Osemiring__1(T_b) % 112.23/112.03 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_na_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_na_2,hAPP(V_inc_2,V_i_2)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_max__Suc1,axiom, % 112.23/112.03 ! [V_m_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2) ). % 112.23/112.03 % 112.23/112.03 fof(fact_max__Suc2,axiom, % 112.23/112.03 ! [V_na_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2) ). % 112.23/112.03 % 112.23/112.03 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 112.23/112.03 ! [V_na_2,V_m_2] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_na_2)) % 112.23/112.03 <=> 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_na_2)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_diff__Suc,axiom, % 112.23/112.03 ! [V_na_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_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_na_2)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_min__Suc2,axiom, % 112.23/112.03 ! [V_na_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2) ). % 112.23/112.03 % 112.23/112.03 fof(fact_min__Suc1,axiom, % 112.23/112.03 ! [V_m_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2) ). % 112.23/112.03 % 112.23/112.03 fof(fact_nat__rec__number__of,axiom, % 112.23/112.03 ! [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)))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 112.23/112.03 ! [V_f_2,V_A_2,T_b] : % 112.23/112.03 ( ! [B_x] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.23/112.03 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 112.23/112.03 ! [V_f_2,V_A_2,T_b] : % 112.23/112.03 ( ! [B_x] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.23/112.03 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_of__int__num,axiom, % 112.23/112.03 ! [V_k_2,T_b] : % 112.23/112.03 ( class_Rings_Oring__1(T_b) % 112.23/112.03 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.23/112.03 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) ) % 112.23/112.03 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.23/112.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.23/112.03 => 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))) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.23/112.03 => 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))))) ) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_adjust__eq,axiom, % 112.23/112.03 ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_divmod__int__mod__div,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_sup__Un__eq2,axiom, % 112.23/112.03 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 112.23/112.03 ( 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)) % 112.23/112.03 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_pred__subset__eq2,axiom, % 112.23/112.03 ! [V_S_2,V_R_2,T_c,T_b] : % 112.23/112.03 ( 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))) % 112.23/112.03 <=> 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_bot__empty__eq2,axiom, % 112.23/112.03 ! [V_y_2,V_x_2,T_c,T_b] : % 112.23/112.03 ( 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)) % 112.23/112.03 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_pred__equals__eq2,axiom, % 112.23/112.03 ! [V_S_2,V_R_2,T_c,T_b] : % 112.23/112.03 ( 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) % 112.23/112.03 <=> V_R_2 = V_S_2 ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_inf__Int__eq2,axiom, % 112.23/112.03 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] : % 112.23/112.03 ( 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)) % 112.23/112.03 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_adjust__def,axiom, % 112.23/112.03 ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_Nitpick_OFrac__def,axiom, % 112.23/112.03 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)))) ). % 112.23/112.03 % 112.23/112.03 fof(fact_pair__imageI,axiom, % 112.23/112.03 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2)) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_norm__frac_Osimps,axiom, % 112.23/112.03 ! [V_a_2,V_b_2] : % 112.23/112.03 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.23/112.03 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) % 112.23/112.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.23/112.03 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.23/112.03 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 112.23/112.03 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 112.23/112.03 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.23/112.03 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 112.23/112.03 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 112.23/112.03 ! [V_w] : % 112.23/112.03 ( 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))) % 112.23/112.03 => ( ( 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)))) % 112.23/112.03 => 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))) ) % 112.23/112.03 & ( ~ 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)))) % 112.23/112.03 => 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)))) ) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_sup2E,axiom, % 112.23/112.03 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 112.23/112.03 ( 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)) % 112.23/112.03 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 112.23/112.03 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_sup2CI,axiom, % 112.23/112.03 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] : % 112.23/112.03 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 112.23/112.03 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 112.23/112.03 => 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)) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_inf2E,axiom, % 112.23/112.03 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 112.23/112.03 ( 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)) % 112.23/112.03 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 112.23/112.03 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_inf2I,axiom, % 112.23/112.03 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 112.23/112.03 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 112.23/112.03 => 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)) ) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_mem__splitI,axiom, % 112.23/112.03 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2))) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_splitI,axiom, % 112.23/112.03 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_prod__caseI,axiom, % 112.23/112.03 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] : % 112.23/112.03 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 112.23/112.03 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ). % 112.23/112.03 % 112.23/112.03 fof(fact_bot2E,axiom, % 112.23/112.03 ! [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)) ). % 112.23/112.03 % 112.23/112.03 fof(fact_splitD,axiom, % 112.26/112.03 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) % 112.26/112.03 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_splitD_H,axiom, % 112.26/112.03 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2)) % 112.26/112.03 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_sup2I1,axiom, % 112.26/112.03 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 112.26/112.03 => 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)) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_sup2I2,axiom, % 112.26/112.03 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 112.26/112.03 => 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)) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_less__by__empty,axiom, % 112.26/112.03 ! [V_B_2,T_b,V_A_2] : % 112.26/112.03 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) % 112.26/112.03 => 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)) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_rev__predicate2D,axiom, % 112.26/112.03 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 112.26/112.03 => ( 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)) % 112.26/112.03 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_predicate2D,axiom, % 112.26/112.03 ! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_c,T_b] : % 112.26/112.03 ( 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)) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 112.26/112.03 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_inf2D2,axiom, % 112.26/112.03 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 112.26/112.03 ( 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)) % 112.26/112.03 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_inf2D1,axiom, % 112.26/112.03 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] : % 112.26/112.03 ( 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)) % 112.26/112.03 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_Pair__inject,axiom, % 112.26/112.03 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 112.26/112.03 ( 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) % 112.26/112.03 => ~ ( V_a = V_a_H % 112.26/112.03 => V_b != V_b_H ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_Pair__eq,axiom, % 112.26/112.03 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.03 ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2) % 112.26/112.03 <=> ( V_a_2 = V_a_H_2 % 112.26/112.03 & V_b_2 = V_b_H_2 ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_split__paired__All,axiom, % 112.26/112.03 ! [T_c,T_b,V_Pa_2] : % 112.26/112.03 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 112.26/112.03 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_split__weak__cong,axiom, % 112.26/112.03 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] : % 112.26/112.03 ( V_p_2 = V_q_2 % 112.26/112.03 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_split__twice,axiom, % 112.26/112.03 ! [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) ). % 112.26/112.03 % 112.26/112.03 fof(fact_prod_Osimps_I2_J,axiom, % 112.26/112.03 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 112.26/112.03 % 112.26/112.03 fof(fact_split__conv,axiom, % 112.26/112.03 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ). % 112.26/112.03 % 112.26/112.03 fof(fact_negDivAlg__div__mod,axiom, % 112.26/112.03 ! [V_l,V_k] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 112.26/112.03 => 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)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_negDivAlg__minus1,axiom, % 112.26/112.03 ! [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))) ). % 112.26/112.03 % 112.26/112.03 fof(fact_split__eta,axiom, % 112.26/112.03 ! [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 ). % 112.26/112.03 % 112.26/112.03 fof(fact_negDivAlg_Osimps,axiom, % 112.26/112.03 ! [V_b,V_a] : % 112.26/112.03 ( ( ( 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))) % 112.26/112.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 112.26/112.03 => 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)) ) % 112.26/112.03 & ( ~ ( 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))) % 112.26/112.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 112.26/112.03 => 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))) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_negDivAlg__eqn,axiom, % 112.26/112.03 ! [V_a,V_b] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.03 => ( ( 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))) % 112.26/112.03 => 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)) ) % 112.26/112.03 & ( ~ 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))) % 112.26/112.03 => 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))) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_negDivAlg__eqn__number__of,axiom, % 112.26/112.03 ! [V_w,V_v] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( ( 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)))) % 112.26/112.03 => 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))) ) % 112.26/112.03 & ( ~ 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)))) % 112.26/112.03 => 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)))) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_in__rel__def,axiom, % 112.26/112.03 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2)) % 112.26/112.03 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_div__mod__code__numeral__def,axiom, % 112.26/112.03 ! [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)) ). % 112.26/112.03 % 112.26/112.03 fof(fact_Nitpick_Orefl_H__def,axiom, % 112.26/112.03 ! [V_r_2,T_b] : % 112.26/112.03 ( c_Nitpick_Orefl_H(T_b,V_r_2) % 112.26/112.03 <=> ! [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)) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 112.26/112.03 ! [V_w] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( ( 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))) % 112.26/112.03 => 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)) ) % 112.26/112.03 & ( ~ 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))) % 112.26/112.03 => 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)))) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_posDivAlg__0,axiom, % 112.26/112.03 ! [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)) ). % 112.26/112.03 % 112.26/112.03 fof(fact_posDivAlg__div__mod,axiom, % 112.26/112.03 ! [V_l,V_k] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 112.26/112.03 => 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)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_posDivAlg__eqn,axiom, % 112.26/112.03 ! [V_a,V_b] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 112.26/112.03 => 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) ) % 112.26/112.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 112.26/112.03 => 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))) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_posDivAlg__eqn__number__of,axiom, % 112.26/112.03 ! [V_w,V_v] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( ( 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))) % 112.26/112.03 => 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)) ) % 112.26/112.03 & ( ~ 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))) % 112.26/112.03 => 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)))) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_posDivAlg_Osimps,axiom, % 112.26/112.03 ! [V_b,V_a] : % 112.26/112.03 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 112.26/112.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 112.26/112.03 => 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) ) % 112.26/112.03 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 112.26/112.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 112.26/112.03 => 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))) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__int__def,axiom, % 112.26/112.03 ! [V_b,V_a] : % 112.26/112.03 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.26/112.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.03 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 112.26/112.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.03 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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)) ) % 112.26/112.03 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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))) ) ) ) ) ) % 112.26/112.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.26/112.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.03 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 112.26/112.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.03 => 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))) ) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__nat__step,axiom, % 112.26/112.03 ! [V_m,V_n] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 112.26/112.03 => 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)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__int__pdivmod,axiom, % 112.26/112.03 ! [V_l_2,V_k_2] : % 112.26/112.03 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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)) ) % 112.26/112.03 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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) ) % 112.26/112.03 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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)))) ) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__int__code,axiom, % 112.26/112.03 ! [V_l_2,V_k_2] : % 112.26/112.03 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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)) ) % 112.26/112.03 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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) ) % 112.26/112.03 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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)))) ) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_negateSnd__def,axiom, % 112.26/112.03 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 112.26/112.03 % 112.26/112.03 fof(fact_apsnd__conv,axiom, % 112.26/112.03 ! [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)) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__nat__zero,axiom, % 112.26/112.03 ! [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) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__nat__base,axiom, % 112.26/112.03 ! [V_n,V_m] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 112.26/112.03 => 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) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_negateSnd__eq,axiom, % 112.26/112.03 ! [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)) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__nat__div__mod,axiom, % 112.26/112.03 ! [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)) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__nat__if,axiom, % 112.26/112.03 ! [V_m_2,V_na_2] : % 112.26/112.03 ( ( ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) % 112.26/112.03 => c_Divides_Odivmod__nat(V_m_2,V_na_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) ) % 112.26/112.03 & ( ~ ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) % 112.26/112.03 => c_Divides_Odivmod__nat(V_m_2,V_na_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_na_2),V_na_2)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_pdivmod__def,axiom, % 112.26/112.03 ! [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))) ). % 112.26/112.03 % 112.26/112.03 fof(fact_pdivmod__posDivAlg,axiom, % 112.26/112.03 ! [V_k,V_l] : % 112.26/112.03 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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)) ) % 112.26/112.03 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 112.26/112.03 ! [V_c,V_r,V_q,V_b,V_a] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 112.26/112.03 => 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)))) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 112.26/112.03 ! [V_a,V_r,V_q,V_c,V_b] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 112.26/112.03 => 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)))) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_negDivAlg_Opsimps,axiom, % 112.26/112.03 ! [V_b_2,V_a_2] : % 112.26/112.03 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 112.26/112.03 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) % 112.26/112.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 112.26/112.03 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) ) % 112.26/112.03 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) % 112.26/112.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 112.26/112.03 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_zmult2__lemma,axiom, % 112.26/112.03 ! [V_c,V_r,V_q,V_b,V_a] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 112.26/112.03 => 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)))) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__nat__rel__unique,axiom, % 112.26/112.03 ! [V_qr_H,V_qr,V_n,V_m] : % 112.26/112.03 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 112.26/112.03 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 112.26/112.03 => V_qr = V_qr_H ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__nat__eq,axiom, % 112.26/112.03 ! [V_qr,V_n,V_m] : % 112.26/112.03 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 112.26/112.03 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 112.26/112.03 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 112.26/112.03 % 112.26/112.03 fof(fact_unique__remainder,axiom, % 112.26/112.03 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( 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))) % 112.26/112.03 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => V_r = V_r_H ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_unique__quotient,axiom, % 112.26/112.03 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( 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))) % 112.26/112.03 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => V_q = V_q_H ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_self__remainder,axiom, % 112.26/112.03 ! [V_r,V_q,V_a] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__int__rel__0,axiom, % 112.26/112.03 ! [V_b] : % 112.26/112.03 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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)))) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__int__rel__neg,axiom, % 112.26/112.03 ! [V_qr,V_b,V_a] : % 112.26/112.03 ( 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)) % 112.26/112.03 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__int__correct,axiom, % 112.26/112.03 ! [V_a,V_b] : % 112.26/112.03 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_mod__eq,axiom, % 112.26/112.03 ! [V_r,V_q,V_n,V_m] : % 112.26/112.03 ( 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))) % 112.26/112.03 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_div__eq,axiom, % 112.26/112.03 ! [V_r,V_q,V_n,V_m] : % 112.26/112.03 ( 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))) % 112.26/112.03 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_self__quotient,axiom, % 112.26/112.03 ! [V_r,V_q,V_a] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__int__rel__mod,axiom, % 112.26/112.03 ! [V_r,V_q,V_b,V_a] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__int__rel__div,axiom, % 112.26/112.03 ! [V_r,V_q,V_b,V_a] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_negDivAlg__correct,axiom, % 112.26/112.03 ! [V_b,V_a] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.03 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__nat__rel,axiom, % 112.26/112.03 ! [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)))) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__int__rel__div__mod,axiom, % 112.26/112.03 ! [V_a,V_b] : % 112.26/112.03 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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)))) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_posDivAlg__correct,axiom, % 112.26/112.03 ! [V_b,V_a] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.03 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_zadd1__lemma,axiom, % 112.26/112.03 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( 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))) % 112.26/112.03 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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)))) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_zminus1__lemma,axiom, % 112.26/112.03 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 112.26/112.03 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2))) % 112.26/112.03 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__int__relI,axiom, % 112.26/112.03 ! [V_r,V_q,V_b,V_a] : % 112.26/112.03 ( 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) % 112.26/112.03 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 112.26/112.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 112.26/112.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 112.26/112.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 112.26/112.03 => 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))) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_zmult1__lemma,axiom, % 112.26/112.03 ! [V_a,V_r,V_q,V_c,V_b] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 => 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)))) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__int__rel__def,axiom, % 112.26/112.03 ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ). % 112.26/112.03 % 112.26/112.03 fof(fact_divmod__nat__rel__add1__eq,axiom, % 112.26/112.03 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( 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))) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 112.26/112.03 => 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)))) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_posDivAlg_Opsimps,axiom, % 112.26/112.03 ! [V_b_2,V_a_2] : % 112.26/112.03 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 112.26/112.03 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 112.26/112.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 112.26/112.03 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) ) % 112.26/112.03 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 112.26/112.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 112.26/112.03 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_norm__frac_Opsimps,axiom, % 112.26/112.03 ! [V_b_2,V_a_2] : % 112.26/112.03 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) % 112.26/112.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.26/112.03 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) % 112.26/112.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.26/112.03 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 112.26/112.03 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) % 112.26/112.03 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 112.26/112.03 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 112.26/112.03 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_negDivAlg_Opinduct,axiom, % 112.26/112.03 ! [V_Pa_2,V_a1_2,V_a0_2] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( ! [B_a,B_b] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( ( ~ ( 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))) % 112.26/112.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 112.26/112.03 => 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))) ) % 112.26/112.03 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 112.26/112.03 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_accp__subset,axiom, % 112.26/112.03 ! [V_R2_2,V_R1_2,T_b] : % 112.26/112.03 ( 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)) % 112.26/112.03 => 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))) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_accp__downward,axiom, % 112.26/112.03 ! [V_a_2,V_b_2,V_r_2,T_b] : % 112.26/112.03 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2)) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 112.26/112.03 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_accp_Oequations,axiom, % 112.26/112.03 ! [V_a_2,V_r_2,T_b] : % 112.26/112.03 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 112.26/112.03 <=> ! [B_x] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 112.26/112.03 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_accp_Osimps,axiom, % 112.26/112.03 ! [V_a_2,V_r_2,T_b] : % 112.26/112.03 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) % 112.26/112.03 <=> ! [B_x] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 112.26/112.03 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_posDivAlg_Opinduct,axiom, % 112.26/112.03 ! [V_Pa_2,V_a1_2,V_a0_2] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( ! [B_a,B_b] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 112.26/112.03 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 112.26/112.03 => 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))) ) % 112.26/112.03 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 112.26/112.03 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_nat__gcd_Opsimps,axiom, % 112.26/112.03 ! [V_y_2,V_x_2] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.03 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 112.26/112.03 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.03 => 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)) ) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_nat_Osize_I2_J,axiom, % 112.26/112.03 ! [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))) ). % 112.26/112.03 % 112.26/112.03 fof(fact_mod__pos__neg__1__number__of,axiom, % 112.26/112.03 ! [V_w] : % 112.26/112.03 ( 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))) % 112.26/112.03 => 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))))) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_snd__conv,axiom, % 112.26/112.03 ! [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 ). % 112.26/112.03 % 112.26/112.03 fof(fact_snd__eqD,axiom, % 112.26/112.03 ! [V_a,V_y,V_x,T_a,T_b] : % 112.26/112.03 ( 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 % 112.26/112.03 => V_y = V_a ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_apsnd__eq__conv,axiom, % 112.26/112.03 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] : % 112.26/112.03 ( 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) % 112.26/112.03 <=> 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)) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_snd__apsnd,axiom, % 112.26/112.03 ! [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)) ). % 112.26/112.03 % 112.26/112.03 fof(fact_snd__def,axiom, % 112.26/112.03 ! [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) ). % 112.26/112.03 % 112.26/112.03 fof(fact_mod__int__def,axiom, % 112.26/112.03 ! [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)) ). % 112.26/112.03 % 112.26/112.03 fof(fact_nat_Osize_I1_J,axiom, % 112.26/112.03 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 112.26/112.03 % 112.26/112.03 fof(fact_mod__neg__pos,axiom, % 112.26/112.03 ! [V_b,V_a] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.03 => 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)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_mod__pos__pos,axiom, % 112.26/112.03 ! [V_b,V_a] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.03 => 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)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_mod__pos__pos__1__number__of,axiom, % 112.26/112.03 ! [V_w] : % 112.26/112.03 ( 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))) % 112.26/112.03 => 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))) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_mod__pos__neg,axiom, % 112.26/112.03 ! [V_b,V_a] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.26/112.03 => 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)))) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_mod__neg__neg,axiom, % 112.26/112.03 ! [V_b,V_a] : % 112.26/112.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.26/112.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.26/112.03 => 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)))) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_in__measure,axiom, % 112.26/112.03 ! [V_f_2,V_y_2,V_x_2,T_b] : % 112.26/112.03 ( 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))) % 112.26/112.03 <=> 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))) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_norm__frac_Opinduct,axiom, % 112.26/112.03 ! [V_Pa_2,V_a1_2,V_a0_2] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( ! [B_a,B_b] : % 112.26/112.03 ( 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))) % 112.26/112.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.26/112.03 => 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))) ) % 112.26/112.03 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) % 112.26/112.03 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 112.26/112.03 % 112.26/112.03 fof(fact_div__pos__neg__1__number__of,axiom, % 112.26/112.03 ! [V_w] : % 112.26/112.03 ( 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))) % 112.26/112.04 => 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))))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_nat__gcd_Opinduct,axiom, % 112.26/112.04 ! [V_Pa_2,V_a1_2,V_a0_2] : % 112.26/112.04 ( 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))) % 112.26/112.04 => ( ! [B_x,B_y] : % 112.26/112.04 ( 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))) % 112.26/112.04 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.04 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 112.26/112.04 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) ) % 112.26/112.04 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_prod__eqI,axiom, % 112.26/112.04 ! [V_q,V_p,T_b,T_a] : % 112.26/112.04 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 112.26/112.04 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 112.26/112.04 => V_p = V_q ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Pair__fst__snd__eq,axiom, % 112.26/112.04 ! [T_c,T_b,V_t_2,V_s_2] : % 112.26/112.04 ( V_s_2 = V_t_2 % 112.26/112.04 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) % 112.26/112.04 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_fst__def,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_fst__apsnd,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_fst__eqD,axiom, % 112.26/112.04 ! [V_a,V_y,V_x,T_b,T_a] : % 112.26/112.04 ( 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 % 112.26/112.04 => V_x = V_a ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_fst__conv,axiom, % 112.26/112.04 ! [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 ). % 112.26/112.04 % 112.26/112.04 fof(fact_pair__collapse,axiom, % 112.26/112.04 ! [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 ). % 112.26/112.04 % 112.26/112.04 fof(fact_surjective__pairing,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_prod__case__beta,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_div__int__def,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_mod__nat__def,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_split__comp__eq,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_split__beta,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_split__def,axiom, % 112.26/112.04 ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_div__neg__pos,axiom, % 112.26/112.04 ! [V_b,V_a] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_div__pos__pos,axiom, % 112.26/112.04 ! [V_b,V_a] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_div__pos__pos__1__number__of,axiom, % 112.26/112.04 ! [V_w] : % 112.26/112.04 ( 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))) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_div__pos__neg,axiom, % 112.26/112.04 ! [V_b,V_a] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.26/112.04 => 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)))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_div__neg__neg,axiom, % 112.26/112.04 ! [V_b,V_a] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 112.26/112.04 => 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)))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_prod__size__simp,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_conjI__realizer,axiom, % 112.26/112.04 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_Pa_2] : % 112.26/112.04 ( hBOOL(hAPP(V_Pa_2,V_p_2)) % 112.26/112.04 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 112.26/112.04 => ( 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)))) % 112.26/112.04 & 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)))) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_exI__realizer,axiom, % 112.26/112.04 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2)) % 112.26/112.04 => 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)))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_div__nat__def,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_divmod__nat__rel__def,axiom, % 112.26/112.04 ! [V_qr_2,V_na_2,V_m_2] : % 112.26/112.04 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_na_2),V_qr_2)) % 112.26/112.04 <=> ( 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_na_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) % 112.26/112.04 & ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.04 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 112.26/112.04 & ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.04 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) % 112.26/112.04 => ( 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))) % 112.26/112.04 & 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_na_2)) ) ) % 112.26/112.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) % 112.26/112.04 & 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))) ) ) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_range,axiom, % 112.26/112.04 ! [V_s,V_k] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_mlex__leq,axiom, % 112.26/112.04 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 112.26/112.04 => ( 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)) % 112.26/112.04 => 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))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_mlex__less,axiom, % 112.26/112.04 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_nat_Osize_I4_J,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_prod_Orecs,axiom, % 112.26/112.04 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 112.26/112.04 % 112.26/112.04 fof(fact_in__lex__prod,axiom, % 112.26/112.04 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2))) % 112.26/112.04 <=> ( 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)) % 112.26/112.04 | ( V_a_2 = V_a_H_2 % 112.26/112.04 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_nat__size,axiom, % 112.26/112.04 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 112.26/112.04 % 112.26/112.04 fof(fact_nat_Osize_I3_J,axiom, % 112.26/112.04 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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_same__fstI,axiom, % 112.26/112.04 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] : % 112.26/112.04 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.04 => ( 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))) % 112.26/112.04 => 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))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_in__finite__psubset,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_b] : % 112.26/112.04 ( 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))) % 112.26/112.04 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.26/112.04 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_setsum__nonneg__0,axiom, % 112.26/112.04 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] : % 112.26/112.04 ( class_Groups_Oordered__ab__group__add(T_c) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 112.26/112.04 => ( ! [B_i] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 112.26/112.04 => ( 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) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 112.26/112.04 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_setsum__nonneg__leq__bound,axiom, % 112.26/112.04 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] : % 112.26/112.04 ( class_Groups_Oordered__ab__group__add(T_c) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 112.26/112.04 => ( ! [B_i] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) ) % 112.26/112.04 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2 % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_sum__diff__distrib,axiom, % 112.26/112.04 ! [V_na_2,V_Pa_2,V_Q_2] : % 112.26/112.04 ( ! [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))) % 112.26/112.04 => 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_na_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_na_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_na_2)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_apfst__apsnd,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_apfst__conv,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_apfst__eq__conv,axiom, % 112.26/112.04 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] : % 112.26/112.04 ( 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) % 112.26/112.04 <=> 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_fst__apfst,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_snd__apfst,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_apsnd__apfst__commute,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_apsnd__apfst,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_pair__lessI2,axiom, % 112.26/112.04 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INFI__fold__inf,axiom, % 112.26/112.04 ! [V_f_2,V_A_2,T_b,T_c] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => 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) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SUPR__fold__sup,axiom, % 112.26/112.04 ! [V_f_2,V_A_2,T_b,T_c] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => 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) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SUP1__I,axiom, % 112.26/112.04 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__I,axiom, % 112.26/112.04 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INF1__D,axiom, % 112.26/112.04 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INF1__E,axiom, % 112.26/112.04 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 112.26/112.04 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 112.26/112.04 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__D,axiom, % 112.26/112.04 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__E,axiom, % 112.26/112.04 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 112.26/112.04 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 112.26/112.04 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INF2__E,axiom, % 112.26/112.04 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 112.26/112.04 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 112.26/112.04 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INF2__D,axiom, % 112.26/112.04 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SUP2__I,axiom, % 112.26/112.04 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__INT,axiom, % 112.26/112.04 ! [V_A_2,T_c,V_I_2,T_b] : % 112.26/112.04 ( ? [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 112.26/112.04 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) ) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Int__UN__distrib2,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__extend__simps_I4_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Int__UN__distrib,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__extend__simps_I5_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__Int__distrib,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__simps_I4_J,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__simps_I5_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__simps_I4_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__simps_I7_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__simps_I6_J,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__Un__distrib,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__extend__simps_I7_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Un__INT__distrib,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__Un,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__extend__simps_I6_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Un__INT__distrib2,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UNION__empty__conv_I1_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b] : % 112.26/112.04 ( 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) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 112.26/112.04 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__empty2,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__constant,axiom, % 112.26/112.04 ! [V_c_2,T_c,T_b,V_A_2] : % 112.26/112.04 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) % 112.26/112.04 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UNION__empty__conv_I2_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_b,T_c] : % 112.26/112.04 ( 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)) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 112.26/112.04 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__Pow__subset,axiom, % 112.26/112.04 ! [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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__extend__simps_I4_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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 ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__subset__iff,axiom, % 112.26/112.04 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : % 112.26/112.04 ( 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))) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 112.26/112.04 => 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))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__subset__iff,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : % 112.26/112.04 ( 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)) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__simps_I10_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__simps_I10_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_image__UN,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__extend__simps_I10_J,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__extend__simps_I10_J,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Inter__def,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__simps_I8_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__simps_I8_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__extend__simps_I8_J,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__extend__simps_I8_J,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Union__def,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__simps_I7_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__simps_I6_J,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__extend__simps_I7_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__extend__simps_I6_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INF__commute,axiom, % 112.26/112.04 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SUP__commute,axiom, % 112.26/112.04 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INFI__apply,axiom, % 112.26/112.04 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SUPR__apply,axiom, % 112.26/112.04 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Compl__INT,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Compl__UN,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Pow__INT__eq,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__extend__simps_I5_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__simps_I5_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_b,T_c] : % 112.26/112.04 ( 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)) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 112.26/112.04 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b] : % 112.26/112.04 ( 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) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 112.26/112.04 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__UN,axiom, % 112.26/112.04 ! [V_B_2,T_c,V_A_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => ( 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))) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__iff,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__iff,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 112.26/112.04 <=> ? [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 112.26/112.04 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INF__INT__eq2,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 112.26/112.04 ( 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)) % 112.26/112.04 <=> 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SUP__UN__eq2,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] : % 112.26/112.04 ( 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)) % 112.26/112.04 <=> 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SUP__le__iff,axiom, % 112.26/112.04 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.04 => ( 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)) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_le__INF__iff,axiom, % 112.26/112.04 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.04 => ( 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))) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_less__SUP__iff,axiom, % 112.26/112.04 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] : % 112.26/112.04 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.04 & class_Orderings_Olinorder(T_b) ) % 112.26/112.04 => ( 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))) % 112.26/112.04 <=> ? [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 112.26/112.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INF__less__iff,axiom, % 112.26/112.04 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] : % 112.26/112.04 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.04 & class_Orderings_Olinorder(T_b) ) % 112.26/112.04 => ( 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)) % 112.26/112.04 <=> ? [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 112.26/112.04 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__insert__distrib,axiom, % 112.26/112.04 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__lower,axiom, % 112.26/112.04 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INF__INT__eq,axiom, % 112.26/112.04 ! [V_x_2,V_r_2,T_c,T_b] : % 112.26/112.04 ( 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)) % 112.26/112.04 <=> 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__absorb,axiom, % 112.26/112.04 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 112.26/112.04 => 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) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SUP__const,axiom, % 112.26/112.04 ! [V_M_2,T_b,V_A_2,T_c] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 112.26/112.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INF__const,axiom, % 112.26/112.04 ! [V_M_2,T_b,V_A_2,T_c] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 112.26/112.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__insert__distrib,axiom, % 112.26/112.04 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__empty,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__constant,axiom, % 112.26/112.04 ! [V_c_2,T_c,T_b,V_A_2] : % 112.26/112.04 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 112.26/112.04 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__extend__simps_I1_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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 ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__extend__simps_I2_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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 ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__upper,axiom, % 112.26/112.04 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SUP__UN__eq,axiom, % 112.26/112.04 ! [V_x_2,V_r_2,T_c,T_b] : % 112.26/112.04 ( 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)) % 112.26/112.04 <=> 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__absorb,axiom, % 112.26/112.04 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) % 112.26/112.04 => 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) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__insert,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__simps_I1_J,axiom, % 112.26/112.04 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__singleton,axiom, % 112.26/112.04 ! [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 ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__extend__simps_I1_J,axiom, % 112.26/112.04 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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))) ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__Un,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__simps_I3_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__simps_I2_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__extend__simps_I3_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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 ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__extend__simps_I2_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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 ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__insert,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_image__Union,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Int__Union,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Int__Union2,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Un__Inter,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Union__image__eq,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UNION__eq__Union__image,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INTER__eq__Inter__image,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Inter__image__eq,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__lessThan__UNIV,axiom, % 112.26/112.04 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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__atMost__UNIV,axiom, % 112.26/112.04 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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__atLeast__UNIV,axiom, % 112.26/112.04 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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INF__subset,axiom, % 112.26/112.04 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.26/112.04 => 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))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SUP__subset,axiom, % 112.26/112.04 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.26/112.04 => 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))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__simps_I2_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__simps_I1_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__simps_I3_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__extend__simps_I3_J,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] : % 112.26/112.04 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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) ) % 112.26/112.04 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_image__eq__UN,axiom, % 112.26/112.04 ! [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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__UN__finite__eq,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INF__leI,axiom, % 112.26/112.04 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 112.26/112.04 => 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))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_le__SUPI,axiom, % 112.26/112.04 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 112.26/112.04 => 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))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Un__Union__image,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Int__Inter__image,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__le__add__shift,axiom, % 112.26/112.04 ! [V_k_2,V_M_2,V_na_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_na_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_na_2),V_k_2))),V_M_2) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__greaterThan__UNIV,axiom, % 112.26/112.04 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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_pair__lessI1,axiom, % 112.26/112.04 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_sup__SUPR__fold__sup,axiom, % 112.26/112.04 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => 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) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inf__INFI__fold__inf,axiom, % 112.26/112.04 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] : % 112.26/112.04 ( class_Complete__Lattice_Ocomplete__lattice(T_c) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => 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) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__le__eq__Un0,axiom, % 112.26/112.04 ! [V_M_2,V_na_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_na_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_na_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_pair__leqI2,axiom, % 112.26/112.04 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_smin__insertI,axiom, % 112.26/112.04 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 112.26/112.04 => ( 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)) % 112.26/112.04 => ( 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)) % 112.26/112.04 => 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)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_smax__insertI,axiom, % 112.26/112.04 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 112.26/112.04 => ( 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)) % 112.26/112.04 => ( 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)) % 112.26/112.04 => 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)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__extend__simps_I9_J,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__extend__simps_I9_J,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INT__simps_I9_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__simps_I9_J,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__UN__flatten,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INF1__iff,axiom, % 112.26/112.04 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SUP1__iff,axiom, % 112.26/112.04 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 112.26/112.04 <=> ? [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.04 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_INF2__iff,axiom, % 112.26/112.04 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SUP2__iff,axiom, % 112.26/112.04 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 112.26/112.04 <=> ? [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.04 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_ball__UN,axiom, % 112.26/112.04 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] : % 112.26/112.04 ( ! [B_x] : % 112.26/112.04 ( 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))) % 112.26/112.04 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 112.26/112.04 => ! [B_xa] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) % 112.26/112.04 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_smin__emptyI,axiom, % 112.26/112.04 ! [V_X_2] : % 112.26/112.04 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_smax__emptyI,axiom, % 112.26/112.04 ! [V_Y_2] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 112.26/112.04 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_pair__leqI1,axiom, % 112.26/112.04 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_wmax__insertI,axiom, % 112.26/112.04 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 112.26/112.04 => ( 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)) % 112.26/112.04 => ( 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)) % 112.26/112.04 => 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)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_wmin__insertI,axiom, % 112.26/112.04 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 112.26/112.04 => ( 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)) % 112.26/112.04 => ( 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)) % 112.26/112.04 => 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)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_nat__def,axiom, % 112.26/112.04 ! [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)))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Rep__Integ__inject,axiom, % 112.26/112.04 ! [V_y_2,V_x_2] : % 112.26/112.04 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 112.26/112.04 <=> V_x_2 = V_y_2 ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_wmax__emptyI,axiom, % 112.26/112.04 ! [V_X_2] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_wmin__emptyI,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_min__weak__def,axiom, % 112.26/112.04 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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_max__weak__def,axiom, % 112.26/112.04 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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__finite2__subset,axiom, % 112.26/112.04 ! [V_B_2,V_k_2,V_A_2,T_b] : % 112.26/112.04 ( ! [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))) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_max__strict__def,axiom, % 112.26/112.04 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 112.26/112.04 % 112.26/112.04 fof(fact_max__ext__additive,axiom, % 112.26/112.04 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] : % 112.26/112.04 ( 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))) % 112.26/112.04 => ( 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))) % 112.26/112.04 => 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))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_min__strict__def,axiom, % 112.26/112.04 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 112.26/112.04 % 112.26/112.04 fof(fact_max__extp__max__ext__eq,axiom, % 112.26/112.04 ! [V_xa_2,V_x_2,V_R_2,T_b] : % 112.26/112.04 ( 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) % 112.26/112.04 <=> 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__finite2__eq,axiom, % 112.26/112.04 ! [V_B_2,V_k_2,V_A_2,T_b] : % 112.26/112.04 ( ! [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) % 112.26/112.04 => 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) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__finite__subset,axiom, % 112.26/112.04 ! [V_C_2,V_A_2,T_b] : % 112.26/112.04 ( ! [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)) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_min__rpair__set,axiom, % 112.26/112.04 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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_max__rpair__set,axiom, % 112.26/112.04 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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_less__than__iff,axiom, % 112.26/112.04 ! [V_y_2,V_x_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than)) % 112.26/112.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_pair__less__def,axiom, % 112.26/112.04 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 112.26/112.04 % 112.26/112.04 fof(fact_mlex__prod__def,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_intrel__iff,axiom, % 112.26/112.04 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 112.26/112.04 ( 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)) % 112.26/112.04 <=> 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) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_rp__inv__image__rp,axiom, % 112.26/112.04 ! [V_f_2,T_c,V_Pa_2,T_b] : % 112.26/112.04 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 112.26/112.04 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_rp__inv__image__def,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_in__inv__image,axiom, % 112.26/112.04 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] : % 112.26/112.04 ( 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))) % 112.26/112.04 <=> 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_equiv__intrel__iff,axiom, % 112.26/112.04 ! [V_y_2,V_x_2] : % 112.26/112.04 ( 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)))) % 112.26/112.04 <=> 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 112.26/112.04 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 112.26/112.04 ( ( class_Groups_Ocomm__monoid__add(T_b) % 112.26/112.04 & class_Groups_Ocomm__monoid__mult(T_b) ) % 112.26/112.04 => ( V_A_2 = V_B_2 % 112.26/112.04 => ( c_Nat__Transfer_Onat__set(V_B_2) % 112.26/112.04 => ( ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 112.26/112.04 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 112.26/112.04 => 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) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Image__UN,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Image__mono,axiom, % 112.26/112.04 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] : % 112.26/112.04 ( 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)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 112.26/112.04 => 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))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Image__Int__subset,axiom, % 112.26/112.04 ! [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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Image__INT__subset,axiom, % 112.26/112.04 ! [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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Un__Image,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Image__Un,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Image__empty,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Image__iff,axiom, % 112.26/112.04 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 112.26/112.04 <=> ? [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 112.26/112.04 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_rev__ImageI,axiom, % 112.26/112.04 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Image__eq__UN,axiom, % 112.26/112.04 ! [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))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Image__singleton__iff,axiom, % 112.26/112.04 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 112.26/112.04 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_measure__def,axiom, % 112.26/112.04 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ). % 112.26/112.04 % 112.26/112.04 fof(fact_of__int,axiom, % 112.26/112.04 ! [V_j_2,V_i_2,T_b] : % 112.26/112.04 ( class_Rings_Oring__1(T_b) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_One__int__def,axiom, % 112.26/112.04 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))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_mult,axiom, % 112.26/112.04 ! [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))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Rep__Integ__inverse,axiom, % 112.26/112.04 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 112.26/112.04 % 112.26/112.04 fof(fact_minus,axiom, % 112.26/112.04 ! [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))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Zero__int__def,axiom, % 112.26/112.04 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))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_int__def,axiom, % 112.26/112.04 ! [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))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_add,axiom, % 112.26/112.04 ! [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))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_nat,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_minus__int__def,axiom, % 112.26/112.04 ! [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))))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_less,axiom, % 112.26/112.04 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 112.26/112.04 ( 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))))))) % 112.26/112.04 <=> 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_le,axiom, % 112.26/112.04 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 112.26/112.04 ( 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))))))) % 112.26/112.04 <=> 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_irrefl__def,axiom, % 112.26/112.04 ! [V_r_2,T_b] : % 112.26/112.04 ( c_Relation_Oirrefl(T_b,V_r_2) % 112.26/112.04 <=> ! [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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_eq__Abs__Integ,axiom, % 112.26/112.04 ! [V_z_2] : % 112.26/112.04 ~ ! [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))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Field__insert,axiom, % 112.26/112.04 ! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Field__Union,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Field__empty,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_mono__Field,axiom, % 112.26/112.04 ! [V_s_2,V_r_2,T_b] : % 112.26/112.04 ( 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)) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Field__Un,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__Field,axiom, % 112.26/112.04 ! [V_r_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 112.26/112.04 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Id__on__def,axiom, % 112.26/112.04 ! [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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_quotient__def,axiom, % 112.26/112.04 ! [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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_ImageE,axiom, % 112.26/112.04 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) % 112.26/112.04 => ~ ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) % 112.26/112.04 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_quotient__empty,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_quotient__is__empty2,axiom, % 112.26/112.04 ! [V_r_2,V_A_2,T_b] : % 112.26/112.04 ( 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) % 112.26/112.04 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_quotient__is__empty,axiom, % 112.26/112.04 ! [V_r_2,V_A_2,T_b] : % 112.26/112.04 ( 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)) % 112.26/112.04 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Id__on__def_H,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Id__on__empty,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Image__Id__on,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_quotientI,axiom, % 112.26/112.04 ! [V_r_2,V_A_2,V_x_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Id__on__iff,axiom, % 112.26/112.04 ! [V_A_2,V_y_2,V_x_2,T_b] : % 112.26/112.04 ( 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))) % 112.26/112.04 <=> ( V_x_2 = V_y_2 % 112.26/112.04 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Id__on__eqI,axiom, % 112.26/112.04 ! [V_A_2,T_b,V_b_2,V_a_2] : % 112.26/112.04 ( V_a_2 = V_b_2 % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_singleton__quotient,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_equiv__class__nondisjoint,axiom, % 112.26/112.04 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_subset__equiv__class,axiom, % 112.26/112.04 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_quotientE,axiom, % 112.26/112.04 ! [V_r_2,V_A_2,V_X_2,T_b] : % 112.26/112.04 ( 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))) % 112.26/112.04 => ~ ! [B_x] : % 112.26/112.04 ( 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)))) % 112.26/112.04 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_equiv__intrel,axiom, % 112.26/112.04 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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Union__quotient,axiom, % 112.26/112.04 ! [V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => 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 ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_equiv__class__self,axiom, % 112.26/112.04 ! [V_a_2,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => 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)))))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_quotient__disj,axiom, % 112.26/112.04 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( 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))) % 112.26/112.04 => ( 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))) % 112.26/112.04 => ( V_X_2 = V_Y_2 % 112.26/112.04 | 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)) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_equiv__class__eq,axiom, % 112.26/112.04 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 112.26/112.04 => hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_quotient__eqI,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( 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))) % 112.26/112.04 => ( 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))) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 112.26/112.04 => ( 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)) % 112.26/112.04 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_quotient__eq__iff,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( 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))) % 112.26/112.04 => ( 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))) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) % 112.26/112.04 => ( V_X_2 = V_Y_2 % 112.26/112.04 <=> 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)) ) ) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_eq__equiv__class,axiom, % 112.26/112.04 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] : % 112.26/112.04 ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 112.26/112.04 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_eq__equiv__class__iff,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 112.26/112.04 => ( 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)))) % 112.26/112.04 <=> 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)) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_equiv__class__eq__iff,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( 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)) % 112.26/112.04 <=> ( 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)))) % 112.26/112.04 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.04 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_equiv__class__subset,axiom, % 112.26/112.04 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_eq__equiv__class__iff2,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 112.26/112.04 => ( 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) % 112.26/112.04 <=> 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)) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__equiv__class2,axiom, % 112.26/112.04 ! [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] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 112.26/112.04 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 112.26/112.04 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2)) % 112.26/112.04 => 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) ) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__equiv__class,axiom, % 112.26/112.04 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => 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) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_equivp__equiv,axiom, % 112.26/112.04 ! [V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2) % 112.26/112.04 <=> 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_identity__equivp,axiom, % 112.26/112.04 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ). % 112.26/112.04 % 112.26/112.04 fof(fact_equivp__def,axiom, % 112.26/112.04 ! [V_R_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 112.26/112.04 <=> ! [B_x,B_y] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 112.26/112.04 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_equivp__reflp,axiom, % 112.26/112.04 ! [V_x_2,V_R_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 112.26/112.04 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_equivp__symp,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_R_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_equivp__transp,axiom, % 112.26/112.04 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_congruent2__implies__congruent,axiom, % 112.26/112.04 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2) % 112.26/112.04 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_congruent2D,axiom, % 112.26/112.04 ! [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] : % 112.26/112.04 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) % 112.26/112.04 => ( 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)) % 112.26/112.04 => ( 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)) % 112.26/112.04 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_congruentD,axiom, % 112.26/112.04 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 112.26/112.04 => ( 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)) % 112.26/112.04 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_congruent2__implies__congruent__UN,axiom, % 112.26/112.04 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 112.26/112.04 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 112.26/112.04 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2)) % 112.26/112.04 => 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)) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__equiv__class__inject,axiom, % 112.26/112.04 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 112.26/112.04 => ( 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) % 112.26/112.04 => ( 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))) % 112.26/112.04 => ( 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))) % 112.26/112.04 => ( ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.04 => ! [B_y] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) % 112.26/112.04 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 112.26/112.04 => 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)) ) ) ) % 112.26/112.04 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__equiv__class__type2,axiom, % 112.26/112.04 ! [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] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) % 112.26/112.04 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) % 112.26/112.04 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 112.26/112.04 => ( 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))) % 112.26/112.04 => ( 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))) % 112.26/112.04 => ( ! [B_x1] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2)) % 112.26/112.04 => ! [B_x2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 112.26/112.04 => 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)) ) ) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__equiv__class__type,axiom, % 112.26/112.04 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) % 112.26/112.04 => ( 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))) % 112.26/112.04 => ( ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 112.26/112.04 => 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)) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Integ__def,axiom, % 112.26/112.04 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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Id__onE,axiom, % 112.26/112.04 ! [V_A_2,V_c_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2))) % 112.26/112.04 => ~ ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.04 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_card__quotient__disjoint,axiom, % 112.26/112.04 ! [V_r_2,V_A_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => ( 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) % 112.26/112.04 => 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) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__empty,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__uminus,axiom, % 112.26/112.04 ! [V_A_2,T_b] : % 112.26/112.04 ( class_Groups_Oordered__ab__group__add(T_b) % 112.26/112.04 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__onD,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 112.26/112.04 => V_x_2 = V_y_2 ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__iff,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 112.26/112.04 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 112.26/112.04 <=> V_x_2 = V_y_2 ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__contraD,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => ( V_x_2 != V_y_2 % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 112.26/112.04 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__id2,axiom, % 112.26/112.04 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__def,axiom, % 112.26/112.04 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.04 => ! [B_xa] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 112.26/112.04 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 112.26/112.04 => B_x = B_xa ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__diff,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__Int,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_subset__inj__on,axiom, % 112.26/112.04 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.26/112.04 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__eq,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 112.26/112.04 <=> V_x_2 = V_y_2 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_injD,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 112.26/112.04 => V_x_2 = V_y_2 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__fun,axiom, % 112.26/112.04 ! [T_d,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__imageD,axiom, % 112.26/112.04 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 112.26/112.04 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) % 112.26/112.04 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__image__eq__iff,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => ( 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) % 112.26/112.04 <=> V_A_2 = V_B_2 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__Un__image__eq__iff,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( 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)) % 112.26/112.04 => ( 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) % 112.26/112.04 <=> V_A_2 = V_B_2 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_card__image,axiom, % 112.26/112.04 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => 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) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__strict__subset,axiom, % 112.26/112.04 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.26/112.04 => 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))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_range__ex1__eq,axiom, % 112.26/112.04 ! [V_b_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 112.26/112.04 <=> ? [B_x] : % 112.26/112.04 ( V_b_2 = hAPP(V_f_2,B_x) % 112.26/112.04 & ! [B_y] : % 112.26/112.04 ( V_b_2 = hAPP(V_f_2,B_y) % 112.26/112.04 => B_y = B_x ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__image__mem__iff,axiom, % 112.26/112.04 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => ( 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))) % 112.26/112.04 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__iff__surj,axiom, % 112.26/112.04 ! [V_A_H_2,T_c,T_b,V_A_2] : % 112.26/112.04 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => ( ? [B_f] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 112.26/112.04 & 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)) ) % 112.26/112.04 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__surj__inj,axiom, % 112.26/112.04 ! [V_f_2,V_A_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => ( 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))) % 112.26/112.04 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_endo__inj__surj,axiom, % 112.26/112.04 ! [V_f_2,V_A_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => ( 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)) % 112.26/112.04 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) % 112.26/112.04 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__UNIV__inj__surj,axiom, % 112.26/112.04 ! [V_f_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 112.26/112.04 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__UNIV__surj__inj,axiom, % 112.26/112.04 ! [V_f_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 112.26/112.04 => ( 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)) % 112.26/112.04 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__image__subset__iff,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => ( 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))) % 112.26/112.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__image__Int,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 112.26/112.04 => 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)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_image__Int,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__iff__eq__card,axiom, % 112.26/112.04 ! [V_f_2,T_c,V_A_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 <=> 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) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_eq__card__imp__inj__on,axiom, % 112.26/112.04 ! [V_f_2,T_c,V_A_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => ( 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) % 112.26/112.04 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__image__set__diff,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) % 112.26/112.04 => 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)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_image__set__diff,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_pigeonhole,axiom, % 112.26/112.04 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( 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))) % 112.26/112.04 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__fun__updI,axiom, % 112.26/112.04 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 112.26/112.04 => c_Fun_Oinj__on(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_A_2) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__singleton,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Rep__Integ,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_card__bij__eq,axiom, % 112.26/112.04 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => ( 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)) % 112.26/112.04 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) % 112.26/112.04 => ( 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)) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 112.26/112.04 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__image__Compl__subset,axiom, % 112.26/112.04 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => 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)))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__insert,axiom, % 112.26/112.04 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) % 112.26/112.04 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 & ~ 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))))))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__Un,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( 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)) % 112.26/112.04 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 112.26/112.04 & 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__iff__card__le,axiom, % 112.26/112.04 ! [V_B_2,T_c,V_A_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 112.26/112.04 => ( ? [B_f] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) % 112.26/112.04 & 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)) ) % 112.26/112.04 <=> 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))) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_card__inj__on__le,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => ( 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)) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 112.26/112.04 => 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))) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_quotient__diff1,axiom, % 112.26/112.04 ! [V_a_2,V_A_2,V_r_2,T_b] : % 112.26/112.04 ( 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) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_image__INT,axiom, % 112.26/112.04 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) % 112.26/112.04 => ( ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) % 112.26/112.04 => 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)) ) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2)) % 112.26/112.04 => 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)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_type__definition__Integ,axiom, % 112.26/112.04 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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_the__inv__into__into,axiom, % 112.26/112.04 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.26/112.04 => 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)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__add__nat,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__Suc,axiom, % 112.26/112.04 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__of__nat,axiom, % 112.26/112.04 ! [T_b] : % 112.26/112.04 ( class_Nat_Osemiring__char__0(T_b) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__int,axiom, % 112.26/112.04 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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_swap__inj__on,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_the__inv__into__f__eq,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.04 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_the__inv__into__f__f,axiom, % 112.26/112.04 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.04 => 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 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_the__inv__f__f,axiom, % 112.26/112.04 ! [V_x_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => 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 ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_the__inv__into__onto,axiom, % 112.26/112.04 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => 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 ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__the__inv__into,axiom, % 112.26/112.04 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_f__the__inv__into__f,axiom, % 112.26/112.04 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 112.26/112.04 => 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 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_type__definition_OAbs__image,axiom, % 112.26/112.04 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 112.26/112.04 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_type__definition_ORep__range,axiom, % 112.26/112.04 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 112.26/112.04 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 112.26/112.04 => 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 ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_type__definition_ORep,axiom, % 112.26/112.04 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 112.26/112.04 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_type__definition_ORep__inject,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 112.26/112.04 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 112.26/112.04 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 112.26/112.04 <=> V_x_2 = V_y_2 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_type__definition_ORep__inverse,axiom, % 112.26/112.04 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 112.26/112.04 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 112.26/112.04 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_type__definition_OAbs__inject,axiom, % 112.26/112.04 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 112.26/112.04 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 112.26/112.04 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 112.26/112.04 <=> V_x_2 = V_y_2 ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_type__definition_OAbs__inverse,axiom, % 112.26/112.04 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] : % 112.26/112.04 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) % 112.26/112.04 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 112.26/112.04 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] : % 112.26/112.04 ( ( class_Groups_Ocomm__monoid__add(T_b) % 112.26/112.04 & class_Groups_Ocomm__monoid__mult(T_b) ) % 112.26/112.04 => ( V_A_2 = V_B_2 % 112.26/112.04 => ( c_Nat__Transfer_Onat__set(V_B_2) % 112.26/112.04 => ( ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 112.26/112.04 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 112.26/112.04 => 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) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_accp__acc__eq,axiom, % 112.26/112.04 ! [V_x_2,V_r_2,T_b] : % 112.26/112.04 ( 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)) % 112.26/112.04 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_max__extp_Oequations,axiom, % 112.26/112.04 ! [V_a2_2,V_a1_2,V_R_2,T_b] : % 112.26/112.04 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) % 112.26/112.04 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 112.26/112.04 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 112.26/112.04 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 & ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 112.26/112.04 => ? [B_xa] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 112.26/112.04 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_acc__subset,axiom, % 112.26/112.04 ! [V_R2_2,V_R1_2,T_b] : % 112.26/112.04 ( 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)) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_acc__downward,axiom, % 112.26/112.04 ! [V_a_2,V_r_2,V_b_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_acc_Osimps,axiom, % 112.26/112.04 ! [V_r_2,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 112.26/112.04 <=> ! [B_x] : % 112.26/112.04 ( 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)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_max__ext_Ointros,axiom, % 112.26/112.04 ! [V_R_2,V_Y_2,V_X_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) % 112.26/112.04 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => ( ! [B_x] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) % 112.26/112.04 => ? [B_xa] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) % 112.26/112.04 & 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)) ) ) % 112.26/112.04 => 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))) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Nitpick_Ozero__frac__def,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__Inter,axiom, % 112.26/112.04 ! [V_f_2,T_c,T_b,V_S_2] : % 112.26/112.04 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) % 112.26/112.04 => ( ! [B_A] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2)) % 112.26/112.04 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) ) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Nitpick_Oone__frac__def,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Nitpick_Ofrac__def,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_the__elem__def,axiom, % 112.26/112.04 ! [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))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Rep__Integ__induct,axiom, % 112.26/112.04 ! [V_Pa_2,V_y_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 112.26/112.04 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x))) % 112.26/112.04 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Rep__Integ__cases,axiom, % 112.26/112.04 ! [V_y_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 112.26/112.04 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_The__split__eq,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_split__paired__The,axiom, % 112.26/112.04 ! [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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_the__inv__into__def,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_fold__def,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_divmod__nat__def,axiom, % 112.26/112.04 ! [V_na_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_na_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_na_2)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_fold1__def,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_The__split,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_flat__lub__def,axiom, % 112.26/112.04 ! [V_b_2,V_A_2,T_b] : % 112.26/112.04 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 112.26/112.04 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 ) % 112.26/112.04 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) % 112.26/112.04 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__vimage__singleton,axiom, % 112.26/112.04 ! [V_a_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => 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))))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__on__INTER,axiom, % 112.26/112.04 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] : % 112.26/112.04 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => ( ! [B_i] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2)) % 112.26/112.04 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) ) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimageI,axiom, % 112.26/112.04 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] : % 112.26/112.04 ( hAPP(V_f_2,V_a_2) = V_b_2 % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__UNIV,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__mono,axiom, % 112.26/112.04 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__Int,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__Compl,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__code,axiom, % 112.26/112.04 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2)) % 112.26/112.04 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__ident,axiom, % 112.26/112.04 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__INT,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__Un,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__empty,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__UN,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimageI2,axiom, % 112.26/112.04 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimageD,axiom, % 112.26/112.04 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2))) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__eq,axiom, % 112.26/112.04 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) % 112.26/112.04 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__Diff,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_image__vimage__subset,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_surj__image__vimage__eq,axiom, % 112.26/112.04 ! [V_A_2,V_f_2,T_b,T_c] : % 112.26/112.04 ( 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)) % 112.26/112.04 => 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 ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__Union,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__singleton__eq,axiom, % 112.26/112.04 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) % 112.26/112.04 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__insert,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__vimageD,axiom, % 112.26/112.04 ! [V_F_2,V_h_2,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) % 112.26/112.04 => ( 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)) % 112.26/112.04 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__subsetD,axiom, % 112.26/112.04 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] : % 112.26/112.04 ( 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)) % 112.26/112.04 => ( 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)) % 112.26/112.04 => 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))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_image__vimage__eq,axiom, % 112.26/112.04 ! [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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__vimageI,axiom, % 112.26/112.04 ! [V_h_2,T_c,V_F_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) % 112.26/112.04 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.04 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_inj__vimage__image__eq,axiom, % 112.26/112.04 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => 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 ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__const,axiom, % 112.26/112.04 ! [T_c,V_A_2,V_c_2,T_b] : % 112.26/112.04 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 112.26/112.04 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 112.26/112.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 112.26/112.04 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__eq__UN,axiom, % 112.26/112.04 ! [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))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__subsetI,axiom, % 112.26/112.04 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 112.26/112.04 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.04 => ( 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))) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__if,axiom, % 112.26/112.04 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] : % 112.26/112.04 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 112.26/112.04 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 112.26/112.04 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) % 112.26/112.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 112.26/112.04 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 112.26/112.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) % 112.26/112.04 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 112.26/112.04 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) ) % 112.26/112.04 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) % 112.26/112.04 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_image__split__eq__Sigma,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_card__less__Suc,axiom, % 112.26/112.04 ! [V_i_2,V_M_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 112.26/112.04 => 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))))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_card__less,axiom, % 112.26/112.04 ! [V_i_2,V_M_2] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 112.26/112.04 => 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) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_CollectI,axiom, % 112.26/112.04 ! [T_b,V_a_2,V_Pa_2] : % 112.26/112.04 ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__Collect__conjI,axiom, % 112.26/112.04 ! [V_Q_2,V_Pa_2,T_b] : % 112.26/112.04 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 112.26/112.04 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) % 112.26/112.04 => 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)))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__Collect__less__nat,axiom, % 112.26/112.04 ! [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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__Collect__le__nat,axiom, % 112.26/112.04 ! [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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SigmaI,axiom, % 112.26/112.04 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__Collect__eq,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Sigma__Diff__distrib1,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Times__Diff__distrib1,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Sigma__Diff__distrib2,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Collect__mem__eq,axiom, % 112.26/112.04 ! [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 ). % 112.26/112.04 % 112.26/112.04 fof(fact_mem__Collect__eq,axiom, % 112.26/112.04 ! [V_Pa_2,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 112.26/112.04 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Times__eq__cancel2,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 112.26/112.04 => ( 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)) % 112.26/112.04 <=> V_A_2 = V_B_2 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_CollectD,axiom, % 112.26/112.04 ! [V_Pa_2,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 112.26/112.04 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_CollectE,axiom, % 112.26/112.04 ! [V_Pa_2,V_a_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 112.26/112.04 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_insert__Collect,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Collect__split,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SetCompr__Sigma__eq,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_empty__def,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Collect__empty__eq,axiom, % 112.26/112.04 ! [V_Pa_2,T_b] : % 112.26/112.04 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_empty__Collect__eq,axiom, % 112.26/112.04 ! [V_Pa_2,T_b] : % 112.26/112.04 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2) % 112.26/112.04 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Collect__disj__eq,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Collect__conj__eq,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Collect__neg__eq,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Collect__def,axiom, % 112.26/112.04 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__Collect__disjI,axiom, % 112.26/112.04 ! [V_Q_2,V_Pa_2,T_b] : % 112.26/112.04 ( 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)))) % 112.26/112.04 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 112.26/112.04 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Sigma__Union,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UNIV__def,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Sigma__empty1,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_card__cartesian__product,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_setsum__cartesian__product,axiom, % 112.26/112.04 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 112.26/112.04 ( class_Groups_Ocomm__monoid__add(T_b) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Times__empty,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b] : % 112.26/112.04 ( 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)) % 112.26/112.04 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Sigma__empty2,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Compl__Times__UNIV2,axiom, % 112.26/112.04 ! [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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Compl__Times__UNIV1,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_setprod__cartesian__product,axiom, % 112.26/112.04 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] : % 112.26/112.04 ( class_Groups_Ocomm__monoid__mult(T_b) % 112.26/112.04 => 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))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_insert__compr__raw,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_insert__compr,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Un__def,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Int__Collect,axiom, % 112.26/112.04 ! [V_Pa_2,V_A_2,V_x_2,T_b] : % 112.26/112.04 ( 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)))) % 112.26/112.04 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.04 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Int__def,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Sigma__Un__distrib1,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Times__Un__distrib1,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Sigma__Un__distrib2,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_singleton__conv2,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_singleton__conv,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Collect__conv__if2,axiom, % 112.26/112.04 ! [T_b,V_a_2,V_Pa_2] : % 112.26/112.04 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 112.26/112.04 => 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))) ) % 112.26/112.04 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Collect__conv__if,axiom, % 112.26/112.04 ! [T_b,V_a_2,V_Pa_2] : % 112.26/112.04 ( ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 112.26/112.04 => 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))) ) % 112.26/112.04 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_set__diff__eq,axiom, % 112.26/112.04 ! [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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__Collect__not,axiom, % 112.26/112.04 ! [V_Pa_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 112.26/112.04 => ( 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)))) % 112.26/112.04 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_insert__def,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_swap__product,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__cartesian__product,axiom, % 112.26/112.04 ! [V_B_2,T_c,V_A_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 112.26/112.04 => 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)))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Compl__eq,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_vimage__def,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_equiv__type,axiom, % 112.26/112.04 ! [V_r_2,V_A_2,T_b] : % 112.26/112.04 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.04 => 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)))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Sigma__Int__distrib1,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Times__Int__distrib1,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Sigma__Int__distrib2,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Collect__imp__eq,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Id__on__subset__Times,axiom, % 112.26/112.04 ! [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)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__M__bounded__by__nat,axiom, % 112.26/112.04 ! [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))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UNIV__Times__UNIV,axiom, % 112.26/112.04 ! [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)) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SigmaE2,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 112.26/112.04 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SigmaD2,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_SigmaD1,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 112.26/112.04 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_mem__Sigma__iff,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 112.26/112.04 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.04 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_card__cartesian__product__singleton,axiom, % 112.26/112.04 ! [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) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Times__subset__cancel2,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) % 112.26/112.04 => ( 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)))) % 112.26/112.04 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Image__subset,axiom, % 112.26/112.04 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 112.26/112.04 ( 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)))) % 112.26/112.04 => 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)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_setsum__setsum__restrict,axiom, % 112.26/112.04 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] : % 112.26/112.04 ( class_Groups_Ocomm__monoid__add(T_d) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 112.26/112.04 => 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) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__cartesian__productD2,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b] : % 112.26/112.04 ( 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)))) % 112.26/112.04 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__cartesian__productD1,axiom, % 112.26/112.04 ! [V_B_2,V_A_2,T_c,T_b] : % 112.26/112.04 ( 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)))) % 112.26/112.04 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 112.26/112.04 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_if__image__distrib,axiom, % 112.26/112.04 ! [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))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_fst__image__times,axiom, % 112.26/112.04 ! [V_A_2,T_c,T_b,V_B_2] : % 112.26/112.04 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) % 112.26/112.04 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_snd__image__times,axiom, % 112.26/112.04 ! [V_B_2,T_c,T_b,V_A_2] : % 112.26/112.04 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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)) ) % 112.26/112.04 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.04 => 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 ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_nat__seg__image__imp__finite,axiom, % 112.26/112.04 ! [V_na_2,V_f_2,T_b,V_A_2] : % 112.26/112.04 ( 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_na_2))) % 112.26/112.04 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_setsum__restrict__set_H,axiom, % 112.26/112.04 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] : % 112.26/112.04 ( class_Groups_Ocomm__monoid__add(T_c) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => 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) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_insert__times__insert,axiom, % 112.26/112.04 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_setsum__image__gen,axiom, % 112.26/112.04 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] : % 112.26/112.04 ( class_Groups_Ocomm__monoid__add(T_c) % 112.26/112.04 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.26/112.04 => 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)) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__equiv__class,axiom, % 112.26/112.04 ! [V_X_2,V_r_2,V_A_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => ( 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)))) % 112.26/112.04 => ( 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))) % 112.26/112.04 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ). % 112.26/112.04 % 112.26/112.04 fof(fact_UN__Times__distrib,axiom, % 112.26/112.04 ! [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))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_Sigma__def,axiom, % 112.26/112.04 ! [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))))) ). % 112.26/112.04 % 112.26/112.04 fof(fact_finite__quotient,axiom, % 112.26/112.04 ! [V_r_2,V_A_2,T_b] : % 112.26/112.04 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.04 => ( 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)))) % 112.26/112.04 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Image__singleton,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setsum__cases,axiom, % 112.26/112.05 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__add(T_c) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => 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))))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_card__less__Suc2,axiom, % 112.26/112.05 ! [V_i_2,V_M_2] : % 112.26/112.05 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 112.26/112.05 => 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))))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 112.26/112.05 ! [V_A_2,V_I_2,T_c,T_b] : % 112.26/112.05 ? [B_f] : % 112.26/112.05 ( 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)) % 112.26/112.05 & 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_fold__image__Sigma,axiom, % 112.26/112.05 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__mult(T_d) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setsum__multicount,axiom, % 112.26/112.05 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) % 112.26/112.05 => ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2)) % 112.26/112.05 => 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 ) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__Collect__subsets,axiom, % 112.26/112.05 ! [V_A_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Pow__def,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_inj__graph,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__psubset__def,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_inv__image__def,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nitpick_Oprod__def,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_int__ge__less__than2__def,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_int__ge__less__than__def,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setprod__Sigma,axiom, % 112.26/112.05 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__mult(T_d) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setsum__Sigma,axiom, % 112.26/112.05 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__add(T_d) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_card__SigmaI,axiom, % 112.26/112.05 ! [V_B_2,T_c,V_A_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) % 112.26/112.05 => 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) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,T_b] : % 112.26/112.05 ( class_Orderings_Olinorder(T_b) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.26/112.05 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => 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))))))) ) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,T_b] : % 112.26/112.05 ( class_Orderings_Olinorder(T_b) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.26/112.05 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => 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))))))) ) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 112.26/112.05 ! [V_x_2,V_A_2,T_b] : % 112.26/112.05 ( class_Orderings_Olinorder(T_b) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => 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))))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__Collect__bounded__ex,axiom, % 112.26/112.05 ! [V_Q_2,T_c,V_Pa_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 112.26/112.05 => ( 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))))) % 112.26/112.05 <=> ! [B_y] : % 112.26/112.05 ( hBOOL(hAPP(V_Pa_2,B_y)) % 112.26/112.05 => 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)))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__image__set,axiom, % 112.26/112.05 ! [V_f_2,T_c,V_Pa_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) % 112.26/112.05 => 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))))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Pow__Compl,axiom, % 112.26/112.05 ! [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))))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_add__Max__commute,axiom, % 112.26/112.05 ! [V_k_2,V_N_2,T_b] : % 112.26/112.05 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 112.26/112.05 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => 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))))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_add__Min__commute,axiom, % 112.26/112.05 ! [V_k_2,V_N_2,T_b] : % 112.26/112.05 ( class_Groups_Olinordered__ab__semigroup__add(T_b) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) % 112.26/112.05 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => 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))))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_sup__Inf2__distrib,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,T_b] : % 112.26/112.05 ( class_Lattices_Odistrib__lattice(T_b) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.26/112.05 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => 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))))))) ) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_sup__Inf1__distrib,axiom, % 112.26/112.05 ! [V_x_2,V_A_2,T_b] : % 112.26/112.05 ( class_Lattices_Odistrib__lattice(T_b) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => 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))))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_inf__Sup1__distrib,axiom, % 112.26/112.05 ! [V_x_2,V_A_2,T_b] : % 112.26/112.05 ( class_Lattices_Odistrib__lattice(T_b) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => 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))))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_inf__Sup2__distrib,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,T_b] : % 112.26/112.05 ( class_Lattices_Odistrib__lattice(T_b) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.26/112.05 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => 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))))))) ) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 112.26/112.05 ! [V_x_2,V_A_2,T_b] : % 112.26/112.05 ( class_Orderings_Olinorder(T_b) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 => 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))))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setsum__mult__setsum__if__inj,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : % 112.26/112.05 ( class_Rings_Osemiring__0(T_d) % 112.26/112.05 => ( 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))) % 112.26/112.05 => 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))))))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__SigmaI,axiom, % 112.26/112.05 ! [V_B_2,T_c,V_A_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( ! [B_a] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 112.26/112.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setsum__multicount__gen,axiom, % 112.26/112.05 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2)) % 112.26/112.05 => ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2)) % 112.26/112.05 => 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) ) % 112.26/112.05 => 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) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_inj__on__id,axiom, % 112.26/112.05 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ). % 112.26/112.05 % 112.26/112.05 fof(fact_id__apply,axiom, % 112.26/112.05 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 112.26/112.05 % 112.26/112.05 fof(fact_apsnd__id,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_id__def,axiom, % 112.26/112.05 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 112.26/112.05 % 112.26/112.05 fof(fact_apfst__id,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_vimage__id,axiom, % 112.26/112.05 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ). % 112.26/112.05 % 112.26/112.05 fof(fact_image__id,axiom, % 112.26/112.05 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ). % 112.26/112.05 % 112.26/112.05 fof(fact_of__int__eq__id,axiom, % 112.26/112.05 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 112.26/112.05 % 112.26/112.05 fof(fact_surj__id,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_split__Pair,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setsum__reindex__id,axiom, % 112.26/112.05 ! [V_B_2,V_f_2,T_b,T_c] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__add(T_c) % 112.26/112.05 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setprod__reindex__id,axiom, % 112.26/112.05 ! [V_B_2,V_f_2,T_b,T_c] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.26/112.05 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_SigmaE,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) % 112.26/112.05 => ~ ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.05 => ! [B_y] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x))) % 112.26/112.05 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_map__pair__surj,axiom, % 112.26/112.05 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ( 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)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__conv__nat__seg__image,axiom, % 112.26/112.05 ! [V_A_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 <=> ? [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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_map__pair__imageI,axiom, % 112.26/112.05 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_map__pair_Oid,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_map__pair_Oidentity,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_map__pair__simp,axiom, % 112.26/112.05 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_snd__prod__fun,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_map__pair__ident,axiom, % 112.26/112.05 ! [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 ). % 112.26/112.05 % 112.26/112.05 fof(fact_fst__map__pair,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_apfst__def,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_apsnd__def,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_map__pair__def,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_map__pair__surj__on,axiom, % 112.26/112.05 ! [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] : % 112.26/112.05 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 % 112.26/112.05 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2 % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_map__pair__inj__on,axiom, % 112.26/112.05 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.05 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_prod__fun__imageE,axiom, % 112.26/112.05 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2))) % 112.26/112.05 => ~ ! [B_x,B_y] : % 112.26/112.05 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 112.26/112.05 => ~ 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__comp__def,axiom, % 112.26/112.05 ! [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))))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__Collect__split,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__compI,axiom, % 112.26/112.05 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_RangeI,axiom, % 112.26/112.05 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__Id__on,axiom, % 112.26/112.05 ! [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 ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__comp__empty2,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__comp__empty1,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__comp__distrib,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__comp__distrib2,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_O__assoc,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__comp__mono,axiom, % 112.26/112.05 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ( 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)) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__comp__UNION__distrib,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__comp__UNION__distrib2,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_union__comp__emptyL,axiom, % 112.26/112.05 ! [V_B_2,V_C_2,V_A_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ( 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)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_union__comp__emptyR,axiom, % 112.26/112.05 ! [V_C_2,V_B_2,V_A_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ( 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)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__Union,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__empty__iff,axiom, % 112.26/112.05 ! [V_r_2,T_b,T_c] : % 112.26/112.05 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__empty,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__comp__subset__Sigma,axiom, % 112.26/112.05 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => ( 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)))) % 112.26/112.05 => 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)))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__Un__eq,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__Range,axiom, % 112.26/112.05 ! [V_r_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 112.26/112.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_snd__eq__Range,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__iff,axiom, % 112.26/112.05 ! [V_r_2,T_c,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 112.26/112.05 <=> ? [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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__insert,axiom, % 112.26/112.05 ! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__Int__subset,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__Diff__subset,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_max__ext__compat,axiom, % 112.26/112.05 ! [V_S_2,V_R_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_min__ext__compat,axiom, % 112.26/112.05 ! [V_S_2,V_R_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_RangeP__Range__eq,axiom, % 112.26/112.05 ! [V_x_2,V_r_2,T_c,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_RangeE,axiom, % 112.26/112.05 ! [V_r_2,T_c,V_b_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) % 112.26/112.05 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_pred__comp__rel__comp__eq,axiom, % 112.26/112.05 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(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)) % 112.26/112.05 <=> 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_pred__comp_Ointros,axiom, % 112.26/112.05 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_c_2)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_RangeP_Ointros,axiom, % 112.26/112.05 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 112.26/112.05 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_RangeP_Oequations,axiom, % 112.26/112.05 ! [V_a2_2,V_r_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2)) % 112.26/112.05 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_pred__comp_Oequations,axiom, % 112.26/112.05 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2)) % 112.26/112.05 <=> ? [B_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 112.26/112.05 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_reduction__pairI,axiom, % 112.26/112.05 ! [V_S_2,V_R_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_R_2) % 112.26/112.05 => ( 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)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__on__def,axiom, % 112.26/112.05 ! [V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 112.26/112.05 <=> ( 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)))) % 112.26/112.05 & ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__Collect__split,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__less__than,axiom, % 112.26/112.05 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__empty,axiom, % 112.26/112.05 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__inv__image,axiom, % 112.26/112.05 ! [V_f_2,T_c,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__lex__prod,axiom, % 112.26/112.05 ! [V_rb_2,T_c,V_ra_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_ra_2) % 112.26/112.05 => ( c_Wellfounded_Owf(T_c,V_rb_2) % 112.26/112.05 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__measure,axiom, % 112.26/112.05 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_DomainI,axiom, % 112.26/112.05 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__comp__self,axiom, % 112.26/112.05 ! [V_R_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_R_2) % 112.26/112.05 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_min__ext__wf,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__subset,axiom, % 112.26/112.05 ! [V_p_2,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => ( 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)) % 112.26/112.05 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__less,axiom, % 112.26/112.05 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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__on__Id__on,axiom, % 112.26/112.05 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__Id__on,axiom, % 112.26/112.05 ! [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 ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__finite__psubset,axiom, % 112.26/112.05 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_max__ext__wf,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__pair__less,axiom, % 112.26/112.05 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__Int2,axiom, % 112.26/112.05 ! [V_r_H_2,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => 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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__Int1,axiom, % 112.26/112.05 ! [V_r_H_2,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => 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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__mlex,axiom, % 112.26/112.05 ! [V_f_2,V_R_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_R_2) % 112.26/112.05 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__irrefl,axiom, % 112.26/112.05 ! [V_a_2,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => ~ 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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__asym,axiom, % 112.26/112.05 ! [V_x_2,V_a_2,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => ( 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)) % 112.26/112.05 => ~ 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__not__sym,axiom, % 112.26/112.05 ! [V_x_2,V_a_2,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => ( 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)) % 112.26/112.05 => ~ 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__not__refl,axiom, % 112.26/112.05 ! [V_a_2,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => ~ 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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__int__ge__less__than2,axiom, % 112.26/112.05 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__int__ge__less__than,axiom, % 112.26/112.05 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__Un,axiom, % 112.26/112.05 ! [V_s_2,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => ( c_Wellfounded_Owf(T_b,V_s_2) % 112.26/112.05 => ( 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)) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__acc__iff,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_acc__wfD,axiom, % 112.26/112.05 ! [V_x_2,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__no__loop,axiom, % 112.26/112.05 ! [V_R_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__union__merge,axiom, % 112.26/112.05 ! [V_S_2,V_R_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 <=> 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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__empty__iff,axiom, % 112.26/112.05 ! [V_r_2,T_c,T_b] : % 112.26/112.05 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__empty,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__mono,axiom, % 112.26/112.05 ! [V_s_2,V_r_2,T_c,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__Un__eq,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__Domain,axiom, % 112.26/112.05 ! [V_r_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) % 112.26/112.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__on__empty,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__on__Un,axiom, % 112.26/112.05 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 112.26/112.05 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_fst__eq__Domain,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__on__Int,axiom, % 112.26/112.05 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 112.26/112.05 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 <=> ~ ? [B_f] : % 112.26/112.05 ! [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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wfE__pf,axiom, % 112.26/112.05 ! [V_A_2,V_R_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_R_2) % 112.26/112.05 => ( 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))) % 112.26/112.05 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__union__compatible,axiom, % 112.26/112.05 ! [V_S_2,V_R_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_R_2) % 112.26/112.05 => ( c_Wellfounded_Owf(T_b,V_S_2) % 112.26/112.05 => ( 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)) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__iff,axiom, % 112.26/112.05 ! [V_r_2,T_c,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 112.26/112.05 <=> ? [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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf,axiom, % 112.26/112.05 ! [T_b] : % 112.26/112.05 ( class_Orderings_Owellorder(T_b) % 112.26/112.05 => 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__insert,axiom, % 112.26/112.05 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_reduction__pair__def,axiom, % 112.26/112.05 ! [V_Pa_2,T_b] : % 112.26/112.05 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 112.26/112.05 <=> ( 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)) % 112.26/112.05 & 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__onD,axiom, % 112.26/112.05 ! [V_a_2,V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__onD1,axiom, % 112.26/112.05 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 112.26/112.05 => ( 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)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__onD2,axiom, % 112.26/112.05 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 112.26/112.05 => ( 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)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_reduction__pair__lemma,axiom, % 112.26/112.05 ! [V_S_2,V_R_2,V_Pa_2,T_b] : % 112.26/112.05 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2) % 112.26/112.05 => ( 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))) % 112.26/112.05 => ( 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))) % 112.26/112.05 => ( c_Wellfounded_Owf(T_b,V_S_2) % 112.26/112.05 => 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)) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__Int__subset,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__Diff__subset,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Field__def,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__map__pair__image,axiom, % 112.26/112.05 ! [V_f_2,T_c,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__Union,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_reflp__def,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Predicate_Oreflp(T_b,V_r_2) % 112.26/112.05 <=> 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_DomainP__Domain__eq,axiom, % 112.26/112.05 ! [V_x_2,V_r_2,T_c,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__lenlex,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_DomainP_Ointros,axiom, % 112.26/112.05 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 112.26/112.05 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_reflpE,axiom, % 112.26/112.05 ! [V_x_2,V_r_2,T_b] : % 112.26/112.05 ( c_Predicate_Oreflp(T_b,V_r_2) % 112.26/112.05 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_DomainP_Oequations,axiom, % 112.26/112.05 ! [V_a1_2,V_r_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2)) % 112.26/112.05 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_pred__nat__def,axiom, % 112.26/112.05 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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__lex,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__onI,axiom, % 112.26/112.05 ! [V_A_2,V_r_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.05 => 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)) ) % 112.26/112.05 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__pred__nat,axiom, % 112.26/112.05 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lex__def,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__lexn,axiom, % 112.26/112.05 ! [V_na_2,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_na_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_DomainE,axiom, % 112.26/112.05 ! [V_r_2,T_c,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) % 112.26/112.05 => ~ ! [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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lexn_Osimps_I1_J,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__same__fst,axiom, % 112.26/112.05 ! [T_b,V_R_2,T_c,V_Pa_2] : % 112.26/112.05 ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(V_Pa_2,B_x)) % 112.26/112.05 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) ) % 112.26/112.05 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__if__measure,axiom, % 112.26/112.05 ! [T_b,V_g_2,V_f_2,V_Pa_2] : % 112.26/112.05 ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(V_Pa_2,B_x)) % 112.26/112.05 => 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))) ) % 112.26/112.05 => 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))))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wfP__def,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_OwfP(T_b,V_r_2) % 112.26/112.05 <=> 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wfP__empty,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wfP__accp__iff,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_OwfP(T_b,V_r_2) % 112.26/112.05 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_accp__wfPD,axiom, % 112.26/112.05 ! [V_x_2,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_OwfP(T_b,V_r_2) % 112.26/112.05 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wfP__subset,axiom, % 112.26/112.05 ! [V_p_2,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_OwfP(T_b,V_r_2) % 112.26/112.05 => ( 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)) % 112.26/112.05 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__in__rel,axiom, % 112.26/112.05 ! [V_R_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_R_2) % 112.26/112.05 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wfP__wf__eq,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wfP__acyclicP,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_OwfP(T_b,V_r_2) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_the__sym__eq__trivial,axiom, % 112.26/112.05 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 112.26/112.05 % 112.26/112.05 fof(fact_the__eq__trivial,axiom, % 112.26/112.05 ! [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 ). % 112.26/112.05 % 112.26/112.05 fof(fact_acyclic__subset,axiom, % 112.26/112.05 ! [V_r_2,V_s_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Oacyclic(T_b,V_s_2) % 112.26/112.05 => ( 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)) % 112.26/112.05 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__acyclic,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__iff__acyclic__if__finite,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 112.26/112.05 => ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__acyclic__wf,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 112.26/112.05 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 112.26/112.05 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nitpick_Owf_H__def,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Nitpick_Owf_H(T_b,V_r_2) % 112.26/112.05 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 112.26/112.05 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 112.26/112.05 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_pigeonhole__infinite,axiom, % 112.26/112.05 ! [V_f_2,T_c,V_A_2,T_b] : % 112.26/112.05 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 112.26/112.05 => ? [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.05 & ~ 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)))))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__on__def_H,axiom, % 112.26/112.05 ! [V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 112.26/112.05 <=> ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 112.26/112.05 => 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)) ) % 112.26/112.05 & ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Powp__def,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2)) % 112.26/112.05 <=> ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) % 112.26/112.05 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_INFI__bool__eq,axiom, % 112.26/112.05 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ). % 112.26/112.05 % 112.26/112.05 fof(fact_ball__empty,axiom, % 112.26/112.05 ! [V_Pa_2,T_b,B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 112.26/112.05 => hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Collect__ball__eq,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_congruent__def,axiom, % 112.26/112.05 ! [V_f_2,V_r_2,T_c,T_b] : % 112.26/112.05 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) % 112.26/112.05 <=> ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_INTER__def,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Inf__Sup,axiom, % 112.26/112.05 ! [V_A_2,T_b] : % 112.26/112.05 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.05 => 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))))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Sup__Inf,axiom, % 112.26/112.05 ! [V_A_2,T_b] : % 112.26/112.05 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.05 => 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)))))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Abs__Integ__cases,axiom, % 112.26/112.05 ! [V_x_2] : % 112.26/112.05 ~ ! [B_y] : % 112.26/112.05 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 112.26/112.05 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Abs__Integ__induct,axiom, % 112.26/112.05 ! [V_x_2,V_Pa_2] : % 112.26/112.05 ( ! [B_y] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 112.26/112.05 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 112.26/112.05 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__UN__I,axiom, % 112.26/112.05 ! [V_B_2,T_c,V_A_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( ! [B_a] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 112.26/112.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) ) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Inter__eq,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_inj__on__diff__nat,axiom, % 112.26/112.05 ! [V_k_2,V_N_2] : % 112.26/112.05 ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 112.26/112.05 => 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) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wfP__SUP,axiom, % 112.26/112.05 ! [T_b,V_r_2,T_c] : % 112.26/112.05 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i)) % 112.26/112.05 => ( ! [B_i,B_j] : % 112.26/112.05 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 112.26/112.05 => 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)) ) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_mem__splitE,axiom, % 112.26/112.05 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2))) % 112.26/112.05 => ~ ! [B_x,B_y] : % 112.26/112.05 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) % 112.26/112.05 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_mem__splitI2,axiom, % 112.26/112.05 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] : % 112.26/112.05 ( ! [B_a,B_b] : % 112.26/112.05 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) ) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_vimage__Times,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Eps__split,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_exE__some,axiom, % 112.26/112.05 ! [T_b,V_c_2,V_Pa_2] : % 112.26/112.05 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 112.26/112.05 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2) % 112.26/112.05 => hBOOL(hAPP(V_Pa_2,V_c_2)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_inj__on__imageI2,axiom, % 112.26/112.05 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] : % 112.26/112.05 ( 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) % 112.26/112.05 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_inj__comp,axiom, % 112.26/112.05 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.05 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_inj__on__imageI,axiom, % 112.26/112.05 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] : % 112.26/112.05 ( 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) % 112.26/112.05 => 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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_comp__inj__on,axiom, % 112.26/112.05 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.05 => ( 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)) % 112.26/112.05 => 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) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_comp__inj__on__iff,axiom, % 112.26/112.05 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.05 => ( 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)) % 112.26/112.05 <=> 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) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_image__compose,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_comp__surj,axiom, % 112.26/112.05 ! [V_g_2,T_d,V_f_2,T_b,T_c] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ( 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)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_vimage__compose,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_apfst__compose,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_K__record__comp,axiom, % 112.26/112.05 ! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2 ). % 112.26/112.05 % 112.26/112.05 fof(fact_o__def,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_some__sym__eq__trivial,axiom, % 112.26/112.05 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 112.26/112.05 % 112.26/112.05 fof(fact_some__eq__trivial,axiom, % 112.26/112.05 ! [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 ). % 112.26/112.05 % 112.26/112.05 fof(fact_some__eq__ex,axiom, % 112.26/112.05 ! [T_b,V_Pa_2] : % 112.26/112.05 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) % 112.26/112.05 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_someI__ex,axiom, % 112.26/112.05 ! [T_b,V_Pa_2] : % 112.26/112.05 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 112.26/112.05 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_apsnd__compose,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_o__eq__dest__lhs,axiom, % 112.26/112.05 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] : % 112.26/112.05 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2 % 112.26/112.05 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_o__assoc,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_o__apply,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_o__eq__dest,axiom, % 112.26/112.05 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] : % 112.26/112.05 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2) % 112.26/112.05 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_o__eq__elim,axiom, % 112.26/112.05 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] : % 112.26/112.05 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2) % 112.26/112.05 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_comp__cong,axiom, % 112.26/112.05 ! [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] : % 112.26/112.05 ( 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)) % 112.26/112.05 => 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) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_fun__upd__comp,axiom, % 112.26/112.05 ! [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),c_Fun_Ofun__upd(T_b,T_d,V_g_2,V_x_2,V_y_2)) = 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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 112.26/112.05 ! [V_x_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 112.26/112.05 => 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) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 112.26/112.05 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 112.26/112.05 => 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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_tfl__some,axiom, % 112.26/112.05 ! [T_b,B_P] : % 112.26/112.05 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 112.26/112.05 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_someI,axiom, % 112.26/112.05 ! [T_b,V_x_2,V_Pa_2] : % 112.26/112.05 ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.05 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_map__pair_Ocompositionality,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_map__pair__compose,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_map__pair_Ocomp,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_o__eq__id__dest,axiom, % 112.26/112.05 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] : % 112.26/112.05 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2) % 112.26/112.05 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_id__o,axiom, % 112.26/112.05 ! [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 ). % 112.26/112.05 % 112.26/112.05 fof(fact_o__id,axiom, % 112.26/112.05 ! [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 ). % 112.26/112.05 % 112.26/112.05 fof(fact_setsum__reindex,axiom, % 112.26/112.05 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__add(T_d) % 112.26/112.05 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 112.26/112.05 => 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) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setprod__reindex,axiom, % 112.26/112.05 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__mult(T_d) % 112.26/112.05 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) % 112.26/112.05 => 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) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setprod__reindex__cong,axiom, % 112.26/112.05 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__mult(T_d) % 112.26/112.05 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.05 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 112.26/112.05 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2) % 112.26/112.05 => 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) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_split__paired__Eps,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Eps__split__eq,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setsum_Oreindex,axiom, % 112.26/112.05 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__add(T_c) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 112.26/112.05 => 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) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setprod_Oreindex,axiom, % 112.26/112.05 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__mult(T_c) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 112.26/112.05 => 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) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_the__inv__into__comp,axiom, % 112.26/112.05 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) % 112.26/112.05 => ( 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)))) % 112.26/112.05 => 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) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_fold__image__reindex,axiom, % 112.26/112.05 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] : % 112.26/112.05 ( class_Groups_Oab__semigroup__mult(T_d) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2) % 112.26/112.05 => 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) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Oremove,axiom, % 112.26/112.05 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding__image_Oreindex,axiom, % 112.26/112.05 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 112.26/112.05 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2) % 112.26/112.05 => 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) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Ounion,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.26/112.05 => ( 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)) % 112.26/112.05 => 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)) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 112.26/112.05 ! [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] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2) % 112.26/112.05 => 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) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Ocommute__comp,axiom, % 112.26/112.05 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => 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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Ocommute__left__comp,axiom, % 112.26/112.05 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => 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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_UN__o,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_fst__comp__map__pair,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_snd__comp__map__pair,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding__image_Odistrib,axiom, % 112.26/112.05 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_split__comp,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 112.26/112.05 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Ocommute__comp_H_H,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Ocommute__left__comp_H,axiom, % 112.26/112.05 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Ocommute__comp_H,axiom, % 112.26/112.05 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Oempty,axiom, % 112.26/112.05 ! [V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Oeq__fold,axiom, % 112.26/112.05 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => 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) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding__image_Oeq__fold,axiom, % 112.26/112.05 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 112.26/112.05 => 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) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Oinsert,axiom, % 112.26/112.05 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Ounion__inter,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding_Oinsert__remove,axiom, % 112.26/112.05 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setsum__reindex__nonzero,axiom, % 112.26/112.05 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__add(T_d) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) % 112.26/112.05 => ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 112.26/112.05 => ! [B_y] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2)) % 112.26/112.05 => ( B_x != B_y % 112.26/112.05 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 112.26/112.05 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) % 112.26/112.05 => 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) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding__idem_Ounion__idem,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 112.26/112.05 => 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) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding__idem_Oidem__comp,axiom, % 112.26/112.05 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => 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) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding__idem_Oidem__left__comp,axiom, % 112.26/112.05 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => 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) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding__idem_Oin__comp__idem,axiom, % 112.26/112.05 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.05 => 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) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_folding__idem_Oinsert__idem,axiom, % 112.26/112.05 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] : % 112.26/112.05 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) % 112.26/112.05 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_strong__setprod__reindex__cong,axiom, % 112.26/112.05 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__mult(T_d) % 112.26/112.05 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.05 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 112.26/112.05 => ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.05 => 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) ) % 112.26/112.05 => 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) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wfI__pf,axiom, % 112.26/112.05 ! [V_R_2,T_b] : % 112.26/112.05 ( ! [B_A] : % 112.26/112.05 ( 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))) % 112.26/112.05 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 112.26/112.05 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Sigma__mono,axiom, % 112.26/112.05 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) % 112.26/112.05 => ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.05 => 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))) ) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_not__acc__down,axiom, % 112.26/112.05 ! [V_R_2,V_x_2,T_b] : % 112.26/112.05 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2))) % 112.26/112.05 => ~ ! [B_z] : % 112.26/112.05 ( 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)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_acc_OaccI,axiom, % 112.26/112.05 ! [V_r_2,V_x_2,T_b] : % 112.26/112.05 ( ! [B_y] : % 112.26/112.05 ( 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)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) ) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_max__ext_Osimps,axiom, % 112.26/112.05 ! [V_R_2,V_a2_2,V_a1_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 112.26/112.05 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 112.26/112.05 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.05 & ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 112.26/112.05 => ? [B_xa] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 112.26/112.05 & 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)) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__no__infinite__down__chainE,axiom, % 112.26/112.05 ! [V_f_2,V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => ~ ! [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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_iterate_Osimps,axiom, % 112.26/112.05 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 112.26/112.05 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 112.26/112.05 => 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) ) % 112.26/112.05 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_setsum__reindex__cong,axiom, % 112.26/112.05 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] : % 112.26/112.05 ( class_Groups_Ocomm__monoid__add(T_d) % 112.26/112.05 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.05 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) % 112.26/112.05 => ( ! [B_a] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 112.26/112.05 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 112.26/112.05 => 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) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_scomp__apply,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_scomp__scomp,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_scomp__Pair,axiom, % 112.26/112.05 ! [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 ). % 112.26/112.05 % 112.26/112.05 fof(fact_Pair__scomp,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_scomp__def,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_scomp__unfold,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_less__eq,axiom, % 112.26/112.05 ! [V_na_2,V_m_2] : % 112.26/112.05 ( 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_na_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) % 112.26/112.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__eq__minimal,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 <=> ! [B_Q] : % 112.26/112.05 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 112.26/112.05 => ? [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) % 112.26/112.05 & ! [B_y] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_transfer__nat__int__set__cong,axiom, % 112.26/112.05 ! [V_P_H_2,V_Pa_2] : % 112.26/112.05 ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 112.26/112.05 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 112.26/112.05 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 112.26/112.05 => 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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__trancl,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_less__than__def,axiom, % 112.26/112.05 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 112.26/112.05 % 112.26/112.05 fof(fact_acyclic__def,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 112.26/112.05 <=> ! [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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl_Or__into__trancl,axiom, % 112.26/112.05 ! [V_r_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__subset__Field2,axiom, % 112.26/112.05 ! [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))))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__Int__subset,axiom, % 112.26/112.05 ! [V_s_2,V_r_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ( 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)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_r__into__trancl_H,axiom, % 112.26/112.05 ! [V_r_2,V_p_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__empty,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__domain,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__range,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__trancl,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 112.26/112.05 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__trans,axiom, % 112.26/112.05 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 112.26/112.05 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__into__trancl2,axiom, % 112.26/112.05 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_r__r__into__trancl,axiom, % 112.26/112.05 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2)) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__mono,axiom, % 112.26/112.05 ! [V_s_2,V_r_2,V_p_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 112.26/112.05 => ( 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)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__unfold,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__subset__Sigma,axiom, % 112.26/112.05 ! [V_A_2,V_r_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__insert,axiom, % 112.26/112.05 ! [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)))))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_reflcl__set__eq,axiom, % 112.26/112.05 ! [V_y_2,V_x_2,V_r_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 <=> 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_acyclicI,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( ! [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))) % 112.26/112.05 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_r__into__rtrancl,axiom, % 112.26/112.05 ! [V_r_2,V_p_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl_Ortrancl__refl,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_IdI,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__into__rtrancl,axiom, % 112.26/112.05 ! [V_r_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__rtrancl__absorb,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__trancl__absorb,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_reflcl__trancl,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__reflcl,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__unfold__right,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__unfold__left,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__Int__subset,axiom, % 112.26/112.05 ! [V_r_2,V_s_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ( 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)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_r__comp__rtrancl__eq,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__idemp__self__comp,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__unfold,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_in__rtrancl__UnI,axiom, % 112.26/112.05 ! [V_S_2,V_R_2,V_x_2,T_b] : % 112.26/112.05 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 112.26/112.05 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) ) % 112.26/112.05 => 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__Un__subset,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__reflcl,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__Un__rtrancl,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__reflcl__absorb,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__subset__rtrancl,axiom, % 112.26/112.05 ! [V_s_2,V_r_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__subset,axiom, % 112.26/112.05 ! [V_S_2,V_R_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ( 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))) % 112.26/112.05 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__mono,axiom, % 112.26/112.05 ! [V_s_2,V_r_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Image__closed__trancl,axiom, % 112.26/112.05 ! [V_X_2,V_r_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__idemp,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__trans,axiom, % 112.26/112.05 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 112.26/112.05 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 112.26/112.05 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__r__diff__Id,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__rtrancl,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__rtrancl,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__rtrancl,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__empty,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Image__Id,axiom, % 112.26/112.05 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ). % 112.26/112.05 % 112.26/112.05 fof(fact_Id__O__R,axiom, % 112.26/112.05 ! [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 ). % 112.26/112.05 % 112.26/112.05 fof(fact_R__O__Id,axiom, % 112.26/112.05 ! [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 ). % 112.26/112.05 % 112.26/112.05 fof(fact_pair__in__Id__conv,axiom, % 112.26/112.05 ! [V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b))) % 112.26/112.05 <=> V_a_2 = V_b_2 ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__trancl__trancl,axiom, % 112.26/112.05 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => ( 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))) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__rtrancl__trancl,axiom, % 112.26/112.05 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__into__trancl1,axiom, % 112.26/112.05 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtranclD,axiom, % 112.26/112.05 ! [V_R_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 112.26/112.05 => ( V_a_2 = V_b_2 % 112.26/112.05 | ( V_a_2 != V_b_2 % 112.26/112.05 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__into__trancl2,axiom, % 112.26/112.05 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__eq__or__trancl,axiom, % 112.26/112.05 ! [V_R_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 <=> ( V_x_2 = V_y_2 % 112.26/112.05 | ( V_x_2 != V_y_2 % 112.26/112.05 & 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))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__Id,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__Id,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__Id,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_pair__leq__def,axiom, % 112.26/112.05 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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Not__Domain__rtrancl,axiom, % 112.26/112.05 ! [V_y_2,V_R_2,V_x_2,T_b] : % 112.26/112.05 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2))) % 112.26/112.05 => ( 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))) % 112.26/112.05 <=> V_x_2 = V_y_2 ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_acc__downwards__aux,axiom, % 112.26/112.05 ! [V_r_2,V_a_2,V_b_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_acc__downwards,axiom, % 112.26/112.05 ! [V_b_2,V_r_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__insert,axiom, % 112.26/112.05 ! [V_r_2,V_x_2,V_y_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 <=> ( c_Wellfounded_Owf(T_b,V_r_2) % 112.26/112.05 & ~ 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_acyclic__insert,axiom, % 112.26/112.05 ! [V_r_2,V_x_2,V_y_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 112.26/112.05 & ~ 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__reflcl,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Id__def,axiom, % 112.26/112.05 ! [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))))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_irrefl__diff__Id,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_pred__nat__trancl__eq__le,axiom, % 112.26/112.05 ! [V_na_2,V_m_2] : % 112.26/112.05 ( 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_na_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) % 112.26/112.05 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__subset__Sigma__aux,axiom, % 112.26/112.05 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) % 112.26/112.05 => ( 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)))) % 112.26/112.05 => ( V_a_2 = V_b_2 % 112.26/112.05 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_irrefl__tranclI,axiom, % 112.26/112.05 ! [V_x_2,V_r_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ~ 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_sequence__trans,axiom, % 112.26/112.05 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] : % 112.26/112.05 ( ! [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))) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_total__on__diff__Id,axiom, % 112.26/112.05 ! [V_r_2,V_A_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__converse,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converse__Id,axiom, % 112.26/112.05 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converse__INTER,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converse__iff,axiom, % 112.26/112.05 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 112.26/112.05 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converseI,axiom, % 112.26/112.05 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converseD,axiom, % 112.26/112.05 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_acyclic__converse,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 112.26/112.05 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converse__UNION,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converse__rel__comp,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converse__Un,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converse__Id__on,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converse__inv__image,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_total__on__converse,axiom, % 112.26/112.05 ! [V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 112.26/112.05 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converse__converse,axiom, % 112.26/112.05 ! [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 ). % 112.26/112.05 % 112.26/112.05 fof(fact_converse__Int,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__converse,axiom, % 112.26/112.05 ! [V_r_2,T_c,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) % 112.26/112.05 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Field__converse,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__on__converse,axiom, % 112.26/112.05 ! [V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 112.26/112.05 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__converse,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__converse__trancl,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 112.26/112.05 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_equiv__comp__eq,axiom, % 112.26/112.05 ! [V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.05 => 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 ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__converse,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Domain__converse,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Range__def,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_total__on__empty,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__converseI,axiom, % 112.26/112.05 ! [V_r_2,V_x_2,V_y_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__converseD,axiom, % 112.26/112.05 ! [V_r_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__converseI,axiom, % 112.26/112.05 ! [V_r_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__converseD,axiom, % 112.26/112.05 ! [V_r_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Image__subset__eq,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 <=> 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))))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_refl__on__comp__subset,axiom, % 112.26/112.05 ! [V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_comp__equivI,axiom, % 112.26/112.05 ! [V_A_2,V_r_2,T_b] : % 112.26/112.05 ( 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 % 112.26/112.05 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2 % 112.26/112.05 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__acyclic__wf__converse,axiom, % 112.26/112.05 ! [V_r_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) % 112.26/112.05 => ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 112.26/112.05 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_total__on__def,axiom, % 112.26/112.05 ! [V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2) % 112.26/112.05 <=> ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.05 => ! [B_xa] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) % 112.26/112.05 => ( B_x != B_xa % 112.26/112.05 => ( 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)) % 112.26/112.05 | 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)) ) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converse__def,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Image__INT__eq,axiom, % 112.26/112.05 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] : % 112.26/112.05 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) % 112.26/112.05 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 112.26/112.05 ! [V_R_2,V_p_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 112.26/112.05 => 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_single__valued__Id,axiom, % 112.26/112.05 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__pow__commute,axiom, % 112.26/112.05 ! [V_na_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_na_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_na_2),V_R_2)),V_R_2) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__pow__1,axiom, % 112.26/112.05 ! [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 ). % 112.26/112.05 % 112.26/112.05 fof(fact_single__valued__rel__pow,axiom, % 112.26/112.05 ! [V_na_2,V_R_2,T_b] : % 112.26/112.05 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2) % 112.26/112.05 => c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_funpow__swap1,axiom, % 112.26/112.05 ! [V_x_2,V_na_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),V_f_2),hAPP(V_f_2,V_x_2)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_funpow__mult,axiom, % 112.26/112.05 ! [V_f_2,V_m_2,V_na_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_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_na_2)),V_f_2) ). % 112.26/112.05 % 112.26/112.05 fof(fact_single__valued__subset,axiom, % 112.26/112.05 ! [V_s_2,V_r_2,T_c,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 112.26/112.05 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_wf__exp,axiom, % 112.26/112.05 ! [V_R_2,V_na_2,T_b] : % 112.26/112.05 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)) % 112.26/112.05 => c_Wellfounded_Owf(T_b,V_R_2) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_single__valued__rel__comp,axiom, % 112.26/112.05 ! [V_s_2,T_d,V_r_2,T_c,T_b] : % 112.26/112.05 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 112.26/112.05 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_comp__funpow,axiom, % 112.26/112.05 ! [V_f_2,V_na_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_na_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_na_2),V_f_2)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__pow__imp__rtrancl,axiom, % 112.26/112.05 ! [V_R_2,V_na_2,V_p_2,T_b] : % 112.26/112.05 ( 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_na_2),V_R_2))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__power,axiom, % 112.26/112.05 ! [V_R_2,V_p_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) % 112.26/112.05 <=> ? [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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_single__valued__Id__on,axiom, % 112.26/112.05 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_relpow_Osimps_I2_J,axiom, % 112.26/112.05 ! [V_R_2,V_na_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_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_na_2),V_R_2)),V_R_2) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__pow__add,axiom, % 112.26/112.05 ! [V_R_2,V_na_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_na_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_na_2),V_R_2)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_relpow_Osimps_I1_J,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__pow__0__I,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__pow__0__E,axiom, % 112.26/112.05 ! [V_R_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => V_x_2 = V_y_2 ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__pow__Suc__I2,axiom, % 112.26/112.05 ! [V_na_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ( 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_na_2),V_R_2))) % 112.26/112.05 => 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_na_2)),V_R_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__pow__Suc__I,axiom, % 112.26/112.05 ! [V_z_2,V_R_2,V_na_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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_na_2),V_R_2))) % 112.26/112.05 => ( 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)) % 112.26/112.05 => 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_na_2)),V_R_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_funpow_Osimps_I2_J,axiom, % 112.26/112.05 ! [V_f_2,V_na_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_na_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_na_2),V_f_2)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_funpow__add,axiom, % 112.26/112.05 ! [V_f_2,V_na_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_na_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_na_2),V_f_2)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_single__valuedD,axiom, % 112.26/112.05 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] : % 112.26/112.05 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 112.26/112.05 => ( 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)) % 112.26/112.05 => ( 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)) % 112.26/112.05 => V_y_2 = V_z_2 ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_single__valued__def,axiom, % 112.26/112.05 ! [V_r_2,T_c,T_b] : % 112.26/112.05 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2) % 112.26/112.05 <=> ! [B_x,B_y] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ! [B_z] : % 112.26/112.05 ( 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)) % 112.26/112.05 => B_y = B_z ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_funpow_Osimps_I1_J,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_trancl__power,axiom, % 112.26/112.05 ! [V_R_2,V_p_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2))) % 112.26/112.05 <=> ? [B_n] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 112.26/112.05 & 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_single__valued__confluent,axiom, % 112.26/112.05 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] : % 112.26/112.05 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2) % 112.26/112.05 => ( 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))) % 112.26/112.05 => ( 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))) % 112.26/112.05 => ( 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))) % 112.26/112.05 | 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))) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Image__Int__eq,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : % 112.26/112.05 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2)) % 112.26/112.05 => 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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_funpow__code__def,axiom, % 112.26/112.05 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__pow__E,axiom, % 112.26/112.05 ! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] : % 112.26/112.05 ( 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_na_2),V_R_2))) % 112.26/112.05 => ( ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.05 => V_x_2 != V_z_2 ) % 112.26/112.05 => ~ ! [B_y,B_m] : % 112.26/112.05 ( V_na_2 = hAPP(c_Nat_OSuc,B_m) % 112.26/112.05 => ( 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))) % 112.26/112.05 => ~ 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)) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__pow__E2,axiom, % 112.26/112.05 ! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] : % 112.26/112.05 ( 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_na_2),V_R_2))) % 112.26/112.05 => ( ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.05 => V_x_2 != V_z_2 ) % 112.26/112.05 => ~ ! [B_y,B_m] : % 112.26/112.05 ( V_na_2 = hAPP(c_Nat_OSuc,B_m) % 112.26/112.05 => ( 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)) % 112.26/112.05 => ~ 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))) ) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__Un__separator__converseE,axiom, % 112.26/112.05 ! [V_Q_2,V_Pa_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Q_2)))) % 112.26/112.05 => ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) % 112.26/112.05 => ! [B_y] : % 112.26/112.05 ( 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)) % 112.26/112.05 => B_y = B_x ) ) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__Un__separatorE,axiom, % 112.26/112.05 ! [V_Q_2,V_Pa_2,V_b_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Q_2)))) % 112.26/112.05 => ( ! [B_x] : % 112.26/112.05 ( 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))) % 112.26/112.05 => ! [B_y] : % 112.26/112.05 ( 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)) % 112.26/112.05 => B_x = B_y ) ) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__pow__Suc__D2,axiom, % 112.26/112.05 ! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] : % 112.26/112.05 ( 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_na_2)),V_R_2))) % 112.26/112.05 => ? [B_y] : % 112.26/112.05 ( 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)) % 112.26/112.05 & 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_na_2),V_R_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__pow__Suc__E,axiom, % 112.26/112.05 ! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] : % 112.26/112.05 ( 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_na_2)),V_R_2))) % 112.26/112.05 => ~ ! [B_y] : % 112.26/112.05 ( 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_na_2),V_R_2))) % 112.26/112.05 => ~ 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__pow__Suc__E2,axiom, % 112.26/112.05 ! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] : % 112.26/112.05 ( 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_na_2)),V_R_2))) % 112.26/112.05 => ~ ! [B_y] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ~ 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_na_2),V_R_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_tranclD,axiom, % 112.26/112.05 ! [V_R_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => ? [B_z] : % 112.26/112.05 ( 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)) % 112.26/112.05 & 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_tranclD2,axiom, % 112.26/112.05 ! [V_R_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => ? [B_z] : % 112.26/112.05 ( 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))) % 112.26/112.05 & 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_IdE,axiom, % 112.26/112.05 ! [V_p_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b))) % 112.26/112.05 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Int__Collect__mono,axiom, % 112.26/112.05 ! [V_Q_2,V_Pa_2,V_B_2,V_A_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.26/112.05 => ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.05 => ( hBOOL(hAPP(V_Pa_2,B_x)) % 112.26/112.05 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 112.26/112.05 => 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)))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rel__compE,axiom, % 112.26/112.05 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => ~ ! [B_x,B_y,B_z] : % 112.26/112.05 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z) % 112.26/112.05 => ( 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)) % 112.26/112.05 => ~ 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_converseE,axiom, % 112.26/112.05 ! [V_r_2,V_yx_2,T_c,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => ~ ! [B_x,B_y] : % 112.26/112.05 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x) % 112.26/112.05 => ~ 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nitpick_Oplus__frac__def,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_internal__split__def,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_internal__split__conv,axiom, % 112.26/112.05 ! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nitpick_Otimes__frac__def,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nitpick_Oof__frac__def,axiom, % 112.26/112.05 ! [V_q,T_a,T_b] : % 112.26/112.05 ( ( class_Rings_Oinverse(T_b) % 112.26/112.05 & class_Rings_Oring__1(T_b) ) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nitpick_Oless__frac__def,axiom, % 112.26/112.05 ! [V_r_2,V_q_2,T_b] : % 112.26/112.05 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2) % 112.26/112.05 <=> 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 112.26/112.05 ! [V_r_2,V_q_2,T_b] : % 112.26/112.05 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2) % 112.26/112.05 <=> 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nitpick_Onum__def,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Nitpick_Odenom__def,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_bool_Osize_I2_J,axiom, % 112.26/112.05 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 112.26/112.05 % 112.26/112.05 fof(fact_bool_Osize_I1_J,axiom, % 112.26/112.05 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__less__ub,axiom, % 112.26/112.05 ! [V_u_2,V_f_2] : % 112.26/112.05 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 112.26/112.05 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_f_2)),V_u_2)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lenlex__def,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_neq__if__length__neq,axiom, % 112.26/112.05 ! [V_ys,V_xs,T_a] : % 112.26/112.05 ( 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) % 112.26/112.05 => V_xs != V_ys ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lexn__length,axiom, % 112.26/112.05 ! [V_na_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.05 ( 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_na_2))) % 112.26/112.05 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_na_2 % 112.26/112.05 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_na_2 ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lenlex__conv,axiom, % 112.26/112.05 ! [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)))))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_length__sublist,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lexn_Osimps_I2_J,axiom, % 112.26/112.05 ! [V_na_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_na_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_na_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_na_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_na_2)))))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_impossible__Cons,axiom, % 112.26/112.05 ! [V_x,V_ys,V_xs,T_a] : % 112.26/112.05 ( 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))) % 112.26/112.05 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_list_Oinject,axiom, % 112.26/112.05 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] : % 112.26/112.05 ( 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) % 112.26/112.05 <=> ( V_a_2 = V_a_H_2 % 112.26/112.05 & V_list_2 = V_list_H_2 ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_not__Cons__self2,axiom, % 112.26/112.05 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 112.26/112.05 % 112.26/112.05 fof(fact_not__Cons__self,axiom, % 112.26/112.05 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 112.26/112.05 % 112.26/112.05 fof(fact_list_Osize_I4_J,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Cons__in__lex,axiom, % 112.26/112.05 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 <=> ( ( 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)) % 112.26/112.05 & 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) ) % 112.26/112.05 | ( V_x_2 = V_y_2 % 112.26/112.05 & 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))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_set__Cons__def,axiom, % 112.26/112.05 ! [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)))))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_pick_Osimps,axiom, % 112.26/112.05 ! [V_xs,V_x,T_a,V_i] : % 112.26/112.05 ( ( 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))) % 112.26/112.05 => 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) ) % 112.26/112.05 & ( ~ 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))) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_select__weight__cons__zero,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lexord__cons__cons,axiom, % 112.26/112.05 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) % 112.26/112.05 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 112.26/112.05 | ( V_a_2 = V_b_2 % 112.26/112.05 & 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))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lexord__lex,axiom, % 112.26/112.05 ! [V_r_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 <=> ( 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))) % 112.26/112.05 & 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) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 112.26/112.05 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => ( 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)))) % 112.26/112.05 => 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)))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_list_Osize_I2_J,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Cons__acc__listrel1I,axiom, % 112.26/112.05 ! [V_xs_2,V_r_2,V_x_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) % 112.26/112.05 => ( 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)))) % 112.26/112.05 => 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)))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel1__converse,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel1__mono,axiom, % 112.26/112.05 ! [V_s_2,V_r_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel1I2,axiom, % 112.26/112.05 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 112.26/112.05 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel1__eq__len,axiom, % 112.26/112.05 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => 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) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__listrel1__eq__len,axiom, % 112.26/112.05 ! [V_r_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => 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) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_in__listrel1__converse,axiom, % 112.26/112.05 ! [V_r_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 <=> 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Cons__listrel1__Cons,axiom, % 112.26/112.05 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 <=> ( ( 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)) % 112.26/112.05 & V_xs_2 = V_ys_2 ) % 112.26/112.05 | ( V_x_2 = V_y_2 % 112.26/112.05 & 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))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel1I1,axiom, % 112.26/112.05 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__Cons,axiom, % 112.26/112.05 ! [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))))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lexord__linear,axiom, % 112.26/112.05 ! [V_y_2,V_x_2,V_r_2,T_b] : % 112.26/112.05 ( ! [B_a,B_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 | B_a = B_b % 112.26/112.05 | 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)) ) % 112.26/112.05 => ( 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))) % 112.26/112.05 | V_x_2 = V_y_2 % 112.26/112.05 | 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__rtrancl__refl,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__mono,axiom, % 112.26/112.05 ! [V_s_2,V_r_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__eq__len,axiom, % 112.26/112.05 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => 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) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__rtrancl__trans,axiom, % 112.26/112.05 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => ( 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)))) % 112.26/112.05 => 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)))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__reflcl__if__listrel1,axiom, % 112.26/112.05 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel1__subset__listrel,axiom, % 112.26/112.05 ! [V_r_H_2,V_r_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 112.26/112.05 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel_OCons,axiom, % 112.26/112.05 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 => ( 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))) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrelp__listrel__eq,axiom, % 112.26/112.05 ! [V_xa_2,V_x_2,V_r_2,T_b] : % 112.26/112.05 ( 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) % 112.26/112.05 <=> 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__Cons1,axiom, % 112.26/112.05 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => ~ ! [B_y,B_ys] : % 112.26/112.05 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys) % 112.26/112.05 => ( 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)) % 112.26/112.05 => ~ 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))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrelp_Oequations_I2_J,axiom, % 112.26/112.05 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] : % 112.26/112.05 ( 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)) % 112.26/112.05 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 112.26/112.05 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrelp_OCons,axiom, % 112.26/112.05 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 112.26/112.05 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2) % 112.26/112.05 => 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)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__Cons2,axiom, % 112.26/112.05 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 => ~ ! [B_x,B_xs] : % 112.26/112.05 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) % 112.26/112.05 => ( 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)) % 112.26/112.05 => ~ 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))) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__subset,axiom, % 112.26/112.05 ! [V_A_2,V_r_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => 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))))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lists__UNIV,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lists__mono,axiom, % 112.26/112.05 ! [V_B_2,V_A_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_equiv__listrel,axiom, % 112.26/112.05 ! [V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.05 => 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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__refl__on,axiom, % 112.26/112.05 ! [V_r_2,V_A_2,T_b] : % 112.26/112.05 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 112.26/112.05 => 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)) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_Cons__in__lists__iff,axiom, % 112.26/112.05 ! [V_A_2,V_xs_2,V_x_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.05 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lists__accI,axiom, % 112.26/112.05 ! [V_r_2,V_xs_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lists__accD,axiom, % 112.26/112.05 ! [V_r_2,V_xs_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__iff__nth,axiom, % 112.26/112.05 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 <=> ( 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) % 112.26/112.05 & ! [B_n] : % 112.26/112.05 ( 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))) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lexord__irreflexive,axiom, % 112.26/112.05 ! [V_y_2,V_r_2,T_b] : % 112.26/112.05 ( ! [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)) % 112.26/112.05 => ~ 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_infinite__UNIV__listI,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_list__eq__iff__nth__eq,axiom, % 112.26/112.05 ! [T_b,V_ys_2,V_xs_2] : % 112.26/112.05 ( V_xs_2 = V_ys_2 % 112.26/112.05 <=> ( 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) % 112.26/112.05 & ! [B_i] : % 112.26/112.05 ( 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))) % 112.26/112.05 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_nth__Cons__Suc,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_nth__Cons__0,axiom, % 112.26/112.05 ! [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 ). % 112.26/112.05 % 112.26/112.05 fof(fact_nth_Osimps,axiom, % 112.26/112.05 ! [V_na_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_na_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_na_2) ). % 112.26/112.05 % 112.26/112.05 fof(fact_nth__Cons_H,axiom, % 112.26/112.05 ! [V_xs,V_x,T_a,V_n] : % 112.26/112.05 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.05 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 112.26/112.05 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_nth__Cons__number__of,axiom, % 112.26/112.05 ! [V_xs,V_x,T_a,V_v] : % 112.26/112.05 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.05 => 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 ) % 112.26/112.05 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lexord__take__index__conv,axiom, % 112.26/112.05 ! [V_r_2,V_y_2,V_x_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 <=> ( ( 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))) % 112.26/112.05 & 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 ) % 112.26/112.05 | ? [B_i] : % 112.26/112.05 ( 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)))) % 112.26/112.05 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2) % 112.26/112.05 & 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_set__sublist,axiom, % 112.26/112.05 ! [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))))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__set,axiom, % 112.26/112.05 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_set__subset__Cons,axiom, % 112.26/112.05 ! [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)))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_take__all,axiom, % 112.26/112.05 ! [V_n,V_xs,T_a] : % 112.26/112.05 ( 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)) % 112.26/112.05 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_set__take__subset,axiom, % 112.26/112.05 ! [V_xs_2,V_na_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_na_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_set__take__subset__set__take,axiom, % 112.26/112.05 ! [V_xs_2,T_b,V_na_2,V_m_2] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 112.26/112.05 => 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_na_2),V_xs_2)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_set__sublist__subset,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_nth__take,axiom, % 112.26/112.05 ! [V_xs,T_a,V_n,V_i] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 112.26/112.05 => 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) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_take__Suc__Cons,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_notin__set__sublistI,axiom, % 112.26/112.05 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 112.26/112.05 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.05 => ~ 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)))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_in__set__takeD,axiom, % 112.26/112.05 ! [V_xs_2,V_na_2,V_x_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2)))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_in__set__sublistD,axiom, % 112.26/112.05 ! [V_I_2,V_xs_2,V_x_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_set__ConsD,axiom, % 112.26/112.05 ! [V_xs_2,V_x_2,V_y_2,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => ( V_y_2 = V_x_2 % 112.26/112.05 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_length__take,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_take__take,axiom, % 112.26/112.05 ! [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) ). % 112.26/112.05 % 112.26/112.05 fof(fact_List_Oset_Osimps_I2_J,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_sublist__upt__eq__take,axiom, % 112.26/112.05 ! [V_na_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2)) = hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_l_2) ). % 112.26/112.05 % 112.26/112.05 fof(fact_card__length,axiom, % 112.26/112.05 ! [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))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_all__set__conv__all__nth,axiom, % 112.26/112.05 ! [V_Pa_2,V_xs_2,T_b] : % 112.26/112.05 ( ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.05 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.05 <=> ! [B_i] : % 112.26/112.05 ( 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))) % 112.26/112.05 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_list__size__estimation,axiom, % 112.26/112.05 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_list__size__estimation_H,axiom, % 112.26/112.05 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.05 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 112.26/112.05 => 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))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_in__lists__conv__set,axiom, % 112.26/112.05 ! [V_A_2,V_xs_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 112.26/112.05 <=> ! [B_x] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_length__pos__if__in__set,axiom, % 112.26/112.05 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.05 => 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))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_in__set__conv__nth,axiom, % 112.26/112.05 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.05 <=> ? [B_i] : % 112.26/112.05 ( 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))) % 112.26/112.05 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_nth__mem,axiom, % 112.26/112.05 ! [V_xs_2,T_b,V_na_2] : % 112.26/112.05 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_na_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_lists__eq__set,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_set__conv__nth,axiom, % 112.26/112.05 ! [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))))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__lists__length__eq,axiom, % 112.26/112.05 ! [V_na_2,V_A_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => 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_na_2))))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_finite__lists__length__le,axiom, % 112.26/112.05 ! [V_na_2,V_A_2,T_b] : % 112.26/112.05 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.05 => 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_na_2))))) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_listrel__iff__zip,axiom, % 112.26/112.05 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.05 ( 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))) % 112.26/112.05 <=> ( 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) % 112.26/112.05 & ! [B_x] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => 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)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_set__zip,axiom, % 112.26/112.05 ! [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)))))) ). % 112.26/112.05 % 112.26/112.05 fof(fact_take__zip,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_length__zip,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_zip__Cons__Cons,axiom, % 112.26/112.05 ! [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)) ). % 112.26/112.05 % 112.26/112.05 fof(fact_list__eq__iff__zip__eq,axiom, % 112.26/112.05 ! [T_b,V_ys_2,V_xs_2] : % 112.26/112.05 ( V_xs_2 = V_ys_2 % 112.26/112.05 <=> ( 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) % 112.26/112.05 & ! [B_x] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_in__set__zipE,axiom, % 112.26/112.05 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 112.26/112.05 ( 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)))) % 112.26/112.05 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.05 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ). % 112.26/112.05 % 112.26/112.05 fof(fact_set__zip__rightD,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 112.26/112.06 ( 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)))) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__zip__leftD,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] : % 112.26/112.06 ( 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)))) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__same,axiom, % 112.26/112.06 ! [V_xs_2,V_b_2,V_a_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2)))) % 112.26/112.06 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 & V_a_2 = V_b_2 ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__zip,axiom, % 112.26/112.06 ! [V_ys,T_b,V_xs,T_a,V_i] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ( 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))) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_greaterThanLessThan__upto,axiom, % 112.26/112.06 ! [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)))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__setsum__nth,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( class_Groups_Ocomm__monoid__add(T_b) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__upto,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_atLeastAtMost__upto,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 112.26/112.06 ! [V_ns_2] : % 112.26/112.06 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 <=> ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 112.26/112.06 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__simps_I2_J,axiom, % 112.26/112.06 ! [V_xs,V_x,T_a] : % 112.26/112.06 ( class_Groups_Omonoid__add(T_a) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_elem__le__listsum__nat,axiom, % 112.26/112.06 ! [V_ns,V_k] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_atLeastLessThan__upto,axiom, % 112.26/112.06 ! [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)))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_greaterThanAtMost__upto,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nat__list__def,axiom, % 112.26/112.06 ! [V_l_2] : % 112.26/112.06 ( c_List_Onat__list(V_l_2) % 112.26/112.06 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__size__pointwise,axiom, % 112.26/112.06 ! [V_g_2,V_f_2,V_xs_2,T_b] : % 112.26/112.06 ( ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__update__nat,axiom, % 112.26/112.06 ! [V_n,V_ns,V_k] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_butlast__take,axiom, % 112.26/112.06 ! [V_xs,T_a,V_n] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update__beyond,axiom, % 112.26/112.06 ! [V_x,V_i,V_xs,T_a] : % 112.26/112.06 ( 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)) % 112.26/112.06 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update__id,axiom, % 112.26/112.06 ! [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 ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__list__update__neq,axiom, % 112.26/112.06 ! [V_x,V_xs,T_a,V_j,V_i] : % 112.26/112.06 ( V_i != V_j % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_butlast__list__update,axiom, % 112.26/112.06 ! [V_x,V_xs,T_a,V_k] : % 112.26/112.06 ( ( 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)) % 112.26/112.06 => 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) ) % 112.26/112.06 & ( 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)) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__list__update,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__update,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_update__zip,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update__swap,axiom, % 112.26/112.06 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 112.26/112.06 ( V_i != V_i_H % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update__overwrite,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update_Osimps_I2_J,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update__code_I3_J,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update__code_I2_J,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_in__set__butlastD,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__update__subsetI,axiom, % 112.26/112.06 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] : % 112.26/112.06 ( 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)) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__update__subset__insert,axiom, % 112.26/112.06 ! [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)))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__list__update,axiom, % 112.26/112.06 ! [V_x,V_j,V_xs,T_a,V_i] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ( ( V_i = V_j % 112.26/112.06 => 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 ) % 112.26/112.06 & ( V_i != V_j % 112.26/112.06 => 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) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update__same__conv,axiom, % 112.26/112.06 ! [V_x_2,V_xs_2,T_b,V_i_2] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 112.26/112.06 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__list__update__eq,axiom, % 112.26/112.06 ! [V_x,V_xs,T_a,V_i] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__butlast,axiom, % 112.26/112.06 ! [V_xs,T_a,V_n] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__butlast,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__update__memI,axiom, % 112.26/112.06 ! [V_x_2,V_xs_2,T_b,V_na_2] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 112.26/112.06 => 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_na_2),V_x_2)))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_butlast__conv__take,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listrel1__iff__update,axiom, % 112.26/112.06 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 <=> ? [B_y,B_n] : % 112.26/112.06 ( 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)) % 112.26/112.06 & 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))) % 112.26/112.06 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__list__update,axiom, % 112.26/112.06 ! [V_i_2,V_a_2,V_xs_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 => ( ~ 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)))))) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__upto,axiom, % 112.26/112.06 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__take,axiom, % 112.26/112.06 ! [V_i,V_xs,T_a] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__sublistI,axiom, % 112.26/112.06 ! [V_I_2,V_xs_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__zipI2,axiom, % 112.26/112.06 ! [V_xs,T_b,V_ys,T_a] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__zipI1,axiom, % 112.26/112.06 ! [V_ys,T_b,V_xs,T_a] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct_Osimps_I2_J,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) % 112.26/112.06 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__card,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_card__distinct,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( 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) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__conv__nth,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 <=> ! [B_i] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ! [B_j] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ( B_i != B_j % 112.26/112.06 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__eq__iff__index__eq,axiom, % 112.26/112.06 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 => ( 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))) % 112.26/112.06 => ( 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))) % 112.26/112.06 => ( 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) % 112.26/112.06 <=> V_i_2 = V_j_2 ) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__listsum__conv__Setsum,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( class_Groups_Ocomm__monoid__add(T_b) % 112.26/112.06 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Nitpick_Ocard_H__def,axiom, % 112.26/112.06 ! [V_A_2,T_b] : % 112.26/112.06 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.06 => 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)))) ) % 112.26/112.06 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.06 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__take__lemma,axiom, % 112.26/112.06 ! [V_ys,V_xs,T_a,V_k] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ( 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))) % 112.26/112.06 => ( ! [B_i] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 112.26/112.06 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 112.26/112.06 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__remove1__eq,axiom, % 112.26/112.06 ! [V_x_2,V_xs_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 => 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)))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__Cons__number__of,axiom, % 112.26/112.06 ! [V_xs,V_x,T_a,V_v] : % 112.26/112.06 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 => 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) ) % 112.26/112.06 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_lists_ONil,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listrel__Nil2,axiom, % 112.26/112.06 ! [V_r_2,V_xs_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listrel__Nil1,axiom, % 112.26/112.06 ! [V_r_2,V_xs_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 => V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__butlast,axiom, % 112.26/112.06 ! [T_a,V_xs] : % 112.26/112.06 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct_Osimps_I1_J,axiom, % 112.26/112.06 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__remove1,axiom, % 112.26/112.06 ! [V_x,V_xs,T_a] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_butlast_Osimps_I1_J,axiom, % 112.26/112.06 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 112.26/112.06 % 112.26/112.06 fof(fact_butlast_Osimps_I2_J,axiom, % 112.26/112.06 ! [V_x,T_a,V_xs] : % 112.26/112.06 ( ( V_xs = c_List_Olist_ONil(T_a) % 112.26/112.06 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 112.26/112.06 & ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remove1_Osimps_I2_J,axiom, % 112.26/112.06 ! [V_xs,T_a,V_y,V_x] : % 112.26/112.06 ( ( V_x = V_y % 112.26/112.06 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 112.26/112.06 & ( V_x != V_y % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list_Osimps_I3_J,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list_Osimps_I2_J,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upto__empty,axiom, % 112.26/112.06 ! [V_i,V_j] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 112.26/112.06 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__Nil,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__eq__Nil,axiom, % 112.26/112.06 ! [V_xs_2,V_na_2,T_b] : % 112.26/112.06 ( hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2) = c_List_Olist_ONil(T_b) % 112.26/112.06 <=> ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__0,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sublist__nil,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remove1_Osimps_I1_J,axiom, % 112.26/112.06 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remove1__commute,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listrelp_ONil,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listrelp_Oequations_I1_J,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip_Osimps_I1_J,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__Nil,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__simps_I1_J,axiom, % 112.26/112.06 ! [T_a] : % 112.26/112.06 ( class_Groups_Omonoid__add(T_a) % 112.26/112.06 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__0__conv,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list_Osize_I3_J,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__empty,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.06 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__empty2,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2) % 112.26/112.06 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_List_Oset_Osimps_I1_J,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update__nonempty,axiom, % 112.26/112.06 ! [V_x_2,V_k_2,V_xs_2,T_b] : % 112.26/112.06 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b) % 112.26/112.06 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update_Osimps_I1_J,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update__code_I1_J,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list_Osize_I1_J,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remove1__idem,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_notin__set__remove1,axiom, % 112.26/112.06 ! [V_y_2,V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => ~ 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)))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_in__set__remove1,axiom, % 112.26/112.06 ! [V_xs_2,T_b,V_b_2,V_a_2] : % 112.26/112.06 ( V_a_2 != V_b_2 % 112.26/112.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2)))) % 112.26/112.06 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sublist__empty,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__remove1__subset,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__greater__0__conv,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__1__Cons,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_not__listrel1__Nil,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_not__Nil__listrel1,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listrel_ONil,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_lexord__Nil__right,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Nil2__notin__lex,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Nil__notin__lex,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__Cons,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,V_na_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_na_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_na_2) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upto_Osimps,axiom, % 112.26/112.06 ! [V_j,V_i] : % 112.26/112.06 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 112.26/112.06 => 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)) ) % 112.26/112.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 112.26/112.06 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sublist__singleton,axiom, % 112.26/112.06 ! [V_x_2,T_b,V_A_2] : % 112.26/112.06 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 112.26/112.06 => 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)) ) % 112.26/112.06 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_lists__empty,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__Cons_H,axiom, % 112.26/112.06 ! [V_xs,V_x,T_a,V_n] : % 112.26/112.06 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 => 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) ) % 112.26/112.06 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upto__rec__number__of,axiom, % 112.26/112.06 ! [V_n,V_m] : % 112.26/112.06 ( ( 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))) % 112.26/112.06 => 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))) ) % 112.26/112.06 & ( ~ 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))) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listrel__Nil,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__Cons__sing__Nil,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__remove1,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => 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)) ) % 112.26/112.06 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upto_Opsimps,axiom, % 112.26/112.06 ! [V_j_2,V_i_2] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 112.26/112.06 => 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)) ) % 112.26/112.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 112.26/112.06 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_select,axiom, % 112.26/112.06 ! [V_s_2,T_b,V_xs_2] : % 112.26/112.06 ( V_xs_2 != c_List_Olist_ONil(T_b) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listset_Osimps_I1_J,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__Cons,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list_Osimps_I5_J,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list_Osimps_I4_J,axiom, % 112.26/112.06 ! [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 ). % 112.26/112.06 % 112.26/112.06 fof(fact_listset_Osimps_I2_J,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__Cons1,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__list__of__set__remove,axiom, % 112.26/112.06 ! [V_x_2,V_A_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upto_Opinduct,axiom, % 112.26/112.06 ! [V_Pa_2,V_a1_2,V_a0_2] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ( ! [B_i,B_j] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 112.26/112.06 => 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)) ) % 112.26/112.06 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) % 112.26/112.06 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__list__of__set__empty,axiom, % 112.26/112.06 ! [T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_anamorph_Osimps,axiom, % 112.26/112.06 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] : % 112.26/112.06 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 112.26/112.06 => hAPP(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) ) % 112.26/112.06 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 112.26/112.06 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = 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))))),hAPP(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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sublist__Cons,axiom, % 112.26/112.06 ! [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)))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append1__eq__conv,axiom, % 112.26/112.06 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 <=> ( V_xs_2 = V_ys_2 % 112.26/112.06 & V_x_2 = V_y_2 ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Cons__eq__append__conv,axiom, % 112.26/112.06 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( 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) % 112.26/112.06 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 112.26/112.06 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 ) % 112.26/112.06 | ? [B_ys_H] : % 112.26/112.06 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 % 112.26/112.06 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__eq__Cons__conv,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] : % 112.26/112.06 ( 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) % 112.26/112.06 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b) % 112.26/112.06 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) % 112.26/112.06 | ? [B_ys_H] : % 112.26/112.06 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) % 112.26/112.06 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Cons__eq__appendI,axiom, % 112.26/112.06 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 112.26/112.06 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 112.26/112.06 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 112.26/112.06 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__Cons,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__in__lists__conv,axiom, % 112.26/112.06 ! [V_A_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) % 112.26/112.06 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__assoc,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__eq__append__conv2,axiom, % 112.26/112.06 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( 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) % 112.26/112.06 <=> ? [B_us] : % 112.26/112.06 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) % 112.26/112.06 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 ) % 112.26/112.06 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 % 112.26/112.06 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_same__append__eq,axiom, % 112.26/112.06 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( 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) % 112.26/112.06 <=> V_ys_2 = V_zs_2 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__same__eq,axiom, % 112.26/112.06 ! [V_zs_2,V_xs_2,V_ys_2,T_b] : % 112.26/112.06 ( 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) % 112.26/112.06 <=> V_ys_2 = V_zs_2 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__eq__appendI,axiom, % 112.26/112.06 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 112.26/112.06 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 112.26/112.06 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 112.26/112.06 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__append,axiom, % 112.26/112.06 ! [V_ys,V_xs,T_a] : % 112.26/112.06 ( class_Groups_Omonoid__add(T_a) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__append,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__append,axiom, % 112.26/112.06 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 112.26/112.06 ( 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) % 112.26/112.06 => ( 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) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__append,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_eq__Nil__appendI,axiom, % 112.26/112.06 ! [T_a,V_ys,V_xs] : % 112.26/112.06 ( V_xs = V_ys % 112.26/112.06 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__self__conv2,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2 % 112.26/112.06 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__self__conv,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2 % 112.26/112.06 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__is__Nil__conv,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b) % 112.26/112.06 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 112.26/112.06 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_self__append__conv2,axiom, % 112.26/112.06 ! [V_xs_2,T_b,V_ys_2] : % 112.26/112.06 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 112.26/112.06 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_self__append__conv,axiom, % 112.26/112.06 ! [V_ys_2,T_b,V_xs_2] : % 112.26/112.06 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 112.26/112.06 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__Nil2,axiom, % 112.26/112.06 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 112.26/112.06 % 112.26/112.06 fof(fact_Nil__is__append__conv,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) % 112.26/112.06 <=> ( V_xs_2 = c_List_Olist_ONil(T_b) % 112.26/112.06 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__Nil,axiom, % 112.26/112.06 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 112.26/112.06 % 112.26/112.06 fof(fact_butlast__append,axiom, % 112.26/112.06 ! [V_xs,T_a,V_ys] : % 112.26/112.06 ( ( V_ys = c_List_Olist_ONil(T_a) % 112.26/112.06 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 112.26/112.06 & ( V_ys != c_List_Olist_ONil(T_a) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__append__length,axiom, % 112.26/112.06 ! [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 ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__append__length__plus,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__append,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update__append1,axiom, % 112.26/112.06 ! [V_x,V_ys,V_xs,T_a,V_i] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update__length,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remove1__append,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => 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) ) % 112.26/112.06 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_in__set__butlast__appendI,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) % 112.26/112.06 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) ) % 112.26/112.06 => 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))))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_butlast__snoc,axiom, % 112.26/112.06 ! [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 ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__listrel1I,axiom, % 112.26/112.06 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( ( ( 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))) % 112.26/112.06 & V_us_2 = V_vs_2 ) % 112.26/112.06 | ( V_xs_2 = V_ys_2 % 112.26/112.06 & 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))) ) ) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_lexord__append__leftI,axiom, % 112.26/112.06 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__append,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) % 112.26/112.06 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 112.26/112.06 & 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__append,axiom, % 112.26/112.06 ! [V_ys,V_xs,T_a,V_n] : % 112.26/112.06 ( ( 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))) % 112.26/112.06 => 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) ) % 112.26/112.06 & ( ~ 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))) % 112.26/112.06 => 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))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__update__append,axiom, % 112.26/112.06 ! [V_x,V_ys,V_xs,T_a,V_n] : % 112.26/112.06 ( ( 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))) % 112.26/112.06 => 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) ) % 112.26/112.06 & ( ~ 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))) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sublist__append,axiom, % 112.26/112.06 ! [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)))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listrel1I,axiom, % 112.26/112.06 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] : % 112.26/112.06 ( 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)) % 112.26/112.06 => ( 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)) % 112.26/112.06 => ( 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)) % 112.26/112.06 => 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))) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_lexord__append__left__rightI,axiom, % 112.26/112.06 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__Suc__conv__app__nth,axiom, % 112.26/112.06 ! [V_xs,T_a,V_i] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_snoc__listrel1__snoc__iff,axiom, % 112.26/112.06 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 <=> ( ( 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))) % 112.26/112.06 & V_x_2 = V_y_2 ) % 112.26/112.06 | ( V_xs_2 = V_ys_2 % 112.26/112.06 & 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)) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listrel1E,axiom, % 112.26/112.06 ! [V_r_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ~ ! [B_x,B_y] : % 112.26/112.06 ( 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)) % 112.26/112.06 => ! [B_us,B_vs] : % 112.26/112.06 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs)) % 112.26/112.06 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_lexord__append__leftD,axiom, % 112.26/112.06 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ( ! [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)) % 112.26/112.06 => 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))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate1__def,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upd__conv__take__nth__drop,axiom, % 112.26/112.06 ! [V_a,V_xs,T_a,V_i] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__take__drop__id,axiom, % 112.26/112.06 ! [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 ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__Suc__Cons,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__1__Cons,axiom, % 112.26/112.06 ! [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 ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__via__drop,axiom, % 112.26/112.06 ! [V_ys,V_y,V_xs,V_n,T_a] : % 112.26/112.06 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 112.26/112.06 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct1__rotate,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2))) % 112.26/112.06 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__drop,axiom, % 112.26/112.06 ! [V_i,V_xs,T_a] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__butlast,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_butlast__drop,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__take,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__drop,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__0,axiom, % 112.26/112.06 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__drop,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__zip,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__rotate1,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__drop,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__rotate1,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_in__set__dropD,axiom, % 112.26/112.06 ! [V_xs_2,V_na_2,V_x_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_na_2),V_xs_2)))) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__drop__subset,axiom, % 112.26/112.06 ! [V_xs_2,V_na_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_na_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate1__is__Nil__conv,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 112.26/112.06 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__Nil,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__drop__subset__set__drop,axiom, % 112.26/112.06 ! [V_xs_2,T_b,V_m_2,V_na_2] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_m_2)) % 112.26/112.06 => 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_na_2),V_xs_2)))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__all,axiom, % 112.26/112.06 ! [V_n,V_xs,T_a] : % 112.26/112.06 ( 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)) % 112.26/112.06 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__eq__Nil,axiom, % 112.26/112.06 ! [V_xs_2,V_na_2,T_b] : % 112.26/112.06 ( hAPP(hAPP(c_List_Odrop(T_b),V_na_2),V_xs_2) = c_List_Olist_ONil(T_b) % 112.26/112.06 <=> 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_na_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__append,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__eq__conv__conj,axiom, % 112.26/112.06 ! [V_zs_2,V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2 % 112.26/112.06 <=> ( 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) % 112.26/112.06 & 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__Cons,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,V_na_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_na_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_na_2) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__Cons_H,axiom, % 112.26/112.06 ! [V_xs,V_x,T_a,V_n] : % 112.26/112.06 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 => 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) ) % 112.26/112.06 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__drop,axiom, % 112.26/112.06 ! [V_xs,T_a,V_i,V_n] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__eq__append__conv__if,axiom, % 112.26/112.06 ! [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] : % 112.26/112.06 ( 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) % 112.26/112.06 <=> ( ( 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))) % 112.26/112.06 => ( 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) % 112.26/112.06 & 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) ) ) % 112.26/112.06 & ( ~ 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))) % 112.26/112.06 => ( 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 % 112.26/112.06 & 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 ) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__drop_H,axiom, % 112.26/112.06 ! [V_xs,T_a,V_i] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate__simps,axiom, % 112.26/112.06 ! [V_xs,V_x,T_b,T_a] : % 112.26/112.06 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 112.26/112.06 & 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__Cons__number__of,axiom, % 112.26/112.06 ! [V_xs,V_x,T_a,V_v] : % 112.26/112.06 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 => 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) ) % 112.26/112.06 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__add,axiom, % 112.26/112.06 ! [V_xs,T_a,V_j,V_i] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate1__length01,axiom, % 112.26/112.06 ! [V_xs,T_a] : % 112.26/112.06 ( 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))) % 112.26/112.06 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__append2,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__append1,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_id__take__nth__drop,axiom, % 112.26/112.06 ! [V_xs,T_a,V_i] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__hd__drop,axiom, % 112.26/112.06 ! [V_xs,T_a,V_n] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_hd__drop__conv__nth,axiom, % 112.26/112.06 ! [V_n,T_a,V_xs] : % 112.26/112.06 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => ( 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))) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_hd_Osimps,axiom, % 112.26/112.06 ! [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 ). % 112.26/112.06 % 112.26/112.06 fof(fact_hd__append,axiom, % 112.26/112.06 ! [V_ys,T_a,V_xs] : % 112.26/112.06 ( ( V_xs = c_List_Olist_ONil(T_a) % 112.26/112.06 => 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) ) % 112.26/112.06 & ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_hd__append2,axiom, % 112.26/112.06 ! [V_ys,T_a,V_xs] : % 112.26/112.06 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_hd__in__set,axiom, % 112.26/112.06 ! [T_b,V_xs_2] : % 112.26/112.06 ( V_xs_2 != c_List_Olist_ONil(T_b) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_hd__conv__nth,axiom, % 112.26/112.06 ! [T_a,V_xs] : % 112.26/112.06 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate1__hd__tl,axiom, % 112.26/112.06 ! [T_a,V_xs] : % 112.26/112.06 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_hd__rotate__conv__nth,axiom, % 112.26/112.06 ! [V_n,T_a,V_xs] : % 112.26/112.06 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_tl__drop,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__tl,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_tl_Osimps_I2_J,axiom, % 112.26/112.06 ! [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 ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__rotate,axiom, % 112.26/112.06 ! [V_xs_2,V_na_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_na_2),V_xs_2))) % 112.26/112.06 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__tl,axiom, % 112.26/112.06 ! [V_xs,T_a] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate__rotate,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate0,axiom, % 112.26/112.06 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate__add,axiom, % 112.26/112.06 ! [V_na_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_na_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_na_2)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__rotate,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__rotate,axiom, % 112.26/112.06 ! [V_xs_2,V_na_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_na_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate__is__Nil__conv,axiom, % 112.26/112.06 ! [V_xs_2,V_na_2,T_b] : % 112.26/112.06 ( hAPP(c_List_Orotate(T_b,V_na_2),V_xs_2) = c_List_Olist_ONil(T_b) % 112.26/112.06 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_tl_Osimps_I1_J,axiom, % 112.26/112.06 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate1__rotate__swap,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate__def,axiom, % 112.26/112.06 ! [V_na_2,T_b] : c_List_Orotate(T_b,V_na_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_na_2),c_List_Orotate1(T_b)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_tl__append2,axiom, % 112.26/112.06 ! [V_ys,T_a,V_xs] : % 112.26/112.06 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__tl,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate__conv__mod,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__Suc,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate__Suc,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_tl__append,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate__id,axiom, % 112.26/112.06 ! [V_xs,T_a,V_n] : % 112.26/112.06 ( 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) % 112.26/112.06 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate__length01,axiom, % 112.26/112.06 ! [V_n,V_xs,T_a] : % 112.26/112.06 ( 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))) % 112.26/112.06 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__tl,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_tl__take,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__Suc,axiom, % 112.26/112.06 ! [V_n,T_a,V_xs] : % 112.26/112.06 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate__drop__take,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_fold1__set,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( class_Lattices_Oab__semigroup__idem__mult(T_b) % 112.26/112.06 => ( V_xs_2 != c_List_Olist_ONil(T_b) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_lexord__append__rightI,axiom, % 112.26/112.06 ! [V_r_2,V_x_2,T_b,V_y_2] : % 112.26/112.06 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldl__Nil,axiom, % 112.26/112.06 ! [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 ). % 112.26/112.06 % 112.26/112.06 fof(fact_start__le__sum,axiom, % 112.26/112.06 ! [V_ns_2,V_na_2,V_m_2] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) % 112.26/112.06 => 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_na_2),V_ns_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldl__absorb0,axiom, % 112.26/112.06 ! [V_zs_2,V_x_2,T_b] : % 112.26/112.06 ( class_Groups_Omonoid__add(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldl__assoc,axiom, % 112.26/112.06 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 112.26/112.06 ( class_Groups_Osemigroup__add(T_b) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldl__Cons,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldl__append,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__foldl,axiom, % 112.26/112.06 ! [T_b] : % 112.26/112.06 ( class_Groups_Omonoid__add(T_b) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sum__eq__0__conv,axiom, % 112.26/112.06 ! [V_ns_2,V_m_2] : % 112.26/112.06 ( 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) % 112.26/112.06 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 & ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 112.26/112.06 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 112.26/112.06 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Sup__set__fold,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Inf__set__fold,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Sup__fin__set__fold,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( class_Lattices_Olattice(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Inf__fin__set__fold,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( class_Lattices_Olattice(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Min__fin__set__fold,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Max__fin__set__fold,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_min__max_OInf__fin__set__fold,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_min__max_OSup__fin__set__fold,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_SUPR__set__fold,axiom, % 112.26/112.06 ! [V_f_2,V_xs_2,T_c,T_b] : % 112.26/112.06 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_INFI__set__fold,axiom, % 112.26/112.06 ! [V_f_2,V_xs_2,T_c,T_b] : % 112.26/112.06 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_elem__le__sum,axiom, % 112.26/112.06 ! [V_ns_2,V_na_2] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_na_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__list__of__set__insert,axiom, % 112.26/112.06 ! [V_x_2,V_A_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.06 => 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)))))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_lexord__Nil__left,axiom, % 112.26/112.06 ! [V_r_2,V_y_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_insort__key_Osimps_I1_J,axiom, % 112.26/112.06 ! [V_x_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_insort__key_Osimps_I2_J,axiom, % 112.26/112.06 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( ( 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))) % 112.26/112.06 => 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)) ) % 112.26/112.06 & ( ~ 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))) % 112.26/112.06 => 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)) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__insort,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__insort,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_fun__left__comm__insort,axiom, % 112.26/112.06 ! [T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_insort__left__comm,axiom, % 112.26/112.06 ! [V_xs_2,V_y_2,V_x_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_insort__key__left__comm,axiom, % 112.26/112.06 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remove1__insort,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => 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 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_insort__not__Nil,axiom, % 112.26/112.06 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__insort,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => ( 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))) % 112.26/112.06 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_insort__insert__insort__key,axiom, % 112.26/112.06 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( ~ 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)))) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_insort__insert__insort,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__insort__insert,axiom, % 112.26/112.06 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 => 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))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_insort__insert__triv,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__insort__insert,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_insort__insert__key__triv,axiom, % 112.26/112.06 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( 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)))) % 112.26/112.06 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_last__list__update,axiom, % 112.26/112.06 ! [V_x,V_k,T_a,V_xs] : % 112.26/112.06 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => ( ( 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)) % 112.26/112.06 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 112.26/112.06 & ( 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)) % 112.26/112.06 => 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) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_last__conv__nth,axiom, % 112.26/112.06 ! [T_a,V_xs] : % 112.26/112.06 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_last__ConsL,axiom, % 112.26/112.06 ! [V_x,T_a,V_xs] : % 112.26/112.06 ( V_xs = c_List_Olist_ONil(T_a) % 112.26/112.06 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_last__ConsR,axiom, % 112.26/112.06 ! [V_x,T_a,V_xs] : % 112.26/112.06 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_last_Osimps,axiom, % 112.26/112.06 ! [V_x,T_a,V_xs] : % 112.26/112.06 ( ( V_xs = c_List_Olist_ONil(T_a) % 112.26/112.06 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 112.26/112.06 & ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_last__appendL,axiom, % 112.26/112.06 ! [V_xs,T_a,V_ys] : % 112.26/112.06 ( V_ys = c_List_Olist_ONil(T_a) % 112.26/112.06 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_last__appendR,axiom, % 112.26/112.06 ! [V_xs,T_a,V_ys] : % 112.26/112.06 ( V_ys != c_List_Olist_ONil(T_a) % 112.26/112.06 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_last__append,axiom, % 112.26/112.06 ! [V_xs,T_a,V_ys] : % 112.26/112.06 ( ( V_ys = c_List_Olist_ONil(T_a) % 112.26/112.06 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 112.26/112.06 & ( V_ys != c_List_Olist_ONil(T_a) % 112.26/112.06 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_last__in__set,axiom, % 112.26/112.06 ! [T_b,V_as_2] : % 112.26/112.06 ( V_as_2 != c_List_Olist_ONil(T_b) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_last__snoc,axiom, % 112.26/112.06 ! [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 ). % 112.26/112.06 % 112.26/112.06 fof(fact_last__drop,axiom, % 112.26/112.06 ! [V_xs,T_a,V_n] : % 112.26/112.06 ( 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))) % 112.26/112.06 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_snoc__eq__iff__butlast,axiom, % 112.26/112.06 ! [V_ys_2,V_x_2,V_xs_2,T_b] : % 112.26/112.06 ( 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 % 112.26/112.06 <=> ( V_ys_2 != c_List_Olist_ONil(T_b) % 112.26/112.06 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2 % 112.26/112.06 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__butlast__last__id,axiom, % 112.26/112.06 ! [T_a,V_xs] : % 112.26/112.06 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => 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 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_lists_Osimps,axiom, % 112.26/112.06 ! [V_A_2,V_a_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2))) % 112.26/112.06 <=> ( V_a_2 = c_List_Olist_ONil(T_b) % 112.26/112.06 | ? [B_a,B_l] : % 112.26/112.06 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) % 112.26/112.06 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) % 112.26/112.06 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_select__weigth__select,axiom, % 112.26/112.06 ! [T_b,V_xs_2] : % 112.26/112.06 ( V_xs_2 != c_List_Olist_ONil(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_inj__mapI,axiom, % 112.26/112.06 ! [V_f_2,T_c,T_b] : % 112.26/112.06 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_last__map,axiom, % 112.26/112.06 ! [V_f_2,T_c,T_b,V_xs_2] : % 112.26/112.06 ( V_xs_2 != c_List_Olist_ONil(T_b) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldl__map,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__tl,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rotate__map,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,T_c,V_na_2,T_b] : hAPP(c_List_Orotate(T_b,V_na_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_na_2),V_xs_2)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__same__conv__map,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__map__map,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__map1,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__zip__map,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__zip__map2,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__map2,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Nil__is__map__conv,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) % 112.26/112.06 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map_Osimps_I1_J,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__is__Nil__conv,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b) % 112.26/112.06 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__update,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__eq__conv,axiom, % 112.26/112.06 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( 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) % 112.26/112.06 <=> ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) % 112.26/112.06 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__eq__imp__length__eq,axiom, % 112.26/112.06 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( 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) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__map,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__addf,axiom, % 112.26/112.06 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( class_Groups_Ocomm__monoid__add(T_b) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__0,axiom, % 112.26/112.06 ! [V_xs_2,T_c,T_b] : % 112.26/112.06 ( class_Groups_Omonoid__add(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__const__mult,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] : % 112.26/112.06 ( class_Rings_Osemiring__0(T_b) % 112.26/112.06 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__mult__const,axiom, % 112.26/112.06 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( class_Rings_Osemiring__0(T_b) % 112.26/112.06 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__subtractf,axiom, % 112.26/112.06 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( class_Groups_Oab__group__add(T_b) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__injective,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( 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) % 112.26/112.06 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.06 => V_xs_2 = V_ys_2 ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_inj__map__eq__map,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.06 => ( 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) % 112.26/112.06 <=> V_xs_2 = V_ys_2 ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__ident,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__map,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,T_c,V_na_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_na_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_na_2),V_xs_2)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__butlast,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__map,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map_Osimps_I2_J,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__append,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_hd__map,axiom, % 112.26/112.06 ! [V_f_2,T_c,T_b,V_xs_2] : % 112.26/112.06 ( V_xs_2 != c_List_Olist_ONil(T_b) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__map,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,T_c,V_na_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_na_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_na_2),V_xs_2)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_List_Omap_Oidentity,axiom, % 112.26/112.06 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__map,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_List_Omap_Ocompositionality,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__comp__map,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_List_Omap_Ocomp,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__size__map,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_List_Omap_Oid,axiom, % 112.26/112.06 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_inj__on__map__eq__map,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ( 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) % 112.26/112.06 <=> V_xs_2 = V_ys_2 ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__inj__on,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( 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) % 112.26/112.06 => ( 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))) % 112.26/112.06 => V_xs_2 = V_ys_2 ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__map,axiom, % 112.26/112.06 ! [V_f_2,T_c,V_xs_2,T_b,V_na_2] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 112.26/112.06 => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_na_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_na_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__fun__upd,axiom, % 112.26/112.06 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] : % 112.26/112.06 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => hAPP(hAPP(c_List_Omap(T_b,T_c),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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__map,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) % 112.26/112.06 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) % 112.26/112.06 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__abs,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( class_Groups_Oordered__ab__group__add__abs(T_b) % 112.26/112.06 => 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)))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_uminus__listsum__map,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( class_Groups_Oab__group__add(T_b) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_inj__on__mapI,axiom, % 112.26/112.06 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_inj__map,axiom, % 112.26/112.06 ! [V_f_2,T_c,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_inj__mapD,axiom, % 112.26/112.06 ! [V_f_2,T_c,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 112.26/112.06 ! [V_f_2,V_xs_2,T_b,T_c] : % 112.26/112.06 ( class_Groups_Ocomm__monoid__add(T_c) % 112.26/112.06 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__triv,axiom, % 112.26/112.06 ! [V_xs_2,V_r_2,T_c,T_b] : % 112.26/112.06 ( class_Rings_Osemiring__1(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__map__remove1,axiom, % 112.26/112.06 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] : % 112.26/112.06 ( class_Groups_Ocomm__monoid__add(T_c) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => 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)))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Nitpick_Osetsum_H__def,axiom, % 112.26/112.06 ! [V_f_2,V_A_2,T_b,T_c] : % 112.26/112.06 ( class_Groups_Ocomm__monoid__add(T_c) % 112.26/112.06 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.06 => 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))))) ) % 112.26/112.06 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.06 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_pick__same,axiom, % 112.26/112.06 ! [V_xs_2,T_b,V_l_2] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_times__code__numeral__code,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 112.26/112.06 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 112.26/112.06 ! [V_m_2,V_na_2] : % 112.26/112.06 ( hAPP(c_Code__Numeral_Oof__nat,V_na_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 112.26/112.06 <=> V_na_2 = V_m_2 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zero__code__numeral__def,axiom, % 112.26/112.06 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_one__code__numeral__def,axiom, % 112.26/112.06 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_less__code__numeral__code,axiom, % 112.26/112.06 ! [V_m_2,V_na_2] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_na_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) % 112.26/112.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_code__numeral_Oof__nat__inject,axiom, % 112.26/112.06 ! [V_y_2,V_x_2] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 112.26/112.06 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 112.26/112.06 <=> V_x_2 = V_y_2 ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__fst__zip,axiom, % 112.26/112.06 ! [V_ys_2,T_c,V_xs_2,T_b] : % 112.26/112.06 ( 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) % 112.26/112.06 => 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 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__snd__zip,axiom, % 112.26/112.06 ! [V_ys_2,T_c,V_xs_2,T_b] : % 112.26/112.06 ( 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) % 112.26/112.06 => 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 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_number__of__code__numeral__def,axiom, % 112.26/112.06 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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__map__fst__snd,axiom, % 112.26/112.06 ! [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 ). % 112.26/112.06 % 112.26/112.06 fof(fact_plus__code__numeral__code,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_less__eq__code__numeral__code,axiom, % 112.26/112.06 ! [V_m_2,V_na_2] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_na_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) % 112.26/112.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_m_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_subtract__code__numeral__code,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_pick__member,axiom, % 112.26/112.06 ! [V_xs_2,T_b,V_i_2] : % 112.26/112.06 ( 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)))) % 112.26/112.06 => 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)))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__eq__conv,axiom, % 112.26/112.06 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] : % 112.26/112.06 ( 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) % 112.26/112.06 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2 % 112.26/112.06 <=> ( 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 % 112.26/112.06 & 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 ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__size__conv__listsum,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_code__numeral__not__eq__zero,axiom, % 112.26/112.06 ! [V_i_2] : % 112.26/112.06 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 112.26/112.06 <=> 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 112.26/112.06 ! [V_l_2,V_k_2,V_f_2,T_b] : % 112.26/112.06 ( class_Groups_Ocomm__monoid__add(T_b) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 112.26/112.06 ! [V_j_2,V_i_2,V_f_2,T_b] : % 112.26/112.06 ( class_Groups_Ocomm__monoid__add(T_b) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_select__weight__member,axiom, % 112.26/112.06 ! [V_s_2,V_xs_2,T_b] : % 112.26/112.06 ( 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)))) % 112.26/112.06 => 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)))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_select__weight__def,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_select__def,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsum__mono,axiom, % 112.26/112.06 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] : % 112.26/112.06 ( ( class_Groups_Omonoid__add(T_c) % 112.26/112.06 & class_Groups_Oordered__ab__semigroup__add(T_c) ) % 112.26/112.06 => ( ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 112.26/112.06 => 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)))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nat__of__of__nat,axiom, % 112.26/112.06 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 112.26/112.06 % 112.26/112.06 fof(fact_of__nat__nat__of,axiom, % 112.26/112.06 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 112.26/112.06 % 112.26/112.06 fof(fact_nat__of__inverse,axiom, % 112.26/112.06 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 112.26/112.06 % 112.26/112.06 fof(fact_code__numeral_Onat__of__inject,axiom, % 112.26/112.06 ! [V_y_2,V_x_2] : % 112.26/112.06 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 112.26/112.06 <=> V_x_2 = V_y_2 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 112.26/112.06 ! [V_l_2,V_k_2] : % 112.26/112.06 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 112.26/112.06 <=> V_k_2 = V_l_2 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_times__code__numeral__def,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_type__definition__code__numeral,axiom, % 112.26/112.06 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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_less__code__numeral__def,axiom, % 112.26/112.06 ! [V_m_2,V_na_2] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_na_2),V_m_2)) % 112.26/112.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_na_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nat__of,axiom, % 112.26/112.06 ! [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)))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nat__of__number,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_int__of__def,axiom, % 112.26/112.06 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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_less__eq__code__numeral__def,axiom, % 112.26/112.06 ! [V_m_2,V_na_2] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_na_2),V_m_2)) % 112.26/112.06 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_na_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nat__of__code,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nat__of__aux__def,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Suc__code__numeral__def,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_minus__code__numeral__def,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_of__nat__inverse,axiom, % 112.26/112.06 ! [V_y_2] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 112.26/112.06 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_plus__code__numeral__def,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_div__code__numeral__def,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_mod__code__numeral__def,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_code__numeral__decr,axiom, % 112.26/112.06 ! [V_k] : % 112.26/112.06 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_partition__set,axiom, % 112.26/112.06 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 112.26/112.06 ( 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) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_partition__P,axiom, % 112.26/112.06 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] : % 112.26/112.06 ( 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) % 112.26/112.06 => ( ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2))) % 112.26/112.06 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.06 & ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2))) % 112.26/112.06 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_partition_Osimps_I1_J,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_partition_Osimps_I2_J,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_lists__Int__eq,axiom, % 112.26/112.06 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,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_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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(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_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(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))),c_List_Olists(T_b,V_B_2))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_lists__IntI,axiom, % 112.26/112.06 ! [V_B_2,V_A_2,V_l_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2))) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2))) % 112.26/112.06 => hBOOL(hAPP(c_List_Olistsp(T_b,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_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))),V_l_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsp_ONil,axiom, % 112.26/112.06 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsp_Oequations_I1_J,axiom, % 112.26/112.06 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_in__listsp__conv__set,axiom, % 112.26/112.06 ! [V_xs_2,V_A_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) % 112.26/112.06 <=> ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsp__conj__eq,axiom, % 112.26/112.06 ! [V_x_2,V_B_2,V_A_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Olistsp(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_A_2)),V_B_2)),V_x_2)) % 112.26/112.06 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2)) % 112.26/112.06 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsp__infI,axiom, % 112.26/112.06 ! [V_B_2,V_l_2,V_A_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2)) % 112.26/112.06 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2)) % 112.26/112.06 => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsp__inf__eq,axiom, % 112.26/112.06 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(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_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsp_Oequations_I2_J,axiom, % 112.26/112.06 ! [V_a2_2,V_a1_2,V_A_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2))) % 112.26/112.06 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 112.26/112.06 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_append__in__listsp__conv,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_A_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) % 112.26/112.06 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) % 112.26/112.06 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsp__mono,axiom, % 112.26/112.06 ! [V_B_2,V_A_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_listsp__lists__eq,axiom, % 112.26/112.06 ! [V_x_2,V_A_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Olistsp(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)) % 112.26/112.06 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_product_Osimps_I2_J,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : c_Enum_Oproduct(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_b,T_c)),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__def,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 112.26/112.06 <=> ( 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) % 112.26/112.06 & ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),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)))) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__map1,axiom, % 112.26/112.06 ! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2) % 112.26/112.06 <=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_Pa_2),V_f_2),V_as_2,V_bs_2) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__map2,axiom, % 112.26/112.06 ! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2)) % 112.26/112.06 <=> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_Pa_2)),V_f_2),V_as_2,V_bs_2) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__dropI,axiom, % 112.26/112.06 ! [V_na_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2) % 112.26/112.06 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Odrop(T_b),V_na_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_na_2),V_bs_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__appendI,axiom, % 112.26/112.06 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) % 112.26/112.06 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_c_2,V_d_2) % 112.26/112.06 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__append,axiom, % 112.26/112.06 ! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] : % 112.26/112.06 ( 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) % 112.26/112.06 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2)) % 112.26/112.06 <=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 112.26/112.06 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__Cons,axiom, % 112.26/112.06 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) % 112.26/112.06 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 112.26/112.06 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__takeI,axiom, % 112.26/112.06 ! [V_na_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 112.26/112.06 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_na_2),V_ys_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__eq,axiom, % 112.26/112.06 ! [T_b,V_ys_2,V_xs_2] : % 112.26/112.06 ( V_xs_2 = V_ys_2 % 112.26/112.06 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__lengthD,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__Nil2,axiom, % 112.26/112.06 ! [V_xs_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_c)) % 112.26/112.06 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__Nil,axiom, % 112.26/112.06 ! [V_ys_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,c_List_Olist_ONil(T_b),V_ys_2) % 112.26/112.06 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_product_Osimps_I1_J,axiom, % 112.26/112.06 ! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__conv__all__nth,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 112.26/112.06 <=> ( 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) % 112.26/112.06 & ! [B_i] : % 112.26/112.06 ( 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))) % 112.26/112.06 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__nthD,axiom, % 112.26/112.06 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 112.26/112.06 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__nthD2,axiom, % 112.26/112.06 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))) % 112.26/112.06 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__update__cong,axiom, % 112.26/112.06 ! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_c,V_xs_2,T_b,V_i_2] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 112.26/112.06 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__update__cong2,axiom, % 112.26/112.06 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) % 112.26/112.06 => ( 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))) % 112.26/112.06 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__product,axiom, % 112.26/112.06 ! [V_ys,T_b,V_xs,T_a] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 112.26/112.06 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_product__list__set,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_List_Oset(T_c),V_ys_2))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sublists__powset,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__sublists,axiom, % 112.26/112.06 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sublists_Osimps_I1_J,axiom, % 112.26/112.06 ! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sublists_Osimps_I2_J,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : c_Enum_Osublists(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_Enum_Osublists(T_b,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_b)),tc_fun(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(tc_List_Olist(T_b))),c_List_Oappend(tc_List_Olist(T_b))),hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_b))))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__set__sublists,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__n__lists,axiom, % 112.26/112.06 ! [V_xs_2,V_na_2,T_b] : hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_na_2,V_xs_2)) = 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_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_na_2))),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))),hAPP(c_List_Oset(T_b),V_xs_2)))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_enum__the__def,axiom, % 112.26/112.06 ! [V_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__n__lists,axiom, % 112.26/112.06 ! [V_n,V_xs,T_a] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_n__lists__Nil,axiom, % 112.26/112.06 ! [T_a,V_n] : % 112.26/112.06 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ) % 112.26/112.06 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_n__lists_Osimps_I1_J,axiom, % 112.26/112.06 ! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__n__lists,axiom, % 112.26/112.06 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__n__lists__elem,axiom, % 112.26/112.06 ! [V_xs_2,V_na_2,V_ys_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_na_2,V_xs_2)))) % 112.26/112.06 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_na_2 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2I,axiom, % 112.26/112.06 ! [V_Pa_2,V_b_2,V_a_2,T_c,T_b] : % 112.26/112.06 ( ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_a_2),V_b_2)))) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) % 112.26/112.06 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2) % 112.26/112.06 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_all__nth__imp__all__set,axiom, % 112.26/112.06 ! [V_x_2,V_Pa_2,V_xs_2,T_b] : % 112.26/112.06 ( ! [B_i] : % 112.26/112.06 ( 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))) % 112.26/112.06 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 112.26/112.06 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) % 112.26/112.06 => 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),c_List_Oremdups(T_b,V_xs_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__removeAll__inj__on,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__remdups,axiom, % 112.26/112.06 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__remdups__leq,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remdups__id__iff__distinct,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2 % 112.26/112.06 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__removeAll,axiom, % 112.26/112.06 ! [V_x,V_xs,T_a] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__remdups__id,axiom, % 112.26/112.06 ! [V_xs,T_a] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 112.26/112.06 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__remdups,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__remdups__eq,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 112.26/112.06 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remdups__remdups,axiom, % 112.26/112.06 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remdups_Osimps_I1_J,axiom, % 112.26/112.06 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remdups__eq__nil__right__iff,axiom, % 112.26/112.06 ! [V_x_2,T_b] : % 112.26/112.06 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2) % 112.26/112.06 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_removeAll_Osimps_I1_J,axiom, % 112.26/112.06 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remdups__eq__nil__iff,axiom, % 112.26/112.06 ! [V_x_2,T_b] : % 112.26/112.06 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b) % 112.26/112.06 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_removeAll_Osimps_I2_J,axiom, % 112.26/112.06 ! [V_xs,T_a,V_y,V_x] : % 112.26/112.06 ( ( V_x = V_y % 112.26/112.06 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) % 112.26/112.06 & ( V_x != V_y % 112.26/112.06 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_removeAll__append,axiom, % 112.26/112.06 ! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remdups__map__remdups,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remove1__remdups,axiom, % 112.26/112.06 ! [V_x,V_xs,T_a] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 112.26/112.06 => c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_removeAll__id,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__remove1__removeAll,axiom, % 112.26/112.06 ! [V_x,V_xs,T_a] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 112.26/112.06 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remdups_Osimps_I2_J,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) ) % 112.26/112.06 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => c_List_Oremdups(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),c_List_Oremdups(T_b,V_xs_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__remdups__card__conv,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__removeAll__inj,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.06 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__removeAll,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_OremoveAll(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)))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__remdups__concat,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),c_List_Oremdups(T_b,V_xs_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sort__key__simps_I1_J,axiom, % 112.26/112.06 ! [V_f_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldl__conv__concat,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_concat__conv__foldl,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__sort,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__sort,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__sort,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2))) % 112.26/112.06 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_concat_Osimps_I1_J,axiom, % 112.26/112.06 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 112.26/112.06 % 112.26/112.06 fof(fact_concat_Osimps_I2_J,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Nil__eq__concat__conv,axiom, % 112.26/112.06 ! [V_xss_2,T_b] : % 112.26/112.06 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2) % 112.26/112.06 <=> ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 112.26/112.06 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_concat__eq__Nil__conv,axiom, % 112.26/112.06 ! [V_xss_2,T_b] : % 112.26/112.06 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b) % 112.26/112.06 <=> ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) % 112.26/112.06 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__concat,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__concat,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__concat,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sort__key__simps_I2_J,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_concat__append,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sort__foldl__insort,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(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_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))),c_List_Olist_ONil(T_b)),V_xs_2) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_concat__eq__concat__iff,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( ! [B_x] : % 112.26/112.06 ( 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)))) % 112.26/112.06 => 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)) ) % 112.26/112.06 => ( 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) % 112.26/112.06 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 112.26/112.06 <=> V_xs_2 = V_ys_2 ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_concat__injective,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) % 112.26/112.06 => ( 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) % 112.26/112.06 => ( ! [B_x] : % 112.26/112.06 ( 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)))) % 112.26/112.06 => 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)) ) % 112.26/112.06 => V_xs_2 = V_ys_2 ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_concat__map__singleton,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_n__lists_Osimps_I2_J,axiom, % 112.26/112.06 ! [V_xs_2,V_na_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_na_2),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))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_na_2,V_xs_2))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose_Osimps_I3_J,axiom, % 112.26/112.06 ! [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))))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose__aux__filter__head,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter__concat,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter__sort,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,V_Pa_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__filter,axiom, % 112.26/112.06 ! [V_Pa_2,V_xs_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sum__length__filter__compl,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter__is__subset,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter__id__conv,axiom, % 112.26/112.06 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.06 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2 % 112.26/112.06 <=> ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__filter__le,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter__filter,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remove1__filter__not,axiom, % 112.26/112.06 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 112.26/112.06 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter__remove1,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter__insort__triv,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_partition__filter1,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_partition__filter2,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_partition__filter__conv,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter__map,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose_Osimps_I1_J,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter_Osimps_I1_J,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter_Osimps_I2_J,axiom, % 112.26/112.06 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 112.26/112.06 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.06 => 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)) ) % 112.26/112.06 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter__append,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter__empty__conv,axiom, % 112.26/112.06 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.06 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b) % 112.26/112.06 <=> ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__filter__map,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_removeAll__filter__not,axiom, % 112.26/112.06 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 112.26/112.06 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.06 => hAPP(c_List_OremoveAll(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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_remdups__filter,axiom, % 112.26/112.06 ! [V_xs_2,V_Pa_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_removeAll__filter__not__eq,axiom, % 112.26/112.06 ! [V_x_2,T_b] : c_List_OremoveAll(T_b,V_x_2) = c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(c_fequal,V_x_2))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose_Osimps_I2_J,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__transpose,axiom, % 112.26/112.06 ! [V_xs_2,T_b,V_i_2] : % 112.26/112.06 ( 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)))) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose__map__map,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__filter,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__filter__less,axiom, % 112.26/112.06 ! [V_Pa_2,V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.06 => 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))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__minus__filter__out,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter__in__sublist,axiom, % 112.26/112.06 ! [V_s_2,V_xs_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose__empty,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b)) % 112.26/112.06 <=> ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 112.26/112.06 => B_x = c_List_Olist_ONil(T_b) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__filter__conv__card,axiom, % 112.26/112.06 ! [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))))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose__aux__filter__tail,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose_Opsimps_I3_J,axiom, % 112.26/112.06 ! [V_xss_2,V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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))))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose_Opsimps_I2_J,axiom, % 112.26/112.06 ! [V_xss_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sublist__shift__lemma__Suc,axiom, % 112.26/112.06 ! [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)))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_select__weigth__drop__zero,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_pick__drop__zero,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose_Opsimps_I1_J,axiom, % 112.26/112.06 ! [T_b] : % 112.26/112.06 ( 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)))) % 112.26/112.06 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose__max__length,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose__aux__max,axiom, % 112.26/112.06 ! [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)))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldr_Osimps_I1_J,axiom, % 112.26/112.06 ! [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 ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldr_Osimps_I2_J,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldr__append,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldr__conv__foldl,axiom, % 112.26/112.06 ! [V_a_2,V_xs_2,T_b] : % 112.26/112.06 ( class_Groups_Oab__semigroup__add(T_b) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldr__map,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldl__foldr1__lemma,axiom, % 112.26/112.06 ! [V_xs_2,V_a_2,T_b] : % 112.26/112.06 ( class_Groups_Omonoid__add(T_b) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_foldl__foldr1,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( class_Groups_Omonoid__add(T_b) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__transpose,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sublist__def,axiom, % 112.26/112.06 ! [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))))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sublist__shift__lemma,axiom, % 112.26/112.06 ! [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))))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__upt,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_atLeastLessThan__upt,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upt__Suc__append,axiom, % 112.26/112.06 ! [V_j,V_i] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upt__Suc,axiom, % 112.26/112.06 ! [V_j,V_i] : % 112.26/112.06 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 112.26/112.06 => 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))) ) % 112.26/112.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 112.26/112.06 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upt__add__eq__append,axiom, % 112.26/112.06 ! [V_k,V_j,V_i] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upt__rec,axiom, % 112.26/112.06 ! [V_j,V_i] : % 112.26/112.06 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 112.26/112.06 => 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)) ) % 112.26/112.06 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 112.26/112.06 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upt__conv__Cons,axiom, % 112.26/112.06 ! [V_j,V_i] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upt__eq__Nil__conv,axiom, % 112.26/112.06 ! [V_j_2,V_i_2] : % 112.26/112.06 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 112.26/112.06 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.06 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upt__conv__Nil,axiom, % 112.26/112.06 ! [V_i,V_j] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 112.26/112.06 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upt__0,axiom, % 112.26/112.06 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 112.26/112.06 % 112.26/112.06 fof(fact_take__upt,axiom, % 112.26/112.06 ! [V_n,V_m,V_i] : % 112.26/112.06 ( 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)) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__list__of__set__range,axiom, % 112.26/112.06 ! [V_na_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_na_2)) = c_List_Oupt(V_m_2,V_na_2) ). % 112.26/112.06 % 112.26/112.06 fof(fact_hd__upt,axiom, % 112.26/112.06 ! [V_j,V_i] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 112.26/112.06 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_drop__upt,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__upt,axiom, % 112.26/112.06 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_length__upt,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upt__rec__number__of,axiom, % 112.26/112.06 ! [V_n,V_m] : % 112.26/112.06 ( ( 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))) % 112.26/112.06 => 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))) ) % 112.26/112.06 & ( ~ 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))) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_upt__eq__Cons__conv,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 112.26/112.06 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 112.26/112.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 112.26/112.06 & V_i_2 = V_x_2 % 112.26/112.06 & 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 ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_last__upt,axiom, % 112.26/112.06 ! [V_j,V_i] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__Suc__upt,axiom, % 112.26/112.06 ! [V_na_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_na_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_na_2)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_atLeastAtMost__upt,axiom, % 112.26/112.06 ! [V_m_2,V_na_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_na_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_na_2,hAPP(c_Nat_OSuc,V_m_2))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_atLeast__upt,axiom, % 112.26/112.06 ! [V_na_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__upt,axiom, % 112.26/112.06 ! [V_j,V_k,V_i] : % 112.26/112.06 ( 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)) % 112.26/112.06 => 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) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_greaterThanAtMost__upt,axiom, % 112.26/112.06 ! [V_m_2,V_na_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_na_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_na_2),hAPP(c_Nat_OSuc,V_m_2))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_greaterThanLessThan__upt,axiom, % 112.26/112.06 ! [V_m_2,V_na_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_na_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_na_2),V_m_2)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_atMost__upto,axiom, % 112.26/112.06 ! [V_na_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__nth,axiom, % 112.26/112.06 ! [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 ). % 112.26/112.06 % 112.26/112.06 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 112.26/112.06 ! [V_na_2,V_m_2,V_f_2,T_b] : % 112.26/112.06 ( class_Groups_Ocomm__monoid__add(T_b) % 112.26/112.06 => 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_na_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_na_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 112.26/112.06 ! [V_na_2,V_m_2,V_f_2,T_b] : % 112.26/112.06 ( class_Groups_Ocomm__monoid__add(T_b) % 112.26/112.06 => 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_na_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_na_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__map__upt,axiom, % 112.26/112.06 ! [V_f_2,T_b,V_m_2,V_na_2,V_i_2] : % 112.26/112.06 ( 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_na_2),V_m_2))) % 112.26/112.06 => 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_na_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose__rectangle,axiom, % 112.26/112.06 ! [V_na_2,T_b,V_xs_2] : % 112.26/112.06 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 112.26/112.06 => V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 112.26/112.06 => ( ! [B_i] : % 112.26/112.06 ( 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))) % 112.26/112.06 => 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_na_2 ) % 112.26/112.06 => 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_na_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_insort__key__remove1,axiom, % 112.26/112.06 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 112.26/112.06 => ( 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 % 112.26/112.06 => 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 ) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted_ONil,axiom, % 112.26/112.06 ! [T_a] : % 112.26/112.06 ( class_Orderings_Olinorder(T_a) % 112.26/112.06 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__single,axiom, % 112.26/112.06 ! [V_x,T_a] : % 112.26/112.06 ( class_Orderings_Olinorder(T_a) % 112.26/112.06 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__upt,axiom, % 112.26/112.06 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__sort,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__insort__insert,axiom, % 112.26/112.06 ! [V_x_2,V_xs_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 112.26/112.06 => 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)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__drop,axiom, % 112.26/112.06 ! [V_n,V_xs,T_a] : % 112.26/112.06 ( class_Orderings_Olinorder(T_a) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 112.26/112.06 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__upto,axiom, % 112.26/112.06 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__take,axiom, % 112.26/112.06 ! [V_n,V_xs,T_a] : % 112.26/112.06 ( class_Orderings_Olinorder(T_a) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 112.26/112.06 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__remove1,axiom, % 112.26/112.06 ! [V_a,V_xs,T_a] : % 112.26/112.06 ( class_Orderings_Olinorder(T_a) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 112.26/112.06 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__tl,axiom, % 112.26/112.06 ! [V_xs,T_a] : % 112.26/112.06 ( class_Orderings_Olinorder(T_a) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 112.26/112.06 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__insort,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( 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)) % 112.26/112.06 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__butlast,axiom, % 112.26/112.06 ! [V_xs,T_a] : % 112.26/112.06 ( class_Orderings_Olinorder(T_a) % 112.26/112.06 => ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 112.26/112.06 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted_Oequations_I1_J,axiom, % 112.26/112.06 ! [T_a] : % 112.26/112.06 ( class_Orderings_Olinorder(T_a) % 112.26/112.06 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__many,axiom, % 112.26/112.06 ! [V_zs,V_y,V_x,T_a] : % 112.26/112.06 ( class_Orderings_Olinorder(T_a) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 112.26/112.06 => 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))) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__many__eq,axiom, % 112.26/112.06 ! [V_zs_2,V_y_2,V_x_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( 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))) % 112.26/112.06 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) % 112.26/112.06 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__remdups,axiom, % 112.26/112.06 ! [V_l,T_a] : % 112.26/112.06 ( class_Orderings_Olinorder(T_a) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 112.26/112.06 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__distinct__set__unique,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 112.26/112.06 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 112.26/112.06 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) % 112.26/112.06 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 112.26/112.06 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__sort__key,axiom, % 112.26/112.06 ! [V_xs_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Osort__key(T_c,T_b,V_f_2,V_xs_2))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__insort__insert__key,axiom, % 112.26/112.06 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 112.26/112.06 => 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))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__map__remove1,axiom, % 112.26/112.06 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 112.26/112.06 => 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))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__insort__key,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( 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))) % 112.26/112.06 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__filter,axiom, % 112.26/112.06 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 112.26/112.06 => 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))) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__map__same,axiom, % 112.26/112.06 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => 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))) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__same,axiom, % 112.26/112.06 ! [V_xs_2,V_g_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__Cons,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 112.26/112.06 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 112.26/112.06 & ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__append,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 112.26/112.06 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 112.26/112.06 & c_List_Olinorder__class_Osorted(T_b,V_ys_2) % 112.26/112.06 & ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => ! [B_xa] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2))) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_filter__insort,axiom, % 112.26/112.06 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) % 112.26/112.06 => ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.06 => 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)) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted_Oequations_I2_J,axiom, % 112.26/112.06 ! [V_a1_2,V_a2_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2)) % 112.26/112.06 <=> ( ! [B_x] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2))) % 112.26/112.06 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) % 112.26/112.06 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__list__of__set,axiom, % 112.26/112.06 ! [V_A_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.06 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 % 112.26/112.06 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) % 112.26/112.06 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_insort__remove1,axiom, % 112.26/112.06 ! [V_xs_2,V_a_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 112.26/112.06 => 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 ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__nth__mono,axiom, % 112.26/112.06 ! [V_j,V_i,V_xs,T_a] : % 112.26/112.06 ( class_Orderings_Olinorder(T_a) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 112.26/112.06 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 112.26/112.06 => ( 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))) % 112.26/112.06 => 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))) ) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_sorted__equals__nth__mono,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( class_Orderings_Olinorder(T_b) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 112.26/112.06 <=> ! [B_j] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ! [B_i] : % 112.26/112.06 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 112.26/112.06 => 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))) ) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_map__sorted__distinct__set__unique,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : % 112.26/112.06 ( class_Orderings_Olinorder(T_c) % 112.26/112.06 => ( 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))) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) % 112.26/112.06 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))) % 112.26/112.06 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)) % 112.26/112.06 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))) % 112.26/112.06 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) % 112.26/112.06 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_transpose__column,axiom, % 112.26/112.06 ! [V_i_2,V_xs_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ( 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))) % 112.26/112.06 => 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) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_nth__nth__transpose__sorted,axiom, % 112.26/112.06 ! [V_j_2,V_i_2,V_xs_2,T_b] : % 112.26/112.06 ( 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))) % 112.26/112.06 => ( 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)))) % 112.26/112.06 => ( 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)))) % 112.26/112.06 => 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) ) ) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_inj__on__rev,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_distinct__rev,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2))) % 112.26/112.06 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rev_Osimps_I1_J,axiom, % 112.26/112.06 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 112.26/112.06 % 112.26/112.06 fof(fact_Nil__is__rev__conv,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2) % 112.26/112.06 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rev__is__Nil__conv,axiom, % 112.26/112.06 ! [V_xs_2,T_b] : % 112.26/112.06 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b) % 112.26/112.06 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rev__singleton__conv,axiom, % 112.26/112.06 ! [V_x_2,V_xs_2,T_b] : % 112.26/112.06 ( 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)) % 112.26/112.06 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_singleton__rev__conv,axiom, % 112.26/112.06 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.06 ( 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) % 112.26/112.06 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rev__append,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rev__concat,axiom, % 112.26/112.06 ! [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))) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rev__map,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_rev__filter,axiom, % 112.26/112.06 ! [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)) ). % 112.26/112.06 % 112.26/112.06 fof(fact_zip__rev,axiom, % 112.26/112.06 ! [V_ys,T_b,V_xs,T_a] : % 112.26/112.06 ( 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) % 112.26/112.06 => 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)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_set__rev,axiom, % 112.26/112.06 ! [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) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__rev1,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2) % 112.26/112.06 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ). % 112.26/112.06 % 112.26/112.06 fof(fact_list__all2__rev,axiom, % 112.26/112.06 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : % 112.26/112.06 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2)) % 112.26/112.06 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ). % 112.26/112.06 % 112.26/112.07 fof(fact_rev__is__rev__conv,axiom, % 112.26/112.07 ! [V_ys_2,V_xs_2,T_b] : % 112.26/112.07 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2) % 112.26/112.07 <=> V_xs_2 = V_ys_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_rev__swap,axiom, % 112.26/112.07 ! [V_ys_2,V_xs_2,T_b] : % 112.26/112.07 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2 % 112.26/112.07 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_rev__rev__ident,axiom, % 112.26/112.07 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 112.26/112.07 % 112.26/112.07 fof(fact_listsum__rev,axiom, % 112.26/112.07 ! [V_xs,T_a] : % 112.26/112.07 ( class_Groups_Ocomm__monoid__add(T_a) % 112.26/112.07 => 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) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_length__rev,axiom, % 112.26/112.07 ! [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) ). % 112.26/112.07 % 112.26/112.07 fof(fact_foldl__foldr,axiom, % 112.26/112.07 ! [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) ). % 112.26/112.07 % 112.26/112.07 fof(fact_foldr__foldl,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_rev_Osimps_I2_J,axiom, % 112.26/112.07 ! [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))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_rev__eq__Cons__iff,axiom, % 112.26/112.07 ! [V_ys_2,V_y_2,V_xs_2,T_b] : % 112.26/112.07 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) % 112.26/112.07 <=> 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))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_last__rev,axiom, % 112.26/112.07 ! [T_a,V_xs] : % 112.26/112.07 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.07 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_hd__rev,axiom, % 112.26/112.07 ! [T_a,V_xs] : % 112.26/112.07 ( V_xs != c_List_Olist_ONil(T_a) % 112.26/112.07 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sorted__transpose,axiom, % 112.26/112.07 ! [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)))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_rev__foldl__cons,axiom, % 112.26/112.07 ! [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) ). % 112.26/112.07 % 112.26/112.07 fof(fact_rev__drop,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_rev__take,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_rotate__rev,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_rev__nth,axiom, % 112.26/112.07 ! [V_xs,T_a,V_n] : % 112.26/112.07 ( 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))) % 112.26/112.07 => 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))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_rev__update,axiom, % 112.26/112.07 ! [V_y,V_xs,T_a,V_k] : % 112.26/112.07 ( 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))) % 112.26/112.07 => 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) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sorted__rev__nth__mono,axiom, % 112.26/112.07 ! [V_j,V_i,V_xs,T_a] : % 112.26/112.07 ( class_Orderings_Olinorder(T_a) % 112.26/112.07 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 112.26/112.07 => ( 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))) % 112.26/112.07 => 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))) ) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_foldr__max__sorted,axiom, % 112.26/112.07 ! [V_y_2,V_xs_2,T_b] : % 112.26/112.07 ( class_Orderings_Olinorder(T_b) % 112.26/112.07 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2)) % 112.26/112.07 => ( ( V_xs_2 = c_List_Olist_ONil(T_b) % 112.26/112.07 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 ) % 112.26/112.07 & ( V_xs_2 != c_List_Olist_ONil(T_b) % 112.26/112.07 => 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) ) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_length__transpose__sorted,axiom, % 112.26/112.07 ! [V_xs_2,T_b] : % 112.26/112.07 ( 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))) % 112.26/112.07 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) % 112.26/112.07 => 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) ) % 112.26/112.07 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b)) % 112.26/112.07 => 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))) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_transpose__column__length,axiom, % 112.26/112.07 ! [V_i_2,V_xs_2,T_b] : % 112.26/112.07 ( 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))) % 112.26/112.07 => ( 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))) % 112.26/112.07 => 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)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_transpose__transpose,axiom, % 112.26/112.07 ! [V_xs_2,T_b] : % 112.26/112.07 ( 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))) % 112.26/112.07 => 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) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 112.26/112.07 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sorted__takeWhile,axiom, % 112.26/112.07 ! [V_Pa_2,V_xs_2,T_b] : % 112.26/112.07 ( class_Orderings_Olinorder(T_b) % 112.26/112.07 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 112.26/112.07 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_length__takeWhile__le,axiom, % 112.26/112.07 ! [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))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile__eq__all__conv,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2 % 112.26/112.07 <=> ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_set__takeWhileD,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,V_x_2,T_b] : % 112.26/112.07 ( 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)))) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_zip__takeWhile__snd,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_zip__takeWhile__fst,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile__map,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile__tail,axiom, % 112.26/112.07 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] : % 112.26/112.07 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 => 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) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile_Osimps_I2_J,axiom, % 112.26/112.07 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 112.26/112.07 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 => 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)) ) % 112.26/112.07 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 => 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) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile_Osimps_I1_J,axiom, % 112.26/112.07 ! [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) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile__eq__take,axiom, % 112.26/112.07 ! [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) ). % 112.26/112.07 % 112.26/112.07 fof(fact_distinct__takeWhile,axiom, % 112.26/112.07 ! [V_Pa_2,V_xs_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.07 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_return__list__def,axiom, % 112.26/112.07 ! [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) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile__append1,axiom, % 112.26/112.07 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 => 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) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile__nth,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b,V_j_2] : % 112.26/112.07 ( 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)))) % 112.26/112.07 => 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) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_nth__length__takeWhile,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( 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))) % 112.26/112.07 => ~ 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))))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile__not__last,axiom, % 112.26/112.07 ! [T_b,V_xs_2] : % 112.26/112.07 ( V_xs_2 != c_List_Olist_ONil(T_b) % 112.26/112.07 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.07 => 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) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 112.26/112.07 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( class_Orderings_Olinorder(T_b) % 112.26/112.07 => ( 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))) % 112.26/112.07 => 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) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_transfer__nat__int__list__return__embed,axiom, % 112.26/112.07 ! [V_l] : % 112.26/112.07 ( c_List_Onat__list(V_l) % 112.26/112.07 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 112.26/112.07 ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_embed__list__def,axiom, % 112.26/112.07 ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile__neq__rev,axiom, % 112.26/112.07 ! [V_x_2,V_xs_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => 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),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(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_x_2)),V_xs_2))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dropWhile__neq__rev,axiom, % 112.26/112.07 ! [V_x_2,V_xs_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => c_List_OdropWhile(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_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),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),V_x_2)),V_xs_2))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile__dropWhile__id,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2 ). % 112.26/112.07 % 112.26/112.07 fof(fact_sorted__dropWhile,axiom, % 112.26/112.07 ! [V_Pa_2,V_xs_2,T_b] : % 112.26/112.07 ( class_Orderings_Olinorder(T_b) % 112.26/112.07 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 112.26/112.07 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_length__dropWhile__le,axiom, % 112.26/112.07 ! [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_OdropWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dropWhile__eq__Nil__conv,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b) % 112.26/112.07 <=> ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dropWhile_Osimps_I2_J,axiom, % 112.26/112.07 ! [V_xs_2,T_b,V_x_2,V_Pa_2] : % 112.26/112.07 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) ) % 112.26/112.07 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 => c_List_OdropWhile(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),V_xs_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dropWhile_Osimps_I1_J,axiom, % 112.26/112.07 ! [V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ). % 112.26/112.07 % 112.26/112.07 fof(fact_distinct__dropWhile,axiom, % 112.26/112.07 ! [V_Pa_2,V_xs_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 112.26/112.07 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_hd__dropWhile,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b) % 112.26/112.07 => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dropWhile__map,axiom, % 112.26/112.07 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OdropWhile(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_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dropWhile__append1,axiom, % 112.26/112.07 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 => c_List_OdropWhile(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),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dropWhile__eq__Cons__conv,axiom, % 112.26/112.07 ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) % 112.26/112.07 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) % 112.26/112.07 & ~ hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dropWhile__eq__drop,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(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) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dropWhile__nth,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b,V_j_2] : % 112.26/112.07 ( 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_OdropWhile(T_b,V_Pa_2,V_xs_2)))) % 112.26/112.07 => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_listsum__map__filter,axiom, % 112.26/112.07 ! [V_f_2,V_Pa_2,V_xs_2,T_b,T_c] : % 112.26/112.07 ( class_Groups_Omonoid__add(T_c) % 112.26/112.07 => ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => ( ~ hBOOL(hAPP(V_Pa_2,B_x)) % 112.26/112.07 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) % 112.26/112.07 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sorted__nth__monoI,axiom, % 112.26/112.07 ! [V_xs,T_a] : % 112.26/112.07 ( class_Orderings_Olinorder(T_a) % 112.26/112.07 => ( ! [B_i,B_j] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) ) % 112.26/112.07 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile__eq__filter,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) % 112.26/112.07 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.07 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile__eq__take__P__nth,axiom, % 112.26/112.07 ! [V_Pa_2,V_xs_2,T_b,V_na_2] : % 112.26/112.07 ( ! [B_i] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_na_2)) % 112.26/112.07 => ( 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))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) % 112.26/112.07 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 112.26/112.07 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_na_2))) ) % 112.26/112.07 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_length__takeWhile__less__P__nth,axiom, % 112.26/112.07 ! [V_xs_2,T_b,V_Pa_2,V_j_2] : % 112.26/112.07 ( ! [B_i] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sorted_Osimps,axiom, % 112.26/112.07 ! [V_a_2,T_b] : % 112.26/112.07 ( class_Orderings_Olinorder(T_b) % 112.26/112.07 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2) % 112.26/112.07 <=> ( V_a_2 = c_List_Olist_ONil(T_b) % 112.26/112.07 | ? [B_xs,B_x] : % 112.26/112.07 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) % 112.26/112.07 & ! [B_xa] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs))) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) % 112.26/112.07 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_List_Oinsert__def,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.07 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) % 112.26/112.07 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_not__in__set__insert,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.07 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_insert__remdups,axiom, % 112.26/112.07 ! [V_xs,V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_distinct__insert,axiom, % 112.26/112.07 ! [V_x,V_xs,T_a] : % 112.26/112.07 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 112.26/112.07 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_in__set__insert,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_List_Oset__insert,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oinsert(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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_insert__Nil,axiom, % 112.26/112.07 ! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_concat__map__maps,axiom, % 112.26/112.07 ! [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)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) ). % 112.26/112.07 % 112.26/112.07 fof(fact_maps__def,axiom, % 112.26/112.07 ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_maps__simps_I2_J,axiom, % 112.26/112.07 ! [V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ). % 112.26/112.07 % 112.26/112.07 fof(fact_maps__simps_I1_J,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omaps(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_Oappend(T_b),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_c,T_b,V_f_2,V_xs_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_distinct__concat,axiom, % 112.26/112.07 ! [V_xs_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2)) % 112.26/112.07 => ( ! [B_ys] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 112.26/112.07 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) ) % 112.26/112.07 => ( ! [B_ys] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 112.26/112.07 => ! [B_zs] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) % 112.26/112.07 => ( B_ys != B_zs % 112.26/112.07 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),B_ys)),hAPP(c_List_Oset(T_b),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) % 112.26/112.07 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_measures__lesseq,axiom, % 112.26/112.07 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] : % 112.26/112.07 ( 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))) % 112.26/112.07 => ( 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_List_Omeasures(T_b,V_fs_2))) % 112.26/112.07 => 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_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_wf__measures,axiom, % 112.26/112.07 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_in__measures_I1_J,axiom, % 112.26/112.07 ! [V_y_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_y_2)),c_List_Omeasures(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_Nat_Onat))))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_measures__def,axiom, % 112.26/112.07 ! [V_fs_2,T_b] : c_List_Omeasures(T_b,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_b),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_b),c_List_Omap(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_b,tc_Nat_Onat),T_b,tc_Nat_Onat),c_COMBI(tc_fun(T_b,tc_Nat_Onat))))),V_fs_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_in__measures_I2_J,axiom, % 112.26/112.07 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] : % 112.26/112.07 ( 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_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) % 112.26/112.07 <=> ( 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))) % 112.26/112.07 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 112.26/112.07 & 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_List_Omeasures(T_b,V_fs_2))) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_measures__less,axiom, % 112.26/112.07 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] : % 112.26/112.07 ( 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))) % 112.26/112.07 => 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_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_foldl__apply,axiom, % 112.26/112.07 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] : % 112.26/112.07 ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => hAPP(c_Fun_Ocomp(T_d,T_d,T_c,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_h_2),hAPP(V_g_2,B_x)) ) % 112.26/112.07 => hAPP(c_List_Ofoldl(T_d,T_b,hAPP(c_COMBC(T_b,T_d,T_d),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_g_2),V_s_2),V_xs_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_order__fun_I2_J,axiom, % 112.26/112.07 ! [V_g_2,V_f_2,T_b,T_c] : % 112.26/112.07 ( ( class_Orderings_Oorder(T_c) % 112.26/112.07 & class_Enum_Oenum(T_b) ) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 112.26/112.07 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 112.26/112.07 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(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_g_2)))) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_enum__ex__prod__def,axiom, % 112.26/112.07 ! [V_Pa_2,T_b,T_c] : % 112.26/112.07 ( ( class_Enum_Oenum(T_c) % 112.26/112.07 & class_Enum_Oenum(T_b) ) % 112.26/112.07 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2)) % 112.26/112.07 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),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))))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_exists__code,axiom, % 112.26/112.07 ! [V_Pa_2,T_b] : % 112.26/112.07 ( class_Enum_Oenum(T_b) % 112.26/112.07 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 112.26/112.07 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_enum__ex,axiom, % 112.26/112.07 ! [V_Pa_2,T_b] : % 112.26/112.07 ( class_Enum_Oenum(T_b) % 112.26/112.07 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) % 112.26/112.07 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_zip__obtain__same__length,axiom, % 112.26/112.07 ! [V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] : % 112.26/112.07 ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Otake(T_c),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))),V_ys_2)) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),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))),V_ys_2)))) ) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_pos__not__random__dseq__def,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dropWhile__append2,axiom, % 112.26/112.07 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] : % 112.26/112.07 ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.07 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_ys_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__all2__all__nthI,axiom, % 112.26/112.07 ! [V_Pa_2,V_b_2,T_c,V_a_2,T_b] : % 112.26/112.07 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2) % 112.26/112.07 => ( ! [B_n] : % 112.26/112.07 ( 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_a_2))) % 112.26/112.07 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n))) ) % 112.26/112.07 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_finite__sorted__distinct__unique,axiom, % 112.26/112.07 ! [V_A_2,T_b] : % 112.26/112.07 ( class_Orderings_Olinorder(T_b) % 112.26/112.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.07 => ? [B_x] : % 112.26/112.07 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2 % 112.26/112.07 & c_List_Olinorder__class_Osorted(T_b,B_x) % 112.26/112.07 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x)) % 112.26/112.07 & ! [B_y] : % 112.26/112.07 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2 % 112.26/112.07 & c_List_Olinorder__class_Osorted(T_b,B_y) % 112.26/112.07 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) ) % 112.26/112.07 => B_y = B_x ) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_takeWhile__append2,axiom, % 112.26/112.07 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] : % 112.26/112.07 ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.07 => c_List_OtakeWhile(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),V_xs_2),c_List_OtakeWhile(T_b,V_Pa_2,V_ys_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_insort__is__Cons,axiom, % 112.26/112.07 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] : % 112.26/112.07 ( class_Orderings_Olinorder(T_c) % 112.26/112.07 => ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 112.26/112.07 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_xs_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_filter__eq__Cons__iff,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] : % 112.26/112.07 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) % 112.26/112.07 <=> ? [B_us,B_vs] : % 112.26/112.07 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) % 112.26/112.07 & ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) % 112.26/112.07 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Cons__eq__filter__iff,axiom, % 112.26/112.07 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] : % 112.26/112.07 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2) % 112.26/112.07 <=> ? [B_us,B_vs] : % 112.26/112.07 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) % 112.26/112.07 & ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) % 112.26/112.07 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_order__fun_I1_J,axiom, % 112.26/112.07 ! [V_g_2,V_f_2,T_b,T_c] : % 112.26/112.07 ( ( class_Orderings_Oorder(T_c) % 112.26/112.07 & class_Enum_Oenum(T_b) ) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) % 112.26/112.07 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_enum__all,axiom, % 112.26/112.07 ! [V_Pa_2,T_b] : % 112.26/112.07 ( class_Enum_Oenum(T_b) % 112.26/112.07 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) % 112.26/112.07 <=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_all__code,axiom, % 112.26/112.07 ! [V_Pa_2,T_b] : % 112.26/112.07 ( class_Enum_Oenum(T_b) % 112.26/112.07 => ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) % 112.26/112.07 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_enum__all__prod__def,axiom, % 112.26/112.07 ! [V_Pa_2,T_b,T_c] : % 112.26/112.07 ( ( class_Enum_Oenum(T_c) % 112.26/112.07 & class_Enum_Oenum(T_b) ) % 112.26/112.07 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2)) % 112.26/112.07 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),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))))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ball__nth,axiom, % 112.26/112.07 ! [V_Pa_2,V_xs_2,T_b,V_na_2] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) % 112.26/112.07 => ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_na_2))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sorted_OCons,axiom, % 112.26/112.07 ! [V_x_2,V_xs_2,T_b] : % 112.26/112.07 ( class_Orderings_Olinorder(T_b) % 112.26/112.07 => ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) % 112.26/112.07 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2) % 112.26/112.07 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ex__length,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 112.26/112.07 <=> ? [B_n] : % 112.26/112.07 ( 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))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_in__set__conv__decomp,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ex__simps_I2_J,axiom, % 112.26/112.07 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ex__append,axiom, % 112.26/112.07 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 112.26/112.07 <=> ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 112.26/112.07 | c_List_Olist__ex(T_b,V_Pa_2,V_ys_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ex__iff,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 112.26/112.07 <=> ? [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ex__rev,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) % 112.26/112.07 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ex__simps_I1_J,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 112.26/112.07 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_in__set__conv__decomp__first,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 <=> ? [B_ys] : % 112.26/112.07 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) % 112.26/112.07 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_in__set__conv__decomp__last,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 <=> ? [B_ys,B_zs] : % 112.26/112.07 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) % 112.26/112.07 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__all__length,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 112.26/112.07 <=> ! [B_n] : % 112.26/112.07 ( 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))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_measure__function__int,axiom, % 112.26/112.07 c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__all__simps_I2_J,axiom, % 112.26/112.07 ! [V_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__all__append,axiom, % 112.26/112.07 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) % 112.26/112.07 <=> ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 112.26/112.07 & c_List_Olist__all(T_b,V_Pa_2,V_ys_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_measure__size,axiom, % 112.26/112.07 ! [T_b] : % 112.26/112.07 ( class_Nat_Osize(T_b) % 112.26/112.07 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_is__measure_Ointros,axiom, % 112.26/112.07 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ). % 112.26/112.07 % 112.26/112.07 fof(fact_is__measure_Oequations,axiom, % 112.26/112.07 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ). % 112.26/112.07 % 112.26/112.07 fof(fact_is__measure_Osimps,axiom, % 112.26/112.07 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__all__iff,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 112.26/112.07 <=> ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_measure__fst,axiom, % 112.26/112.07 ! [T_c,V_f_2,T_b] : % 112.26/112.07 ( c_FunDef_Ois__measure(T_b,V_f_2) % 112.26/112.07 => c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_measure__snd,axiom, % 112.26/112.07 ! [T_c,V_f_2,T_b] : % 112.26/112.07 ( c_FunDef_Ois__measure(T_b,V_f_2) % 112.26/112.07 => c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__all__rev,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) % 112.26/112.07 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__all__simps_I1_J,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 112.26/112.07 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 & c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Ball__set__list__all,axiom, % 112.26/112.07 ! [V_Pa_2,V_xs_2,T_b] : % 112.26/112.07 ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.07 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__all__iff__raw,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2) % 112.26/112.07 <=> ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ex1__simps_I2_J,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) % 112.26/112.07 <=> ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 => c_List_Olist__all(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_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))),hAPP(c_fequal,V_x_2)),V_xs_2) ) % 112.26/112.07 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 => c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_transfer__morphism__int__nat,axiom, % 112.26/112.07 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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ex1__simps_I1_J,axiom, % 112.26/112.07 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bool_Osize_I3_J,axiom, % 112.26/112.07 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bool_Osize_I4_J,axiom, % 112.26/112.07 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ex1__iff,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) % 112.26/112.07 <=> ? [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,B_x)) % 112.26/112.07 & ! [B_y] : % 112.26/112.07 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,B_y)) ) % 112.26/112.07 => B_y = B_x ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 112.26/112.07 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 112.26/112.07 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 112.26/112.07 => 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) ) % 112.26/112.07 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 112.26/112.07 => 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)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 112.26/112.07 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] : % 112.26/112.07 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 112.26/112.07 => 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) ) % 112.26/112.07 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 112.26/112.07 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(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)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_New__DSequence_Opos__empty__def,axiom, % 112.26/112.07 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 112.26/112.07 % 112.26/112.07 fof(fact_pos__empty__def,axiom, % 112.26/112.07 ! [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) ). % 112.26/112.07 % 112.26/112.07 fof(fact_neg__bind__def,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_New__DSequence_Opos__bind__def,axiom, % 112.26/112.07 ! [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) = hAPP(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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_neg__map__def,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_neg__single__def,axiom, % 112.26/112.07 ! [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) ). % 112.26/112.07 % 112.26/112.07 fof(fact_pos__bind__def,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_New__DSequence_Oneg__single__def,axiom, % 112.26/112.07 ! [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) ). % 112.26/112.07 % 112.26/112.07 fof(fact_pos__map__def,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_pos__single__def,axiom, % 112.26/112.07 ! [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) ). % 112.26/112.07 % 112.26/112.07 fof(fact_length__splice,axiom, % 112.26/112.07 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_splice_Osimps_I3_J,axiom, % 112.26/112.07 ! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_splice__Nil2,axiom, % 112.26/112.07 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 112.26/112.07 % 112.26/112.07 fof(fact_splice_Osimps_I1_J,axiom, % 112.26/112.07 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 112.26/112.07 % 112.26/112.07 fof(fact_splice_Osimps_I2_J,axiom, % 112.26/112.07 ! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va) ). % 112.26/112.07 % 112.26/112.07 fof(fact_New__DSequence_Opos__single__def,axiom, % 112.26/112.07 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x) ). % 112.26/112.07 % 112.26/112.07 fof(fact_acyclicP__converse,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( 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),c_Predicate_Oconversep(T_b,T_b,V_r_2)))) % 112.26/112.07 <=> 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))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_converse__meet,axiom, % 112.26/112.07 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_converse__join,axiom, % 112.26/112.07 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_conversep__noteq,axiom, % 112.26/112.07 ! [V_y_2,V_x_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2)) % 112.26/112.07 <=> V_x_2 != V_y_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_conversep__eq,axiom, % 112.26/112.07 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ). % 112.26/112.07 % 112.26/112.07 fof(fact_conversep__conversep,axiom, % 112.26/112.07 ! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2 ). % 112.26/112.07 % 112.26/112.07 fof(fact_conversep__iff,axiom, % 112.26/112.07 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2)) % 112.26/112.07 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_conversep_Oequations,axiom, % 112.26/112.07 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2)) % 112.26/112.07 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_conversep_Ointros,axiom, % 112.26/112.07 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_conversepD,axiom, % 112.26/112.07 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2)) % 112.26/112.07 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_converse__pred__comp,axiom, % 112.26/112.07 ! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_conversep__converse__eq,axiom, % 112.26/112.07 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(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),V_y_2)) % 112.26/112.07 <=> 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_Relation_Oconverse(T_b,T_c),V_r_2))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_,axiom, % 112.26/112.07 ! [V_s2_2,V_s1_2,T_c,T_b] : c_Lazy__Sequence_Oproduct(T_b,T_c,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_b,tc_prod(T_b,T_c),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_b),c_Lazy__Sequence_Obind(T_c,tc_prod(T_b,T_c),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_c),c_Lazy__Sequence_Osingle(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_tl__replicate,axiom, % 112.26/112.07 ! [V_x,T_a,V_n] : % 112.26/112.07 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.07 => hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_replicate__length__filter,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,T_b] : c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2) ). % 112.26/112.07 % 112.26/112.07 fof(fact_length__replicate,axiom, % 112.26/112.07 ! [V_x,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x)) = V_n ). % 112.26/112.07 % 112.26/112.07 fof(fact_map__replicate__const,axiom, % 112.26/112.07 ! [V_lst_2,V_k_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_k_2)),V_lst_2) = c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_lst_2),V_k_2) ). % 112.26/112.07 % 112.26/112.07 fof(fact_replicate__app__Cons__same,axiom, % 112.26/112.07 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),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_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_replicate__Suc,axiom, % 112.26/112.07 ! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_rev__replicate,axiom, % 112.26/112.07 ! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x) ). % 112.26/112.07 % 112.26/112.07 fof(fact_drop__replicate,axiom, % 112.26/112.07 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x) ). % 112.26/112.07 % 112.26/112.07 fof(fact_hd__replicate,axiom, % 112.26/112.07 ! [V_x,T_a,V_n] : % 112.26/112.07 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.07 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_last__replicate,axiom, % 112.26/112.07 ! [V_x,T_a,V_n] : % 112.26/112.07 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.07 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_take__replicate,axiom, % 112.26/112.07 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x) ). % 112.26/112.07 % 112.26/112.07 fof(fact_zip__replicate,axiom, % 112.26/112.07 ! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Bex__set__replicate,axiom, % 112.26/112.07 ! [V_Pa_2,V_a_2,V_na_2,T_b] : % 112.26/112.07 ( ? [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_a_2)))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.07 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 112.26/112.07 & V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Ball__set__replicate,axiom, % 112.26/112.07 ! [V_Pa_2,V_a_2,V_na_2,T_b] : % 112.26/112.07 ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_a_2)))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.07 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2)) % 112.26/112.07 | V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_replicate__eq__replicate,axiom, % 112.26/112.07 ! [V_y_2,V_na_2,V_x_2,V_m_2,T_b] : % 112.26/112.07 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_na_2,V_y_2) % 112.26/112.07 <=> ( V_m_2 = V_na_2 % 112.26/112.07 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.07 => V_x_2 = V_y_2 ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_nth__replicate,axiom, % 112.26/112.07 ! [V_x,T_a,V_n,V_i] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 112.26/112.07 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_append__replicate__commute,axiom, % 112.26/112.07 ! [V_k,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_replicate__add,axiom, % 112.26/112.07 ! [V_x,V_m,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_filter__replicate,axiom, % 112.26/112.07 ! [V_na_2,T_b,V_x_2,V_Pa_2] : % 112.26/112.07 ( ( hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_na_2,V_x_2)) = c_List_Oreplicate(T_b,V_na_2,V_x_2) ) % 112.26/112.07 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2)) % 112.26/112.07 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_na_2,V_x_2)) = c_List_Olist_ONil(T_b) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_concat__replicate__trivial,axiom, % 112.26/112.07 ! [V_i,T_a] : c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a) ). % 112.26/112.07 % 112.26/112.07 fof(fact_replicate__0,axiom, % 112.26/112.07 ! [V_x,T_a] : c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a) ). % 112.26/112.07 % 112.26/112.07 fof(fact_empty__replicate,axiom, % 112.26/112.07 ! [V_x_2,V_na_2,T_b] : % 112.26/112.07 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_na_2,V_x_2) % 112.26/112.07 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_replicate__empty,axiom, % 112.26/112.07 ! [V_x_2,V_na_2,T_b] : % 112.26/112.07 ( c_List_Oreplicate(T_b,V_na_2,V_x_2) = c_List_Olist_ONil(T_b) % 112.26/112.07 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_map__replicate,axiom, % 112.26/112.07 ! [V_x_2,V_na_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oreplicate(T_c,V_na_2,V_x_2)) = c_List_Oreplicate(T_b,V_na_2,hAPP(V_f_2,V_x_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_in__set__replicate,axiom, % 112.26/112.07 ! [V_y_2,V_na_2,V_x_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_y_2)))) % 112.26/112.07 <=> ( V_x_2 = V_y_2 % 112.26/112.07 & V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_replicate__append__same,axiom, % 112.26/112.07 ! [V_x,V_i,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_map__replicate__trivial,axiom, % 112.26/112.07 ! [V_i_2,V_x_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_COMBK(T_b,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_b,V_i_2,V_x_2) ). % 112.26/112.07 % 112.26/112.07 fof(fact_set__replicate__conv__if,axiom, % 112.26/112.07 ! [V_x_2,T_b,V_na_2] : % 112.26/112.07 ( ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.07 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 112.26/112.07 & ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.07 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,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))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_set__replicate,axiom, % 112.26/112.07 ! [V_x_2,T_b,V_na_2] : % 112.26/112.07 ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.07 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,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))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_set__replicate__Suc,axiom, % 112.26/112.07 ! [V_x_2,V_na_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_na_2),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))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_small__lazy__list_Osimps,axiom, % 112.26/112.07 ! [V_d_2,T_b] : % 112.26/112.07 ( class_Lazy__Sequence_Osmall__lazy(T_b) % 112.26/112.07 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_b),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),c_Lazy__Sequence_Oproduct(T_b,tc_List_Olist(T_b),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_b)))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_eq__comp__r,axiom, % 112.26/112.07 ! [V_R_2,T_b] : c_Predicate_Opred__comp(T_b,T_b,T_b,c_fequal,c_Predicate_Opred__comp(T_b,T_b,T_b,V_R_2,c_fequal)) = V_R_2 ). % 112.26/112.07 % 112.26/112.07 fof(fact_small__lazy__prod__def,axiom, % 112.26/112.07 ! [V_d,T_b,T_a] : % 112.26/112.07 ( ( class_Lazy__Sequence_Osmall__lazy(T_a) % 112.26/112.07 & class_Lazy__Sequence_Osmall__lazy(T_b) ) % 112.26/112.07 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_New__DSequence_Opos__union__def,axiom, % 112.26/112.07 ! [V_i_2,V_yq_2,V_xq_2,T_b] : hAPP(c_New__DSequence_Opos__union(T_b,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_b,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 112.26/112.07 ! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 112.26/112.07 % 112.26/112.07 fof(fact__01,axiom, % 112.26/112.07 ! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_lazy__sequence_Oinject,axiom, % 112.26/112.07 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] : % 112.26/112.07 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2) % 112.26/112.07 <=> ( V_a_2 = V_a_H_2 % 112.26/112.07 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_pos__union__def,axiom, % 112.26/112.07 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_b] : c_New__Random__Sequence_Opos__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_b,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 112.26/112.07 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_small__lazy_H_Osimps,axiom, % 112.26/112.07 ! [V_i,V_d] : % 112.26/112.07 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 112.26/112.07 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 112.26/112.07 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 112.26/112.07 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_small__lazy_H_Opsimps,axiom, % 112.26/112.07 ! [V_i_2,V_d_2] : % 112.26/112.07 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2))) % 112.26/112.07 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 112.26/112.07 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 112.26/112.07 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 112.26/112.07 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_small__lazy__int__def,axiom, % 112.26/112.07 ! [V_d] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_small__lazy_H_Opinduct,axiom, % 112.26/112.07 ! [V_Pa_2,V_a1_2,V_a0_2] : % 112.26/112.07 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) % 112.26/112.07 => ( ! [B_d,B_i] : % 112.26/112.07 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i))) % 112.26/112.07 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 112.26/112.07 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) % 112.26/112.07 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),B_i)) ) ) % 112.26/112.07 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_size__code,axiom, % 112.26/112.07 ! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),T_b),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_lazy__sequence__size__code,axiom, % 112.26/112.07 ! [V_xq_2,V_s_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_b,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_b),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_seq__case,axiom, % 112.26/112.07 ! [V_xq_2,V_g_2,V_f_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_b,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),T_b),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_yieldn__def,axiom, % 112.26/112.07 ! [T_b] : c_Lazy__Sequence_Oyieldn(T_b) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_b),T_b,c_Lazy__Sequence_Oyield(T_b)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 112.26/112.07 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ). % 112.26/112.07 % 112.26/112.07 fof(fact_refl__on__INTER,axiom, % 112.26/112.07 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] : % 112.26/112.07 ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 112.26/112.07 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) ) % 112.26/112.07 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_List_Omember__def,axiom, % 112.26/112.07 ! [V_x_2,V_xs_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) % 112.26/112.07 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_member__rec_I2_J,axiom, % 112.26/112.07 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_member__set,axiom, % 112.26/112.07 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ). % 112.26/112.07 % 112.26/112.07 fof(fact_member__rec_I1_J,axiom, % 112.26/112.07 ! [V_y_2,V_xs_2,V_x_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_y_2)) % 112.26/112.07 <=> ( V_x_2 = V_y_2 % 112.26/112.07 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_in__set__member,axiom, % 112.26/112.07 ! [V_xs_2,V_x_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ex1__iff__raw,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) % 112.26/112.07 <=> ? [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,B_x)) % 112.26/112.07 & ! [B_y] : % 112.26/112.07 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,B_y)) ) % 112.26/112.07 => B_y = B_x ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_setsum__UNION__zero,axiom, % 112.26/112.07 ! [V_f_2,V_S_2,T_b,T_c] : % 112.26/112.07 ( class_Groups_Ocomm__monoid__add(T_c) % 112.26/112.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2)) % 112.26/112.07 => ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2)) % 112.26/112.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) ) % 112.26/112.07 => ( ! [B_T1] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2)) % 112.26/112.07 => ! [B_T2] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2)) % 112.26/112.07 => ( B_T1 != B_T2 % 112.26/112.07 => ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1)) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2)) % 112.26/112.07 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) % 112.26/112.07 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2)),V_S_2) ) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_THE__default__def,axiom, % 112.26/112.07 ! [V_d_2,T_b,V_Pa_2] : % 112.26/112.07 ( ( ? [B_x] : % 112.26/112.07 ( hBOOL(hAPP(V_Pa_2,B_x)) % 112.26/112.07 & ! [B_y] : % 112.26/112.07 ( hBOOL(hAPP(V_Pa_2,B_y)) % 112.26/112.07 => B_y = B_x ) ) % 112.26/112.07 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ) % 112.26/112.07 & ( ~ ? [B_x] : % 112.26/112.07 ( hBOOL(hAPP(V_Pa_2,B_x)) % 112.26/112.07 & ! [B_y] : % 112.26/112.07 ( hBOOL(hAPP(V_Pa_2,B_y)) % 112.26/112.07 => B_y = B_x ) ) % 112.26/112.07 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = V_d_2 ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_SUP2__E,axiom, % 112.26/112.07 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 112.26/112.07 => ~ ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.07 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_INF2__I,axiom, % 112.26/112.07 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,T_b] : % 112.26/112.07 ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.07 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) % 112.26/112.07 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_finite__maxlen,axiom, % 112.26/112.07 ! [V_M_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2)) % 112.26/112.07 => ? [B_n] : % 112.26/112.07 ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2)) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_x)),B_n)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_lazy__sequence_Osize_I3_J,axiom, % 112.26/112.07 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 112.26/112.07 % 112.26/112.07 fof(fact_lazy__sequence_Osize_I1_J,axiom, % 112.26/112.07 ! [V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 112.26/112.07 % 112.26/112.07 fof(fact__02,axiom, % 112.26/112.07 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ). % 112.26/112.07 % 112.26/112.07 fof(fact_lazy__sequence_Osimps_I3_J,axiom, % 112.26/112.07 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) != c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ). % 112.26/112.07 % 112.26/112.07 fof(fact_lazy__sequence_Osimps_I2_J,axiom, % 112.26/112.07 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) ). % 112.26/112.07 % 112.26/112.07 fof(fact_lazy__sequence_Osimps_I4_J,axiom, % 112.26/112.07 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__all__iff__all__interval__int,axiom, % 112.26/112.07 ! [V_j_2,V_i_2,V_Pa_2] : % 112.26/112.07 ( c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2)) % 112.26/112.07 <=> c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ex__iff__not__all__inverval__int,axiom, % 112.26/112.07 ! [V_j_2,V_i_2,V_Pa_2] : % 112.26/112.07 ( c_List_Olist__ex(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2)) % 112.26/112.07 <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_Pa_2),V_i_2,V_j_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_all__interval__int__def,axiom, % 112.26/112.07 ! [V_j_2,V_i_2,V_Pa_2] : % 112.26/112.07 ( c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) % 112.26/112.07 <=> ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_code__numeral_Orecs_I2_J,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Random_Osimps,axiom, % 112.26/112.07 ! [V_size_2,V_g_2,T_b,V_nrandom_2] : % 112.26/112.07 ( ( 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))) % 112.26/112.07 => 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)) ) % 112.26/112.07 & ( ~ 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))) % 112.26/112.07 => 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))))))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_code__numeral_Orecs_I1_J,axiom, % 112.26/112.07 ! [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 ). % 112.26/112.07 % 112.26/112.07 fof(fact_Random__Sequence_Oempty__def,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Random__Sequence_Osingle__def,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Random__Sequence_Omap__def,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_exE__realizer,axiom, % 112.26/112.07 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_Pa_2] : % 112.26/112.07 ( 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))) % 112.26/112.07 => ( ! [B_x,B_y] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x)) % 112.26/112.07 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) ) % 112.26/112.07 => 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))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Image__Collect__split,axiom, % 112.26/112.07 ! [V_A_2,V_Pa_2,T_b,T_c] : hAPP(c_Relation_OImage(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))),V_A_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_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_A_2)))),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2)))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_lexord__trans,axiom, % 112.26/112.07 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] : % 112.26/112.07 ( 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))) % 112.26/112.07 => ( 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_z_2)),c_List_Olexord(T_b,V_r_2))) % 112.26/112.07 => ( c_Relation_Otrans(T_b,V_r_2) % 112.26/112.07 => 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_z_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__less__than,axiom, % 112.26/112.07 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__lex__prod,axiom, % 112.26/112.07 ! [V_R2_2,T_c,V_R1_2,T_b] : % 112.26/112.07 ( c_Relation_Otrans(T_b,V_R1_2) % 112.26/112.07 => ( c_Relation_Otrans(T_c,V_R2_2) % 112.26/112.07 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__def,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Otrans(T_b,V_r_2) % 112.26/112.07 <=> ! [B_x,B_y] : % 112.26/112.07 ( 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)) % 112.26/112.07 => ! [B_z] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2)) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2)) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_transD,axiom, % 112.26/112.07 ! [V_c_2,V_b_2,V_a_2,V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Otrans(T_b,V_r_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2)) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),V_r_2)) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__rtrancl,axiom, % 112.26/112.07 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__finite__psubset,axiom, % 112.26/112.07 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__Id__on,axiom, % 112.26/112.07 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__trancl,axiom, % 112.26/112.07 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trancl__id,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Otrans(T_b,V_r_2) % 112.26/112.07 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__Id,axiom, % 112.26/112.07 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_lexord__transI,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Otrans(T_b,V_r_2) % 112.26/112.07 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__converse,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 112.26/112.07 <=> c_Relation_Otrans(T_b,V_r_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bex__empty,axiom, % 112.26/112.07 ! [V_Pa_2,T_b] : % 112.26/112.07 ~ ? [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,B_x)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_listrel__trans,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Otrans(T_b,V_r_2) % 112.26/112.07 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_finite__Collect__bex,axiom, % 112.26/112.07 ! [V_Q_2,T_c,V_A_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.07 => ( 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),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_Q_2))))) % 112.26/112.07 <=> ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.07 => 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_x)))) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bex__UNIV,axiom, % 112.26/112.07 ! [V_Pa_2,T_b] : % 112.26/112.07 ( ? [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.07 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__Int,axiom, % 112.26/112.07 ! [V_s_2,V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Otrans(T_b,V_r_2) % 112.26/112.07 => ( c_Relation_Otrans(T_b,V_s_2) % 112.26/112.07 => c_Relation_Otrans(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_s_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_SUPR__bool__eq,axiom, % 112.26/112.07 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__O__subset,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Otrans(T_b,V_r_2) % 112.26/112.07 => 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_r_2)),V_r_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__inv__image,axiom, % 112.26/112.07 ! [V_f_2,T_c,V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Otrans(T_b,V_r_2) % 112.26/112.07 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__reflclI,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Otrans(T_b,V_r_2) % 112.26/112.07 => c_Relation_Otrans(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))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Union__eq,axiom, % 112.26/112.07 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(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_OEx(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_fconj),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)))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Bex__set__list__ex,axiom, % 112.26/112.07 ! [V_Pa_2,V_xs_2,T_b] : % 112.26/112.07 ( ? [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.07 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ex__iff__raw,axiom, % 112.26/112.07 ! [V_xs_2,V_Pa_2,T_b] : % 112.26/112.07 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) % 112.26/112.07 <=> ? [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_UN__eq,axiom, % 112.26/112.07 ! [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_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),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_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_INT__eq,axiom, % 112.26/112.07 ! [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_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),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_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Sup__apply,axiom, % 112.26/112.07 ! [V_x_2,V_A_2,T_c,T_b] : % 112.26/112.07 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.07 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Sup__fun__def,axiom, % 112.26/112.07 ! [V_x_2,V_A_2,T_c,T_b] : % 112.26/112.07 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.07 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Inf__apply,axiom, % 112.26/112.07 ! [V_x_2,V_A_2,T_c,T_b] : % 112.26/112.07 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.07 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Inf__fun__def,axiom, % 112.26/112.07 ! [V_x_2,V_A_2,T_c,T_b] : % 112.26/112.07 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 112.26/112.07 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_max__extp_Ointros,axiom, % 112.26/112.07 ! [V_R_2,V_Y_2,V_X_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) % 112.26/112.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) % 112.26/112.07 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.07 => ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) % 112.26/112.07 => ? [B_xa] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) % 112.26/112.07 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) % 112.26/112.07 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_transp__def,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Predicate_Otransp(T_b,V_r_2) % 112.26/112.07 <=> c_Relation_Otrans(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))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_transpE,axiom, % 112.26/112.07 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] : % 112.26/112.07 ( c_Predicate_Otransp(T_b,V_r_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2)) % 112.26/112.07 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_equivp__reflp__symp__transp,axiom, % 112.26/112.07 ! [V_R_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 112.26/112.07 <=> ( c_Predicate_Oreflp(T_b,V_R_2) % 112.26/112.07 & c_Predicate_Osymp(T_b,V_R_2) % 112.26/112.07 & c_Predicate_Otransp(T_b,V_R_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_equivpI,axiom, % 112.26/112.07 ! [V_R_2,T_b] : % 112.26/112.07 ( c_Predicate_Oreflp(T_b,V_R_2) % 112.26/112.07 => ( c_Predicate_Osymp(T_b,V_R_2) % 112.26/112.07 => ( c_Predicate_Otransp(T_b,V_R_2) % 112.26/112.07 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sympE,axiom, % 112.26/112.07 ! [V_y_2,V_x_2,V_r_2,T_b] : % 112.26/112.07 ( c_Predicate_Osymp(T_b,V_r_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 112.26/112.07 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_equivpE,axiom, % 112.26/112.07 ! [V_R_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 112.26/112.07 => ~ ( c_Predicate_Oreflp(T_b,V_R_2) % 112.26/112.07 => ( c_Predicate_Osymp(T_b,V_R_2) % 112.26/112.07 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_max__extp_Osimps,axiom, % 112.26/112.07 ! [V_a2_2,V_a1_2,V_R_2,T_b] : % 112.26/112.07 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) % 112.26/112.07 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) % 112.26/112.07 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) % 112.26/112.07 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 112.26/112.07 & ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) % 112.26/112.07 => ? [B_xa] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) % 112.26/112.07 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_trans__diff__Id,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Otrans(T_b,V_r_2) % 112.26/112.07 => ( c_Relation_Oantisym(T_b,V_r_2) % 112.26/112.07 => c_Relation_Otrans(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))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_antisym__Id__on,axiom, % 112.26/112.07 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_antisym__empty,axiom, % 112.26/112.07 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_antisym__converse,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 112.26/112.07 <=> c_Relation_Oantisym(T_b,V_r_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_antisym__Id,axiom, % 112.26/112.07 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_antisym__subset,axiom, % 112.26/112.07 ! [V_s_2,V_r_2,T_b] : % 112.26/112.07 ( 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)) % 112.26/112.07 => ( c_Relation_Oantisym(T_b,V_s_2) % 112.26/112.07 => c_Relation_Oantisym(T_b,V_r_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_antisymD,axiom, % 112.26/112.07 ! [V_b_2,V_a_2,V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Oantisym(T_b,V_r_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2)) % 112.26/112.07 => V_a_2 = V_b_2 ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_antisym__def,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Oantisym(T_b,V_r_2) % 112.26/112.07 <=> ! [B_x,B_y] : % 112.26/112.07 ( 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)) % 112.26/112.07 => ( 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)) % 112.26/112.07 => B_x = B_y ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_antisym__reflcl,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Oantisym(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))) % 112.26/112.07 <=> c_Relation_Oantisym(T_b,V_r_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_acyclic__impl__antisym__rtrancl,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Wellfounded_Oacyclic(T_b,V_r_2) % 112.26/112.07 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_fun__lub__def,axiom, % 112.26/112.07 ! [V_x_2,V_A_2,V_L_2,T_d,T_b,T_c] : c_Partial__Function_Ofun__lub(T_c,T_b,T_d,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_d,T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_d,T_c),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_d,T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_d,T_c))),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_fun(T_d,T_c))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),T_d,T_c),c_COMBI(tc_fun(T_d,T_c))),V_x_2)))))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sym__trans__comp__subset,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Osym(T_b,V_r_2) % 112.26/112.07 => ( c_Relation_Otrans(T_b,V_r_2) % 112.26/112.07 => 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_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)),V_r_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sym__def,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Osym(T_b,V_r_2) % 112.26/112.07 <=> ! [B_x,B_y] : % 112.26/112.07 ( 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)) % 112.26/112.07 => 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)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_symD,axiom, % 112.26/112.07 ! [V_b_2,V_a_2,V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Osym(T_b,V_r_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sym__Int__converse,axiom, % 112.26/112.07 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sym__rtrancl,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Osym(T_b,V_r_2) % 112.26/112.07 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sym__Id__on,axiom, % 112.26/112.07 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sym__trancl,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Osym(T_b,V_r_2) % 112.26/112.07 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sym__Un,axiom, % 112.26/112.07 ! [V_s_2,V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Osym(T_b,V_r_2) % 112.26/112.07 => ( c_Relation_Osym(T_b,V_s_2) % 112.26/112.07 => c_Relation_Osym(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)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sym__Id,axiom, % 112.26/112.07 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sym__converse,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) % 112.26/112.07 <=> c_Relation_Osym(T_b,V_r_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sym__conv__converse__eq,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Osym(T_b,V_r_2) % 112.26/112.07 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_listrel__sym,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Osym(T_b,V_r_2) % 112.26/112.07 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sym__Int,axiom, % 112.26/112.07 ! [V_s_2,V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Osym(T_b,V_r_2) % 112.26/112.07 => ( c_Relation_Osym(T_b,V_s_2) % 112.26/112.07 => c_Relation_Osym(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_s_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sym__Un__converse,axiom, % 112.26/112.07 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_sym__inv__image,axiom, % 112.26/112.07 ! [V_f_2,T_c,V_r_2,T_b] : % 112.26/112.07 ( c_Relation_Osym(T_b,V_r_2) % 112.26/112.07 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_equivE,axiom, % 112.26/112.07 ! [V_r_2,V_A_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.07 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 112.26/112.07 => ( c_Relation_Osym(T_b,V_r_2) % 112.26/112.07 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_equivI,axiom, % 112.26/112.07 ! [V_r_2,V_A_2,T_b] : % 112.26/112.07 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 112.26/112.07 => ( c_Relation_Osym(T_b,V_r_2) % 112.26/112.07 => ( c_Relation_Otrans(T_b,V_r_2) % 112.26/112.07 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_equiv__def,axiom, % 112.26/112.07 ! [V_r_2,V_A_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) % 112.26/112.07 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2) % 112.26/112.07 & c_Relation_Osym(T_b,V_r_2) % 112.26/112.07 & c_Relation_Otrans(T_b,V_r_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_symp__def,axiom, % 112.26/112.07 ! [V_r_2,T_b] : % 112.26/112.07 ( c_Predicate_Osymp(T_b,V_r_2) % 112.26/112.07 <=> c_Relation_Osym(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))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_part__equivp__refl__symp__transp,axiom, % 112.26/112.07 ! [V_R_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 112.26/112.07 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 112.26/112.07 & c_Predicate_Osymp(T_b,V_R_2) % 112.26/112.07 & c_Predicate_Otransp(T_b,V_R_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_part__equivpI,axiom, % 112.26/112.07 ! [T_b,V_R_2] : % 112.26/112.07 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 112.26/112.07 => ( c_Predicate_Osymp(T_b,V_R_2) % 112.26/112.07 => ( c_Predicate_Otransp(T_b,V_R_2) % 112.26/112.07 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_part__equivp__def,axiom, % 112.26/112.07 ! [V_R_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 112.26/112.07 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 112.26/112.07 & ! [B_x,B_y] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 112.26/112.07 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 112.26/112.07 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y)) % 112.26/112.07 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_part__equivp__symp,axiom, % 112.26/112.07 ! [V_y_2,V_x_2,V_R_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 112.26/112.07 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_part__equivp__transp,axiom, % 112.26/112.07 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 112.26/112.07 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_equivp__implies__part__equivp,axiom, % 112.26/112.07 ! [V_R_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 112.26/112.07 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_part__equivpE,axiom, % 112.26/112.07 ! [V_R_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 112.26/112.07 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) % 112.26/112.07 => ( c_Predicate_Osymp(T_b,V_R_2) % 112.26/112.07 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_part__equivp__typedef,axiom, % 112.26/112.07 ! [V_R_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2) % 112.26/112.07 => ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),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_COMBS(T_b,T_b,tc_HOL_Obool),V_R_2),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),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_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_R_2))))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__o__cancel,axiom, % 112.26/112.07 ! [V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.07 => hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inj__iff,axiom, % 112.26/112.07 ! [V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.07 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inj__imp__surj__inv,axiom, % 112.26/112.07 ! [V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.07 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),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)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_image__inv__f__f,axiom, % 112.26/112.07 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.07 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__image__comp,axiom, % 112.26/112.07 ! [V_X_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.07 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_X_2)) = V_X_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_surj__imp__inj__inv,axiom, % 112.26/112.07 ! [V_f_2,T_b,T_c] : % 112.26/112.07 ( 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)) % 112.26/112.07 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__def,axiom, % 112.26/112.07 ! [V_y_2,V_f_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(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_y_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__id,axiom, % 112.26/112.07 ! [T_b] : c_Hilbert__Choice_Oinv__into(T_b,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Fun_Oid(T_b)) = c_Fun_Oid(T_b) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__f__f,axiom, % 112.26/112.07 ! [V_x_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.07 => hAPP(c_Hilbert__Choice_Oinv__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 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__f__eq,axiom, % 112.26/112.07 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.07 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 112.26/112.07 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__into__f__f,axiom, % 112.26/112.07 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.07 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__into__f__eq,axiom, % 112.26/112.07 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 112.26/112.07 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 112.26/112.07 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__into__injective,axiom, % 112.26/112.07 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] : % 112.26/112.07 ( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) % 112.26/112.07 => V_x_2 = V_y_2 ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__into__into,axiom, % 112.26/112.07 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_x_2)),V_A_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_f__inv__into__f,axiom, % 112.26/112.07 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) % 112.26/112.07 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_image__surj__f__inv__f,axiom, % 112.26/112.07 ! [V_A_2,V_f_2,T_b,T_c] : % 112.26/112.07 ( 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)) % 112.26/112.07 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_surj__f__inv__f,axiom, % 112.26/112.07 ! [V_y_2,V_f_2,T_b,T_c] : % 112.26/112.07 ( 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)) % 112.26/112.07 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_surj__iff__all,axiom, % 112.26/112.07 ! [V_f_2,T_b,T_c] : % 112.26/112.07 ( 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)) % 112.26/112.07 <=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_x)) = B_x ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_image__inv__into__cancel,axiom, % 112.26/112.07 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] : % 112.26/112.07 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2)) % 112.26/112.07 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2 ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__into__def,axiom, % 112.26/112.07 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(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))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__into__image__cancel,axiom, % 112.26/112.07 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2)) % 112.26/112.07 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = V_S_2 ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inj__on__inv__into,axiom, % 112.26/112.07 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] : % 112.26/112.07 ( 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))) % 112.26/112.07 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_B_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_o__inv__o__cancel,axiom, % 112.26/112.07 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.07 => hAPP(c_Fun_Ocomp(T_c,T_d,T_b,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__into__comp,axiom, % 112.26/112.07 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] : % 112.26/112.07 ( 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)) % 112.26/112.07 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) % 112.26/112.07 => ( 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)))) % 112.26/112.07 => hAPP(c_Hilbert__Choice_Oinv__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_Hilbert__Choice_Oinv__into(T_d,T_b,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__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) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_surj__iff,axiom, % 112.26/112.07 ! [V_f_2,T_b,T_c] : % 112.26/112.07 ( 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)) % 112.26/112.07 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,V_f_2),c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_b) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inj__transfer,axiom, % 112.26/112.07 ! [V_x_2,V_Pa_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.07 => ( ! [B_y] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y))) ) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_fold__image__UN__disjoint,axiom, % 112.26/112.07 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] : % 112.26/112.07 ( class_Groups_Ocomm__monoid__mult(T_d) % 112.26/112.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2)) % 112.26/112.07 => ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 112.26/112.07 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) ) % 112.26/112.07 => ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 112.26/112.07 => ! [B_xa] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2)) % 112.26/112.07 => ( B_x != B_xa % 112.26/112.07 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) % 112.26/112.07 => hAPP(hAPP(hAPP(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)),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(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_b),hAPP(hAPP(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_A_2)),c_Groups_Oone__class_Oone(T_d)),V_I_2) ) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_nat__of__cases,axiom, % 112.26/112.07 ! [V_y_2] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 112.26/112.07 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_nat__of__induct,axiom, % 112.26/112.07 ! [V_Pa_2,V_y_2] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 112.26/112.07 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Onat__of,B_x))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_of__nat__cases,axiom, % 112.26/112.07 ! [V_x_2] : % 112.26/112.07 ~ ! [B_y] : % 112.26/112.07 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y) % 112.26/112.07 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_of__nat__induct,axiom, % 112.26/112.07 ! [V_x_2,V_Pa_2] : % 112.26/112.07 ( ! [B_y] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) ) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_lazy__sequence_Orecs_I1_J,axiom, % 112.26/112.07 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ). % 112.26/112.07 % 112.26/112.07 fof(fact_beyond__def,axiom, % 112.26/112.07 ! [V_l,V_k] : % 112.26/112.07 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 112.26/112.07 => c_Quickcheck_Obeyond(V_k,V_l) = V_l ) % 112.26/112.07 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 112.26/112.07 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_beyond__zero,axiom, % 112.26/112.07 ! [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) ). % 112.26/112.07 % 112.26/112.07 fof(fact_lazy__sequence_Orecs_I2_J,axiom, % 112.26/112.07 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,V_lazy__sequence_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__image__Collect__eq,axiom, % 112.26/112.07 ! [V_Pa_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_Pa_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_curry__def,axiom, % 112.26/112.07 ! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_curryI,axiom, % 112.26/112.07 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] : % 112.26/112.07 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__id,axiom, % 112.26/112.07 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__inv__into,axiom, % 112.26/112.07 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 112.26/112.07 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__into__inv__into__eq,axiom, % 112.26/112.07 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 112.26/112.07 => hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inv__inv__eq,axiom, % 112.26/112.07 ! [V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 => c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) = V_f_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__imp__bij__inv,axiom, % 112.26/112.07 ! [V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),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))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_o__inv__distrib,axiom, % 112.26/112.07 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 => ( c_Fun_Obij__betw(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.07 => c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__comp__iff,axiom, % 112.26/112.07 ! [V_A_H_H_2,V_f_H_2,T_d,V_A_H_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 112.26/112.07 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2) % 112.26/112.07 <=> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__trans,axiom, % 112.26/112.07 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 112.26/112.07 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2) % 112.26/112.07 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2,V_C_2) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__comp,axiom, % 112.26/112.07 ! [V_g_2,T_d,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 => ( c_Fun_Obij__betw(T_c,T_d,V_g_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))) % 112.26/112.07 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__comp__iff2,axiom, % 112.26/112.07 ! [V_A_2,V_f_2,T_d,V_A_H_H_2,V_A_H_2,V_f_H_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),V_A_H_2)) % 112.26/112.07 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2) % 112.26/112.07 <=> c_Fun_Obij__betw(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_curry__conv,axiom, % 112.26/112.07 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_curryD,axiom, % 112.26/112.07 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) % 112.26/112.07 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_curryE,axiom, % 112.26/112.07 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) % 112.26/112.07 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__image__Compl__eq,axiom, % 112.26/112.07 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 => 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)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__def,axiom, % 112.26/112.07 ! [V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.07 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bijI,axiom, % 112.26/112.07 ! [V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 112.26/112.07 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 112.26/112.07 => c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__subset,axiom, % 112.26/112.07 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 112.26/112.07 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2 % 112.26/112.07 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__imp__surj,axiom, % 112.26/112.07 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__is__surj,axiom, % 112.26/112.07 ! [V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_inj__on__imp__bij__betw,axiom, % 112.26/112.07 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.07 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__def,axiom, % 112.26/112.07 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 112.26/112.07 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.07 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__imp__inj__on,axiom, % 112.26/112.07 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 112.26/112.07 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__is__inj,axiom, % 112.26/112.07 ! [V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__the__inv__into,axiom, % 112.26/112.07 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 112.26/112.07 => c_Fun_Obij__betw(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__same__card,axiom, % 112.26/112.07 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 112.26/112.07 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__empty2,axiom, % 112.26/112.07 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__empty1,axiom, % 112.26/112.07 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_A_2) % 112.26/112.07 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__finite,axiom, % 112.26/112.07 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 112.26/112.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.07 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_BIJ,axiom, % 112.26/112.07 ! [V_B_2,T_c,V_A_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) % 112.26/112.07 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2) % 112.26/112.07 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__id__iff,axiom, % 112.26/112.07 ! [V_B_2,V_A_2,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2) % 112.26/112.07 <=> V_A_2 = V_B_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__id,axiom, % 112.26/112.07 ! [T_b] : c_Fun_Obij__betw(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))) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__Disj__Un,axiom, % 112.26/112.07 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] : % 112.26/112.07 ( 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)) % 112.26/112.07 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 112.26/112.07 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) % 112.26/112.07 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) % 112.26/112.07 => c_Fun_Obij__betw(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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2)) ) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__betw__combine,axiom, % 112.26/112.07 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) % 112.26/112.07 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2) % 112.26/112.07 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 112.26/112.07 => c_Fun_Obij__betw(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_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2)) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_finite__vimage__iff,axiom, % 112.26/112.07 ! [V_F_2,V_h_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(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))) % 112.26/112.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) % 112.26/112.07 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_split__curry,axiom, % 112.26/112.07 ! [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 ). % 112.26/112.07 % 112.26/112.07 fof(fact_curry__split,axiom, % 112.26/112.07 ! [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 ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__image__INT,axiom, % 112.26/112.07 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 => 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)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_vimage__subset__eq,axiom, % 112.26/112.07 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 => ( 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)) % 112.26/112.07 <=> 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))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bij__vimage__eq__inv__image,axiom, % 112.26/112.07 ! [V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 112.26/112.07 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_A_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_ex__bij__betw__nat__finite__1,axiom, % 112.26/112.07 ! [V_M_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 112.26/112.07 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Cantor__Bernstein,axiom, % 112.26/112.07 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) % 112.26/112.07 => ( 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)) % 112.26/112.07 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) % 112.26/112.07 => ( 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)) % 112.26/112.07 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_ex__bij__betw__nat__finite,axiom, % 112.26/112.07 ! [V_M_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 112.26/112.07 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_ex__bij__betw__finite__nat,axiom, % 112.26/112.07 ! [V_M_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) % 112.26/112.07 => ? [B_h] : c_Fun_Obij__betw(T_b,tc_Nat_Onat,B_h,V_M_2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_refl__on__UNION,axiom, % 112.26/112.07 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] : % 112.26/112.07 ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) % 112.26/112.07 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) ) % 112.26/112.07 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bex__reg__eqv,axiom, % 112.26/112.07 ! [V_Pa_2,V_R_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 112.26/112.07 => ( ? [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.07 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_in__respects,axiom, % 112.26/112.07 ! [V_R_2,V_x_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2))) % 112.26/112.07 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Respects__def,axiom, % 112.26/112.07 ! [V_x_2,V_R_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2)) % 112.26/112.07 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_bex__reg__right,axiom, % 112.26/112.07 ! [V_Pa_2,V_Q_2,V_R_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 112.26/112.07 => ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(V_Q_2,B_x)) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) % 112.26/112.07 => ( ? [B_x1] : hBOOL(hAPP(V_Q_2,B_x1)) % 112.26/112.07 => ? [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) % 112.26/112.07 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_babs__reg__eqv,axiom, % 112.26/112.07 ! [V_Pa_2,T_c,V_R_2,T_b] : % 112.26/112.07 ( c_Equiv__Relations_Oequivp(T_b,V_R_2) % 112.26/112.07 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_Pa_2) = V_Pa_2 ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_Babs__def,axiom, % 112.26/112.07 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2)) % 112.26/112.07 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_wf__weak__decr__stable,axiom, % 112.26/112.07 ! [V_r_2,V_f_2,T_b] : % 112.26/112.07 ( ! [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))) % 112.26/112.07 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) % 112.26/112.07 => ? [B_i] : % 112.26/112.07 ! [B_k] : hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),B_k)) = hAPP(V_f_2,B_i) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_INT__anti__mono,axiom, % 112.26/112.07 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 112.26/112.07 => ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 112.26/112.07 => 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_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_g_2))) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_INT__greatest,axiom, % 112.26/112.07 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : % 112.26/112.07 ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x))) ) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_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))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_converse__rtranclE2,axiom, % 112.26/112.07 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] : % 112.26/112.07 ( 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_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 112.26/112.07 => ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2) % 112.26/112.07 => ~ ! [B_a,B_b] : % 112.26/112.07 ( 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_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),V_r_2)) % 112.26/112.07 => ~ 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),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_rtrancl__induct2,axiom, % 112.26/112.07 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] : % 112.26/112.07 ( 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_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) % 112.26/112.07 => ( ! [B_a,B_b] : % 112.26/112.07 ( 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_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 112.26/112.07 => ! [B_aa,B_ba] : % 112.26/112.07 ( 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),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2)) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) % 112.26/112.07 => hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) ) ) ) % 112.26/112.07 => hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_converse__rtrancl__induct2,axiom, % 112.26/112.07 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] : % 112.26/112.07 ( 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_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) % 112.26/112.07 => ( ! [B_a,B_b,B_aa,B_ba] : % 112.26/112.07 ( 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),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2)) % 112.26/112.07 => ( 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),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) % 112.26/112.07 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) ) % 112.26/112.07 => hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_congruent2I_H,axiom, % 112.26/112.07 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] : % 112.26/112.07 ( ! [B_y1,B_z1] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y1),B_z1)),V_r1_2)) % 112.26/112.07 => ! [B_y2,B_z2] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y2),B_z2)),V_r2_2)) % 112.26/112.07 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) ) % 112.26/112.07 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_congruentI,axiom, % 112.26/112.07 ! [T_c,V_f_2,V_r_2,T_b] : % 112.26/112.07 ( ! [B_y,B_z] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2)) % 112.26/112.07 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) ) % 112.26/112.07 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact__03,axiom, % 112.26/112.07 ! [V_xqq,V_xq,T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(T_a),V_xq,V_xqq)) = c_Lazy__Sequence_Oappend(T_a,V_xq,c_Lazy__Sequence_Oflat(T_a,V_xqq)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_all__interval__nat__def,axiom, % 112.26/112.07 ! [V_j_2,V_i_2,V_Pa_2] : % 112.26/112.07 ( c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) % 112.26/112.07 <=> ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2))) % 112.26/112.07 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact__04,axiom, % 112.26/112.07 ! [T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(T_a))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__all__iff__all__interval__nat,axiom, % 112.26/112.07 ! [V_j_2,V_i_2,V_Pa_2] : % 112.26/112.07 ( c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2)) % 112.26/112.07 <=> c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_list__ex__iff__not__all__inverval__nat,axiom, % 112.26/112.07 ! [V_j_2,V_i_2,V_Pa_2] : % 112.26/112.07 ( c_List_Olist__ex(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2)) % 112.26/112.07 <=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_Pa_2),V_i_2,V_j_2) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact__05,axiom, % 112.26/112.07 ! [V_f_2,V_xq_2,T_b,T_c] : hAPP(c_Lazy__Sequence_Obind(T_c,T_b,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_b,c_Lazy__Sequence_Omap(T_c,tc_Lazy__Sequence_Olazy__sequence(T_b),V_f_2,V_xq_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_folding__image_Ocong,axiom, % 112.26/112.07 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] : % 112.26/112.07 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) % 112.26/112.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) % 112.26/112.07 => ( ! [B_x] : % 112.26/112.07 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 112.26/112.07 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 112.26/112.07 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact__06,axiom, % 112.26/112.07 ! [V_xq_2,V_x_2,V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,hAPP(V_f_2,V_x_2),c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,V_xq_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact__07,axiom, % 112.26/112.07 ! [V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b) ). % 112.26/112.07 % 112.26/112.07 fof(fact_New__DSequence_Opos__map__def,axiom, % 112.26/112.07 ! [V_i_2,V_xq_2,V_f_2,T_b,T_c] : c_New__DSequence_Opos__map(T_c,T_b,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,hAPP(V_xq_2,V_i_2)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_power__dvd__imp__le,axiom, % 112.26/112.07 ! [V_n,V_m,V_i] : % 112.26/112.07 ( 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))) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i)) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dvd_Oorder__refl,axiom, % 112.26/112.07 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dvd__0__right,axiom, % 112.26/112.07 ! [V_a,T_a] : % 112.26/112.07 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.07 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dvd__1__left,axiom, % 112.26/112.07 ! [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)) ). % 112.26/112.07 % 112.26/112.07 fof(fact_dvd__setprod,axiom, % 112.26/112.07 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] : % 112.26/112.07 ( class_Rings_Ocomm__semiring__1(T_c) % 112.26/112.07 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 112.26/112.07 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) % 112.26/112.07 => 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))) ) ) ) ). % 112.26/112.07 % 112.26/112.07 fof(fact_unity__coeff__ex,axiom, % 112.26/112.07 ! [V_l_2,V_Pa_2,T_b] : % 112.26/112.07 ( ( class_Rings_Odvd(T_b) % 112.26/112.07 & class_Rings_Osemiring__0(T_b) ) % 112.26/112.07 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x))) % 112.26/112.08 <=> ? [B_x] : % 112.26/112.08 ( 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)))) % 112.26/112.08 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_nat__mult__dvd__cancel__disj,axiom, % 112.26/112.08 ! [V_na_2,V_m_2,V_k_2] : % 112.26/112.08 ( 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_na_2))) % 112.26/112.08 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 112.26/112.08 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__mult__cancel__left,axiom, % 112.26/112.08 ! [V_b_2,V_a_2,V_c_2,T_b] : % 112.26/112.08 ( class_Rings_Oidom(T_b) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) % 112.26/112.08 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 112.26/112.08 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__mult__cancel__right,axiom, % 112.26/112.08 ! [V_b_2,V_c_2,V_a_2,T_b] : % 112.26/112.08 ( class_Rings_Oidom(T_b) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))) % 112.26/112.08 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b) % 112.26/112.08 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__mult__right,axiom, % 112.26/112.08 ! [V_c,V_b,V_a,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => ( 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)) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__mult__left,axiom, % 112.26/112.08 ! [V_c,V_b,V_a,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => ( 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)) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvdI,axiom, % 112.26/112.08 ! [V_k,V_b,V_a,T_a] : % 112.26/112.08 ( class_Rings_Odvd(T_a) % 112.26/112.08 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_mult__dvd__mono,axiom, % 112.26/112.08 ! [V_d,V_c,V_b,V_a,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d)) % 112.26/112.08 => 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))) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__mult,axiom, % 112.26/112.08 ! [V_b,V_c,V_a,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) % 112.26/112.08 => 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))) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__mult2,axiom, % 112.26/112.08 ! [V_c,V_b,V_a,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 112.26/112.08 => 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))) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__triv__right,axiom, % 112.26/112.08 ! [V_b,V_a,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => 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))) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__triv__left,axiom, % 112.26/112.08 ! [V_b,V_a,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => 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))) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_div__mult__div__if__dvd,axiom, % 112.26/112.08 ! [V_w,V_z,V_x,V_y,T_a] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w)) % 112.26/112.08 => 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)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__div__mult,axiom, % 112.26/112.08 ! [V_c,V_b,V_a,T_a] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 112.26/112.08 => 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) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__div__mult__self,axiom, % 112.26/112.08 ! [V_b,V_a,T_a] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 112.26/112.08 => 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 ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_div__mult__swap,axiom, % 112.26/112.08 ! [V_a,V_b,V_c,T_a] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) % 112.26/112.08 => 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) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__mult__div__cancel,axiom, % 112.26/112.08 ! [V_b,V_a,T_a] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 112.26/112.08 => 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 ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_inf__period_I4_J,axiom, % 112.26/112.08 ! [V_t_2,V_D_2,V_d_2,T_b] : % 112.26/112.08 ( ( class_Rings_Ocomm__ring(T_b) % 112.26/112.08 & class_Rings_Odvd(T_b) ) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) % 112.26/112.08 => ! [B_x,B_k] : % 112.26/112.08 ( 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))) % 112.26/112.08 <=> 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))) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_inf__period_I3_J,axiom, % 112.26/112.08 ! [V_t_2,V_D_2,V_d_2,T_b] : % 112.26/112.08 ( ( class_Rings_Ocomm__ring(T_b) % 112.26/112.08 & class_Rings_Odvd(T_b) ) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) % 112.26/112.08 => ! [B_x,B_k] : % 112.26/112.08 ( 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))) % 112.26/112.08 <=> 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))) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom, % 112.26/112.08 ! [V_b_2,V_a_2] : % 112.26/112.08 ( V_a_2 = V_b_2 % 112.26/112.08 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OatLeastAtMost__singleton,axiom, % 112.26/112.08 ! [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))) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom, % 112.26/112.08 ! [V_c_2,V_b_2,V_a_2] : % 112.26/112.08 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) % 112.26/112.08 <=> ( V_a_2 = V_b_2 % 112.26/112.08 & V_b_2 = V_c_2 ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OatLeastatMost__empty,axiom, % 112.26/112.08 ! [V_a_2,V_b_2] : % 112.26/112.08 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) % 112.26/112.08 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OatLeastatMost__empty__iff,axiom, % 112.26/112.08 ! [V_b_2,V_a_2] : % 112.26/112.08 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) % 112.26/112.08 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom, % 112.26/112.08 ! [V_b_2,V_a_2] : % 112.26/112.08 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) % 112.26/112.08 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom, % 112.26/112.08 ! [V_l_2,V_k_2] : % 112.26/112.08 ( 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) % 112.26/112.08 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom, % 112.26/112.08 ! [V_l_2,V_k_2] : % 112.26/112.08 ( 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)) % 112.26/112.08 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OgreaterThanAtMost__empty,axiom, % 112.26/112.08 ! [V_k_2,V_l_2] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) % 112.26/112.08 => 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)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom, % 112.26/112.08 ! [V_b_2,V_a_2] : % 112.26/112.08 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) % 112.26/112.08 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom, % 112.26/112.08 ! [V_b_2,V_a_2] : % 112.26/112.08 ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) % 112.26/112.08 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OgreaterThanLessThan__empty,axiom, % 112.26/112.08 ! [V_k_2,V_l_2] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) % 112.26/112.08 => 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)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OatLeastLessThan__empty,axiom, % 112.26/112.08 ! [V_a_2,V_b_2] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) % 112.26/112.08 => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__1__iff__1,axiom, % 112.26/112.08 ! [V_m_2] : % 112.26/112.08 ( 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)))) % 112.26/112.08 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__minus__iff,axiom, % 112.26/112.08 ! [V_y_2,V_x_2,T_b] : % 112.26/112.08 ( class_Rings_Ocomm__ring__1(T_b) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) % 112.26/112.08 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_minus__dvd__iff,axiom, % 112.26/112.08 ! [V_y_2,V_x_2,T_b] : % 112.26/112.08 ( class_Rings_Ocomm__ring__1(T_b) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2)) % 112.26/112.08 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__diff,axiom, % 112.26/112.08 ! [V_z,V_y,V_x,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__ring__1(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z)) % 112.26/112.08 => 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))) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__diff__nat,axiom, % 112.26/112.08 ! [V_n,V_m,V_k] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 112.26/112.08 => 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))) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_div__add,axiom, % 112.26/112.08 ! [V_y,V_x,V_z,T_a] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y)) % 112.26/112.08 => 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)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__neg__div,axiom, % 112.26/112.08 ! [V_x,V_y,T_a] : % 112.26/112.08 ( class_Divides_Oring__div(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 112.26/112.08 => 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)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__div__neg,axiom, % 112.26/112.08 ! [V_x,V_y,T_a] : % 112.26/112.08 ( class_Divides_Oring__div(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 112.26/112.08 => 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)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__if__abs__eq,axiom, % 112.26/112.08 ! [V_k,V_l,T_a] : % 112.26/112.08 ( class_Rings_Olinordered__idom(T_a) % 112.26/112.08 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_abs__dvd__iff,axiom, % 112.26/112.08 ! [V_k_2,V_m_2,T_b] : % 112.26/112.08 ( class_Rings_Olinordered__idom(T_b) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2)) % 112.26/112.08 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__abs__iff,axiom, % 112.26/112.08 ! [V_k_2,V_m_2,T_b] : % 112.26/112.08 ( class_Rings_Olinordered__idom(T_b) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2))) % 112.26/112.08 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_one__dvd,axiom, % 112.26/112.08 ! [V_a,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__refl,axiom, % 112.26/112.08 ! [V_a,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oeq__iff,axiom, % 112.26/112.08 ! [V_y_2,V_x_2] : % 112.26/112.08 ( V_x_2 = V_y_2 % 112.26/112.08 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 112.26/112.08 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Ole__less,axiom, % 112.26/112.08 ! [V_y_2,V_x_2] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 112.26/112.08 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 112.26/112.08 | V_x_2 = V_y_2 ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oless__le,axiom, % 112.26/112.08 ! [V_y_2,V_x_2] : % 112.26/112.08 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 112.26/112.08 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 112.26/112.08 & V_x_2 != V_y_2 ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oneq__le__trans,axiom, % 112.26/112.08 ! [V_b,V_a] : % 112.26/112.08 ( V_a != V_b % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oeq__refl,axiom, % 112.26/112.08 ! [V_y,V_x] : % 112.26/112.08 ( V_x = V_y % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oantisym__conv,axiom, % 112.26/112.08 ! [V_x_2,V_y_2] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 112.26/112.08 <=> V_x_2 = V_y_2 ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Ole__imp__less__or__eq,axiom, % 112.26/112.08 ! [V_y,V_x] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 112.26/112.08 | V_x = V_y ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Ole__neq__trans,axiom, % 112.26/112.08 ! [V_b,V_a] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 112.26/112.08 => ( V_a != V_b % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oord__eq__le__trans,axiom, % 112.26/112.08 ! [V_c,V_b,V_a] : % 112.26/112.08 ( V_a = V_b % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oord__le__eq__trans,axiom, % 112.26/112.08 ! [V_c,V_b,V_a] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 112.26/112.08 => ( V_b = V_c % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__trans,axiom, % 112.26/112.08 ! [V_c,V_b,V_a,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__antisym,axiom, % 112.26/112.08 ! [V_n,V_m] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) % 112.26/112.08 => V_m = V_n ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oantisym,axiom, % 112.26/112.08 ! [V_y,V_x] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 112.26/112.08 => V_x = V_y ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oorder__trans,axiom, % 112.26/112.08 ! [V_z,V_y,V_x] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oord__eq__less__trans,axiom, % 112.26/112.08 ! [V_c,V_b,V_a] : % 112.26/112.08 ( V_a = V_b % 112.26/112.08 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) ) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Ole__less__trans,axiom, % 112.26/112.08 ! [V_z,V_y,V_x] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) ) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oless__imp__neq,axiom, % 112.26/112.08 ! [V_y,V_x] : % 112.26/112.08 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 112.26/112.08 => V_x != V_y ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oless__not__sym,axiom, % 112.26/112.08 ! [V_y,V_x] : % 112.26/112.08 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 112.26/112.08 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oless__imp__le,axiom, % 112.26/112.08 ! [V_y,V_x] : % 112.26/112.08 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oless__imp__not__less,axiom, % 112.26/112.08 ! [V_y,V_x] : % 112.26/112.08 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 112.26/112.08 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oless__imp__not__eq,axiom, % 112.26/112.08 ! [V_y,V_x] : % 112.26/112.08 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 112.26/112.08 => V_x != V_y ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oless__imp__not__eq2,axiom, % 112.26/112.08 ! [V_y,V_x] : % 112.26/112.08 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 112.26/112.08 => V_y != V_x ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oord__less__eq__trans,axiom, % 112.26/112.08 ! [V_c,V_b,V_a] : % 112.26/112.08 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) % 112.26/112.08 => ( V_b = V_c % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oless__le__trans,axiom, % 112.26/112.08 ! [V_z,V_y,V_x] : % 112.26/112.08 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oless__asym_H,axiom, % 112.26/112.08 ! [V_b,V_a] : % 112.26/112.08 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) % 112.26/112.08 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oless__trans,axiom, % 112.26/112.08 ! [V_z,V_y,V_x] : % 112.26/112.08 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 112.26/112.08 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) ) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Oless__asym,axiom, % 112.26/112.08 ! [V_y,V_x] : % 112.26/112.08 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) % 112.26/112.08 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__0__left,axiom, % 112.26/112.08 ! [V_a,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 112.26/112.08 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_div__dvd__div,axiom, % 112.26/112.08 ! [V_c_2,V_b_2,V_a_2,T_b] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_b) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2))) % 112.26/112.08 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__mod__imp__dvd,axiom, % 112.26/112.08 ! [V_n,V_m,V_k,T_a] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__mod,axiom, % 112.26/112.08 ! [V_n,V_m,V_k,T_a] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n)) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_mod__mod__cancel,axiom, % 112.26/112.08 ! [V_a,V_b,V_c,T_a] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) % 112.26/112.08 => 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) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__mod__iff,axiom, % 112.26/112.08 ! [V_m_2,V_na_2,V_k_2,T_b] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_b) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_na_2)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_na_2))) % 112.26/112.08 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__power__same,axiom, % 112.26/112.08 ! [V_n,V_y,V_x,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 112.26/112.08 => 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))) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_nat__dvd__1__iff__1,axiom, % 112.26/112.08 ! [V_m_2] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 112.26/112.08 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__reduce,axiom, % 112.26/112.08 ! [V_na_2,V_k_2] : % 112.26/112.08 ( 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_na_2),V_k_2))) % 112.26/112.08 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_na_2)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__add,axiom, % 112.26/112.08 ! [V_c,V_b,V_a,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) % 112.26/112.08 => 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))) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OatLeastatMost__psubset__iff,axiom, % 112.26/112.08 ! [V_d_2,V_c_2,V_b_2,V_a_2] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2))) % 112.26/112.08 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) % 112.26/112.08 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) % 112.26/112.08 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) % 112.26/112.08 & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2)) ) % 112.26/112.08 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2)) ) ) ) ) % 112.26/112.08 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__eq__mod__eq__0,axiom, % 112.26/112.08 ! [V_b_2,V_a_2,T_b] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_b) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) % 112.26/112.08 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__imp__mod__0,axiom, % 112.26/112.08 ! [V_b,V_a,T_a] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) % 112.26/112.08 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_div__power,axiom, % 112.26/112.08 ! [V_n,V_x,V_y,T_a] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) % 112.26/112.08 => 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)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_nat__dvd__not__less,axiom, % 112.26/112.08 ! [V_n,V_m] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 112.26/112.08 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OatMost__iff,axiom, % 112.26/112.08 ! [V_k_2,V_i_2] : % 112.26/112.08 ( 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))) % 112.26/112.08 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OatLeast__iff,axiom, % 112.26/112.08 ! [V_k_2,V_i_2] : % 112.26/112.08 ( 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))) % 112.26/112.08 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OlessThan__iff,axiom, % 112.26/112.08 ! [V_k_2,V_i_2] : % 112.26/112.08 ( 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))) % 112.26/112.08 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OgreaterThan__iff,axiom, % 112.26/112.08 ! [V_k_2,V_i_2] : % 112.26/112.08 ( 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))) % 112.26/112.08 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__diffD1,axiom, % 112.26/112.08 ! [V_n,V_m,V_k] : % 112.26/112.08 ( 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))) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__diffD,axiom, % 112.26/112.08 ! [V_n,V_m,V_k] : % 112.26/112.08 ( 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))) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_OatLeastatMost__subset__iff,axiom, % 112.26/112.08 ! [V_d_2,V_c_2,V_b_2,V_a_2] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2))) % 112.26/112.08 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) % 112.26/112.08 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) % 112.26/112.08 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_le__imp__power__dvd,axiom, % 112.26/112.08 ! [V_a,V_n,V_m,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 112.26/112.08 => 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))) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__power__le,axiom, % 112.26/112.08 ! [V_m,V_n,V_y,V_x,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 112.26/112.08 => 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))) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_power__le__dvd,axiom, % 112.26/112.08 ! [V_m,V_b,V_n,V_a,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => ( 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)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 112.26/112.08 => 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)) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__div__div__eq__mult,axiom, % 112.26/112.08 ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_b) % 112.26/112.08 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) % 112.26/112.08 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2)) % 112.26/112.08 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2) % 112.26/112.08 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__div__eq__mult,axiom, % 112.26/112.08 ! [V_c_2,V_b_2,V_a_2,T_b] : % 112.26/112.08 ( class_Divides_Osemiring__div(T_b) % 112.26/112.08 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) % 112.26/112.08 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2 % 112.26/112.08 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__eq__mod__eq__0__number__of,axiom, % 112.26/112.08 ! [V_y_2,V_x_2,T_b] : % 112.26/112.08 ( ( class_Divides_Osemiring__div(T_b) % 112.26/112.08 & class_Int_Onumber(T_b) ) % 112.26/112.08 => ( 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))) % 112.26/112.08 <=> 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) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_setprod__dvd__setprod__subset,axiom, % 112.26/112.08 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] : % 112.26/112.08 ( ( class_Groups_Ocomm__monoid__mult(T_c) % 112.26/112.08 & class_Rings_Odvd(T_c) ) % 112.26/112.08 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) % 112.26/112.08 => 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))) ) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__mult__cancel,axiom, % 112.26/112.08 ! [V_n,V_m,V_k] : % 112.26/112.08 ( 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))) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_nat__mult__dvd__cancel1,axiom, % 112.26/112.08 ! [V_na_2,V_m_2,V_k_2] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 112.26/112.08 => ( 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_na_2))) % 112.26/112.08 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__imp__le,axiom, % 112.26/112.08 ! [V_n,V_k] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__power,axiom, % 112.26/112.08 ! [V_x,V_n,T_a] : % 112.26/112.08 ( class_Rings_Ocomm__semiring__1(T_a) % 112.26/112.08 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 112.26/112.08 | V_x = c_Groups_Oone__class_Oone(T_a) ) % 112.26/112.08 => 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))) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__mult__cancel2,axiom, % 112.26/112.08 ! [V_na_2,V_m_2] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 112.26/112.08 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),V_m_2)),V_m_2)) % 112.26/112.08 <=> V_na_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd__mult__cancel1,axiom, % 112.26/112.08 ! [V_na_2,V_m_2] : % 112.26/112.08 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 112.26/112.08 => ( 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_na_2)),V_m_2)) % 112.26/112.08 <=> V_na_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 112.26/112.08 % 112.26/112.08 fof(fact_dvd_Ostrict__monoD,axiom, % 112.26/112.08 ! [V_y_2,V_x_2,V_f_2,T_b] : % 112.26/112.08 ( class_Orderings_Oorder(T_b) % 112.26/112.08 => ( 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) % 112.26/112.08 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) % 112.26/112.08 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) % 112.26/112.08 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ). % 112.26/112.08 % 112.26/112.08 %----Arity declarations (220) % 112.26/112.08 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 112.26/112.08 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Lattices_Obounded__lattice(T_1) % 112.26/112.08 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 112.26/112.08 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Lattices_Obounded__lattice(T_1) % 112.26/112.08 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Lattices_Obounded__lattice(T_1) % 112.26/112.08 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Lattices_Olattice(T_1) % 112.26/112.08 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Lattices_Olattice(T_1) % 112.26/112.08 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Lattices_Odistrib__lattice(T_1) % 112.26/112.08 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Lattices_Oboolean__algebra(T_1) % 112.26/112.08 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Orderings_Opreorder,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Orderings_Opreorder(T_1) % 112.26/112.08 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Finite__Set_Ofinite,axiom, % 112.26/112.08 ! [T_1,T_2] : % 112.26/112.08 ( ( class_Finite__Set_Ofinite(T_2) % 112.26/112.08 & class_Finite__Set_Ofinite(T_1) ) % 112.26/112.08 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Lattices_Olattice,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Lattices_Olattice(T_1) % 112.26/112.08 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Orderings_Oorder,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Orderings_Oorder(T_1) % 112.26/112.08 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Orderings_Otop,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Orderings_Otop(T_1) % 112.26/112.08 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Orderings_Oord,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Orderings_Oord(T_1) % 112.26/112.08 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Orderings_Obot,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Orderings_Obot(T_1) % 112.26/112.08 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Groups_Ouminus,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Groups_Ouminus(T_1) % 112.26/112.08 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Groups_Ominus,axiom, % 112.26/112.08 ! [T_2,T_1] : % 112.26/112.08 ( class_Groups_Ominus(T_1) % 112.26/112.08 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_fun__Enum_Oenum,axiom, % 112.26/112.08 ! [T_1,T_2] : % 112.26/112.08 ( ( class_Enum_Oenum(T_2) % 112.26/112.08 & class_Enum_Oenum(T_1) ) % 112.26/112.08 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Com__Ocom__Nat_Osize,axiom, % 112.26/112.08 class_Nat_Osize(tc_Com_Ocom) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 112.26/112.08 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 112.26/112.08 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 112.26/112.08 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 112.26/112.08 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 112.26/112.08 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 112.26/112.08 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 112.26/112.08 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 112.26/112.08 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 112.26/112.08 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 112.26/112.08 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 112.26/112.08 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 112.26/112.08 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 112.26/112.08 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 112.26/112.08 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 112.26/112.08 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 112.26/112.08 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 112.26/112.08 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 112.26/112.08 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom, % 112.26/112.08 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 112.26/112.08 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 112.26/112.08 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 112.26/112.08 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 112.26/112.08 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 112.26/112.08 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 112.26/112.08 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 112.26/112.08 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 112.26/112.08 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 112.26/112.08 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 112.26/112.08 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 112.26/112.08 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 112.26/112.08 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 112.26/112.08 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 112.26/112.08 class_Divides_Osemiring__div(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 112.26/112.08 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 112.26/112.08 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 112.26/112.08 class_Groups_Oab__group__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 112.26/112.08 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 112.26/112.08 class_Rings_Oordered__ring(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 112.26/112.08 class_Orderings_Opreorder(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 112.26/112.08 class_Orderings_Olinorder(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 112.26/112.08 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 112.26/112.08 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 112.26/112.08 class_Groups_Omonoid__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 112.26/112.08 class_Rings_Osemiring__1(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 112.26/112.08 class_Rings_Osemiring__0(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 112.26/112.08 class_Lattices_Olattice(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 112.26/112.08 class_Groups_Ogroup__add(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 112.26/112.08 class_Divides_Oring__div(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 112.26/112.08 class_Rings_Omult__zero(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom, % 112.26/112.08 class_Rings_Ocomm__ring(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 112.26/112.08 class_Orderings_Oorder(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 112.26/112.08 class_Int_Oring__char__0(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 112.26/112.08 class_Int_Onumber__ring(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 112.26/112.08 class_Rings_Osemiring(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Orderings_Oord,axiom, % 112.26/112.08 class_Orderings_Oord(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 112.26/112.08 class_Groups_Ouminus(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 112.26/112.08 class_Groups_Osgn__if(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 112.26/112.08 class_Groups_Oabs__if(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 112.26/112.08 class_Rings_Oring__1(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Ominus,axiom, % 112.26/112.08 class_Groups_Ominus(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Power_Opower,axiom, % 112.26/112.08 class_Power_Opower(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Ozero,axiom, % 112.26/112.08 class_Groups_Ozero(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Oring,axiom, % 112.26/112.08 class_Rings_Oring(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Oidom,axiom, % 112.26/112.08 class_Rings_Oidom(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Int_Onumber,axiom, % 112.26/112.08 class_Int_Onumber(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Groups_Oone,axiom, % 112.26/112.08 class_Groups_Oone(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Int__Oint__Rings_Odvd,axiom, % 112.26/112.08 class_Rings_Odvd(tc_Int_Oint) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 112.26/112.08 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 112.26/112.08 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 112.26/112.08 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 112.26/112.08 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 112.26/112.08 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 112.26/112.08 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 112.26/112.08 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 112.26/112.08 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 112.26/112.08 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 112.26/112.08 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 112.26/112.08 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 112.26/112.08 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 112.26/112.08 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 112.26/112.08 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 112.26/112.08 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 112.26/112.08 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 112.26/112.08 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 112.26/112.08 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 112.26/112.08 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 112.26/112.08 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 112.26/112.08 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 112.26/112.08 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 112.26/112.08 class_Orderings_Owellorder(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 112.26/112.08 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 112.26/112.08 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 112.26/112.08 class_Orderings_Opreorder(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 112.26/112.08 class_Orderings_Olinorder(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 112.26/112.08 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 112.26/112.08 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 112.26/112.08 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 112.26/112.08 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 112.26/112.08 class_Lattices_Olattice(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 112.26/112.08 class_Rings_Omult__zero(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 112.26/112.08 class_Orderings_Oorder(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 112.26/112.08 class_Rings_Osemiring(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 112.26/112.08 class_Orderings_Oord(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 112.26/112.08 class_Orderings_Obot(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 112.26/112.08 class_Groups_Ominus(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Power_Opower,axiom, % 112.26/112.08 class_Power_Opower(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 112.26/112.08 class_Groups_Ozero(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Int_Onumber,axiom, % 112.26/112.08 class_Int_Onumber(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Groups_Oone,axiom, % 112.26/112.08 class_Groups_Oone(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Rings_Odvd,axiom, % 112.26/112.08 class_Rings_Odvd(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nat__Onat__Nat_Osize,axiom, % 112.26/112.08 class_Nat_Osize(tc_Nat_Onat) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 112.26/112.08 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 112.26/112.08 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 112.26/112.08 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 112.26/112.08 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 112.26/112.08 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 112.26/112.08 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 112.26/112.08 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 112.26/112.08 class_Orderings_Opreorder(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 112.26/112.08 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 112.26/112.08 class_Lattices_Olattice(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 112.26/112.08 class_Orderings_Oorder(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 112.26/112.08 class_Orderings_Otop(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 112.26/112.08 class_Orderings_Oord(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 112.26/112.08 class_Orderings_Obot(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 112.26/112.08 class_Groups_Ouminus(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 112.26/112.08 class_Groups_Ominus(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 112.26/112.08 class_Enum_Oenum(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_HOL__Obool__Nat_Osize,axiom, % 112.26/112.08 class_Nat_Osize(tc_HOL_Obool) ). % 112.26/112.08 % 112.26/112.08 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom, % 112.26/112.08 ! [T_1] : % 112.26/112.08 ( class_Lazy__Sequence_Osmall__lazy(T_1) % 112.26/112.08 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_List__Olist__Nat_Osize,axiom, % 112.26/112.08 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 112.26/112.08 % 112.26/112.08 fof(arity_sum__Finite__Set_Ofinite,axiom, % 112.26/112.08 ! [T_1,T_2] : % 112.26/112.08 ( ( class_Finite__Set_Ofinite(T_2) % 112.26/112.08 & class_Finite__Set_Ofinite(T_1) ) % 112.26/112.08 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_sum__Enum_Oenum,axiom, % 112.26/112.08 ! [T_1,T_2] : % 112.26/112.08 ( ( class_Enum_Oenum(T_2) % 112.26/112.08 & class_Enum_Oenum(T_1) ) % 112.26/112.08 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_sum__Nat_Osize,axiom, % 112.26/112.08 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 112.26/112.08 ! [T_1] : % 112.26/112.08 ( class_Finite__Set_Ofinite(T_1) % 112.26/112.08 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 112.26/112.08 ! [T_1] : % 112.26/112.08 ( class_Enum_Oenum(T_1) % 112.26/112.08 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Option__Ooption__Nat_Osize,axiom, % 112.26/112.08 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom, % 112.26/112.08 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ). % 112.26/112.08 % 112.26/112.08 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom, % 112.26/112.08 ! [T_1,T_2] : % 112.26/112.08 ( ( class_Lazy__Sequence_Osmall__lazy(T_2) % 112.26/112.08 & class_Lazy__Sequence_Osmall__lazy(T_1) ) % 112.26/112.08 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_prod__Finite__Set_Ofinite,axiom, % 112.26/112.08 ! [T_1,T_2] : % 112.26/112.08 ( ( class_Finite__Set_Ofinite(T_2) % 112.26/112.08 & class_Finite__Set_Ofinite(T_1) ) % 112.26/112.08 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_prod__Enum_Oenum,axiom, % 112.26/112.08 ! [T_1,T_2] : % 112.26/112.08 ( ( class_Enum_Oenum(T_2) % 112.26/112.08 & class_Enum_Oenum(T_1) ) % 112.26/112.08 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 112.26/112.08 % 112.26/112.08 fof(arity_prod__Nat_Osize,axiom, % 112.26/112.08 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom, % 112.26/112.08 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 112.26/112.08 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 112.26/112.08 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 112.26/112.08 class_Nat_Osize(tc_Product__Type_Ounit) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 112.26/112.08 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 112.26/112.08 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 112.26/112.08 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 112.26/112.08 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 112.26/112.08 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 112.26/112.08 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 112.26/112.08 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 112.26/112.08 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 112.26/112.08 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 112.26/112.08 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 112.26/112.08 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 112.26/112.08 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 112.26/112.08 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 112.26/112.08 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 112.26/112.08 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 112.26/112.08 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 112.26/112.08 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 112.26/112.08 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 112.26/112.08 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 112.26/112.08 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 112.26/112.08 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 112.26/112.08 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 112.26/112.08 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 112.26/112.08 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 112.26/112.08 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 112.26/112.08 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 112.26/112.08 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 112.26/112.08 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 112.26/112.08 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 112.26/112.08 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 112.26/112.08 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 112.26/112.08 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 112.26/112.08 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 112.26/112.08 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 112.26/112.08 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 112.26/112.08 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 112.26/112.08 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom, % 112.26/112.08 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 112.26/112.08 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 112.26/112.08 % 112.26/112.08 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 112.26/112.08 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 112.26/112.08 % 112.26/112.08 %----Helper facts (20) % 112.26/112.08 fof(help_c__COMBI__1,axiom, % 112.26/112.08 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 112.26/112.08 % 112.26/112.08 fof(help_c__COMBK__1,axiom, % 112.26/112.08 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 112.26/112.08 % 112.26/112.08 fof(help_c__COMBB__1,axiom, % 112.26/112.08 ! [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)) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__COMBC__1,axiom, % 112.26/112.08 ! [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) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__COMBS__1,axiom, % 112.26/112.08 ! [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)) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fequal__1,axiom, % 112.26/112.08 ! [V_y_2,V_x_2] : % 112.26/112.08 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 112.26/112.08 | V_x_2 = V_y_2 ) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fequal__2,axiom, % 112.26/112.08 ! [V_y_2,V_x_2] : % 112.26/112.08 ( V_x_2 != V_y_2 % 112.26/112.08 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fFalse__1,axiom, % 112.26/112.08 ~ hBOOL(c_fFalse) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fTrue__1,axiom, % 112.26/112.08 hBOOL(c_fTrue) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fNot__1,axiom, % 112.26/112.08 ! [V_Pa_2] : % 112.26/112.08 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2)) % 112.26/112.08 | ~ hBOOL(V_Pa_2) ) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fNot__2,axiom, % 112.26/112.08 ! [V_Pa_2] : % 112.26/112.08 ( ~ ~ hBOOL(V_Pa_2) % 112.26/112.08 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fconj__1,axiom, % 112.26/112.08 ! [V_Q_2,V_Pa_2] : % 112.26/112.08 ( ~ hBOOL(V_Pa_2) % 112.26/112.08 | ~ hBOOL(V_Q_2) % 112.26/112.08 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) ) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fconj__2,axiom, % 112.26/112.08 ! [V_Q_2,V_Pa_2] : % 112.26/112.08 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) % 112.26/112.08 | hBOOL(V_Pa_2) ) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fconj__3,axiom, % 112.26/112.08 ! [V_Q_2,V_Pa_2] : % 112.26/112.08 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) % 112.26/112.08 | hBOOL(V_Q_2) ) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fdisj__1,axiom, % 112.26/112.08 ! [V_Q_2,V_Pa_2] : % 112.26/112.08 ( ~ hBOOL(V_Pa_2) % 112.26/112.08 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fdisj__2,axiom, % 112.26/112.08 ! [V_Pa_2,V_Q_2] : % 112.26/112.08 ( ~ hBOOL(V_Q_2) % 112.26/112.08 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fdisj__3,axiom, % 112.26/112.08 ! [V_Q_2,V_Pa_2] : % 112.26/112.08 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) % 112.26/112.08 | hBOOL(V_Pa_2) % 112.26/112.08 | hBOOL(V_Q_2) ) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fimplies__1,axiom, % 112.26/112.08 ! [V_Q_2,V_Pa_2] : % 112.26/112.08 ( hBOOL(V_Pa_2) % 112.26/112.08 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fimplies__2,axiom, % 112.26/112.08 ! [V_Pa_2,V_Q_2] : % 112.26/112.08 ( ~ hBOOL(V_Q_2) % 112.26/112.08 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ). % 112.26/112.08 % 112.26/112.08 fof(help_c__fimplies__3,axiom, % 112.26/112.08 ! [V_Q_2,V_Pa_2] : % 112.26/112.08 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) % 112.26/112.08 | ~ hBOOL(V_Pa_2) % 112.26/112.08 | hBOOL(V_Q_2) ) ). % 112.26/112.08 % 112.26/112.08 %----Conjectures (4) % 112.26/112.08 fof(conj_0,hypothesis, % 112.26/112.08 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)) ). % 112.26/112.08 % 112.26/112.08 fof(conj_1,hypothesis, % 112.26/112.08 v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U) ). % 112.26/112.08 % 112.26/112.08 fof(conj_2,hypothesis, % 112.26/112.08 hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)) ). % 112.26/112.08 % 112.26/112.08 fof(conj_3,conjecture, % 112.26/112.08 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ). % 112.26/112.08 % 112.26/112.08 %------------------------------------------------------------------------------ % 112.26/112.08 %------------------------------------------- % 112.26/112.08 % Proof found % 112.26/112.08 % SZS status Theorem for theBenchmark % 112.26/112.08 % SZS output start Proof % 112.26/112.08 %ClaNum:10400(EqnAxiom:3041) % 112.26/112.08 %VarNum:70804(SingletonVarNum:20416) % 112.26/112.08 %MaxLitNum:8 % 112.26/112.08 %MaxfuncDepth:13 % 112.26/112.08 %SharedTerms:1000 % 112.26/112.08 %goalClause: 4641 % 112.26/112.08 %singleGoalClaCount:1 % 112.26/112.08 [3045]P1(a177) % 112.26/112.08 [3046]P2(a895) % 112.26/112.08 [3047]P2(a898) % 112.26/112.08 [3048]P65(a895) % 112.26/112.08 [3049]P65(a899) % 112.26/112.08 [3050]P65(a1) % 112.26/112.08 [3051]P65(a89) % 112.26/112.08 [3052]P66(a895) % 112.26/112.08 [3053]P66(a899) % 112.26/112.08 [3054]P107(a895) % 112.26/112.08 [3055]P107(a899) % 112.26/112.08 [3056]P107(a1) % 112.26/112.08 [3057]P107(a89) % 112.26/112.08 [3058]P108(a899) % 112.26/112.08 [3059]P108(a1) % 112.26/112.08 [3060]P108(a89) % 112.26/112.08 [3061]P109(a895) % 112.26/112.08 [3062]P109(a899) % 112.26/112.08 [3063]P109(a1) % 112.26/112.08 [3064]P109(a89) % 112.26/112.08 [3065]P67(a895) % 112.26/112.08 [3066]P67(a899) % 112.26/112.08 [3067]P67(a1) % 112.26/112.08 [3068]P67(a89) % 112.26/112.08 [3069]P79(a1) % 112.26/112.08 [3070]P68(a1) % 112.26/112.08 [3071]P110(a1) % 112.26/112.08 [3072]P69(a899) % 112.26/112.08 [3073]P69(a1) % 112.26/112.08 [3074]P69(a89) % 112.26/112.08 [3075]P83(a899) % 112.26/112.08 [3076]P83(a1) % 112.26/112.08 [3077]P83(a89) % 112.26/112.08 [3078]P70(a899) % 112.26/112.08 [3079]P70(a1) % 112.26/112.08 [3080]P70(a89) % 112.26/112.08 [3081]P80(a899) % 112.26/112.08 [3082]P80(a1) % 112.26/112.08 [3083]P80(a89) % 112.26/112.08 [3084]P75(a899) % 112.26/112.08 [3085]P75(a1) % 112.26/112.08 [3086]P75(a89) % 112.26/112.08 [3087]P82(a899) % 112.26/112.08 [3088]P82(a1) % 112.26/112.08 [3089]P82(a89) % 112.26/112.08 [3090]P71(a899) % 112.26/112.08 [3091]P71(a1) % 112.26/112.08 [3092]P71(a89) % 112.26/112.08 [3093]P72(a899) % 112.26/112.08 [3094]P72(a1) % 112.26/112.08 [3095]P72(a89) % 112.26/112.08 [3096]P73(a899) % 112.26/112.08 [3097]P73(a1) % 112.26/112.08 [3098]P73(a89) % 112.26/112.08 [3099]P84(a899) % 112.26/112.08 [3100]P84(a1) % 112.26/112.08 [3101]P84(a89) % 112.26/112.08 [3102]P85(a899) % 112.26/112.08 [3103]P85(a1) % 112.26/112.08 [3104]P85(a89) % 112.26/112.08 [3105]P76(a1) % 112.26/112.08 [3106]P111(a1) % 112.26/112.08 [3107]P112(a1) % 112.26/112.08 [3108]P113(a899) % 112.26/112.08 [3109]P113(a1) % 112.26/112.08 [3110]P113(a89) % 112.26/112.08 [3111]P139(a899) % 112.26/112.08 [3112]P139(a1) % 112.26/112.08 [3113]P139(a89) % 112.26/112.08 [3114]P126(a899) % 112.26/112.08 [3115]P126(a1) % 112.26/112.08 [3116]P126(a89) % 112.26/112.08 [3117]P119(a899) % 112.26/112.08 [3118]P119(a1) % 112.26/112.08 [3119]P119(a89) % 112.26/112.08 [3120]P143(a899) % 112.26/112.08 [3121]P143(a1) % 112.26/112.08 [3122]P129(a1) % 112.26/112.08 [3123]P132(a899) % 112.26/112.08 [3124]P132(a1) % 112.26/112.08 [3125]P132(a89) % 112.26/112.08 [3126]P87(a899) % 112.26/112.08 [3127]P87(a1) % 112.26/112.08 [3128]P87(a89) % 112.26/112.08 [3129]P81(a899) % 112.26/112.08 [3130]P81(a1) % 112.26/112.08 [3131]P81(a89) % 112.26/112.08 [3132]P77(a1) % 112.26/112.08 [3133]P133(a899) % 112.26/112.08 [3134]P133(a1) % 112.26/112.08 [3135]P133(a89) % 112.26/112.08 [3136]P140(a1) % 112.26/112.08 [3137]P144(a899) % 112.26/112.08 [3138]P144(a1) % 112.26/112.08 [3139]P144(a89) % 112.26/112.08 [3140]P88(a899) % 112.26/112.08 [3141]P88(a1) % 112.26/112.08 [3142]P88(a89) % 112.26/112.08 [3143]P135(a899) % 112.26/112.08 [3144]P135(a1) % 112.26/112.08 [3145]P135(a89) % 112.26/112.08 [3146]P137(a899) % 112.26/112.08 [3147]P137(a1) % 112.26/112.08 [3148]P137(a89) % 112.26/112.08 [3149]P136(a899) % 112.26/112.08 [3150]P136(a1) % 112.26/112.08 [3151]P136(a89) % 112.26/112.08 [3152]P127(a1) % 112.26/112.08 [3153]P128(a1) % 112.26/112.08 [3154]P134(a899) % 112.26/112.08 [3155]P134(a1) % 112.26/112.08 [3156]P134(a89) % 112.26/112.08 [3157]P120(a899) % 112.26/112.08 [3158]P120(a1) % 112.26/112.08 [3159]P120(a89) % 112.26/112.08 [3160]P130(a899) % 112.26/112.08 [3161]P130(a1) % 112.26/112.08 [3162]P130(a89) % 112.26/112.08 [3163]P131(a1) % 112.26/112.08 [3164]P141(a1) % 112.26/112.08 [3165]P92(a1) % 112.26/112.08 [3166]P93(a899) % 112.26/112.08 [3167]P93(a1) % 112.26/112.08 [3168]P93(a89) % 112.26/112.08 [3169]P94(a1) % 112.26/112.08 [3170]P95(a899) % 112.26/112.08 [3171]P95(a1) % 112.26/112.08 [3172]P95(a89) % 112.26/112.08 [3173]P145(a899) % 112.26/112.08 [3174]P145(a1) % 112.26/112.08 [3175]P145(a89) % 112.26/112.08 [3176]P86(a1) % 112.26/112.08 [3177]P138(a1) % 112.26/112.08 [3178]P96(a895) % 112.26/112.08 [3179]P89(a895) % 112.26/112.08 [3180]P89(a1) % 112.26/112.08 [3181]P121(a1) % 112.26/112.08 [3182]P114(a1) % 112.26/112.08 [3183]P142(a1) % 112.26/112.08 [3184]P74(a1) % 112.26/112.08 [3185]P90(a1) % 112.26/112.08 [3186]P3(a899) % 112.26/112.08 [3187]P3(a1) % 112.26/112.08 [3188]P3(a89) % 112.26/112.08 [3189]P4(a1) % 112.26/112.08 [3190]P115(a899) % 112.26/112.08 [3191]P115(a1) % 112.26/112.08 [3192]P115(a89) % 112.26/112.08 [3193]P146(a899) % 112.26/112.08 [3194]P146(a1) % 112.26/112.08 [3195]P146(a89) % 112.26/112.08 [3196]P98(a895) % 112.26/112.08 [3197]P98(a899) % 112.26/112.08 [3198]P98(a1) % 112.26/112.08 [3199]P99(a895) % 112.26/112.08 [3200]P99(a899) % 112.26/112.08 [3201]P99(a1) % 112.26/112.08 [3202]P100(a895) % 112.26/112.08 [3203]P102(a895) % 112.26/112.08 [3204]P116(a895) % 112.26/112.08 [3205]P5(a895) % 112.26/112.08 [3206]P103(a895) % 112.26/112.08 [3207]P103(a899) % 112.26/112.08 [3208]P103(a1) % 112.26/112.08 [3209]P104(a895) % 112.26/112.08 [3210]P104(a899) % 112.26/112.08 [3211]P104(a1) % 112.26/112.08 [3212]P78(a899) % 112.26/112.08 [3213]P78(a1) % 112.26/112.08 [3214]P78(a89) % 112.26/112.08 [3215]P117(a899) % 112.26/112.08 [3216]P91(a899) % 112.26/112.08 [3217]P91(a1) % 112.26/112.08 [3218]P91(a89) % 112.26/112.08 [3219]P60(a895) % 112.26/112.08 [3220]P60(a898) % 112.26/112.08 [3221]P106(a895) % 112.26/112.08 [3222]P106(a896) % 112.26/112.08 [3223]P106(a899) % 112.26/112.08 [3224]P106(a89) % 112.26/112.08 [3225]P106(a898) % 112.26/112.08 [3226]P106(a313) % 112.26/112.08 [3227]P105(a1) % 112.26/112.08 [3228]P105(a898) % 112.26/112.08 [3229]P122(a899) % 112.26/112.08 [3230]P122(a1) % 112.26/112.08 [3231]P122(a89) % 112.26/112.08 [3232]P118(a1) % 112.26/112.08 [3233]P101(a895) % 112.26/112.08 [3247]P36(a899,a230) % 112.26/112.08 [3248]P36(a899,a307) % 112.26/112.08 [3249]P37(a899,a230) % 112.26/112.08 [4574]~E(a87,a77) % 112.26/112.08 [4575]~P1(a229) % 112.26/112.08 [3042]E(f2(a1),a77) % 112.26/112.08 [3043]E(f3(a89),a4) % 112.26/112.08 [3044]E(f90(a89),a5) % 112.26/112.08 [3234]E(f178(a899),f2(a899)) % 112.26/112.08 [3235]E(f223(a899),f91(a899)) % 112.26/112.08 [3236]E(f228(a899),f92(a899)) % 112.26/112.08 [3237]E(f93(a1),f25(a1)) % 112.26/112.08 [3238]E(f78(a229),f2(a899)) % 112.26/112.08 [3239]E(f78(a177),f2(a899)) % 112.26/112.08 [3240]P6(f72(a1)) % 112.26/112.08 [3241]P6(f2(a1)) % 112.26/112.08 [3295]P36(f905(a899,a899),a26) % 112.26/112.08 [3638]E(f310(a899,a899,a230,a230),a26) % 112.26/112.08 [4576]~E(f72(a1),f2(a1)) % 112.26/112.08 [3242]E(f6(f2(a89)),f2(a899)) % 112.26/112.08 [3243]E(f101(f2(a899)),f2(a899)) % 112.26/112.08 [3251]E(f317(f73(a1),a77),a77) % 112.26/112.08 [3254]E(f317(a102,f2(a899)),f72(a899)) % 112.26/112.08 [3255]E(f317(a95,f72(a1)),f72(a899)) % 112.26/112.08 [3256]E(f317(a5,f72(a899)),f72(a89)) % 112.26/112.08 [3258]E(f317(a5,f2(a899)),f2(a89)) % 112.26/112.08 [3260]E(f317(f94(a1),a77),f2(a1)) % 112.26/112.08 [3261]E(f317(f94(a89),a77),f2(a89)) % 112.26/112.08 [3262]E(f317(a95,f2(a1)),f2(a899)) % 112.26/112.08 [3263]E(f317(f94(a899),a77),f2(a899)) % 112.26/112.08 [3264]E(f317(f179(a895),a229),f2(a899)) % 112.26/112.08 [3265]E(f317(f179(a895),a177),f2(a899)) % 112.26/112.08 [3271]E(f317(f73(a1),f72(a1)),a87) % 112.26/112.08 [3278]E(f317(f90(a1),f72(a899)),f72(a1)) % 112.26/112.08 [3279]E(f317(f90(a1),f2(a899)),f2(a1)) % 112.26/112.08 [3280]E(f317(f73(a1),f2(a1)),f2(a1)) % 112.26/112.08 [3282]E(f317(f179(a89),f2(a89)),f2(a899)) % 112.26/112.08 [3292]E(f317(a95,f72(a1)),f317(a102,f2(a899))) % 112.26/112.08 [3293]E(f308(f905(a899,a899),a26),a27) % 112.26/112.08 [3294]E(f309(f905(a899,a899),a26),a28) % 112.26/112.08 [3296]P1(f317(f29(a897),a907)) % 112.26/112.08 [3322]E(f317(f272(a899),f2(a899)),f178(f906(a899,a895))) % 112.26/112.08 [3323]E(f317(f273(a899),f2(a899)),f232(f906(a899,a895))) % 112.26/112.08 [3331]P39(f178(f906(a1,a895))) % 112.26/112.08 [3365]E(f317(f317(f3(a89),f2(a89)),f72(a89)),f2(a89)) % 112.26/112.08 [3441]P1(f317(f317(f225(a1),a87),f2(a1))) % 112.26/112.08 [3461]E(f317(f300(a897,a894,a910),a907),a908) % 112.26/112.08 [3466]P1(f317(f317(f224(a1),f2(a1)),f72(a1))) % 112.26/112.08 [3468]P1(f317(f317(f225(a1),f2(a1)),f72(a1))) % 112.26/112.08 [3669]E(f317(f317(f279(a899,a899,a899),a307),f297(a899,a307)),a230) % 112.26/112.08 [3706]P40(a1,a899,a95,f317(f224(a1),f2(a1))) % 112.26/112.08 [3710]E(f317(f317(f35(a899,f906(a899,a895)),f232(f906(a899,a895))),f294(a899)),f178(f906(a899,a895))) % 112.26/112.08 [3711]E(f317(f317(f36(a899,f906(a899,a895)),f232(f906(a899,a895))),f291(a899)),f232(f906(a899,a895))) % 112.26/112.08 [3712]E(f317(f317(f36(a899,f906(a899,a895)),f232(f906(a899,a895))),f272(a899)),f232(f906(a899,a895))) % 112.26/112.08 [3713]E(f317(f317(f36(a899,f906(a899,a895)),f232(f906(a899,a895))),f273(a899)),f232(f906(a899,a895))) % 112.26/112.08 [3728]P24(a899,a1,f90(a1),f232(f906(a899,a895))) % 112.26/112.08 [3742]P40(a899,a1,f90(a1),f317(f18(a895,a899),a177)) % 112.26/112.08 [3877]E(f317(f67(a899,a89,a1,a5),a95),f94(a89)) % 112.26/112.08 [4096]P56(a89,a899,a22,a5,f232(f906(a899,a895))) % 112.26/112.08 [4100]P56(a1,f906(f905(a899,a899),a895),a98,a83,a88) % 112.26/112.08 [4354]E(f248(a1,a1,a1,a1,f25(a1),f73(a1)),a47) % 112.26/112.08 [4585]~E(f317(f94(a1),a87),f317(f94(a1),a77)) % 112.26/112.08 [4586]~P1(f317(a183,f72(a1))) % 112.26/112.08 [4587]~P1(f317(a183,f2(a1))) % 112.26/112.08 [4612]~P1(f317(f317(f225(a1),a77),f2(a1))) % 112.26/112.08 [3314]E(f317(f317(f3(a1),a87),a87),a77) % 112.26/112.08 [3329]E(f317(f90(a1),f317(a102,f2(a899))),f72(a1)) % 112.26/112.08 [3394]E(f317(f30(a898),f232(f906(a898,a895))),f72(a899)) % 112.26/112.08 [3414]P1(f317(a183,f317(f94(a1),a87))) % 112.26/112.08 [3416]P1(f317(f317(f224(a1),a87),a77)) % 112.26/112.08 [3418]P1(f317(f317(f319(a897),a909),a907)) % 112.26/112.08 [3419]P1(f317(f317(f225(a1),a87),a77)) % 112.26/112.08 [3476]E(f317(f317(f299(a899),f2(a899)),f178(f906(a899,a895))),f317(f291(a899),f2(a899))) % 112.26/112.08 [3529]P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),a77))) % 112.26/112.08 [3541]E(f317(f300(a899,a899,a102),f232(f906(a899,a895))),f317(f294(a899),f2(a899))) % 112.26/112.08 [3576]P8(f905(a899,a899),f232(f906(f905(a899,a899),a895)),a99) % 112.26/112.08 [3884]E(f317(f67(a899,a1,a89,f90(a1)),a22),a24) % 112.26/112.08 [3943]P36(a899,f317(f252(f905(a899,a899)),f317(f247(a899,a899,a895),f225(a899)))) % 112.26/112.08 [4603]~P1(f317(a183,f317(f94(a1),a77))) % 112.26/112.08 [4604]~P1(f317(f317(f224(a1),a77),a87)) % 112.26/112.08 [4605]~P1(f317(f317(f225(a1),a77),a77)) % 112.26/112.08 [4606]~P1(f317(f317(f225(a1),a77),a87)) % 112.26/112.08 [4607]~P1(f317(f317(f225(a1),a87),a87)) % 112.26/112.08 [4616]~P1(f317(f29(a899),f232(f906(a899,a895)))) % 112.26/112.08 [4617]~P1(f317(f29(a1),f232(f906(a1,a895)))) % 112.26/112.08 [4641]~P1(f317(f317(f224(f906(a894,a895)),f317(f317(f299(a894),f317(a910,a909)),f178(f906(a894,a895)))),f317(f300(a897,a894,a910),a907))) % 112.26/112.08 [4520]E(f317(f247(a1,a1,a895),f317(f317(f10(f906(a1,a895),f906(a1,a895),a1),f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f225(a1),f2(a1))))),f317(f317(f9(a1,a1,f906(a1,a895)),f317(f317(f10(f906(a1,f906(a1,a895)),f906(a1,f906(a1,a895)),a1),f9(a1,a1,a895)),f317(f317(f10(f906(a1,a1),f906(a1,f906(a1,a895)),a1),f317(f10(a1,f906(a1,a895),a1),a314)),a207))),f72(a1)))),a203) % 112.26/112.08 [3613]E(f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87),f317(f73(a1),a87)) % 112.26/112.08 [3651]E(f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87),f317(f317(f3(a1),a77),a87)) % 112.26/112.08 [3811]E(f317(f317(f56(f905(a899,a899)),f232(f906(f905(a899,a899),a895))),a99),a88) % 112.26/112.08 [3840]E(f317(f94(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f72(a1)) % 112.26/112.08 [3841]E(f317(f94(a89),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f72(a89)) % 112.26/112.08 [3842]E(f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f72(a899)) % 112.26/112.08 [3845]E(f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(a102,f2(a899))) % 112.26/112.08 [4222]E(f317(f317(f91(f906(f905(f905(a899,a899),f905(a899,a899)),a895)),a26),f297(f905(a899,a899),f178(f906(f905(f905(a899,a899),f905(a899,a899)),a895)))),a65) % 112.26/112.08 [4288]E(f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),f72(a899)),f2(a899))),f178(f906(f905(a899,a899),a895))))),f72(a1)) % 112.26/112.08 [4289]E(f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),f2(a899)),f2(a899))),f178(f906(f905(a899,a899),a895))))),f2(a1)) % 112.26/112.08 [4302]E(f317(f252(f905(a899,a899)),f317(f247(a899,a899,a895),f317(f317(f10(a899,f906(a899,a895),a899),f317(f9(a899,a899,a895),a314)),a102))),a307) % 112.26/112.08 [4274]E(f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),f317(a102,f317(a102,f2(a899)))) % 112.26/112.08 [4277]E(f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),f317(f317(f74(a899),f72(a899)),f72(a899))) % 112.26/112.08 [4278]E(f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),f317(f30(a895),f232(f906(a895,a895)))) % 112.26/112.08 [4341]P6(f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))) % 112.26/112.08 [4410]P26(f906(f905(a899,a899),a895),f317(f317(f242(f906(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),a895),f906(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),a895)),a27),a66)) % 112.26/112.08 [4411]P26(f906(f905(a899,a899),a895),f317(f317(f242(f906(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),a895),f906(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),a895)),a28),a64)) % 112.26/112.08 [4451]E(f317(f317(f91(f906(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),a895)),f309(f905(a899,a899),a65)),f317(f317(f299(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),f178(f906(f905(a899,a899),a895))),f178(f906(f905(a899,a899),a895)))),f178(f906(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),a895)))),a64) % 112.26/112.08 [4452]E(f317(f317(f91(f906(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),a895)),f308(f905(a899,a899),a65)),f317(f317(f299(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),f178(f906(f905(a899,a899),a895))),f178(f906(f905(a899,a899),a895)))),f178(f906(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),a895)))),a66) % 112.26/112.08 [4343]E(f317(a95,f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(a102,f317(a102,f2(a899)))) % 112.26/112.08 [4388]E(f317(f90(a1),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))) % 112.26/112.08 [4421]P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))) % 112.26/112.08 [4422]E(f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),a87)),f317(a102,f317(a102,f317(a102,f2(a899))))) % 112.26/112.08 [4466]P6(f317(f94(a1),f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))) % 112.26/112.08 [4492]E(f317(f90(a1),f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),f317(f94(a1),f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))) % 112.26/112.08 [4505]P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),a87)))) % 112.26/112.08 [3250]P7(x32501,a314) % 112.26/112.08 [3639]P24(a899,a899,a102,x36391) % 112.26/112.08 [3244]P106(f902(x32441)) % 112.26/112.08 [3245]P106(f900(x32451)) % 112.26/112.08 [3246]P106(f901(x32461)) % 112.26/112.08 [3266]P36(a1,f96(x32661)) % 112.26/112.08 [3267]P36(a1,f97(x32671)) % 112.26/112.08 [3318]P36(f906(x33181,a895),f304(x33181)) % 112.26/112.08 [3319]P37(f906(x33191,a895),f304(x33191)) % 112.26/112.08 [3343]E(f233(x33431,x33431,a314),a314) % 112.26/112.08 [3358]E(f41(a1,x33581,x33581),f2(a1)) % 112.26/112.08 [3411]P14(x34111,f906(x34111,a895),f299(x34111)) % 112.26/112.08 [4578]~E(f317(a102,x45781),x45781) % 112.26/112.08 [4584]~E(f317(a102,x45841),f2(a899)) % 112.26/112.08 [3252]E(f317(f94(a1),x32521),x32521) % 112.26/112.08 [3253]E(f317(f179(a899),x32531),x32531) % 112.26/112.08 [3268]E(f317(a83,f318(x32681)),x32681) % 112.26/112.08 [3269]E(f317(a5,f563(x32691)),x32691) % 112.26/112.08 [3270]E(f231(x32701,f2(a89)),f2(a89)) % 112.26/112.08 [3283]E(f104(x32831,f103(x32831)),f103(x32831)) % 112.26/112.08 [3284]E(f142(x32841,f103(x32841)),f103(x32841)) % 112.26/112.08 [3289]E(f317(f157(x32891),f103(x32891)),f103(x32891)) % 112.26/112.08 [3290]E(f317(f161(x32901),f103(x32901)),f103(x32901)) % 112.26/112.08 [3291]E(f317(f158(x32911),f103(x32911)),f103(x32911)) % 112.26/112.08 [3297]E(f317(f94(a1),x32971),f317(f93(a1),x32971)) % 112.26/112.08 [3298]E(f317(a83,f317(a98,x32981)),x32981) % 112.26/112.08 [3300]E(f317(a5,f317(a22,x33001)),x33001) % 112.26/112.08 [3301]E(f317(a22,f317(a5,x33011)),x33011) % 112.26/112.08 [3303]P6(f317(f90(a1),x33031)) % 112.26/112.08 [3312]E(f317(f179(f900(x33121)),f103(x33121)),f2(a899)) % 112.26/112.08 [3313]E(f317(f179(f901(x33131)),f109(x33131)),f2(a899)) % 112.26/112.08 [3334]E(f317(f317(f3(a899),x33341),f2(a899)),x33341) % 112.26/112.08 [3335]E(f317(f317(f74(a899),x33351),f2(a899)),x33351) % 112.26/112.08 [3336]E(f317(f317(f74(a1),x33361),f2(a1)),x33361) % 112.26/112.08 [3337]E(f317(f317(f75(a899),x33371),f72(a899)),x33371) % 112.26/112.08 [3338]E(f317(f317(f75(a1),x33381),f72(a1)),x33381) % 112.26/112.08 [3339]E(f317(f317(f223(a899),x33391),f2(a899)),x33391) % 112.26/112.08 [3340]E(f317(f317(f75(a899),x33401),f2(a899)),f2(a899)) % 112.26/112.08 [3341]E(f317(f317(f228(a899),x33411),f2(a899)),f2(a899)) % 112.26/112.08 [3342]E(f317(f317(f31(a1),x33421),f2(a1)),f2(a1)) % 112.26/112.08 [3349]E(f317(f162(x33491),f103(x33491)),f178(f906(x33491,a895))) % 112.26/112.08 [3353]P1(f317(f127(x33531),f103(x33531))) % 112.26/112.08 [3359]E(f317(f144(x33591,x33591),f7(x33591)),f25(f900(x33591))) % 112.26/112.08 [3360]E(f317(f144(x33601,x33601),f25(x33601)),f25(f900(x33601))) % 112.26/112.08 [3361]E(f41(a1,x33611,f2(a1)),x33611) % 112.26/112.08 [3362]E(f317(f224(a899),f317(a102,x33621)),f317(f225(a899),x33621)) % 112.26/112.08 [3363]E(f317(f272(a899),f317(a102,x33631)),f317(f291(a899),x33631)) % 112.26/112.08 [3364]E(f317(f273(a899),f317(a102,x33641)),f317(f294(a899),x33641)) % 112.26/112.08 [3366]E(f41(a1,f2(a1),x33661),f2(a1)) % 112.26/112.08 [3379]E(f317(f317(f74(a899),x33791),f72(a899)),f317(a102,x33791)) % 112.26/112.08 [3388]E(f317(f292(a899,x33881),f2(a899)),f178(f906(a899,a895))) % 112.26/112.08 [3400]E(f293(a899,f2(a899),x34001),f317(f291(a899),x34001)) % 112.26/112.08 [3444]E(f317(f317(f3(a899),f317(a102,x34441)),f72(a899)),x34441) % 112.26/112.08 [3456]E(f43(f2(a1),x34561),f317(f317(f242(a1,a1),f2(a1)),f2(a1))) % 112.26/112.08 [3504]P1(f317(f317(f225(a899),x35041),f317(a102,x35041))) % 112.26/112.08 [3516]P1(f317(f317(f225(a899),f2(a899)),f317(a102,x35161))) % 112.26/112.08 [3741]E(f85(x37411,x37411,f232(f906(x37411,a895)),f25(x37411)),f25(x37411)) % 112.26/112.08 [3798]E(f317(f317(f3(a89),f317(a5,f317(a102,f317(a22,x37981)))),f72(a89)),x37981) % 112.26/112.08 [3868]P1(f317(f317(f224(a1),f317(f73(a1),f317(f90(a1),x38681))),f2(a1))) % 112.26/112.08 [4011]P1(f317(f317(f225(a1),f317(f73(a1),f317(f90(a1),f317(a102,x40111)))),f2(a1))) % 112.26/112.08 [4592]~E(f232(f906(x45921,a895)),f178(f906(x45921,a895))) % 112.26/112.08 [4615]~P1(f317(f317(f225(a899),x46151),f2(a899))) % 112.26/112.08 [4626]~P1(f317(f317(f225(a1),f317(f90(a1),x46261)),f2(a1))) % 112.26/112.08 [3302]E(f110(x33021,f109(f901(x33021))),f109(x33021)) % 112.26/112.08 [3317]E(f169(x33171,f103(f900(x33171))),f103(f900(x33171))) % 112.26/112.08 [3320]E(f317(f317(f75(a1),a77),x33201),a77) % 112.26/112.08 [3321]E(f317(f317(f74(a1),a77),x33211),x33211) % 112.26/112.08 [3324]E(f317(a95,f317(f90(a1),x33241)),x33241) % 112.26/112.08 [3325]E(f317(f317(f3(a1),x33251),a77),x33251) % 112.26/112.08 [3326]E(f317(f317(f74(a1),x33261),a77),x33261) % 112.26/112.08 [3328]E(f317(f317(f3(a899),x33281),x33281),f2(a899)) % 112.26/112.08 [3332]E(f317(f30(a899),f317(f272(a899),x33321)),x33321) % 112.26/112.08 [3333]E(f317(f73(a1),f317(f73(a1),x33331)),x33331) % 112.26/112.08 [3344]E(f317(f317(f74(a899),f2(a899)),x33441),x33441) % 112.26/112.08 [3345]E(f317(f317(f74(a1),f2(a1)),x33451),x33451) % 112.26/112.08 [3346]E(f317(f317(f75(a899),f72(a899)),x33461),x33461) % 112.26/112.08 [3347]E(f317(f317(f75(a1),f72(a1)),x33471),x33471) % 112.26/112.08 [3348]E(f317(f317(f223(a899),f2(a899)),x33481),x33481) % 112.26/112.08 [3354]E(f317(f317(f3(a899),f2(a899)),x33541),f2(a899)) % 112.26/112.08 [3355]E(f317(f317(f75(a899),f2(a899)),x33551),f2(a899)) % 112.26/112.08 [3356]E(f317(f317(f228(a899),f2(a899)),x33561),f2(a899)) % 112.26/112.08 [3357]E(f317(f317(f31(a1),f2(a1)),x33571),f2(a1)) % 112.26/112.08 [3367]E(f118(x33671,f317(f73(a1),x33671)),f122(a1,x33671)) % 112.26/112.08 [3372]E(f317(f292(a899,f2(a899)),x33721),f317(f272(a899),x33721)) % 112.26/112.08 [3373]E(f317(f317(f75(a1),a87),x33731),f317(f73(a1),x33731)) % 112.26/112.08 [3381]E(f317(a95,f317(f94(a1),x33811)),f317(f94(a899),x33811)) % 112.26/112.08 [3382]E(f317(a22,f317(f94(a89),x33821)),f317(f94(a899),x33821)) % 112.26/112.08 [3383]E(f317(f30(a899),f317(f291(a899),x33831)),f317(a102,x33831)) % 112.26/112.08 [3392]E(f317(f317(f74(a899),f72(a899)),x33921),f317(a102,x33921)) % 112.26/112.08 [3396]E(f317(f70(a1),f317(f90(a1),x33961)),f317(f90(a1),x33961)) % 112.26/112.08 [3397]E(f317(f93(a1),f317(f90(a1),x33971)),f317(f90(a1),x33971)) % 112.26/112.08 [3401]E(f317(f30(x34011),f178(f906(x34011,a895))),f2(a899)) % 112.26/112.08 [3403]E(f317(f317(f31(a899),x34031),f317(a102,f2(a899))),x34031) % 112.26/112.08 [3412]E(f41(a899,x34121,f317(a102,f2(a899))),f2(a899)) % 112.26/112.08 [3413]E(f41(a1,x34131,f317(f94(a1),a87)),f2(a1)) % 112.26/112.08 [3428]E(f317(f317(f31(a1),x34281),f317(f94(a1),a87)),f317(f73(a1),x34281)) % 112.26/112.08 [3432]E(f129(a899,f317(f292(a899,x34321),f2(a899))),f103(a899)) % 112.26/112.08 [3433]E(f317(f317(f74(a1),x34331),f72(a1)),f317(f317(f3(a1),x34331),a87)) % 112.26/112.08 [3434]E(f317(f317(f3(a1),x34341),f72(a1)),f317(f317(f74(a1),x34341),a87)) % 112.26/112.08 [3438]P1(f317(f317(f224(a899),x34381),x34381)) % 112.26/112.08 [3439]P1(f317(f317(f224(a1),x34391),x34391)) % 112.26/112.08 [3440]P1(f317(f317(f277(a899),x34401),x34401)) % 112.26/112.08 [3445]E(f317(f73(a1),f317(f94(a1),x34451)),f317(f94(a1),f317(f73(a1),x34451))) % 112.26/112.08 [3446]P1(f317(f29(a899),f317(f291(a899),x34461))) % 112.26/112.08 [3447]P1(f317(f29(a899),f317(f272(a899),x34471))) % 112.26/112.08 [3454]E(f151(x34541,f232(f906(x34541,a895))),f232(f906(f900(x34541),a895))) % 112.26/112.08 [3459]P1(f317(f317(f224(a899),f2(a899)),x34591)) % 112.26/112.08 [3470]E(f317(f317(f74(a899),f101(x34701)),f317(a102,f2(a899))),f101(f317(a102,x34701))) % 112.26/112.08 [3471]E(f317(f252(x34711),f317(f18(a895,x34711),a229)),f178(f906(x34711,a895))) % 112.26/112.08 [3472]E(f317(f252(x34721),f317(f18(a895,x34721),a177)),f232(f906(x34721,a895))) % 112.26/112.08 [3475]E(f317(f317(f299(a899),x34751),f317(f272(a899),x34751)),f317(f272(a899),f317(a102,x34751))) % 112.26/112.08 [3487]E(f317(f317(f74(a1),f72(a1)),f317(f90(a1),x34871)),f317(f90(a1),f317(a102,x34871))) % 112.26/112.08 [3489]E(f317(f317(f141(f900(x34891)),f103(x34891)),f103(f900(x34891))),f50(x34891,f103(x34891))) % 112.26/112.08 [3507]E(f178(f906(f905(x35071,x35071),a895)),f253(x35071,f178(f906(x35071,a895)))) % 112.26/112.08 [3508]E(f317(f298(x35081),f232(f906(x35081,a895))),f232(f906(f906(x35081,a895),a895))) % 112.26/112.08 [3509]E(f317(f73(f906(x35091,a895)),f178(f906(x35091,a895))),f232(f906(x35091,a895))) % 112.26/112.08 [3510]E(f317(f73(f906(x35101,a895)),f232(f906(x35101,a895))),f178(f906(x35101,a895))) % 112.26/112.08 [3512]P1(f317(f29(x35121),f178(f906(x35121,a895)))) % 112.26/112.08 [3514]E(f317(f292(a899,x35141),f317(a102,x35141)),f317(f317(f299(a899),x35141),f178(f906(a899,a895)))) % 112.26/112.08 [3515]E(f79(f905(a899,a899),f44(x35151,f2(a899))),f317(f317(f242(a899,a899),f2(a899)),x35151)) % 112.26/112.08 [3528]E(f317(f317(f299(a899),f317(a102,x35281)),f317(f291(a899),x35281)),f317(f291(a899),f317(a102,x35281))) % 112.26/112.08 [3532]P36(x35321,f178(f906(f905(x35321,x35321),a895))) % 112.26/112.08 [3533]P38(x35331,f178(f906(f905(x35331,x35331),a895))) % 112.26/112.08 [3536]P1(f317(f317(f224(a1),f2(a1)),f317(f90(a1),x35361))) % 112.26/112.08 [3543]E(f317(f317(f74(a899),f317(f179(a899),x35431)),f317(a102,f2(a899))),f317(f179(a899),f317(a102,x35431))) % 112.26/112.08 [3646]P39(f317(f300(a899,a1,f90(a1)),x36461)) % 112.26/112.08 [3684]P52(x36841,f178(f906(x36841,a895)),f178(f906(f905(x36841,x36841),a895))) % 112.26/112.08 [3702]E(f317(f317(f242(a1,a1),f317(f94(a1),a87)),f317(f317(f3(a1),x37021),f72(a1))),f46(f317(f94(a1),a87),x37021)) % 112.26/112.08 [3754]P59(x37541,f317(f18(f906(x37541,a895),x37541),f317(f18(a895,x37541),a229))) % 112.26/112.08 [3766]E(f280(a899,f277(a899),x37661,x37661),f317(f317(f299(a899),x37661),f178(f906(a899,a895)))) % 112.26/112.08 [3955]P1(f317(f317(f319(f906(f905(a899,a899),a895)),f318(x39551)),a88)) % 112.26/112.08 [3980]P1(f317(f317(f319(f906(f905(a899,a899),a895)),f317(a98,x39801)),a88)) % 112.26/112.08 [4109]P24(x41091,f906(x41091,a895),f317(f317(f9(x41091,f906(x41091,a895),f906(x41091,a895)),f299(x41091)),f178(f906(x41091,a895))),f232(f906(x41091,a895))) % 112.26/112.08 [4589]~E(f317(f317(f74(a1),x45891),x45891),a87) % 112.26/112.08 [4602]~E(f317(a5,f317(a102,f317(a22,x46021))),f2(a89)) % 112.26/112.08 [4608]~P1(f317(a183,f317(f90(a1),x46081))) % 112.26/112.08 [4611]~P1(f317(f317(f225(a899),x46111),x46111)) % 112.26/112.08 [4619]~P1(f317(f317(f224(a899),f317(a102,x46191)),x46191)) % 112.26/112.08 [3462]E(f317(a95,f317(f73(a1),f317(f90(a1),x34621))),f2(a899)) % 112.26/112.08 [3465]E(f317(f317(f74(a1),f317(f73(a1),x34651)),x34651),f2(a1)) % 112.26/112.08 [3469]E(f317(f30(a1),f317(f292(a1,f2(a1)),x34691)),f317(a95,x34691)) % 112.26/112.08 [3480]E(f317(f317(f234(a899),f317(a102,f2(a899))),x34801),f317(a102,f2(a899))) % 112.26/112.08 [3573]E(f317(f271(x35731),f178(f906(f905(x35731,x35731),a895))),f178(f906(x35731,a895))) % 112.26/112.08 [3581]E(f32(f906(x35811,a895),f178(f906(f906(x35811,a895),a895))),f178(f906(x35811,a895))) % 112.26/112.08 [3582]E(f32(f906(x35821,a895),f232(f906(f906(x35821,a895),a895))),f232(f906(x35821,a895))) % 112.26/112.08 [3583]E(f33(f906(x35831,a895),f178(f906(f906(x35831,a895),a895))),f232(f906(x35831,a895))) % 112.26/112.08 [3584]E(f33(f906(x35841,a895),f232(f906(f906(x35841,a895),a895))),f178(f906(x35841,a895))) % 112.26/112.08 [3588]P1(f317(f317(f277(a899),f317(a102,f2(a899))),x35881)) % 112.26/112.08 [3629]E(f317(f317(f299(f900(x36291)),f103(x36291)),f178(f906(f900(x36291),a895))),f151(x36291,f178(f906(x36291,a895)))) % 112.26/112.08 [3630]E(f317(f317(f299(f900(x36301)),f103(x36301)),f178(f906(f900(x36301),a895))),f152(x36301,f103(f906(x36301,a895)))) % 112.26/112.08 [3668]E(f317(f317(f74(a899),f6(x36681)),f317(a102,f2(a899))),f6(f317(a5,f317(a102,f317(a22,x36681))))) % 112.26/112.08 [3693]E(f317(f30(a1),f317(f300(a899,a1,f90(a1)),x36931)),f317(f30(a899),x36931)) % 112.26/112.08 [3696]P1(f317(f317(f224(a899),x36961),f317(f317(f75(a899),x36961),x36961))) % 112.26/112.08 [3732]E(f317(f300(a1,a899,a95),f293(a1,f2(a1),f317(f90(a1),x37321))),f317(f291(a899),x37321)) % 112.26/112.08 [3749]E(f317(f317(f31(a899),f317(a102,f2(a899))),f317(f94(a899),x37491)),f317(a95,f317(f317(f31(a1),f72(a1)),f317(f94(a1),x37491)))) % 112.26/112.08 [3751]E(f317(f162(a899),f129(a899,f317(f292(a899,f2(a899)),f317(a102,x37511)))),f317(f291(a899),x37511)) % 112.26/112.08 [3752]E(f317(f317(f74(a899),f317(f179(a89),x37521)),f317(a102,f2(a899))),f317(f179(a89),f317(a5,f317(a102,f317(a22,x37521))))) % 112.26/112.08 [3772]P38(x37721,f297(x37721,f178(f906(f905(x37721,x37721),a895)))) % 112.26/112.08 [3773]P51(x37731,f297(x37731,f178(f906(f905(x37731,x37731),a895)))) % 112.26/112.08 [3774]E(f317(f300(a1,a899,a95),f317(f300(a899,a1,f90(a1)),x37741)),x37741) % 112.26/112.08 [3804]E(f317(f317(f299(a899),f2(a899)),f317(f300(a899,a899,a102),f317(f272(a899),x38041))),f317(f272(a899),f317(a102,x38041))) % 112.26/112.08 [3810]P54(x38101,x38101,f297(x38101,f178(f906(f905(x38101,x38101),a895)))) % 112.26/112.08 [3816]P1(f317(a183,f317(f73(a1),f317(f90(a1),f317(a102,x38161))))) % 112.26/112.08 [3826]E(f317(f317(f3(f906(a899,a895)),f317(f273(a899),x38261)),f317(f317(f299(a899),x38261),f178(f906(a899,a895)))),f317(f273(a899),f317(a102,x38261))) % 112.26/112.08 [3843]E(f317(f317(f74(a1),f317(f317(f3(a1),a77),x38431)),f317(f317(f3(a1),a77),x38431)),f317(f317(f3(a1),a77),f317(f317(f74(a1),x38431),x38431))) % 112.26/112.08 [3857]E(f317(f317(f299(f906(x38571,a895)),f178(f906(x38571,a895))),f178(f906(f906(x38571,a895),a895))),f317(f298(x38571),f178(f906(x38571,a895)))) % 112.26/112.08 [3885]E(f317(f317(f3(f906(a899,a895)),f317(f294(a899),x38851)),f317(f317(f299(a899),f317(a102,x38851)),f178(f906(a899,a895)))),f317(f294(a899),f317(a102,x38851))) % 112.26/112.08 [3992]E(f317(f94(a899),f317(f317(f74(a1),x39921),x39921)),f317(f317(f80(a899,a899),f317(f94(a899),x39921)),f317(f317(f20(a899,a899,a899),f74(a899)),f7(a899)))) % 112.26/112.08 [4363]P14(x43631,f906(x43631,a895),f317(f317(f10(f906(x43631,a895),f906(f906(x43631,a895),f906(x43631,a895)),x43631),f317(f9(f906(x43631,a895),f906(x43631,a895),f906(x43631,a895)),f3(f906(x43631,a895)))),f317(f317(f9(x43631,f906(x43631,a895),f906(x43631,a895)),f299(x43631)),f178(f906(x43631,a895))))) % 112.26/112.08 [4450]E(f317(f252(f905(a1,a1)),f317(f247(a1,a1,a895),f317(f317(f10(f906(a1,a895),f906(a1,a895),a1),f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f224(a1),x44501)))),f225(a1)))),f96(x44501)) % 112.26/112.08 [4483]E(f317(f252(f905(a1,a1)),f317(f247(a1,a1,a895),f317(f317(f20(a1,f906(a1,a895),f906(a1,a895)),f317(f317(f10(f906(a895,a895),f906(f906(a1,a895),f906(a1,a895)),a1),f10(a895,a895,a1)),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f224(a1),x44831)))),f225(a1)))),f97(x44831)) % 112.26/112.08 [4536]E(f317(f252(f905(f906(x45361,a895),f906(x45361,a895))),f317(f247(f906(x45361,a895),f906(x45361,a895),a895),f317(f317(f9(f906(x45361,a895),f906(f906(x45361,a895),a895),f906(f906(x45361,a895),a895)),f317(f317(f10(f906(f906(x45361,a895),f906(a895,a895)),f906(f906(f906(x45361,a895),a895),f906(f906(x45361,a895),a895)),f906(x45361,a895)),f20(f906(x45361,a895),a895,a895)),f317(f317(f10(f906(f906(x45361,a895),a895),f906(f906(x45361,a895),f906(a895,a895)),f906(x45361,a895)),f317(f10(a895,f906(a895,a895),f906(x45361,a895)),a315)),f225(f906(x45361,a895))))),f29(x45361)))),f304(x45361)) % 112.26/112.08 [4623]~P1(f317(f29(f900(x46231)),f232(f906(f900(x46231),a895)))) % 112.26/112.08 [4635]~P1(f317(f317(f224(a1),f2(a1)),f317(f73(a1),f317(f90(a1),f317(a102,x46351))))) % 112.26/112.08 [3608]E(f317(f317(f3(a1),f317(f317(f74(a1),x36081),a87)),a87),x36081) % 112.26/112.08 [3622]E(f317(f162(a899),f129(a899,f317(f292(a899,f2(a899)),x36221))),f317(f272(a899),x36221)) % 112.26/112.08 [3864]E(f317(f317(f74(a1),f317(f317(f74(a1),f72(a1)),x38641)),x38641),f317(f317(f3(a1),f317(f317(f74(a1),x38641),x38641)),a87)) % 112.26/112.08 [3912]E(f317(f276(x39121,x39121),f297(x39121,f178(f906(f905(x39121,x39121),a895)))),f297(x39121,f178(f906(f905(x39121,x39121),a895)))) % 112.26/112.08 [3958]P1(f317(f317(f224(a899),x39581),f317(f317(f75(a899),x39581),f317(f317(f75(a899),x39581),x39581)))) % 112.26/112.08 [4226]P1(f317(f29(a899),f317(f252(a899),f317(f317(f9(a899,a899,a895),f224(a899)),x42261)))) % 112.26/112.08 [4227]P1(f317(f29(a899),f317(f252(a899),f317(f317(f9(a899,a899,a895),f225(a899)),x42271)))) % 112.26/112.08 [4499]E(f317(f252(f905(x44991,x44991)),f317(f317(f10(f906(x44991,a895),a895,f905(x44991,x44991)),f81(x44991)),f317(f317(f9(f905(x44991,x44991),f906(x44991,f905(x44991,x44991)),f906(x44991,a895)),f317(f317(f10(f906(f905(x44991,x44991),a895),f906(f906(x44991,f905(x44991,x44991)),f906(x44991,a895)),f905(x44991,x44991)),f10(f905(x44991,x44991),a895,x44991)),a314)),f317(f317(f20(x44991,x44991,f905(x44991,x44991)),f242(x44991,x44991)),f7(x44991))))),f297(x44991,f178(f906(f905(x44991,x44991),a895)))) % 112.26/112.08 [4625]~E(f317(f317(f3(a1),f317(f317(f74(a1),x46251),x46251)),a87),a77) % 112.26/112.08 [4627]~E(f317(f317(f74(a1),f317(f317(f74(a1),f72(a1)),x46271)),x46271),f2(a1)) % 112.26/112.08 [4002]E(f317(f317(f74(a1),f317(f317(f3(a1),a87),x40021)),f317(f317(f3(a1),a87),x40021)),f317(f317(f3(a1),a87),f317(f317(f3(a1),f317(f317(f74(a1),x40021),x40021)),a87))) % 112.26/112.08 [4117]E(f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),a87),x41171)),f317(f317(f3(a1),a87),x41171))),a87),f317(f317(f3(a1),a87),f317(f317(f74(a1),x41171),x41171))) % 112.26/112.08 [4149]E(f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f74(a1),x41491),a87)),f317(f317(f74(a1),x41491),a87))),a87),f317(f317(f74(a1),f317(f317(f74(a1),x41491),x41491)),a87)) % 112.26/112.08 [4187]E(f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),a87),x41871)),f317(f317(f3(a1),a87),x41871))),a87),f317(f317(f3(a1),a77),f317(f317(f3(a1),f317(f317(f74(a1),x41871),x41871)),a87))) % 112.26/112.08 [4284]E(f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x42841),f2(a899))),f178(f906(f905(a899,a899),a895))))),f317(f90(a1),x42841)) % 112.26/112.08 [4294]E(f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),f322(x42941)),f492(x42941))),f178(f906(f905(a899,a899),a895))))),x42941) % 112.26/112.08 [4327]E(f317(f252(a1),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f224(a1),f2(a1)))),x43271)),f317(f300(a899,a1,f90(a1)),f317(f252(a899),f317(f317(f10(a1,a895,a899),x43271),f90(a1))))) % 112.26/112.08 [4371]P39(f317(f252(a1),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f224(a1),f2(a1)))),x43711))) % 112.26/112.08 [4391]P1(f317(f317(f319(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),x43911),f178(f906(f905(a899,a899),a895)))),a66)) % 112.26/112.08 [4396]E(f317(f300(a1,a899,a95),f317(f252(a1),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f224(a1),f2(a1)))),f317(f317(f10(a899,a895,a1),x43961),a95)))),f317(f252(a899),x43961)) % 112.26/112.08 [4551]E(f302(a899,f317(f317(f36(f905(a899,a899),f906(a899,a895)),f317(a98,x45511)),f317(f247(a899,a899,f906(a899,a895)),f317(f317(f9(a899,f906(a899,a895),f906(a899,f906(a899,a895))),f317(f317(f10(f906(a899,f906(f906(a899,a895),f906(a899,a895))),f906(f906(a899,a895),f906(a899,f906(a899,a895))),a899),f9(a899,f906(a899,a895),f906(a899,a895))),f317(f317(f10(f906(a899,a899),f906(a899,f906(f906(a899,a895),f906(a899,a895))),a899),f317(f10(a899,f906(f906(a899,a895),f906(a899,a895)),a899),f299(a899))),f3(a899)))),f178(f906(a899,a895)))))),f317(a95,x45511)) % 112.26/112.08 [4047]E(f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),x40471),x40471)),a87)),a87),f317(f317(f74(a1),x40471),x40471)) % 112.26/112.08 [4097]E(f317(f317(f3(a1),f317(f317(f3(a1),f317(f317(f74(a1),x40971),x40971)),a87)),a87),f317(f317(f74(a1),f317(f317(f3(a1),x40971),a87)),f317(f317(f3(a1),x40971),a87))) % 112.26/112.08 [4300]E(f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f74(a1),f317(f73(a1),x43001)),a87)),f317(f317(f74(a1),f317(f73(a1),x43001)),a87))),a87),f317(f73(a1),f317(f317(f3(a1),f317(f317(f74(a1),x43001),x43001)),a87))) % 112.26/112.08 [4344]E(f317(f317(f74(a899),x43441),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(a102,f317(a102,x43441))) % 112.26/112.08 [4345]E(f317(f317(f75(a899),x43451),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f74(a899),x43451),x43451)) % 112.26/112.08 [4346]E(f317(f317(f31(a899),f317(f317(f74(a899),x43461),x43461)),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x43461) % 112.26/112.08 [4424]E(f41(a899,f317(a102,f317(a102,x44241)),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f41(a899,x44241,f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))) % 112.26/112.08 [4565]E(f317(a83,f317(f317(f36(f905(a899,a899),f906(f905(a899,a899),a895)),f317(a98,x45651)),f317(f247(a899,a899,f906(f905(a899,a899),a895)),f317(f317(f10(f906(a899,f906(f905(a899,a899),a895)),f906(a899,f906(f905(a899,a899),a895)),a899),f317(f10(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895),a899),f275(f905(a899,a899),f905(a899,a899),a99))),f317(f317(f9(a899,f906(f905(a899,a899),a895),f906(a899,f906(f905(a899,a899),a895))),f317(f317(f10(f906(a899,f906(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f906(f906(f905(a899,a899),a895),f906(a899,f906(f905(a899,a899),a895))),a899),f9(a899,f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f10(f906(a899,f905(a899,a899)),f906(a899,f906(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),a899),f317(f10(f905(a899,a899),f906(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),a899),f299(f905(a899,a899)))),f317(f9(a899,a899,f905(a899,a899)),f242(a899,a899))))),f178(f906(f905(a899,a899),a895))))))),f317(f73(a1),x45651)) % 112.26/112.08 [4419]E(f317(f317(f74(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x44191),f317(a102,f317(a102,x44191))) % 112.26/112.08 [4420]E(f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x44201),f317(f317(f74(a899),x44201),x44201)) % 112.26/112.08 [4456]E(f317(f317(f31(a899),f317(a102,f317(a102,x44561))),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(a102,f317(f317(f31(a899),x44561),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))) % 112.26/112.08 [4506]E(f317(f317(f74(a899),f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),x45061),f317(a102,f317(a102,f317(a102,x45061)))) % 112.26/112.08 [4572]E(f317(f247(a1,a1,f905(a1,a1)),f317(f317(f20(a1,f906(a1,f905(a1,a1)),f906(a1,f905(a1,a1))),f317(f317(f10(f906(a1,f906(f905(a1,a1),f905(a1,a1))),f906(f906(a1,f905(a1,a1)),f906(a1,f905(a1,a1))),a1),f20(a1,f905(a1,a1),f905(a1,a1))),f317(f317(f10(f906(a1,f905(a1,a1)),f906(a1,f906(f905(a1,a1),f905(a1,a1))),a1),f317(f20(a1,f905(a1,a1),f906(f905(a1,a1),f905(a1,a1))),f317(f317(f10(a895,f906(f905(a1,a1),f906(f905(a1,a1),f905(a1,a1))),a1),f86(f905(a1,a1))),f317(f317(f10(a1,a895,a1),f317(f224(a1),f2(a1))),f317(f317(f9(a1,a1,a1),f3(a1)),x45721))))),f317(f317(f9(a1,f906(a1,a1),f906(a1,f905(a1,a1))),f317(f317(f10(f906(a1,f905(a1,a1)),f906(f906(a1,a1),f906(a1,f905(a1,a1))),a1),f10(a1,f905(a1,a1),a1)),f317(f317(f10(a1,f906(a1,f905(a1,a1)),a1),f242(a1,a1)),f317(f317(f9(a1,a1,a1),f317(f317(f10(a1,f906(a1,a1),a1),f74(a1)),f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f72(a1))))),f317(f317(f9(a1,a1,a1),f3(a1)),x45721))))),f317(f317(f10(a1,f906(a1,f905(a1,a1)),a1),f242(a1,a1)),f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))))),f39(x45721)) % 112.26/112.08 [3286]P106(f904(x32861,x32862)) % 112.26/112.08 [3287]P106(f905(x32871,x32872)) % 112.26/112.08 [3288]P106(f903(x32881,x32882)) % 112.26/112.08 [3306]P13(a1,f168(x33061,x33062)) % 112.26/112.08 [3307]P36(x33071,f143(x33071,x33072)) % 112.26/112.08 [3308]P37(x33081,f253(x33081,x33082)) % 112.26/112.08 [3309]P37(x33091,f297(x33091,x33092)) % 112.26/112.08 [3310]P38(x33101,f253(x33101,x33102)) % 112.26/112.08 [3311]P51(x33111,f253(x33111,x33112)) % 112.26/112.08 [3374]P30(x33741,x33742,f103(x33741)) % 112.26/112.08 [3407]P52(x34071,x34072,f253(x34071,x34072)) % 112.26/112.08 [3408]P54(x34081,x34081,f253(x34081,x34082)) % 112.26/112.08 [3671]P24(x36711,x36711,f7(x36711),x36712) % 112.26/112.08 [3672]P24(x36721,x36721,f25(x36721),x36722) % 112.26/112.08 [3680]P31(x36801,x36802,f103(x36801),f103(x36801)) % 112.26/112.08 [3687]P24(f900(x36871),f900(x36871),f158(x36871),x36872) % 112.26/112.08 [4087]P25(x40871,x40871,f25(x40871),x40872,x40872) % 112.26/112.08 [4597]~P32(x45971,x45972,f103(x45971)) % 112.26/112.08 [4598]~P34(x45981,x45982,f103(x45981)) % 112.26/112.08 [3272]E(f317(f7(x32721),x32722),x32722) % 112.26/112.08 [3273]E(f317(f252(x32731),x32732),x32732) % 112.26/112.08 [3275]E(f317(f25(x32751),x32752),x32752) % 112.26/112.08 [3285]E(f317(f181(x32851),x32852),f105(x32851)) % 112.26/112.08 [3304]E(f79(x33041,f317(a314,x33042)),x33042) % 112.26/112.08 [3305]E(f84(x33051,f317(a314,x33052)),x33052) % 112.26/112.08 [3327]E(f317(f115(x33271,x33272),f109(x33271)),f2(a899)) % 112.26/112.08 [3330]E(f317(f126(x33301,x33302),f103(x33301)),f103(x33301)) % 112.26/112.08 [3350]E(f297(x33501,f297(x33501,x33502)),f297(x33501,x33502)) % 112.26/112.08 [3351]E(f142(x33511,f142(x33511,x33512)),f142(x33511,x33512)) % 112.26/112.08 [3369]E(f317(f317(f124(x33691),x33692),f103(x33691)),x33692) % 112.26/112.08 [3375]E(f163(x33751,x33752,f103(x33751)),x33752) % 112.26/112.08 [3376]E(f163(x33761,f103(x33761),x33762),x33762) % 112.26/112.08 [3377]E(f106(x33771,f109(x33771),x33772),x33772) % 112.26/112.08 [3378]E(f159(x33781,f2(a899),x33782),f103(x33781)) % 112.26/112.08 [3384]E(f317(f317(f165(x33841),x33842),f103(x33841)),f103(x33841)) % 112.26/112.09 [3385]E(f317(f317(f128(x33851),x33852),f103(x33851)),f103(x33851)) % 112.26/112.09 [3387]E(f145(x33871,x33872,f103(x33871)),f2(a899)) % 112.26/112.09 [3389]E(f160(x33891,x33892,f103(x33891)),f103(x33891)) % 112.26/112.09 [3390]E(f167(x33901,x33902,f103(x33901)),f103(x33901)) % 112.26/112.09 [3391]E(f166(x33911,f103(x33911),x33912),f103(x33911)) % 112.26/112.09 [3395]E(f317(f162(x33951),f142(x33951,x33952)),f317(f162(x33951),x33952)) % 112.26/112.09 [3398]E(f317(f274(x33981,x33981),f253(x33981,x33982)),x33982) % 112.26/112.09 [3399]E(f317(f254(x33991,x33991),f253(x33991,x33992)),x33992) % 112.26/112.09 [3406]E(f317(f276(x34061,x34061),f253(x34061,x34062)),f253(x34061,x34062)) % 112.26/112.09 [3420]E(f297(f900(x34201),f147(x34201,x34202)),f148(x34201,f297(x34201,x34202))) % 112.26/112.09 [3422]P1(f317(f127(a1),f168(x34221,x34222))) % 112.26/112.09 [3430]E(f317(f274(x34301,x34301),f297(x34301,x34302)),f232(f906(x34301,a895))) % 112.26/112.09 [3431]E(f317(f254(x34311,x34311),f297(x34311,x34312)),f232(f906(x34311,a895))) % 112.26/112.09 [3435]P1(f317(f127(x34351),f142(x34351,x34352))) % 112.26/112.09 [3437]P1(f317(f150(x34371,x34372),f103(x34371))) % 112.26/112.09 [3443]E(f317(f162(a1),f168(x34431,x34432)),f293(a1,x34431,x34432)) % 112.26/112.09 [3457]P55(x34571,f178(f906(x34571,a895)),x34572) % 112.26/112.09 [3463]E(f317(f246(a1,a1),f42(x34631,x34632)),f41(a1,x34631,x34632)) % 112.26/112.09 [3464]E(f317(f292(a899,x34641),f317(a102,x34642)),f293(a899,x34641,x34642)) % 112.26/112.09 [3479]E(f317(f317(f141(x34791),x34792),f103(x34791)),f130(x34791,x34792,f103(x34791))) % 112.26/112.09 [3491]E(f293(a899,f317(a102,x34911),x34912),f295(a899,x34911,x34912)) % 112.26/112.09 [3492]P52(x34921,f232(f906(x34921,a895)),f297(x34921,x34922)) % 112.26/112.09 [3554]E(f317(f317(f3(a899),x35541),f317(a102,x35542)),f317(f30(a899),f296(a899,x35542,x35541))) % 112.26/112.09 [3609]E(f156(x36091,x36092,f103(x36091)),f317(f317(f242(f900(x36091),f900(x36091)),f103(x36091)),f103(x36091))) % 112.26/112.09 [3627]E(f317(f247(x36271,x36272,f905(x36271,x36272)),f242(x36271,x36272)),f25(f905(x36271,x36272))) % 112.26/112.09 [3631]P1(f317(f317(f319(f900(x36311)),f103(x36311)),f151(x36311,x36312))) % 112.26/112.09 [3632]E(f317(f179(f900(x36321)),f104(x36321,x36322)),f317(f317(f3(a899),f317(f179(f900(x36321)),x36322)),f72(a899))) % 112.26/112.09 [3640]P1(f317(f29(a899),f296(a899,x36401,x36402))) % 112.26/112.09 [3641]P1(f317(f29(a899),f293(a899,x36411,x36412))) % 112.26/112.09 [3642]P1(f317(f29(a899),f295(a899,x36421,x36422))) % 112.26/112.09 [3643]P1(f317(f29(a1),f296(a1,x36431,x36432))) % 112.26/112.09 [3644]P1(f317(f29(a1),f293(a1,x36441,x36442))) % 112.26/112.09 [3645]P1(f317(f29(a1),f295(a1,x36451,x36452))) % 112.26/112.09 [3748]E(f317(f300(a899,a899,a102),f293(a899,x37481,x37482)),f293(a899,f317(a102,x37481),f317(a102,x37482))) % 112.26/112.09 [3768]E(f317(f317(f279(x37681,x37681,x37681),f297(x37681,x37682)),f297(x37681,x37682)),f297(x37681,x37682)) % 112.26/112.09 [3802]E(f317(f317(f242(a1,a1),f317(f317(f31(a1),x38021),x38022)),f41(a1,x38021,x38022)),f42(x38021,x38022)) % 112.26/112.09 [3803]E(f317(f317(f242(a89,a89),f317(f317(f31(a89),x38031),x38032)),f41(a89,x38031,x38032)),f23(x38031,x38032)) % 112.26/112.09 [3830]E(f317(f317(f242(a899,a899),f317(f317(f31(a899),x38301),x38302)),f41(a899,x38301,x38302)),f79(f905(a899,a899),f44(x38301,x38302))) % 112.26/112.09 [3881]P1(f317(f317(f225(a899),f317(f317(f3(a899),x38811),x38812)),f317(a102,x38811))) % 112.26/112.09 [3929]P37(x39291,f317(f317(f279(x39291,x39291,x39291),x39292),f297(x39291,x39292))) % 112.26/112.09 [3979]E(f317(f317(f74(a1),f317(f317(f75(a1),x39791),f317(f317(f31(a1),x39792),x39791))),f41(a1,x39792,x39791)),x39792) % 112.26/112.09 [3983]E(f317(f317(f36(a899,f906(f905(f900(x39831),f900(x39831)),a895)),f232(f906(a899,a895))),f133(x39831,x39832)),f135(x39831,x39832)) % 112.26/112.09 [4203]P1(f317(f317(f319(f905(f900(x42031),f900(x42031))),f317(f317(f242(f900(x42031),f900(x42031)),f103(x42031)),f103(x42031))),f148(x42031,x42032))) % 112.26/112.09 [4312]E(f243(x43121,x43121,x43121,a314,f243(x43121,x43121,x43121,x43122,a314)),x43122) % 112.26/112.09 [4356]E(f248(x43561,x43561,x43562,x43562,f7(x43561),f7(x43562)),f25(f905(x43561,x43562))) % 112.26/112.09 [4358]E(f248(x43581,x43581,x43582,x43582,f25(x43581),f25(x43582)),f25(f905(x43581,x43582))) % 112.26/112.09 [3368]E(f317(f158(x33681),f317(f158(x33681),x33682)),x33682) % 112.26/112.09 [3370]E(f317(f317(f128(x33701),f2(a899)),x33702),x33702) % 112.26/112.09 [3386]E(f317(f317(f165(x33861),f2(a899)),x33862),f103(x33861)) % 112.26/112.09 [3393]E(f317(f317(f124(x33931),f103(x33931)),x33932),x33932) % 112.26/112.09 [3402]E(f32(f906(x34021,a895),f317(f298(x34021),x34022)),x34022) % 112.26/112.09 [3404]E(f317(f162(x34041),f317(f157(x34041),x34042)),f317(f162(x34041),x34042)) % 112.26/112.09 [3405]E(f317(f162(x34051),f317(f158(x34051),x34052)),f317(f162(x34051),x34052)) % 112.26/112.09 [3410]E(f317(f317(f3(a89),x34101),x34102),f317(f317(a4,x34101),x34102)) % 112.26/112.09 [3424]E(f317(f317(f74(a899),x34241),x34242),f317(f317(f74(a899),x34242),x34241)) % 112.26/112.09 [3425]E(f317(f317(f74(a1),x34251),x34252),f317(f317(f74(a1),x34252),x34251)) % 112.26/112.09 [3426]E(f317(f317(f75(a899),x34261),x34262),f317(f317(f75(a899),x34262),x34261)) % 112.26/112.09 [3427]E(f317(f317(f75(a1),x34271),x34272),f317(f317(f75(a1),x34272),x34271)) % 112.26/112.09 [3449]E(f317(f317(f173(x34491,x34491),f2(a899)),x34492),f25(x34491)) % 112.26/112.09 [3450]E(f317(f179(f900(x34501)),f317(f157(x34501),x34502)),f317(f179(f900(x34501)),x34502)) % 112.26/112.09 [3451]E(f317(f179(f900(x34511)),f317(f158(x34511),x34512)),f317(f179(f900(x34511)),x34512)) % 112.26/112.09 [3452]E(f166(x34521,x34522,f178(f906(a899,a895))),f103(x34521)) % 112.26/112.09 [3453]E(f317(f317(f144(x34531,x34531),f7(x34531)),x34532),x34532) % 112.26/112.09 [3455]E(f317(f241(a1,a1),f42(x34551,x34552)),f317(f317(f31(a1),x34551),x34552)) % 112.26/112.09 [3473]E(f317(f179(f900(x34731)),f142(x34731,x34732)),f317(f30(x34731),f317(f162(x34731),x34732))) % 112.26/112.09 [3474]E(f317(f271(x34741),f317(f276(x34741,x34741),x34742)),f317(f271(x34741),x34742)) % 112.26/112.09 [3478]P1(f317(f29(x34781),f317(f162(x34781),x34782))) % 112.26/112.09 [3486]E(f317(f317(f74(a1),x34861),f317(f73(a1),x34862)),f317(f317(f3(a1),x34861),x34862)) % 112.26/112.09 [3493]E(f317(f300(x34931,x34931,f7(x34931)),x34932),x34932) % 112.26/112.09 [3494]E(f317(f300(x34941,x34941,f25(x34941)),x34942),x34942) % 112.26/112.09 [3495]E(f317(f301(x34951,x34951,f7(x34951)),x34952),x34952) % 112.26/112.09 [3496]E(f317(f301(x34961,x34961,f25(x34961)),x34962),x34962) % 112.26/112.09 [3497]P1(f317(f232(f906(x34971,a895)),x34972)) % 112.26/112.09 [3499]E(f317(f30(a899),f317(f292(a899,x34991),x34992)),f317(f317(f3(a899),x34992),x34991)) % 112.26/112.09 [3500]E(f317(f292(a899,f317(a102,x35001)),x35002),f296(a899,x35001,x35002)) % 112.26/112.09 [3513]E(f317(f317(f299(x35131),x35132),f178(f906(x35131,a895))),f317(f252(x35131),f317(a314,x35132))) % 112.26/112.09 [3518]E(f297(x35181,f317(f276(x35181,x35181),x35182)),f317(f276(x35181,x35181),f297(x35181,x35182))) % 112.26/112.09 [3523]E(f317(f317(f74(a899),f317(a102,x35231)),x35232),f317(f317(f74(a899),x35231),f317(a102,x35232))) % 112.26/112.09 [3524]E(f317(f317(f3(a899),f317(a102,x35241)),f317(a102,x35242)),f317(f317(f3(a899),x35241),x35242)) % 112.26/112.09 [3530]E(f51(x35301,f2(a899),x35302),f317(f317(f141(f900(x35301)),f103(x35301)),f103(f900(x35301)))) % 112.26/112.09 [3531]E(f317(f30(a899),f295(a899,x35311,x35312)),f317(f317(f3(a899),x35312),x35311)) % 112.26/112.09 [3540]P36(x35401,f317(f317(f278(a899,x35401),a230),x35402)) % 112.26/112.09 [3542]P13(a899,f129(a899,f317(f292(a899,x35421),x35422))) % 112.26/112.09 [3544]P1(f317(f29(a899),f317(f292(a899,x35441),x35442))) % 112.26/112.09 [3545]P1(f317(f29(a1),f317(f292(a1,x35451),x35452))) % 112.26/112.09 [3548]E(f317(f276(f900(x35481),f900(x35481)),f147(x35481,x35482)),f147(x35481,f317(f276(x35481,x35481),x35482))) % 112.26/112.09 [3550]E(f317(f292(a1,x35501),f317(f317(f74(a1),x35502),f72(a1))),f293(a1,x35501,x35502)) % 112.26/112.09 [3553]E(f317(f317(f31(a1),f317(f73(a1),x35531)),f317(f73(a1),x35532)),f317(f317(f31(a1),x35531),x35532)) % 112.26/112.09 [3561]E(f317(f317(f173(f905(x35611,x35611),a895),f72(a899)),x35612),x35612) % 112.26/112.09 [3563]E(f317(f317(f3(f906(x35631,a895)),x35632),f178(f906(x35631,a895))),x35632) % 112.26/112.09 [3564]E(f317(f317(f91(f906(x35641,a895)),x35642),f178(f906(x35641,a895))),x35642) % 112.26/112.09 [3565]E(f317(f317(f92(f906(x35651,a895)),x35652),f232(f906(x35651,a895))),x35652) % 112.26/112.09 [3566]E(f317(f241(a899,a899),f79(f905(a899,a899),f44(x35661,x35662))),f317(f317(f31(a899),x35661),x35662)) % 112.26/112.09 [3572]E(f293(a1,f317(f317(f74(a1),x35721),f72(a1)),x35722),f295(a1,x35721,x35722)) % 112.26/112.09 [3577]E(f317(f246(a899,a899),f79(f905(a899,a899),f44(x35771,x35772))),f41(a899,x35771,x35772)) % 112.26/112.09 [3587]P1(f317(f317(f319(x35871),x35872),f232(f906(x35871,a895)))) % 112.26/112.09 [3592]E(f317(f317(f3(a899),f317(a102,x35921)),x35922),f317(f30(a899),f293(a899,x35922,x35921))) % 112.26/112.09 [3618]E(f317(f317(f3(f906(x36181,a895)),x36182),f232(f906(x36181,a895))),f178(f906(x36181,a895))) % 112.26/112.09 [3619]E(f317(f317(f91(f906(x36191,a895)),x36192),f232(f906(x36191,a895))),f232(f906(x36191,a895))) % 112.26/112.09 [3620]E(f317(f317(f92(f906(x36201,a895)),x36202),f178(f906(x36201,a895))),f178(f906(x36201,a895))) % 112.26/112.09 [3635]E(f41(a1,f317(f90(a1),x36351),f317(f90(a1),x36352)),f317(f90(a1),f41(a899,x36351,x36352))) % 112.26/112.09 [3636]E(f41(a1,f317(f73(a1),x36361),f317(f73(a1),x36362)),f317(f73(a1),f41(a1,x36361,x36362))) % 112.26/112.09 [3647]E(f317(f179(f900(x36471)),f317(f161(x36471),x36472)),f317(f317(f3(a899),f317(f179(f900(x36471)),x36472)),f72(a899))) % 112.26/112.09 [3673]E(f317(f317(f31(a1),f41(a1,x36731,x36732)),x36732),f2(a1)) % 112.26/112.09 [3682]E(f317(a5,f41(a899,f317(a22,x36821),f317(a22,x36822))),f41(a89,x36821,x36822)) % 112.26/112.09 [3715]E(f317(a5,f317(f317(f3(a899),f317(a22,x37151)),f317(a22,x37152))),f317(f317(f3(a89),x37151),x37152)) % 112.26/112.09 [3716]E(f317(a5,f317(f317(f74(a899),f317(a22,x37161)),f317(a22,x37162))),f317(f317(f74(a89),x37161),x37162)) % 112.26/112.09 [3717]E(f317(a5,f317(f317(f75(a899),f317(a22,x37171)),f317(a22,x37172))),f317(f317(f75(a89),x37171),x37172)) % 112.26/112.09 [3718]E(f317(a5,f317(f317(f31(a899),f317(a22,x37181)),f317(a22,x37182))),f317(f317(f31(a89),x37181),x37182)) % 112.26/112.09 [3726]E(f317(f300(a899,a899,a102),f317(f292(a899,x37261),x37262)),f317(f292(a899,f317(a102,x37261)),f317(a102,x37262))) % 112.26/112.09 [3753]P1(f317(f44(x37531,x37532),f79(f905(a899,a899),f44(x37531,x37532)))) % 112.26/112.09 [3777]E(f41(a899,f317(a102,f41(a899,x37771,x37772)),x37772),f41(a899,f317(a102,x37771),x37772)) % 112.26/112.09 [3789]E(f317(f317(f36(f906(x37891,a895),f906(x37891,a895)),x37892),f7(f906(x37891,a895))),f32(f906(x37891,a895),x37892)) % 112.26/112.09 [3790]E(f317(f317(f35(f906(x37901,a895),f906(x37901,a895)),x37902),f7(f906(x37901,a895))),f33(f906(x37901,a895),x37902)) % 112.26/112.09 [3791]E(f317(f300(f900(x37911),f906(x37911,a895),f162(x37911)),f317(f162(f900(x37911)),f50(x37911,x37912))),f317(f298(x37911),f317(f162(x37911),x37912))) % 112.26/112.09 [3795]P1(f317(f317(f319(f906(x37951,a895)),x37952),f317(f298(x37951),x37952))) % 112.26/112.09 [3801]E(f41(a1,f317(f73(a1),f41(a1,x38011,x38012)),x38012),f41(a1,f317(f73(a1),x38011),x38012)) % 112.26/112.09 [3812]P1(f317(f317(f224(f906(x38121,a895)),x38122),f232(f906(x38121,a895)))) % 112.26/112.09 [3814]E(f317(f317(f279(x38141,x38141,x38141),f297(x38141,x38142)),f297(x38141,f297(x38141,x38142))),f297(x38141,x38142)) % 112.26/112.09 [3815]E(f317(f317(f91(f906(x38151,a895)),f317(f254(x38151,x38151),x38152)),f317(f274(x38151,x38151),x38152)),f317(f271(x38151),x38152)) % 112.26/112.09 [3836]E(f303(x38361,x38362,f232(f906(x38361,a895)),f232(f906(x38362,a895))),f232(f906(f904(x38361,x38362),a895))) % 112.26/112.09 [3886]P1(f317(f317(f224(a899),f41(a899,x38861,x38862)),x38861)) % 112.26/112.09 [3910]P1(f317(f317(f224(a1),f317(f73(a1),f317(f90(a1),x39101))),f317(f90(a1),x39102))) % 112.26/112.09 [3934]P1(f317(f317(f319(f906(x39341,a895)),f178(f906(x39341,a895))),f317(f298(x39341),x39342))) % 112.26/112.09 [3939]E(f297(x39391,f317(f317(f279(x39391,x39391,x39391),x39392),f297(x39391,x39392))),f297(x39391,x39392)) % 112.26/112.09 [3942]E(f317(f317(f279(x39421,x39421,x39421),f297(x39421,x39422)),x39422),f317(f317(f279(x39421,x39421,x39421),x39422),f297(x39421,x39422))) % 112.26/112.09 [3944]E(f317(a95,f317(f317(f74(a1),f317(f317(f3(a1),x39441),x39442)),f72(a1))),f317(f30(a1),f293(a1,x39442,x39441))) % 112.26/112.09 [3959]E(f317(f274(x39591,x39591),f317(f317(f279(x39591,x39591,x39591),x39592),f297(x39591,x39592))),f317(f274(x39591,x39591),x39592)) % 112.26/112.09 [3960]E(f317(f254(x39601,x39601),f317(f317(f279(x39601,x39601,x39601),x39602),f297(x39601,x39602))),f317(f254(x39601,x39601),x39602)) % 112.26/112.09 [3978]E(f317(f132(f900(x39781),f900(x39781),f124(x39781),f103(x39781)),f159(f900(x39781),x39782,f103(x39781))),f103(x39781)) % 112.26/112.09 [3987]P24(a899,a899,f317(f317(f9(a899,a899,a899),f74(a899)),x39871),x39872) % 112.26/112.09 [3989]P13(a899,f317(f158(a899),f317(f317(f144(f900(x39891),a899),f179(f900(x39891))),f169(x39891,x39892)))) % 112.26/112.09 [4019]P51(x40191,f317(f317(f91(f906(f905(x40191,x40191),a895)),x40192),f317(f276(x40191,x40191),x40192))) % 112.26/112.09 [4020]P51(x40201,f317(f317(f92(f906(f905(x40201,x40201),a895)),x40202),f317(f276(x40201,x40201),x40202))) % 112.26/112.09 [4031]P1(f317(f317(f225(a1),f317(f73(a1),f317(f90(a1),f317(a102,x40311)))),f317(f90(a1),x40312))) % 112.26/112.09 [4076]E(f317(f132(f900(x40761),x40761,f317(f9(x40761,f900(x40761),f900(x40761)),f141(x40761)),f103(x40761)),x40762),f317(f158(x40761),x40762)) % 112.26/112.09 [4124]P1(f317(f317(f224(f906(f905(f900(x41241),f900(x41241)),a895)),f148(x41241,x41242)),f297(f900(x41241),f147(x41241,x41242)))) % 112.26/112.09 [4153]P1(f317(f44(x41531,x41532),f317(f317(f242(a899,a899),f317(f317(f31(a899),x41531),x41532)),f41(a899,x41531,x41532)))) % 112.26/112.09 [4165]P1(f317(f317(f224(f906(f905(f900(x41651),f900(x41651)),a895)),f147(x41651,f297(x41651,x41652))),f297(f900(x41651),f147(x41651,x41652)))) % 112.26/112.09 [4381]E(f317(f317(f249(f905(a89,a89),a89,f905(a89,a89),f905(x43811,f905(a89,a89))),f257(f317(f155(a89),f317(f317(f144(f905(a89,x43811),a89),f241(a89,x43811)),x43812)))),f317(f317(f10(x43811,f906(f905(a89,a89),f905(x43811,f905(a89,a89))),a89),f242(x43811,f905(a89,a89))),f258(x43811,x43812))),f256(x43811,x43812)) % 112.26/112.09 [4458]E(f213(a899,f905(x44581,f901(x44581)),f2(a899),f317(f247(x44581,f901(x44581),a899),f317(f18(f906(f901(x44581),a899),x44581),f317(f317(f9(f901(x44581),a899,a899),f317(f317(f10(a899,f906(a899,a899),f901(x44581)),f74(a899)),f179(f901(x44581)))),f72(a899)))),f317(f125(x44581),x44582)),f317(f179(f901(x44581)),x44582)) % 112.26/112.09 [4564]E(f317(f247(f906(f905(x45641,x45641),a895),f906(f905(x45641,x45641),a895),f906(f906(x45642,x45641),f905(f906(f905(x45642,x45642),a895),f906(f905(x45642,x45642),a895)))),f317(f317(f9(f906(f905(x45641,x45641),a895),f906(f906(f905(x45641,x45641),a895),f906(f906(x45642,x45641),f906(f905(x45642,x45642),a895))),f906(f906(f905(x45641,x45641),a895),f906(f906(x45642,x45641),f905(f906(f905(x45642,x45642),a895),f906(f905(x45642,x45642),a895))))),f317(f317(f10(f906(f906(f906(x45642,x45641),f906(f905(x45642,x45642),a895)),f906(f906(x45642,x45641),f905(f906(f905(x45642,x45642),a895),f906(f905(x45642,x45642),a895)))),f906(f906(f906(f905(x45641,x45641),a895),f906(f906(x45642,x45641),f906(f905(x45642,x45642),a895))),f906(f906(f905(x45641,x45641),a895),f906(f906(x45642,x45641),f905(f906(f905(x45642,x45642),a895),f906(f905(x45642,x45642),a895))))),f906(f905(x45641,x45641),a895)),f10(f906(f906(x45642,x45641),f906(f905(x45642,x45642),a895)),f906(f906(x45642,x45641),f905(f906(f905(x45642,x45642),a895),f906(f905(x45642,x45642),a895))),f906(f905(x45641,x45641),a895))),f317(f317(f10(f906(f906(x45642,x45641),f906(f906(f905(x45642,x45642),a895),f905(f906(f905(x45642,x45642),a895),f906(f905(x45642,x45642),a895)))),f906(f906(f906(x45642,x45641),f906(f905(x45642,x45642),a895)),f906(f906(x45642,x45641),f905(f906(f905(x45642,x45642),a895),f906(f905(x45642,x45642),a895)))),f906(f905(x45641,x45641),a895)),f20(f906(x45642,x45641),f906(f905(x45642,x45642),a895),f905(f906(f905(x45642,x45642),a895),f906(f905(x45642,x45642),a895)))),f317(f317(f10(f906(f906(x45642,x45641),f906(f905(x45642,x45642),a895)),f906(f906(x45642,x45641),f906(f906(f905(x45642,x45642),a895),f905(f906(f905(x45642,x45642),a895),f906(f905(x45642,x45642),a895)))),f906(f905(x45641,x45641),a895)),f317(f10(f906(f905(x45642,x45642),a895),f906(f906(f905(x45642,x45642),a895),f905(f906(f905(x45642,x45642),a895),f906(f905(x45642,x45642),a895))),f906(x45642,x45641)),f242(f906(f905(x45642,x45642),a895),f906(f905(x45642,x45642),a895)))),f278(x45641,x45642))))),f278(x45641,x45642))),f68(x45641,x45642)) % 112.26/112.09 [4609]~E(f317(f298(x46091),x46092),f178(f906(f906(x46091,a895),a895))) % 112.26/112.09 [4618]~P1(f317(f317(f162(x46181),f103(x46181)),x46182)) % 112.26/112.09 [4622]~P1(f317(f317(f319(x46221),x46222),f178(f906(x46221,a895)))) % 112.26/112.09 [4630]~P1(f317(f317(f225(f906(x46301,a895)),x46302),f178(f906(x46301,a895)))) % 112.26/112.09 [3502]E(f317(f317(f3(a899),x35021),f317(f317(f74(a899),x35021),x35022)),f2(a899)) % 112.26/112.09 [3505]E(f317(f317(f91(f906(x35051,a895)),x35052),x35052),x35052) % 112.26/112.09 [3506]E(f317(f317(f92(f906(x35061,a895)),x35062),x35062),x35062) % 112.26/112.09 [3534]E(f317(f317(f3(f906(x35341,a895)),x35342),x35342),f178(f906(x35341,a895))) % 112.26/112.09 [3537]E(f317(f133(x35371,x35372),f2(a899)),f178(f906(f905(f900(x35371),f900(x35371)),a895))) % 112.26/112.09 [3538]E(f317(f317(f74(a899),x35381),f317(a102,x35382)),f317(a102,f317(f317(f74(a899),x35381),x35382))) % 112.26/112.09 [3549]E(f184(f317(f90(a1),x35491),f317(f90(a1),x35492)),f317(f90(a1),f317(f317(f3(a899),x35491),x35492))) % 112.26/112.09 [3552]E(f317(f317(f31(a1),f317(f73(a1),x35521)),x35522),f317(f317(f31(a1),x35521),f317(f73(a1),x35522))) % 112.26/112.09 [3556]E(f317(f30(a1),f317(f292(a1,x35561),x35562)),f317(a95,f317(f317(f3(a1),x35562),x35561))) % 112.26/112.09 [3559]E(f317(f317(f74(a899),f317(a102,x35591)),x35592),f317(a102,f317(f317(f74(a899),x35591),x35592))) % 112.26/112.09 [3562]E(f317(f73(f906(x35621,a895)),f317(f73(f906(x35621,a895)),x35622)),x35622) % 112.26/112.09 [3574]E(f169(x35741,f317(f317(f141(f900(x35741)),f103(x35741)),x35742)),f169(x35741,x35742)) % 112.26/112.09 [3578]E(f317(f317(f74(a899),x35781),f317(f317(f75(a899),x35781),x35782)),f317(f317(f75(a899),x35781),f317(a102,x35782))) % 112.26/112.09 [3585]E(f317(f317(a4,f317(a5,x35851)),f317(a5,x35852)),f317(a5,f317(f317(f3(a899),x35851),x35852))) % 112.26/112.09 [3600]E(f317(f317(f75(a1),f317(f73(a1),x36001)),x36002),f317(f73(a1),f317(f317(f75(a1),x36001),x36002))) % 112.26/112.09 [3602]E(f317(f317(f234(a1),f317(f90(a1),x36021)),x36022),f317(f90(a1),f317(f317(f234(a899),x36021),x36022))) % 112.26/112.09 [3603]E(f317(f317(f74(a89),f317(a5,x36031)),f317(a5,x36032)),f317(a5,f317(f317(f74(a899),x36031),x36032))) % 112.26/112.09 [3604]E(f317(f317(f75(a89),f317(a5,x36041)),f317(a5,x36042)),f317(a5,f317(f317(f75(a899),x36041),x36042))) % 112.26/112.09 [3605]E(f317(f317(f228(a899),f317(a102,x36051)),f317(a102,x36052)),f317(a102,f317(f317(f228(a899),x36051),x36052))) % 112.26/112.09 [3606]E(f317(f317(f223(a899),f317(a102,x36061)),f317(a102,x36062)),f317(a102,f317(f317(f223(a899),x36061),x36062))) % 112.26/112.09 [3611]E(f317(f162(a899),f129(a899,f317(f292(a899,x36111),x36112))),f317(f292(a899,x36111),x36112)) % 112.26/112.09 [3612]E(f302(x36121,f317(f317(f299(x36121),x36122),f178(f906(x36121,a895)))),x36122) % 112.26/112.09 [3616]E(f317(f274(x36161,x36162),f178(f906(f905(x36161,x36162),a895))),f178(f906(x36162,a895))) % 112.26/112.09 [3617]E(f317(f254(x36171,x36172),f178(f906(f905(x36171,x36172),a895))),f178(f906(x36171,a895))) % 112.26/112.09 [3621]E(f317(a95,f317(f317(f3(a1),x36211),x36212)),f317(f30(a1),f295(a1,x36212,x36211))) % 112.26/112.09 [3626]E(f317(f317(f74(a899),x36261),f317(f317(f75(a899),x36262),x36261)),f317(f317(f75(a899),f317(a102,x36262)),x36261)) % 112.26/112.09 [3628]E(f317(f317(f56(x36281),f178(f906(x36281,a895))),x36282),f178(f906(f906(x36281,a895),a895))) % 112.26/112.09 [3637]E(f317(f179(f900(a899)),f129(a899,f317(f292(a899,x36371),x36372))),f317(f317(f3(a899),x36372),x36371)) % 112.26/112.09 [3652]E(f317(f317(f91(f906(x36521,a895)),f178(f906(x36521,a895))),x36522),x36522) % 112.26/112.09 [3653]E(f317(f317(f92(f906(x36531,a895)),f232(f906(x36531,a895))),x36532),x36532) % 112.26/112.09 [3656]E(f317(f317(f74(a1),f317(f73(a1),x36561)),f317(f73(a1),x36562)),f317(f73(a1),f317(f317(f74(a1),x36561),x36562))) % 112.26/112.09 [3658]E(f317(f317(f74(a1),f317(f94(a1),x36581)),f317(f94(a1),x36582)),f317(f94(a1),f317(f317(f74(a1),x36581),x36582))) % 112.26/112.09 [3660]E(f317(f317(f74(a1),f317(f90(a1),x36601)),f317(f90(a1),x36602)),f317(f90(a1),f317(f317(f74(a899),x36601),x36602))) % 112.26/112.09 [3661]E(f317(f317(f75(a1),f317(f94(a1),x36611)),f317(f94(a1),x36612)),f317(f94(a1),f317(f317(f75(a1),x36611),x36612))) % 112.26/112.09 [3663]E(f317(f317(f75(a1),f317(f90(a1),x36631)),f317(f90(a1),x36632)),f317(f90(a1),f317(f317(f75(a899),x36631),x36632))) % 112.26/112.09 [3664]E(f317(f317(f31(a1),f317(f90(a1),x36641)),f317(f90(a1),x36642)),f317(f90(a1),f317(f317(f31(a899),x36641),x36642))) % 112.26/112.09 [3683]E(f317(f317(f8(x36831,a899),f317(f18(a899,x36831),f72(a899))),x36832),f317(f30(x36831),x36832)) % 112.26/112.09 [3688]E(f317(f73(a1),f41(a1,f317(f73(a1),x36881),x36882)),f41(a1,x36881,f317(f73(a1),x36882))) % 112.26/112.09 [3690]E(f317(f162(a1),f168(x36901,f317(f317(f3(a1),x36902),f72(a1)))),f317(f292(a1,x36901),x36902)) % 112.26/112.09 [3694]P1(f317(f317(f224(a899),x36941),f317(f317(f74(a899),x36942),x36941))) % 112.26/112.09 [3695]P1(f317(f317(f224(a899),x36951),f317(f317(f74(a899),x36951),x36952))) % 112.26/112.09 [3698]E(f317(f317(f3(f906(x36981,a895)),f178(f906(x36981,a895))),x36982),f178(f906(x36981,a895))) % 112.26/112.09 [3699]E(f317(f317(f91(f906(x36991,a895)),f232(f906(x36991,a895))),x36992),f232(f906(x36991,a895))) % 112.26/112.09 [3700]E(f317(f317(f92(f906(x37001,a895)),f178(f906(x37001,a895))),x37002),f178(f906(x37001,a895))) % 112.26/112.09 [3707]E(f317(f317(f242(a1,a1),x37071),f317(f73(a1),x37072)),f317(a47,f317(f317(f242(a1,a1),x37071),x37072))) % 112.26/112.09 [3708]E(f317(f292(a1,f317(f317(f74(a1),x37081),f72(a1))),x37082),f296(a1,x37081,x37082)) % 112.26/112.09 [3719]E(f317(f317(f75(a899),x37191),f317(f317(f31(a899),x37192),x37191)),f317(f317(f3(a899),x37192),f41(a899,x37192,x37191))) % 112.26/112.09 [3720]E(f317(f317(f75(a1),x37201),f317(f317(f31(a1),x37202),x37201)),f317(f317(f3(a1),x37202),f41(a1,x37202,x37201))) % 112.26/112.09 [3723]E(f317(f162(a1),f168(f317(f317(f74(a1),x37231),f72(a1)),x37232)),f295(a1,x37231,x37232)) % 112.26/112.09 [3727]P1(f317(f317(f224(f906(x37271,a895)),x37272),x37272)) % 112.26/112.09 [3730]E(f317(f317(f91(f906(x37301,a895)),x37302),f317(f73(f906(x37301,a895)),x37302)),f232(f906(x37301,a895))) % 112.26/112.09 [3731]E(f317(f317(f92(f906(x37311,a895)),x37312),f317(f73(f906(x37311,a895)),x37312)),f178(f906(x37311,a895))) % 112.26/112.09 [3739]E(f317(f317(f3(a899),f317(f317(f3(a899),x37391),f72(a899))),x37392),f317(f317(f3(a899),x37391),f317(a102,x37392))) % 112.26/112.09 [3745]E(f317(f317(f3(f906(x37451,a895)),f232(f906(x37451,a895))),x37452),f317(f73(f906(x37451,a895)),x37452)) % 112.26/112.09 [3746]E(f317(f317(f3(a1),f317(f94(a1),x37461)),f317(f94(a1),x37462)),f317(f94(a1),f317(f317(f74(a1),x37461),f317(f73(a1),x37462)))) % 112.26/112.09 [3759]E(f317(f162(a899),f129(a899,f317(f292(a899,x37591),f317(a102,x37592)))),f293(a899,x37591,x37592)) % 112.26/112.09 [3775]E(f317(f179(f900(f900(x37751))),f50(x37751,x37752)),f317(f317(f234(a899),f317(a102,f317(a102,f2(a899)))),f317(f179(f900(x37751)),x37752))) % 112.26/112.09 [3793]E(f317(f317(f173(f905(x37931,x37931),a895),f2(a899)),x37932),f297(x37931,f178(f906(f905(x37931,x37931),a895)))) % 112.26/112.09 [3797]P1(f317(f127(a899),f129(a899,f317(f292(a899,x37971),x37972)))) % 112.26/112.09 [3813]E(f317(f300(a1,a899,a95),f293(a1,f317(f90(a1),x38131),f317(f90(a1),x38132))),f293(a899,x38131,x38132)) % 112.26/112.09 [3822]E(f175(a899,f2(a899),f7(a899),f317(f317(f3(a899),x38221),x38222)),f317(f317(f3(a899),x38221),f317(a102,x38222))) % 112.26/112.09 [3823]E(f317(a95,f317(f317(f3(a1),x38231),f317(f317(f74(a1),x38232),f72(a1)))),f317(f30(a1),f296(a1,x38232,x38231))) % 112.26/112.09 [3858]E(f317(f317(f144(a899,a899),a102),f129(a899,f317(f292(a899,x38581),x38582))),f129(a899,f317(f292(a899,f317(a102,x38581)),f317(a102,x38582)))) % 112.26/112.09 [3866]E(f317(f162(a1),f168(f317(f317(f74(a1),x38661),f72(a1)),f317(f317(f3(a1),x38662),f72(a1)))),f296(a1,x38661,x38662)) % 112.26/112.09 [3878]P1(f317(f317(f224(f906(x38781,a895)),f178(f906(x38781,a895))),x38782)) % 112.26/112.09 [3882]E(f79(x38821,f317(f317(f9(x38821,x38821,a895),a314),x38822)),x38822) % 112.26/112.09 [3883]E(f84(x38831,f317(f317(f9(x38831,x38831,a895),a314),x38832)),x38832) % 112.26/112.09 [3887]E(f317(f162(a899),f129(a899,f317(f292(a899,f317(a102,x38871)),f317(a102,x38872)))),f295(a899,x38871,x38872)) % 112.26/112.09 [3913]E(f317(f317(f244(x39131,x39132),f232(f906(x39131,a895))),f317(f18(f906(x39132,a895),x39131),f232(f906(x39132,a895)))),f232(f906(f905(x39131,x39132),a895))) % 112.26/112.09 [3946]E(f317(f252(x39461),f317(f317(f10(a895,a895,x39461),a312),x39462)),f317(f73(f906(x39461,a895)),f317(f252(x39461),x39462))) % 112.26/112.09 [3949]E(f317(f252(x39491),f317(f317(f9(x39491,x39491,a895),a314),x39492)),f317(f317(f299(x39491),x39492),f178(f906(x39491,a895)))) % 112.26/112.09 [3956]E(f317(f317(f74(a1),f317(f317(f3(a1),x39561),x39562)),f317(f317(f3(a1),x39561),x39562)),f317(f317(f3(a1),f317(f317(f74(a1),x39561),x39561)),f317(f317(f74(a1),x39562),x39562))) % 112.26/112.09 [3957]E(f317(f317(f74(a1),f317(f317(f74(a1),x39571),x39571)),f317(f317(f74(a1),x39572),x39572)),f317(f317(f74(a1),f317(f317(f74(a1),x39571),x39572)),f317(f317(f74(a1),x39571),x39572))) % 112.26/112.09 [3973]P1(f317(f317(f224(a899),f317(f30(x39731),f317(f162(x39731),x39732))),f317(f179(f900(x39731)),x39732))) % 112.26/112.09 [3974]P1(f317(f317(f224(a899),f317(f179(f900(x39741)),f142(x39741,x39742))),f317(f179(f900(x39741)),x39742))) % 112.26/112.09 [3984]E(f317(f252(x39841),f317(f317(f9(x39841,f906(x39841,a895),a895),f319(x39841)),x39842)),x39842) % 112.26/112.09 [3998]E(f317(f317(f165(x39981),f317(f317(f3(a899),f317(f179(f900(x39981)),x39982)),f72(a899))),x39982),f104(x39981,x39982)) % 112.26/112.09 [4018]E(f175(a899,f2(a899),f317(f317(f10(a899,a899,a899),a102),f317(f228(a899),x40181)),x40182),f317(f317(f228(a899),f317(a102,x40181)),x40182)) % 112.26/112.09 [4023]E(f32(f906(x40231,a895),f317(f300(f906(f905(x40231,x40231),a895),f906(x40231,a895),f271(x40231)),x40232)),f317(f271(x40231),f32(f906(f905(x40231,x40231),a895),x40232))) % 112.26/112.09 [4024]E(f175(a899,f317(a102,x40241),f317(f317(f10(a899,a899,a899),a102),f317(f223(a899),x40241)),x40242),f317(f317(f223(a899),f317(a102,x40241)),x40242)) % 112.26/112.09 [4026]E(f317(f317(f242(a1,a1),f317(f317(f31(a1),f317(f70(a1),x40261)),f317(f70(a1),x40262))),f41(a1,f317(f70(a1),x40261),f317(f70(a1),x40262))),f49(x40261,x40262)) % 112.26/112.09 [4049]P1(f317(f317(f224(f906(f906(x40491,a895),a895)),x40492),f317(f298(x40491),f32(f906(x40491,a895),x40492)))) % 112.26/112.09 [4081]E(f317(f317(f36(x40811,f906(x40811,a895)),x40812),f317(f317(f9(x40811,f906(x40811,a895),f906(x40811,a895)),f299(x40811)),f178(f906(x40811,a895)))),x40812) % 112.26/112.09 [4082]E(f317(f317(f279(x40821,x40821,x40821),f317(f276(x40821,x40821),x40822)),f297(x40821,f317(f276(x40821,x40821),x40822))),f317(f276(x40821,x40821),f317(f317(f279(x40821,x40821,x40821),x40822),f297(x40821,x40822)))) % 112.26/112.09 [4145]E(f317(f162(x41451),f317(f132(f900(x41451),f900(x41451),f124(x41451),f103(x41451)),x41452)),f317(f317(f36(f900(x41451),f906(x41451,a895)),f317(f162(f900(x41451)),x41452)),f162(x41451))) % 112.26/112.09 [4176]E(f317(f317(f91(f906(f905(x41761,x41761),a895)),f297(x41761,f178(f906(f905(x41761,x41761),a895)))),f317(f317(f279(x41761,x41761,x41761),f297(x41761,x41762)),x41762)),f297(x41761,x41762)) % 112.26/112.09 [4212]E(f317(f317(f171(x42121,x42121),x42122),x42122),f317(f317(f144(x42121,f905(x42121,x42121)),f317(f317(f20(x42121,x42121,f905(x42121,x42121)),f242(x42121,x42121)),f7(x42121))),x42122)) % 112.26/112.09 [4323]E(f317(f132(a899,f900(x43231),f317(f9(f900(x43231),a899,a899),f317(f317(f10(a899,f906(a899,a899),f900(x43231)),f223(a899)),f179(f900(x43231)))),f2(a899)),f317(f158(f900(x43231)),x43232)),f317(f179(f900(f900(x43231))),f169(x43231,x43232))) % 112.26/112.09 [4395]E(f317(f317(f278(f905(a899,f900(x43951)),f900(x43951)),f310(a899,f900(x43951),a230,f135(x43951,x43952))),f317(f317(f20(f900(x43951),f900(x43951),f905(a899,f900(x43951))),f317(f317(f10(a899,f906(f900(x43951),f905(a899,f900(x43951))),f900(x43951)),f242(a899,f900(x43951))),f179(f900(x43951)))),f7(f900(x43951)))),f136(x43951,x43952)) % 112.26/112.09 [4522]E(f317(f252(x45221),f317(f317(f10(f906(f906(x45221,a895),a895),a895,x45221),f81(f906(x45221,a895))),f317(f317(f10(f906(f906(x45221,a895),a895),f906(f906(x45221,a895),a895),x45221),f317(f20(f906(x45221,a895),a895,a895),f317(f317(f10(a895,f906(a895,a895),f906(x45221,a895)),a315),f317(f317(f9(f906(x45221,a895),f906(f906(x45221,a895),a895),a895),f319(f906(x45221,a895))),x45222)))),f319(x45221)))),f32(f906(x45221,a895),x45222)) % 112.26/112.09 [4523]E(f317(f252(x45231),f317(f317(f10(f906(f906(x45231,a895),a895),a895,x45231),f82(f906(x45231,a895))),f317(f317(f10(f906(f906(x45231,a895),a895),f906(f906(x45231,a895),a895),x45231),f317(f20(f906(x45231,a895),a895,a895),f317(f317(f10(a895,f906(a895,a895),f906(x45231,a895)),a320),f317(f317(f9(f906(x45231,a895),f906(f906(x45231,a895),a895),a895),f319(f906(x45231,a895))),x45232)))),f319(x45231)))),f33(f906(x45231,a895),x45232)) % 112.26/112.09 [4631]~P1(f317(f317(f225(a1),f317(f90(a1),x46311)),f317(f73(a1),f317(f90(a1),x46312)))) % 112.26/112.09 [3624]E(f317(f317(f3(a899),f317(f317(f74(a899),x36241),x36242)),x36242),x36241) % 112.26/112.09 [3625]E(f317(f317(f3(a899),f317(f317(f74(a899),x36251),x36252)),x36251),x36252) % 112.26/112.09 [3689]E(f317(f317(f74(a899),f317(f317(f3(a899),x36891),x36892)),x36892),f317(f317(f223(a899),x36891),x36892)) % 112.26/112.09 [3800]E(f317(f317(f75(a899),f317(f317(f31(a899),x38001),x38002)),x38002),f317(f317(f3(a899),x38001),f41(a899,x38001,x38002))) % 112.26/112.09 [3827]E(f317(f162(a899),f129(a899,f317(f292(a899,f317(a102,x38271)),x38272))),f296(a899,x38271,x38272)) % 112.26/112.09 [3835]E(f317(f90(a1),f206(f317(a95,f317(f70(a1),x38351)),f317(a95,f317(f70(a1),x38352)))),f317(f317(a207,x38351),x38352)) % 112.26/112.09 [3837]E(f317(f317(f91(f906(x38371,a895)),f317(f73(f906(x38371,a895)),x38372)),x38372),f232(f906(x38371,a895))) % 112.26/112.09 [3838]E(f317(f317(f92(f906(x38381,a895)),f317(f73(f906(x38381,a895)),x38382)),x38382),f178(f906(x38381,a895))) % 112.26/112.09 [3854]P1(f317(f317(f224(a899),f317(f317(f3(a899),x38541),x38542)),x38541)) % 112.26/112.09 [3855]P1(f317(f317(f224(a899),f317(f317(f31(a899),x38551),x38552)),x38551)) % 112.26/112.09 [3879]P1(f317(f317(f225(a899),x38791),f317(a102,f317(f317(f74(a899),x38792),x38791)))) % 112.26/112.09 [3880]P1(f317(f317(f225(a899),x38801),f317(a102,f317(f317(f74(a899),x38801),x38802)))) % 112.26/112.09 [3897]E(f317(f317(f75(a899),f317(a95,f317(f70(a1),x38971))),f317(a95,f317(f70(a1),x38972))),f317(a95,f317(f70(a1),f317(f317(f75(a1),x38971),x38972)))) % 112.26/112.09 [3909]P1(f317(f317(f224(a1),f2(a1)),f317(f317(f234(a1),f317(f70(a1),x39091)),x39092))) % 112.26/112.09 [3977]E(f317(f275(f900(x39771),f900(x39771),f148(x39771,x39772)),f317(f317(f299(f900(x39771)),f103(x39771)),f178(f906(f900(x39771),a895)))),f317(f317(f299(f900(x39771)),f103(x39771)),f178(f906(f900(x39771),a895)))) % 112.26/112.09 [3996]E(f317(f317(f91(f906(f905(x39961,x39961),a895)),f297(x39961,x39962)),f297(x39961,f178(f906(f905(x39961,x39961),a895)))),f297(x39961,x39962)) % 112.26/112.09 [4008]E(f317(f317(f31(a1),f317(f94(a1),f317(f317(f74(a1),x40081),x40081))),f317(f94(a1),f317(f317(f74(a1),x40082),x40082))),f317(f317(f31(a1),f317(f94(a1),x40081)),f317(f94(a1),x40082))) % 112.26/112.09 [4071]E(f317(f317(f234(a1),x40711),f317(f94(a899),f317(f317(f74(a1),x40712),x40712))),f317(f317(f80(a1,a1),f317(f317(f234(a1),x40711),f317(f94(a899),x40712))),f317(f317(f20(a1,a1,a1),f75(a1)),f7(a1)))) % 112.26/112.09 [4077]E(f317(f252(f906(x40771,a895)),f317(f317(f9(f906(x40771,a895),f906(x40771,a895),a895),f224(f906(x40771,a895))),x40772)),f317(f298(x40771),x40772)) % 112.26/112.09 [4093]E(f317(f317(f144(a1,a899),a95),f317(f317(f124(a1),f317(f317(f144(a899,a1),f90(a1)),x40931)),f317(f317(f144(a899,a1),f90(a1)),x40932))),f317(f317(f124(a899),x40931),x40932)) % 112.26/112.09 [4123]E(f317(f300(a1,a1,f317(f317(f9(a1,a1,a1),f74(a1)),x41231)),f317(f292(a1,f2(a1)),f317(f317(f3(a1),x41232),x41231))),f317(f292(a1,x41231),x41232)) % 112.26/112.09 [4125]P53(x41251,f317(f317(f3(f906(f905(x41251,x41251),a895)),x41252),f297(x41251,f178(f906(f905(x41251,x41251),a895))))) % 112.26/112.09 [4143]E(f317(f179(f900(x41431)),f317(f132(f900(x41431),f900(x41431),f124(x41431),f103(x41431)),x41432)),f317(f155(a899),f317(f317(f144(f900(x41431),a899),f179(f900(x41431))),x41432))) % 112.26/112.09 [4147]P52(x41471,f232(f906(x41471,a895)),f317(f317(f91(f906(f905(x41471,x41471),a895)),x41472),f297(x41471,f178(f906(f905(x41471,x41471),a895))))) % 112.26/112.09 [4192]E(f175(a899,f2(a899),f317(f317(f10(a899,a899,a899),a102),f317(f317(f9(a899,a899,a899),f228(a899)),x41921)),x41922),f317(f317(f228(a899),x41922),f317(a102,x41921))) % 112.26/112.09 [4195]E(f175(a899,f317(a102,x41951),f317(f317(f10(a899,a899,a899),a102),f317(f317(f9(a899,a899,a899),f223(a899)),x41951)),x41952),f317(f317(f223(a899),x41952),f317(a102,x41951))) % 112.26/112.09 [4198]E(f317(f300(x41981,f900(x41981),f317(f317(f9(x41981,f900(x41981),f900(x41981)),f141(x41981)),f103(x41981))),x41982),f164(x41981,x41982,f317(f317(f299(f900(x41981)),f103(x41981)),f178(f906(f900(x41981),a895))))) % 112.26/112.09 [4200]E(f317(f317(f91(f906(f905(x42001,x42001),a895)),f317(f317(f279(x42001,x42001,x42001),x42002),f297(x42001,x42002))),f297(x42001,f178(f906(f905(x42001,x42001),a895)))),f297(x42001,x42002)) % 112.26/112.09 [4207]P1(f317(f317(f224(f906(f905(x42071,x42071),a895)),f253(x42071,x42072)),f317(f317(f244(x42071,x42071),x42072),f317(f18(f906(x42071,a895),x42071),x42072)))) % 112.26/112.09 [4210]E(f317(f300(a1,a899,a95),f317(f317(f91(f906(a1,a895)),f317(f300(a899,a1,f90(a1)),x42101)),f317(f300(a899,a1,f90(a1)),x42102))),f317(f317(f91(f906(a899,a895)),x42101),x42102)) % 112.26/112.09 [4211]E(f317(f300(a1,a899,a95),f317(f317(f92(f906(a1,a895)),f317(f300(a899,a1,f90(a1)),x42111)),f317(f300(a899,a1,f90(a1)),x42112))),f317(f317(f92(f906(a899,a895)),x42111),x42112)) % 112.26/112.09 [4214]E(f317(f252(x42141),f317(f317(f10(a895,a895,x42141),a312),f317(f317(f9(x42141,f906(x42141,a895),a895),f319(x42141)),x42142))),f317(f73(f906(x42141,a895)),x42142)) % 112.26/112.09 [4241]E(f317(f132(f900(x42411),f900(x42411),f124(x42411),f103(x42411)),f317(f317(f144(f900(x42411),f900(x42411)),f158(x42411)),f317(f158(f900(x42411)),x42412))),f317(f158(x42411),f317(f132(f900(x42411),f900(x42411),f124(x42411),f103(x42411)),x42412))) % 112.26/112.09 [4267]E(f317(f317(f36(a899,f906(f905(x42671,x42671),a895)),f232(f906(a899,a895))),f317(f317(f9(a899,f906(f905(x42671,x42671),a895),f906(f905(x42671,x42671),a895)),f173(f905(x42671,x42671),a895)),x42672)),f297(x42671,x42672)) % 112.26/112.09 [4285]E(f79(x42851,f317(f317(f10(f906(x42851,a895),a895,x42851),f317(a314,x42852)),f317(f317(f9(x42851,f906(x42851,a895),f906(x42851,a895)),f299(x42851)),f178(f906(x42851,a895))))),f302(x42851,x42852)) % 112.26/112.09 [4293]E(f317(f179(f900(x42931)),f142(x42931,f317(f132(f900(x42931),f900(x42931),f124(x42931),f103(x42931)),x42932))),f317(f30(x42931),f317(f317(f36(f900(x42931),f906(x42931,a895)),f317(f162(f900(x42931)),x42932)),f162(x42931)))) % 112.26/112.09 [4307]E(f317(f317(f91(f906(f905(x43071,x43071),a895)),x43072),f317(f317(f279(x43071,x43071,x43071),f317(f317(f279(x43071,x43071,x43071),x43072),f297(x43071,x43072))),x43072)),f317(f317(f279(x43071,x43071,x43071),x43072),f297(x43071,x43072))) % 112.26/112.09 [4331]P1(f317(f317(f224(f906(f905(x43311,x43311),a895)),f317(f317(f279(x43311,x43311,x43311),x43312),f297(x43311,x43312))),f317(f317(f244(x43311,x43311),f317(f271(x43311),x43312)),f317(f18(f906(x43311,a895),x43311),f317(f271(x43311),x43312))))) % 112.26/112.09 [4372]E(f317(f252(f900(x43721)),f317(f317(f9(f900(x43721),f906(x43721,a895),a895),f317(f317(f10(f906(x43721,a895),f906(f906(x43721,a895),a895),f900(x43721)),f224(f906(x43721,a895))),f162(x43721))),x43722)),f151(x43721,x43722)) % 112.26/112.09 [4383]E(f317(f146(f900(x43831),x43831,f103(x43831),f317(f317(f10(f900(x43831),f906(f900(x43831),f900(x43831)),x43831),f317(f9(f900(x43831),f900(x43831),f900(x43831)),f124(x43831))),f317(f317(f9(x43831,f900(x43831),f900(x43831)),f141(x43831)),f103(x43831)))),x43832),f317(f157(x43831),x43832)) % 112.26/112.09 [4423]P24(f906(x44231,x44232),f906(f905(x44231,x44232),a895),f317(f317(f10(f906(f905(x44231,x44232),a895),f906(f905(x44231,x44232),a895),f906(x44231,x44232)),f252(f905(x44231,x44232))),f317(f317(f10(f906(x44231,f906(x44232,a895)),f906(f905(x44231,x44232),a895),f906(x44231,x44232)),f247(x44231,x44232,a895)),f317(f10(x44232,f906(x44232,a895),x44231),f317(f9(x44232,x44232,a895),a314)))),f232(f906(f906(x44231,x44232),a895))) % 112.26/112.09 [4428]E(f41(a1,f317(f94(a1),f317(f317(f74(a1),x44281),x44281)),f317(f94(a1),f317(f317(f74(a1),x44282),x44282))),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f41(a1,f317(f94(a1),x44281),f317(f94(a1),x44282)))) % 112.26/112.09 [4472]E(f317(f317(f36(x44721,f906(f905(x44721,x44721),a895)),x44722),f317(f317(f9(x44721,f906(f905(x44721,x44721),a895),f906(f905(x44721,x44721),a895)),f317(f317(f10(f905(x44721,x44721),f906(f906(f905(x44721,x44721),a895),f906(f905(x44721,x44721),a895)),x44721),f299(f905(x44721,x44721))),f317(f317(f20(x44721,x44721,f905(x44721,x44721)),f242(x44721,x44721)),f7(x44721)))),f178(f906(f905(x44721,x44721),a895)))),f253(x44721,x44722)) % 112.26/112.09 [4480]E(f192(x44801,f317(f317(f242(a1,a1),f317(f73(a1),f317(f317(f67(f905(a1,a1),a1,x44801,f241(a1,a1)),f202(x44801)),x44802))),f317(f317(f67(f905(a1,a1),a1,x44801,f246(a1,a1)),f202(x44801)),x44802))),f217(x44801,x44802)) % 112.26/112.09 [4561]E(f317(f252(f906(x45611,a895)),f317(f317(f10(f906(f906(x45611,a895),a895),a895,f906(x45611,a895)),f81(f906(x45611,a895))),f317(f317(f9(f906(x45611,a895),f906(f906(x45611,a895),a895),f906(f906(x45611,a895),a895)),f317(f317(f10(f906(f906(x45611,a895),f906(a895,a895)),f906(f906(f906(x45611,a895),a895),f906(f906(x45611,a895),a895)),f906(x45611,a895)),f20(f906(x45611,a895),a895,a895)),f317(f317(f10(f906(f906(x45611,a895),a895),f906(f906(x45611,a895),f906(a895,a895)),f906(x45611,a895)),f317(f10(a895,f906(a895,a895),f906(x45611,a895)),a315)),f317(f317(f9(f906(x45611,a895),f906(f906(x45611,a895),f906(x45611,a895)),f906(f906(x45611,a895),a895)),f317(f317(f10(f906(f906(x45611,a895),a895),f906(f906(f906(x45611,a895),f906(x45611,a895)),f906(f906(x45611,a895),a895)),f906(x45611,a895)),f10(f906(x45611,a895),a895,f906(x45611,a895))),a314)),f73(f906(x45611,a895)))))),f317(f317(f10(f906(f906(x45611,a895),a895),a895,f906(x45611,a895)),f317(f319(f906(x45611,a895)),x45612)),f298(x45611))))),f317(f298(x45611),f317(f73(f906(x45611,a895)),x45612))) % 112.26/112.09 [4629]~E(f317(f317(f74(a1),x46291),x46291),f317(f317(f3(a1),f317(f317(f74(a1),x46292),x46292)),a87)) % 112.26/112.09 [4633]~P1(f317(f317(f225(a899),f317(f317(f74(a899),x46331),x46332)),x46332)) % 112.26/112.09 [4634]~P1(f317(f317(f225(a899),f317(f317(f74(a899),x46341),x46342)),x46341)) % 112.26/112.09 [3914]E(f317(f317(f3(a899),x39141),f317(f317(f75(a899),f317(f317(f31(a899),x39141),x39142)),x39142)),f41(a899,x39141,x39142)) % 112.26/112.09 [3915]E(f317(f317(f3(a1),x39151),f317(f317(f75(a1),f317(f317(f31(a1),x39151),x39152)),x39152)),f41(a1,x39151,x39152)) % 112.26/112.09 [3947]E(f317(f317(f144(a899,x39471),f317(f154(x39471),x39472)),f129(a899,f317(f292(a899,f2(a899)),f317(f179(f900(x39471)),x39472)))),x39472) % 112.26/112.09 [4004]E(f317(f275(x40041,x40041,f297(x40041,f178(f906(f905(x40041,x40041),a895)))),x40042),x40042) % 112.26/112.09 [4128]E(f297(x41281,f317(f317(f3(f906(f905(x41281,x41281),a895)),x41282),f297(x41281,f178(f906(f905(x41281,x41281),a895))))),f297(x41281,x41282)) % 112.26/112.09 [4129]E(f297(x41291,f317(f317(f91(f906(f905(x41291,x41291),a895)),x41292),f297(x41291,f178(f906(f905(x41291,x41291),a895))))),f297(x41291,x41292)) % 112.26/112.09 [4179]E(f317(f317(f3(a1),f317(f317(f3(a1),f317(f317(f74(a1),x41791),x41791)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),x41792),x41792)),a87)),f317(f317(f74(a1),f317(f317(f3(a1),x41791),x41792)),f317(f317(f3(a1),x41791),x41792))) % 112.26/112.09 [4219]E(f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f74(a1),x42191),x42192)),f317(f317(f74(a1),x42191),x42192))),a87),f317(f317(f74(a1),f317(f317(f74(a1),x42191),x42191)),f317(f317(f3(a1),f317(f317(f74(a1),x42192),x42192)),a87))) % 112.26/112.09 [4244]E(f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),x42441),x42441)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),x42442),x42442)),a87)),f317(f317(f74(a1),f317(f317(f74(a1),x42441),f317(f317(f3(a1),x42442),a87))),f317(f317(f74(a1),x42441),f317(f317(f3(a1),x42442),a87)))) % 112.26/112.09 [4255]E(f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),x42551),x42552)),f317(f317(f3(a1),x42551),x42552))),a87),f317(f317(f3(a1),f317(f317(f3(a1),f317(f317(f74(a1),x42551),x42551)),a87)),f317(f317(f74(a1),x42552),x42552))) % 112.26/112.09 [4256]E(f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f74(a1),x42561),x42562)),f317(f317(f74(a1),x42561),x42562))),a87),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),x42561),x42561)),a87)),f317(f317(f74(a1),x42562),x42562))) % 112.26/112.09 [4304]E(f317(f90(a1),f317(f317(f31(a899),f317(f317(f75(a899),f317(a95,f317(f70(a1),x43041))),f317(a95,f317(f70(a1),x43042)))),f206(f317(a95,f317(f70(a1),x43041)),f317(a95,f317(f70(a1),x43042))))),f208(x43041,x43042)) % 112.26/112.09 [4349]E(f317(f317(f249(f905(a89,a89),a89,f905(a89,a89),f905(x43491,f905(a89,a89))),f257(f317(a5,f317(f179(f900(x43491)),x43492)))),f317(f317(f10(x43491,f906(f905(a89,a89),f905(x43491,f905(a89,a89))),a89),f242(x43491,f905(a89,a89))),f317(f317(f10(a899,x43491,a89),f317(f154(x43491),x43492)),a22))),f265(x43491,x43492)) % 112.26/112.09 [4429]E(f317(f132(a899,f900(x44291),f317(f9(f900(x44291),a899,a899),f317(f317(f10(a899,f906(a899,a899),f900(x44291)),f223(a899)),f179(f900(x44291)))),f2(a899)),f317(f158(f900(x44291)),f169(x44291,x44292))),f317(f179(f900(f900(x44291))),f317(f126(f900(x44291),f317(f317(f10(a895,a895,f900(x44291)),a312),f317(f317(f9(f900(x44291),f900(x44291),a895),a314),f103(x44291)))),x44292))) % 112.26/112.09 [4435]E(f317(f317(f36(a899,f906(x44351,a895)),f232(f906(a899,a895))),f317(f317(f9(a899,f906(a899,f906(x44351,a895)),f906(x44351,a895)),f317(f317(f10(f906(a899,a895),f906(f906(a899,f906(x44351,a895)),f906(x44351,a895)),a899),f36(a899,f906(x44351,a895))),f292(a899,f2(a899)))),x44352)),f317(f317(f36(a899,f906(x44351,a895)),f232(f906(a899,a895))),x44352)) % 112.26/112.09 [4457]P1(f317(f29(a899),f317(f252(a899),f317(f317(f20(a899,a895,a895),f317(f317(f10(a895,f906(a895,a895),a899),a315),x44571)),f317(f317(f9(a899,a899,a895),f225(a899)),x44572))))) % 112.26/112.09 [4569]E(f317(f252(f905(f900(x45691),f900(x45691))),f317(f247(f900(x45691),f900(x45691),a895),f317(f317(f20(f900(x45691),f906(f900(x45691),a895),f906(f900(x45691),a895)),f317(f317(f10(f906(f900(x45691),f906(a895,a895)),f906(f906(f900(x45691),a895),f906(f900(x45691),a895)),f900(x45691)),f20(f900(x45691),a895,a895)),f317(f317(f10(f906(f900(x45691),a895),f906(f900(x45691),f906(a895,a895)),f900(x45691)),f317(f10(a895,f906(a895,a895),f900(x45691)),a316)),f317(f317(f9(f900(x45691),f906(f900(x45691),a899),f906(f900(x45691),a895)),f317(f317(f10(f906(a899,a895),f906(f906(f900(x45691),a899),f906(f900(x45691),a895)),f900(x45691)),f10(a899,a895,f900(x45691))),f317(f317(f10(a899,f906(a899,a895),f900(x45691)),f225(a899)),f179(f900(x45691))))),f179(f900(x45691)))))),f317(f317(f20(f900(x45691),f906(f900(x45691),a895),f906(f900(x45691),a895)),f317(f317(f10(f906(f900(x45691),f906(a895,a895)),f906(f906(f900(x45691),a895),f906(f900(x45691),a895)),f900(x45691)),f20(f900(x45691),a895,a895)),f317(f317(f10(f906(f900(x45691),a895),f906(f900(x45691),f906(a895,a895)),f900(x45691)),f317(f10(a895,f906(a895,a895),f900(x45691)),a315)),f317(f317(f9(f900(x45691),f906(f900(x45691),a899),f906(f900(x45691),a895)),f317(f317(f10(f906(a899,a895),f906(f906(f900(x45691),a899),f906(f900(x45691),a895)),f900(x45691)),f10(a899,a895,f900(x45691))),f317(f317(f10(a899,f906(a899,a895),f900(x45691)),a314),f179(f900(x45691))))),f179(f900(x45691)))))),f317(f317(f9(f900(x45691),f906(f905(f900(x45691),f900(x45691)),a895),f906(f900(x45691),a895)),f317(f317(f10(f906(f900(x45691),f906(f906(f905(f900(x45691),f900(x45691)),a895),a895)),f906(f906(f905(f900(x45691),f900(x45691)),a895),f906(f900(x45691),a895)),f900(x45691)),f9(f900(x45691),f906(f905(f900(x45691),f900(x45691)),a895),a895)),f317(f317(f10(f906(f900(x45691),f905(f900(x45691),f900(x45691))),f906(f900(x45691),f906(f906(f905(f900(x45691),f900(x45691)),a895),a895)),f900(x45691)),f317(f10(f905(f900(x45691),f900(x45691)),f906(f906(f905(f900(x45691),f900(x45691)),a895),a895),f900(x45691)),f319(f905(f900(x45691),f900(x45691))))),f242(f900(x45691),f900(x45691))))),f135(x45691,x45692)))))),f136(x45691,x45692)) % 112.26/112.09 [4247]E(f317(f317(f74(a1),f317(f317(f74(a1),f317(f317(f75(a1),x42471),x42472)),f317(f317(f75(a1),x42471),x42472))),x42472),f317(f317(f75(a1),f317(f317(f3(a1),f317(f317(f74(a1),x42471),x42471)),a87)),x42472)) % 112.26/112.09 [4348]E(f317(a95,f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x43481),x43482)),f178(f906(f905(a899,a899),a895)))))),f317(f317(f3(a899),x43481),x43482)) % 112.26/112.09 [4352]E(f317(f317(f279(x43521,x43521,x43521),f317(f317(f91(f906(f905(x43521,x43521),a895)),x43522),f297(x43521,f178(f906(f905(x43521,x43521),a895))))),f297(x43521,f317(f317(f91(f906(f905(x43521,x43521),a895)),x43522),f297(x43521,f178(f906(f905(x43521,x43521),a895)))))),f297(x43521,x43522)) % 112.26/112.09 [4389]E(f258(x43891,f317(f126(f905(a89,x43891),f317(f247(a89,x43891,a895),f317(f317(f10(a895,f906(x43891,a895),a89),f18(a895,x43891)),f317(f225(a89),f2(a89))))),x43892)),f258(x43891,x43892)) % 112.26/112.09 [4390]E(f256(x43901,f317(f126(f905(a89,x43901),f317(f247(a89,x43901,a895),f317(f317(f10(a895,f906(x43901,a895),a89),f18(a895,x43901)),f317(f225(a89),f2(a89))))),x43902)),f256(x43901,x43902)) % 112.26/112.09 [4392]E(f317(f73(a1),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x43921),x43922)),f178(f906(f905(a899,a899),a895)))))),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x43922),x43921)),f178(f906(f905(a899,a899),a895)))))) % 112.26/112.09 [4448]E(f317(f317(f278(f900(a899),x44481),f135(a899,a230)),f317(f317(f9(x44481,f900(f906(x44481,a899)),f900(a899)),f317(f317(f10(f906(f906(x44481,a899),a899),f906(f900(f906(x44481,a899)),f900(a899)),x44481),f144(f906(x44481,a899),a899)),f317(f9(f906(x44481,a899),x44481,a899),f7(f906(x44481,a899))))),x44482)),f143(x44481,x44482)) % 112.26/112.09 [4469]E(f317(f317(f80(a1,a899),f317(f94(a1),f317(f317(f74(a1),x44691),a87))),f317(f317(f20(a1,a899,a899),f317(f317(f9(a1,a899,f906(a899,a899)),f317(f317(f10(a895,f906(a899,f906(a899,a899)),a1),f86(a899)),a183)),f2(a899))),f317(f317(f10(a899,a899,a1),a102),f317(f317(f10(a899,a899,a1),f317(f228(a899),x44692)),a95)))),f317(f317(f228(a899),f317(a102,x44692)),f317(f94(a899),x44691))) % 112.26/112.09 [4470]E(f317(f317(f80(a1,a899),f317(f94(a1),f317(f317(f74(a1),x44701),a87))),f317(f317(f20(a1,a899,a899),f317(f317(f9(a1,a899,f906(a899,a899)),f317(f317(f10(a895,f906(a899,f906(a899,a899)),a1),f86(a899)),a183)),f317(a102,x44702))),f317(f317(f10(a899,a899,a1),a102),f317(f317(f10(a899,a899,a1),f317(f223(a899),x44702)),a95)))),f317(f317(f223(a899),f317(a102,x44702)),f317(f94(a899),x44701))) % 112.26/112.09 [4490]E(f317(f132(f900(x44901),f900(x44901),f124(x44901),f103(x44901)),f317(f317(f144(f900(x44901),f900(x44901)),f146(f900(x44901),x44901,f103(x44901),f317(f317(f10(f900(x44901),f906(f900(x44901),f900(x44901)),x44901),f18(f900(x44901),f900(x44901))),f317(f317(f9(x44901,f900(x44901),f900(x44901)),f141(x44901)),f103(x44901))))),x44902)),f317(f317(f144(f900(x44901),x44901),f131(x44901)),f317(f126(f900(x44901),f317(f317(f10(a895,a895,f900(x44901)),a312),f317(f317(f9(f900(x44901),f900(x44901),a895),a314),f103(x44901)))),x44902))) % 112.26/112.09 [4552]E(f317(f247(a1,a1,a895),f317(f317(f9(a1,f906(a1,a895),f906(a1,a895)),f317(f317(f10(f906(a1,f906(a895,a895)),f906(f906(a1,a895),f906(a1,a895)),a1),f20(a1,a895,a895)),f317(f317(f10(f906(a1,a895),f906(a1,f906(a895,a895)),a1),f317(f10(a895,f906(a895,a895),a1),a315)),f317(f317(f10(f906(a1,a1),f906(a1,a895),a1),f317(f10(a1,a895,a1),f317(a314,x45521))),f317(f317(f10(a1,f906(a1,a1),a1),f74(a1)),f317(f75(a1),x45522)))))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f317(f10(a895,a895,a1),f317(a320,f317(f317(f225(a1),f2(a1)),x45522))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f224(a1),f2(a1)))),f317(f317(f9(a1,a1,a895),f225(a1)),x45522))))),f317(f317(f10(a895,a895,a1),f317(a320,f317(a312,f317(f317(f225(a1),f2(a1)),x45522)))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f225(a1),x45522))),f317(f317(f9(a1,a1,a895),f224(a1)),f2(a1))))))),f45(x45521,x45522)) % 112.26/112.09 [4555]E(f317(f252(x45551),f317(f317(f10(f906(a899,a895),a895,x45551),f81(a899)),f317(f317(f9(x45551,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),x45551),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),x45551),f317(f10(a895,f906(a895,a895),a899),a315)),f317(f317(f9(x45551,f906(a899,x45551),f906(a899,a895)),f317(f317(f10(f906(x45551,a895),f906(f906(a899,x45551),f906(a899,a895)),x45551),f10(x45551,a895,a899)),a314)),f317(f154(x45551),x45552))))),f317(f317(f9(a899,a899,a895),f225(a899)),f317(f179(f900(x45551)),x45552))))),f317(f162(x45551),x45552)) % 112.26/112.09 [4362]E(f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),x43621),a87)),x43622)),f317(f317(f3(a1),f317(f317(f74(a1),x43621),a87)),x43622))),a87),f317(f317(f3(a1),f317(f317(f74(a1),x43621),x43621)),f317(f317(f3(a1),f317(f317(f74(a1),x43622),x43622)),a87))) % 112.26/112.09 [4485]E(f317(f132(f900(f900(x44851)),f900(f900(x44851)),f124(f900(x44851)),f103(f900(x44851))),f317(f317(f144(f900(x44851),f900(f900(x44851))),f146(f900(f900(x44851)),x44851,f103(f900(x44851)),f317(f18(f906(f900(x44851),f900(f900(x44851))),x44851),f317(f317(f9(f900(x44851),f900(f900(x44851)),f900(f900(x44851))),f141(f900(x44851))),f103(f900(x44851)))))),x44852)),f317(f317(f144(f900(x44851),f900(x44851)),f161(x44851)),f317(f126(f900(x44851),f317(f317(f10(a895,a895,f900(x44851)),a312),f317(f317(f9(f900(x44851),f900(x44851),a895),a314),f103(x44851)))),x44852))) % 112.26/112.09 [4495]E(f317(f317(f80(a1,a899),f317(f94(a1),f317(f317(f74(a1),x44951),a87))),f317(f317(f20(a1,a899,a899),f317(f317(f9(a1,a899,f906(a899,a899)),f317(f317(f10(a895,f906(a899,f906(a899,a899)),a1),f86(a899)),a183)),f2(a899))),f317(f317(f10(a899,a899,a1),a102),f317(f317(f9(a1,a899,a899),f317(f317(f10(a899,f906(a899,a899),a1),f228(a899)),a95)),x44952)))),f317(f317(f228(a899),f317(f94(a899),x44951)),f317(a102,x44952))) % 112.26/112.09 [4496]E(f317(f317(f80(a1,a899),f317(f94(a1),f317(f317(f74(a1),x44961),a87))),f317(f317(f20(a1,a899,a899),f317(f317(f9(a1,a899,f906(a899,a899)),f317(f317(f10(a895,f906(a899,f906(a899,a899)),a1),f86(a899)),a183)),f317(a102,x44962))),f317(f317(f10(a899,a899,a1),a102),f317(f317(f9(a1,a899,a899),f317(f317(f10(a899,f906(a899,a899),a1),f223(a899)),a95)),x44962)))),f317(f317(f223(a899),f317(f94(a899),x44961)),f317(a102,x44962))) % 112.26/112.09 [4484]E(f317(f247(x44841,x44841,a895),f317(f317(f20(x44841,a895,f906(x44841,a895)),f317(f317(f10(f906(x44841,f906(a895,a895)),f906(a895,f906(x44841,a895)),x44841),f9(x44841,a895,a895)),f317(f317(f10(f906(x44841,a895),f906(x44841,f906(a895,a895)),x44841),f317(f10(a895,f906(a895,a895),x44841),a315)),a314))),x44842)),f253(x44841,x44842)) % 112.26/112.09 [4529]E(f317(f317(f31(a899),x45291),f317(f317(f74(a899),f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),x45292)),f317(f317(f31(a899),x45291),f317(a102,f317(a102,f317(a102,x45292))))) % 112.26/112.09 [4530]E(f41(a899,x45301,f317(f317(f74(a899),f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),x45302)),f41(a899,x45301,f317(a102,f317(a102,f317(a102,x45302))))) % 112.26/112.09 [4531]E(f41(a899,f317(f317(f74(a899),f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),x45311),x45312),f41(a899,f317(a102,f317(a102,f317(a102,x45311))),x45312)) % 112.26/112.09 [4543]E(f113(f317(x45431,f317(f317(f75(a89),f317(f94(a89),f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),x45432))),f317(f190(x45431),x45432)) % 112.26/112.09 [4544]E(f317(f317(f31(a899),f317(f317(f74(a899),f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),x45441)),x45442),f317(f317(f31(a899),f317(a102,f317(a102,f317(a102,x45441)))),x45442)) % 112.26/112.09 [4596]~E(f116(x45961,x45962,x45963),f109(x45961)) % 112.26/112.09 [3352]E(f317(f182(x33521,x33522),x33523),f111(x33521,x33522)) % 112.26/112.09 [3371]E(f317(f189(x33711,x33712),x33713),f317(f119(x33711),x33712)) % 112.26/112.09 [3448]E(f317(f317(f144(x34481,x34482),x34483),f103(x34481)),f103(x34482)) % 112.26/112.09 [3488]E(f317(f174(x34881,x34882,x34883),f2(a899)),x34882) % 112.26/112.09 [3490]E(f317(f317(f171(x34901,x34902),x34903),f103(x34902)),f103(f905(x34901,x34902))) % 112.26/112.09 [3503]E(f317(f179(f900(x35031)),f159(x35031,x35032,x35033)),x35032) % 112.26/112.09 [3522]E(f79(x35221,f57(x35221,x35222,x35223)),f317(f58(x35221,x35222),x35223)) % 112.26/112.09 [3526]E(f233(x35261,x35262,f233(x35262,x35261,x35263)),x35263) % 112.26/112.09 [3546]E(f317(f158(x35461),f159(x35461,x35462,x35463)),f159(x35461,x35462,x35463)) % 112.26/112.09 [3571]E(f130(x35711,x35712,f142(x35711,x35713)),f142(x35711,f130(x35711,x35712,x35713))) % 112.26/112.09 [3590]E(f317(f241(f900(x35901),f900(x35901)),f156(x35901,x35902,x35903)),f317(f126(x35901,x35902),x35903)) % 112.26/112.09 [3633]E(f317(f317(f141(x36331),x36332),f159(x36331,x36333,x36332)),f159(x36331,f317(a102,x36333),x36332)) % 112.26/112.09 [3665]E(f19(x36651,x36652,x36653,f2(a89)),x36652) % 112.26/112.09 [3666]E(f175(x36661,x36662,x36663,f2(a899)),x36662) % 112.26/112.09 [3667]E(f21(x36671,x36672,x36673,f2(a89)),x36672) % 112.26/112.09 [3674]E(f153(x36741,x36742,x36743,f103(x36741)),f103(x36742)) % 112.26/112.09 [3675]E(f120(x36751,x36752,x36753,f109(x36751)),f109(x36752)) % 112.26/112.09 [3681]E(f317(f317(f154(x36811),f317(f317(f141(x36811),x36812),x36813)),f2(a899)),x36812) % 112.26/112.09 [3709]E(f55(x37091,x37092,f103(x37091),x37093),f103(f905(x37091,x37092))) % 112.26/112.09 [3729]P24(x37291,x37292,x37293,f178(f906(x37291,a895))) % 112.26/112.09 [3831]E(f255(x38311,x38312,x38313),f317(f242(f906(a89,f906(a895,f902(f901(x38311)))),f905(a89,a89)),f37(x38311))) % 112.26/112.09 [3888]E(f317(f67(x38881,x38882,x38881,x38883),f25(x38881)),x38883) % 112.26/112.09 [4063]P1(f317(f317(f319(f905(x40631,x40631)),f317(f317(f242(x40631,x40631),x40632),x40632)),f297(x40631,x40633))) % 112.26/112.09 [4638]~P1(f317(f317(f319(f905(f900(x46381),f900(x46381))),f317(f317(f242(f900(x46381),f900(x46381)),x46382),f103(x46381))),f135(x46381,x46383))) % 112.26/112.09 [4639]~P1(f317(f317(f319(f905(f900(x46391),f900(x46391))),f317(f317(f242(f900(x46391),f900(x46391)),x46392),f103(x46391))),f137(x46391,x46393))) % 112.26/112.09 [4640]~P1(f317(f317(f319(f905(f900(x46401),f900(x46401))),f317(f317(f242(f900(x46401),f900(x46401)),x46402),f103(x46401))),f147(x46401,x46403))) % 112.26/112.09 [4642]~P1(f317(f317(f319(f905(f900(x46421),f900(x46421))),f317(f317(f242(f900(x46421),f900(x46421)),f103(x46421)),x46422)),f135(x46421,x46423))) % 112.26/112.09 [4643]~P1(f317(f317(f319(f905(f900(x46431),f900(x46431))),f317(f317(f242(f900(x46431),f900(x46431)),f103(x46431)),x46432)),f147(x46431,x46433))) % 112.26/112.09 [3423]E(f317(f317(f191(x34231),x34232),x34233),f192(x34231,f205(x34232,x34233))) % 112.26/112.09 [3477]E(f317(f276(x34771,x34772),f317(f276(x34772,x34771),x34773)),x34773) % 112.26/112.09 [3498]E(f317(f317(f171(x34981,x34982),f103(x34981)),x34983),f103(f905(x34981,x34982))) % 112.26/112.09 [3501]E(f166(x35011,x35012,f317(f272(a899),x35013)),f317(f317(f165(x35011),x35013),x35012)) % 112.26/112.09 [3519]E(f142(x35191,f317(f126(x35191,x35192),x35193)),f317(f126(x35191,x35192),f142(x35191,x35193))) % 112.26/112.09 [3520]E(f317(f274(x35201,x35202),f317(f276(x35202,x35201),x35203)),f317(f254(x35202,x35201),x35203)) % 112.26/112.09 [3521]E(f317(f254(x35211,x35212),f317(f276(x35212,x35211),x35213)),f317(f274(x35212,x35211),x35213)) % 112.26/112.09 [3539]E(f317(f126(x35391,x35392),f317(f158(x35391),x35393)),f317(f158(x35391),f317(f126(x35391,x35392),x35393))) % 112.26/112.09 [3551]E(f317(f317(f128(x35511),x35512),f317(f161(x35511),x35513)),f317(f317(f128(x35511),f317(a102,x35512)),x35513)) % 112.26/112.09 [3567]E(f317(f300(x35671,x35672,x35673),f178(f906(x35671,a895))),f178(f906(x35672,a895))) % 112.26/112.09 [3568]E(f317(f275(x35681,x35682,x35683),f178(f906(x35681,a895))),f178(f906(x35682,a895))) % 112.26/112.09 [3569]E(f317(f301(x35691,x35692,x35693),f178(f906(x35692,a895))),f178(f906(x35691,a895))) % 112.26/112.09 [3570]E(f317(f301(x35701,x35702,x35703),f232(f906(x35702,a895))),f232(f906(x35701,a895))) % 112.26/112.09 [3596]E(f110(x35961,f116(f901(x35961),x35962,x35963)),f106(x35961,x35962,f110(x35961,x35963))) % 112.26/112.09 [3598]E(f317(f317(f299(x35981),x35982),f317(f162(x35981),x35983)),f317(f162(x35981),f130(x35981,x35982,x35983))) % 112.26/112.09 [3685]E(f317(f300(f905(x36851,x36852),x36852,f246(x36851,x36852)),x36853),f317(f274(x36851,x36852),x36853)) % 112.26/112.09 [3686]E(f317(f300(f905(x36861,x36862),x36861,f241(x36861,x36862)),x36863),f317(f254(x36861,x36862),x36863)) % 112.26/112.09 [3701]E(f317(f162(x37011),f159(x37011,f317(a102,x37012),x37013)),f317(f317(f299(x37011),x37013),f178(f906(x37011,a895)))) % 112.26/112.09 [3758]E(f317(f317(f242(x37581,x37582),f317(f241(x37581,x37582),x37583)),f317(f246(x37581,x37582),x37583)),x37583) % 112.26/112.09 [3765]E(f317(f179(f901(x37651)),f116(x37651,x37652,x37653)),f317(f317(f74(a899),f317(f179(f901(x37651)),x37653)),f317(a102,f2(a899)))) % 112.26/112.09 [3767]E(f317(f317(f247(x37671,x37672,x37671),f18(x37671,x37672)),x37673),f317(f241(x37671,x37672),x37673)) % 112.26/112.09 [3893]E(f317(f67(x38931,x38931,x38932,f25(x38931)),x38933),x38933) % 112.26/112.09 [3900]E(f317(f317(f124(x39001),f159(x39001,x39002,x39003)),f317(f317(f141(x39001),x39003),f103(x39001))),f317(f317(f141(x39001),x39003),f159(x39001,x39002,x39003))) % 112.26/112.09 [4072]P1(f317(f317(f224(f906(x40721,a895)),f317(f162(x40721),f317(f126(x40721,x40722),x40723))),f317(f162(x40721),x40723))) % 112.26/112.09 [4114]P1(f317(f317(f224(f906(x41141,a895)),f317(f162(x41141),f317(f317(f165(x41141),x41142),x41143))),f317(f162(x41141),x41143))) % 112.26/112.09 [4115]P1(f317(f317(f224(f906(x41151,a895)),f317(f162(x41151),f317(f317(f128(x41151),x41152),x41153))),f317(f162(x41151),x41153))) % 112.26/112.09 [4119]P1(f317(f317(f224(f906(x41191,a895)),f317(f162(x41191),f166(x41191,x41192,x41193))),f317(f162(x41191),x41192))) % 112.26/112.09 [4120]P1(f317(f317(f224(f906(x41201,a895)),f317(f162(x41201),f160(x41201,x41202,x41203))),f317(f162(x41201),x41203))) % 112.26/112.09 [4141]P24(f905(x41411,x41412),f905(x41412,x41411),f317(f247(x41411,x41412,f905(x41412,x41411)),f317(f9(x41412,x41411,f905(x41412,x41411)),f242(x41412,x41411))),x41413) % 112.26/112.09 [4152]E(f317(f317(f317(f173(f900(x41521),f900(x41521)),f41(a899,x41522,f317(f179(f900(x41521)),x41523))),f157(x41521)),x41523),f317(f317(f317(f173(f900(x41521),f900(x41521)),x41522),f157(x41521)),x41523)) % 112.26/112.09 [4196]P1(f317(f317(f319(f905(f900(x41961),f900(x41961))),f317(f317(f242(f900(x41961),f900(x41961)),x41962),x41962)),f148(x41961,f297(x41961,x41963)))) % 112.26/112.09 [4335]E(f79(f905(x43351,x43352),f317(f317(f20(f905(x43351,x43352),x43352,a895),f317(f317(f10(x43351,f906(x43352,a895),f905(x43351,x43352)),x43353),f241(x43351,x43352))),f246(x43351,x43352))),f79(f905(x43351,x43352),f317(f247(x43351,x43352,a895),x43353))) % 112.26/112.09 [4336]E(f84(f905(x43361,x43362),f317(f317(f20(f905(x43361,x43362),x43362,a895),f317(f317(f10(x43361,f906(x43362,a895),f905(x43361,x43362)),x43363),f241(x43361,x43362))),f246(x43361,x43362))),f84(f905(x43361,x43362),f317(f247(x43361,x43362,a895),x43363))) % 112.26/112.09 [4369]E(f317(f317(f278(f905(a899,x43691),x43691),f310(a899,x43691,a230,x43692)),f317(f317(f20(x43691,x43691,f905(a899,x43691)),f317(f317(f10(a899,f906(x43691,f905(a899,x43691)),x43691),f242(a899,x43691)),x43693)),f7(x43691))),f311(x43691,x43693,x43692)) % 112.26/112.09 [4431]E(f317(f248(x44311,x44311,x44312,x44312,f7(x44311),f7(x44312)),x44313),x44313) % 112.26/112.09 [4504]E(f317(f132(f900(f900(x45041)),f900(f900(x45041)),f124(f900(x45041)),f103(f900(x45041))),f317(f317(f144(f900(x45041),f900(f900(x45041))),f317(f317(f9(f900(x45041),f900(x45041),f900(f900(x45041))),f317(f317(f10(f906(x45041,f900(x45041)),f906(f900(x45041),f900(f900(x45041))),f900(x45041)),f144(x45041,f900(x45041))),f317(f9(x45041,f900(x45041),f900(x45041)),f141(x45041)))),x45042)),f51(x45041,x45043,x45042))),f51(x45041,f317(a102,x45043),x45042)) % 112.26/112.09 [4560]E(f213(a899,f905(x45601,f901(x45601)),f2(a899),f317(f247(x45601,f901(x45601),a899),f317(f317(f9(x45601,a899,f906(f901(x45601),a899)),f317(f317(f10(f906(f901(x45601),f906(a899,a899)),f906(a899,f906(f901(x45601),a899)),x45601),f9(f901(x45601),a899,a899)),f317(f317(f10(f906(f901(x45601),a899),f906(f901(x45601),f906(a899,a899)),x45601),f317(f10(a899,f906(a899,a899),f901(x45601)),f74(a899))),f317(f317(f9(x45601,f906(f901(x45601),a899),f906(f901(x45601),a899)),f317(f317(f10(f906(a899,a899),f906(f906(f901(x45601),a899),f906(f901(x45601),a899)),x45601),f10(a899,a899,f901(x45601))),f317(f317(f10(a899,f906(a899,a899),x45601),f74(a899)),x45602))),f115(x45601,x45602))))),f72(a899))),f317(f125(x45601),x45603)),f317(f115(x45601,x45602),x45603)) % 112.26/112.09 [4568]E(f317(f317(f80(a1,x45681),f208(f317(f317(f67(f905(a1,a1),a1,x45681,f246(a1,a1)),f202(x45681)),x45682),f317(f317(f67(f905(a1,a1),a1,x45681,f246(a1,a1)),f202(x45681)),x45683))),f317(f317(f20(a1,a1,x45681),f317(f317(f10(a1,f906(a1,x45681),a1),f191(x45681)),f317(f317(f20(a1,a1,a1),f317(f317(f10(a1,f906(a1,a1),a1),f74(a1)),f317(f317(f10(a1,a1,a1),f317(f75(a1),f317(f317(f67(f905(a1,a1),a1,x45681,f241(a1,a1)),f202(x45681)),x45682))),f317(f317(f9(a1,a1,a1),f31(a1)),f317(f317(f67(f905(a1,a1),a1,x45681,f246(a1,a1)),f202(x45681)),x45682))))),f317(f317(f10(a1,a1,a1),f317(f75(a1),f317(f317(f67(f905(a1,a1),a1,x45681,f241(a1,a1)),f202(x45681)),x45683))),f317(f317(f9(a1,a1,a1),f31(a1)),f317(f317(f67(f905(a1,a1),a1,x45681,f246(a1,a1)),f202(x45681)),x45683)))))),f7(a1))),f220(x45681,x45682,x45683)) % 112.26/112.09 [4591]~E(f317(f317(f141(x45911),x45912),x45913),x45913) % 112.26/112.09 [4594]~E(f317(f317(f141(x45941),x45942),x45943),f103(x45941)) % 112.26/112.09 [4600]~E(f317(f317(f299(x46001),x46002),x46003),f178(f906(x46001,a895))) % 112.26/112.09 [4620]~E(f317(f300(x46201,f906(x46201,a895),x46202),x46203),f317(f298(x46201),x46203)) % 112.26/112.09 [3482]E(f317(f317(f149(x34821,f103(x34821)),x34822),x34823),f103(x34821)) % 112.26/112.09 [3483]E(f317(f131(x34831),f317(f317(f141(x34831),x34832),x34833)),x34832) % 112.26/112.09 [3484]E(f317(f161(x34841),f317(f317(f141(x34841),x34842),x34843)),x34843) % 112.26/112.09 [3525]E(f317(f317(f128(x35251),f72(a899)),f317(f317(f141(x35251),x35252),x35253)),x35253) % 112.26/112.09 [3558]E(f104(x35581,f317(f317(f128(x35581),x35582),x35583)),f317(f317(f128(x35581),x35582),f104(x35581,x35583))) % 112.26/112.09 [3560]E(f317(f317(f149(x35601,x35602),x35603),f317(f317(f154(x35601),x35602),x35603)),x35602) % 112.26/112.09 [3580]E(f317(f317(f299(x35801),x35802),f317(f317(f299(x35801),x35802),x35803)),f317(f317(f299(x35801),x35802),x35803)) % 112.26/112.09 [3593]E(f317(f317(f299(x35931),x35932),f317(f162(x35931),x35933)),f317(f162(x35931),f317(f317(f141(x35931),x35932),x35933))) % 112.26/112.09 [3595]E(f317(f317(f128(x35951),x35952),f317(f161(x35951),x35953)),f317(f161(x35951),f317(f317(f128(x35951),x35952),x35953))) % 112.26/112.09 [3607]E(f317(f317(f165(x36071),f72(a899)),f317(f317(f141(x36071),x36072),x36073)),f317(f317(f141(x36071),x36072),f103(x36071))) % 112.26/112.09 [3650]E(f317(f58(x36501,x36502),f317(f317(f299(x36501),x36503),f178(f906(x36501,a895)))),x36503) % 112.26/112.09 [3691]E(f317(f317(f74(a899),x36911),f317(f317(f74(a899),x36912),x36913)),f317(f317(f74(a899),x36912),f317(f317(f74(a899),x36911),x36913))) % 112.26/112.09 [3692]E(f317(f317(f74(a1),x36921),f317(f317(f74(a1),x36922),x36923)),f317(f317(f74(a1),x36922),f317(f317(f74(a1),x36921),x36923))) % 112.26/112.09 [3697]E(f317(f317(f244(x36971,x36972),f178(f906(x36971,a895))),x36973),f178(f906(f905(x36971,x36972),a895))) % 112.26/112.09 [3721]E(f317(f317(f91(f906(x37211,a895)),x37212),x37213),f317(f317(f91(f906(x37211,a895)),x37213),x37212)) % 112.26/112.09 [3722]E(f317(f317(f92(f906(x37221,a895)),x37222),x37223),f317(f317(f92(f906(x37221,a895)),x37223),x37222)) % 112.26/112.09 [3724]E(f317(f317(f124(x37241),x37242),f317(f317(f141(x37241),x37243),f103(x37241))),f317(f157(x37241),f317(f317(f141(x37241),x37243),x37242))) % 112.26/112.09 [3725]E(f317(f317(f124(x37251),f317(f158(x37251),x37252)),f317(f158(x37251),x37253)),f317(f158(x37251),f317(f317(f124(x37251),x37253),x37252))) % 112.26/112.09 [3735]E(f317(f161(x37351),f317(f317(f165(x37351),f317(a102,x37352)),x37353)),f317(f317(f165(x37351),x37352),f317(f161(x37351),x37353))) % 112.26/112.09 [3743]P1(f317(f317(f319(x37431),x37432),f317(f317(f299(x37431),x37432),x37433))) % 112.26/112.09 [3747]E(f317(f317(f35(x37471,f906(x37472,a895)),f178(f906(x37471,a895))),x37473),f232(f906(x37472,a895))) % 112.26/112.09 [3750]E(f317(f275(x37501,x37501,f253(x37501,x37502)),x37503),f317(f317(f92(f906(x37501,a895)),x37502),x37503)) % 112.26/112.09 [3764]E(f317(f179(f900(x37641)),f317(f317(f141(x37641),x37642),x37643)),f317(f317(f74(a899),f317(f179(f900(x37641)),x37643)),f317(a102,f2(a899)))) % 112.26/112.09 [3769]E(f104(x37691,f317(f317(f124(x37691),x37692),f317(f317(f141(x37691),x37693),f103(x37691)))),x37692) % 112.26/112.09 [3770]E(f134(x37701,f317(f317(f124(x37701),x37702),f317(f317(f141(x37701),x37703),f103(x37701)))),x37703) % 112.26/112.09 [3778]E(f317(f317(f124(x37781),f317(f317(f165(x37781),x37782),x37783)),f317(f317(f128(x37781),x37782),x37783)),x37783) % 112.26/112.09 [3787]E(f317(f317(f3(a899),f317(f317(f74(a899),x37871),x37872)),f317(f317(f74(a899),x37873),x37872)),f317(f317(f3(a899),x37871),x37873)) % 112.26/112.09 [3788]E(f317(f317(f3(a899),f317(f317(f74(a899),x37881),x37882)),f317(f317(f74(a899),x37881),x37883)),f317(f317(f3(a899),x37882),x37883)) % 112.26/112.09 [3794]E(f317(f317(f124(x37941),f317(f158(x37941),x37942)),f317(f317(f141(x37941),x37943),f103(x37941))),f317(f158(x37941),f317(f317(f141(x37941),x37943),x37942))) % 112.26/112.09 [3796]E(f317(f317(f74(a899),f317(f179(f900(x37961)),x37962)),f317(f179(f900(x37961)),x37963)),f317(f179(f900(x37961)),f317(f317(f124(x37961),x37962),x37963))) % 112.26/112.09 [3799]E(f317(f317(f74(a899),f317(f179(f900(x37991)),x37992)),f317(f179(f900(x37991)),x37993)),f317(f179(f900(x37991)),f163(x37991,x37992,x37993))) % 112.26/112.09 [3806]E(f317(f317(f91(f906(x38061,a895)),f317(f162(x38061),x38062)),f317(f162(x38061),x38063)),f317(f162(x38061),f317(f317(f124(x38061),x38062),x38063))) % 112.26/112.09 [3807]E(f41(a899,f317(f317(f75(a899),x38071),x38072),f317(f317(f75(a899),x38071),x38073)),f317(f317(f75(a899),x38071),f41(a899,x38072,x38073))) % 112.26/112.09 [3819]E(f317(f317(f165(x38191),f317(f317(f3(a899),x38192),f72(a899))),f317(f161(x38191),x38193)),f317(f161(x38191),f317(f317(f165(x38191),x38192),x38193))) % 112.26/112.09 [3824]E(f317(f317(f92(f906(x38241,a895)),x38242),f317(f73(f906(x38241,a895)),x38243)),f317(f317(f3(f906(x38241,a895)),x38242),x38243)) % 112.26/112.09 [3825]E(f317(f317(f3(f906(x38251,a895)),x38252),f317(f73(f906(x38251,a895)),x38253)),f317(f317(f92(f906(x38251,a895)),x38252),x38253)) % 112.26/112.09 [3847]E(f317(f317(f244(x38471,x38472),x38473),f317(f18(f906(x38472,a895),x38471),f178(f906(x38472,a895)))),f178(f906(f905(x38471,x38472),a895))) % 112.26/112.09 [3849]E(f317(f317(f3(a899),f317(f317(f75(a899),x38491),x38492)),f317(f317(f75(a899),x38491),x38493)),f317(f317(f75(a899),x38491),f317(f317(f3(a899),x38492),x38493))) % 112.26/112.09 [3850]E(f317(f317(f74(a899),f317(f317(f75(a899),x38501),x38502)),f317(f317(f75(a899),x38501),x38503)),f317(f317(f75(a899),x38501),f317(f317(f74(a899),x38502),x38503))) % 112.26/112.09 [3851]E(f317(f317(f3(a1),f317(f317(f75(a1),x38511),x38512)),f317(f317(f75(a1),x38511),x38513)),f317(f317(f75(a1),x38511),f317(f317(f3(a1),x38512),x38513))) % 112.26/112.09 [3852]E(f317(f317(f74(a1),f317(f317(f75(a1),x38521),x38522)),f317(f317(f75(a1),x38521),x38523)),f317(f317(f75(a1),x38521),f317(f317(f74(a1),x38522),x38523))) % 112.26/112.09 [3853]E(f317(f317(f75(a1),f317(f317(f234(a1),x38531),x38532)),f317(f317(f234(a1),x38531),x38533)),f317(f317(f234(a1),x38531),f317(f317(f74(a899),x38532),x38533))) % 112.26/112.09 [3867]E(f317(f317(f36(x38671,f906(x38672,a895)),x38673),f317(f18(f906(x38672,a895),x38671),f178(f906(x38672,a895)))),f178(f906(x38672,a895))) % 112.26/112.09 [3869]E(f41(a899,f317(f317(f75(a899),x38691),x38692),f317(f317(f75(a899),x38693),x38692)),f317(f317(f75(a899),f41(a899,x38691,x38693)),x38692)) % 112.26/112.09 [3874]E(f41(a1,f317(f317(f3(a1),x38741),f41(a1,x38742,x38743)),x38743),f41(a1,f317(f317(f3(a1),x38741),x38742),x38743)) % 112.26/112.09 [3875]E(f41(a1,f317(f317(f75(a1),x38751),f41(a1,x38752,x38753)),x38753),f41(a1,f317(f317(f75(a1),x38751),x38752),x38753)) % 112.26/112.09 [3876]P1(f317(f317(f224(f906(x38761,a895)),x38762),f317(f317(f299(x38761),x38763),x38762))) % 112.26/112.09 [3951]E(f317(f317(f35(f906(x39511,a895),f906(x39511,a895)),x39512),f317(f91(f906(x39511,a895)),x39513)),f317(f317(f91(f906(x39511,a895)),x39513),f33(f906(x39511,a895),x39512))) % 112.26/112.09 [3952]E(f317(f317(f36(f906(x39521,a895),f906(x39521,a895)),x39522),f317(f92(f906(x39521,a895)),x39523)),f317(f317(f92(f906(x39521,a895)),x39523),f32(f906(x39521,a895),x39522))) % 112.26/112.09 [3964]E(f317(f162(x39641),f317(f317(f317(f173(f900(x39641),f900(x39641)),x39642),f157(x39641)),x39643)),f317(f162(x39641),x39643)) % 112.26/112.09 [3968]E(f317(f317(f165(x39681),f317(f179(f900(x39681)),f167(x39681,x39682,x39683))),x39683),f167(x39681,x39682,x39683)) % 112.26/112.09 [3972]E(f317(f179(f900(x39721)),f317(f317(f317(f173(f900(x39721),f900(x39721)),x39722),f157(x39721)),x39723)),f317(f179(f900(x39721)),x39723)) % 112.26/112.09 [3975]E(f317(f317(f247(x39751,x39752,x39752),f317(f18(f906(x39752,x39752),x39751),f7(x39752))),x39753),f317(f246(x39751,x39752),x39753)) % 112.26/112.09 [3981]E(f41(a1,f317(f317(f3(a1),f41(a1,x39811,x39812)),x39813),x39812),f41(a1,f317(f317(f3(a1),x39811),x39813),x39812)) % 112.26/112.09 [3982]E(f41(a1,f317(f317(f234(a1),f41(a1,x39821,x39822)),x39823),x39822),f41(a1,f317(f317(f234(a1),x39821),x39823),x39822)) % 112.26/112.09 [3985]E(f317(f317(f36(f906(f905(x39851,x39852),a895),f906(x39852,a895)),x39853),f274(x39851,x39852)),f317(f274(x39851,x39852),f32(f906(f905(x39851,x39852),a895),x39853))) % 112.26/112.09 [3986]E(f317(f317(f36(f906(f905(x39861,x39862),a895),f906(x39861,a895)),x39863),f254(x39861,x39862)),f317(f254(x39861,x39862),f32(f906(f905(x39861,x39862),a895),x39863))) % 112.26/112.09 [4009]E(f317(f67(x40091,x40091,x40091,x40092),f317(f317(f173(x40091,x40091),x40093),x40092)),f317(f317(f173(x40091,x40091),f317(a102,x40093)),x40092)) % 112.26/112.09 [4027]E(f317(f317(f128(x40271),f317(f317(f3(a899),f317(f179(f900(x40271)),x40272)),x40273)),f317(f158(x40271),x40272)),f317(f158(x40271),f317(f317(f165(x40271),x40273),x40272))) % 112.26/112.09 [4028]E(f317(f317(f165(x40281),f317(f317(f3(a899),f317(f179(f900(x40281)),x40282)),x40283)),f317(f158(x40281),x40282)),f317(f158(x40281),f317(f317(f128(x40281),x40283),x40282))) % 112.26/112.09 [4030]E(f317(f317(f74(a899),f317(f155(a899),f317(f317(f144(x40301,a899),x40302),x40303))),f317(f179(f900(x40301)),x40303)),f145(x40301,x40302,x40303)) % 112.26/112.09 [4050]E(f317(f157(x40501),f317(f317(f317(f173(f900(x40501),f900(x40501)),x40502),f157(x40501)),x40503)),f317(f317(f317(f173(f900(x40501),f900(x40501)),f317(a102,x40502)),f157(x40501)),x40503)) % 112.26/112.09 [4064]P1(f317(f317(f224(a899),f317(f179(f900(x40641)),f317(f126(x40641,x40642),x40643))),f317(f179(f900(x40641)),x40643))) % 112.26/112.09 [4080]E(f317(f317(f91(f906(f906(x40801,a895),a895)),f317(f298(x40801),x40802)),f317(f300(f906(x40801,a895),f906(x40801,a895),f317(f299(x40801),x40803)),f317(f298(x40801),x40802))),f317(f298(x40801),f317(f317(f299(x40801),x40803),x40802))) % 112.26/112.09 [4111]P1(f317(f317(f224(a899),f317(f179(f900(x41111)),f167(x41111,x41112,x41113))),f317(f179(f900(x41111)),x41113))) % 112.26/112.09 [4118]E(f317(f254(x41181,x41182),f317(f252(f905(x41181,x41182)),f317(f247(x41181,x41182,a895),x41183))),f317(f252(x41181),f317(f317(f10(f906(x41182,a895),a895,x41181),f81(x41182)),x41183))) % 112.26/112.09 [4130]E(f317(f300(a899,a899,f317(f317(f9(a899,a899,a899),f74(a899)),x41301)),f293(a899,x41302,x41303)),f293(a899,f317(f317(f74(a899),x41302),x41301),f317(f317(f74(a899),x41303),x41301))) % 112.26/112.09 [4144]E(f317(f300(a899,a899,f317(f317(f9(a899,a899,a899),f74(a899)),x41441)),f317(f292(a899,x41442),x41443)),f317(f292(a899,f317(f317(f74(a899),x41442),x41441)),f317(f317(f74(a899),x41443),x41441))) % 112.26/112.09 [4162]E(f317(f317(f171(x41621,x41622),f317(f317(f144(f905(x41621,x41622),x41621),f241(x41621,x41622)),x41623)),f317(f317(f144(f905(x41621,x41622),x41622),f246(x41621,x41622)),x41623)),x41623) % 112.26/112.09 [4167]E(f317(f317(f74(a899),f317(f317(f75(a899),x41671),f41(a899,f317(f317(f31(a899),x41672),x41671),x41673))),f41(a899,x41672,x41671)),f41(a899,x41672,f317(f317(f75(a899),x41671),x41673))) % 112.26/112.09 [4180]E(f317(f317(f124(x41801),x41802),f317(f132(f900(x41801),f900(x41801),f124(x41801),f103(x41801)),x41803)),f317(f132(f900(x41801),f900(x41801),f124(x41801),x41802),x41803)) % 112.26/112.09 [4201]P1(f317(f317(f319(f905(x42011,x42011)),f317(f317(f242(x42011,x42011),x42012),x42012)),f317(f317(f173(f905(x42011,x42011),a895),f2(a899)),x42013))) % 112.26/112.09 [4206]E(f317(f252(x42061),f317(f317(f10(f906(x42062,a895),a895,x42061),f81(x42062)),f317(f9(x42062,x42061,a895),x42063))),f317(f274(x42062,x42061),f317(f252(f905(x42062,x42061)),f317(f247(x42062,x42061,a895),x42063)))) % 112.26/112.09 [4223]E(f317(f317(f91(f906(x42231,a895)),f317(f317(f36(a899,f906(x42231,a895)),f293(a899,f72(a899),x42232)),x42233)),f317(x42233,f2(a899))),f317(f317(f36(a899,f906(x42231,a895)),f317(f291(a899),x42232)),x42233)) % 112.26/112.09 [4238]E(f317(f132(f900(x42381),f900(x42381),f124(x42381),f103(x42381)),f317(f317(f144(f900(x42381),f900(x42381)),f126(x42381,x42382)),x42383)),f317(f126(x42381,x42382),f317(f132(f900(x42381),f900(x42381),f124(x42381),f103(x42381)),x42383))) % 112.26/112.09 [4242]E(f317(f246(f900(x42421),f900(x42421)),f156(x42421,x42422,x42423)),f317(f126(x42421,f317(f67(a895,a895,x42421,a312),x42422)),x42423)) % 112.26/112.09 [4287]E(f317(f317(f74(a1),f317(f317(f74(a1),f317(f317(f75(a1),x42871),f317(f317(f31(a1),x42872),x42871))),f41(a1,x42872,x42871))),x42873),f317(f317(f74(a1),x42872),x42873)) % 112.26/112.09 [4324]E(f317(f317(f74(a1),f317(f317(f74(a1),f317(f317(f75(a1),f317(f317(f31(a1),x43241),x43242)),x43242)),f41(a1,x43241,x43242))),x43243),f317(f317(f74(a1),x43241),x43243)) % 112.26/112.09 [4350]E(f79(f905(x43501,x43502),f317(f247(x43501,x43502,a895),f317(f317(f10(f906(x43502,f905(x43501,x43502)),f906(x43502,a895),x43501),f317(f10(f905(x43501,x43502),a895,x43502),x43503)),f242(x43501,x43502)))),f79(f905(x43501,x43502),x43503)) % 112.26/112.09 [4351]E(f84(f905(x43511,x43512),f317(f247(x43511,x43512,a895),f317(f317(f10(f906(x43512,f905(x43511,x43512)),f906(x43512,a895),x43511),f317(f10(f905(x43511,x43512),a895,x43512),x43513)),f242(x43511,x43512)))),f84(f905(x43511,x43512),x43513)) % 112.26/112.09 [4378]P1(f317(f317(f224(f906(x43781,a895)),f32(f906(x43781,a895),f317(f317(f92(f906(f906(x43781,a895),a895)),x43782),x43783))),f317(f317(f92(f906(x43781,a895)),f32(f906(x43781,a895),x43782)),f32(f906(x43781,a895),x43783)))) % 112.26/112.09 [4379]E(f317(f158(x43791),f317(f317(f317(f173(f900(x43791),f900(x43791)),f317(f317(f3(a899),f317(f179(f900(x43791)),x43792)),f41(a899,x43793,f317(f179(f900(x43791)),x43792)))),f157(x43791)),x43792)),f317(f317(f317(f173(f900(x43791),f900(x43791)),x43793),f157(x43791)),f317(f158(x43791),x43792))) % 112.26/112.09 [4416]P1(f317(f317(f224(a899),f317(f179(f900(x44161)),f317(f317(f128(x44161),f317(f179(f900(x44161)),f167(x44161,x44162,x44163))),x44163))),f317(f179(f900(x44161)),x44163))) % 112.26/112.09 [4632]~P1(f317(f57(x46321,x46322,f178(f906(x46321,a895))),x46323)) % 112.26/112.09 [4637]~P1(f317(f317(f319(f905(x46371,x46371)),f317(f317(f242(x46371,x46371),x46372),x46373)),f143(x46371,f103(f906(x46371,a899))))) % 112.26/112.09 [3736]E(f317(f179(f900(x37361)),f317(f317(f165(x37361),x37362),x37363)),f317(f317(f228(a899),f317(f179(f900(x37361)),x37363)),x37362)) % 112.26/112.09 [3737]E(f317(f179(f900(x37371)),f317(f317(f128(x37371),x37372),x37373)),f317(f317(f3(a899),f317(f179(f900(x37371)),x37373)),x37372)) % 112.26/112.09 [3763]E(f317(f179(f900(f900(x37631))),f51(x37631,x37632,x37633)),f317(f317(f234(a899),f317(f179(f900(x37631)),x37633)),x37632)) % 112.26/112.09 [3780]E(f317(f317(f31(a899),f317(f317(f31(a899),x37801),x37802)),x37803),f317(f317(f31(a899),x37801),f317(f317(f75(a899),x37802),x37803))) % 112.26/112.09 [3781]E(f317(f317(f3(a899),f317(f317(f3(a899),x37811),x37812)),x37813),f317(f317(f3(a899),x37811),f317(f317(f74(a899),x37812),x37813))) % 112.26/112.09 [3782]E(f317(f317(f74(a899),f317(f317(f74(a899),x37821),x37822)),x37823),f317(f317(f74(a899),x37821),f317(f317(f74(a899),x37822),x37823))) % 112.26/112.09 [3783]E(f317(f317(f74(a1),f317(f317(f74(a1),x37831),x37832)),x37833),f317(f317(f74(a1),x37831),f317(f317(f74(a1),x37832),x37833))) % 112.26/112.09 [3784]E(f317(f317(f75(a899),f317(f317(f75(a899),x37841),x37842)),x37843),f317(f317(f75(a899),x37841),f317(f317(f75(a899),x37842),x37843))) % 112.26/112.09 [3785]E(f317(f317(f75(a1),f317(f317(f75(a1),x37851),x37852)),x37853),f317(f317(f75(a1),x37851),f317(f317(f75(a1),x37852),x37853))) % 112.26/112.09 [3786]E(f317(f317(f234(a1),f317(f317(f234(a1),x37861),x37862)),x37863),f317(f317(f234(a1),x37861),f317(f317(f75(a899),x37862),x37863))) % 112.26/112.09 [3805]E(f152(x38051,f317(f317(f141(f906(x38051,a895)),x38052),x38053)),f164(x38051,x38052,f152(x38051,x38053))) % 112.26/112.09 [3848]E(f317(f317(f3(a899),f317(f317(f3(a899),x38481),x38482)),x38483),f317(f317(f3(a899),f317(f317(f3(a899),x38481),x38483)),x38482)) % 112.26/112.09 [3856]E(f317(f317(f92(f906(x38561,a895)),x38562),f317(f317(f3(f906(x38561,a895)),x38563),x38562)),f178(f906(x38561,a895))) % 112.26/112.09 [3860]E(f317(f317(f144(a899,x38601),f317(f18(x38601,a899),x38602)),f129(a899,f317(f292(a899,f2(a899)),x38603))),f159(x38601,x38603,x38602)) % 112.26/112.09 [3898]E(f32(f906(x38981,a895),f317(f317(f299(f906(x38981,a895)),x38982),x38983)),f317(f317(f91(f906(x38981,a895)),x38982),f32(f906(x38981,a895),x38983))) % 112.26/112.09 [3899]E(f33(f906(x38991,a895),f317(f317(f299(f906(x38991,a895)),x38992),x38993)),f317(f317(f92(f906(x38991,a895)),x38992),f33(f906(x38991,a895),x38993))) % 112.26/112.09 [3901]E(f159(x39011,f317(f179(f900(x39011)),f317(f126(x39011,f317(a314,x39012)),x39013)),x39012),f317(f126(x39011,f317(a314,x39012)),x39013)) % 112.26/112.09 [3903]E(f317(f317(f3(a899),f317(f317(f75(a899),x39031),x39032)),f317(f317(f75(a899),x39033),x39032)),f317(f317(f75(a899),f317(f317(f3(a899),x39031),x39033)),x39032)) % 112.26/112.09 [3904]E(f317(f317(f74(a899),f317(f317(f75(a899),x39041),x39042)),f317(f317(f75(a899),x39043),x39042)),f317(f317(f75(a899),f317(f317(f74(a899),x39041),x39043)),x39042)) % 112.26/112.09 [3905]E(f317(f317(f3(a1),f317(f317(f75(a1),x39051),x39052)),f317(f317(f75(a1),x39053),x39052)),f317(f317(f75(a1),f317(f317(f3(a1),x39051),x39053)),x39052)) % 112.26/112.09 [3906]E(f317(f317(f74(a1),f317(f317(f75(a1),x39061),x39062)),f317(f317(f75(a1),x39063),x39062)),f317(f317(f75(a1),f317(f317(f74(a1),x39061),x39063)),x39062)) % 112.26/112.09 [3908]E(f317(f317(f228(a899),f317(f317(f3(a899),x39081),x39082)),f317(f317(f3(a899),x39083),x39082)),f317(f317(f3(a899),f317(f317(f228(a899),x39081),x39083)),x39082)) % 112.26/112.09 [3928]E(f317(f317(f92(f906(f900(x39281),a895)),f150(x39281,x39282)),f150(x39281,x39283)),f150(x39281,f317(f317(f92(f906(x39281,a895)),x39282),x39283))) % 112.26/112.09 [3931]E(f317(f317(f91(f906(x39311,a895)),x39312),f317(f317(f3(f906(x39311,a895)),x39313),x39312)),f317(f317(f91(f906(x39311,a895)),x39312),x39313)) % 112.26/112.09 [3932]E(f317(f317(f91(f906(x39321,a895)),x39322),f317(f317(f91(f906(x39321,a895)),x39322),x39323)),f317(f317(f91(f906(x39321,a895)),x39322),x39323)) % 112.26/112.09 [3933]E(f317(f317(f92(f906(x39331,a895)),x39332),f317(f317(f92(f906(x39331,a895)),x39332),x39333)),f317(f317(f92(f906(x39331,a895)),x39332),x39333)) % 112.26/112.09 [3945]E(f317(f317(f279(x39451,x39452,x39452),x39453),f297(x39452,f178(f906(f905(x39452,x39452),a895)))),x39453) % 112.26/112.09 [3948]E(f317(f317(f91(f906(x39481,a895)),f317(f317(f299(x39481),x39482),f178(f906(x39481,a895)))),x39483),f317(f317(f299(x39481),x39482),x39483)) % 112.26/112.09 [3967]E(f317(f317(f3(a899),f317(f317(f3(a899),f317(a102,x39671)),x39672)),f317(a102,x39673)),f317(f317(f3(a899),f317(f317(f3(a899),x39671),x39672)),x39673)) % 112.26/112.09 [3994]E(f317(f317(f92(f906(f906(x39941,a895),a895)),f317(f298(x39941),x39942)),f317(f298(x39941),x39943)),f317(f298(x39941),f317(f317(f92(f906(x39941,a895)),x39942),x39943))) % 112.26/112.09 [3997]E(f317(f317(f91(f906(x39971,a895)),f317(f73(f906(x39971,a895)),x39972)),x39973),f317(f73(f906(x39971,a895)),f317(f317(f3(f906(x39971,a895)),x39972),x39973))) % 112.26/112.09 [4006]E(f317(f317(f299(x40061),x40062),f317(f317(f3(f906(x40061,a895)),x40063),f317(f317(f299(x40061),x40062),f178(f906(x40061,a895))))),f317(f317(f299(x40061),x40062),x40063)) % 112.26/112.09 [4016]P1(f317(f317(f224(f906(x40161,a895)),x40162),f317(f317(f91(f906(x40161,a895)),x40163),x40162))) % 112.26/112.09 [4017]P1(f317(f317(f224(f906(x40171,a895)),x40172),f317(f317(f91(f906(x40171,a895)),x40172),x40173))) % 112.26/112.09 [4021]E(f317(f317(f92(f906(x40211,a895)),f317(f73(f906(x40211,a895)),x40212)),f317(f73(f906(x40211,a895)),x40213)),f317(f73(f906(x40211,a895)),f317(f317(f91(f906(x40211,a895)),x40212),x40213))) % 112.26/112.09 [4022]E(f317(f317(f91(f906(x40221,a895)),f317(f73(f906(x40221,a895)),x40222)),f317(f73(f906(x40221,a895)),x40223)),f317(f73(f906(x40221,a895)),f317(f317(f92(f906(x40221,a895)),x40222),x40223))) % 112.26/112.09 [4036]P1(f317(f317(f224(f906(x40361,a895)),f317(f162(x40361),x40362)),f317(f162(x40361),f317(f317(f141(x40361),x40363),x40362)))) % 112.26/112.09 [4048]E(f317(f317(f91(f906(x40481,a895)),f317(f317(f3(f906(x40481,a895)),x40482),x40483)),f317(f317(f92(f906(x40481,a895)),x40482),x40483)),x40482) % 112.26/112.09 [4098]E(f317(f317(f8(x40981,a1),f317(f317(f10(a899,a1,x40981),f90(a1)),x40982)),x40983),f317(f90(a1),f317(f317(f8(x40981,a899),x40982),x40983))) % 112.26/112.09 [4099]E(f317(f317(f11(x40991,a1),f317(f317(f10(a899,a1,x40991),f90(a1)),x40992)),x40993),f317(f90(a1),f317(f317(f11(x40991,a899),x40992),x40993))) % 112.26/112.09 [4146]E(f317(f317(f124(x41461),f167(x41461,x41462,x41463)),f317(f317(f128(x41461),f317(f179(f900(x41461)),f167(x41461,x41462,x41463))),x41463)),x41463) % 112.26/112.09 [4150]E(f317(f73(f906(f905(x41501,x41502),a895)),f317(f317(f244(x41501,x41502),x41503),f317(f18(f906(x41502,a895),x41501),f232(f906(x41502,a895))))),f317(f317(f244(x41501,x41502),f317(f73(f906(x41501,a895)),x41503)),f317(f18(f906(x41502,a895),x41501),f232(f906(x41502,a895))))) % 112.26/112.09 [4151]E(f317(f73(f906(f905(x41511,x41512),a895)),f317(f317(f244(x41511,x41512),f232(f906(x41511,a895))),f317(f18(f906(x41512,a895),x41511),x41513))),f317(f317(f244(x41511,x41512),f232(f906(x41511,a895))),f317(f18(f906(x41512,a895),x41511),f317(f73(f906(x41512,a895)),x41513)))) % 112.26/112.09 [4202]E(f317(f317(f36(f906(x42021,a895),f906(x42021,a895)),x42022),f317(f317(f9(f906(x42021,a895),f906(x42021,a895),f906(x42021,a895)),f92(f906(x42021,a895))),x42023)),f317(f317(f92(f906(x42021,a895)),f32(f906(x42021,a895),x42022)),x42023)) % 112.26/112.09 [4208]E(f317(f132(f900(x42081),f900(x42081),f124(x42081),f103(x42081)),f317(f317(f141(f900(x42081)),x42082),x42083)),f317(f317(f124(x42081),x42082),f317(f132(f900(x42081),f900(x42081),f124(x42081),f103(x42081)),x42083))) % 112.26/112.09 [4229]E(f317(f317(f299(f906(x42291,a895)),f317(f275(x42291,x42291,x42292),f317(f317(f299(x42291),x42293),f178(f906(x42291,a895))))),f178(f906(f906(x42291,a895),a895))),f317(f317(f56(x42291),f317(f317(f299(x42291),x42293),f178(f906(x42291,a895)))),x42292)) % 112.26/112.09 [4239]E(f317(f317(f74(a899),f317(f317(f75(a899),x42391),f317(f317(f31(a899),x42392),x42393))),f317(f317(f31(a899),f317(f317(f75(a899),x42391),f41(a899,x42392,x42393))),x42393)),f317(f317(f31(a899),f317(f317(f75(a899),x42391),x42392)),x42393)) % 112.26/112.09 [4240]E(f317(f317(f74(a1),f317(f317(f75(a1),x42401),f317(f317(f31(a1),x42402),x42403))),f317(f317(f31(a1),f317(f317(f75(a1),x42401),f41(a1,x42402,x42403))),x42403)),f317(f317(f31(a1),f317(f317(f75(a1),x42401),x42402)),x42403)) % 112.26/112.09 [4272]E(f317(f317(f3(f906(x42721,a895)),f317(f162(x42721),x42722)),f317(f317(f299(x42721),x42723),f178(f906(x42721,a895)))),f317(f162(x42721),f317(f126(x42721,f317(f317(f10(a895,a895,x42721),a312),f317(a314,x42723))),x42722))) % 112.26/112.09 [4322]E(f317(f317(f124(x43221),f317(f132(f900(x43221),f900(x43221),f124(x43221),f103(x43221)),x43222)),f317(f132(f900(x43221),f900(x43221),f124(x43221),f103(x43221)),x43223)),f317(f132(f900(x43221),f900(x43221),f124(x43221),f103(x43221)),f317(f317(f124(f900(x43221)),x43222),x43223))) % 112.26/112.09 [4325]E(f317(f317(f242(f900(x43251),f900(x43251)),f317(f126(x43251,x43252),x43253)),f317(f126(x43251,f317(f67(a895,a895,x43251,a312),x43252)),x43253)),f156(x43251,x43252,x43253)) % 112.26/112.09 [4328]E(f317(f317(f74(a899),f317(f317(f74(a899),f317(f317(f31(a899),x43281),x43282)),f317(f317(f31(a899),x43283),x43282))),f317(f317(f31(a899),f317(f317(f74(a899),f41(a899,x43281,x43282)),f41(a899,x43283,x43282))),x43282)),f317(f317(f31(a899),f317(f317(f74(a899),x43281),x43283)),x43282)) % 112.26/112.09 [4329]E(f317(f317(f74(a1),f317(f317(f74(a1),f317(f317(f31(a1),x43291),x43292)),f317(f317(f31(a1),x43293),x43292))),f317(f317(f31(a1),f317(f317(f74(a1),f41(a1,x43291,x43292)),f41(a1,x43293,x43292))),x43292)),f317(f317(f31(a1),f317(f317(f74(a1),x43291),x43293)),x43292)) % 112.26/112.09 [4382]E(f317(f317(f92(f906(f900(x43821),a895)),f317(f317(f9(f900(x43821),f906(f900(x43821),a895),a895),f319(f900(x43821))),f151(x43821,x43822))),f317(f317(f9(f900(x43821),f906(f900(x43821),a895),a895),f319(f900(x43821))),f151(x43821,x43823))),f150(x43821,f317(f317(f92(f906(x43821,a895)),f317(f317(f9(x43821,f906(x43821,a895),a895),f319(x43821)),x43822)),f317(f317(f9(x43821,f906(x43821,a895),a895),f319(x43821)),x43823)))) % 112.26/112.09 [4394]E(f317(f252(x43941),f317(f317(f20(x43941,a895,a895),f317(f317(f10(a895,f906(a895,a895),x43941),a316),f317(f317(f9(x43941,x43941,a895),a314),x43942))),f317(f317(f9(x43941,f906(x43941,a895),a895),f319(x43941)),x43943))),f317(f317(f299(x43941),x43942),x43943)) % 112.26/112.09 [4414]E(f317(f317(f80(f900(f900(x44141)),f900(f900(x44141))),f50(x44141,x44142)),f317(f317(f20(f900(f900(x44141)),f900(f900(x44141)),f900(f900(x44141))),f317(f317(f10(f900(f900(x44141)),f906(f900(f900(x44141)),f900(f900(x44141))),f900(f900(x44141))),f124(f900(x44141))),f317(f144(f900(x44141),f900(x44141)),f317(f141(x44141),x44143)))),f7(f900(f900(x44141))))),f50(x44141,f317(f317(f141(x44141),x44143),x44142))) % 112.26/112.09 [4417]E(f317(f252(x44171),f317(f317(f20(x44171,a895,a895),f317(f317(f10(a895,f906(a895,a895),x44171),a316),f317(f317(f9(x44171,f906(x44171,a895),a895),f319(x44171)),x44172))),f317(f317(f9(x44171,f906(x44171,a895),a895),f319(x44171)),x44173))),f317(f317(f91(f906(x44171,a895)),x44172),x44173)) % 112.26/112.09 [4418]E(f317(f252(x44181),f317(f317(f20(x44181,a895,a895),f317(f317(f10(a895,f906(a895,a895),x44181),a315),f317(f317(f9(x44181,f906(x44181,a895),a895),f319(x44181)),x44182))),f317(f317(f9(x44181,f906(x44181,a895),a895),f319(x44181)),x44183))),f317(f317(f92(f906(x44181,a895)),x44182),x44183)) % 112.26/112.09 [4507]E(f317(f317(f36(x45071,f906(f906(x45071,a895),a895)),x45072),f317(f317(f9(x45071,f906(f906(x45071,a895),a895),f906(f906(x45071,a895),a895)),f317(f317(f10(f906(x45071,a895),f906(f906(f906(x45071,a895),a895),f906(f906(x45071,a895),a895)),x45071),f299(f906(x45071,a895))),f317(f317(f10(f906(x45071,a895),f906(x45071,a895),x45071),f275(x45071,x45071,x45073)),f317(f317(f9(x45071,f906(x45071,a895),f906(x45071,a895)),f299(x45071)),f178(f906(x45071,a895)))))),f178(f906(f906(x45071,a895),a895)))),f317(f317(f56(x45071),x45072),x45073)) % 112.26/112.09 [4509]E(f317(f317(f191(x45091),f317(f317(f75(a1),f317(f317(f67(f905(a1,a1),a1,x45091,f241(a1,a1)),f202(x45091)),x45092)),f317(f317(f67(f905(a1,a1),a1,x45091,f241(a1,a1)),f202(x45091)),x45093))),f317(f317(f75(a1),f317(f317(f67(f905(a1,a1),a1,x45091,f246(a1,a1)),f202(x45091)),x45092)),f317(f317(f67(f905(a1,a1),a1,x45091,f246(a1,a1)),f202(x45091)),x45093))),f218(x45091,x45092,x45093)) % 112.26/112.09 [4512]E(f317(f252(f900(x45121)),f317(f317(f20(f900(x45121),a895,a895),f317(f317(f10(a895,f906(a895,a895),f900(x45121)),a315),f317(f317(f9(f900(x45121),a899,a895),f317(f317(f10(a899,f906(a899,a895),f900(x45121)),a314),f179(f900(x45121)))),x45122))),f317(f317(f9(f900(x45121),f906(x45121,a895),a895),f317(f317(f10(f906(x45121,a895),f906(f906(x45121,a895),a895),f900(x45121)),f224(f906(x45121,a895))),f162(x45121))),f317(f162(x45121),x45123)))),f317(f162(f900(x45121)),f51(x45121,x45122,x45123))) % 112.26/112.09 [3921]E(f41(a899,f317(f317(f74(a899),f317(f317(f75(a899),x39211),x39212)),x39213),x39212),f41(a899,x39213,x39212)) % 112.26/112.09 [3966]E(f129(a899,f317(f292(a899,f317(f317(f74(a899),x39661),x39662)),x39663)),f317(f317(f128(a899),x39662),f129(a899,f317(f292(a899,x39661),x39663)))) % 112.26/112.09 [4005]E(f317(f317(f74(a1),f317(f90(a1),x40051)),f317(f317(f74(a1),f317(f90(a1),x40052)),x40053)),f317(f317(f74(a1),f317(f90(a1),f317(f317(f74(a899),x40051),x40052))),x40053)) % 112.26/112.09 [4012]E(f317(f317(f3(f906(x40121,a895)),f317(f317(f3(f906(x40121,a895)),x40122),x40123)),x40123),f317(f317(f3(f906(x40121,a895)),x40122),x40123)) % 112.26/112.09 [4013]E(f317(f317(f91(f906(x40131,a895)),f317(f317(f3(f906(x40131,a895)),x40132),x40133)),x40133),f317(f317(f91(f906(x40131,a895)),x40132),x40133)) % 112.26/112.09 [4037]E(f317(f317(f279(x40371,x40371,x40372),f297(x40371,f178(f906(f905(x40371,x40371),a895)))),x40373),x40373) % 112.26/112.09 [4045]E(f317(f317(f91(f906(x40451,a895)),f317(f271(x40451),x40452)),f317(f271(x40451),x40453)),f317(f271(x40451),f317(f317(f91(f906(f905(x40451,x40451),a895)),x40452),x40453))) % 112.26/112.09 [4055]E(f256(x40551,f317(f317(f141(f905(a89,x40551)),f317(f317(f242(a89,x40551),f2(a89)),x40552)),x40553)),f256(x40551,x40553)) % 112.26/112.09 [4057]E(f317(f317(f91(f906(x40571,a895)),f32(f906(x40571,a895),x40572)),f32(f906(x40571,a895),x40573)),f32(f906(x40571,a895),f317(f317(f91(f906(f906(x40571,a895),a895)),x40572),x40573))) % 112.26/112.09 [4058]E(f317(f317(f92(f906(x40581,a895)),f33(f906(x40581,a895),x40582)),f33(f906(x40581,a895),x40583)),f33(f906(x40581,a895),f317(f317(f91(f906(f906(x40581,a895),a895)),x40582),x40583))) % 112.26/112.09 [4095]E(f317(f317(f279(x40951,x40951,x40951),f317(f317(f173(f905(x40951,x40951),a895),x40952),x40953)),x40953),f317(f317(f173(f905(x40951,x40951),a895),f317(a102,x40952)),x40953)) % 112.26/112.09 [4138]P1(f317(f317(f224(f906(x41381,a895)),f317(f317(f3(f906(x41381,a895)),x41382),x41383)),x41382)) % 112.26/112.09 [4139]P1(f317(f317(f224(f906(x41391,a895)),f317(f317(f92(f906(x41391,a895)),x41392),x41393)),x41393)) % 112.26/112.09 [4140]P1(f317(f317(f224(f906(x41401,a895)),f317(f317(f92(f906(x41401,a895)),x41402),x41403)),x41402)) % 112.26/112.09 [4164]E(f297(x41641,f317(f317(f91(f906(f905(x41641,x41641),a895)),f297(x41641,x41642)),f297(x41641,x41643))),f297(x41641,f317(f317(f91(f906(f905(x41641,x41641),a895)),x41642),x41643))) % 112.26/112.09 [4168]E(f32(f906(x41681,a895),f317(f317(f299(f906(x41681,a895)),x41682),f317(f317(f299(f906(x41681,a895)),x41683),f178(f906(f906(x41681,a895),a895))))),f317(f317(f91(f906(x41681,a895)),x41682),x41683)) % 112.26/112.09 [4169]E(f33(f906(x41691,a895),f317(f317(f299(f906(x41691,a895)),x41692),f317(f317(f299(f906(x41691,a895)),x41693),f178(f906(f906(x41691,a895),a895))))),f317(f317(f92(f906(x41691,a895)),x41692),x41693)) % 112.26/112.09 [4174]E(f317(f317(f279(x41741,x41741,x41741),f317(f317(f173(f905(x41741,x41741),a895),x41742),x41743)),x41743),f317(f317(f279(x41741,x41741,x41741),x41743),f317(f317(f173(f905(x41741,x41741),a895),x41742),x41743))) % 112.26/112.09 [4243]E(f317(f317(f91(f906(x42431,a895)),f317(f252(x42431),f317(f317(f9(x42431,x42431,a895),a314),x42432))),x42433),f317(f317(f299(x42431),x42432),x42433)) % 112.26/112.09 [4245]E(f317(a95,f317(f317(f8(x42451,a1),f317(f317(f10(a899,a1,x42451),f90(a1)),x42452)),x42453)),f317(f317(f8(x42451,a899),x42452),x42453)) % 112.26/112.09 [4246]E(f317(a95,f317(f317(f11(x42461,a1),f317(f317(f10(a899,a1,x42461),f90(a1)),x42462)),x42463)),f317(f317(f11(x42461,a899),x42462),x42463)) % 112.26/112.09 [4319]E(f317(f146(f900(x43191),x43191,f317(f161(x43191),x43192),f317(f18(f906(f900(x43191),f900(x43191)),x43191),f317(f317(f9(f900(x43191),f900(x43191),f900(x43191)),f124(x43191)),x43192))),x43193),f317(f161(x43191),f317(f317(f124(x43191),x43193),x43192))) % 112.26/112.09 [4347]P1(f317(f317(f224(f906(f906(x43471,a895),a895)),f317(f317(f91(f906(f906(x43471,a895),a895)),f317(f298(x43471),x43472)),f317(f298(x43471),x43473))),f317(f298(x43471),f317(f317(f91(f906(x43471,a895)),x43472),x43473)))) % 112.26/112.09 [4436]E(f317(f252(x44361),f317(f317(f20(x44361,a895,a895),f317(f317(f10(a895,f906(a895,a895),x44361),a315),f317(f317(f9(x44361,f906(x44361,a895),a895),f319(x44361)),x44362))),f317(f317(f10(a895,a895,x44361),a312),f317(f317(f9(x44361,f906(x44361,a895),a895),f319(x44361)),x44363)))),f317(f317(f3(f906(x44361,a895)),x44362),x44363)) % 112.26/112.09 [4460]E(f317(f30(a899),f317(f252(a899),f317(f317(f20(a899,a895,a895),f317(f317(f10(a895,f906(a895,a895),a899),a315),f317(f317(f9(a899,a899,a895),f225(a899)),f317(f179(f900(x44601)),x44602)))),f317(f317(f10(x44601,a895,a899),x44603),f317(f154(x44601),x44602))))),f317(f179(f900(x44601)),f317(f126(x44601,x44603),x44602))) % 112.26/112.09 [4462]E(f317(f179(f900(x44621)),f166(x44621,x44622,x44623)),f317(f30(a899),f317(f252(a899),f317(f317(f20(a899,a895,a895),f317(f317(f10(a895,f906(a895,a895),a899),a315),f317(f317(f9(a899,a899,a895),f225(a899)),f317(f179(f900(x44621)),x44622)))),f317(f317(f9(a899,f906(a899,a895),a895),f319(a899)),x44623))))) % 112.26/112.09 [4558]E(f317(f317(f92(f906(f905(f900(x45581),f900(x45581)),a895)),f317(f300(f905(f905(x45581,f900(x45581)),f905(x45581,f900(x45581))),f905(f900(x45581),f900(x45581)),f248(f905(x45581,f900(x45581)),f900(x45581),f905(x45581,f900(x45581)),f900(x45581),f317(f247(x45581,f900(x45581),f900(x45581)),f141(x45581)),f317(f247(x45581,f900(x45581),f900(x45581)),f141(x45581)))),f310(x45581,f900(x45581),x45582,f317(f133(x45581,x45582),x45583)))),f317(f252(f905(f900(x45581),f900(x45581))),f317(f247(f900(x45581),f900(x45581),a895),f317(f317(f9(f900(x45581),f906(f900(x45581),a895),f906(f900(x45581),a895)),f317(f317(f10(f906(a895,a895),f906(f906(f900(x45581),a895),f906(f900(x45581),a895)),f900(x45581)),f10(a895,a895,f900(x45581))),f317(f317(f10(a895,f906(a895,a895),f900(x45581)),a315),f317(f317(f9(f900(x45581),a899,a895),f317(f317(f10(a899,f906(a899,a895),f900(x45581)),a314),f179(f900(x45581)))),f317(a102,x45583))))),f317(f317(f9(f900(x45581),a899,a895),f317(f317(f10(a899,f906(a899,a895),f900(x45581)),a314),f179(f900(x45581)))),f317(a102,x45583)))))),f317(f133(x45581,x45582),f317(a102,x45583))) % 112.26/112.09 [4059]E(f41(a899,f317(a102,f317(f317(f74(a899),f317(f317(f75(a899),x40591),x40592)),x40593)),x40592),f41(a899,f317(a102,x40593),x40592)) % 112.26/112.09 [4305]E(f317(f252(x43051),f317(f317(f20(x43051,a895,a895),f317(f317(f10(a895,f906(a895,a895),x43051),a315),x43052)),x43053)),f317(f317(f92(f906(x43051,a895)),f317(f252(x43051),x43052)),f317(f252(x43051),x43053))) % 112.26/112.09 [4306]E(f317(f252(x43061),f317(f317(f20(x43061,a895,a895),f317(f317(f10(a895,f906(a895,a895),x43061),a316),x43062)),x43063)),f317(f317(f91(f906(x43061,a895)),f317(f252(x43061),x43062)),f317(f252(x43061),x43063))) % 112.26/112.09 [4308]E(f317(f317(f124(x43081),f317(f317(f128(x43081),f41(a899,x43082,f317(f179(f900(x43081)),x43083))),x43083)),f317(f317(f165(x43081),f41(a899,x43082,f317(f179(f900(x43081)),x43083))),x43083)),f317(f317(f317(f173(f900(x43081),f900(x43081)),x43082),f157(x43081)),x43083)) % 112.26/112.09 [4314]E(f317(f252(x43141),f317(f317(f20(x43141,a895,a895),f317(f317(f10(a895,f906(a895,a895),x43141),a320),x43142)),x43143)),f317(f317(f91(f906(x43141,a895)),f317(f73(f906(x43141,a895)),f317(f252(x43141),x43142))),f317(f252(x43141),x43143))) % 112.26/112.09 [4330]E(f317(f317(f74(a899),f317(f179(f900(x43301)),f317(f126(x43301,x43302),x43303))),f317(f179(f900(x43301)),f317(f126(x43301,f317(f317(f10(a895,a895,x43301),a312),x43302)),x43303))),f317(f179(f900(x43301)),x43303)) % 112.26/112.09 [4353]P1(f317(f317(f224(f906(x43531,a895)),f317(f317(f91(f906(x43531,a895)),f33(f906(x43531,a895),x43532)),f33(f906(x43531,a895),x43533))),f33(f906(x43531,a895),f317(f317(f92(f906(f906(x43531,a895),a895)),x43532),x43533)))) % 112.26/112.09 [4367]E(f317(f162(x43671),f317(f126(x43671,f317(f317(f10(a895,a895,x43671),a312),f317(f317(f9(x43671,x43671,a895),a314),x43672))),x43673)),f317(f317(f3(f906(x43671,a895)),f317(f162(x43671),x43673)),f317(f317(f299(x43671),x43672),f178(f906(x43671,a895))))) % 112.26/112.09 [4376]P1(f317(f317(f224(f906(f905(x43761,x43761),a895)),f317(f317(f91(f906(f905(x43761,x43761),a895)),f297(x43761,x43762)),f297(x43761,x43763))),f297(x43761,f317(f317(f91(f906(f905(x43761,x43761),a895)),x43762),x43763)))) % 112.26/112.09 [4399]E(f317(f317(f75(a899),f317(a102,f317(a102,f2(a899)))),f317(f317(f8(a899,a899),f317(f317(f10(a899,a899,a899),f317(f74(a899),x43991)),f317(f317(f9(a899,a899,a899),f75(a899)),x43992))),f317(f272(a899),x43993))),f317(f317(f75(a899),x43993),f317(f317(f74(a899),x43991),f317(f317(f74(a899),x43991),f317(f317(f75(a899),f317(f317(f3(a899),x43993),f72(a899))),x43992))))) % 112.26/112.09 [4409]E(f317(f252(x44091),f317(f317(f20(x44091,a895,a895),f317(f317(f10(a895,f906(a895,a895),x44091),a315),f317(f317(f9(x44091,f906(x44091,a895),a895),f319(x44091)),f317(f162(x44091),x44092)))),x44093)),f317(f162(x44091),f317(f126(x44091,x44093),x44092))) % 112.26/112.09 [4557]E(f317(f252(x45571),f317(f317(f10(f906(a899,a895),a895,x45571),f81(a899)),f317(f317(f9(x45571,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),x45571),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),x45571),f317(f10(a895,f906(a895,a895),a899),a315)),f317(f317(f9(x45571,f906(a899,x45571),f906(a899,a895)),f317(f317(f10(f906(x45571,a895),f906(f906(a899,x45571),f906(a899,a895)),x45571),f10(x45571,a895,a899)),a314)),f317(f154(x45571),x45572))))),f317(f317(f20(a899,a895,a895),f317(f317(f10(a895,f906(a895,a895),a899),a315),f317(f317(f9(a899,a899,a895),f225(a899)),f317(f179(f900(x45571)),x45572)))),f317(f317(f9(a899,f906(a899,a895),a895),f319(a899)),x45573))))),f317(f162(x45571),f166(x45571,x45572,x45573))) % 112.26/112.09 [4449]E(f317(f252(x44491),f317(f317(f20(x44491,a895,a895),f317(f317(f10(a895,f906(a895,a895),x44491),a320),f317(f317(f10(a895,a895,x44491),a312),f317(f317(f9(x44491,x44491,a895),a314),x44492)))),x44493)),f317(f317(f299(x44491),x44492),f317(f252(x44491),x44493))) % 112.26/112.09 [4481]E(f317(f317(f144(f905(x44811,a899),x44811),f241(x44811,a899)),f317(f126(f905(x44811,a899),f317(f317(f9(f905(x44811,a899),f906(a899,a895),a895),f317(f317(f10(a899,f906(f906(a899,a895),a895),f905(x44811,a899)),f319(a899)),f246(x44811,a899))),x44812)),f317(f317(f171(x44811,a899),x44813),f129(a899,f317(f292(a899,f2(a899)),f317(f179(f900(x44811)),x44813)))))),f166(x44811,x44813,x44812)) % 112.26/112.09 [4508]E(f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f8(a899,a1),f317(f317(f10(a1,a1,a899),f317(f74(a1),x45081)),f317(f317(f9(a899,a1,a1),f317(f317(f10(a1,f906(a1,a1),a899),f75(a1)),f90(a1))),x45082))),f317(f272(a899),x45083))),f317(f317(f75(a1),f317(f90(a1),x45083)),f317(f317(f74(a1),x45081),f317(f317(f74(a1),x45081),f317(f317(f75(a1),f317(f90(a1),f317(f317(f3(a899),x45083),f72(a899)))),x45082))))) % 112.26/112.09 [4550]E(f317(f252(f905(x45501,x45502)),f317(f247(x45501,x45502,a895),f317(f317(f9(x45501,f906(f905(x45502,x45501),a895),f906(x45502,a895)),f317(f317(f10(f906(x45502,f906(f906(f905(x45502,x45501),a895),a895)),f906(f906(f905(x45502,x45501),a895),f906(x45502,a895)),x45501),f9(x45502,f906(f905(x45502,x45501),a895),a895)),f317(f317(f10(f906(x45502,f905(x45502,x45501)),f906(x45502,f906(f906(f905(x45502,x45501),a895),a895)),x45501),f317(f10(f905(x45502,x45501),f906(f906(f905(x45502,x45501),a895),a895),x45502),f319(f905(x45502,x45501)))),f317(f9(x45502,x45501,f905(x45502,x45501)),f242(x45502,x45501))))),x45503))),f317(f276(x45502,x45501),x45503)) % 112.26/112.09 [4570]E(f317(f252(f900(x45701)),f317(f317(f10(f906(x45701,a895),a895,f900(x45701)),f81(x45701)),f317(f317(f10(f906(x45701,f906(f900(x45701),a895)),f906(x45701,a895),f900(x45701)),f317(f10(f906(f900(x45701),a895),a895,x45701),f81(f900(x45701)))),f317(f317(f9(f900(x45701),f906(x45701,f906(f900(x45701),a895)),f906(x45701,f906(f900(x45701),a895))),f317(f317(f10(f906(x45701,f906(f906(f900(x45701),a895),f906(f900(x45701),a895))),f906(f906(x45701,f906(f900(x45701),a895)),f906(x45701,f906(f900(x45701),a895))),f900(x45701)),f20(x45701,f906(f900(x45701),a895),f906(f900(x45701),a895))),f317(f317(f10(f906(x45701,f906(f900(x45701),f906(a895,a895))),f906(x45701,f906(f906(f900(x45701),a895),f906(f900(x45701),a895))),f900(x45701)),f317(f10(f906(f900(x45701),f906(a895,a895)),f906(f906(f900(x45701),a895),f906(f900(x45701),a895)),x45701),f20(f900(x45701),a895,a895))),f317(f317(f10(f906(x45701,f906(f900(x45701),a895)),f906(x45701,f906(f900(x45701),f906(a895,a895))),f900(x45701)),f317(f10(f906(f900(x45701),a895),f906(f900(x45701),f906(a895,a895)),x45701),f317(f10(a895,f906(a895,a895),f900(x45701)),a315))),f317(f317(f9(f900(x45701),f906(x45701,f906(f900(x45701),f900(x45701))),f906(x45701,f906(f900(x45701),a895))),f317(f317(f10(f906(f906(f900(x45701),f900(x45701)),f906(f900(x45701),a895)),f906(f906(x45701,f906(f900(x45701),f900(x45701))),f906(x45701,f906(f900(x45701),a895))),f900(x45701)),f10(f906(f900(x45701),f900(x45701)),f906(f900(x45701),a895),x45701)),f317(f317(f10(f906(f900(x45701),a895),f906(f906(f900(x45701),f900(x45701)),f906(f900(x45701),a895)),f900(x45701)),f10(f900(x45701),a895,f900(x45701))),a314))),f141(x45701)))))),f317(f317(f9(x45701,f906(f900(x45701),a895),f906(f900(x45701),a895)),f317(f317(f10(f906(a895,a895),f906(f906(f900(x45701),a895),f906(f900(x45701),a895)),x45701),f10(a895,a895,f900(x45701))),f317(f317(f10(a895,f906(a895,a895),x45701),a315),f317(f317(f9(x45701,f906(x45701,a895),a895),f319(x45701)),x45702)))),f317(f317(f9(f900(x45701),f906(f900(x45701),a895),a895),f319(f900(x45701))),x45703)))))),f164(x45701,x45702,x45703)) % 112.26/112.09 [4567]E(f317(f317(f80(a1,f905(a1,a1)),f317(f317(f3(a1),x45671),x45672)),f317(f317(f9(a1,f905(a1,a1),f905(a1,a1)),f317(f317(f20(a1,f905(a1,a1),f906(f905(a1,a1),f905(a1,a1))),f317(f317(f10(a895,f906(f905(a1,a1),f906(f905(a1,a1),f905(a1,a1))),a1),f86(f905(a1,a1))),f317(f224(a1),f2(a1)))),f317(f242(a1,a1),f317(f317(f74(a1),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x45673)),f72(a1))))),f317(f317(f242(a1,a1),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x45673)),x45671))),f317(f39(x45672),f317(f317(f242(a1,a1),x45673),x45671))) % 112.26/112.09 [3623]E(f106(x36231,f317(x36232,x36233),f317(x36234,x36233)),f317(f193(x36231,x36232,x36234),x36233)) % 112.26/112.09 [3676]E(f317(f317(f235(x36761,x36762,x36763),x36764),f2(a899)),x36762) % 112.26/112.09 [3714]E(f175(x37141,x37142,x37143,f317(a102,x37144)),f317(x37143,x37144)) % 112.26/112.09 [3755]E(f160(x37551,x37552,f160(x37551,x37553,x37554)),f160(x37551,x37553,f160(x37551,x37552,x37554))) % 112.26/112.09 [3756]E(f116(x37561,x37562,f106(x37561,x37563,x37564)),f106(x37561,f116(x37561,x37562,x37563),x37564)) % 112.26/112.09 [3889]E(f317(f146(x38891,x38892,x38893,x38894),f103(x38892)),x38893) % 112.26/112.09 [3890]E(f317(f132(x38901,x38902,x38903,x38904),f103(x38902)),x38904) % 112.26/112.09 [3927]E(f317(f179(f903(x39271,x39272)),f210(x39271,x39272,x39273,x39274)),f2(a899)) % 112.26/112.09 [3950]E(f317(f247(x39501,x39502,x39503),f245(x39501,x39502,x39503,x39504)),x39504) % 112.26/112.09 [3993]E(f317(f317(f124(x39931),f159(x39931,x39932,x39933)),f159(x39931,x39934,x39933)),f317(f317(f124(x39931),f159(x39931,x39934,x39933)),f159(x39931,x39932,x39933))) % 112.26/112.09 [4078]E(f317(f317(f249(x40781,x40782,x40783,f905(x40782,x40783)),x40784),f242(x40782,x40783)),x40784) % 112.26/112.09 [4088]E(f117(x40881,x40882,x40883,x40884,f109(x40882)),x40883) % 112.26/112.09 [4094]E(f69(x40941,x40942,x40943,x40944,f317(x40943,x40944)),x40943) % 112.26/112.09 [4360]P41(x43601,x43602,x43603,x43604,f178(f906(x43601,a895)),x43604) % 112.26/112.09 [3429]E(f317(f317(f18(x34291,x34292),x34293),x34294),x34293) % 112.26/112.09 [3704]E(f160(x37041,x37042,f317(f126(x37041,x37043),x37044)),f317(f126(x37041,x37043),f160(x37041,x37042,x37044))) % 112.26/112.09 [3738]E(f317(f317(f59(x37381,x37382,x37383),x37384),f178(f906(x37381,a895))),x37384) % 112.26/112.09 [3762]E(f317(f317(f154(x37621),f317(f317(f141(x37621),x37622),x37623)),f317(a102,x37624)),f317(f317(f154(x37621),x37623),x37624)) % 112.26/112.09 [3829]E(f317(f317(x38291,x38292),f317(f174(x38293,x38294,x38291),x38292)),f317(f174(x38293,x38294,x38291),f317(a102,x38292))) % 112.26/112.09 [3870]E(f245(x38701,x38702,x38703,f317(f247(x38701,x38702,x38703),x38704)),x38704) % 112.26/112.09 [3925]E(f317(f317(f149(x39251,f317(f317(f141(x39251),x39252),x39253)),f2(a899)),x39254),f317(f317(f141(x39251),x39254),x39253)) % 112.26/112.09 [3935]E(f317(f317(f36(f906(x39351,a895),f906(x39352,a895)),x39353),f300(x39351,x39352,x39354)),f317(f300(x39351,x39352,x39354),f32(f906(x39351,a895),x39353))) % 112.26/112.09 [3936]E(f317(f317(f36(f906(x39361,a895),f906(x39362,a895)),x39363),f301(x39362,x39361,x39364)),f317(f301(x39362,x39361,x39364),f32(f906(x39361,a895),x39363))) % 112.26/112.09 [3961]E(f110(x39611,f120(x39612,f901(x39611),x39613,x39614)),f317(f108(x39612,x39611,x39614),x39613)) % 112.26/112.09 [4033]E(f317(f115(x40331,x40332),f116(x40331,x40333,x40334)),f317(f317(f74(a899),f317(f317(f74(a899),f317(x40332,x40333)),f317(f115(x40331,x40332),x40334))),f317(a102,f2(a899)))) % 112.26/112.09 [4054]E(f317(f132(x40541,x40542,f317(f9(x40542,x40541,x40541),x40543),x40544),f317(f158(x40542),f103(x40542))),x40544) % 112.26/112.09 [4158]E(f213(x41581,f905(x41582,f901(x41582)),x41583,f317(f247(x41582,f901(x41582),x41581),x41584),f317(f125(x41582),f109(x41582))),x41583) % 112.26/112.09 [4290]E(f317(f247(x42901,x42902,x42903),f317(f317(f10(f906(x42902,f905(x42901,x42902)),f906(x42902,x42903),x42901),f317(f10(f905(x42901,x42902),x42903,x42902),x42904)),f242(x42901,x42902))),x42904) % 112.26/112.09 [3614]E(f317(f246(x36141,x36142),f317(f317(f242(x36141,x36142),x36143),x36144)),x36144) % 112.26/112.09 [3615]E(f317(f241(x36151,x36152),f317(f317(f242(x36151,x36152),x36153),x36154)),x36153) % 112.26/112.09 [3648]E(f317(f179(f900(x36481)),f317(f317(f149(x36481,x36482),x36483),x36484)),f317(f179(f900(x36481)),x36482)) % 112.26/112.09 [3649]E(f317(f179(f900(x36491)),f317(f317(f144(x36492,x36491),x36493),x36494)),f317(f179(f900(x36492)),x36494)) % 112.26/112.09 [3670]E(f317(f317(f128(x36701),f317(a102,x36702)),f317(f317(f141(x36701),x36703),x36704)),f317(f317(f128(x36701),x36702),x36704)) % 112.26/112.09 [3733]E(f317(f317(f165(x37331),x37332),f159(x37331,x37333,x37334)),f159(x37331,f317(f317(f228(a899),x37332),x37333),x37334)) % 112.26/112.09 [3734]E(f317(f317(f128(x37341),x37342),f159(x37341,x37343,x37344)),f159(x37341,f317(f317(f3(a899),x37343),x37342),x37344)) % 112.26/112.09 [3740]E(f317(f317(f299(x37401),x37402),f317(f317(f299(x37401),x37403),x37404)),f317(f317(f299(x37401),x37403),f317(f317(f299(x37401),x37402),x37404))) % 112.26/112.09 [3744]E(f317(f317(f144(x37441,x37442),x37443),f104(x37441,x37444)),f104(x37442,f317(f317(f144(x37441,x37442),x37443),x37444))) % 112.26/112.09 [3760]E(f317(f158(x37601),f317(f317(f144(x37602,x37601),x37603),x37604)),f317(f317(f144(x37602,x37601),x37603),f317(f158(x37602),x37604))) % 112.26/112.09 [3761]E(f317(f317(f144(x37611,x37612),x37613),f317(f161(x37611),x37614)),f317(f161(x37612),f317(f317(f144(x37611,x37612),x37613),x37614))) % 112.26/112.09 [3776]E(f317(f317(f165(x37761),f317(a102,x37762)),f317(f317(f141(x37761),x37763),x37764)),f317(f317(f141(x37761),x37763),f317(f317(f165(x37761),x37762),x37764))) % 112.26/112.09 [3779]E(f317(f162(x37791),f317(f317(f144(x37792,x37791),x37793),x37794)),f317(f300(x37792,x37791,x37793),f317(f162(x37792),x37794))) % 112.26/112.09 [3792]E(f317(f317(f144(x37921,x37922),f317(f18(x37922,x37921),x37923)),x37924),f159(x37922,f317(f179(f900(x37921)),x37924),x37923)) % 112.26/112.09 [3828]E(f19(x38281,x38282,x38283,f317(a5,f317(a102,f317(a22,x38284)))),f317(x38283,x38284)) % 112.26/112.09 [3832]E(f317(f317(f124(x38321),f317(f126(x38321,x38322),x38323)),f317(f126(x38321,x38322),x38324)),f317(f126(x38321,x38322),f317(f317(f124(x38321),x38323),x38324))) % 112.26/112.09 [3844]E(f142(x38441,f317(f317(f144(x38442,x38441),x38443),f142(x38442,x38444))),f142(x38441,f317(f317(f144(x38442,x38441),x38443),x38444))) % 112.26/112.09 [3859]E(f317(f276(x38591,x38591),f317(f317(f278(x38592,x38591),x38593),x38594)),f317(f317(f278(x38592,x38591),f317(f276(x38592,x38592),x38593)),x38594)) % 112.26/112.09 [3871]E(f317(f317(f279(x38711,x38712,x38713),x38714),f178(f906(f905(x38712,x38713),a895))),f178(f906(f905(x38711,x38713),a895))) % 112.26/112.09 [3872]E(f317(f317(f165(x38721),f317(f317(f3(a899),x38722),x38723)),f317(f317(f128(x38721),x38723),x38724)),f317(f317(f128(x38721),x38723),f317(f317(f165(x38721),x38722),x38724))) % 112.26/112.09 [3891]E(f317(f317(f124(x38911),f159(x38911,x38912,x38913)),f159(x38911,x38914,x38913)),f159(x38911,f317(f317(f74(a899),x38912),x38914),x38913)) % 112.26/112.09 [3892]E(f317(f317(f317(f268(x38921),x38922),x38923),x38924),f317(f242(f906(a89,f906(a895,f902(f901(x38921)))),f905(a89,a89)),f317(f38(x38921),x38922))) % 112.26/112.09 [3918]E(f32(f906(x39181,a895),f317(f300(x39182,f906(x39181,a895),x39183),x39184)),f317(f317(f36(x39182,f906(x39181,a895)),x39184),x39183)) % 112.26/112.09 [3919]E(f33(f906(x39191,a895),f317(f300(x39192,f906(x39191,a895),x39193),x39194)),f317(f317(f35(x39192,f906(x39191,a895)),x39194),x39193)) % 112.26/112.09 [3920]E(f317(f179(f900(f905(x39201,x39202))),f317(f317(f171(x39201,x39202),x39203),x39204)),f317(f317(f228(a899),f317(f179(f900(x39201)),x39203)),f317(f179(f900(x39202)),x39204))) % 112.26/112.09 [3922]E(f317(f301(x39221,x39222,x39223),f317(f73(f906(x39222,a895)),x39224)),f317(f73(f906(x39221,a895)),f317(f301(x39221,x39222,x39223),x39224))) % 112.26/112.09 [3971]E(f317(f301(x39711,x39712,x39713),f317(f252(x39712),x39714)),f317(f252(x39711),f317(f317(f10(x39712,a895,x39711),x39714),x39713))) % 112.26/112.09 [3988]E(f317(f317(f154(x39881),f317(f317(f124(x39881),x39882),f317(f317(f141(x39881),x39883),x39884))),f317(f179(f900(x39881)),x39882)),x39883) % 112.26/112.09 [4010]E(f317(f300(x40101,x40102,x40103),f317(f301(x40101,x40102,x40103),x40104)),f317(f317(f92(f906(x40102,a895)),x40104),f317(f300(x40101,x40102,x40103),f232(f906(x40101,a895))))) % 112.26/112.09 [4029]P1(f317(f317(f319(x40291),f317(x40292,x40293)),f317(f300(x40294,x40291,x40292),f232(f906(x40294,a895))))) % 112.26/112.09 [4038]E(f21(x40381,x40382,x40383,f317(a5,f317(a102,f317(a22,x40384)))),f317(f317(x40383,x40384),f21(x40381,x40382,x40383,x40384))) % 112.26/112.09 [4042]E(f317(f317(f124(x40421),f159(x40421,x40422,x40423)),f317(f317(f141(x40421),x40423),x40424)),f317(f317(f141(x40421),x40423),f317(f317(f124(x40421),f159(x40421,x40422,x40423)),x40424))) % 112.26/112.09 [4044]E(f317(f317(f244(x40441,x40442),f317(f162(x40441),x40443)),f317(f18(f906(x40442,a895),x40441),f317(f162(x40442),x40444))),f317(f162(f905(x40441,x40442)),f55(x40441,x40442,x40443,x40444))) % 112.26/112.09 [4056]E(f145(x40561,x40562,f317(f317(f141(x40561),x40563),x40564)),f317(f317(f74(a899),f317(f317(f74(a899),f317(x40562,x40563)),f145(x40561,x40562,x40564))),f317(a102,f2(a899)))) % 112.26/112.09 [4069]E(f175(f900(x40691),f317(f317(f141(x40691),x40692),x40693),f317(f317(f9(a899,f900(x40691),f900(x40691)),f128(x40691)),x40693),x40694),f317(f317(f128(x40691),x40694),f317(f317(f141(x40691),x40692),x40693))) % 112.26/112.09 [4070]P24(x40701,f905(x40702,x40701),f321(x40703,x40704,x40702,x40701),f317(f317(f36(x40702,f906(x40701,a895)),x40704),x40703)) % 112.26/112.09 [4079]E(f317(f317(f3(f906(x40791,a895)),f317(f317(f3(f906(x40791,a895)),x40792),x40793)),f317(f317(f299(x40791),x40794),f178(f906(x40791,a895)))),f317(f317(f3(f906(x40791,a895)),x40792),f317(f317(f299(x40791),x40794),x40793))) % 112.26/112.09 [4092]E(f317(f317(f173(f906(x40921,x40922),f906(x40921,x40922)),x40923),f67(x40922,x40922,x40921,x40924)),f67(x40922,x40922,x40921,f317(f317(f173(x40922,x40922),x40923),x40924))) % 112.26/112.09 [4163]E(f317(f317(f317(f173(f900(x41631),f900(x41631)),x41632),f157(x41631)),f317(f317(f317(f173(f900(x41631),f900(x41631)),x41633),f157(x41631)),x41634)),f317(f317(f317(f173(f900(x41631),f900(x41631)),f317(f317(f74(a899),x41632),x41633)),f157(x41631)),x41634)) % 112.26/112.09 [4248]P1(f317(f317(f224(f906(x42481,a895)),f317(f162(x42481),f317(f317(f149(x42481,x42482),x42483),x42484))),f317(f317(f299(x42481),x42484),f317(f162(x42481),x42482)))) % 112.26/112.09 [4280]E(f317(f317(f36(f906(x42801,a895),f906(f905(x42801,x42802),a895)),x42803),f317(f317(f9(f906(x42801,a895),f906(x42801,f906(x42802,a895)),f906(f905(x42801,x42802),a895)),f244(x42801,x42802)),x42804)),f317(f317(f244(x42801,x42802),f32(f906(x42801,a895),x42803)),x42804)) % 112.26/112.09 [4318]E(f199(x43181,x43182,x43183,f317(f67(x43182,f906(a89,f906(a89,f906(f905(a89,a89),f906(a89,f901(x43182))))),x43181,f198(x43182)),x43184)),f200(x43181,x43182,x43184,x43183)) % 112.26/112.09 [4333]E(f195(x43331,x43332,x43333,f317(f67(x43332,f906(a89,f906(a89,f906(f905(a89,a89),f906(a89,f901(f902(x43332)))))),x43331,f194(x43332)),x43334)),f196(x43331,x43332,x43334,x43333)) % 112.26/112.09 [4338]P1(f317(f61(x43381,x43382,x43383,x43384,f178(f906(x43381,a895))),x43384)) % 112.26/112.09 [4377]E(f317(f317(f36(x43771,f906(x43772,a895)),x43773),f317(f317(f9(x43771,f906(x43772,a895),f906(x43772,a895)),f317(f317(f10(x43772,f906(f906(x43772,a895),f906(x43772,a895)),x43771),f299(x43772)),x43774)),f178(f906(x43772,a895)))),f317(f300(x43771,x43772,x43774),x43773)) % 112.26/112.09 [4384]P1(f317(f317(f224(f906(x43841,a895)),f317(f274(x43842,x43841),f317(f317(f92(f906(f905(x43842,x43841),a895)),x43843),x43844))),f317(f317(f92(f906(x43841,a895)),f317(f274(x43842,x43841),x43843)),f317(f274(x43842,x43841),x43844)))) % 112.26/112.09 [4385]P1(f317(f317(f224(f906(x43851,a895)),f317(f254(x43851,x43852),f317(f317(f92(f906(f905(x43851,x43852),a895)),x43853),x43854))),f317(f317(f92(f906(x43851,a895)),f317(f254(x43851,x43852),x43853)),f317(f254(x43851,x43852),x43854)))) % 112.26/112.09 [4445]P1(f317(f317(f224(f906(f905(x44451,x44452),a895)),f317(f300(x44452,f905(x44451,x44452),f321(x44453,x44454,x44451,x44452)),f317(f317(f36(x44451,f906(x44452,a895)),x44454),x44453))),f317(f317(f244(x44451,x44452),x44454),x44453))) % 112.26/112.09 [4446]E(f317(f108(x44461,f905(x44461,x44462),x44463),f317(f317(f10(f906(x44462,f901(f905(x44461,x44462))),f901(f905(x44461,x44462)),x44461),f108(x44462,f905(x44461,x44462),x44464)),f317(f317(f10(f906(x44462,f905(x44461,x44462)),f906(x44462,f901(f905(x44461,x44462))),x44461),f317(f10(f905(x44461,x44462),f901(f905(x44461,x44462)),x44462),f119(f905(x44461,x44462)))),f242(x44461,x44462)))),f121(x44461,x44462,x44463,x44464)) % 112.26/112.09 [4447]E(f266(x44471,x44472,x44473,f317(f67(x44472,f906(a89,f906(a89,f906(f905(a89,a89),f905(f906(a89,f906(a895,f902(f901(x44472)))),f905(a89,a89))))),x44471,f268(x44472)),x44474)),f269(x44471,x44472,x44474,x44473)) % 112.26/112.09 [4487]E(f79(f905(x44871,x44872),f317(f247(x44871,x44872,a895),f317(f317(f9(x44871,f906(x44872,a895),f906(x44872,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x44872,a895),f906(x44872,a895)),x44871),f10(a895,a895,x44872)),f317(f317(f10(a895,f906(a895,a895),x44871),a315),f317(a314,x44873)))),f317(a314,x44874)))),f317(f317(f242(x44871,x44872),x44873),x44874)) % 112.26/112.09 [4488]E(f84(f905(x44881,x44882),f317(f247(x44881,x44882,a895),f317(f317(f9(x44881,f906(x44882,a895),f906(x44882,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x44882,a895),f906(x44882,a895)),x44881),f10(a895,a895,x44882)),f317(f317(f10(a895,f906(a895,a895),x44881),a315),f317(a314,x44883)))),f317(a314,x44884)))),f317(f317(f242(x44881,x44882),x44883),x44884)) % 112.26/112.09 [4559]E(f317(f317(f247(f900(x45591),f900(x45591),f905(f900(x45591),f900(x45591))),f317(f317(f20(f900(x45591),f906(f900(x45591),f905(f900(x45591),f900(x45591))),f906(f900(x45591),f905(f900(x45591),f900(x45591)))),f317(f317(f10(f906(f900(x45591),f906(f905(f900(x45591),f900(x45591)),f905(f900(x45591),f900(x45591)))),f906(f906(f900(x45591),f905(f900(x45591),f900(x45591))),f906(f900(x45591),f905(f900(x45591),f900(x45591)))),f900(x45591)),f20(f900(x45591),f905(f900(x45591),f900(x45591)),f905(f900(x45591),f900(x45591)))),f317(f317(f10(f906(f900(x45591),f905(f900(x45591),f900(x45591))),f906(f900(x45591),f906(f905(f900(x45591),f900(x45591)),f905(f900(x45591),f900(x45591)))),f900(x45591)),f317(f10(f905(f900(x45591),f900(x45591)),f906(f905(f900(x45591),f900(x45591)),f905(f900(x45591),f900(x45591))),f900(x45591)),f317(f86(f905(f900(x45591),f900(x45591))),f317(x45592,x45593)))),f317(f317(f10(f900(x45591),f906(f900(x45591),f905(f900(x45591),f900(x45591))),f900(x45591)),f242(f900(x45591),f900(x45591))),f317(f141(x45591),x45593))))),f317(f317(f9(f900(x45591),f906(f900(x45591),f900(x45591)),f906(f900(x45591),f905(f900(x45591),f900(x45591)))),f317(f317(f10(f906(f900(x45591),f905(f900(x45591),f900(x45591))),f906(f906(f900(x45591),f900(x45591)),f906(f900(x45591),f905(f900(x45591),f900(x45591)))),f900(x45591)),f10(f900(x45591),f905(f900(x45591),f900(x45591)),f900(x45591))),f242(f900(x45591),f900(x45591)))),f317(f141(x45591),x45593)))),f156(x45591,x45592,x45594)),f156(x45591,x45592,f317(f317(f141(x45591),x45593),x45594))) % 112.26/112.09 [3808]E(f317(f317(f165(x38081),x38082),f317(f317(f165(x38081),x38083),x38084)),f317(f317(f165(x38081),f317(f317(f228(a899),x38082),x38083)),x38084)) % 112.26/112.09 [3809]E(f317(f317(f128(x38091),x38092),f317(f317(f128(x38091),x38093),x38094)),f317(f317(f128(x38091),f317(f317(f74(a899),x38092),x38093)),x38094)) % 112.26/112.09 [3820]E(f317(f317(f124(x38201),f317(f317(f141(x38201),x38202),x38203)),x38204),f317(f317(f141(x38201),x38202),f317(f317(f124(x38201),x38203),x38204))) % 112.26/112.09 [3821]E(f317(f317(f124(x38211),f317(f317(f124(x38211),x38212),x38213)),x38214),f317(f317(f124(x38211),x38212),f317(f317(f124(x38211),x38213),x38214))) % 112.26/112.09 [3902]E(f317(f317(f154(x39021),f317(f317(f141(x39021),x39022),x39023)),x39024),f175(x39021,x39022,f317(f154(x39021),x39023),x39024)) % 112.26/112.09 [3911]E(f317(f317(f173(x39111,x39111),x39112),f317(f317(f173(x39111,x39111),x39113),x39114)),f317(f317(f173(x39111,x39111),f317(f317(f75(a899),x39113),x39112)),x39114)) % 112.26/112.09 [3938]E(f317(f317(f91(f906(x39381,a895)),x39382),f317(f317(f299(x39381),x39383),x39384)),f317(f317(f299(x39381),x39383),f317(f317(f91(f906(x39381,a895)),x39382),x39384))) % 112.26/112.09 [3953]E(f317(f317(f317(f173(x39531,x39531),x39532),x39533),f317(x39533,x39534)),f317(x39533,f317(f317(f317(f173(x39531,x39531),x39532),x39533),x39534))) % 112.26/112.09 [3962]E(f317(f317(f279(x39621,x39622,x39623),f178(f906(f905(x39621,x39622),a895))),x39624),f178(f906(f905(x39621,x39623),a895))) % 112.26/112.09 [3976]E(f317(f317(f91(f906(x39761,a895)),f317(f317(f299(x39761),x39762),x39763)),x39764),f317(f317(f299(x39761),x39762),f317(f317(f91(f906(x39761,a895)),x39763),x39764))) % 112.26/112.09 [3995]E(f317(f30(f905(x39951,x39952)),f317(f317(f244(x39951,x39952),x39953),f317(f18(f906(x39952,a895),x39951),x39954))),f317(f317(f75(a899),f317(f30(x39951),x39953)),f317(f30(x39952),x39954))) % 112.26/112.09 [4001]E(f317(f317(f92(f906(x40011,a895)),f317(f317(f299(x40011),x40012),x40013)),f317(f317(f299(x40011),x40012),x40014)),f317(f317(f299(x40011),x40012),f317(f317(f92(f906(x40011,a895)),x40013),x40014))) % 112.26/112.09 [4014]E(f317(f317(f91(f906(x40141,a895)),x40142),f317(f317(f91(f906(x40141,a895)),x40143),x40144)),f317(f317(f91(f906(x40141,a895)),x40143),f317(f317(f91(f906(x40141,a895)),x40142),x40144))) % 112.26/112.09 [4015]E(f317(f317(f92(f906(x40151,a895)),x40152),f317(f317(f92(f906(x40151,a895)),x40153),x40154)),f317(f317(f92(f906(x40151,a895)),x40153),f317(f317(f92(f906(x40151,a895)),x40152),x40154))) % 112.26/112.09 [4025]E(f59(x40251,x40252,f317(f317(f10(x40252,f906(x40252,x40252),x40251),x40253),x40254)),f317(f60(x40252,x40251,x40253),x40254)) % 112.26/112.09 [4034]E(f169(x40341,f317(f317(f144(f900(x40342),f900(x40341)),f317(f144(x40342,x40341),x40343)),x40344)),f317(f317(f144(f900(x40342),f900(x40341)),f317(f144(x40342,x40341),x40343)),f169(x40342,x40344))) % 112.26/112.09 [4053]E(f317(f132(f900(x40531),f900(x40531),f124(x40531),f103(x40531)),f317(f317(f144(x40532,f900(x40531)),x40533),x40534)),f153(x40532,x40531,x40533,x40534)) % 112.26/112.09 [4110]E(f317(f67(x41101,x41101,x41101,f317(f317(f173(x41101,x41101),x41102),x41103)),f317(f317(f173(x41101,x41101),x41104),x41103)),f317(f317(f173(x41101,x41101),f317(f317(f74(a899),x41102),x41104)),x41103)) % 112.26/112.09 [4133]E(f317(f317(f92(f906(x41331,a895)),f317(f317(f3(f906(x41331,a895)),x41332),x41333)),f317(f317(f3(f906(x41331,a895)),x41332),x41334)),f317(f317(f3(f906(x41331,a895)),x41332),f317(f317(f91(f906(x41331,a895)),x41333),x41334))) % 112.26/112.09 [4134]E(f317(f317(f91(f906(x41341,a895)),f317(f317(f3(f906(x41341,a895)),x41342),x41343)),f317(f317(f3(f906(x41341,a895)),x41342),x41344)),f317(f317(f3(f906(x41341,a895)),x41342),f317(f317(f92(f906(x41341,a895)),x41343),x41344))) % 112.26/112.09 [4135]E(f317(f317(f92(f906(x41351,a895)),f317(f317(f91(f906(x41351,a895)),x41352),x41353)),f317(f317(f91(f906(x41351,a895)),x41352),x41354)),f317(f317(f91(f906(x41351,a895)),x41352),f317(f317(f92(f906(x41351,a895)),x41353),x41354))) % 112.26/112.09 [4136]E(f317(f317(f3(f906(x41361,a895)),f317(f317(f92(f906(x41361,a895)),x41362),x41363)),f317(f317(f92(f906(x41361,a895)),x41362),x41364)),f317(f317(f92(f906(x41361,a895)),x41362),f317(f317(f3(f906(x41361,a895)),x41363),x41364))) % 112.26/112.09 [4137]E(f317(f317(f91(f906(x41371,a895)),f317(f317(f92(f906(x41371,a895)),x41372),x41373)),f317(f317(f92(f906(x41371,a895)),x41372),x41374)),f317(f317(f92(f906(x41371,a895)),x41372),f317(f317(f91(f906(x41371,a895)),x41373),x41374))) % 112.26/112.09 [4142]E(f317(f30(f905(x41421,x41422)),f317(f317(f244(x41421,x41422),f317(f317(f299(x41421),x41423),f178(f906(x41421,a895)))),f317(f18(f906(x41422,a895),x41421),x41424))),f317(f30(x41422),x41424)) % 112.26/112.09 [4177]E(f317(f317(f36(x41771,f906(x41772,a895)),x41773),f317(f317(f10(f906(x41772,a895),f906(x41772,a895),x41771),f73(f906(x41772,a895))),x41774)),f317(f73(f906(x41772,a895)),f317(f317(f35(x41771,f906(x41772,a895)),x41773),x41774))) % 112.26/112.09 [4178]E(f317(f317(f35(x41781,f906(x41782,a895)),x41783),f317(f317(f10(f906(x41782,a895),f906(x41782,a895),x41781),f73(f906(x41782,a895))),x41784)),f317(f73(f906(x41782,a895)),f317(f317(f36(x41781,f906(x41782,a895)),x41783),x41784))) % 112.26/112.09 [4194]E(f317(f317(f279(x41941,x41941,x41941),f317(f317(f173(f905(x41941,x41941),a895),x41942),x41943)),f317(f317(f173(f905(x41941,x41941),a895),x41944),x41943)),f317(f317(f173(f905(x41941,x41941),a895),f317(f317(f74(a899),x41942),x41944)),x41943)) % 112.26/112.09 [4224]E(f317(f317(f35(x42241,f906(f906(x42242,a895),a895)),x42243),f317(f317(f10(f906(x42242,a895),f906(f906(x42242,a895),a895),x42241),f298(x42242)),x42244)),f317(f298(x42242),f317(f317(f35(x42241,f906(x42242,a895)),x42243),x42244))) % 112.26/112.09 [4253]E(f317(f317(f35(f906(x42531,a895),f906(x42532,a895)),x42533),f317(f317(f9(f906(x42531,a895),f906(x42531,f906(x42532,a895)),f906(x42532,a895)),f35(x42531,f906(x42532,a895))),x42534)),f317(f317(f35(x42531,f906(x42532,a895)),f32(f906(x42531,a895),x42533)),x42534)) % 112.26/112.09 [4254]E(f317(f317(f36(f906(x42541,a895),f906(x42542,a895)),x42543),f317(f317(f9(f906(x42541,a895),f906(x42541,f906(x42542,a895)),f906(x42542,a895)),f36(x42541,f906(x42542,a895))),x42544)),f317(f317(f36(x42541,f906(x42542,a895)),f32(f906(x42541,a895),x42543)),x42544)) % 112.26/112.09 [4259]E(f317(f317(f144(x42591,x42592),x42593),f317(f132(f900(x42591),f900(x42591),f124(x42591),f103(x42591)),x42594)),f317(f132(f900(x42592),f900(x42592),f124(x42592),f103(x42592)),f317(f317(f144(f900(x42591),f900(x42592)),f317(f144(x42591,x42592),x42593)),x42594))) % 112.26/112.09 [4261]E(f175(f900(x42611),f103(x42611),f317(f317(f10(f900(x42611),f900(x42611),a899),f317(f141(x42611),x42612)),f317(f317(f9(a899,f900(x42611),f900(x42611)),f165(x42611)),x42613)),x42614),f317(f317(f165(x42611),x42614),f317(f317(f141(x42611),x42612),x42613))) % 112.26/112.09 [4299]P1(f317(f317(f224(f906(x42991,a895)),f317(f300(x42992,x42991,x42993),f317(f301(x42992,x42991,x42993),x42994))),x42994)) % 112.26/112.09 [4301]E(f317(f300(f905(x43011,x43012),f905(x43012,x43011),f317(f247(x43011,x43012,f905(x43012,x43011)),f317(f9(x43012,x43011,f905(x43012,x43011)),f242(x43012,x43011)))),f317(f317(f244(x43011,x43012),x43013),f317(f18(f906(x43012,a895),x43011),x43014))),f317(f317(f244(x43012,x43011),x43014),f317(f18(f906(x43011,a895),x43012),x43013))) % 112.26/112.09 [4310]E(f317(f317(f36(x43101,f906(x43102,a895)),x43103),f317(f317(f10(f906(x43101,a895),f906(x43102,a895),x43101),f275(x43101,x43102,x43104)),f317(f317(f9(x43101,f906(x43101,a895),f906(x43101,a895)),f299(x43101)),f178(f906(x43101,a895))))),f317(f275(x43101,x43102,x43104),x43103)) % 112.26/112.09 [4311]E(f317(f317(f36(x43111,f906(x43112,a895)),x43113),f317(f317(f10(f906(x43111,a895),f906(x43112,a895),x43111),f301(x43112,x43111,x43114)),f317(f317(f9(x43111,f906(x43111,a895),f906(x43111,a895)),f299(x43111)),f178(f906(x43111,a895))))),f317(f301(x43112,x43111,x43114),x43113)) % 112.26/112.09 [4398]E(f317(f317(f92(f906(x43981,a895)),f317(f317(f92(f906(x43981,a895)),f317(f317(f91(f906(x43981,a895)),x43982),x43983)),f317(f317(f91(f906(x43981,a895)),x43983),x43984))),f317(f317(f91(f906(x43981,a895)),x43984),x43982)),f317(f317(f91(f906(x43981,a895)),f317(f317(f91(f906(x43981,a895)),f317(f317(f92(f906(x43981,a895)),x43982),x43983)),f317(f317(f92(f906(x43981,a895)),x43983),x43984))),f317(f317(f92(f906(x43981,a895)),x43984),x43982))) % 112.26/112.09 [4461]E(f317(f132(f900(x44611),f900(x44611),f124(x44611),f103(x44611)),f317(f317(f144(x44612,f900(x44611)),f317(f317(f9(x44612,f900(x44611),f900(x44611)),f317(f317(f10(x44611,f906(f900(x44611),f900(x44611)),x44612),f141(x44611)),x44613)),f103(x44611))),x44614)),f317(f317(f144(x44612,x44611),x44613),x44614)) % 112.26/112.09 [4471]E(f317(f317(f80(a1,x44711),f317(f94(a1),f317(f317(f74(a1),x44712),a87))),f317(f317(f20(a1,x44711,x44711),f317(f317(f9(a1,x44711,f906(x44711,x44711)),f317(f317(f10(a895,f906(x44711,f906(x44711,x44711)),a1),f86(x44711)),a183)),x44713)),f317(f317(f10(a899,x44711,a1),x44714),a95))),f175(x44711,x44713,x44714,f317(f94(a899),x44712))) % 112.26/112.09 [4502]E(f317(f252(x45021),f317(f317(f10(f906(x45022,a895),a895,x45021),f81(x45022)),f317(f317(f10(f906(x45022,a895),f906(x45022,a895),x45021),f317(f20(x45022,a895,a895),f317(f317(f10(a895,f906(a895,a895),x45022),a315),f317(f317(f9(x45022,f906(x45022,a895),a895),f319(x45022)),x45023)))),f317(f9(x45022,x45021,a895),x45024)))),f317(f275(x45022,x45021,f317(f252(f905(x45022,x45021)),f317(f247(x45022,x45021,a895),x45024))),x45023)) % 112.26/112.09 [4636]~P1(f317(f317(f178(f906(x46361,f906(x46362,a895))),x46363),x46364)) % 112.26/112.09 [3965]E(f317(f317(f154(x39651),f317(f317(f124(x39651),x39652),x39653)),f317(f317(f74(a899),f317(f179(f900(x39651)),x39652)),x39654)),f317(f317(f154(x39651),x39653),x39654)) % 112.26/112.09 [3970]E(f317(f317(f128(x39701),x39702),f317(f317(f165(x39701),f317(f317(f74(a899),x39703),x39702)),x39704)),f317(f317(f165(x39701),x39703),f317(f317(f128(x39701),x39702),x39704))) % 112.26/112.09 [4067]E(f317(f317(f91(f906(x40671,a895)),f317(f274(x40672,x40671),x40673)),f317(f274(x40672,x40671),x40674)),f317(f274(x40672,x40671),f317(f317(f91(f906(f905(x40672,x40671),a895)),x40673),x40674))) % 112.26/112.09 [4068]E(f317(f317(f91(f906(x40681,a895)),f317(f254(x40681,x40682),x40683)),f317(f254(x40681,x40682),x40684)),f317(f254(x40681,x40682),f317(f317(f91(f906(f905(x40681,x40682),a895)),x40683),x40684))) % 112.26/112.09 [4073]E(f317(f317(f3(f906(x40731,a895)),f317(f317(f92(f906(x40731,a895)),x40732),x40733)),x40734),f317(f317(f92(f906(x40731,a895)),x40732),f317(f317(f3(f906(x40731,a895)),x40733),x40734))) % 112.26/112.09 [4074]E(f317(f317(f91(f906(x40741,a895)),f317(f317(f91(f906(x40741,a895)),x40742),x40743)),x40744),f317(f317(f91(f906(x40741,a895)),x40742),f317(f317(f91(f906(x40741,a895)),x40743),x40744))) % 112.26/112.09 [4075]E(f317(f317(f92(f906(x40751,a895)),f317(f317(f92(f906(x40751,a895)),x40752),x40753)),x40754),f317(f317(f92(f906(x40751,a895)),x40752),f317(f317(f92(f906(x40751,a895)),x40753),x40754))) % 112.26/112.09 [4112]E(f317(f317(f91(f906(f905(x41121,x41122),a895)),f317(f276(x41122,x41121),x41123)),f317(f276(x41122,x41121),x41124)),f317(f276(x41122,x41121),f317(f317(f91(f906(f905(x41122,x41121),a895)),x41123),x41124))) % 112.26/112.09 [4113]E(f317(f317(f92(f906(f905(x41131,x41132),a895)),f317(f276(x41132,x41131),x41133)),f317(f276(x41132,x41131),x41134)),f317(f276(x41132,x41131),f317(f317(f92(f906(f905(x41132,x41131),a895)),x41133),x41134))) % 112.26/112.09 [4126]E(f317(f317(f91(f906(x41261,f906(x41262,a895))),f233(x41262,x41261,x41263)),f233(x41262,x41261,x41264)),f233(x41262,x41261,f317(f317(f91(f906(x41262,f906(x41261,a895))),x41263),x41264))) % 112.26/112.09 [4127]E(f317(f317(f92(f906(x41271,f906(x41272,a895))),f233(x41272,x41271,x41273)),f233(x41272,x41271,x41274)),f233(x41272,x41271,f317(f317(f92(f906(x41272,f906(x41271,a895))),x41273),x41274))) % 112.26/112.09 [4181]E(f317(f317(f91(f906(x41811,a895)),f317(f317(f3(f906(x41811,a895)),x41812),x41813)),f317(f317(f3(f906(x41811,a895)),x41814),x41813)),f317(f317(f3(f906(x41811,a895)),f317(f317(f91(f906(x41811,a895)),x41812),x41814)),x41813)) % 112.26/112.09 [4182]E(f317(f317(f92(f906(x41821,a895)),f317(f317(f91(f906(x41821,a895)),x41822),x41823)),f317(f317(f91(f906(x41821,a895)),x41824),x41823)),f317(f317(f91(f906(x41821,a895)),f317(f317(f92(f906(x41821,a895)),x41822),x41824)),x41823)) % 112.26/112.09 [4183]E(f317(f317(f3(f906(x41831,a895)),f317(f317(f92(f906(x41831,a895)),x41832),x41833)),f317(f317(f92(f906(x41831,a895)),x41834),x41833)),f317(f317(f92(f906(x41831,a895)),f317(f317(f3(f906(x41831,a895)),x41832),x41834)),x41833)) % 112.26/112.09 [4184]E(f317(f317(f91(f906(x41841,a895)),f317(f317(f92(f906(x41841,a895)),x41842),x41843)),f317(f317(f92(f906(x41841,a895)),x41844),x41843)),f317(f317(f92(f906(x41841,a895)),f317(f317(f91(f906(x41841,a895)),x41842),x41844)),x41843)) % 112.26/112.09 [4185]E(f317(f317(f3(f906(x41851,a895)),f317(f317(f92(f906(x41851,a895)),x41852),x41853)),f317(f317(f92(f906(x41851,a895)),x41854),x41853)),f317(f317(f3(f906(x41851,a895)),f317(f317(f92(f906(x41851,a895)),x41852),x41853)),x41854)) % 112.26/112.09 [4197]E(f317(f317(f3(f906(x41971,a895)),f317(f317(f3(f906(x41971,a895)),x41972),f317(f317(f299(x41971),x41973),f178(f906(x41971,a895))))),x41974),f317(f317(f3(f906(x41971,a895)),x41972),f317(f317(f299(x41971),x41973),x41974))) % 112.26/112.09 [4250]E(f317(f317(f91(f906(x42501,a895)),f317(f317(f299(x42501),x42502),f317(f317(f299(x42501),x42503),f178(f906(x42501,a895))))),f317(f271(x42501),x42504)),f317(f271(x42501),f317(f317(f299(f905(x42501,x42501)),f317(f317(f242(x42501,x42501),x42502),x42503)),x42504))) % 112.26/112.09 [4275]E(f317(f317(f36(a899,f906(x42751,a895)),f317(f291(a899),x42752)),f317(f317(f10(a899,f906(x42751,a895),a899),x42753),f317(f317(f9(a899,a899,a899),f74(a899)),x42754))),f317(f317(f36(a899,f906(x42751,a895)),f293(a899,x42754,f317(f317(f74(a899),x42752),x42754))),x42753)) % 112.26/112.09 [4276]E(f164(x42761,f317(f275(x42761,x42761,x42762),f317(f317(f299(x42761),x42763),f178(f906(x42761,a895)))),f317(f275(f900(x42761),f900(x42761),f148(x42761,x42762)),f317(f317(f299(f900(x42761)),x42764),f178(f906(f900(x42761),a895))))),f317(f275(f900(x42761),f900(x42761),f148(x42761,x42762)),f317(f317(f299(f900(x42761)),f317(f317(f141(x42761),x42763),x42764)),f178(f906(f900(x42761),a895))))) % 112.26/112.09 [4340]E(f317(f252(x43401),f317(f317(f9(x43401,f906(x43402,a895),a895),f317(f317(f10(x43402,f906(f906(x43402,a895),a895),x43401),f319(x43402)),x43403)),x43404)),f317(f301(x43401,x43402,x43403),x43404)) % 112.26/112.09 [4430]E(f317(f252(x44301),f317(f317(f9(x44301,f906(f905(x44302,x44301),a895),a895),f317(f317(f10(f905(x44302,x44301),f906(f906(f905(x44302,x44301),a895),a895),x44301),f319(f905(x44302,x44301))),f317(f242(x44302,x44301),x44303))),x44304)),f317(f275(x44302,x44301,x44304),f317(f317(f299(x44302),x44303),f178(f906(x44302,a895))))) % 112.26/112.09 [4444]E(f317(f317(f144(f905(x44441,a899),x44441),f241(x44441,a899)),f317(f126(f905(x44441,a899),f317(f317(f10(a899,a895,f905(x44441,a899)),x44442),f317(f317(f10(a899,a899,f905(x44441,a899)),a102),f246(x44441,a899)))),f317(f317(f171(x44441,a899),x44443),x44444))),f317(f317(f144(f905(x44441,a899),x44441),f241(x44441,a899)),f317(f126(f905(x44441,a899),f317(f317(f10(a899,a895,f905(x44441,a899)),x44442),f246(x44441,a899))),f317(f317(f171(x44441,a899),x44443),f317(f317(f144(a899,a899),a102),x44444))))) % 112.26/112.09 [4453]P1(f317(f317(f224(f906(f906(x44531,a895),a895)),f317(f317(f36(x44532,f906(f906(x44531,a895),a895)),x44533),f317(f317(f10(f906(x44531,a895),f906(f906(x44531,a895),a895),x44532),f298(x44531)),x44534))),f317(f298(x44531),f317(f317(f36(x44532,f906(x44531,a895)),x44533),x44534)))) % 112.26/112.09 [4494]E(f317(f317(f80(a1,x44941),f317(f94(a1),f317(f317(f74(a1),x44942),a87))),f317(f317(f20(a1,x44941,x44941),f317(f317(f9(a1,x44941,f906(x44941,x44941)),f317(f317(f10(a895,f906(x44941,f906(x44941,x44941)),a1),f86(x44941)),a183)),x44943)),f317(f317(f20(a1,x44941,x44941),f317(f317(f10(a899,f906(x44941,x44941),a1),x44944),a95)),f317(f317(f10(a899,x44941,a1),f174(x44941,x44943,x44944)),a95)))),f317(f174(x44941,x44943,x44944),f317(f94(a899),x44942))) % 112.26/112.09 [4518]E(f317(f252(f905(x45181,x45182)),f317(f247(x45181,x45182,a895),f317(f317(f9(x45181,f906(x45182,a895),f906(x45182,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x45182,a895),f906(x45182,a895)),x45181),f10(a895,a895,x45182)),f317(f317(f10(a895,f906(a895,a895),x45181),a315),f317(f317(f9(x45181,f906(x45181,a895),a895),f319(x45181)),x45183)))),f317(f317(f9(x45182,f906(x45182,a895),a895),f319(x45182)),x45184)))),f219(x45181,x45182,x45183,x45184)) % 112.26/112.09 [4554]E(f317(f317(f36(x45541,f906(f905(x45541,x45542),a895)),x45543),f317(f317(f20(x45541,f906(x45542,f906(f905(x45541,x45542),a895)),f906(f905(x45541,x45542),a895)),f317(f317(f10(f906(x45542,a895),f906(f906(x45542,f906(f905(x45541,x45542),a895)),f906(f905(x45541,x45542),a895)),x45541),f36(x45542,f906(f905(x45541,x45542),a895))),x45544)),f317(f317(f9(x45541,f906(f905(x45541,x45542),a895),f906(x45542,f906(f905(x45541,x45542),a895))),f317(f317(f10(f906(x45542,f906(f906(f905(x45541,x45542),a895),f906(f905(x45541,x45542),a895))),f906(f906(f905(x45541,x45542),a895),f906(x45542,f906(f905(x45541,x45542),a895))),x45541),f9(x45542,f906(f905(x45541,x45542),a895),f906(f905(x45541,x45542),a895))),f317(f317(f10(f906(x45542,f905(x45541,x45542)),f906(x45542,f906(f906(f905(x45541,x45542),a895),f906(f905(x45541,x45542),a895))),x45541),f317(f10(f905(x45541,x45542),f906(f906(f905(x45541,x45542),a895),f906(f905(x45541,x45542),a895)),x45542),f299(f905(x45541,x45542)))),f242(x45541,x45542)))),f178(f906(f905(x45541,x45542),a895))))),f317(f317(f244(x45541,x45542),x45543),x45544)) % 112.26/112.09 [4121]E(f317(f317(f124(x41211),f317(f317(f165(x41211),x41212),x41213)),f317(f317(f165(x41211),f317(f317(f3(a899),x41212),f317(f179(f900(x41211)),x41213))),x41214)),f317(f317(f165(x41211),x41212),f317(f317(f124(x41211),x41213),x41214))) % 112.26/112.09 [4122]E(f317(f317(f124(x41221),f317(f317(f128(x41221),x41222),x41223)),f317(f317(f128(x41221),f317(f317(f3(a899),x41222),f317(f179(f900(x41221)),x41223))),x41224)),f317(f317(f128(x41221),x41222),f317(f317(f124(x41221),x41223),x41224))) % 112.26/112.09 [4171]E(f317(f317(f74(a899),f317(f317(f75(a899),x41711),x41712)),f317(f317(f74(a899),f317(f317(f75(a899),x41713),x41712)),x41714)),f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f74(a899),x41711),x41713)),x41712)),x41714)) % 112.26/112.09 [4316]E(f84(x43161,f317(f317(f9(x43161,x43162,a895),f317(f317(f10(x43162,f906(x43162,a895),x43161),a314),x43163)),x43164)),f317(f85(x43161,x43162,f232(f906(x43161,a895)),x43163),x43164)) % 112.26/112.09 [4364]P1(f317(f317(f224(f906(x43641,a895)),f317(f317(f3(f906(x43641,a895)),f317(f274(x43642,x43641),x43643)),f317(f274(x43642,x43641),x43644))),f317(f274(x43642,x43641),f317(f317(f3(f906(f905(x43642,x43641),a895)),x43643),x43644)))) % 112.26/112.09 [4365]P1(f317(f317(f224(f906(x43651,a895)),f317(f317(f3(f906(x43651,a895)),f317(f254(x43651,x43652),x43653)),f317(f254(x43651,x43652),x43654))),f317(f254(x43651,x43652),f317(f317(f3(f906(f905(x43651,x43652),a895)),x43653),x43654)))) % 112.26/112.09 [4473]E(f317(f317(f74(a1),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x44731),x44732)),f178(f906(f905(a899,a899),a895)))))),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x44733),x44734)),f178(f906(f905(a899,a899),a895)))))),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),f317(f317(f74(a899),x44731),x44733)),f317(f317(f74(a899),x44732),x44734))),f178(f906(f905(a899,a899),a895)))))) % 112.26/112.09 [4513]E(f317(f317(f75(a1),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x45131),x45132)),f178(f906(f905(a899,a899),a895)))))),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x45133),x45134)),f178(f906(f905(a899,a899),a895)))))),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),f317(f317(f74(a899),f317(f317(f75(a899),x45131),x45133)),f317(f317(f75(a899),x45132),x45134))),f317(f317(f74(a899),f317(f317(f75(a899),x45131),x45134)),f317(f317(f75(a899),x45132),x45133)))),f178(f906(f905(a899,a899),a895)))))) % 112.26/112.09 [4534]E(f317(f252(x45341),f317(f317(f10(f906(x45342,a895),a895,x45341),f82(x45342)),f317(f317(f10(f906(x45342,a895),f906(x45342,a895),x45341),f317(f20(x45342,a895,a895),f317(f317(f10(a895,f906(a895,a895),x45342),a320),f317(f317(f9(x45342,f906(x45342,a895),a895),f319(x45342)),x45343)))),f317(f317(f9(x45341,f906(x45342,f906(x45341,a895)),f906(x45342,a895)),f317(f317(f10(f906(f906(x45341,a895),a895),f906(f906(x45342,f906(x45341,a895)),f906(x45342,a895)),x45341),f10(f906(x45341,a895),a895,x45342)),f319(x45341))),x45344)))),f317(f317(f35(x45342,f906(x45341,a895)),x45343),x45344)) % 112.26/112.09 [4566]E(f317(f317(f279(x45661,x45661,x45661),f317(f317(f299(f905(x45661,x45661)),f317(f317(f242(x45661,x45661),x45662),x45663)),x45664)),f297(x45661,f317(f317(f299(f905(x45661,x45661)),f317(f317(f242(x45661,x45661),x45662),x45663)),x45664))),f317(f317(f91(f906(f905(x45661,x45661),a895)),f317(f317(f279(x45661,x45661,x45661),x45664),f297(x45661,x45664))),f317(f252(f905(x45661,x45661)),f317(f247(x45661,x45661,a895),f317(f317(f9(x45661,f906(x45661,a895),f906(x45661,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x45661,a895),f906(x45661,a895)),x45661),f10(a895,a895,x45661)),f317(f317(f10(a895,f906(a895,a895),x45661),a315),f317(f317(f9(x45661,f906(f905(x45661,x45661),a895),a895),f317(f317(f10(f905(x45661,x45661),f906(f906(f905(x45661,x45661),a895),a895),x45661),f319(f905(x45661,x45661))),f317(f317(f9(x45661,x45661,f905(x45661,x45661)),f242(x45661,x45661)),x45662))),f297(x45661,x45664))))),f317(f317(f9(x45661,f906(f905(x45661,x45661),a895),a895),f317(f317(f10(f905(x45661,x45661),f906(f906(f905(x45661,x45661),a895),a895),x45661),f319(f905(x45661,x45661))),f317(f242(x45661,x45661),x45663))),f297(x45661,x45664))))))) % 112.26/112.09 [4366]E(f317(f126(x43661,f317(f317(f20(x43661,a895,a895),f317(f317(f10(a895,f906(a895,a895),x43661),a315),x43662)),x43663)),x43664),f317(f126(x43661,x43663),f317(f126(x43661,x43662),x43664))) % 112.26/112.09 [4467]E(f317(f317(f124(x44671),f317(f317(f317(f86(f900(x44671)),f317(f317(f319(a899),f2(a899)),x44672)),f317(f317(f141(x44671),x44673),f103(x44671))),f103(x44671))),f166(x44671,x44674,f317(f252(a899),f317(f317(f9(a899,f906(a899,a895),a895),f317(f317(f10(a899,f906(f906(a899,a895),a895),a899),f319(a899)),a102)),x44672)))),f166(x44671,f317(f317(f141(x44671),x44673),x44674),x44672)) % 112.26/112.09 [4562]E(f317(f252(f905(x45621,x45622)),f317(f317(f10(f906(a899,a895),a895,f905(x45621,x45622)),f81(a899)),f317(f317(f9(f905(x45621,x45622),f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),f905(x45621,x45622)),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),f905(x45621,x45622)),f317(f10(a895,f906(a895,a895),a899),a315)),f317(f317(f9(f905(x45621,x45622),f906(a899,f905(x45621,x45622)),f906(a899,a895)),f317(f317(f10(f906(f905(x45621,x45622),a895),f906(f906(a899,f905(x45621,x45622)),f906(a899,a895)),f905(x45621,x45622)),f10(f905(x45621,x45622),a895,a899)),a314)),f317(f317(f20(a899,x45622,f905(x45621,x45622)),f317(f317(f10(x45621,f906(x45622,f905(x45621,x45622)),a899),f242(x45621,x45622)),f317(f154(x45621),x45623))),f317(f154(x45622),x45624)))))),f317(f317(f9(a899,a899,a895),f225(a899)),f317(f317(f228(a899),f317(f179(f900(x45621)),x45623)),f317(f179(f900(x45622)),x45624)))))),f317(f162(f905(x45621,x45622)),f317(f317(f171(x45621,x45622),x45623),x45624))) % 112.26/112.09 [4486]E(f317(f252(f905(x44861,x44862)),f317(f247(x44861,x44862,a895),f317(f317(f9(x44861,f906(x44862,a895),f906(x44862,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x44862,a895),f906(x44862,a895)),x44861),f10(a895,a895,x44862)),f317(f317(f10(a895,f906(a895,a895),x44861),a315),x44863))),x44864))),f317(f317(f244(x44861,x44862),f317(f252(x44861),x44863)),f317(f18(f906(x44862,a895),x44861),f317(f252(x44862),x44864)))) % 112.26/112.09 [4489]E(f317(f252(f905(x44891,x44892)),f317(f247(x44891,x44892,a895),f317(f317(f20(x44891,f906(x44892,a895),f906(x44892,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x44892,a895),f906(x44892,a895)),x44891),f10(a895,a895,x44892)),f317(f317(f10(a895,f906(a895,a895),x44891),a315),x44893))),x44894))),f317(f317(f244(x44891,x44892),f317(f252(x44891),x44893)),f317(f317(f10(f906(x44892,a895),f906(x44892,a895),x44891),f252(x44892)),x44894))) % 112.26/112.09 [4501]E(f317(f252(x45011),f317(f317(f10(f906(x45012,a895),a895,x45011),f82(x45012)),f317(f317(f10(f906(x45012,a895),f906(x45012,a895),x45011),f317(f20(x45012,a895,a895),f317(f317(f10(a895,f906(a895,a895),x45012),a320),f317(f317(f9(x45012,f906(x45012,a895),a895),f319(x45012)),x45013)))),x45014))),f317(f317(f35(x45012,f906(x45011,a895)),x45013),f317(f317(f10(f906(x45011,a895),f906(x45011,a895),x45012),f252(x45011)),f317(f9(x45011,x45012,a895),x45014)))) % 112.26/112.09 [4546]E(f317(f317(f144(f905(x45461,a899),x45461),f241(x45461,a899)),f317(f126(f905(x45461,a899),f317(f317(f9(f905(x45461,a899),f906(a899,a895),a895),f317(f317(f10(a899,f906(f906(a899,a895),a895),f905(x45461,a899)),f319(a899)),f246(x45461,a899))),x45462)),f317(f317(f171(x45461,a899),x45463),f129(a899,f317(f292(a899,x45464),f317(f317(f74(a899),x45464),f317(f179(f900(x45461)),x45463))))))),f317(f317(f144(f905(x45461,a899),x45461),f241(x45461,a899)),f317(f126(f905(x45461,a899),f317(f317(f9(f905(x45461,a899),f906(a899,a895),a895),f317(f317(f10(a899,f906(f906(a899,a895),a895),f905(x45461,a899)),f319(a899)),f317(f317(f9(f905(x45461,a899),a899,a899),f317(f317(f10(a899,f906(a899,a899),f905(x45461,a899)),f74(a899)),f246(x45461,a899))),x45464))),x45462)),f317(f317(f171(x45461,a899),x45463),f129(a899,f317(f292(a899,f2(a899)),f317(f179(f900(x45461)),x45463))))))) % 112.26/112.09 [4547]E(f317(a102,f317(f317(f223(a899),f317(f179(f900(x45471)),x45472)),f317(f132(a899,f900(x45473),f317(f9(f900(x45473),a899,a899),f317(f317(f10(a899,f906(a899,a899),f900(x45473)),f223(a899)),f317(f317(f9(f900(x45473),a899,a899),f317(f317(f10(a899,f906(a899,a899),f900(x45473)),f3(a899)),f179(f900(x45473)))),f317(a102,f2(a899))))),f2(a899)),f317(f158(f900(x45473)),f317(f126(f900(x45473),f317(f317(f10(a895,a895,f900(x45473)),a312),f317(f317(f9(f900(x45473),f900(x45473),a895),a314),f103(x45473)))),x45474))))),f317(f317(f223(a899),f317(a102,f317(f179(f900(x45471)),x45472))),f317(f132(a899,f900(x45473),f317(f9(f900(x45473),a899,a899),f317(f317(f10(a899,f906(a899,a899),f900(x45473)),f223(a899)),f179(f900(x45473)))),f2(a899)),f317(f158(f900(x45473)),x45474)))) % 112.26/112.09 [4500]E(f317(f317(f124(x45001),f166(x45001,x45002,x45003)),f166(x45001,x45004,f317(f252(a899),f317(f317(f9(a899,f906(a899,a895),a895),f317(f317(f10(a899,f906(f906(a899,a895),a895),a899),f319(a899)),f317(f317(f9(a899,a899,a899),f74(a899)),f317(f179(f900(x45001)),x45002)))),x45003)))),f166(x45001,f317(f317(f124(x45001),x45002),x45004),x45003)) % 112.26/112.09 [4548]E(f33(f906(x45481,a895),f317(f252(f906(x45481,a895)),f317(f317(f10(f906(x45482,a895),a895,f906(x45481,a895)),f81(x45482)),f317(f317(f10(f906(x45482,a895),f906(x45482,a895),f906(x45481,a895)),f317(f20(x45482,a895,a895),f317(f317(f10(a895,f906(a895,a895),x45482),a315),f317(f317(f9(x45482,f906(x45482,a895),a895),f319(x45482)),x45483)))),f317(f317(f9(f906(x45481,a895),f906(x45482,f906(x45481,a895)),f906(x45482,a895)),f317(f317(f10(f906(f906(x45481,a895),a895),f906(f906(x45482,f906(x45481,a895)),f906(x45482,a895)),f906(x45481,a895)),f10(f906(x45481,a895),a895,x45482)),a314)),x45484))))),f317(f317(f35(x45482,f906(x45481,a895)),x45483),x45484)) % 112.26/112.09 [4549]E(f32(f906(x45491,a895),f317(f252(f906(x45491,a895)),f317(f317(f10(f906(x45492,a895),a895,f906(x45491,a895)),f81(x45492)),f317(f317(f10(f906(x45492,a895),f906(x45492,a895),f906(x45491,a895)),f317(f20(x45492,a895,a895),f317(f317(f10(a895,f906(a895,a895),x45492),a315),f317(f317(f9(x45492,f906(x45492,a895),a895),f319(x45492)),x45493)))),f317(f317(f9(f906(x45491,a895),f906(x45492,f906(x45491,a895)),f906(x45492,a895)),f317(f317(f10(f906(f906(x45491,a895),a895),f906(f906(x45492,f906(x45491,a895)),f906(x45492,a895)),f906(x45491,a895)),f10(f906(x45491,a895),a895,x45492)),a314)),x45494))))),f317(f317(f36(x45492,f906(x45491,a895)),x45493),x45494)) % 112.26/112.09 [4556]E(f317(f317(f141(f900(x45561)),f317(f317(f141(x45561),x45562),f317(f132(f900(x45561),f900(x45561),f124(x45561),f103(x45561)),f317(f317(f144(f900(x45561),f900(x45561)),f146(f900(x45561),x45561,f103(x45561),f317(f317(f10(f900(x45561),f906(f900(x45561),f900(x45561)),x45561),f18(f900(x45561),f900(x45561))),f317(f317(f9(x45561,f900(x45561),f900(x45561)),f141(x45561)),f103(x45561))))),x45563)))),f169(x45561,f317(f317(f141(f900(x45561)),x45564),f317(f132(f900(f900(x45561)),f900(f900(x45561)),f124(f900(x45561)),f103(f900(x45561))),f317(f317(f144(f900(x45561),f900(f900(x45561))),f146(f900(f900(x45561)),x45561,f103(f900(x45561)),f317(f18(f906(f900(x45561),f900(f900(x45561))),x45561),f317(f317(f9(f900(x45561),f900(f900(x45561)),f900(f900(x45561))),f141(f900(x45561))),f103(f900(x45561)))))),x45563))))),f169(x45561,f317(f317(f141(f900(x45561)),f317(f317(f141(x45561),x45562),x45564)),x45563))) % 112.26/112.09 [4563]E(f317(f252(f905(x45631,x45631)),f317(f247(x45631,x45631,a895),f317(f317(f9(x45631,f906(f905(x45632,x45632),a895),f906(x45631,a895)),f317(f317(f10(f906(x45631,f906(f906(f905(x45632,x45632),a895),a895)),f906(f906(f905(x45632,x45632),a895),f906(x45631,a895)),x45631),f9(x45631,f906(f905(x45632,x45632),a895),a895)),f317(f317(f10(f906(x45631,f905(x45632,x45632)),f906(x45631,f906(f906(f905(x45632,x45632),a895),a895)),x45631),f317(f10(f905(x45632,x45632),f906(f906(f905(x45632,x45632),a895),a895),x45631),f319(f905(x45632,x45632)))),f317(f317(f9(x45631,f906(x45631,x45632),f906(x45631,f905(x45632,x45632))),f317(f317(f10(f906(x45632,f905(x45632,x45632)),f906(f906(x45631,x45632),f906(x45631,f905(x45632,x45632))),x45631),f10(x45632,f905(x45632,x45632),x45631)),f317(f317(f10(x45632,f906(x45632,f905(x45632,x45632)),x45631),f242(x45632,x45632)),x45633))),x45633)))),x45634))),f317(f317(f278(x45632,x45631),x45634),x45633)) % 112.26/112.09 [3705]E(f317(f317(f144(x37051,x37052),x37053),f159(x37051,x37054,x37055)),f159(x37052,x37054,f317(x37053,x37055))) % 112.26/112.09 [4035]E(f120(x40351,x40352,x40353,f116(x40351,x40354,x40355)),f116(x40352,f317(x40353,x40354),f120(x40351,x40352,x40353,x40355))) % 112.26/112.09 [4265]E(f317(f69(x42651,x42652,x42653,x42654,x42655),x42654),x42655) % 112.26/112.09 [4317]E(f243(x43171,x43172,x43173,f233(x43172,x43171,x43174),f233(x43173,x43172,x43175)),f233(x43173,x43171,f243(x43173,x43172,x43171,x43175,x43174))) % 112.26/112.09 [3896]E(f317(f317(f247(x38961,x38962,x38963),x38964),x38965),f317(f317(x38964,f317(f241(x38961,x38962),x38965)),f317(f246(x38961,x38962),x38965))) % 112.26/112.09 [3930]E(f317(f317(f317(f60(x39301,x39302,x39303),x39304),x39305),f178(f906(x39302,a895))),x39305) % 112.26/112.09 [4205]E(f317(f67(f900(x42051),f900(x42052),f900(x42053),f317(f144(x42051,x42052),x42054)),f317(f144(x42053,x42051),x42055)),f317(f144(x42053,x42052),f317(f67(x42051,x42052,x42053,x42054),x42055))) % 112.26/112.09 [4279]E(f79(x42791,f61(x42792,x42791,x42793,x42794,x42795)),f317(f317(f59(x42792,x42791,x42793),x42794),x42795)) % 112.26/112.09 [4313]E(f317(f317(f74(a899),f317(f317(f74(a899),f317(x43131,f317(f241(x43132,x43133),x43134))),f317(x43135,f317(f246(x43132,x43133),x43134)))),f317(a102,f2(a899))),f251(x43132,x43133,x43131,x43135,x43134)) % 112.26/112.09 [3833]E(f317(f317(f165(x38331),x38332),f317(f317(f144(x38333,x38331),x38334),x38335)),f317(f317(f144(x38333,x38331),x38334),f317(f317(f165(x38333),x38332),x38335))) % 112.26/112.09 [3834]E(f317(f317(f128(x38341),x38342),f317(f317(f144(x38343,x38341),x38344),x38345)),f317(f317(f144(x38343,x38341),x38344),f317(f317(f128(x38343),x38342),x38345))) % 112.26/112.09 [3865]E(f317(f317(f144(x38651,x38652),x38653),f317(f317(f141(x38651),x38654),x38655)),f317(f317(f141(x38652),f317(x38653,x38654)),f317(f317(f144(x38651,x38652),x38653),x38655))) % 112.26/112.09 [3926]E(f317(f300(x39261,x39262,x39263),f317(f317(f299(x39261),x39264),x39265)),f317(f317(f299(x39262),f317(x39263,x39264)),f317(f300(x39261,x39262,x39263),x39265))) % 112.26/112.09 [3954]E(f163(x39541,f317(f317(f141(x39541),x39542),x39543),f317(f317(f141(x39541),x39544),x39545)),f317(f317(f141(x39541),x39542),f317(f317(f141(x39541),x39544),f163(x39541,x39543,x39545)))) % 112.26/112.09 [3990]E(f317(f317(f171(x39901,x39902),f317(f317(f165(x39901),x39903),x39904)),f317(f317(f165(x39902),x39903),x39905)),f317(f317(f165(f905(x39901,x39902)),x39903),f317(f317(f171(x39901,x39902),x39904),x39905))) % 112.26/112.09 [3991]E(f317(f317(f171(x39911,x39912),f317(f317(f128(x39911),x39913),x39914)),f317(f317(f128(x39912),x39913),x39915)),f317(f317(f128(f905(x39911,x39912)),x39913),f317(f317(f171(x39911,x39912),x39914),x39915))) % 112.26/112.09 [4000]E(f317(f317(f149(x40001,f317(f317(f141(x40001),x40002),x40003)),f317(a102,x40004)),x40005),f317(f317(f141(x40001),x40002),f317(f317(f149(x40001,x40003),x40004),x40005))) % 112.26/112.09 [4003]E(f317(f317(f124(x40031),f317(f317(f144(x40032,x40031),x40033),x40034)),f317(f317(f144(x40032,x40031),x40033),x40035)),f317(f317(f144(x40032,x40031),x40033),f317(f317(f124(x40032),x40034),x40035))) % 112.26/112.09 [4007]E(f317(f317(x40071,x40072),f317(f317(f235(x40073,x40074,x40071),x40072),x40075)),f317(f317(f235(x40073,x40074,x40071),x40072),f317(a102,x40075))) % 112.26/112.09 [4039]E(f153(x40391,x40392,x40393,f317(f317(f141(x40391),x40394),x40395)),f317(f317(f124(x40392),f317(x40393,x40394)),f153(x40391,x40392,x40393,x40395))) % 112.26/112.09 [4051]E(f317(f317(f279(x40511,x40512,x40513),f317(f276(x40512,x40511),x40514)),f317(f276(x40513,x40512),x40515)),f317(f276(x40513,x40511),f317(f317(f279(x40513,x40512,x40511),x40515),x40514))) % 112.26/112.09 [4083]E(f317(f317(f317(f173(f900(x40831),f900(x40831)),x40832),f157(x40831)),f317(f317(f144(x40833,x40831),x40834),x40835)),f317(f317(f144(x40833,x40831),x40834),f317(f317(f317(f173(f900(x40833),f900(x40833)),x40832),f157(x40833)),x40835))) % 112.26/112.09 [4084]E(f317(f317(f249(x40841,x40842,x40841,x40843),f317(f242(x40842,x40841),x40844)),x40845),f317(x40845,x40844)) % 112.26/112.09 [4107]E(f145(x41071,x41072,f317(f317(f144(x41073,x41071),x41074),x41075)),f145(x41073,f317(f67(x41071,a899,x41073,x41072),x41074),x41075)) % 112.26/112.09 [4170]E(f167(f905(x41701,x41702),f317(f67(x41702,a895,f905(x41701,x41702),x41703),f246(x41701,x41702)),f317(f317(f171(x41701,x41702),x41704),x41705)),f317(f317(f171(x41701,x41702),x41704),f167(x41702,x41703,x41705))) % 112.26/112.09 [4175]E(f317(f300(x41751,x41752,f317(f317(f10(x41753,x41752,x41751),x41754),x41755)),f232(f906(x41751,a895))),f317(f300(x41753,x41752,x41754),f317(f300(x41751,x41753,x41755),f232(f906(x41751,a895))))) % 112.26/112.09 [4188]E(f167(f905(x41881,x41882),f317(f67(x41881,a895,f905(x41881,x41882),x41883),f241(x41881,x41882)),f317(f317(f171(x41881,x41882),x41884),x41885)),f317(f317(f171(x41881,x41882),f167(x41881,x41883,x41884)),x41885)) % 112.26/112.09 [4209]E(f317(f317(f91(f906(x42091,a895)),f317(f301(x42091,x42092,x42093),f317(f317(f299(x42092),x42094),f178(f906(x42092,a895))))),f317(f301(x42091,x42092,x42093),x42095)),f317(f301(x42091,x42092,x42093),f317(f317(f299(x42092),x42094),x42095))) % 112.26/112.09 [4264]E(f317(f317(f124(f905(x42641,x42642)),f317(f317(f144(x42642,f905(x42641,x42642)),f317(f242(x42641,x42642),x42643)),x42644)),f55(x42641,x42642,x42645,x42644)),f55(x42641,x42642,f317(f317(f141(x42641),x42643),x42645),x42644)) % 112.26/112.09 [4266]E(f317(f317(f144(x42661,x42662),x42663),f167(x42661,f317(f67(x42662,a895,x42661,x42664),x42663),x42665)),f167(x42662,x42664,f317(f317(f144(x42661,x42662),x42663),x42665))) % 112.26/112.09 [4271]E(f317(f132(x42711,x42712,f317(f9(x42712,x42711,x42711),f317(f9(x42711,x42712,x42711),x42713)),x42714),f317(f158(x42712),f317(f158(x42712),x42715))),f317(f132(x42711,x42712,x42713,x42714),x42715)) % 112.26/112.09 [4374]P1(f317(f317(f224(f906(x43741,a895)),f317(f300(x43742,x43741,x43743),f317(f317(f92(f906(x43742,a895)),x43744),x43745))),f317(f317(f92(f906(x43741,a895)),f317(f300(x43742,x43741,x43743),x43744)),f317(f300(x43742,x43741,x43743),x43745)))) % 112.26/112.09 [4375]P1(f317(f317(f224(f906(x43751,a895)),f317(f275(x43752,x43751,x43753),f317(f317(f92(f906(x43752,a895)),x43754),x43755))),f317(f317(f92(f906(x43751,a895)),f317(f275(x43752,x43751,x43753),x43754)),f317(f275(x43752,x43751,x43753),x43755)))) % 112.26/112.09 [4474]E(f317(f246(x44741,x44742),f317(f248(x44743,x44741,x44742,x44742,x44744,f25(x44742)),x44745)),f317(f246(x44743,x44742),x44745)) % 112.26/112.09 [4475]E(f317(f241(x44751,x44752),f317(f248(x44751,x44751,x44753,x44752,f25(x44751),x44754),x44755)),f317(f241(x44751,x44753),x44755)) % 112.26/112.09 [3677]E(f317(f317(f317(f317(f194(x36771),x36772),x36773),x36774),x36775),f182(x36771,x36772)) % 112.26/112.09 [3678]E(f317(f317(f317(f317(f198(x36781),x36782),x36783),x36784),x36785),f189(x36781,x36782)) % 112.26/112.09 [4040]E(f317(f317(f35(x40401,f906(x40402,a895)),f317(f317(f299(x40401),x40403),x40404)),x40405),f317(f317(f92(f906(x40402,a895)),f317(x40405,x40403)),f317(f317(f35(x40401,f906(x40402,a895)),x40404),x40405))) % 112.26/112.09 [4041]E(f317(f317(f36(x40411,f906(x40412,a895)),f317(f317(f299(x40411),x40413),x40414)),x40415),f317(f317(f91(f906(x40412,a895)),f317(x40415,x40413)),f317(f317(f36(x40411,f906(x40412,a895)),x40414),x40415))) % 112.26/112.09 [4091]E(f317(f108(x40911,x40912,f317(x40913,x40914)),f317(f317(f9(x40911,a89,f901(x40912)),x40915),x40914)),f317(f187(x40911,x40912,x40913,x40915),x40914)) % 112.26/112.09 [4101]E(f317(f317(f91(f906(x41011,a895)),f317(f300(x41012,x41011,x41013),x41014)),f317(f300(x41012,x41011,x41013),x41015)),f317(f300(x41012,x41011,x41013),f317(f317(f91(f906(x41012,a895)),x41014),x41015))) % 112.26/112.09 [4102]E(f317(f317(f91(f906(x41021,a895)),f317(f275(x41022,x41021,x41023),x41024)),f317(f275(x41022,x41021,x41023),x41025)),f317(f275(x41022,x41021,x41023),f317(f317(f91(f906(x41022,a895)),x41024),x41025))) % 112.26/112.09 [4103]E(f317(f317(f3(f906(x41031,a895)),f317(f301(x41031,x41032,x41033),x41034)),f317(f301(x41031,x41032,x41033),x41035)),f317(f301(x41031,x41032,x41033),f317(f317(f3(f906(x41032,a895)),x41034),x41035))) % 112.26/112.09 [4104]E(f317(f317(f91(f906(x41041,a895)),f317(f301(x41041,x41042,x41043),x41044)),f317(f301(x41041,x41042,x41043),x41045)),f317(f301(x41041,x41042,x41043),f317(f317(f91(f906(x41042,a895)),x41044),x41045))) % 112.26/112.09 [4105]E(f317(f317(f92(f906(x41051,a895)),f317(f301(x41051,x41052,x41053),x41054)),f317(f301(x41051,x41052,x41053),x41055)),f317(f301(x41051,x41052,x41053),f317(f317(f92(f906(x41052,a895)),x41054),x41055))) % 112.26/112.09 [4166]E(f317(f317(f149(x41661,f317(f317(f124(x41661),x41662),f317(f317(f141(x41661),x41663),x41664))),f317(f179(f900(x41661)),x41662)),x41665),f317(f317(f124(x41661),x41662),f317(f317(f141(x41661),x41665),x41664))) % 112.26/112.09 [4173]E(f317(f317(f35(x41731,f906(x41732,a895)),x41733),f317(f317(f10(f906(x41732,a895),f906(x41732,a895),x41731),f317(f299(x41732),x41734)),x41735)),f317(f317(f299(x41732),x41734),f317(f317(f35(x41731,f906(x41732,a895)),x41733),x41735))) % 112.26/112.09 [4326]E(f317(f317(f144(x43261,x43262),x43263),f317(f126(x43261,f317(f67(x43262,a895,x43261,x43264),x43263)),x43265)),f317(f126(x43262,x43264),f317(f317(f144(x43261,x43262),x43263),x43265))) % 112.26/112.09 [4332]E(f317(f179(f900(x43321)),f317(f126(x43321,x43322),f317(f317(f144(x43323,x43321),x43324),x43325))),f317(f179(f900(x43323)),f317(f126(x43323,f317(f67(x43321,a895,x43323,x43322),x43324)),x43325))) % 112.26/112.09 [4539]E(f317(f146(f900(f905(x45391,x45392)),x45392,f103(f905(x45391,x45392)),f317(f317(f9(x45392,f906(f900(x45392),f900(f905(x45391,x45392))),f906(f900(x45392),f900(f905(x45391,x45392)))),f317(f317(f10(f906(f900(f905(x45391,x45392)),f900(f905(x45391,x45392))),f906(f906(f900(x45392),f900(f905(x45391,x45392))),f906(f900(x45392),f900(f905(x45391,x45392)))),x45392),f10(f900(f905(x45391,x45392)),f900(f905(x45391,x45392)),f900(x45392))),f317(f317(f10(f905(x45391,x45392),f906(f900(f905(x45391,x45392)),f900(f905(x45391,x45392))),x45392),f141(f905(x45391,x45392))),f317(f242(x45391,x45392),x45393)))),f317(f171(x45391,x45392),x45394))),x45395),f317(f317(f171(x45391,x45392),f317(f317(f141(x45391),x45393),x45394)),x45395)) % 112.26/112.09 [4032]E(f317(f317(f149(x40321,f317(f317(f149(x40321,x40322),x40323),x40324)),x40323),x40325),f317(f317(f149(x40321,x40322),x40323),x40325)) % 112.26/112.09 [4085]E(f317(f274(x40851,x40852),f317(f317(f299(f905(x40851,x40852)),f317(f317(f242(x40851,x40852),x40853),x40854)),x40855)),f317(f317(f299(x40852),x40854),f317(f274(x40851,x40852),x40855))) % 112.26/112.09 [4086]E(f317(f254(x40861,x40862),f317(f317(f299(f905(x40861,x40862)),f317(f317(f242(x40861,x40862),x40863),x40864)),x40865)),f317(f317(f299(x40861),x40863),f317(f254(x40861,x40862),x40865))) % 112.26/112.09 [4131]E(f112(x41311,x41312,f317(x41313,x41314),f317(f317(f9(x41311,a89,f901(f902(x41312))),x41315),x41314)),f317(f185(x41311,x41312,x41313,x41315),x41314)) % 112.26/112.09 [4159]E(f317(f317(f3(f906(f905(x41591,x41592),a895)),f317(f317(f244(x41591,x41592),x41593),x41594)),f317(f317(f244(x41591,x41592),x41595),x41594)),f317(f317(f244(x41591,x41592),f317(f317(f3(f906(x41591,a895)),x41593),x41595)),x41594)) % 112.26/112.09 [4160]E(f317(f317(f91(f906(f905(x41601,x41602),a895)),f317(f317(f244(x41601,x41602),x41603),x41604)),f317(f317(f244(x41601,x41602),x41605),x41604)),f317(f317(f244(x41601,x41602),f317(f317(f91(f906(x41601,a895)),x41603),x41605)),x41604)) % 112.26/112.09 [4161]E(f317(f317(f92(f906(f905(x41611,x41612),a895)),f317(f317(f244(x41611,x41612),x41613),x41614)),f317(f317(f244(x41611,x41612),x41615),x41614)),f317(f317(f244(x41611,x41612),f317(f317(f92(f906(x41611,a895)),x41613),x41615)),x41614)) % 112.26/112.09 [4220]E(f317(f317(f92(f906(x42201,a895)),f317(f317(f35(x42202,f906(x42201,a895)),x42203),x42204)),f317(f317(f35(x42202,f906(x42201,a895)),x42205),x42204)),f317(f317(f35(x42202,f906(x42201,a895)),f317(f317(f91(f906(x42202,a895)),x42203),x42205)),x42204)) % 112.26/112.09 [4221]E(f317(f317(f91(f906(x42211,a895)),f317(f317(f36(x42212,f906(x42211,a895)),x42213),x42214)),f317(f317(f36(x42212,f906(x42211,a895)),x42215),x42214)),f317(f317(f36(x42212,f906(x42211,a895)),f317(f317(f91(f906(x42212,a895)),x42213),x42215)),x42214)) % 112.26/112.09 [4235]E(f317(f317(f35(x42351,f906(x42352,a895)),x42353),f317(f317(f10(f906(x42352,a895),f906(x42352,a895),x42351),f317(f91(f906(x42352,a895)),x42354)),x42355)),f317(f317(f91(f906(x42352,a895)),x42354),f317(f317(f35(x42351,f906(x42352,a895)),x42353),x42355))) % 112.26/112.09 [4236]E(f317(f317(f36(x42361,f906(x42362,a895)),x42363),f317(f317(f10(f906(x42362,a895),f906(x42362,a895),x42361),f317(f3(f906(x42362,a895)),x42364)),x42365)),f317(f317(f3(f906(x42362,a895)),x42364),f317(f317(f35(x42361,f906(x42362,a895)),x42363),x42365))) % 112.26/112.09 [4237]E(f317(f317(f36(x42371,f906(x42372,a895)),x42373),f317(f317(f10(f906(x42372,a895),f906(x42372,a895),x42371),f317(f92(f906(x42372,a895)),x42374)),x42375)),f317(f317(f92(f906(x42372,a895)),x42374),f317(f317(f36(x42371,f906(x42372,a895)),x42373),x42375))) % 112.26/112.09 [4291]E(f175(f900(x42911),f317(f317(f141(x42911),x42912),x42913),f317(f317(f10(f900(x42911),f900(x42911),a899),f317(f141(x42911),x42914)),f317(f317(f9(a899,x42911,f900(x42911)),f149(x42911,x42913)),x42912)),x42915),f317(f317(f149(x42911,f317(f317(f141(x42911),x42914),x42913)),x42915),x42912)) % 112.26/112.09 [4295]E(f317(f317(f35(x42951,f906(f905(x42952,x42953),a895)),x42954),f317(f317(f10(f906(f905(x42953,x42952),a895),f906(f905(x42952,x42953),a895),x42951),f276(x42953,x42952)),x42955)),f317(f276(x42953,x42952),f317(f317(f35(x42951,f906(f905(x42953,x42952),a895)),x42954),x42955))) % 112.26/112.09 [4296]E(f317(f317(f36(x42961,f906(f905(x42962,x42963),a895)),x42964),f317(f317(f10(f906(f905(x42963,x42962),a895),f906(f905(x42962,x42963),a895),x42961),f276(x42963,x42962)),x42965)),f317(f276(x42963,x42962),f317(f317(f36(x42961,f906(f905(x42963,x42962),a895)),x42964),x42965))) % 112.26/112.09 [4397]P1(f317(f317(f224(f906(x43971,a895)),f317(f317(f3(f906(x43971,a895)),f317(f300(x43972,x43971,x43973),x43974)),f317(f300(x43972,x43971,x43973),x43975))),f317(f300(x43972,x43971,x43973),f317(f317(f3(f906(x43972,a895)),x43974),x43975)))) % 112.26/112.09 [4542]E(f317(f146(f900(f905(x45421,x45422)),x45421,f103(f905(x45421,x45422)),f317(f317(f9(x45421,f906(f900(x45421),f900(f905(x45421,x45422))),f906(f900(x45421),f900(f905(x45421,x45422)))),f317(f317(f10(f906(f900(f905(x45421,x45422)),f900(f905(x45421,x45422))),f906(f906(f900(x45421),f900(f905(x45421,x45422))),f906(f900(x45421),f900(f905(x45421,x45422)))),x45421),f10(f900(f905(x45421,x45422)),f900(f905(x45421,x45422)),f900(x45421))),f317(f317(f10(f905(x45421,x45422),f906(f900(f905(x45421,x45422)),f900(f905(x45421,x45422))),x45421),f141(f905(x45421,x45422))),f317(f317(f9(x45421,x45422,f905(x45421,x45422)),f242(x45421,x45422)),x45423)))),f317(f317(f9(f900(x45421),f900(x45422),f900(f905(x45421,x45422))),f171(x45421,x45422)),x45424))),x45425),f317(f317(f171(x45421,x45422),x45425),f317(f317(f141(x45422),x45423),x45424))) % 112.26/112.09 [4260]E(f317(f317(f91(f906(x42601,a895)),f317(f275(x42602,x42601,x42603),x42604)),f317(f275(x42602,x42601,x42605),x42604)),f317(f275(x42602,x42601,f317(f317(f91(f906(f905(x42602,x42601),a895)),x42603),x42605)),x42604)) % 112.26/112.09 [4297]E(f317(f317(f124(f905(x42971,x42972)),f317(f317(f171(x42971,x42972),x42973),f317(f317(f165(x42972),f317(f179(f900(x42971)),x42973)),x42974))),f317(f317(f171(x42971,x42972),x42975),f317(f317(f128(x42972),f317(f179(f900(x42971)),x42973)),x42974))),f317(f317(f171(x42971,x42972),f317(f317(f124(x42971),x42973),x42975)),x42974)) % 112.26/112.09 [4400]E(f317(f317(f244(x44001,x44002),x44003),f317(f317(f20(x44001,f906(x44002,a895),f906(x44002,a895)),f317(f317(f10(f906(x44002,a895),f906(f906(x44002,a895),f906(x44002,a895)),x44001),f3(f906(x44002,a895))),x44004)),x44005)),f317(f317(f3(f906(f905(x44001,x44002),a895)),f317(f317(f244(x44001,x44002),x44003),x44004)),f317(f317(f244(x44001,x44002),x44003),x44005))) % 112.26/112.09 [4401]E(f317(f317(f244(x44011,x44012),x44013),f317(f317(f20(x44011,f906(x44012,a895),f906(x44012,a895)),f317(f317(f10(f906(x44012,a895),f906(f906(x44012,a895),f906(x44012,a895)),x44011),f91(f906(x44012,a895))),x44014)),x44015)),f317(f317(f91(f906(f905(x44011,x44012),a895)),f317(f317(f244(x44011,x44012),x44013),x44014)),f317(f317(f244(x44011,x44012),x44013),x44015))) % 112.26/112.09 [4402]E(f317(f317(f244(x44021,x44022),x44023),f317(f317(f20(x44021,f906(x44022,a895),f906(x44022,a895)),f317(f317(f10(f906(x44022,a895),f906(f906(x44022,a895),f906(x44022,a895)),x44021),f92(f906(x44022,a895))),x44024)),x44025)),f317(f317(f92(f906(f905(x44021,x44022),a895)),f317(f317(f244(x44021,x44022),x44023),x44024)),f317(f317(f244(x44021,x44022),x44023),x44025))) % 112.26/112.09 [4406]E(f317(f317(f35(x44061,f906(x44062,a895)),x44063),f317(f317(f9(x44061,f906(x44062,a895),f906(x44062,a895)),f317(f317(f10(f906(x44062,a895),f906(f906(x44062,a895),f906(x44062,a895)),x44061),f91(f906(x44062,a895))),x44064)),x44065)),f317(f317(f91(f906(x44062,a895)),f317(f317(f35(x44061,f906(x44062,a895)),x44063),x44064)),x44065)) % 112.26/112.09 [4407]E(f317(f317(f36(x44071,f906(x44072,a895)),x44073),f317(f317(f9(x44071,f906(x44072,a895),f906(x44072,a895)),f317(f317(f10(f906(x44072,a895),f906(f906(x44072,a895),f906(x44072,a895)),x44071),f3(f906(x44072,a895))),x44074)),x44075)),f317(f317(f3(f906(x44072,a895)),f317(f317(f36(x44071,f906(x44072,a895)),x44073),x44074)),x44075)) % 112.26/112.09 [4408]E(f317(f317(f36(x44081,f906(x44082,a895)),x44083),f317(f317(f9(x44081,f906(x44082,a895),f906(x44082,a895)),f317(f317(f10(f906(x44082,a895),f906(f906(x44082,a895),f906(x44082,a895)),x44081),f92(f906(x44082,a895))),x44084)),x44085)),f317(f317(f92(f906(x44082,a895)),f317(f317(f36(x44081,f906(x44082,a895)),x44083),x44084)),x44085)) % 112.26/112.09 [4412]E(f317(f317(f35(x44121,f906(x44122,a895)),x44123),f317(f317(f20(x44121,f906(x44122,a895),f906(x44122,a895)),f317(f317(f10(f906(x44122,a895),f906(f906(x44122,a895),f906(x44122,a895)),x44121),f92(f906(x44122,a895))),x44124)),x44125)),f317(f317(f92(f906(x44122,a895)),f317(f317(f35(x44121,f906(x44122,a895)),x44123),x44124)),f317(f317(f35(x44121,f906(x44122,a895)),x44123),x44125))) % 112.26/112.09 [4413]E(f317(f317(f36(x44131,f906(x44132,a895)),x44133),f317(f317(f20(x44131,f906(x44132,a895),f906(x44132,a895)),f317(f317(f10(f906(x44132,a895),f906(f906(x44132,a895),f906(x44132,a895)),x44131),f91(f906(x44132,a895))),x44134)),x44135)),f317(f317(f91(f906(x44132,a895)),f317(f317(f36(x44131,f906(x44132,a895)),x44133),x44134)),f317(f317(f36(x44131,f906(x44132,a895)),x44133),x44135))) % 112.26/112.09 [4426]E(f317(f317(f35(x44261,f906(x44262,a895)),x44263),f317(f317(f20(x44261,f906(x44262,a895),f906(x44262,a895)),f317(f317(f10(f906(x44262,a895),f906(f906(x44262,a895),f906(x44262,a895)),x44261),f92(f906(x44262,a895))),x44264)),x44265)),f317(f317(f92(f906(x44262,a895)),f33(f906(x44262,a895),f317(f300(x44261,f906(x44262,a895),x44264),x44263))),f33(f906(x44262,a895),f317(f300(x44261,f906(x44262,a895),x44265),x44263)))) % 112.26/112.09 [4427]E(f317(f317(f36(x44271,f906(x44272,a895)),x44273),f317(f317(f20(x44271,f906(x44272,a895),f906(x44272,a895)),f317(f317(f10(f906(x44272,a895),f906(f906(x44272,a895),f906(x44272,a895)),x44271),f91(f906(x44272,a895))),x44274)),x44275)),f317(f317(f91(f906(x44272,a895)),f32(f906(x44272,a895),f317(f300(x44271,f906(x44272,a895),x44274),x44273))),f32(f906(x44272,a895),f317(f300(x44271,f906(x44272,a895),x44275),x44273)))) % 112.26/112.09 [4463]E(f317(f317(f128(x44631),f317(f179(f900(x44631)),f167(x44631,x44632,f317(f317(f144(x44633,x44631),x44634),x44635)))),f317(f317(f144(x44633,x44631),x44634),x44635)),f317(f317(f144(x44633,x44631),x44634),f317(f317(f128(x44633),f317(f179(f900(x44633)),f167(x44633,f317(f67(x44631,a895,x44633,x44632),x44634),x44635))),x44635))) % 112.26/112.09 [4339]E(f317(f317(f124(f905(x43391,x43392)),f317(f317(f171(x43391,x43392),f317(f317(f165(x43391),f317(f179(f900(x43392)),x43393)),x43394)),x43393)),f317(f317(f171(x43391,x43392),f317(f317(f128(x43391),f317(f179(f900(x43392)),x43393)),x43394)),x43395)),f317(f317(f171(x43391,x43392),x43394),f317(f317(f124(x43392),x43393),x43395))) % 112.26/112.09 [4454]E(f79(x44541,f317(f317(f20(x44541,a895,a895),f317(f317(f10(a895,f906(a895,a895),x44541),a315),f317(f317(f9(x44541,f906(x44541,a895),a895),f319(x44541)),x44542))),f317(f317(f9(x44541,x44543,a895),f317(f317(f10(x44543,f906(x44543,a895),x44541),a314),x44544)),x44545))),f317(f71(x44541,x44543,x44542,x44544),x44545)) % 112.26/112.09 [4455]E(f84(x44551,f317(f317(f20(x44551,a895,a895),f317(f317(f10(a895,f906(a895,a895),x44551),a315),f317(f317(f9(x44551,f906(x44551,a895),a895),f319(x44551)),x44552))),f317(f317(f9(x44551,x44553,a895),f317(f317(f10(x44553,f906(x44553,a895),x44551),a314),x44554)),x44555))),f317(f85(x44551,x44553,x44552,x44554),x44555)) % 112.26/112.09 [4503]E(f317(f317(f80(a1,x45031),f317(f94(a1),f317(f317(f74(a1),x45032),a87))),f317(f317(f20(a1,x45031,x45031),f317(f317(f9(a1,x45031,f906(x45031,x45031)),f317(f317(f10(a895,f906(x45031,f906(x45031,x45031)),a1),f86(x45031)),a183)),f175(x45031,x45033,x45034,x45035))),f317(f317(f10(a899,x45031,a1),x45034),f317(f317(f9(a1,a899,a899),f317(f317(f10(a899,f906(a899,a899),a1),f74(a899)),a95)),x45035)))),f175(x45031,x45033,x45034,f317(f317(f74(a899),f317(f94(a899),x45032)),x45035))) % 112.26/112.09 [4538]E(f317(f317(f80(a1,x45381),f317(f94(a1),f317(f317(f74(a1),x45382),a87))),f317(f317(f20(a1,x45381,x45381),f317(f317(f9(a1,x45381,f906(x45381,x45381)),f317(f317(f10(a895,f906(x45381,f906(x45381,x45381)),a1),f86(x45381)),a183)),f317(f174(x45381,x45383,x45384),x45385))),f317(f317(f20(a1,x45381,x45381),f317(f317(f10(a899,f906(x45381,x45381),a1),x45384),f317(f317(f9(a1,a899,a899),f317(f317(f10(a899,f906(a899,a899),a1),f74(a899)),a95)),x45385))),f317(f317(f10(a899,x45381,a1),f174(x45381,x45383,x45384)),f317(f317(f9(a1,a899,a899),f317(f317(f10(a899,f906(a899,a899),a1),f74(a899)),a95)),x45385))))),f317(f174(x45381,x45383,x45384),f317(f317(f74(a899),f317(f94(a899),x45382)),x45385))) % 112.26/112.09 [4571]E(f317(f252(f905(x45711,x45712)),f317(f247(x45711,x45712,a895),f317(f317(f10(f906(x45712,f906(x45713,a895)),f906(x45712,a895),x45711),f317(f10(f906(x45713,a895),a895,x45712),f81(x45713))),f317(f317(f9(x45711,f906(x45712,f906(x45713,a895)),f906(x45712,f906(x45713,a895))),f317(f317(f10(f906(f906(x45713,a895),f906(x45713,a895)),f906(f906(x45712,f906(x45713,a895)),f906(x45712,f906(x45713,a895))),x45711),f10(f906(x45713,a895),f906(x45713,a895),x45712)),f317(f317(f10(f906(x45713,f906(a895,a895)),f906(f906(x45713,a895),f906(x45713,a895)),x45711),f20(x45713,a895,a895)),f317(f317(f10(f906(x45713,a895),f906(x45713,f906(a895,a895)),x45711),f317(f10(a895,f906(a895,a895),x45713),a315)),f317(f317(f9(x45711,f906(f905(x45711,x45713),a895),f906(x45713,a895)),f317(f317(f10(f906(x45713,f906(f906(f905(x45711,x45713),a895),a895)),f906(f906(f905(x45711,x45713),a895),f906(x45713,a895)),x45711),f9(x45713,f906(f905(x45711,x45713),a895),a895)),f317(f317(f10(f906(x45713,f905(x45711,x45713)),f906(x45713,f906(f906(f905(x45711,x45713),a895),a895)),x45711),f317(f10(f905(x45711,x45713),f906(f906(f905(x45711,x45713),a895),a895),x45713),f319(f905(x45711,x45713)))),f242(x45711,x45713)))),x45714))))),f317(f317(f9(x45712,f906(f905(x45713,x45712),a895),f906(x45713,a895)),f317(f317(f10(f906(x45713,f906(f906(f905(x45713,x45712),a895),a895)),f906(f906(f905(x45713,x45712),a895),f906(x45713,a895)),x45712),f9(x45713,f906(f905(x45713,x45712),a895),a895)),f317(f317(f10(f906(x45713,f905(x45713,x45712)),f906(x45713,f906(f906(f905(x45713,x45712),a895),a895)),x45712),f317(f10(f905(x45713,x45712),f906(f906(f905(x45713,x45712),a895),a895),x45713),f319(f905(x45713,x45712)))),f317(f9(x45713,x45712,f905(x45713,x45712)),f242(x45713,x45712))))),x45715))))),f317(f317(f279(x45711,x45713,x45712),x45714),x45715)) % 112.26/112.09 [4189]E(f214(x41891,x41892,x41893,x41894,f210(x41891,x41892,x41895,x41896)),f317(f317(x41894,x41895),x41896)) % 112.26/112.09 [4190]E(f215(x41901,x41902,x41903,x41904,f210(x41901,x41902,x41905,x41906)),f317(f317(x41904,x41905),x41906)) % 112.26/112.09 [4315]E(f117(x43151,x43152,x43153,x43154,f116(x43152,x43155,x43156)),f317(f317(f317(x43154,x43155),x43156),f117(x43151,x43152,x43153,x43154,x43156))) % 112.26/112.09 [4334]E(f69(x43341,x43342,f69(x43341,x43342,x43343,x43344,x43345),x43344,x43346),f69(x43341,x43342,x43343,x43344,x43346)) % 112.26/112.09 [4442]E(f317(f67(f905(x44421,x44422),x44422,f905(x44423,x44424),f246(x44421,x44422)),f248(x44423,x44421,x44424,x44422,x44425,x44426)),f317(f67(x44424,x44422,f905(x44423,x44424),x44426),f246(x44423,x44424))) % 112.26/112.09 [4443]E(f317(f67(f905(x44431,x44432),x44431,f905(x44433,x44434),f241(x44431,x44432)),f248(x44433,x44431,x44434,x44432,x44435,x44436)),f317(f67(x44433,x44431,f905(x44433,x44434),x44435),f241(x44433,x44434))) % 112.26/112.09 [4061]E(f317(f317(f67(x40611,x40612,x40613,x40614),x40615),x40616),f317(x40614,f317(x40615,x40616))) % 112.26/112.09 [4199]E(f213(x41991,f905(x41992,f901(x41992)),x41993,f317(f247(x41992,f901(x41992),x41991),x41994),f317(f125(x41992),f116(x41992,x41995,x41996))),f317(f317(x41994,x41995),x41996)) % 112.26/112.09 [4249]E(f216(x42491,x42492,x42493,x42494,f210(x42491,x42492,x42495,x42496)),f317(f317(f74(a899),f317(f317(f74(a899),f317(x42493,x42495)),f317(x42494,x42496))),f317(a102,f2(a899)))) % 112.26/112.09 [3863]E(f317(f317(f247(x38631,x38632,x38633),x38634),f317(f317(f242(x38631,x38632),x38635),x38636)),f317(f317(x38634,x38635),x38636)) % 112.26/112.09 [3923]E(f317(f317(f317(f10(x39231,x39232,x39233),x39234),x39235),x39236),f317(x39234,f317(x39235,x39236))) % 112.26/112.09 [3924]E(f317(f317(f317(f9(x39241,x39242,x39243),x39244),x39245),x39246),f317(f317(x39244,x39246),x39245)) % 112.26/112.09 [3940]E(f317(f317(f317(f20(x39401,x39402,x39403),x39404),x39405),x39406),f317(f317(x39404,x39406),f317(x39405,x39406))) % 112.26/112.09 [3963]E(f317(f146(x39631,x39632,x39633,x39634),f317(f317(f141(x39632),x39635),x39636)),f317(f317(x39634,x39635),x39636)) % 112.26/112.09 [3999]E(f159(f905(x39991,x39992),f317(f317(f228(a899),x39993),x39994),f317(f317(f242(x39991,x39992),x39995),x39996)),f317(f317(f171(x39991,x39992),f159(x39991,x39993,x39995)),f159(x39992,x39994,x39996))) % 112.26/112.09 [4065]E(f317(f317(f141(f905(x40651,x40652)),f317(f317(f242(x40651,x40652),x40653),x40654)),f317(f317(f171(x40651,x40652),x40655),x40656)),f317(f317(f171(x40651,x40652),f317(f317(f141(x40651),x40653),x40655)),f317(f317(f141(x40652),x40654),x40656))) % 112.26/112.09 [4066]E(f317(f317(f144(x40661,x40662),x40663),f317(f317(f149(x40661,x40664),x40665),x40666)),f317(f317(f149(x40662,f317(f317(f144(x40661,x40662),x40663),x40664)),x40665),f317(x40663,x40666))) % 112.26/112.09 [4090]E(f317(f317(f245(x40901,x40902,x40903,x40904),x40905),x40906),f317(x40904,f317(f317(f242(x40901,x40902),x40905),x40906))) % 112.26/112.09 [4106]E(f317(f132(x41061,x41062,x41063,x41064),f317(f317(f141(x41062),x41065),x41066)),f317(f132(x41061,x41062,x41063,f317(f317(x41063,x41064),x41065)),x41066)) % 112.26/112.09 [4132]E(f250(x41321,x41322,x41323,x41324,f317(f317(f242(x41321,x41322),x41325),x41326)),f317(f317(x41324,x41325),x41326)) % 112.26/112.09 [4213]E(f317(f317(f36(x42131,f906(x42132,a895)),x42133),f317(f67(x42134,f906(x42132,a895),x42131,x42135),x42136)),f317(f317(f36(x42134,f906(x42132,a895)),f317(f300(x42131,x42134,x42136),x42133)),x42135)) % 112.26/112.09 [4263]E(f317(f317(f144(x42631,x42632),x42633),f317(f317(f144(x42634,x42631),x42635),x42636)),f317(f317(f144(x42634,x42632),f317(f67(x42631,x42632,x42634,x42633),x42635)),x42636)) % 112.26/112.09 [4269]E(f317(f300(x42691,x42692,f317(f67(x42693,x42692,x42691,x42694),x42695)),x42696),f317(f300(x42693,x42692,x42694),f317(f300(x42691,x42693,x42695),x42696))) % 112.26/112.09 [4270]E(f317(f301(x42701,x42702,f317(f67(x42703,x42702,x42701,x42704),x42705)),x42706),f317(f301(x42701,x42703,x42705),f317(f301(x42703,x42702,x42704),x42706))) % 112.26/112.09 [4298]E(f317(f132(x42981,x42982,x42983,f317(f132(x42981,x42982,x42983,x42984),x42985)),x42986),f317(f132(x42981,x42982,x42983,x42984),f317(f317(f124(x42982),x42985),x42986))) % 112.26/112.09 [4432]E(f317(f248(x44321,x44321,x44322,x44323,f25(x44321),x44324),f317(f317(f242(x44321,x44322),x44325),x44326)),f317(f317(f242(x44321,x44323),x44325),f317(x44324,x44326))) % 112.26/112.09 [4433]E(f317(f248(x44331,x44332,x44333,x44333,x44334,f25(x44333)),f317(f317(f242(x44331,x44333),x44335),x44336)),f317(f317(f242(x44332,x44333),f317(x44334,x44335)),x44336)) % 112.26/112.09 [4521]E(f317(f317(f144(f905(x45211,x45212),f905(x45211,x45213)),f317(f247(x45211,x45212,f905(x45211,x45213)),f317(f317(f9(x45211,f906(x45212,x45213),f906(x45212,f905(x45211,x45213))),f317(f317(f10(f906(x45213,f905(x45211,x45213)),f906(f906(x45212,x45213),f906(x45212,f905(x45211,x45213))),x45211),f10(x45213,f905(x45211,x45213),x45212)),f242(x45211,x45213))),x45214))),f317(f317(f171(x45211,x45212),x45215),x45216)),f317(f317(f171(x45211,x45213),x45215),f317(f317(f144(x45212,x45213),x45214),x45216))) % 112.26/112.09 [4116]E(f317(f317(f67(x41161,x41162,x41163,f317(f18(x41162,x41161),x41164)),x41165),x41166),x41164) % 112.26/112.09 [4148]E(f317(f300(x41481,x41482,x41483),f317(f300(x41484,x41481,x41485),x41486)),f317(f300(x41484,x41482,f317(f317(f10(x41481,x41482,x41484),x41483),x41485)),x41486)) % 112.26/112.09 [4154]E(f317(f317(f35(x41541,f906(x41542,a895)),f317(f300(x41543,x41541,x41544),x41545)),x41546),f317(f317(f35(x41543,f906(x41542,a895)),x41545),f317(f317(f10(x41541,f906(x41542,a895),x41543),x41546),x41544))) % 112.26/112.09 [4155]E(f317(f317(f36(x41551,f906(x41552,a895)),f317(f300(x41553,x41551,x41554),x41555)),x41556),f317(f317(f36(x41553,f906(x41552,a895)),x41555),f317(f317(f10(x41551,f906(x41552,a895),x41553),x41556),x41554))) % 112.26/112.09 [4156]E(f317(f317(f35(x41561,f906(x41562,a895)),x41563),f317(f317(f10(x41564,f906(x41562,a895),x41561),x41565),x41566)),f317(f317(f35(x41564,f906(x41562,a895)),f317(f300(x41561,x41564,x41566),x41563)),x41565)) % 112.26/112.09 [4157]E(f317(f317(f36(x41571,f906(x41572,a895)),x41573),f317(f317(f10(x41574,f906(x41572,a895),x41571),x41575),x41576)),f317(f317(f36(x41574,f906(x41572,a895)),f317(f300(x41571,x41574,x41576),x41573)),x41575)) % 112.26/112.09 [4215]E(f317(f317(f36(x42151,f906(x42152,a895)),x42153),f317(f317(f10(f906(x42154,a895),f906(x42152,a895),x42151),f300(x42154,x42152,x42155)),x42156)),f317(f300(x42154,x42152,x42155),f317(f317(f36(x42151,f906(x42154,a895)),x42153),x42156))) % 112.26/112.09 [4216]E(f317(f317(f36(x42161,f906(x42162,a895)),x42163),f317(f317(f10(f906(x42164,a895),f906(x42162,a895),x42161),f275(x42164,x42162,x42165)),x42166)),f317(f275(x42164,x42162,x42165),f317(f317(f36(x42161,f906(x42164,a895)),x42163),x42166))) % 112.26/112.09 [4217]E(f317(f317(f35(x42171,f906(x42172,a895)),x42173),f317(f317(f10(f906(x42174,a895),f906(x42172,a895),x42171),f301(x42172,x42174,x42175)),x42176)),f317(f301(x42172,x42174,x42175),f317(f317(f35(x42171,f906(x42174,a895)),x42173),x42176))) % 112.26/112.09 [4218]E(f317(f317(f36(x42181,f906(x42182,a895)),x42183),f317(f317(f10(f906(x42184,a895),f906(x42182,a895),x42181),f301(x42182,x42184,x42185)),x42186)),f317(f301(x42182,x42184,x42185),f317(f317(f36(x42181,f906(x42184,a895)),x42183),x42186))) % 112.26/112.09 [4303]E(f317(f132(x43031,x43032,f317(f9(x43032,x43031,x43031),x43033),x43034),f317(f158(x43032),f317(f317(f141(x43032),x43035),x43036))),f317(f317(x43033,x43035),f317(f132(x43031,x43032,f317(f9(x43032,x43031,x43031),x43033),x43034),f317(f158(x43032),x43036)))) % 112.26/112.09 [4361]E(f317(f317(f20(f905(x43611,x43612),x43612,x43613),f317(f317(f10(x43614,f906(x43612,x43613),f905(x43611,x43612)),x43615),f317(f317(f10(x43611,x43614,f905(x43611,x43612)),x43616),f241(x43611,x43612)))),f246(x43611,x43612)),f317(f247(x43611,x43612,x43613),f317(f317(f10(x43614,f906(x43612,x43613),x43611),x43615),x43616))) % 112.26/112.09 [4368]E(f317(f132(x43681,x43682,f317(f9(x43682,x43681,x43681),x43683),f317(f132(x43681,x43682,f317(f9(x43682,x43681,x43681),x43683),x43684),f317(f158(x43682),x43685))),f317(f158(x43682),x43686)),f317(f132(x43681,x43682,f317(f9(x43682,x43681,x43681),x43683),x43684),f317(f158(x43682),f317(f317(f124(x43682),x43686),x43685)))) % 112.26/112.09 [4370]E(f317(f317(f144(f905(x43701,x43702),f905(x43703,x43702)),f317(f247(x43701,x43702,f905(x43703,x43702)),f317(f317(f10(x43703,f906(x43702,f905(x43703,x43702)),x43701),f242(x43703,x43702)),x43704))),f317(f317(f171(x43701,x43702),x43705),x43706)),f317(f317(f171(x43703,x43702),f317(f317(f144(x43701,x43703),x43704),x43705)),x43706)) % 112.26/112.09 [4415]P1(f317(f317(f224(f906(x44151,a895)),f317(f275(x44152,x44151,x44153),f317(f317(f35(x44154,f906(x44152,a895)),x44155),x44156))),f317(f317(f35(x44154,f906(x44151,a895)),x44155),f317(f317(f10(f906(x44152,a895),f906(x44151,a895),x44154),f275(x44152,x44151,x44153)),x44156)))) % 112.26/112.09 [4228]E(f317(f317(f171(x42281,x42282),f317(f317(f149(x42281,x42283),x42284),f317(f241(x42281,x42282),x42285))),f317(f317(f149(x42282,x42286),x42284),f317(f246(x42281,x42282),x42285))),f317(f317(f149(f905(x42281,x42282),f317(f317(f171(x42281,x42282),x42283),x42286)),x42284),x42285)) % 112.26/112.09 [4286]E(f317(f317(f91(f906(f905(x42861,x42862),a895)),f317(f317(f279(x42861,x42863,x42862),x42864),x42865)),f317(f317(f279(x42861,x42863,x42862),x42864),x42866)),f317(f317(f279(x42861,x42863,x42862),x42864),f317(f317(f91(f906(f905(x42863,x42862),a895)),x42865),x42866))) % 112.26/112.09 [4380]E(f317(f317(f299(f905(x43801,x43802)),f317(f317(f242(x43801,x43802),x43803),x43804)),f317(f317(f91(f906(f905(x43801,x43802),a895)),f317(f317(f244(x43801,x43802),x43805),f317(f18(f906(x43802,a895),x43801),f317(f317(f299(x43802),x43804),x43806)))),f317(f317(f244(x43801,x43802),f317(f317(f299(x43801),x43803),x43805)),f317(f18(f906(x43802,a895),x43801),x43806)))),f317(f317(f244(x43801,x43802),f317(f317(f299(x43801),x43803),x43805)),f317(f18(f906(x43802,a895),x43801),f317(f317(f299(x43802),x43804),x43806)))) % 112.26/112.09 [4459]E(f317(f317(f92(f906(x44591,a895)),f317(f301(x44591,x44592,f317(f67(f905(x44592,x44593),x44592,x44591,f241(x44592,x44593)),x44594)),x44595)),f317(f301(x44591,x44593,f317(f67(f905(x44592,x44593),x44593,x44591,f246(x44592,x44593)),x44594)),x44596)),f317(f301(x44591,f905(x44592,x44593),x44594),f317(f317(f244(x44592,x44593),x44595),f317(f18(f906(x44593,a895),x44592),x44596)))) % 112.26/112.09 [4309]E(f317(f317(f91(f906(f905(x43091,x43092),a895)),f317(f317(f279(x43091,x43093,x43092),x43094),x43095)),f317(f317(f279(x43091,x43093,x43092),x43096),x43095)),f317(f317(f279(x43091,x43093,x43092),f317(f317(f91(f906(f905(x43091,x43093),a895)),x43094),x43096)),x43095)) % 112.26/112.09 [4440]E(f317(f317(f35(x44401,f906(x44402,a895)),x44403),f317(f317(f9(x44401,f906(x44404,f906(x44402,a895)),f906(x44402,a895)),f317(f317(f10(f906(x44404,a895),f906(f906(x44404,f906(x44402,a895)),f906(x44402,a895)),x44401),f35(x44404,f906(x44402,a895))),x44405)),x44406)),f317(f317(f35(x44404,f906(x44402,a895)),f317(f317(f36(x44401,f906(x44404,a895)),x44403),x44405)),x44406)) % 112.26/112.09 [4441]E(f317(f317(f36(x44411,f906(x44412,a895)),x44413),f317(f317(f9(x44411,f906(x44414,f906(x44412,a895)),f906(x44412,a895)),f317(f317(f10(f906(x44414,a895),f906(f906(x44414,f906(x44412,a895)),f906(x44412,a895)),x44411),f36(x44414,f906(x44412,a895))),x44415)),x44416)),f317(f317(f36(x44414,f906(x44412,a895)),f317(f317(f36(x44411,f906(x44414,a895)),x44413),x44415)),x44416)) % 112.26/112.09 [4493]E(f317(f247(x44931,x44932,f905(x44933,x44934)),f317(f317(f9(x44931,f906(x44932,x44934),f906(x44932,f905(x44933,x44934))),f317(f317(f10(f906(x44934,f905(x44933,x44934)),f906(f906(x44932,x44934),f906(x44932,f905(x44933,x44934))),x44931),f10(x44934,f905(x44933,x44934),x44932)),f317(f317(f10(x44933,f906(x44934,f905(x44933,x44934)),x44931),f242(x44933,x44934)),x44935))),x44936)),f248(x44931,x44933,x44932,x44934,x44935,x44936)) % 112.26/112.09 [4516]E(f317(f300(x45161,x45162,f317(f317(f20(x45161,x45162,x45162),f317(f317(f20(x45161,x45162,f906(x45162,x45162)),f317(f317(f10(a895,f906(x45162,f906(x45162,x45162)),x45161),f86(x45162)),x45163)),x45164)),x45165)),x45166),f317(f317(f91(f906(x45162,a895)),f317(f300(x45161,x45162,x45164),f317(f317(f92(f906(x45161,a895)),x45166),f317(f252(x45161),x45163)))),f317(f300(x45161,x45162,x45165),f317(f317(f92(f906(x45161,a895)),x45166),f317(f252(x45161),f317(f317(f10(a895,a895,x45161),a312),x45163)))))) % 112.26/112.09 [4528]E(f317(f300(x45281,f905(x45282,x45283),f317(f317(f20(x45281,x45283,f905(x45282,x45283)),f317(f317(f10(x45282,f906(x45283,f905(x45282,x45283)),x45281),f242(x45282,x45283)),x45284)),x45285)),x45286),f317(f317(f244(x45282,x45283),f317(f300(x45281,x45282,x45284),x45286)),f317(f317(f10(f906(x45281,a895),f906(x45283,a895),x45282),f300(x45281,x45283,x45285)),f317(f317(f9(x45282,f906(x45281,a895),f906(x45281,a895)),f317(f317(f10(f906(x45281,a895),f906(f906(x45281,a895),f906(x45281,a895)),x45282),f92(f906(x45281,a895))),f317(f317(f10(f906(x45282,a895),f906(x45281,a895),x45282),f301(x45281,x45282,x45284)),f317(f317(f9(x45282,f906(x45282,a895),f906(x45282,a895)),f299(x45282)),f178(f906(x45282,a895)))))),x45286)))) % 112.26/112.09 [4553]E(f236(x45531,x45532,x45533,x45534,x45535,x45536),f317(x45534,f317(f252(x45531),f317(f317(f10(f906(f906(x45533,x45531),a895),a895,x45531),f81(f906(x45533,x45531))),f317(f317(f10(f906(f906(x45533,x45531),a895),f906(f906(x45533,x45531),a895),x45531),f317(f20(f906(x45533,x45531),a895,a895),f317(f317(f10(a895,f906(a895,a895),f906(x45533,x45531)),a315),f317(f317(f9(f906(x45533,x45531),f906(f906(x45533,x45531),a895),a895),f319(f906(x45533,x45531))),x45535)))),f317(f317(f9(x45531,f906(f906(x45533,x45531),x45531),f906(f906(x45533,x45531),a895)),f317(f317(f10(f906(x45531,a895),f906(f906(f906(x45533,x45531),x45531),f906(f906(x45533,x45531),a895)),x45531),f10(x45531,a895,f906(x45533,x45531))),a314)),f317(f317(f9(f906(x45533,x45531),x45533,x45531),f7(f906(x45533,x45531))),x45536))))))) % 112.26/112.09 [4342]E(f317(f67(x43421,x43422,x43423,x43424),f69(x43423,x43421,x43425,x43426,x43427)),f69(x43423,x43422,f317(f67(x43421,x43422,x43423,x43424),x43425),x43426,f317(x43424,x43427))) % 112.26/112.09 [4476]E(f317(f246(x44761,x44762),f317(f248(x44763,x44761,x44764,x44762,x44765,x44766),x44767)),f317(x44766,f317(f246(x44763,x44764),x44767))) % 112.26/112.09 [4477]E(f317(f241(x44771,x44772),f317(f248(x44773,x44771,x44774,x44772,x44775,x44776),x44777)),f317(x44775,f317(f241(x44773,x44774),x44777))) % 112.26/112.09 [4191]E(f317(f317(f171(x41911,x41912),f317(f317(f149(x41911,x41913),x41914),x41915)),f317(f317(f149(x41912,x41916),x41914),x41917)),f317(f317(f149(f905(x41911,x41912),f317(f317(f171(x41911,x41912),x41913),x41916)),x41914),f317(f317(f242(x41911,x41912),x41915),x41917))) % 112.26/112.09 [4258]E(f317(f317(f317(f249(x42581,x42582,x42583,x42584),x42585),x42586),x42587),f317(f317(f247(x42582,x42583,x42584),x42586),f317(x42585,x42587))) % 112.26/112.09 [4268]E(f317(f317(f317(f249(x42681,x42682,x42683,x42684),x42685),x42686),x42687),f317(f317(x42686,f317(f241(x42682,x42683),f317(x42685,x42687))),f317(f246(x42682,x42683),f317(x42685,x42687)))) % 112.26/112.09 [4320]E(f317(f67(x43201,x43202,x43203,x43204),f317(f67(x43205,x43201,x43203,x43206),x43207)),f317(f67(x43205,x43202,x43203,f317(f67(x43201,x43202,x43205,x43204),x43206)),x43207)) % 112.26/112.09 [4497]E(f317(f248(x44971,x44972,x44973,x44973,x44974,f25(x44973)),f317(f248(x44971,x44971,x44975,x44973,f25(x44971),x44976),x44977)),f317(f317(f242(x44972,x44973),f317(x44974,f317(f241(x44971,x44975),x44977))),f317(x44976,f317(f246(x44971,x44975),x44977)))) % 112.26/112.09 [4498]E(f317(f248(x44981,x44981,x44982,x44983,f25(x44981),x44984),f317(f248(x44985,x44981,x44982,x44982,x44986,f25(x44982)),x44987)),f317(f317(f242(x44981,x44983),f317(x44986,f317(f241(x44985,x44982),x44987))),f317(x44984,f317(f246(x44985,x44982),x44987)))) % 112.26/112.09 [4514]E(f317(f248(x45141,x45142,x45143,x45143,x45144,f25(x45143)),f317(f248(x45145,x45141,x45143,x45143,x45146,f25(x45143)),x45147)),f317(f248(x45145,x45142,x45143,x45143,f317(f67(x45141,x45142,x45145,x45144),x45146),f25(x45143)),x45147)) % 112.26/112.09 [4515]E(f317(f248(x45151,x45151,x45152,x45153,f25(x45151),x45154),f317(f248(x45151,x45151,x45155,x45152,f25(x45151),x45156),x45157)),f317(f248(x45151,x45151,x45155,x45153,f25(x45151),f317(f67(x45152,x45153,x45155,x45154),x45156)),x45157)) % 112.26/112.09 [4525]E(f317(f248(x45251,x45252,x45253,x45253,x45254,f25(x45253)),f317(f248(x45251,x45251,x45255,x45253,f25(x45251),x45256),x45257)),f317(f248(x45252,x45252,x45255,x45253,f25(x45252),x45256),f317(f248(x45251,x45252,x45255,x45255,x45254,f25(x45255)),x45257))) % 112.26/112.09 [4225]E(f317(f317(f279(x42251,x42252,x42253),f317(f317(f279(x42251,x42254,x42252),x42255),x42256)),x42257),f317(f317(f279(x42251,x42254,x42253),x42255),f317(f317(f279(x42254,x42252,x42253),x42256),x42257))) % 112.26/112.09 [4292]E(f317(f317(f247(x42921,x42922,x42923),f317(f67(x42924,f906(x42922,x42923),x42921,x42925),x42926)),x42927),f317(f317(x42925,f317(x42926,f317(f241(x42921,x42922),x42927))),f317(f246(x42921,x42922),x42927))) % 112.26/112.09 [4373]E(f317(f132(x43731,x43732,f317(f9(x43732,x43731,x43731),x43733),x43734),f317(f158(x43732),f317(f317(f144(x43735,x43732),x43736),x43737))),f317(f132(x43731,x43735,f317(f9(x43735,x43731,x43731),f317(f67(x43732,f906(x43731,x43731),x43735,x43733),x43736)),x43734),f317(f158(x43735),x43737))) % 112.26/112.09 [4321]E(f317(f317(f36(x43211,f906(f905(x43212,x43213),a895)),x43214),f317(f317(f10(f906(f905(x43215,x43213),a895),f906(f905(x43212,x43213),a895),x43211),f317(f279(x43212,x43215,x43213),x43216)),x43217)),f317(f317(f279(x43212,x43215,x43213),x43216),f317(f317(f36(x43211,f906(f905(x43215,x43213),a895)),x43214),x43217))) % 112.26/112.09 [4464]E(f317(f317(f36(x44641,f906(f905(x44642,x44643),a895)),x44644),f317(f317(f9(x44641,f906(f905(x44645,x44643),a895),f906(f905(x44642,x44643),a895)),f317(f317(f10(f906(f905(x44642,x44645),a895),f906(f906(f905(x44645,x44643),a895),f906(f905(x44642,x44643),a895)),x44641),f279(x44642,x44645,x44643)),x44646)),x44647)),f317(f317(f279(x44642,x44645,x44643),f317(f317(f36(x44641,f906(f905(x44642,x44645),a895)),x44644),x44646)),x44647)) % 112.26/112.09 [4465]E(f317(f132(x44651,x44652,f317(f317(f9(x44651,f906(x44652,x44653),f906(x44652,x44651)),f317(f317(f10(f906(x44653,x44651),f906(f906(x44652,x44653),f906(x44652,x44651)),x44651),f10(x44653,x44651,x44652)),x44654)),x44655),x44656),x44657),f317(f132(x44651,x44653,x44654,x44656),f317(f317(f144(x44652,x44653),x44655),x44657))) % 112.26/112.09 [4526]E(f317(f317(f35(x45261,f906(x45262,a895)),x45263),f317(f317(f10(f906(x45264,f906(x45262,a895)),f906(x45262,a895),x45261),f317(f35(x45264,f906(x45262,a895)),x45265)),f317(f317(f9(x45261,f906(x45264,f906(x45262,a895)),f906(x45264,f906(x45262,a895))),f317(f317(f10(f906(f906(x45262,a895),f906(x45262,a895)),f906(f906(x45264,f906(x45262,a895)),f906(x45264,f906(x45262,a895))),x45261),f10(f906(x45262,a895),f906(x45262,a895),x45264)),f317(f317(f10(f906(x45262,a895),f906(f906(x45262,a895),f906(x45262,a895)),x45261),f91(f906(x45262,a895))),x45266))),x45267))),f317(f317(f91(f906(x45262,a895)),f317(f317(f35(x45261,f906(x45262,a895)),x45263),x45266)),f317(f317(f35(x45264,f906(x45262,a895)),x45265),x45267))) % 112.26/112.09 [4527]E(f317(f317(f36(x45271,f906(x45272,a895)),x45273),f317(f317(f10(f906(x45274,f906(x45272,a895)),f906(x45272,a895),x45271),f317(f36(x45274,f906(x45272,a895)),x45275)),f317(f317(f9(x45271,f906(x45274,f906(x45272,a895)),f906(x45274,f906(x45272,a895))),f317(f317(f10(f906(f906(x45272,a895),f906(x45272,a895)),f906(f906(x45274,f906(x45272,a895)),f906(x45274,f906(x45272,a895))),x45271),f10(f906(x45272,a895),f906(x45272,a895),x45274)),f317(f317(f10(f906(x45272,a895),f906(f906(x45272,a895),f906(x45272,a895)),x45271),f92(f906(x45272,a895))),x45276))),x45277))),f317(f317(f92(f906(x45272,a895)),f317(f317(f36(x45271,f906(x45272,a895)),x45273),x45276)),f317(f317(f36(x45274,f906(x45272,a895)),x45275),x45277))) % 112.26/112.09 [4519]E(f187(x45191,x45192,f317(f317(f317(x45193,x45194),x45195),x45196),f317(f317(f9(x45191,f905(a89,a89),f906(a89,f901(x45192))),f317(f317(f9(x45191,a89,f906(f905(a89,a89),f906(a89,f901(x45192)))),f317(f317(f9(x45191,a89,f906(a89,f906(f905(a89,a89),f906(a89,f901(x45192))))),x45197),x45194)),x45195)),x45196)),f317(f317(f317(f199(x45191,x45192,x45193,x45197),x45194),x45195),x45196)) % 112.26/112.09 [4533]E(f188(x45331,x45332,f317(f317(f317(x45333,x45334),x45335),x45336),f317(f317(f9(x45331,f905(a89,a89),f906(a89,f901(x45332))),f317(f317(f9(x45331,a89,f906(f905(a89,a89),f906(a89,f901(x45332)))),f317(f317(f9(x45331,a89,f906(a89,f906(f905(a89,a89),f906(a89,f901(x45332))))),x45337),x45334)),x45335)),x45336)),f201(x45331,x45332,x45333,x45337,x45334,x45335,x45336)) % 112.26/112.09 [4524]E(f185(x45241,x45242,f317(f317(f317(x45243,x45244),x45245),x45246),f317(f317(f9(x45241,f905(a89,a89),f906(a89,f901(f902(x45242)))),f317(f317(f9(x45241,a89,f906(f905(a89,a89),f906(a89,f901(f902(x45242))))),f317(f317(f9(x45241,a89,f906(a89,f906(f905(a89,a89),f906(a89,f901(f902(x45242)))))),x45247),x45244)),x45245)),x45246)),f317(f317(f317(f195(x45241,x45242,x45243,x45247),x45244),x45245),x45246)) % 112.26/112.09 [4535]E(f186(x45351,x45352,f317(f317(f317(x45353,x45354),x45355),x45356),f317(f317(f9(x45351,f905(a89,a89),f906(a89,f901(f902(x45352)))),f317(f317(f9(x45351,a89,f906(f905(a89,a89),f906(a89,f901(f902(x45352))))),f317(f317(f9(x45351,a89,f906(a89,f906(f905(a89,a89),f906(a89,f901(f902(x45352)))))),x45357),x45354)),x45355)),x45356)),f197(x45351,x45352,x45353,x45357,x45354,x45355,x45356)) % 112.26/112.09 [4434]E(f317(f248(x44341,x44342,x44343,x44344,x44345,x44346),f317(f317(f242(x44341,x44343),x44347),x44348)),f317(f317(f242(x44342,x44344),f317(x44345,x44347)),f317(x44346,x44348))) % 112.26/112.09 [4537]E(f317(f317(f144(f905(x45371,x45372),f905(x45373,x45374)),f317(f247(x45371,x45372,f905(x45373,x45374)),f317(f317(f9(x45371,f906(x45372,x45374),f906(x45372,f905(x45373,x45374))),f317(f317(f10(f906(x45374,f905(x45373,x45374)),f906(f906(x45372,x45374),f906(x45372,f905(x45373,x45374))),x45371),f10(x45374,f905(x45373,x45374),x45372)),f317(f317(f10(x45373,f906(x45374,f905(x45373,x45374)),x45371),f242(x45373,x45374)),x45375))),x45376))),f317(f317(f171(x45371,x45372),x45377),x45378)),f317(f317(f171(x45373,x45374),f317(f317(f144(x45371,x45373),x45375),x45377)),f317(f317(f144(x45372,x45374),x45376),x45378))) % 112.26/112.09 [4540]E(f317(f317(f144(f905(x45401,x45402),x45403),f317(f247(x45401,x45402,x45403),f317(f317(f10(f906(x45402,f905(x45401,x45404)),f906(x45402,x45403),x45401),f317(f10(f905(x45401,x45404),x45403,x45402),x45405)),f317(f317(f9(x45401,f906(x45402,x45404),f906(x45402,f905(x45401,x45404))),f317(f317(f10(f906(x45404,f905(x45401,x45404)),f906(f906(x45402,x45404),f906(x45402,f905(x45401,x45404))),x45401),f10(x45404,f905(x45401,x45404),x45402)),f242(x45401,x45404))),x45406)))),f317(f317(f171(x45401,x45402),x45407),x45408)),f317(f317(f144(f905(x45401,x45404),x45403),x45405),f317(f317(f171(x45401,x45404),x45407),f317(f317(f144(x45402,x45404),x45406),x45408)))) % 112.26/112.09 [4468]E(f317(f317(f144(f905(x44681,x44682),x44683),f317(f247(x44681,x44682,x44683),f317(f317(f10(f906(x44682,f905(x44684,x44682)),f906(x44682,x44683),x44681),f317(f10(f905(x44684,x44682),x44683,x44682),x44685)),f317(f317(f10(x44684,f906(x44682,f905(x44684,x44682)),x44681),f242(x44684,x44682)),x44686)))),f317(f317(f171(x44681,x44682),x44687),x44688)),f317(f317(f144(f905(x44684,x44682),x44683),x44685),f317(f317(f171(x44684,x44682),f317(f317(f144(x44681,x44684),x44686),x44687)),x44688))) % 112.26/112.09 [4425]E(f317(f317(f247(x44251,x44252,x44253),f317(f317(f10(f906(x44252,f905(x44254,x44255)),f906(x44252,x44253),x44251),f317(f10(f905(x44254,x44255),x44253,x44252),f317(f247(x44254,x44255,x44253),x44256))),x44257)),x44258),f317(f317(f247(x44254,x44255,x44253),x44256),f317(f317(f247(x44251,x44252,f905(x44254,x44255)),x44257),x44258))) % 112.26/112.09 [4541]E(f317(f317(f36(f905(x45411,x45412),f906(f905(x45413,x45414),a895)),f317(f317(f244(x45411,x45412),x45415),f317(f18(f906(x45412,a895),x45411),x45416))),f317(f247(x45411,x45412,f906(f905(x45413,x45414),a895)),f317(f317(f9(x45411,f906(x45412,f906(x45413,f906(x45414,a895))),f906(x45412,f906(f905(x45413,x45414),a895))),f317(f317(f10(f906(f906(x45413,f906(x45414,a895)),f906(f905(x45413,x45414),a895)),f906(f906(x45412,f906(x45413,f906(x45414,a895))),f906(x45412,f906(f905(x45413,x45414),a895))),x45411),f10(f906(x45413,f906(x45414,a895)),f906(f905(x45413,x45414),a895),x45412)),f317(f317(f10(f906(x45413,a895),f906(f906(x45413,f906(x45414,a895)),f906(f905(x45413,x45414),a895)),x45411),f244(x45413,x45414)),x45417))),f317(f317(f10(f906(x45414,a895),f906(x45413,f906(x45414,a895)),x45412),f18(f906(x45414,a895),x45413)),x45418)))),f317(f317(f244(x45413,x45414),f317(f317(f36(x45411,f906(x45413,a895)),x45415),x45417)),f317(f18(f906(x45414,a895),x45413),f317(f317(f36(x45412,f906(x45414,a895)),x45416),x45418)))) % 112.26/112.09 [4482]E(f317(f317(f249(x44821,x44822,x44823,x44824),f317(f317(f249(x44821,x44825,x44826,f905(x44822,x44823)),x44827),x44828)),x44829),f317(f317(f249(x44821,x44825,x44826,x44824),x44827),f317(f317(f9(x44825,f906(x44822,f906(x44823,x44824)),f906(x44826,x44824)),f317(f317(f10(f906(x44826,f905(x44822,x44823)),f906(f906(x44822,f906(x44823,x44824)),f906(x44826,x44824)),x44825),f249(x44826,x44822,x44823,x44824)),x44828)),x44829))) % 112.26/112.09 [4511]E(f317(f67(f905(x45111,x45112),f905(x45113,x45114),f905(x45115,x45116),f248(x45111,x45113,x45112,x45114,x45117,x45118)),f248(x45115,x45111,x45116,x45112,x45119,x451110)),f248(x45115,x45113,x45116,x45114,f317(f67(x45111,x45113,x45115,x45117),x45119),f317(f67(x45112,x45114,x45116,x45118),x451110))) % 112.26/112.09 [4517]E(f317(f248(x45171,x45172,x45173,x45174,x45175,x45176),f317(f248(x45177,x45171,x45178,x45173,x45179,x451710),x451711)),f317(f248(x45177,x45172,x45178,x45174,f317(f67(x45171,x45172,x45177,x45175),x45179),f317(f67(x45173,x45174,x45178,x45176),x451710)),x451711)) % 112.26/112.09 [4644]~P2(x46441)+P2(f902(x46441)) % 112.26/112.09 [4645]~P60(x46451)+P60(f902(x46451)) % 112.26/112.09 [4646]~P105(x46461)+P105(f900(x46461)) % 112.26/112.09 [4649]~P144(x46491)+~E(f72(x46491),f2(x46491)) % 112.26/112.09 [4651]~E(x46511,f2(a89))+E(f317(a24,x46511),f2(a1)) % 112.26/112.09 [4652]~E(x46521,f2(a1))+E(f76(a1,x46521),f2(a1)) % 112.26/112.09 [4658]~P145(x46581)+P27(x46581,f2(x46581)) % 112.26/112.09 [4660]~P108(x46601)+P13(x46601,f103(x46601)) % 112.26/112.09 [4669]P1(x46691)+P1(f317(a312,x46691)) % 112.26/112.09 [4723]~P145(x47231)+~P27(x47231,f72(x47231)) % 112.26/112.09 [4760]~P1(x47601)+~P1(f317(a312,x47601)) % 112.26/112.09 [4781]E(f317(a95,x47811),f2(a899))+~P1(f317(a183,x47811)) % 112.26/112.09 [4847]~P70(x48471)+P16(x48471,x48471,f75(x48471)) % 112.26/112.09 [4848]~P97(x48481)+P14(x48481,x48481,f75(x48481)) % 112.26/112.09 [4849]~P108(x48491)+P14(x48491,x48491,f228(x48491)) % 112.26/112.09 [4850]~P108(x48501)+P14(x48501,x48501,f223(x48501)) % 112.26/112.09 [4851]~P98(x48511)+P14(x48511,x48511,f91(x48511)) % 112.26/112.09 [4852]~P104(x48521)+P14(x48521,x48521,f92(x48521)) % 112.26/112.09 [4655]~E(x46551,f2(a899))+E(f317(f90(a1),x46551),f2(a1)) % 112.26/112.09 [4662]~P94(x46621)+E(f317(f94(x46621),a77),f2(x46621)) % 112.26/112.09 [4665]~E(f564(x46651),f2(a899))+E(f317(f155(a899),x46651),f2(a899)) % 112.26/112.09 [4666]~P107(x46661)+E(f226(x46661,f224(x46661)),f228(x46661)) % 112.26/112.09 [4667]~P107(x46671)+E(f227(x46671,f224(x46671)),f223(x46671)) % 112.26/112.09 [4668]~P90(x46681)+E(f76(x46681,f2(x46681)),f2(x46681)) % 112.26/112.09 [4677]~P145(x46771)+E(f317(f90(x46771),f72(a899)),f72(x46771)) % 112.26/112.09 [4678]~P145(x46781)+E(f317(f90(x46781),f2(a899)),f2(x46781)) % 112.26/112.09 [4679]~P141(x46791)+E(f317(f93(x46791),f72(a1)),f72(x46791)) % 112.26/112.09 [4680]~P141(x46801)+E(f317(f93(x46801),f2(a1)),f2(x46801)) % 112.26/112.09 [4681]E(x46811,f2(a899))+~E(f317(f90(a1),x46811),f2(a1)) % 112.26/112.09 [4717]~P112(x47171)+E(f317(f70(x47171),f72(x47171)),f72(x47171)) % 112.26/112.09 [4718]~P86(x47181)+E(f317(f70(x47181),f2(x47181)),f2(x47181)) % 112.26/112.09 [4719]~P96(x47191)+E(f317(f73(x47191),f178(x47191)),f232(x47191)) % 112.26/112.09 [4720]~P76(x47201)+E(f317(f73(x47201),f2(x47201)),f2(x47201)) % 112.26/112.09 [4721]~P96(x47211)+E(f317(f73(x47211),f232(x47211)),f178(x47211)) % 112.26/112.09 [4722]~P81(x47221)+E(f317(f155(x47221),f103(x47221)),f2(x47221)) % 112.26/112.09 [4740]~P35(x47401)+P39(f317(f162(a1),x47401)) % 112.26/112.09 [4765]~P94(x47651)+E(f317(f73(x47651),f72(x47651)),f317(f94(x47651),a87)) % 112.26/112.09 [4780]~P94(x47801)+P27(x47801,f317(f94(x47801),a77)) % 112.26/112.09 [4806]P35(x48061)+~P39(f317(f162(a1),x48061)) % 112.26/112.09 [4853]E(f317(f90(a1),f317(a95,x48531)),x48531)+P1(f317(a183,x48531)) % 112.26/112.09 [4923]~P115(x49231)+E(f235(x49231,f72(x49231),f75(x49231)),f234(x49231)) % 112.26/112.09 [4956]~P94(x49561)+~P27(x49561,f317(f94(x49561),a87)) % 112.26/112.09 [5109]E(f317(f70(a1),x51091),x51091)+P1(f317(f317(f225(a1),x51091),f2(a1))) % 112.26/112.09 [5127]~E(f317(a95,x51271),f2(a899))+P1(f317(f317(f224(a1),x51271),f2(a1))) % 112.26/112.09 [5193]~P1(f317(a183,x51931))+P1(f317(f317(f225(a1),x51931),f2(a1))) % 112.26/112.09 [5233]~P126(x52331)+P1(f317(f317(f224(x52331),f2(x52331)),f72(x52331))) % 112.26/112.09 [5234]~P141(x52341)+P1(f317(f317(f319(x52341),f72(x52341)),f100(x52341))) % 112.26/112.09 [5235]~P145(x52351)+P1(f317(f317(f319(x52351),f72(x52351)),f176(x52351))) % 112.26/112.09 [5236]~P141(x52361)+P1(f317(f317(f319(x52361),f2(x52361)),f100(x52361))) % 112.26/112.09 [5237]~P145(x52371)+P1(f317(f317(f319(x52371),f2(x52371)),f176(x52371))) % 112.26/112.09 [5238]~P126(x52381)+P1(f317(f317(f225(x52381),f2(x52381)),f72(x52381))) % 112.26/112.09 [5290]E(x52901,f72(a899))+~P1(f317(f317(f277(a899),x52901),f72(a899))) % 112.26/112.09 [5291]E(x52911,f2(a899))+~P1(f317(f317(f224(a899),x52911),f2(a899))) % 112.26/112.09 [5333]E(f317(a95,x53331),f2(a899))+~P1(f317(f317(f224(a1),x53331),f2(a1))) % 112.26/112.09 [5391]P1(f317(a183,x53911))+~P1(f317(f317(f225(a1),x53911),f2(a1))) % 112.26/112.09 [5398]~P108(x53981)+P16(x53981,f900(x53981),f138(x53981,x53981,f7(x53981))) % 112.26/112.09 [5416]P39(x54161)+~P1(f317(f317(f224(a1),f2(a1)),f323(x54161))) % 112.26/112.09 [5421]E(f317(f70(a1),x54211),f317(f73(a1),x54211))+~P1(f317(f317(f225(a1),x54211),f2(a1))) % 112.26/112.09 [5593]~P126(x55931)+~P1(f317(f317(f224(x55931),f72(x55931)),f2(x55931))) % 112.26/112.09 [5594]~P126(x55941)+~P1(f317(f317(f225(x55941),f72(x55941)),f2(x55941))) % 112.26/112.09 [5610]~E(x56101,f2(a899))+P1(f317(f317(f224(a1),f317(f90(a1),x56101)),f2(a1))) % 112.26/112.09 [5611]~E(x56111,f2(a1))+P1(f317(f317(f225(a1),f317(f70(a1),x56111)),f72(a1))) % 112.26/112.09 [5733]~P81(x57331)+E(f132(x57331,x57331,f74(x57331),f2(x57331)),f155(x57331)) % 112.26/112.09 [5916]~P95(x59161)+P24(a899,x59161,f90(x59161),f232(f906(a899,a895))) % 112.26/112.09 [6123]E(x61231,f2(a899))+~P1(f317(f317(f224(a1),f317(f90(a1),x61231)),f2(a1))) % 112.26/112.09 [6124]E(x61241,f2(a1))+~P1(f317(f317(f225(a1),f317(f70(a1),x61241)),f72(a1))) % 112.26/112.09 [6946]~P1(f317(f317(f225(a1),x69461),f2(a1)))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x69461),x69461)),f2(a1))) % 112.26/112.09 [7508]P1(f317(f317(f225(a1),x75081),f2(a1)))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),x75081),x75081)),f2(a1))) % 112.26/112.09 [8059]E(x80591,f317(a5,f2(a899)))+P1(f317(f317(f225(a899),f317(f317(f3(a899),f317(a22,x80591)),f317(a102,f2(a899)))),f317(a22,x80591))) % 112.26/112.09 [8826]~P1(f317(f317(f225(a1),x88261),f2(a1)))+P1(f317(f317(f225(a1),f317(f317(f3(a1),f317(f317(f74(a1),x88261),x88261)),a87)),f2(a1))) % 112.26/112.09 [8923]~P1(f317(f317(f225(a1),x89231),f2(a1)))+P1(f317(f317(f225(a1),f317(f317(f74(a1),f317(f317(f74(a1),f72(a1)),x89231)),x89231)),f2(a1))) % 112.26/112.09 [9241]P1(f317(f317(f225(a1),x92411),f2(a1)))+~P1(f317(f317(f225(a1),f317(f317(f3(a1),f317(f317(f74(a1),x92411),x92411)),a87)),f2(a1))) % 112.26/112.09 [9303]P1(f317(f317(f225(a1),x93031),f2(a1)))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),f317(f317(f74(a1),f72(a1)),x93031)),x93031)),f2(a1))) % 112.26/112.09 [4754]~E(a77,x47541)+E(f317(f317(f74(a1),x47541),x47541),a77) % 112.26/112.09 [4755]~E(x47551,a77)+E(f317(f317(f74(a1),x47551),x47551),a77) % 112.26/112.09 [4766]E(x47661,f2(a1))+E(f317(f317(f31(a1),x47661),x47661),f72(a1)) % 112.26/112.09 [4900]E(x49001,a77)+~E(f317(f317(f74(a1),x49001),x49001),a77) % 112.26/112.09 [4901]E(a77,x49011)+~E(f317(f317(f74(a1),x49011),x49011),a77) % 112.26/112.09 [4913]~P5(x49131)+E(f32(x49131,f178(f906(x49131,a895))),f178(x49131)) % 112.26/112.09 [4914]~P5(x49141)+E(f32(x49141,f232(f906(x49141,a895))),f232(x49141)) % 112.26/112.09 [4915]~P5(x49151)+E(f33(x49151,f178(f906(x49151,a895))),f232(x49151)) % 112.26/112.09 [4916]~P5(x49161)+E(f33(x49161,f232(f906(x49161,a895))),f178(x49161)) % 112.26/112.09 [4917]~P108(x49171)+E(f129(x49171,f178(f906(x49171,a895))),f103(x49171)) % 112.26/112.09 [5064]E(x50641,f2(a899))+P1(f317(f317(f225(a899),f2(a899)),x50641)) % 112.26/112.09 [5084]~P6(x50841)+P1(f317(f317(f224(a1),f2(a1)),x50841)) % 112.26/112.09 [5118]~E(f317(f94(a899),x51181),f2(a899))+P1(f317(f317(f224(a1),x51181),a77)) % 112.26/112.09 [5123]P39(x51231)+P1(f317(f317(f319(a1),f323(x51231)),x51231)) % 112.26/112.09 [5124]E(x51241,f317(a5,f2(a899)))+P1(f317(f317(f224(a89),f72(a89)),x51241)) % 112.26/112.09 [5165]P1(f317(a183,x51651))+P1(f317(f317(f224(a1),f2(a1)),x51651)) % 112.26/112.09 [5215]E(f317(f90(a1),f317(a95,x52151)),f2(a1))+P1(f317(f317(f224(a1),f2(a1)),x52151)) % 112.26/112.09 [5272]E(f317(f90(a1),f317(f94(a899),x52721)),f317(f94(a1),x52721))+P1(f317(a183,f317(f94(a1),x52721))) % 112.26/112.09 [5297]E(f317(f94(a899),x52971),f2(a899))+~P1(f317(a183,f317(f94(a1),x52971))) % 112.26/112.09 [5298]E(f317(f94(a899),x52981),f2(a899))+~P1(f317(f317(f224(a1),x52981),a77)) % 112.26/112.09 [5330]P6(x53301)+~P1(f317(f317(f224(a1),f2(a1)),x53301)) % 112.26/112.09 [5386]P149(f222(a896,f34(x53861)))+~P1(f317(f317(f319(a897),x53861),a907)) % 112.26/112.09 [5401]E(f317(a102,f582(x54011)),x54011)+~P1(f317(f317(f225(a899),f2(a899)),x54011)) % 112.26/112.09 [5410]E(f317(a102,f317(f94(a899),x54101)),f72(a899))+~P1(f317(a183,f317(f94(a1),x54101))) % 112.26/112.09 [5417]E(f317(f90(a1),f881(x54171)),x54171)+~P1(f317(f317(f225(a1),f2(a1)),x54171)) % 112.26/112.09 [5424]~E(x54241,f317(a5,f2(a899)))+~P1(f317(f317(f224(a89),f72(a89)),x54241)) % 112.26/112.09 [5431]E(f317(f90(a1),f317(f94(a899),x54311)),f2(a1))+~P1(f317(a183,f317(f94(a1),x54311))) % 112.26/112.09 [5457]E(f317(f155(a899),x54571),f2(a899))+P1(f317(f317(f319(a899),f564(x54571)),f317(f162(a899),x54571))) % 112.26/112.09 [5478]E(f317(f90(a1),f317(a95,x54781)),x54781)+~P1(f317(f317(f224(a1),f2(a1)),x54781)) % 112.26/112.09 [5486]~P1(f317(a183,x54861))+~P1(f317(f317(f224(a1),f2(a1)),x54861)) % 112.26/112.09 [5586]E(f317(f317(f74(a899),f72(a899)),f317(f94(a899),x55861)),f72(a899))+~P1(f317(f317(f225(a1),x55861),a77)) % 112.26/112.09 [5652]E(x56521,f2(a899))+~P1(f317(f317(f225(a899),x56521),f317(a102,f2(a899)))) % 112.26/112.09 [5674]E(x56741,f317(a102,f2(a899)))+~P1(f317(f317(f277(a899),x56741),f317(a102,f2(a899)))) % 112.26/112.09 [5692]E(f317(f317(f3(a899),f317(f94(a899),x56921)),f72(a899)),f2(a899))+~P1(f317(f317(f224(a1),x56921),a77)) % 112.26/112.09 [5693]E(f317(f317(f74(a899),f317(f94(a899),x56931)),f72(a899)),f72(a899))+~P1(f317(f317(f225(a1),x56931),a77)) % 112.26/112.09 [5705]~P39(x57051)+E(f317(f30(a899),f317(f300(a1,a899,a95),x57051)),f317(f30(a1),x57051)) % 112.26/112.09 [5734]~P108(x57341)+E(f227(x57341,f317(f9(x57341,x57341,a895),f224(x57341))),f228(x57341)) % 112.26/112.09 [5735]~P108(x57351)+E(f226(x57351,f317(f9(x57351,x57351,a895),f224(x57351))),f223(x57351)) % 112.26/112.09 [5745]E(f41(a899,f317(a102,f2(a899)),f317(f94(a899),x57451)),f317(a102,f2(a899)))+~P1(f317(a183,f317(f94(a1),x57451))) % 112.26/112.09 [5754]~P1(f317(f317(f225(a1),f2(a1)),x57541))+P1(f317(f317(f224(a1),f72(a1)),x57541)) % 112.26/112.09 [5755]P1(f317(f317(f225(a1),f2(a1)),x57551))+~P1(f317(f317(f224(a1),f72(a1)),x57551)) % 112.26/112.09 [5766]E(f317(a102,f317(f317(f3(a899),x57661),f72(a899))),x57661)+~P1(f317(f317(f225(a899),f2(a899)),x57661)) % 112.26/112.09 [5822]P1(f317(f317(f225(a899),f2(a899)),f881(x58221)))+~P1(f317(f317(f225(a1),f2(a1)),x58221)) % 112.26/112.09 [5883]E(f41(a1,f317(f94(a1),a87),x58831),f317(f317(f3(a1),x58831),f72(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x58831)) % 112.26/112.09 [5929]~P1(f317(f317(f225(a1),a77),x59291))+P1(f317(f317(f225(a899),f2(a899)),f317(f94(a899),x59291))) % 112.26/112.09 [5934]E(f317(a22,f791(x59341)),x59341)+~P1(f317(f317(f319(a899),x59341),f232(f906(a899,a895)))) % 112.26/112.09 [5987]P1(f317(f317(f225(a899),f2(a899)),f317(a95,x59871)))+~P1(f317(f317(f225(a1),f2(a1)),x59871)) % 112.26/112.09 [6038]~P1(f317(f317(f225(a899),f2(a899)),x60381))+P1(f317(f317(f225(a1),f2(a1)),f317(f90(a1),x60381))) % 112.26/112.09 [6074]~P1(f317(f317(f225(a899),f2(a899)),f317(a95,x60741)))+P1(f317(f317(f225(a1),f2(a1)),x60741)) % 112.26/112.09 [6089]~P39(x60891)+E(f317(f300(a899,a1,f90(a1)),f317(f300(a1,a899,a95),x60891)),x60891) % 112.26/112.09 [6102]P1(f317(f317(f225(a1),a77),x61021))+~P1(f317(f317(f225(a899),f2(a899)),f317(f94(a899),x61021))) % 112.26/112.09 [6161]P1(f317(f317(f225(a899),f2(a899)),x61611))+~P1(f317(f317(f225(a1),f2(a1)),f317(f90(a1),x61611))) % 112.26/112.09 [6279]E(f317(f300(a899,a1,f90(a1)),f317(f272(a899),f317(a95,x62791))),f317(f292(a1,f2(a1)),x62791))+~P1(f317(f317(f224(a1),f2(a1)),x62791)) % 112.26/112.09 [6296]~P126(x62961)+P1(f317(f317(f225(x62961),f2(x62961)),f317(f317(f74(x62961),f72(x62961)),f72(x62961)))) % 112.26/112.09 [6347]P1(f317(f317(f225(a899),f317(a102,f2(a899))),f317(a95,x63471)))+~P1(f317(f317(f225(a1),f72(a1)),x63471)) % 112.26/112.09 [6449]E(x64491,f2(a1))+P1(f317(f45(f2(a1),x64491),f317(f317(f242(a1,a1),f2(a1)),f2(a1)))) % 112.26/112.09 [6623]~P1(f317(f317(f225(a899),f317(a102,f2(a899))),f317(a95,x66231)))+P1(f317(f317(f225(a1),f72(a1)),x66231)) % 112.26/112.09 [7063]~P117(x70631)+P36(x70631,f317(f252(f905(x70631,x70631)),f317(f247(x70631,x70631,a895),f225(x70631)))) % 112.26/112.09 [5639]E(f317(f94(a899),f317(f317(f3(a1),x56391),a87)),f317(a102,f317(f94(a899),x56391)))+P1(f317(a183,f317(f94(a1),x56391))) % 112.26/112.09 [5655]~P35(x56551)+E(f317(f317(f144(a899,a1),f90(a1)),f317(f317(f144(a1,a899),a95),x56551)),x56551) % 112.26/112.09 [5772]E(f317(f73(a1),f317(f90(a1),f317(a102,f326(x57721)))),x57721)+~P1(f317(f317(f225(a1),x57721),f2(a1))) % 112.26/112.09 [5782]E(f317(f317(f74(a899),f72(a899)),f317(f94(a899),x57821)),f317(f94(a899),f317(f317(f3(a1),x57821),a87)))+P1(f317(f317(f225(a1),x57821),a77)) % 112.26/112.09 [5824]E(f317(f317(f31(a1),f317(f94(a1),a87)),x58241),f317(f94(a1),a87))+~P1(f317(f317(f225(a1),f2(a1)),x58241)) % 112.26/112.09 [5925]E(f317(f317(f3(a899),f317(f94(a899),x59251)),f72(a899)),f317(f94(a899),f317(f317(f74(a1),x59251),a87)))+P1(f317(f317(f224(a1),x59251),a77)) % 112.26/112.09 [5926]E(f317(f317(f74(a899),f317(f94(a899),x59261)),f72(a899)),f317(f94(a899),f317(f317(f3(a1),x59261),a87)))+P1(f317(f317(f225(a1),x59261),a77)) % 112.26/112.09 [5972]E(f317(a95,f317(f317(f74(a1),f72(a1)),x59721)),f317(a102,f317(a95,x59721)))+~P1(f317(f317(f224(a1),f2(a1)),x59721)) % 112.26/112.09 [6009]E(f317(a102,f317(f317(f3(a899),x60091),f317(a102,f2(a899)))),x60091)+~P1(f317(f317(f225(a899),f2(a899)),x60091)) % 112.26/112.09 [6228]E(f41(a899,f317(a102,f2(a899)),f317(f94(a899),x62281)),f317(a95,f41(a1,f72(a1),f317(f94(a1),x62281))))+P1(f317(a183,f317(f94(a1),x62281))) % 112.26/112.09 [6272]~P1(f317(f317(f224(a1),a77),x62721))+P1(f317(f317(f224(a1),a77),f317(f317(f74(a1),x62721),x62721))) % 112.26/112.09 [6273]~P1(f317(f317(f225(a1),a87),x62731))+P1(f317(f317(f224(a1),a87),f317(f317(f74(a1),x62731),x62731))) % 112.26/112.09 [6274]~P1(f317(f317(f225(a1),a77),x62741))+P1(f317(f317(f225(a1),a77),f317(f317(f74(a1),x62741),x62741))) % 112.26/112.09 [6275]~P1(f317(f317(f225(a1),a87),x62751))+P1(f317(f317(f225(a1),a87),f317(f317(f74(a1),x62751),x62751))) % 112.26/112.09 [6463]~P1(f317(f29(x64631),f232(f906(x64631,a895))))+P1(f317(f29(f902(x64631)),f232(f906(f902(x64631),a895)))) % 112.26/112.09 [6550]~P1(f317(f317(f224(a1),f2(a1)),x65501))+P1(f317(f317(f225(a1),f2(a1)),f317(f317(f74(a1),f72(a1)),x65501))) % 112.26/112.09 [6557]E(f317(f241(a1,a1),f43(f72(a1),f317(f94(a1),x65571))),f317(f317(f31(a1),f72(a1)),f317(f94(a1),x65571)))+~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x65571))) % 112.26/112.09 [6582]E(f317(f246(a1,a1),f43(f72(a1),f317(f94(a1),x65821))),f41(a1,f72(a1),f317(f94(a1),x65821)))+~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x65821))) % 112.26/112.09 [6594]P1(f317(f29(x65941),f232(f906(x65941,a895))))+~P1(f317(f29(f902(x65941)),f232(f906(f902(x65941),a895)))) % 112.26/112.09 [6624]P1(f317(f317(f224(a1),a77),x66241))+~P1(f317(f317(f224(a1),a77),f317(f317(f74(a1),x66241),x66241))) % 112.26/112.09 [6625]P1(f317(f317(f225(a1),a77),x66251))+~P1(f317(f317(f225(a1),a77),f317(f317(f74(a1),x66251),x66251))) % 112.26/112.09 [6626]P1(f317(f317(f225(a1),a87),x66261))+~P1(f317(f317(f224(a1),a87),f317(f317(f74(a1),x66261),x66261))) % 112.26/112.09 [6627]P1(f317(f317(f225(a1),a87),x66271))+~P1(f317(f317(f225(a1),a87),f317(f317(f74(a1),x66271),x66271))) % 112.26/112.09 [6950]~P1(f317(f29(x69501),f232(f906(x69501,a895))))+P1(f317(f317(f225(a899),f2(a899)),f317(f30(x69501),f232(f906(x69501,a895))))) % 112.26/112.09 [7546]P1(f317(f29(a899),x75461))+~P1(f317(f29(a1),f317(f300(a899,a1,f90(a1)),x75461))) % 112.26/112.09 [5562]~E(a87,x55621)+E(f317(f317(f3(a1),f317(f317(f74(a1),x55621),x55621)),a87),a87) % 112.26/112.09 [5563]~E(x55631,a87)+E(f317(f317(f3(a1),f317(f317(f74(a1),x55631),x55631)),a87),a87) % 112.26/112.09 [6097]E(x60971,a87)+~E(f317(f317(f3(a1),f317(f317(f74(a1),x60971),x60971)),a87),a87) % 112.26/112.09 [6098]E(a87,x60981)+~E(f317(f317(f3(a1),f317(f317(f74(a1),x60981),x60981)),a87),a87) % 112.26/112.09 [6519]~E(f317(f94(a899),x65191),f2(a899))+P1(f317(a183,f317(f94(a1),f317(f317(f74(a1),x65191),a87)))) % 112.26/112.09 [6880]~P1(f317(a183,f317(f94(a1),x68801)))+P1(f317(a183,f317(f94(a1),f317(f317(f74(a1),x68801),x68801)))) % 112.26/112.09 [6881]~P1(f317(f317(f224(a1),x68811),a77))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x68811),x68811)),a77)) % 112.26/112.09 [6882]~P1(f317(f317(f224(a1),x68821),a87))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x68821),x68821)),a87)) % 112.26/112.09 [6883]~P1(f317(f317(f225(a1),x68831),a77))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x68831),x68831)),a77)) % 112.26/112.09 [6884]~P1(f317(f317(f224(a1),x68841),a87))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x68841),x68841)),a87)) % 112.26/112.09 [7209]E(f317(f94(a899),x72091),f2(a899))+~P1(f317(a183,f317(f94(a1),f317(f317(f74(a1),x72091),a87)))) % 112.26/112.09 [7461]~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x74611)))+P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),f317(f317(f74(a1),x74611),x74611)))) % 112.26/112.09 [7462]P1(f317(a183,f317(f94(a1),x74621)))+~P1(f317(a183,f317(f94(a1),f317(f317(f74(a1),x74621),x74621)))) % 112.26/112.09 [7463]P1(f317(f317(f224(a1),x74631),a77))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x74631),x74631)),a77)) % 112.26/112.09 [7464]P1(f317(f317(f224(a1),x74641),a87))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x74641),x74641)),a87)) % 112.26/112.09 [7465]P1(f317(f317(f224(a1),x74651),a87))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),x74651),x74651)),a87)) % 112.26/112.09 [7466]P1(f317(f317(f225(a1),x74661),a77))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),x74661),x74661)),a77)) % 112.26/112.09 [7828]E(f317(a98,f512(x78281)),x78281)+~P1(f317(f317(f319(f906(f905(a899,a899),a895)),x78281),a88)) % 112.26/112.09 [6436]~P94(x64361)+E(f317(f94(x64361),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f72(x64361)) % 112.26/112.09 [6930]~P1(f317(a183,f317(f94(a1),x69301)))+E(f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),x69301),x69301)),a87)),f2(a899)) % 112.26/112.09 [8004]~P1(f317(f317(f225(a1),f317(f94(a1),x80041)),f2(a1)))+E(f317(f241(a1,a1),f317(a47,f46(f317(f73(a1),f72(a1)),f317(f73(a1),f317(f94(a1),x80041))))),f317(f317(f31(a1),f72(a1)),f317(f94(a1),x80041))) % 112.26/112.09 [8017]~P1(f317(f317(f225(a1),f317(f94(a1),x80171)),f2(a1)))+E(f317(f246(a1,a1),f317(a47,f46(f317(f73(a1),f72(a1)),f317(f73(a1),f317(f94(a1),x80171))))),f41(a1,f72(a1),f317(f94(a1),x80171))) % 112.26/112.09 [8066]~P1(f317(f317(f224(a1),a77),x80661))+P1(f317(f317(f224(a1),a77),f317(f317(f3(a1),f317(f317(f74(a1),x80661),x80661)),a87))) % 112.26/112.09 [8067]~P1(f317(f317(f224(a1),a87),x80671))+P1(f317(f317(f224(a1),a87),f317(f317(f3(a1),f317(f317(f74(a1),x80671),x80671)),a87))) % 112.26/112.09 [8068]~P1(f317(f317(f224(a1),a77),x80681))+P1(f317(f317(f225(a1),a77),f317(f317(f3(a1),f317(f317(f74(a1),x80681),x80681)),a87))) % 112.26/112.09 [8069]~P1(f317(f317(f225(a1),a87),x80691))+P1(f317(f317(f225(a1),a87),f317(f317(f3(a1),f317(f317(f74(a1),x80691),x80691)),a87))) % 112.26/112.09 [8367]~P94(x83671)+~P27(x83671,f317(f94(x83671),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))) % 112.26/112.09 [8551]P1(f317(f317(f224(a1),a77),x85511))+~P1(f317(f317(f224(a1),a77),f317(f317(f3(a1),f317(f317(f74(a1),x85511),x85511)),a87))) % 112.26/112.09 [8552]P1(f317(f317(f224(a1),a77),x85521))+~P1(f317(f317(f225(a1),a77),f317(f317(f3(a1),f317(f317(f74(a1),x85521),x85521)),a87))) % 112.26/112.09 [8553]P1(f317(f317(f224(a1),a87),x85531))+~P1(f317(f317(f224(a1),a87),f317(f317(f3(a1),f317(f317(f74(a1),x85531),x85531)),a87))) % 112.26/112.09 [8554]P1(f317(f317(f225(a1),a87),x85541))+~P1(f317(f317(f225(a1),a87),f317(f317(f3(a1),f317(f317(f74(a1),x85541),x85541)),a87))) % 112.26/112.09 [8873]E(f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),x88731),x88731)),a87)),f317(f317(f80(a899,a899),f317(f94(a899),x88731)),f317(f317(f10(a899,a899,a899),a102),f317(f317(f20(a899,a899,a899),f74(a899)),f7(a899)))))+P1(f317(a183,f317(f94(a1),x88731))) % 112.26/112.09 [9741]E(x97411,f178(f906(f905(a899,a899),a895)))+P1(f317(f317(f319(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),x97411),f178(f906(f905(a899,a899),a895)))),a27)) % 112.26/112.09 [8800]~P1(f317(a183,f317(f94(a1),x88001)))+P1(f317(a183,f317(f94(a1),f317(f317(f3(a1),f317(f317(f74(a1),x88001),x88001)),a87)))) % 112.26/112.09 [8801]~P1(f317(f317(f225(a1),x88011),a77))+P1(f317(f317(f224(a1),f317(f317(f3(a1),f317(f317(f74(a1),x88011),x88011)),a87)),a77)) % 112.26/112.09 [8802]~P1(f317(f317(f224(a1),x88021),a87))+P1(f317(f317(f224(a1),f317(f317(f3(a1),f317(f317(f74(a1),x88021),x88021)),a87)),a87)) % 112.26/112.09 [8803]~P1(f317(f317(f225(a1),x88031),a77))+P1(f317(f317(f225(a1),f317(f317(f3(a1),f317(f317(f74(a1),x88031),x88031)),a87)),a77)) % 112.26/112.09 [8804]~P1(f317(f317(f225(a1),x88041),a87))+P1(f317(f317(f225(a1),f317(f317(f3(a1),f317(f317(f74(a1),x88041),x88041)),a87)),a87)) % 112.26/112.09 [8914]~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x89141)))+P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),f317(f317(f3(a1),f317(f317(f74(a1),x89141),x89141)),a87)))) % 112.26/112.09 [9072]~P94(x90721)+E(f317(f317(f74(x90721),f72(x90721)),f72(x90721)),f317(f94(x90721),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))) % 112.26/112.09 [9225]P1(f317(a183,f317(f94(a1),x92251)))+~P1(f317(a183,f317(f94(a1),f317(f317(f3(a1),f317(f317(f74(a1),x92251),x92251)),a87)))) % 112.26/112.09 [9226]P1(f317(f317(f224(a1),x92261),a87))+~P1(f317(f317(f224(a1),f317(f317(f3(a1),f317(f317(f74(a1),x92261),x92261)),a87)),a87)) % 112.26/112.09 [9227]P1(f317(f317(f225(a1),x92271),a77))+~P1(f317(f317(f224(a1),f317(f317(f3(a1),f317(f317(f74(a1),x92271),x92271)),a87)),a77)) % 112.26/112.09 [9228]P1(f317(f317(f225(a1),x92281),a77))+~P1(f317(f317(f225(a1),f317(f317(f3(a1),f317(f317(f74(a1),x92281),x92281)),a87)),a77)) % 112.26/112.09 [9229]P1(f317(f317(f225(a1),x92291),a87))+~P1(f317(f317(f225(a1),f317(f317(f3(a1),f317(f317(f74(a1),x92291),x92291)),a87)),a87)) % 112.26/112.09 [9786]~P1(f317(f29(f905(a899,a899)),x97861))+P1(f317(f317(f319(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),f178(f906(f905(a899,a899),a895))),x97861)),a64)) % 112.26/112.09 [9562]~P145(x95621)+E(f317(f317(f234(x95621),f72(x95621)),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f72(x95621)) % 112.26/112.09 [9563]~P145(x95631)+E(f317(f317(f234(x95631),f2(x95631)),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f2(x95631)) % 112.26/112.09 [10011]~P1(f317(f317(f225(a899),f72(a899)),x100111))+P1(f317(f317(f225(a899),f2(a899)),f317(f317(f31(a899),x100111),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))) % 112.26/112.09 [10017]~P1(f317(f317(f225(a899),f2(a899)),x100171))+P1(f317(f317(f225(a899),f2(a899)),f317(f317(f31(a899),f317(f317(f74(a899),x100171),f72(a899))),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))) % 112.26/112.09 [10055]~E(f41(a899,x100551,f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f72(a899))+P1(f317(f317(f225(a899),f2(a899)),f41(a899,x100551,f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))) % 112.26/112.09 [10086]E(f41(a899,x100861,f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f72(a899))+~P1(f317(f317(f225(a899),f2(a899)),f41(a899,x100861,f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))) % 112.26/112.09 [4686]~P7(x46861,x46862)+P42(x46861,x46862) % 112.26/112.09 [4687]~P36(x46871,x46872)+P57(x46871,x46872) % 112.26/112.09 [4688]~P43(x46881,x46882)+P57(x46881,x46882) % 112.26/112.09 [4690]~P7(x46901,x46902)+P49(x46901,x46902) % 112.26/112.09 [4692]~P15(x46921,x46922)+P49(x46921,x46922) % 112.26/112.09 [4694]~P7(x46941,x46942)+P50(x46941,x46942) % 112.26/112.09 [4696]~P15(x46961,x46962)+P50(x46961,x46962) % 112.26/112.09 [4697]~P7(x46971,x46972)+P15(x46971,x46972) % 112.26/112.09 [4647]~E(x46471,x46472)+E(f259(x46471,x46472),f72(a89)) % 112.26/112.09 [4650]E(f206(x46501,x46502),x46501)+~E(x46502,f2(a899)) % 112.26/112.09 [4657]~E(x46572,f103(x46571))+E(f142(x46571,x46572),f103(x46571)) % 112.26/112.09 [4676]~E(f142(x46762,x46761),f103(x46762))+E(x46761,f103(x46762)) % 112.26/112.09 [4701]~P65(x47012)+P65(f906(x47011,x47012)) % 112.26/112.09 [4702]~P66(x47022)+P66(f906(x47021,x47022)) % 112.26/112.09 [4703]~P107(x47032)+P107(f906(x47031,x47032)) % 112.26/112.09 [4704]~P109(x47042)+P109(f906(x47041,x47042)) % 112.26/112.09 [4705]~P67(x47052)+P67(f906(x47051,x47052)) % 112.26/112.09 [4706]~P96(x47062)+P96(f906(x47061,x47062)) % 112.26/112.09 [4707]~P89(x47072)+P89(f906(x47071,x47072)) % 112.26/112.09 [4708]~P99(x47082)+P98(f906(x47081,x47082)) % 112.26/112.09 [4709]~P99(x47092)+P99(f906(x47091,x47092)) % 112.26/112.09 [4710]~P101(x47102)+P100(f906(x47101,x47102)) % 112.26/112.09 [4711]~P101(x47112)+P102(f906(x47111,x47112)) % 112.26/112.09 [4712]~P116(x47122)+P116(f906(x47121,x47122)) % 112.26/112.09 [4713]~P5(x47132)+P5(f906(x47131,x47132)) % 112.26/112.09 [4714]~P103(x47142)+P103(f906(x47141,x47142)) % 112.26/112.09 [4715]~P99(x47152)+P104(f906(x47151,x47152)) % 112.26/112.09 [4716]~P101(x47162)+P101(f906(x47161,x47162)) % 112.26/112.09 [4729]E(x47291,x47292)+~E(f317(a102,x47291),f317(a102,x47292)) % 112.26/112.09 [4730]E(x47301,x47302)+~E(f317(a98,x47301),f317(a98,x47302)) % 112.26/112.09 [4731]E(x47311,x47312)+~E(f317(a5,x47311),f317(a5,x47312)) % 112.26/112.09 [4733]E(x47331,x47332)+~E(f317(a22,x47331),f317(a22,x47332)) % 112.26/112.09 [4782]P38(x47821,x47822)+~E(f688(x47822,x47821),f689(x47822,x47821)) % 112.26/112.09 [4812]~P57(x48121,x48122)+P38(x48121,f297(x48121,x48122)) % 112.26/112.09 [4813]~P51(x48131,x48132)+P51(x48131,f297(x48131,x48132)) % 112.26/112.09 [4826]~P3(x48261)+E(f41(x48261,x48262,x48262),f2(x48261)) % 112.26/112.09 [4860]~P36(x48601,x48602)+P36(f900(x48601),f136(x48601,x48602)) % 112.26/112.09 [4861]~P36(x48611,x48612)+P36(f900(x48611),f135(x48611,x48612)) % 112.26/112.09 [4862]~P37(x48621,x48622)+P37(f900(x48621),f137(x48621,x48622)) % 112.26/112.09 [4863]~P37(x48631,x48632)+P37(f900(x48631),f148(x48631,x48632)) % 112.26/112.09 [4864]~P51(x48641,x48642)+P51(f900(x48641),f148(x48641,x48642)) % 112.26/112.09 [4961]~P36(x49611,x49612)+P36(f906(x49611,a895),f308(x49611,x49612)) % 112.26/112.09 [4962]~P36(x49621,x49622)+P36(f906(x49621,a895),f309(x49621,x49622)) % 112.26/112.09 [5093]~P6(x50931)+P39(f293(a1,x50931,x50932)) % 112.26/112.09 [5196]~P36(x51961,x51962)+P59(x51961,f62(x51961,x51961,x51962)) % 112.26/112.09 [5699]~P79(x56991)+P24(x56991,x56991,f73(x56991),x56992) % 112.26/112.09 [4671]~E(x46712,f103(x46711))+E(f317(f157(x46711),x46712),f103(x46711)) % 112.26/112.09 [4672]~E(x46722,f103(x46721))+E(f317(f158(x46721),x46722),f103(x46721)) % 112.26/112.09 [4735]E(x47351,f317(a95,x47352))+~E(f317(f90(a1),x47351),x47352) % 112.26/112.09 [4738]E(x47381,f103(x47382))+~E(f317(f157(x47382),x47381),f103(x47382)) % 112.26/112.09 [4739]E(x47391,f103(x47392))+~E(f317(f158(x47392),x47391),f103(x47392)) % 112.26/112.09 [4751]~P94(x47511)+E(f317(f94(x47511),x47512),f317(f93(x47511),x47512)) % 112.26/112.09 [4759]~P2(x47591)+P1(f317(f29(x47591),x47592)) % 112.26/112.09 [4767]~E(f647(x47672,x47671),f103(x47671))+E(f169(x47671,x47672),f103(f900(x47671))) % 112.26/112.09 [4776]~E(x47762,f103(x47761))+E(f317(f162(x47761),x47762),f178(f906(x47761,a895))) % 112.26/112.09 [4777]~E(x47772,f103(x47771))+E(f178(f906(x47771,a895)),f317(f162(x47771),x47772)) % 112.26/112.09 [4779]E(x47791,x47792)+~E(f317(f90(a1),x47791),f317(f90(a1),x47792)) % 112.26/112.09 [4783]E(f204(x47831,x47832),f2(a899))+P1(f317(f29(x47831),x47832)) % 112.26/112.09 [4801]~P112(x48011)+E(f76(x48011,f76(x48011,x48012)),f76(x48011,x48012)) % 112.26/112.09 [4815]~P80(x48151)+E(f317(f317(f234(x48151),x48152),f72(a899)),x48152) % 112.26/112.09 [4816]~P119(x48161)+E(f317(f317(f234(x48161),x48162),f72(a899)),x48162) % 112.26/112.09 [4817]~P51(x48171,x48172)+E(f317(f276(x48171,x48171),x48172),x48172) % 112.26/112.09 [4821]E(x48211,x48212)+E(f259(x48211,x48212),f317(f317(f74(a89),x48212),f72(a89))) % 112.26/112.09 [4824]E(f317(f30(x48241),x48242),f2(a899))+P1(f317(f29(x48241),x48242)) % 112.26/112.09 [4827]~E(f142(x48271,x48272),x48272)+P1(f317(f127(x48271),x48272)) % 112.26/112.09 [4830]~P76(x48301)+E(f317(f317(f3(x48301),x48302),f2(x48301)),x48302) % 112.26/112.09 [4831]~P69(x48311)+E(f317(f317(f74(x48311),x48312),f2(x48311)),x48312) % 112.26/112.09 [4832]~P119(x48321)+E(f317(f317(f74(x48321),x48322),f2(x48321)),x48322) % 112.26/112.09 [4833]~P81(x48331)+E(f317(f317(f74(x48331),x48332),f2(x48331)),x48332) % 112.26/112.09 [4834]~P80(x48341)+E(f317(f317(f75(x48341),x48342),f72(x48341)),x48342) % 112.26/112.09 [4835]~P75(x48351)+E(f317(f317(f75(x48351),x48352),f72(x48351)),x48352) % 112.26/112.09 [4836]~P119(x48361)+E(f317(f317(f75(x48361),x48362),f72(x48361)),x48362) % 112.26/112.09 [4837]~P123(x48371)+E(f317(f317(f281(x48371),x48372),f72(x48371)),x48372) % 112.26/112.09 [4838]~P3(x48381)+E(f317(f317(f31(x48381),x48382),f72(x48381)),x48382) % 112.26/112.09 [4839]~P100(x48391)+E(f317(f317(f91(x48391),x48392),f178(x48391)),x48392) % 112.26/112.09 [4840]~P102(x48401)+E(f317(f317(f92(x48401),x48402),f232(x48401)),x48402) % 112.26/112.09 [4841]~P119(x48411)+E(f317(f317(f234(x48411),x48412),f2(a899)),f72(x48411)) % 112.26/112.09 [4842]~P115(x48421)+E(f317(f317(f234(x48421),x48422),f2(a899)),f72(x48421)) % 112.26/112.09 [4843]~E(x48432,f178(f906(x48431,a895)))+E(f317(f30(x48431),x48432),f2(a899)) % 112.26/112.09 [4854]~P3(x48541)+E(f41(x48541,x48542,f2(x48541)),x48542) % 112.26/112.09 [4865]~P119(x48651)+E(f317(f317(f75(x48651),x48652),f2(x48651)),f2(x48651)) % 112.26/112.09 [4866]~P133(x48661)+E(f317(f317(f75(x48661),x48662),f2(x48661)),f2(x48661)) % 112.26/112.09 [4867]~P124(x48671)+E(f317(f317(f281(x48671),x48672),f2(x48671)),f2(x48671)) % 112.26/112.09 [4868]~P3(x48681)+E(f317(f317(f31(x48681),x48682),f2(x48681)),f2(x48681)) % 112.26/112.09 [4869]~P102(x48691)+E(f317(f317(f91(x48691),x48692),f232(x48691)),f232(x48691)) % 112.26/112.09 [4870]~P100(x48701)+E(f317(f317(f92(x48701),x48702),f178(x48701)),f178(x48701)) % 112.26/112.09 [4872]~P3(x48721)+E(f41(x48721,x48722,f72(x48721)),f2(x48721)) % 112.26/112.09 [4873]~P3(x48731)+E(f41(x48731,f2(x48731),x48732),f2(x48731)) % 112.26/112.09 [4902]E(x49021,f2(a899))+E(f51(x49022,x49021,f103(x49022)),f103(f900(x49022))) % 112.26/112.09 [4925]P51(x49251,x49252)+~E(f317(f276(x49251,x49251),x49252),x49252) % 112.26/112.09 [4926]P36(x49261,x49262)+~E(f565(x49262,x49261),f178(f906(x49261,a895))) % 112.26/112.09 [4927]E(x49271,f103(x49272))+~E(f317(f162(x49272),x49271),f178(f906(x49272,a895))) % 112.26/112.09 [4928]E(x49281,f103(x49282))+~E(f178(f906(x49282,a895)),f317(f162(x49282),x49281)) % 112.26/112.09 [4931]~E(x49311,x49312)+P1(f317(f317(a314,x49311),x49312)) % 112.26/112.09 [4941]P1(x49411)+P1(f317(f317(a320,x49411),x49412)) % 112.26/112.09 [4942]E(x49421,f103(x49422))+E(f317(f317(f154(x49422),x49421),f2(a899)),f317(f131(x49422),x49421)) % 112.26/112.09 [4945]E(f142(x49451,x49452),x49452)+~P1(f317(f127(x49451),x49452)) % 112.26/112.09 [4952]~P1(x49522)+P1(f317(f317(a320,x49521),x49522)) % 112.26/112.09 [4953]~P1(x49532)+P1(f317(f317(a316,x49531),x49532)) % 112.26/112.09 [4954]~P1(x49541)+P1(f317(f317(a316,x49541),x49542)) % 112.26/112.09 [4964]~E(f648(x49642,x49641),f652(x49642,x49641))+P1(f317(f127(x49641),x49642)) % 112.26/112.09 [4971]E(f317(f252(x49711),x49712),f178(f906(x49711,a895)))+P1(f317(x49712,f493(x49712))) % 112.26/112.09 [4972]E(f178(f906(x49721,a895)),f317(f252(x49721),x49722))+P1(f317(x49722,f524(x49722))) % 112.26/112.09 [5045]~P112(x50451)+E(f317(f317(f75(x50451),x50452),f76(x50451,x50452)),f317(f70(x50451),x50452)) % 112.26/112.09 [5057]~E(x50571,f2(a1))+E(f42(x50571,x50572),f317(f317(f242(a1,a1),f2(a1)),f2(a1))) % 112.26/112.09 [5089]~P57(x50891,x50892)+P57(x50891,f317(f276(x50891,x50891),x50892)) % 112.26/112.09 [5090]~P37(x50901,x50902)+P37(x50901,f317(f276(x50901,x50901),x50902)) % 112.26/112.09 [5091]~P38(x50911,x50912)+P38(x50911,f317(f276(x50911,x50911),x50912)) % 112.26/112.09 [5092]~P51(x50921,x50922)+P51(x50921,f317(f276(x50921,x50921),x50922)) % 112.26/112.09 [5114]E(x51141,x51142)+~P1(f317(f317(a314,x51141),x51142)) % 112.26/112.09 [5125]P1(x51251)+~P1(f317(f317(a315,x51252),x51251)) % 112.26/112.09 [5126]P1(x51261)+~P1(f317(f317(a315,x51261),x51262)) % 112.26/112.09 [5131]~P116(x51311)+P1(f317(f317(f224(x51311),x51312),f232(x51311))) % 112.26/112.09 [5132]~P119(x51321)+P1(f317(f317(f277(x51321),x51322),f2(x51321))) % 112.26/112.09 [5136]E(x51361,x51362)+~E(f317(x51361,f350(x51362,x51361)),f317(x51362,f350(x51362,x51361))) % 112.26/112.09 [5167]E(x51671,f2(a899))+E(f206(x51671,f41(a899,x51672,x51671)),f206(x51672,x51671)) % 112.26/112.09 [5172]~P108(x51721)+P13(x51721,f317(f317(f141(x51721),x51722),f103(x51721))) % 112.26/112.09 [5174]E(x51741,f2(a1))+P1(f317(f45(x51742,x51741),f42(x51742,x51741))) % 112.26/112.09 [5191]~P15(x51912,x51911)+P1(f317(f317(x51911,f782(x51911)),f782(x51911))) % 112.26/112.09 [5194]~E(x51941,x51942)+P1(f317(f317(f225(a899),x51941),f317(a102,x51942))) % 112.26/112.09 [5204]~E(x52041,f2(a899))+P1(f317(f317(f225(a899),x52041),f317(a102,x52042))) % 112.26/112.09 [5214]P1(f317(x52141,x52142))+P1(f317(f317(f224(a1),f2(a1)),f325(x52141))) % 112.26/112.09 [5277]P57(x52771,x52772)+~P57(x52771,f317(f276(x52771,x52771),x52772)) % 112.26/112.09 [5278]P37(x52781,x52782)+~P37(x52781,f317(f276(x52781,x52781),x52782)) % 112.26/112.09 [5279]P38(x52791,x52792)+~P38(x52791,f317(f276(x52791,x52791),x52792)) % 112.26/112.09 [5280]P51(x52801,x52802)+~P51(x52801,f317(f276(x52801,x52801),x52802)) % 112.26/112.09 [5283]~E(f41(a899,x52832,x52831),f2(a899))+E(f317(f317(f75(a899),x52831),f336(x52831,x52832)),x52832) % 112.26/112.09 [5284]~E(f41(a1,x52842,x52841),f2(a1))+E(f317(f317(f75(a1),x52841),f337(x52841,x52842)),x52842) % 112.26/112.09 [5311]~P1(f317(x53111,x53112))+P1(f317(f317(f224(a1),f2(a1)),f324(x53111))) % 112.26/112.09 [5322]E(f317(f317(f3(a899),f317(a95,x53221)),f317(a95,x53222)),f317(a95,x53221))+~P1(f317(a183,x53222)) % 112.26/112.09 [5345]E(f262(x53451,x53452),f72(a89))+~P1(f317(f317(f224(a89),x53451),f72(a89))) % 112.26/112.09 [5443]E(f317(f317(f154(x54431),x54432),f648(x54432,x54431)),f317(f317(f154(x54431),x54432),f652(x54432,x54431)))+P1(f317(f127(x54431),x54432)) % 112.26/112.09 [5487]~P1(f317(x54871,f84(x54872,x54871)))+P1(f317(x54871,f566(x54872,x54871))) % 112.26/112.09 [5552]P59(x55521,x55522)+~P1(f317(f305(x55521,x55522),f554(x55522,x55521))) % 112.26/112.09 [5696]~P15(x56962,x56961)+P1(f317(f317(x56961,f783(x56961,x56962)),f783(x56961,x56962))) % 112.26/112.09 [5697]~P15(x56972,x56971)+P1(f317(f317(x56971,f786(x56971,x56972)),f786(x56971,x56972))) % 112.26/112.09 [5706]~E(f317(a102,f41(a899,x57061,x57062)),x57062)+E(f41(a899,f317(a102,x57061),x57062),f2(a899)) % 112.26/112.09 [5761]P36(x57611,x57612)+P1(f317(f317(f319(x57611),f585(x57612,x57611)),f586(x57612,x57611))) % 112.26/112.09 [5768]~P94(x57681)+P1(f317(f317(f319(x57681),f317(f94(x57681),x57682)),f100(x57681))) % 112.26/112.09 [5769]~P141(x57691)+P1(f317(f317(f319(x57691),f317(f90(x57691),x57692)),f100(x57691))) % 112.26/112.09 [5770]~P145(x57701)+P1(f317(f317(f319(x57701),f317(f90(x57701),x57702)),f176(x57701))) % 112.26/112.09 [5771]~P141(x57711)+P1(f317(f317(f319(x57711),f317(f93(x57711),x57712)),f100(x57711))) % 112.26/112.09 [5914]~P37(x59141,x59142)+E(f317(f317(f279(x59141,x59141,x59141),x59142),f297(x59141,x59142)),x59142) % 112.26/112.09 [5928]E(f317(a102,f41(a899,x59281,x59282)),x59282)+E(f41(a899,f317(a102,x59281),x59282),f317(a102,f41(a899,x59281,x59282))) % 112.26/112.09 [6360]P36(x63601,x63602)+~P1(f317(f317(f319(x63601),f544(x63602,x63601)),f306(x63601,x63602))) % 112.26/112.09 [6399]~P126(x63991)+~P1(f317(f317(f225(x63991),f317(f90(x63991),x63992)),f2(x63991))) % 112.26/112.09 [6400]~P86(x64001)+~P1(f317(f317(f225(x64001),f317(f70(x64001),x64002)),f2(x64001))) % 112.26/112.09 [6490]P1(f317(f317(f225(a1),x64901),f41(a1,x64902,x64901)))+~P1(f317(f317(f225(a1),x64901),f2(a1))) % 112.26/112.09 [6596]E(f317(f317(f299(a899),f317(a102,x65961)),f293(a899,x65962,x65961)),f293(a899,x65962,f317(a102,x65961)))+~P1(f317(f317(f224(a899),x65962),f317(a102,x65961))) % 112.26/112.09 [6688]~P108(x66881)+P13(x66881,f140(x66881,x66881,f7(x66881),x66882)) % 112.26/112.09 [6820]E(f317(f157(x68201),x68202),x68202)+~P1(f317(f317(f224(a899),f317(f179(f900(x68201)),x68202)),f72(a899))) % 112.26/112.09 [6842]~P86(x68421)+P1(f317(f317(f224(x68421),f317(f73(x68421),f317(f70(x68421),x68422))),f2(x68421))) % 112.26/112.09 [6876]~P36(x68761,x68762)+P36(x68761,f317(f317(f279(x68761,x68761,x68761),x68762),f297(x68761,x68762))) % 112.26/112.09 [6877]~P51(x68771,x68772)+P51(x68771,f317(f317(f279(x68771,x68771,x68771),x68772),f297(x68771,x68772))) % 112.26/112.09 [7103]~P1(f317(f317(f225(a1),x71032),f2(a1)))+P1(f317(f317(f224(a1),f41(a1,x71031,x71032)),f2(a1))) % 112.26/112.09 [7503]~P145(x75031)+E(f180(x75031,f317(f317(f9(x75031,x75031,x75031),f74(x75031)),f72(x75031)),x75032,f2(x75031)),f317(f90(x75031),x75032)) % 112.26/112.09 [7532]~P128(x75321)+~P1(f317(f317(f225(x75321),f317(f317(f75(x75321),x75322),x75322)),f2(x75321))) % 112.26/112.09 [10178]~P112(x101781)+~P1(f317(f317(f225(x101781),f317(f317(f234(x101781),x101782),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f2(x101781))) % 112.26/112.09 [4736]~E(x47362,f103(x47361))+E(f317(f179(f900(x47361)),x47362),f2(a899)) % 112.26/112.09 [4768]~E(x47681,f2(a899))+E(f317(f317(f74(a899),x47681),x47682),x47682) % 112.26/112.09 [4769]~E(x47692,f2(a899))+E(f317(f317(f75(a899),x47691),x47692),f2(a899)) % 112.26/112.09 [4771]~E(x47711,f2(a899))+E(f317(f317(f75(a899),x47711),x47712),f2(a899)) % 112.26/112.09 [4772]~E(x47722,f2(a1))+E(f317(f317(f31(a1),x47721),x47722),f2(a1)) % 112.26/112.09 [4773]~E(x47732,f2(a899))+E(f317(f317(f234(a899),x47731),x47732),f72(a899)) % 112.26/112.09 [4784]E(x47841,f103(x47842))+~E(f317(f179(f900(x47842)),x47841),f2(a899)) % 112.26/112.09 [4786]~P97(x47861)+E(f317(f317(f75(x47861),x47862),x47862),x47862) % 112.26/112.09 [4788]~P108(x47881)+E(f317(f317(f228(x47881),x47882),x47882),x47882) % 112.26/112.09 [4790]~P108(x47901)+E(f317(f317(f223(x47901),x47902),x47902),x47902) % 112.26/112.09 [4792]~P98(x47921)+E(f317(f317(f91(x47921),x47922),x47922),x47922) % 112.26/112.09 [4793]~P99(x47931)+E(f317(f317(f91(x47931),x47932),x47932),x47932) % 112.26/112.09 [4794]~P99(x47941)+E(f317(f317(f92(x47941),x47942),x47942),x47942) % 112.26/112.09 [4796]~P104(x47961)+E(f317(f317(f92(x47961),x47962),x47962),x47962) % 112.26/112.09 [4814]~P76(x48141)+E(f317(f317(f3(x48141),x48142),x48142),f2(x48141)) % 112.26/112.09 [4828]~P76(x48281)+E(f317(f73(x48281),f317(f73(x48281),x48282)),x48282) % 112.26/112.09 [4829]~P96(x48291)+E(f317(f73(x48291),f317(f73(x48291),x48292)),x48292) % 112.26/112.09 [4846]~E(x48462,f2(a899))+E(f317(f317(f234(a899),x48461),x48462),f317(a102,f2(a899))) % 112.26/112.09 [4881]~P69(x48811)+E(f317(f317(f74(x48811),f2(x48811)),x48812),x48812) % 112.26/112.09 [4882]~P119(x48821)+E(f317(f317(f74(x48821),f2(x48821)),x48822),x48822) % 112.26/112.09 [4883]~P81(x48831)+E(f317(f317(f74(x48831),f2(x48831)),x48832),x48832) % 112.26/112.09 [4884]~P80(x48841)+E(f317(f317(f75(x48841),f72(x48841)),x48842),x48842) % 112.26/112.09 [4885]~P75(x48851)+E(f317(f317(f75(x48851),f72(x48851)),x48852),x48852) % 112.26/112.09 [4886]~P119(x48861)+E(f317(f317(f75(x48861),f72(x48861)),x48862),x48862) % 112.26/112.09 [4887]~P100(x48871)+E(f317(f317(f91(x48871),f178(x48871)),x48872),x48872) % 112.26/112.09 [4888]~P102(x48881)+E(f317(f317(f92(x48881),f232(x48881)),x48882),x48882) % 112.26/112.09 [4906]~P119(x49061)+E(f317(f317(f75(x49061),f2(x49061)),x49062),f2(x49061)) % 112.26/112.09 [4907]~P133(x49071)+E(f317(f317(f75(x49071),f2(x49071)),x49072),f2(x49071)) % 112.26/112.09 [4908]~P123(x49081)+E(f317(f317(f281(x49081),f2(x49081)),x49082),f2(x49081)) % 112.26/112.09 [4909]~P3(x49091)+E(f317(f317(f31(x49091),f2(x49091)),x49092),f2(x49091)) % 112.26/112.09 [4910]~P80(x49101)+E(f317(f317(f234(x49101),f72(x49101)),x49102),f72(x49101)) % 112.26/112.09 [4911]~P102(x49111)+E(f317(f317(f91(x49111),f232(x49111)),x49112),f232(x49111)) % 112.26/112.09 [4912]~P100(x49121)+E(f317(f317(f92(x49121),f178(x49121)),x49122),f178(x49121)) % 112.26/112.09 [4920]E(x49201,f103(x49202))+E(f134(x49202,f317(f158(x49202),x49201)),f317(f131(x49202),x49201)) % 112.26/112.09 [4921]E(x49211,f103(x49212))+E(f317(f131(x49212),f317(f158(x49212),x49211)),f134(x49212,x49211)) % 112.26/112.09 [4922]E(x49221,f2(a899))+~E(f317(f317(f74(a899),x49222),x49221),x49222) % 112.26/112.09 [4929]~P94(x49291)+E(f317(f93(x49291),f317(f94(a1),x49292)),f317(f94(x49291),x49292)) % 112.26/112.09 [4930]~P141(x49301)+E(f317(f93(x49301),f317(f90(a1),x49302)),f317(f90(x49301),x49302)) % 112.26/112.09 [4937]E(x49371,f72(a899))+~E(f317(f317(f75(a899),x49372),x49371),f72(a899)) % 112.26/112.09 [4938]E(x49381,f72(a899))+~E(f317(f317(f75(a899),x49381),x49382),f72(a899)) % 112.26/112.09 [4939]E(x49391,f2(a899))+~E(f317(f317(f74(a899),x49392),x49391),f2(a899)) % 112.26/112.09 [4940]E(x49401,f2(a899))+~E(f317(f317(f74(a899),x49401),x49402),f2(a899)) % 112.26/112.09 [4957]~P112(x49571)+E(f317(f70(x49571),f317(f90(x49571),x49572)),f317(f90(x49571),x49572)) % 112.26/112.09 [4958]~P86(x49581)+E(f317(f70(x49581),f317(f70(x49581),x49582)),f317(f70(x49581),x49582)) % 112.26/112.09 [4959]~P86(x49591)+E(f317(f70(x49591),f317(f73(x49591),x49592)),f317(f70(x49591),x49592)) % 112.26/112.09 [4960]~P69(x49601)+E(f317(f155(x49601),f317(f158(x49601),x49602)),f317(f155(x49601),x49602)) % 112.26/112.09 [4965]~E(x49651,f317(a102,f2(a899)))+E(f317(f317(f234(a899),x49651),x49652),f317(a102,f2(a899))) % 112.26/112.09 [4974]~P76(x49741)+E(f317(f317(f3(x49741),f2(x49741)),x49742),f317(f73(x49741),x49742)) % 112.26/112.09 [4975]~E(x49752,f2(a899))+E(f129(a899,f317(f292(a899,x49751),x49752)),f103(a899)) % 112.26/112.09 [4984]~P94(x49841)+E(f317(f317(f74(x49841),x49842),f317(f94(x49841),a77)),x49842) % 112.26/112.09 [4985]E(x49851,f2(a1))+E(f43(f317(f70(a1),x49852),f317(f70(a1),x49851)),f49(x49852,x49851)) % 112.26/112.09 [5001]~E(x50011,x50012)+P1(f317(f317(f224(a899),x50011),x50012)) % 112.26/112.09 [5005]~E(x50051,x50052)+P1(f317(f317(f277(a899),x50051),x50052)) % 112.26/112.09 [5012]~E(x50121,f2(a89))+E(f317(f317(f74(a899),f317(a22,x50121)),x50122),x50122) % 112.26/112.09 [5026]~P6(x50261)+P6(f317(f317(f234(a1),x50261),x50262)) % 112.26/112.09 [5027]~P76(x50271)+E(f317(f317(f74(x50271),x50272),f317(f73(x50271),x50272)),f2(x50271)) % 112.26/112.09 [5028]~P96(x50281)+E(f317(f317(f91(x50281),x50282),f317(f73(x50281),x50282)),f232(x50281)) % 112.26/112.09 [5029]~P96(x50291)+E(f317(f317(f92(x50291),x50292),f317(f73(x50291),x50292)),f178(x50291)) % 112.26/112.09 [5054]E(x50541,f2(a899))+~E(f317(f73(a1),f317(f90(a1),x50542)),f317(f90(a1),x50541)) % 112.26/112.09 [5055]E(x50551,f2(a899))+~E(f317(f73(a1),f317(f90(a1),x50551)),f317(f90(a1),x50552)) % 112.26/112.09 [5065]E(f184(x50651,x50652),f2(a1))+P1(f317(f317(f224(a1),x50652),x50651)) % 112.26/112.09 [5066]E(f168(x50661,x50662),f103(a1))+P1(f317(f317(f224(a1),x50661),x50662)) % 112.26/112.09 [5067]E(f231(x50671,x50672),f2(a89))+P1(f317(f317(f225(a89),x50671),x50672)) % 112.26/112.09 [5080]E(x50801,f317(a102,f2(a899)))+~E(f317(f317(f75(a899),x50802),x50801),f317(a102,f2(a899))) % 112.26/112.09 [5081]E(x50811,f317(a102,f2(a899)))+~E(f317(f317(f75(a899),x50811),x50812),f317(a102,f2(a899))) % 112.26/112.09 [5082]~P65(x50821)+P1(f317(f317(f224(x50821),x50822),x50822)) % 112.26/112.09 [5083]~P119(x50831)+P1(f317(f317(f277(x50831),x50832),x50832)) % 112.26/112.09 [5086]~P94(x50861)+E(f317(f317(f75(x50861),x50862),f317(f94(x50861),a87)),f317(f73(x50861),x50862)) % 112.26/112.09 [5106]~P94(x51061)+E(f317(f73(x51061),f317(f94(x51061),x51062)),f317(f94(x51061),f317(f73(a1),x51062))) % 112.26/112.09 [5107]~P141(x51071)+E(f317(f73(x51071),f317(f93(x51071),x51072)),f317(f93(x51071),f317(f73(a1),x51072))) % 112.26/112.09 [5137]~E(x51371,f317(a102,x51372))+P1(f317(f317(f225(a899),f2(a899)),x51371)) % 112.26/112.09 [5155]~P108(x51551)+E(f317(f73(f906(x51551,a895)),f317(f291(x51551),x51552)),f317(f294(x51551),x51552)) % 112.26/112.09 [5156]~P108(x51561)+E(f317(f73(f906(x51561,a895)),f317(f272(x51561),x51562)),f317(f273(x51561),x51562)) % 112.26/112.09 [5157]~P108(x51571)+E(f317(f73(f906(x51571,a895)),f317(f294(x51571),x51572)),f317(f291(x51571),x51572)) % 112.26/112.09 [5158]~P108(x51581)+E(f317(f73(f906(x51581,a895)),f317(f273(x51581),x51582)),f317(f272(x51581),x51582)) % 112.26/112.09 [5166]~E(f317(f90(a1),x51662),x51661)+P1(f317(f317(f224(a1),f2(a1)),x51661)) % 112.26/112.09 [5173]~E(x51732,f2(a1))+E(f49(x51731,x51732),f317(f317(f242(a1,a1),f2(a1)),f317(f70(a1),x51731))) % 112.26/112.09 [5175]~P66(x51751)+P1(f317(f317(f224(x51751),f178(x51751)),x51752)) % 112.26/112.09 [5176]~P119(x51761)+P1(f317(f317(f277(x51761),f72(x51761)),x51762)) % 112.26/112.09 [5209]E(x52091,x52092)+~E(f317(f317(f74(a1),x52091),x52091),f317(f317(f74(a1),x52092),x52092)) % 112.26/112.09 [5213]~P1(f317(x52131,x52132))+P1(f317(x52131,f317(a95,f324(x52131)))) % 112.26/112.09 [5239]~P112(x52391)+E(f317(f317(f75(x52391),f76(x52391,x52392)),f317(f70(x52391),x52392)),x52392) % 112.26/112.09 [5246]~E(x52462,f2(a899))+E(f79(f905(a899,a899),f44(x52461,x52462)),f317(f317(f242(a899,a899),f2(a899)),x52461)) % 112.26/112.09 [5251]~E(x52511,x52512)+~P1(f317(f317(f225(a899),x52511),x52512)) % 112.26/112.09 [5252]~E(x52521,x52522)+~P1(f317(f317(f225(a1),x52521),x52522)) % 112.26/112.09 [5255]~P145(x52551)+E(f317(f317(f74(x52551),f72(x52551)),f317(f90(x52551),x52552)),f317(f90(x52551),f317(a102,x52552))) % 112.26/112.09 [5259]~E(x52591,f2(a899))+~P1(f317(f317(f225(a899),x52592),x52591)) % 112.26/112.09 [5273]E(f142(x52731,x52732),x52732)+~E(f317(f179(f900(x52731)),f142(x52731,x52732)),f317(f179(f900(x52731)),x52732)) % 112.26/112.09 [5274]E(f317(f30(x52741),f317(f162(x52741),x52742)),f317(f179(f900(x52741)),x52742))+~P1(f317(f127(x52741),x52742)) % 112.26/112.09 [5288]~P1(f317(x52881,f799(x52881)))+P1(f317(x52881,f317(f90(a1),x52882))) % 112.26/112.09 [5299]E(f231(x52991,x52992),x52992)+~P1(f317(f317(f225(a89),x52991),x52992)) % 112.26/112.09 [5301]E(f262(x53011,x53012),f72(a89))+~P1(f317(f317(f225(a89),x53012),x53011)) % 112.26/112.09 [5302]E(f168(x53021,x53022),f103(a1))+~P1(f317(f317(f225(a1),x53022),x53021)) % 112.26/112.09 [5303]E(f118(x53031,x53032),f105(a1))+~P1(f317(f317(f225(a1),x53031),x53032)) % 112.26/112.09 [5305]~P109(x53051)+E(f293(x53051,x53052,x53052),f317(f317(f299(x53051),x53052),f178(f906(x53051,a895)))) % 112.26/112.09 [5325]~E(f317(f317(f3(a899),x53251),x53252),f2(a899))+P1(f317(f317(f224(a899),x53251),x53252)) % 112.26/112.09 [5342]~E(x53422,f2(a899))+E(f51(x53421,x53422,f103(x53421)),f317(f317(f141(f900(x53421)),f103(x53421)),f103(f900(x53421)))) % 112.26/112.09 [5346]~P65(x53461)+~P1(f317(f317(f225(x53461),x53462),x53462)) % 112.26/112.09 [5348]~E(f41(a1,x53481,x53482),f2(a1))+E(f41(a1,x53481,f317(f73(a1),x53482)),f2(a1)) % 112.26/112.09 [5350]~E(f41(a1,x53501,x53502),f2(a1))+E(f41(a1,f317(f73(a1),x53501),x53502),f2(a1)) % 112.26/112.09 [5358]E(f317(f292(a899,x53581),f317(a102,x53582)),f178(f906(a899,a895)))+P1(f317(f317(f224(a899),x53581),x53582)) % 112.26/112.09 [5382]E(f129(a899,f317(f292(a899,x53821),x53822)),f103(a899))+P1(f317(f317(f225(a899),x53821),x53822)) % 112.26/112.09 [5388]~E(f317(f30(x53881),f317(f162(x53881),x53882)),f317(f179(f900(x53881)),x53882))+P1(f317(f127(x53881),x53882)) % 112.26/112.09 [5392]~P1(f317(f127(x53921),x53922))+P1(f317(f127(x53921),f317(f157(x53921),x53922))) % 112.26/112.09 [5393]~P1(f317(f127(x53931),x53932))+P1(f317(f127(x53931),f317(f161(x53931),x53932))) % 112.26/112.09 [5394]~P1(f317(f127(x53941),x53942))+P1(f317(f127(x53941),f317(f158(x53941),x53942))) % 112.26/112.09 [5402]P1(f317(x54021,x54022))+~P1(f317(x54021,f317(a95,f325(x54021)))) % 112.26/112.09 [5403]P1(f317(f317(f224(a899),x54032),x54031))+P1(f317(f317(f224(a899),x54031),x54032)) % 112.26/112.09 [5404]P1(f317(f317(f224(a1),x54042),x54041))+P1(f317(f317(f224(a1),x54041),x54042)) % 112.26/112.09 [5408]~P86(x54081)+P1(f317(f317(f224(x54081),x54082),f317(f70(x54081),x54082))) % 112.26/112.09 [5411]P1(f317(x54111,f878(x54111)))+~P1(f317(x54111,f317(f90(a1),x54112))) % 112.26/112.09 [5435]E(f317(f317(f3(a899),x54351),x54352),f2(a899))+~P1(f317(f317(f224(a899),x54351),x54352)) % 112.26/112.09 [5436]E(f317(f317(f31(a899),x54361),x54362),f2(a899))+~P1(f317(f317(f225(a899),x54361),x54362)) % 112.26/112.09 [5455]E(f41(a899,x54551,x54552),x54551)+~P1(f317(f317(f225(a899),x54551),x54552)) % 112.26/112.09 [5463]E(f41(a1,x54631,f317(f73(a1),x54632)),f282(x54631,x54632))+P1(f317(f317(f224(a1),f2(a1)),x54632)) % 112.26/112.09 [5476]E(f317(f317(f3(a1),x54761),x54762),f184(x54761,x54762))+~P1(f317(f317(f224(a1),x54762),x54761)) % 112.26/112.09 [5496]P1(f317(f317(f224(a1),f2(a1)),f799(x54961)))+P1(f317(x54961,f317(f90(a1),x54962))) % 112.26/112.09 [5509]~P126(x55091)+P1(f317(f317(f224(x55091),f2(x55091)),f317(f90(x55091),x55092))) % 112.26/112.09 [5510]~P86(x55101)+P1(f317(f317(f224(x55101),f2(x55101)),f317(f70(x55101),x55102))) % 112.26/112.09 [5538]E(f317(f317(f74(a899),x55381),f525(x55382,x55381)),x55382)+~P1(f317(f317(f224(a899),x55381),x55382)) % 112.26/112.09 [5553]E(f293(a1,x55531,x55532),f178(f906(a1,a895)))+~P1(f317(f317(f225(a1),x55532),x55531)) % 112.26/112.09 [5555]~P112(x55551)+E(f317(f317(f75(x55551),f317(f70(x55551),x55552)),f317(f70(x55551),x55552)),f317(f317(f75(x55551),x55552),x55552)) % 112.26/112.09 [5561]E(f129(a899,f317(f292(a899,x55611),f317(a102,x55612))),f103(a899))+P1(f317(f317(f224(a899),x55611),x55612)) % 112.26/112.09 [5564]E(f317(f317(f31(a1),x55641),x55642),f283(x55641,x55642))+~P1(f317(f317(f224(a1),f2(a1)),x55642)) % 112.26/112.09 [5584]P1(f317(f127(x55841),x55842))+~P1(f317(f127(x55841),f317(f157(x55841),x55842))) % 112.26/112.09 [5585]P1(f317(f127(x55851),x55852))+~P1(f317(f127(x55851),f317(f158(x55851),x55852))) % 112.26/112.09 [5612]P1(f317(f29(a899),x56121))+P1(f317(f317(f319(a899),f888(x56121,x56122)),x56121)) % 112.26/112.09 [5613]P1(f317(f29(a899),x56131))+P1(f317(f317(f319(a899),f890(x56131,x56132)),x56131)) % 112.26/112.09 [5616]P1(f317(f317(f225(a899),x56162),f317(a102,x56161)))+P1(f317(f317(f225(a899),x56161),x56162)) % 112.26/112.09 [5617]E(f41(a1,x56171,x56172),f282(x56171,x56172))+~P1(f317(f317(f224(a1),f2(a1)),x56172)) % 112.26/112.09 [5620]E(f129(a899,f317(f292(a899,x56201),x56202)),f103(a899))+~P1(f317(f317(f224(a899),x56202),x56201)) % 112.26/112.09 [5621]~P79(x56211)+E(f317(f300(x56211,x56211,f73(x56211)),f317(f291(x56211),x56212)),f317(f273(x56211),f317(f73(x56211),x56212))) % 112.26/112.09 [5622]~P79(x56221)+E(f317(f300(x56221,x56221,f73(x56221)),f317(f272(x56221),x56222)),f317(f294(x56221),f317(f73(x56221),x56222))) % 112.26/112.09 [5623]~P79(x56231)+E(f317(f300(x56231,x56231,f73(x56231)),f317(f294(x56231),x56232)),f317(f272(x56231),f317(f73(x56231),x56232))) % 112.26/112.09 [5624]~P79(x56241)+E(f317(f300(x56241,x56241,f73(x56241)),f317(f273(x56241),x56242)),f317(f291(x56241),f317(f73(x56241),x56242))) % 112.26/112.09 [5635]E(x56351,f178(f906(x56352,a895)))+P1(f317(f317(f319(x56352),f653(x56351,x56352)),x56351)) % 112.26/112.09 [5636]E(x56361,f178(f906(x56362,a895)))+P1(f317(f317(f319(x56362),f526(x56361,x56362)),x56361)) % 112.26/112.09 [5647]~P1(f317(f317(f225(a899),x56471),x56472))+P1(f317(f317(f224(a899),x56471),x56472)) % 112.26/112.09 [5648]~P1(f317(f317(f225(a1),x56481),x56482))+P1(f317(f317(f224(a1),x56481),x56482)) % 112.26/112.09 [5664]E(f43(x56641,x56642),f317(f317(f242(a1,a1),f2(a1)),x56641))+~P1(f317(f317(f225(a1),x56641),x56642)) % 112.26/112.09 [5666]E(f205(f317(f73(a1),x56661),f317(f73(a1),x56662)),f205(x56661,x56662))+~P1(f317(f317(f225(a1),x56662),f2(a1))) % 112.26/112.09 [5678]E(x56781,x56782)+~E(f317(a5,f317(a102,f317(a22,x56781))),f317(a5,f317(a102,f317(a22,x56782)))) % 112.26/112.09 [5683]E(f43(x56831,x56832),f317(f317(f242(a1,a1),f2(a1)),x56831))+~P1(f317(f317(f224(a1),x56832),f2(a1))) % 112.26/112.09 [5712]E(f41(a899,f317(f94(a899),x57121),f317(f94(a899),x57122)),f2(a899))+~P1(f317(a183,f317(f94(a1),x57121))) % 112.26/112.09 [5726]P1(f317(f317(f224(a1),f2(a1)),f878(x57261)))+~P1(f317(x57261,f317(f90(a1),x57262))) % 112.26/112.09 [5759]P39(f293(a1,x57591,x57592))+~P1(f317(f317(f224(a1),f2(a1)),x57591)) % 112.26/112.09 [5764]~P1(f317(f29(x57641),x57642))+P1(f317(f29(f906(x57641,a895)),f317(f298(x57641),x57642))) % 112.26/112.09 [5777]E(f317(f317(f74(a1),x57771),f317(f90(a1),f882(x57772,x57771))),x57772)+~P1(f317(f317(f224(a1),x57771),x57772)) % 112.26/112.09 [5785]P1(f317(f317(f224(a899),x57851),x57852))+P1(f317(f317(f224(a899),f317(a102,x57852)),x57851)) % 112.26/112.09 [5829]E(f317(f317(f31(a899),f317(f94(a899),x58291)),f317(f94(a899),x58292)),f2(a899))+~P1(f317(a183,f317(f94(a1),x58291))) % 112.26/112.09 [5830]E(f317(f317(f75(a899),f317(f94(a899),x58301)),f317(f94(a899),x58302)),f2(a899))+~P1(f317(f317(f225(a1),x58301),a77)) % 112.26/112.09 [5832]P1(f317(f317(f224(a899),x58321),f317(a102,x58322)))+~P1(f317(f317(f224(a899),x58321),x58322)) % 112.26/112.09 [5834]P1(f317(f317(f225(a899),x58341),f317(a102,x58342)))+~P1(f317(f317(f224(a899),x58341),x58342)) % 112.26/112.09 [5836]P1(f317(f317(f225(a899),x58361),f317(a102,x58362)))+~P1(f317(f317(f225(a899),x58361),x58362)) % 112.26/112.09 [5839]~E(x58391,x58392)+P1(f317(f317(f225(a1),x58391),f317(f317(f74(a1),x58392),f72(a1)))) % 112.26/112.09 [5842]E(f41(a1,x58421,x58422),f2(a1))+E(f317(f317(f3(a1),x58422),f41(a1,x58421,x58422)),f41(a1,f317(f73(a1),x58421),x58422)) % 112.26/112.09 [5851]E(x58511,f103(x58512))+P1(f317(f317(f319(x58512),f134(x58512,x58511)),f317(f162(x58512),x58511))) % 112.26/112.09 [5863]E(f79(f905(a899,a899),f44(x58631,x58632)),f317(f317(f242(a899,a899),f2(a899)),x58631))+~P1(f317(f317(f225(a899),x58631),x58632)) % 112.26/112.09 [5907]E(f317(f317(f3(a899),f317(f94(a899),x59071)),f317(f94(a899),x59072)),f317(f94(a899),x59071))+~P1(f317(f317(f225(a1),x59072),a77)) % 112.26/112.09 [5908]E(f317(f317(f74(a899),f317(f94(a899),x59081)),f317(f94(a899),x59082)),f317(f94(a899),x59082))+~P1(f317(f317(f225(a1),x59081),a77)) % 112.26/112.09 [5915]E(f317(a102,f317(f317(f74(a899),x59151),f567(x59152,x59151))),x59152)+~P1(f317(f317(f225(a899),x59151),x59152)) % 112.26/112.09 [5939]P1(f317(x59391,x59392))+~P1(f317(x59391,f317(a83,f568(x59392,x59391)))) % 112.26/112.09 [5940]P1(f317(x59401,x59402))+~P1(f317(x59401,f317(a5,f801(x59402,x59401)))) % 112.26/112.09 [5949]~P1(f317(f317(f225(a899),x59491),f317(a102,x59492)))+P1(f317(f317(f224(a899),x59491),x59492)) % 112.26/112.09 [5999]E(f317(f317(f299(a899),x59991),f317(f292(a899,x59992),x59991)),f317(f292(a899,x59992),f317(a102,x59991)))+~P1(f317(f317(f224(a899),x59992),x59991)) % 112.26/112.09 [6002]E(x60021,f103(x60022))+E(f317(f317(f124(x60022),f104(x60022,x60021)),f317(f317(f141(x60022),f134(x60022,x60021)),f103(x60022))),x60021) % 112.26/112.09 [6019]P1(f317(f29(x60191),x60192))+~P1(f317(f317(f225(a899),f2(a899)),f317(f30(x60191),x60192))) % 112.26/112.09 [6023]~E(x60231,f178(f906(x60232,a895)))+~P1(f317(f317(f225(a899),f2(a899)),f317(f30(x60232),x60231))) % 112.26/112.09 [6035]~P1(f317(f317(f225(a899),x60351),x60352))+P1(f317(f317(f224(a899),f317(a102,x60351)),x60352)) % 112.26/112.09 [6039]~P108(x60391)+E(f140(x60391,x60391,f7(x60391),f142(x60391,x60392)),f129(x60391,f317(f162(x60391),x60392))) % 112.26/112.09 [6042]E(x60421,f103(x60422))+P1(f317(f317(f319(x60422),f317(f131(x60422),x60421)),f317(f162(x60422),x60421))) % 112.26/112.09 [6048]~P126(x60481)+P1(f317(f317(f225(x60481),x60482),f317(f317(f74(x60481),x60482),f72(x60481)))) % 112.26/112.09 [6050]~P86(x60501)+P1(f317(f317(f224(x60501),f317(f73(x60501),x60502)),f317(f70(x60501),x60502))) % 112.26/112.09 [6064]~E(x60641,x60642)+E(f280(a899,f277(a899),x60641,x60642),f317(f317(f299(a899),x60641),f178(f906(a899,a895)))) % 112.26/112.09 [6082]P1(f317(f29(a899),x60821))+~P1(f317(f317(f224(a899),f888(x60821,x60822)),x60822)) % 112.26/112.09 [6083]P1(f317(f29(a899),x60831))+~P1(f317(f317(f225(a899),f890(x60831,x60832)),x60832)) % 112.26/112.09 [6086]~P1(f317(f29(f905(x60861,x60861)),x60862))+P1(f317(f29(x60861),f317(f271(x60861),x60862))) % 112.26/112.09 [6142]E(f280(a899,f277(a899),x61421,x61422),f178(f906(a899,a895)))+P1(f317(f317(f277(a899),x61421),x61422)) % 112.26/112.09 [6145]~P1(f317(f317(f225(a899),x61452),f317(a102,x61451)))+~P1(f317(f317(f225(a899),x61451),x61452)) % 112.26/112.09 [6146]~P109(x61461)+E(f317(f317(f92(f906(x61461,a895)),f317(f291(x61461),x61462)),f317(f273(x61461),x61462)),f317(f317(f299(x61461),x61462),f178(f906(x61461,a895)))) % 112.26/112.09 [6158]P1(f317(f29(x61581),x61582))+~P1(f317(f29(f906(x61581,a895)),f317(f298(x61581),x61582))) % 112.26/112.09 [6180]P1(f317(f317(f224(a899),f317(a102,x61801)),f317(a102,x61802)))+~P1(f317(f317(f224(a899),x61801),x61802)) % 112.26/112.09 [6181]P1(f317(f317(f224(a899),f317(a22,x61811)),f317(a22,x61812)))+~P1(f317(f317(f224(a89),x61811),x61812)) % 112.26/112.09 [6182]P1(f317(f317(f224(a89),f317(a5,x61821)),f317(a5,x61822)))+~P1(f317(f317(f224(a899),x61821),x61822)) % 112.26/112.09 [6184]P1(f317(f317(f225(a899),f317(a102,x61841)),f317(a102,x61842)))+~P1(f317(f317(f225(a899),x61841),x61842)) % 112.26/112.09 [6185]P1(f317(f317(f225(a899),f317(a22,x61851)),f317(a22,x61852)))+~P1(f317(f317(f225(a89),x61851),x61852)) % 112.26/112.09 [6186]P1(f317(f317(f225(a89),f317(a5,x61861)),f317(a5,x61862)))+~P1(f317(f317(f225(a899),x61861),x61862)) % 112.26/112.09 [6191]E(x61911,x61912)+~E(f317(f300(a899,a1,f90(a1)),x61911),f317(f300(a899,a1,f90(a1)),x61912)) % 112.26/112.09 [6207]P1(f317(f317(f224(a899),x62071),x62072))+~P1(f317(f317(f224(a899),f317(a102,x62071)),x62072)) % 112.26/112.09 [6210]P1(f317(f317(f225(a899),x62101),x62102))+~P1(f317(f317(f224(a899),f317(a102,x62101)),x62102)) % 112.26/112.09 [6211]P1(f317(f317(f225(a899),x62111),x62112))+~P1(f317(f317(f225(a899),f317(a102,x62111)),x62112)) % 112.26/112.09 [6231]E(f41(a1,x62311,x62312),f2(a1))+E(f317(f317(f3(a1),f41(a1,x62311,x62312)),x62312),f41(a1,x62311,f317(f73(a1),x62312))) % 112.26/112.09 [6299]E(f317(f30(f906(x62991,a895)),f317(f298(x62991),x62992)),f317(f317(f234(a899),f317(a102,f317(a102,f2(a899)))),f317(f30(x62991),x62992)))+~P1(f317(f29(x62991),x62992)) % 112.26/112.09 [6302]E(x63021,f103(x63022))+E(f317(f317(f154(x63022),x63021),f317(f317(f3(a899),f317(f179(f900(x63022)),x63021)),f72(a899))),f134(x63022,x63021)) % 112.26/112.09 [6324]E(x63241,f103(x63242))+E(f317(f317(f124(x63242),f317(f161(x63242),x63241)),f317(f317(f141(x63242),f317(f131(x63242),x63241)),f103(x63242))),f317(f157(x63242),x63241)) % 112.26/112.09 [6357]~P1(f317(f29(x63571),f32(f906(x63571,a895),x63572)))+P1(f317(f29(f906(x63571,a895)),x63572)) % 112.26/112.09 [6379]P1(f317(f317(f224(a899),f317(f94(a899),x63791)),f317(f94(a899),x63792)))+~P1(f317(f317(f224(a1),x63791),a77)) % 112.26/112.09 [6403]~P1(f317(f317(f225(a1),x64031),x64032))+P1(f317(f317(f224(a1),x64031),f317(f317(f3(a1),x64032),f72(a1)))) % 112.26/112.09 [6404]~P1(f317(f317(f224(a1),x64041),x64042))+P1(f317(f317(f225(a1),x64041),f317(f317(f74(a1),x64042),f72(a1)))) % 112.26/112.09 [6405]~P1(f317(f317(f225(a1),x64051),x64052))+P1(f317(f317(f225(a1),x64051),f317(f317(f74(a1),x64052),f72(a1)))) % 112.26/112.09 [6407]~P1(f317(f317(f224(a1),x64071),x64072))+P1(f317(f317(f224(a899),f317(f94(a899),x64071)),f317(f94(a899),x64072))) % 112.26/112.09 [6408]~P1(f317(f317(f224(a1),x64081),x64082))+P1(f317(f317(f224(a1),f317(f94(a1),x64081)),f317(f94(a1),x64082))) % 112.26/112.09 [6410]~P1(f317(f317(f224(a899),x64101),x64102))+P1(f317(f317(f224(a1),f317(f90(a1),x64101)),f317(f90(a1),x64102))) % 112.26/112.09 [6411]~P1(f317(f317(f225(a1),x64111),x64112))+P1(f317(f317(f225(a1),f317(f94(a1),x64111)),f317(f94(a1),x64112))) % 112.26/112.09 [6413]~P1(f317(f317(f225(a899),x64131),x64132))+P1(f317(f317(f225(a1),f317(f90(a1),x64131)),f317(f90(a1),x64132))) % 112.26/112.09 [6433]~P1(f317(f317(f224(a899),x64331),x64332))+~P1(f317(f317(f224(a899),f317(a102,x64332)),x64331)) % 112.26/112.09 [6476]~P1(f317(f317(f224(a899),f317(a102,x64761)),f317(a102,x64762)))+P1(f317(f317(f224(a899),x64761),x64762)) % 112.26/112.09 [6477]~P1(f317(f317(f224(a89),f317(a5,x64771)),f317(a5,x64772)))+P1(f317(f317(f224(a899),x64771),x64772)) % 112.26/112.09 [6478]~P1(f317(f317(f224(a899),f317(a22,x64781)),f317(a22,x64782)))+P1(f317(f317(f224(a89),x64781),x64782)) % 112.26/112.09 [6480]~P1(f317(f317(f225(a899),f317(a102,x64801)),f317(a102,x64802)))+P1(f317(f317(f225(a899),x64801),x64802)) % 112.26/112.09 [6481]~P1(f317(f317(f225(a89),f317(a5,x64811)),f317(a5,x64812)))+P1(f317(f317(f225(a899),x64811),x64812)) % 112.26/112.09 [6482]~P1(f317(f317(f225(a899),f317(a95,x64821)),f317(a95,x64822)))+P1(f317(f317(f225(a1),x64821),x64822)) % 112.26/112.09 [6483]~P1(f317(f317(f225(a899),f317(a22,x64831)),f317(a22,x64832)))+P1(f317(f317(f225(a89),x64831),x64832)) % 112.26/112.09 [6525]~P1(f317(f317(f225(a899),f317(a95,x65252)),f317(a95,x65251)))+P1(f317(f317(f225(a1),f2(a1)),x65251)) % 112.26/112.09 [6556]P1(f317(f317(f224(a1),f2(a1)),f41(a1,x65561,x65562)))+~P1(f317(f317(f225(a1),f2(a1)),x65562)) % 112.26/112.09 [6722]P36(x67221,x67222)+~E(f317(f317(f279(x67221,x67221,x67221),x67222),x67222),f178(f906(f905(x67221,x67221),a895))) % 112.26/112.09 [6738]~P36(x67381,x67382)+P36(x67381,f317(f317(f279(x67381,x67381,x67381),x67382),x67382)) % 112.26/112.09 [6749]P1(f317(f317(f224(a1),x67491),x67492))+~P1(f317(f317(f225(a1),x67491),f317(f317(f74(a1),x67492),f72(a1)))) % 112.26/112.09 [6750]P1(f317(f317(f225(a1),x67501),x67502))+~P1(f317(f317(f224(a1),x67501),f317(f317(f3(a1),x67502),f72(a1)))) % 112.26/112.09 [6753]P1(f317(f317(f224(a899),x67531),x67532))+~P1(f317(f317(f224(a1),f317(f90(a1),x67531)),f317(f90(a1),x67532))) % 112.26/112.09 [6754]P1(f317(f317(f224(a1),x67541),x67542))+~P1(f317(f317(f224(a1),f317(f94(a1),x67541)),f317(f94(a1),x67542))) % 112.26/112.09 [6756]P1(f317(f317(f225(a899),x67561),x67562))+~P1(f317(f317(f225(a1),f317(f90(a1),x67561)),f317(f90(a1),x67562))) % 112.26/112.09 [6757]P1(f317(f317(f225(a1),x67571),x67572))+~P1(f317(f317(f225(a899),f317(f94(a899),x67571)),f317(f94(a899),x67572))) % 112.26/112.09 [6758]P1(f317(f317(f225(a1),x67581),x67582))+~P1(f317(f317(f225(a1),f317(f94(a1),x67581)),f317(f94(a1),x67582))) % 112.26/112.09 [6831]~E(f280(a899,f277(a899),x68311,x68312),f178(f906(a899,a895)))+~P1(f317(f317(f277(a899),x68311),x68312)) % 112.26/112.09 [6858]~E(f678(x68582,x68581),f103(x68581))+E(f317(f132(f900(x68581),f900(x68581),f124(x68581),f103(x68581)),x68582),f103(x68581)) % 112.26/112.09 [6859]~E(f684(x68592,x68591),f103(x68591))+E(f317(f132(f900(x68591),f900(x68591),f124(x68591),f103(x68591)),x68592),f103(x68591)) % 112.26/112.09 [6863]~P5(x68631)+E(f317(f132(x68631,x68631,f91(x68631),f178(x68631)),x68632),f32(x68631,f317(f162(x68631),x68632))) % 112.26/112.09 [6864]~P5(x68641)+E(f317(f132(x68641,x68641,f92(x68641),f232(x68641)),x68642),f33(x68641,f317(f162(x68641),x68642))) % 112.26/112.09 [6878]E(x68781,f2(a89))+E(f317(f317(f74(a899),f317(a22,f317(f317(f3(a89),x68781),f72(a89)))),f317(a102,x68782)),f317(f317(f74(a899),f317(a22,x68781)),x68782)) % 112.26/112.09 [6927]P1(f317(f317(f225(a1),f317(f317(f3(a1),x69271),x69272)),f2(a1)))+~P1(f317(f317(f225(a1),x69271),x69272)) % 112.26/112.09 [6952]~P108(x69521)+E(f317(f317(f91(f906(x69521,a895)),f317(f317(f299(x69521),x69522),f178(f906(x69521,a895)))),f317(f294(x69521),x69522)),f317(f273(x69521),x69522)) % 112.26/112.09 [7031]~P59(x70311,x70312)+P36(x70311,f317(f252(f905(x70311,x70311)),f317(f247(x70311,x70311,a895),x70312))) % 112.26/112.09 [7032]~P59(x70321,x70322)+P57(x70321,f317(f252(f905(x70321,x70321)),f317(f247(x70321,x70321,a895),x70322))) % 112.26/112.09 [7033]~P49(x70331,x70332)+P37(x70331,f317(f252(f905(x70331,x70331)),f317(f247(x70331,x70331,a895),x70332))) % 112.26/112.09 [7034]~P50(x70341,x70342)+P51(x70341,f317(f252(f905(x70341,x70341)),f317(f247(x70341,x70341,a895),x70342))) % 112.26/112.09 [7035]E(x70351,f178(f906(x70352,a895)))+~P1(f317(f317(f224(f906(x70352,a895)),x70351),f178(f906(x70352,a895)))) % 112.26/112.09 [7119]~P1(f317(f317(f225(a899),f2(a899)),x71192))+P1(f317(f317(f224(a899),f41(a899,x71191,x71192)),x71192)) % 112.26/112.09 [7120]~P1(f317(f317(f224(a1),f2(a1)),x71201))+P1(f317(f317(f224(a1),f41(a1,x71201,x71202)),x71201)) % 112.26/112.09 [7121]~P1(f317(f317(f225(a899),f2(a899)),x71212))+P1(f317(f317(f225(a899),f41(a899,x71211,x71212)),x71212)) % 112.26/112.09 [7123]~P1(f317(f317(f225(a1),f2(a1)),x71232))+P1(f317(f317(f225(a1),f41(a1,x71231,x71232)),x71232)) % 112.26/112.09 [7199]~P109(x71991)+E(f317(f317(f3(f906(x71991,a895)),f317(f317(f299(x71991),x71992),f178(f906(x71991,a895)))),f317(f272(x71991),x71992)),f317(f317(f299(x71991),x71992),f178(f906(x71991,a895)))) % 112.26/112.09 [7274]~P42(x72741,x72742)+P52(x72741,f232(f906(x72741,a895)),f317(f252(f905(x72741,x72741)),f317(f247(x72741,x72741,a895),x72742))) % 112.26/112.09 [7275]P1(f317(x72751,x72752))+P1(f317(f317(f319(f906(f905(a899,a899),a895)),f568(x72752,x72751)),a88)) % 112.26/112.09 [7318]E(f317(f317(f124(a899),f129(a899,f317(f292(a899,x73181),x73182))),f317(f317(f141(a899),x73182),f103(a899))),f129(a899,f317(f292(a899,x73181),f317(a102,x73182))))+~P1(f317(f317(f224(a899),x73181),x73182)) % 112.26/112.09 [7470]E(x74701,f2(a899))+~E(f317(f132(a899,a899,f74(a899),x74701),x74702),f2(a899)) % 112.26/112.09 [7495]~P1(f317(f317(f225(a1),f317(f317(f3(a1),x74951),x74952)),f2(a1)))+P1(f317(f317(f225(a1),x74951),x74952)) % 112.26/112.09 [7524]P36(x75241,x75242)+~P36(x75241,f317(f317(f279(x75241,x75241,x75241),x75242),x75242)) % 112.26/112.09 [7549]~P1(f317(f317(f224(a899),f317(a102,x75491)),x75492))+P1(f175(a895,a229,f317(f224(a899),x75491),x75492)) % 112.26/112.09 [7704]P24(a899,a899,f317(f317(f9(a899,a899,a899),f3(a899)),x77041),x77042)+P1(f317(f317(f319(a899),f570(x77041,x77042)),x77042)) % 112.26/112.09 [7762]E(f317(f317(f317(f60(a899,x77621,f74(a899)),f317(f18(a899,x77621),f72(a899))),f2(a899)),x77622),f317(f30(x77621),x77622))+~P1(f317(f29(x77621),x77622)) % 112.26/112.09 [7804]P24(a899,a899,f317(f317(f9(a899,a899,a899),f3(a899)),x78041),x78042)+~P1(f317(f317(f224(a899),x78041),f570(x78041,x78042))) % 112.26/112.09 [7860]P36(x78601,x78602)+P1(f317(f317(f224(f906(x78601,a895)),f565(x78602,x78601)),f317(f275(x78601,x78601,x78602),f565(x78602,x78601)))) % 112.26/112.09 [7865]P59(x78651,x78652)+~P36(x78651,f317(f252(f905(x78651,x78651)),f317(f247(x78651,x78651,a895),x78652))) % 112.26/112.09 [7866]P49(x78661,x78662)+~P37(x78661,f317(f252(f905(x78661,x78661)),f317(f247(x78661,x78661,a895),x78662))) % 112.26/112.09 [7867]P50(x78671,x78672)+~P51(x78671,f317(f252(f905(x78671,x78671)),f317(f247(x78671,x78671,a895),x78672))) % 112.26/112.09 [7935]P1(f317(f317(f224(a899),f317(a102,x79351)),x79352))+~P1(f175(a895,a229,f317(f224(a899),x79351),x79352)) % 112.26/112.09 [7992]P1(f317(f317(f319(f905(a899,a899)),f317(f317(f242(a899,a899),x79921),x79922)),f297(a899,a307)))+~P1(f317(f317(f224(a899),x79921),x79922)) % 112.26/112.09 [8088]P42(x80881,x80882)+~P52(x80881,f232(f906(x80881,a895)),f317(f252(f905(x80881,x80881)),f317(f247(x80881,x80881,a895),x80882))) % 112.26/112.09 [8143]~P1(f317(f127(x81431),x81432))+P1(f317(f127(f906(x81431,a895)),f317(f317(f144(f900(x81431),f906(x81431,a895)),f162(x81431)),f50(x81431,x81432)))) % 112.26/112.09 [8344]~P36(x83441,f317(f276(x83441,x83441),x83442))+P36(x83441,f317(f276(x83441,x83441),f317(f317(f279(x83441,x83441,x83441),x83442),f297(x83441,x83442)))) % 112.26/112.09 [8356]P150(x83561,f317(f317(f299(a894),f317(a910,x83562)),f178(f906(a894,a895))))+~P150(f317(f317(f299(a894),f317(a910,x83562)),x83561),f317(f317(f299(a894),f911(f222(a896,f34(x83562)))),f178(f906(a894,a895)))) % 112.26/112.09 [8443]P25(x84431,a899,f804(x84432,x84431),x84432,f317(f292(a899,f2(a899)),f317(f30(x84431),x84432)))+~P1(f317(f29(x84431),x84432)) % 112.26/112.09 [8444]P25(a899,x84441,f805(x84442,x84441),f317(f292(a899,f2(a899)),f317(f30(x84441),x84442)),x84442)+~P1(f317(f29(x84441),x84442)) % 112.26/112.09 [8461]P25(a899,x84611,f806(x84612,x84611),f293(a899,f72(a899),f317(f30(x84611),x84612)),x84612)+~P1(f317(f29(x84611),x84612)) % 112.26/112.09 [8471]P1(f317(f29(f905(x84711,x84711)),f317(f317(f279(x84711,x84711,x84711),x84712),f297(x84711,x84712))))+~P1(f317(f29(f905(x84711,x84711)),x84712)) % 112.26/112.09 [8498]E(x84981,f2(a1))+P1(f317(f45(x84982,x84981),f317(f317(f242(a1,a1),f317(f317(f31(a1),x84982),x84981)),f41(a1,x84982,x84981)))) % 112.26/112.09 [8512]~P1(f317(f317(f319(f905(a899,a899)),f317(f317(f242(a899,a899),x85121),x85122)),f297(a899,a307)))+P1(f317(f317(f224(a899),x85121),x85122)) % 112.26/112.09 [8529]~P81(x85291)+E(f317(f132(x85291,x85291,f317(f9(x85291,x85291,x85291),f74(x85291)),f2(x85291)),f317(f158(x85291),x85292)),f317(f132(x85291,x85291,f74(x85291),f2(x85291)),x85292)) % 112.26/112.09 [8700]~P108(x87001)+E(f317(f132(f900(x87001),x87001,f317(f9(x87001,f900(x87001),f900(x87001)),f138(x87001,x87001,f7(x87001))),f103(x87001)),x87002),f140(x87001,x87001,f7(x87001),x87002)) % 112.26/112.09 [8811]~P57(x88111,f317(f252(f905(x88111,x88111)),f317(f247(x88111,x88111,a895),x88112)))+P57(x88111,f317(f252(f905(x88111,x88111)),f317(f247(x88111,x88111,a895),f233(x88111,x88111,x88112)))) % 112.26/112.09 [8825]P1(f317(f317(f319(f905(a899,a899)),f317(f317(f242(a899,a899),x88251),x88252)),f317(f317(f279(a899,a899,a899),a307),f297(a899,a307))))+~P1(f317(f317(f225(a899),x88251),x88252)) % 112.26/112.09 [8871]~P1(f317(f29(f905(x88711,x88711)),f317(f317(f279(x88711,x88711,x88711),x88712),f297(x88711,x88712))))+P1(f317(f29(f905(x88711,x88711)),x88712)) % 112.26/112.09 [8929]~P57(x89291,f317(f252(f905(x89291,x89291)),f317(f247(x89291,x89291,a895),f233(x89291,x89291,x89292))))+P57(x89291,f317(f252(f905(x89291,x89291)),f317(f247(x89291,x89291,a895),x89292))) % 112.26/112.09 [9126]P57(x91261,x91262)+P1(f317(f317(f319(f905(x91261,x91261)),f317(f317(f242(x91261,x91261),f598(x91262,x91261)),f598(x91262,x91261))),f317(f317(f279(x91261,x91261,x91261),x91262),f297(x91261,x91262)))) % 112.26/112.09 [9127]P57(x91271,x91272)+P1(f317(f317(f319(f905(x91271,x91271)),f317(f317(f242(x91271,x91271),f600(x91272,x91271)),f600(x91272,x91271))),f317(f317(f279(x91271,x91271,x91271),x91272),f297(x91271,x91272)))) % 112.26/112.09 [9244]~P1(f317(f317(f319(f905(a899,a899)),f317(f317(f242(a899,a899),x92441),x92442)),f317(f317(f279(a899,a899,a899),a307),f297(a899,a307))))+P1(f317(f317(f225(a899),x92441),x92442)) % 112.26/112.09 [5151]~P94(x51511)+E(f317(f317(f74(x51511),f317(f94(x51511),a77)),x51512),x51512) % 112.26/112.09 [5181]~P68(x51811)+E(f317(f317(f74(x51811),f317(f73(x51811),x51812)),x51812),f2(x51811)) % 112.26/112.09 [5182]~P76(x51821)+E(f317(f317(f74(x51821),f317(f73(x51821),x51822)),x51822),f2(x51821)) % 112.26/112.09 [5183]~P96(x51831)+E(f317(f317(f91(x51831),f317(f73(x51831),x51832)),x51832),f232(x51831)) % 112.26/112.09 [5184]~P96(x51841)+E(f317(f317(f92(x51841),f317(f73(x51841),x51842)),x51842),f178(x51841)) % 112.26/112.09 [5217]~P94(x52171)+E(f317(f317(f75(x52171),f317(f94(x52171),a87)),x52172),f317(f73(x52171),x52172)) % 112.26/112.09 [5374]~P114(x53741)+E(f317(f317(f75(x53741),f317(f73(x53741),f72(x53741))),x53742),f317(f73(x53741),x53742)) % 112.26/112.09 [5420]E(f317(f70(a1),x54201),f72(a1))+~E(f317(f70(a1),f317(f317(f75(a1),x54201),x54202)),f72(a1)) % 112.26/112.09 [5512]~P94(x55121)+E(f317(f317(f74(x55121),f72(x55121)),f317(f94(x55121),x55122)),f317(f94(x55121),f317(f317(f3(a1),x55122),a87))) % 112.26/112.09 [5565]~P108(x55651)+E(f16(x55651,f317(f317(f299(x55651),x55652),f178(f906(x55651,a895)))),x55652) % 112.26/112.09 [5566]~P108(x55661)+E(f17(x55661,f317(f317(f299(x55661),x55662),f178(f906(x55661,a895)))),x55662) % 112.26/112.09 [5567]~P99(x55671)+E(f12(x55671,f317(f317(f299(x55671),x55672),f178(f906(x55671,a895)))),x55672) % 112.26/112.09 [5568]~P5(x55681)+E(f32(x55681,f317(f317(f299(x55681),x55682),f178(f906(x55681,a895)))),x55682) % 112.26/112.09 [5569]~P99(x55691)+E(f13(x55691,f317(f317(f299(x55691),x55692),f178(f906(x55691,a895)))),x55692) % 112.26/112.09 [5570]~P5(x55701)+E(f33(x55701,f317(f317(f299(x55701),x55702),f178(f906(x55701,a895)))),x55702) % 112.26/112.09 [5592]E(f317(f317(f74(a899),x55921),f317(f317(f3(a899),x55922),x55921)),x55922)+P1(f317(f317(f225(a899),x55922),x55921)) % 112.26/112.09 [5630]E(x56301,f103(x56302))+P1(f317(f317(f225(a899),f2(a899)),f317(f179(f900(x56302)),x56301))) % 112.26/112.09 [5756]~P108(x57561)+E(f14(x57561,f223(x57561),f317(f317(f299(x57561),x57562),f178(f906(x57561,a895)))),x57562) % 112.26/112.09 [5757]~P108(x57571)+E(f15(x57571,f228(x57571),f317(f317(f299(x57571),x57572),f178(f906(x57571,a895)))),x57572) % 112.26/112.09 [5818]E(f317(f317(f3(a899),x58181),f317(f317(f3(a899),x58181),x58182)),x58182)+~P1(f317(f317(f224(a899),x58182),x58181)) % 112.26/112.09 [5819]E(f317(f317(f74(a899),x58191),f317(f317(f3(a899),x58192),x58191)),x58192)+~P1(f317(f317(f224(a899),x58191),x58192)) % 112.26/112.09 [5841]E(f41(a899,f317(f317(f3(a899),x58411),x58412),x58412),f41(a899,x58411,x58412))+P1(f317(f317(f225(a899),x58411),x58412)) % 112.26/112.09 [5852]E(f317(f73(a1),f317(f317(f31(a1),x58521),f317(f73(a1),x58522))),f283(x58521,x58522))+P1(f317(f317(f224(a1),f2(a1)),x58522)) % 112.26/112.09 [5854]~E(x58542,f2(a899))+P1(f317(f317(f225(a899),f2(a899)),f317(f317(f234(a899),x58541),x58542))) % 112.26/112.09 [5917]~P94(x59171)+E(f317(f317(f74(x59171),f317(f73(x59171),f72(x59171))),f317(f94(x59171),x59172)),f317(f94(x59171),f317(f317(f74(a1),x59172),a87))) % 112.26/112.09 [5919]E(f317(f317(f234(a899),f317(f94(a899),x59191)),x59192),f317(f317(f234(a899),f2(a899)),x59192))+~P1(f317(a183,f317(f94(a1),x59191))) % 112.26/112.09 [6027]E(f317(f131(a899),f129(a899,f317(f292(a899,x60271),x60272))),x60271)+~P1(f317(f317(f225(a899),x60271),x60272)) % 112.26/112.09 [6043]E(f317(f317(f75(a899),f317(f94(a899),x60431)),f317(f94(a899),x60432)),f317(f94(a899),f317(f317(f75(a1),x60431),x60432)))+P1(f317(f317(f225(a1),x60431),a77)) % 112.26/112.09 [6049]~P128(x60491)+P1(f317(f317(f224(x60491),f2(x60491)),f317(f317(f75(x60491),x60492),x60492))) % 112.26/112.09 [6061]E(f317(f317(f3(a899),f317(a102,x60611)),x60612),f317(a102,f317(f317(f3(a899),x60611),x60612)))+~P1(f317(f317(f224(a899),x60612),x60611)) % 112.26/112.09 [6065]E(f41(a899,f317(f317(f3(a899),x60651),x60652),x60652),f41(a899,x60651,x60652))+~P1(f317(f317(f224(a899),x60652),x60651)) % 112.26/112.09 [6119]E(f317(f317(f234(a899),f317(a95,x61191)),x61192),f317(a95,f317(f317(f234(a1),x61191),x61192)))+~P1(f317(f317(f224(a1),f2(a1)),x61191)) % 112.26/112.09 [6137]P1(f317(f127(x61371),x61372))+P1(f317(f317(f225(a899),f648(x61372,x61371)),f317(f179(f900(x61371)),x61372))) % 112.26/112.09 [6138]P1(f317(f127(x61381),x61382))+P1(f317(f317(f225(a899),f652(x61382,x61381)),f317(f179(f900(x61381)),x61382))) % 112.26/112.09 [6152]~E(x61521,f103(x61522))+~P1(f317(f317(f225(a899),f2(a899)),f317(f179(f900(x61522)),x61521))) % 112.26/112.09 [6163]E(f134(a899,f129(a899,f317(f292(a899,x61631),x61632))),f317(f317(f3(a899),x61632),f72(a899)))+~P1(f317(f317(f225(a899),x61631),x61632)) % 112.26/112.09 [6166]E(f317(f317(f74(a1),x61661),f317(f90(a1),f317(a102,f883(x61662,x61661)))),x61662)+~P1(f317(f317(f225(a1),x61661),x61662)) % 112.26/112.09 [6173]E(x61731,f2(a899))+E(f317(f317(f75(a899),x61732),f317(f317(f234(a899),x61732),f317(f317(f3(a899),x61731),f72(a899)))),f317(f317(f234(a899),x61732),x61731)) % 112.26/112.09 [6201]E(f317(f317(f75(a899),f317(a95,x62011)),f317(a95,x62012)),f317(a95,f317(f317(f75(a1),x62011),x62012)))+~P1(f317(f317(f224(a1),f2(a1)),x62011)) % 112.26/112.09 [6202]E(f317(f317(f31(a899),f317(a95,x62021)),f317(a95,x62022)),f317(a95,f317(f317(f31(a1),x62021),x62022)))+~P1(f317(f317(f224(a1),f2(a1)),x62021)) % 112.26/112.09 [6217]~P119(x62171)+E(f317(f317(f74(x62171),x62172),x62172),f317(f317(f75(x62171),f317(f317(f74(x62171),f72(x62171)),f72(x62171))),x62172)) % 112.26/112.09 [6240]E(f317(f317(f3(a1),f317(f90(a1),x62401)),f317(f90(a1),x62402)),f317(f90(a1),f317(f317(f3(a899),x62401),x62402)))+~P1(f317(f317(f224(a899),x62402),x62401)) % 112.26/112.09 [6242]E(f317(f317(f242(a1,a1),f317(f94(a1),a87)),f317(f317(f74(a1),x62421),x62422)),f46(x62421,x62422))+~P1(f317(f317(f224(a1),x62422),f2(a1))) % 112.26/112.09 [6276]E(f169(x62761,x62762),f103(f900(x62761)))+P1(f317(f317(f319(f900(x62761)),f647(x62762,x62761)),f317(f162(f900(x62761)),x62762))) % 112.26/112.09 [6286]E(f106(a1,f317(f119(a1),x62861),f118(x62862,f317(f317(f74(a1),x62861),f72(a1)))),f118(x62862,x62861))+P1(f317(f317(f225(a1),x62862),x62861)) % 112.26/112.09 [6341]~P1(f317(f317(f277(a899),x63411),x63412))+P1(f317(f317(f277(a899),x63411),f317(f317(f74(a899),x63412),x63411))) % 112.26/112.09 [6363]E(f317(f317(f141(a1),x63631),f168(f317(f317(f74(a1),x63631),f72(a1)),x63632)),f168(x63631,x63632))+~P1(f317(f317(f224(a1),x63631),x63632)) % 112.26/112.09 [6385]P150(x63851,x63852)+~P1(f317(f317(f224(f906(a894,a895)),x63852),x63851)) % 112.26/112.09 [6406]~P1(f317(f317(f225(a899),x64062),x64061))+P1(f317(f317(f225(a899),f2(a899)),f317(f317(f3(a899),x64061),x64062))) % 112.26/112.09 [6438]~P1(f317(f317(f225(a899),x64381),f317(a95,x64382)))+P1(f317(f317(f225(a1),f317(f90(a1),x64381)),x64382)) % 112.26/112.09 [6467]~P108(x64671)+E(f317(f317(f91(f906(x64671,a895)),f317(f272(x64671),x64672)),f317(f317(f299(x64671),x64672),f178(f906(x64671,a895)))),f317(f291(x64671),x64672)) % 112.26/112.09 [6468]~P1(f317(f317(f224(a1),f2(a1)),x64681))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f234(a1),x64681),x64682))) % 112.26/112.09 [6471]~P1(f317(f317(f225(a899),f2(a899)),x64711))+P1(f317(f317(f225(a899),f2(a899)),f317(f317(f234(a899),x64711),x64712))) % 112.26/112.09 [6498]~E(f317(x64981,f2(a899)),f2(a899))+E(f317(f317(f8(a899,a899),x64981),f293(a899,f317(a102,f2(a899)),x64982)),f317(f317(f8(a899,a899),x64981),f293(a899,f2(a899),x64982))) % 112.26/112.09 [6564]~P94(x65641)+E(f317(f317(f75(x65641),f317(f317(f74(x65641),f72(x65641)),f72(x65641))),f317(f94(x65641),x65642)),f317(f94(x65641),f317(f317(f74(a1),x65642),x65642))) % 112.26/112.09 [6584]E(f317(f317(f299(a1),x65841),f293(a1,f317(f317(f74(a1),x65841),f72(a1)),x65842)),f293(a1,x65841,x65842))+P1(f317(f317(f225(a1),x65842),x65841)) % 112.26/112.09 [6585]P1(f317(f317(f225(a899),x65851),f317(a95,x65852)))+~P1(f317(f317(f225(a1),f317(f90(a1),x65851)),x65852)) % 112.26/112.09 [6685]P1(f317(f317(f277(a899),x66851),x66852))+~P1(f317(f317(f277(a899),x66851),f317(f317(f74(a899),x66852),x66851))) % 112.26/112.09 [6690]E(f317(a95,f317(f317(f31(a1),f317(f94(a1),x66901)),f317(f94(a1),x66902))),f317(f317(f31(a899),f317(f94(a899),x66901)),f317(f94(a899),x66902)))+P1(f317(a183,f317(f94(a1),x66901))) % 112.26/112.09 [6751]P1(f317(f317(f225(a899),x67511),x67512))+~P1(f317(f317(f225(a899),f2(a899)),f317(f317(f3(a899),x67512),x67511))) % 112.26/112.09 [6794]P1(f317(f317(f225(a899),f2(a899)),x67941))+~P1(f317(f317(f225(a899),f2(a899)),f317(f317(f75(a899),x67942),x67941))) % 112.26/112.09 [6795]P1(f317(f317(f225(a899),f2(a899)),x67951))+~P1(f317(f317(f225(a899),f2(a899)),f317(f317(f75(a899),x67951),x67952))) % 112.26/112.09 [6814]~P1(f317(f317(f224(a1),x68141),f2(a1)))+E(f317(f317(f75(a899),f317(a95,f317(f73(a1),x68141))),f317(a95,f317(f73(a1),x68142))),f317(a95,f317(f317(f75(a1),x68141),x68142))) % 112.26/112.09 [6875]~E(x68752,f178(f906(x68751,a895)))+P1(f317(f317(f224(f906(x68751,a895)),x68752),f317(f73(f906(x68751,a895)),x68752))) % 112.26/112.09 [6937]~P94(x69371)+E(f317(f317(f74(x69371),f317(f317(f74(x69371),f2(x69371)),f317(f94(x69371),x69372))),f317(f94(x69371),x69372)),f317(f94(x69371),f317(f317(f74(a1),x69372),x69372))) % 112.26/112.09 [6993]~P1(f317(f317(f225(a1),x69931),x69932))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x69931),f72(a1))),x69932)) % 112.26/112.09 [7064]E(x70641,f2(a899))+~P1(f317(f317(f224(a1),f317(f90(a1),x70642)),f317(f73(a1),f317(f90(a1),x70641)))) % 112.26/112.09 [7065]E(x70651,f2(a899))+~P1(f317(f317(f224(a1),f317(f90(a1),x70651)),f317(f73(a1),f317(f90(a1),x70652)))) % 112.26/112.09 [7167]E(f317(f317(f242(a1,a1),f317(f94(a1),a87)),f317(f317(f74(a1),x71671),x71672)),f46(x71671,x71672))+~P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),x71671),x71672))) % 112.26/112.09 [7211]~P26(x72111,x72112)+P36(x72111,f317(f241(f906(f905(x72111,x72111),a895),f906(f905(x72111,x72111),a895)),x72112)) % 112.26/112.09 [7230]~P1(f317(f317(f224(a899),f317(a102,f2(a899))),x72301))+P1(f317(f317(f224(a899),f317(a102,f2(a899))),f317(f317(f234(a899),x72301),x72302))) % 112.26/112.09 [7408]~P1(f317(f317(f224(a1),x74081),x74082))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x74081),x74081)),f317(f317(f74(a1),x74082),x74082))) % 112.26/112.09 [7413]~P1(f317(f317(f225(a1),x74131),x74132))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x74131),x74131)),f317(f317(f74(a1),x74132),x74132))) % 112.26/112.09 [7471]~P1(f317(f317(f225(a899),f2(a899)),x74711))+P1(f317(f317(f225(a899),f317(f317(f3(a899),x74711),f317(a102,x74712))),x74711)) % 112.26/112.09 [7506]P1(f317(f317(f224(a899),f317(a102,f2(a899))),x75061))+~P1(f317(f317(f224(a899),f317(a102,f2(a899))),f317(f317(f75(a899),x75062),x75061))) % 112.26/112.09 [7507]P1(f317(f317(f224(a899),f317(a102,f2(a899))),x75071))+~P1(f317(f317(f224(a899),f317(a102,f2(a899))),f317(f317(f75(a899),x75071),x75072))) % 112.26/112.09 [7511]P1(f317(f317(f224(a899),f317(f317(f154(a899),x75111),x75112)),f317(f155(a899),x75111)))+~P1(f317(f317(f225(a899),x75112),f317(f179(f900(a899)),x75111))) % 112.26/112.09 [7548]P1(f317(f317(f225(a1),x75481),x75482))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x75481),f72(a1))),x75482)) % 112.26/112.09 [7589]P1(f317(f29(x75891),f232(f906(x75891,a895))))+~P1(f317(f29(f906(x75892,x75891)),f232(f906(f906(x75892,x75891),a895)))) % 112.26/112.09 [7590]P1(f317(f29(x75901),f232(f906(x75901,a895))))+~P1(f317(f29(f904(x75902,x75901)),f232(f906(f904(x75902,x75901),a895)))) % 112.26/112.09 [7591]P1(f317(f29(x75911),f232(f906(x75911,a895))))+~P1(f317(f29(f904(x75911,x75912)),f232(f906(f904(x75911,x75912),a895)))) % 112.26/112.09 [7631]E(x76311,f178(f906(x76312,a895)))+~P1(f317(f317(f224(f906(x76312,a895)),x76311),f317(f73(f906(x76312,a895)),x76311))) % 112.26/112.09 [7772]E(f317(f132(f900(x77721),f900(x77721),f124(x77721),f103(x77721)),x77722),f103(x77721))+P1(f317(f317(f319(f900(x77721)),f678(x77722,x77721)),f317(f162(f900(x77721)),x77722))) % 112.26/112.09 [7773]E(f317(f132(f900(x77731),f900(x77731),f124(x77731),f103(x77731)),x77732),f103(x77731))+P1(f317(f317(f319(f900(x77731)),f684(x77732,x77731)),f317(f162(f900(x77731)),x77732))) % 112.26/112.09 [8010]P1(f317(f317(f224(a1),x80101),x80102))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x80101),x80101)),f317(f317(f74(a1),x80102),x80102))) % 112.26/112.09 [8015]P1(f317(f317(f225(a1),x80151),x80152))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),x80151),x80151)),f317(f317(f74(a1),x80152),x80152))) % 112.26/112.09 [8108]~P119(x81081)+E(f317(f317(f75(x81081),f317(f317(f74(x81081),f72(x81081)),f72(x81081))),f317(f317(f8(a899,x81081),f90(x81081)),f293(a899,f72(a899),x81082))),f317(f317(f75(x81081),f317(f90(x81081),x81082)),f317(f317(f74(x81081),f317(f90(x81081),x81082)),f72(x81081)))) % 112.26/112.09 [8157]P1(f317(f317(f319(a899),x81571),x81572))+~P1(f317(f317(f319(a1),f317(f90(a1),x81571)),f317(f300(a899,a1,f90(a1)),x81572))) % 112.26/112.09 [8316]~P1(f317(f29(x83161),x83162))+E(f317(f300(a899,x83161,f527(x83162,x83161)),f317(f252(a899),f317(f317(f9(a899,a899,a895),f225(a899)),f528(x83162,x83161)))),x83162) % 112.26/112.09 [8597]P53(x85971,x85972)+P1(f317(f317(f319(f905(x85971,x85971)),f317(f317(f242(x85971,x85971),f470(x85972,x85971)),f470(x85972,x85971))),x85972)) % 112.26/112.09 [8598]P37(x85981,x85982)+P1(f317(f317(f319(f905(x85981,x85981)),f317(f317(f242(x85981,x85981),f770(x85982,x85981)),f773(x85982,x85981))),x85982)) % 112.26/112.09 [8599]P37(x85991,x85992)+P1(f317(f317(f319(f905(x85991,x85991)),f317(f317(f242(x85991,x85991),f773(x85992,x85991)),f774(x85992,x85991))),x85992)) % 112.26/112.09 [8600]P38(x86001,x86002)+P1(f317(f317(f319(f905(x86001,x86001)),f317(f317(f242(x86001,x86001),f689(x86002,x86001)),f688(x86002,x86001))),x86002)) % 112.26/112.09 [8601]P38(x86011,x86012)+P1(f317(f317(f319(f905(x86011,x86011)),f317(f317(f242(x86011,x86011),f688(x86012,x86011)),f689(x86012,x86011))),x86012)) % 112.26/112.09 [8602]P51(x86021,x86022)+P1(f317(f317(f319(f905(x86021,x86021)),f317(f317(f242(x86021,x86021),f784(x86022,x86021)),f785(x86022,x86021))),x86022)) % 112.26/112.09 [8743]~P94(x87431)+E(f317(f317(f3(x87431),f72(x87431)),f317(f94(x87431),x87432)),f317(f94(x87431),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f73(a1),x87432)))) % 112.26/112.09 [8868]~P1(f317(f317(f225(f906(a899,a895)),x88681),x88682))+P1(f317(f317(f225(f906(a1,a895)),f317(f300(a899,a1,f90(a1)),x88681)),f317(f300(a899,a1,f90(a1)),x88682))) % 112.26/112.09 [8902]~P1(f317(f317(f225(a1),x89021),x89022))+P1(f317(f317(f224(a1),f317(f317(f3(a1),f317(f317(f74(a1),x89021),x89021)),a87)),f317(f317(f74(a1),x89022),x89022))) % 112.26/112.09 [8904]~P1(f317(f317(f225(a1),x89041),x89042))+P1(f317(f317(f225(a1),f317(f317(f3(a1),f317(f317(f74(a1),x89041),x89041)),a87)),f317(f317(f74(a1),x89042),x89042))) % 112.26/112.09 [8977]~P1(f317(f317(f319(a899),x89771),f317(f162(a899),x89772)))+P1(f317(f317(f224(a899),x89771),f317(f132(a899,a899,f74(a899),f2(a899)),x89772))) % 112.26/112.09 [9066]P45(x90661,x90662)+~P1(f317(f317(f319(f905(x90661,x90661)),f317(f317(f242(x90661,x90661),f448(x90662,x90661)),f448(x90662,x90661))),x90662)) % 112.26/112.09 [9067]P37(x90671,x90672)+~P1(f317(f317(f319(f905(x90671,x90671)),f317(f317(f242(x90671,x90671),f770(x90672,x90671)),f774(x90672,x90671))),x90672)) % 112.26/112.09 [9068]P51(x90681,x90682)+~P1(f317(f317(f319(f905(x90681,x90681)),f317(f317(f242(x90681,x90681),f785(x90682,x90681)),f784(x90682,x90681))),x90682)) % 112.26/112.09 [9207]~P1(f317(f317(f224(f906(a1,a895)),f317(f300(a899,a1,f90(a1)),x92071)),f317(f300(a899,a1,f90(a1)),x92072)))+P1(f317(f317(f224(f906(a899,a895)),x92071),x92072)) % 112.26/112.09 [9208]~P1(f317(f317(f225(f906(a1,a895)),f317(f300(a899,a1,f90(a1)),x92081)),f317(f300(a899,a1,f90(a1)),x92082)))+P1(f317(f317(f225(f906(a899,a895)),x92081),x92082)) % 112.26/112.09 [9293]P1(f317(f317(f225(a1),x92931),x92932))+~P1(f317(f317(f224(a1),f317(f317(f3(a1),f317(f317(f74(a1),x92931),x92931)),a87)),f317(f317(f74(a1),x92932),x92932))) % 112.26/112.09 [9295]P1(f317(f317(f225(a1),x92951),x92952))+~P1(f317(f317(f225(a1),f317(f317(f3(a1),f317(f317(f74(a1),x92951),x92951)),a87)),f317(f317(f74(a1),x92952),x92952))) % 112.26/112.09 [10196]~P105(x101961)+E(f106(f900(x101961),f317(f119(f900(x101961)),f103(x101961)),f317(f317(f317(f86(f901(f900(x101961))),f317(f317(f225(a1),f2(a1)),x101962)),f317(f108(f905(x101961,f900(x101961)),f900(x101961),f121(x101961,f900(x101961),f122(x101961,f317(f317(f3(a1),x101962),f72(a1))),f122(f900(x101961),f317(f317(f3(a1),x101962),f72(a1))))),f317(f247(x101961,f900(x101961),f901(f900(x101961))),f317(f317(f10(f906(f900(x101961),f900(x101961)),f906(f900(x101961),f901(f900(x101961))),x101961),f317(f10(f900(x101961),f901(f900(x101961)),f900(x101961)),f119(f900(x101961)))),f141(x101961))))),f105(f900(x101961)))),f122(f900(x101961),x101962)) % 112.26/112.09 [10218]~P1(f317(f29(x102181),x102182))+E(f317(f179(f900(x102181)),f84(f900(x102181),f317(f317(f20(f900(x102181),a895,a895),f317(f317(f10(a895,f906(a895,a895),f900(x102181)),a315),f317(f317(f9(f900(x102181),f906(x102181,a895),a895),f317(f317(f10(f906(x102181,a895),f906(f906(x102181,a895),a895),f900(x102181)),a314),f162(x102181))),x102182))),f127(x102181)))),f204(x102181,x102182)) % 112.26/112.09 [6162]E(f317(f317(f74(a899),f317(f317(f3(a899),x61621),x61622)),x61622),x61621)+~P1(f317(f317(f224(a899),x61622),x61621)) % 112.26/112.09 [6236]E(f317(f317(f31(a899),f317(f317(f75(a899),x62361),x62362)),x62362),x62361)+~P1(f317(f317(f225(a899),f2(a899)),x62362)) % 112.26/112.09 [6237]E(f317(f317(f31(a899),f317(f317(f75(a899),x62371),x62372)),x62371),x62372)+~P1(f317(f317(f225(a899),f2(a899)),x62371)) % 112.26/112.09 [6241]~P69(x62411)+E(f317(f317(f8(a899,x62411),f317(f154(x62411),x62412)),f317(f292(a899,f2(a899)),f317(f179(f900(x62411)),x62412))),f317(f155(x62411),x62412)) % 112.26/112.09 [6355]E(f41(a899,f317(a102,f317(f317(f75(a899),x63551),x63552)),x63551),f72(a899))+~P1(f317(f317(f225(a899),f72(a899)),x63551)) % 112.26/112.09 [6361]E(f317(a102,f317(f317(f74(a899),f317(f94(a899),x63611)),x63612)),f317(f317(f74(a899),f72(a899)),x63612))+~P1(f317(a183,f317(f94(a1),x63611))) % 112.26/112.09 [6391]E(f317(a95,f317(f317(f234(a1),f317(f94(a1),x63911)),x63912)),f317(f317(f234(a899),f317(f94(a899),x63911)),x63912))+P1(f317(a183,f317(f94(a1),x63911))) % 112.26/112.09 [6639]E(f317(f317(f3(a899),x66391),f317(f94(a899),f317(f317(f74(a1),x66392),a87))),f317(f317(f3(a899),f317(a102,x66391)),f317(f94(a899),x66392)))+~P1(f317(f317(f225(a1),a77),x66392)) % 112.26/112.09 [6721]E(x67211,f2(a899))+E(f317(a102,f317(f317(f74(a899),f317(f317(f3(a899),x67211),f72(a899))),x67212)),f317(f317(f74(a899),x67211),x67212)) % 112.26/112.09 [6764]E(x67641,f2(a1))+P1(f317(f317(f225(a1),f2(a1)),f317(f317(f234(a1),f317(f70(a1),x67641)),x67642))) % 112.26/112.09 [6779]~E(x67792,f2(a899))+P1(f317(f317(f225(a1),f2(a1)),f317(f317(f234(a1),f317(f70(a1),x67791)),x67792))) % 112.26/112.09 [6817]E(x68171,f2(a899))+E(f317(f317(f74(a899),x68172),f317(f317(f75(a899),f317(f317(f3(a899),x68171),f72(a899))),x68172)),f317(f317(f75(a899),x68171),x68172)) % 112.26/112.09 [6868]~P1(f317(f317(f224(a1),x68681),x68682))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x68681),a87)),x68682)) % 112.26/112.09 [6997]E(f317(f317(f141(a899),x69971),f129(a899,f317(f292(a899,f317(a102,x69971)),x69972))),f129(a899,f317(f292(a899,x69971),x69972)))+~P1(f317(f317(f225(a899),x69971),x69972)) % 112.26/112.09 [7202]E(x72021,x72022)+~E(f317(f317(f3(a1),f317(f317(f74(a1),x72021),x72021)),a87),f317(f317(f3(a1),f317(f317(f74(a1),x72022),x72022)),a87)) % 112.26/112.09 [7205]E(x72051,f103(x72052))+E(f256(x72052,f317(f317(f144(x72052,f905(a89,x72052)),f317(f242(a89,x72052),f72(a89))),x72051)),f265(x72052,x72051)) % 112.26/112.09 [7441]P1(f317(f317(f224(a1),x74411),x74412))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),x74411),a87)),x74412)) % 112.26/112.09 [7914]~P1(f317(f317(f225(a899),x79141),x79142))+P1(f317(f317(f319(f905(a899,a899)),f317(f317(f242(a899,a899),x79141),x79142)),a230)) % 112.26/112.09 [8134]~P1(f317(f317(f225(a89),f2(a89)),x81341))+P1(f317(f317(f225(a89),f317(f241(a89,f905(a89,a89)),f317(f257(x81341),x81342))),x81341)) % 112.26/112.09 [8398]~P37(x83981,x83982)+P37(x83981,f317(f317(f91(f906(f905(x83981,x83981),a895)),x83982),f297(x83981,f178(f906(f905(x83981,x83981),a895))))) % 112.26/112.09 [8399]~P38(x83991,x83992)+P38(x83991,f317(f317(f91(f906(f905(x83991,x83991),a895)),x83992),f297(x83991,f178(f906(f905(x83991,x83991),a895))))) % 112.26/112.09 [8447]~P86(x84471)+P1(f317(f317(f224(x84471),f317(f70(x84471),f317(f155(x84471),x84472))),f317(f155(x84471),f317(f317(f144(x84471,x84471),f70(x84471)),x84472)))) % 112.26/112.09 [8473]P1(f317(f317(f225(a899),x84731),x84732))+~P1(f317(f317(f319(f905(a899,a899)),f317(f317(f242(a899,a899),x84731),x84732)),a230)) % 112.26/112.09 [8621]E(f317(f317(f242(x86211,x86211),f622(x86212,x86211)),f622(x86212,x86211)),x86212)+~P1(f317(f317(f319(f905(x86211,x86211)),x86212),f297(x86211,f178(f906(f905(x86211,x86211),a895))))) % 112.26/112.09 [8665]E(f317(f292(a899,x86651),f317(f317(f74(a899),x86651),f317(f30(a899),x86652))),x86652)+~P1(f317(f317(f224(f906(a899,a895)),x86652),f317(f292(a899,x86651),f317(f317(f74(a899),x86651),f317(f30(a899),x86652))))) % 112.26/112.09 [8895]P38(x88951,x88952)+~P38(x88951,f317(f317(f91(f906(f905(x88951,x88951),a895)),x88952),f297(x88951,f178(f906(f905(x88951,x88951),a895))))) % 112.26/112.09 [9021]E(f317(f317(f31(a1),f317(f94(a1),f317(f317(f3(a1),f317(f317(f74(a1),x90211),x90211)),a87))),f317(f94(a1),f317(f317(f74(a1),x90212),x90212))),f317(f317(f31(a1),f317(f94(a1),x90211)),f317(f94(a1),x90212)))+~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x90212))) % 112.26/112.09 [9111]~P37(x91111,x91112)+P1(f317(f317(f224(f906(f905(x91111,x91111),a895)),f317(f317(f279(x91111,x91111,x91111),x91112),x91112)),x91112)) % 112.26/112.09 [9137]E(f167(f900(x91371),f317(f317(f10(a895,a895,f900(x91371)),a312),f317(f317(f9(f900(x91371),f900(x91371),a895),a314),f103(x91371))),x91372),f169(x91371,f169(x91371,x91372)))+~P13(a899,f317(f158(a899),f317(f317(f144(f900(x91371),a899),f179(f900(x91371))),x91372))) % 112.26/112.09 [9140]E(f317(f317(f31(a1),f317(f94(a1),f317(f317(f3(a1),f317(f317(f74(a1),x91401),x91401)),a87))),f317(f94(a1),f317(f317(f74(a1),x91402),x91402))),f317(f317(f31(a1),f317(f317(f74(a1),f317(f94(a1),x91401)),f72(a1))),f317(f94(a1),x91402)))+P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x91402))) % 112.26/112.09 [9992]P1(f317(a183,x99922))+E(f317(f317(f80(a1,a899),f317(f317(f3(a1),x99921),x99922)),f317(f317(f20(a1,a899,a899),f317(f317(f9(a1,a899,f906(a899,a899)),f317(f317(f10(a895,f906(a899,f906(a899,a899)),a1),f86(a899)),a183)),f2(a899))),a95)),f317(f317(f3(a899),f317(a95,x99921)),f317(a95,x99922))) % 112.26/112.09 [10000]E(f317(f317(f80(a1,a899),f317(f94(a1),f317(f317(f74(a1),x100001),f317(f73(a1),x100002)))),f317(f317(f20(a1,a899,a899),f317(f317(f9(a1,a899,f906(a899,a899)),f317(f317(f10(a895,f906(a899,f906(a899,a899)),a1),f86(a899)),a183)),f2(a899))),a95)),f317(f317(f3(a899),f317(f94(a899),x100001)),f317(f94(a899),x100002)))+P1(f317(f317(f225(a1),x100002),a77)) % 112.26/112.09 [10001]~P26(x100011,x100012)+P1(f317(f317(f224(f906(f905(x100011,x100011),a895)),f317(f317(f279(x100011,x100011,x100011),f317(f241(f906(f905(x100011,x100011),a895),f906(f905(x100011,x100011),a895)),x100012)),f317(f246(f906(f905(x100011,x100011),a895),f906(f905(x100011,x100011),a895)),x100012))),f317(f241(f906(f905(x100011,x100011),a895),f906(f905(x100011,x100011),a895)),x100012))) % 112.26/112.09 [10056]~E(f317(f30(a899),f317(f252(a899),f317(f317(f20(a899,a895,a895),f317(f317(f10(a895,f906(a895,a895),a899),a315),f317(f317(f9(a899,f906(a899,a895),a895),f319(a899)),x100561))),f317(f317(f9(a899,a899,a895),f225(a899)),f317(a102,x100562))))),f2(a899))+~P1(f317(f317(f319(a899),f2(a899)),x100561)) % 112.26/112.09 [10068]E(f289(a899,f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x100681,x100682),f178(f906(a899,a895)))+~P1(f317(f317(f277(a899),x100682),x100681)) % 112.26/112.09 [10073]E(f287(a899,f277(a899),f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x100731,x100732),f178(f906(a899,a895)))+P1(f317(f317(f277(a899),x100731),x100732)) % 112.26/112.09 [10074]E(f290(a899,f277(a899),f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x100741,x100742),f178(f906(a899,a895)))+P1(f317(f317(f277(a899),x100741),x100742)) % 112.26/112.09 [10078]E(f287(a899,f277(a899),f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x100781,x100782),f178(f906(a899,a895)))+~P1(f317(f317(f277(a899),x100782),x100781)) % 112.26/112.09 [10080]E(f290(a899,f277(a899),f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x100801,x100802),f178(f906(a899,a895)))+~P1(f317(f317(f277(a899),x100802),x100801)) % 112.26/112.09 [10123]E(f41(a1,f317(f94(a1),f317(f317(f3(a1),f317(f317(f74(a1),x101231),x101231)),a87)),f317(f94(a1),f317(f317(f74(a1),x101232),x101232))),f317(f317(f74(a1),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f41(a1,f317(f94(a1),x101231),f317(f94(a1),x101232)))),f72(a1)))+~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x101232))) % 112.26/112.09 [10132]E(f41(a1,f317(f94(a1),f317(f317(f3(a1),f317(f317(f74(a1),x101321),x101321)),a87)),f317(f94(a1),f317(f317(f74(a1),x101322),x101322))),f317(f317(f3(a1),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f41(a1,f317(f317(f74(a1),f317(f94(a1),x101321)),f72(a1)),f317(f94(a1),x101322)))),f72(a1)))+P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x101322))) % 112.26/112.09 [10187]~P5(x101871)+E(f32(x101871,f317(f252(x101871),f317(f317(f10(f906(x101871,a895),a895,x101871),f82(x101871)),f317(f317(f10(f906(x101871,a895),f906(x101871,a895),x101871),f317(f20(x101871,a895,a895),f317(f317(f10(a895,f906(a895,a895),x101871),a320),f317(f317(f9(x101871,f906(x101871,a895),a895),f319(x101871)),x101872)))),f224(x101871))))),f33(x101871,x101872)) % 112.26/112.09 [10211]~P36(x102111,x102112)+P59(x102111,f317(f317(f9(x102111,f906(f905(x102111,x102111),a895),f906(x102111,a895)),f317(f317(f10(f906(x102111,f906(f906(f905(x102111,x102111),a895),a895)),f906(f906(f905(x102111,x102111),a895),f906(x102111,a895)),x102111),f9(x102111,f906(f905(x102111,x102111),a895),a895)),f317(f317(f10(f906(x102111,f905(x102111,x102111)),f906(x102111,f906(f906(f905(x102111,x102111),a895),a895)),x102111),f317(f10(f905(x102111,x102111),f906(f906(f905(x102111,x102111),a895),a895),x102111),f319(f905(x102111,x102111)))),f242(x102111,x102111)))),x102112)) % 112.26/112.09 [10212]~P8(x102121,f232(f906(x102121,a895)),x102122)+P7(x102121,f317(f317(f9(x102121,f906(f905(x102121,x102121),a895),f906(x102121,a895)),f317(f317(f10(f906(x102121,f906(f906(f905(x102121,x102121),a895),a895)),f906(f906(f905(x102121,x102121),a895),f906(x102121,a895)),x102121),f9(x102121,f906(f905(x102121,x102121),a895),a895)),f317(f317(f10(f906(x102121,f905(x102121,x102121)),f906(x102121,f906(f906(f905(x102121,x102121),a895),a895)),x102121),f317(f10(f905(x102121,x102121),f906(f906(f905(x102121,x102121),a895),a895),x102121),f319(f905(x102121,x102121)))),f242(x102121,x102121)))),x102122)) % 112.26/112.09 [10255]P36(x102551,x102552)+~P59(x102551,f317(f317(f9(x102551,f906(f905(x102551,x102551),a895),f906(x102551,a895)),f317(f317(f10(f906(x102551,f906(f906(f905(x102551,x102551),a895),a895)),f906(f906(f905(x102551,x102551),a895),f906(x102551,a895)),x102551),f9(x102551,f906(f905(x102551,x102551),a895),a895)),f317(f317(f10(f906(x102551,f905(x102551,x102551)),f906(x102551,f906(f906(f905(x102551,x102551),a895),a895)),x102551),f317(f10(f905(x102551,x102551),f906(f906(f905(x102551,x102551),a895),a895),x102551),f319(f905(x102551,x102551)))),f242(x102551,x102551)))),x102552)) % 112.26/112.09 [10256]P8(x102561,f232(f906(x102561,a895)),x102562)+~P7(x102561,f317(f317(f9(x102561,f906(f905(x102561,x102561),a895),f906(x102561,a895)),f317(f317(f10(f906(x102561,f906(f906(f905(x102561,x102561),a895),a895)),f906(f906(f905(x102561,x102561),a895),f906(x102561,a895)),x102561),f9(x102561,f906(f905(x102561,x102561),a895),a895)),f317(f317(f10(f906(x102561,f905(x102561,x102561)),f906(x102561,f906(f906(f905(x102561,x102561),a895),a895)),x102561),f317(f10(f905(x102561,x102561),f906(f906(f905(x102561,x102561),a895),a895),x102561),f319(f905(x102561,x102561)))),f242(x102561,x102561)))),x102562)) % 112.26/112.09 [7388]E(f317(f317(f74(a899),f317(f94(a899),f317(f317(f3(a1),x73881),a87))),x73882),f317(a102,f317(f317(f74(a899),f317(f94(a899),x73881)),x73882)))+P1(f317(a183,f317(f94(a1),x73881))) % 112.26/112.09 [7831]~P94(x78311)+E(f317(f317(f74(x78311),f317(f317(f74(x78311),f72(x78311)),f317(f94(x78311),x78312))),f317(f94(x78311),x78312)),f317(f94(x78311),f317(f317(f3(a1),f317(f317(f74(a1),x78312),x78312)),a87))) % 112.26/112.09 [8475]~P1(f317(f317(f224(a1),x84751),x84752))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x84751),x84751)),f317(f317(f3(a1),f317(f317(f74(a1),x84752),x84752)),a87))) % 112.26/112.09 [8477]~P1(f317(f317(f224(a1),x84771),x84772))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x84771),x84771)),f317(f317(f3(a1),f317(f317(f74(a1),x84772),x84772)),a87))) % 112.26/112.09 [8906]P1(f317(f317(f224(a1),x89061),x89062))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x89061),x89061)),f317(f317(f3(a1),f317(f317(f74(a1),x89062),x89062)),a87))) % 112.26/112.09 [8908]P1(f317(f317(f224(a1),x89081),x89082))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),x89081),x89081)),f317(f317(f3(a1),f317(f317(f74(a1),x89082),x89082)),a87))) % 112.26/112.09 [9196]~P1(f317(f317(f224(a1),x91961),x91962))+P1(f317(f317(f224(a1),f317(f317(f3(a1),f317(f317(f74(a1),x91961),x91961)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),x91962),x91962)),a87))) % 112.26/112.09 [9198]~P1(f317(f317(f225(a1),x91981),x91982))+P1(f317(f317(f225(a1),f317(f317(f3(a1),f317(f317(f74(a1),x91981),x91981)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),x91982),x91982)),a87))) % 112.26/112.09 [9470]P1(f317(f317(f224(a1),x94701),x94702))+~P1(f317(f317(f224(a1),f317(f317(f3(a1),f317(f317(f74(a1),x94701),x94701)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),x94702),x94702)),a87))) % 112.26/112.09 [9472]P1(f317(f317(f225(a1),x94721),x94722))+~P1(f317(f317(f225(a1),f317(f317(f3(a1),f317(f317(f74(a1),x94721),x94721)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),x94722),x94722)),a87))) % 112.26/112.09 [9505]~P1(f317(f29(x95051),x95052))+P1(f317(f29(f906(x95051,a895)),f317(f252(f906(x95051,a895)),f317(f317(f9(f906(x95051,a895),f906(x95051,a895),a895),f224(f906(x95051,a895))),x95052)))) % 112.26/112.09 [9557]~E(f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),x95571),f178(f906(f905(a899,a899),a895)))),f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),x95572),f178(f906(f905(a899,a899),a895)))))+P1(f317(f317(f319(f905(f905(a899,a899),f905(a899,a899))),f317(f317(f242(f905(a899,a899),f905(a899,a899)),x95571),x95572)),a99)) % 112.26/112.09 [9651]E(f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),x96511),f178(f906(f905(a899,a899),a895)))),f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),x96512),f178(f906(f905(a899,a899),a895)))))+~P1(f317(f317(f319(f905(f905(a899,a899),f905(a899,a899))),f317(f317(f242(f905(a899,a899),f905(a899,a899)),x96511),x96512)),a99)) % 112.26/112.09 [9688]P1(f317(f317(f224(a1),f2(a1)),f599(x96881,x96882)))+E(f317(f252(a1),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f224(a1),f2(a1)))),x96881)),f317(f252(a1),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f224(a1),f2(a1)))),x96882))) % 112.26/112.09 [10195]~P5(x101951)+E(f33(x101951,f317(f252(x101951),f317(f317(f10(f906(x101951,a895),a895,x101951),f82(x101951)),f317(f317(f10(f906(x101951,a895),f906(x101951,a895),x101951),f317(f20(x101951,a895,a895),f317(f317(f10(a895,f906(a895,a895),x101951),a320),f317(f317(f9(x101951,f906(x101951,a895),a895),f319(x101951)),x101952)))),f317(f9(x101951,x101951,a895),f224(x101951)))))),f32(x101951,x101952)) % 112.26/112.09 [10217]P1(f317(f317(f319(a899),f2(a899)),x102171))+E(f317(f30(a899),f317(f252(a899),f317(f317(f20(a899,a895,a895),f317(f317(f10(a895,f906(a895,a895),a899),a315),f317(f317(f9(a899,f906(a899,a895),a895),f317(f317(f10(a899,f906(f906(a899,a895),a895),a899),f319(a899)),a102)),x102171))),f317(f317(f9(a899,a899,a895),f225(a899)),x102172)))),f317(f30(a899),f317(f252(a899),f317(f317(f20(a899,a895,a895),f317(f317(f10(a895,f906(a895,a895),a899),a315),f317(f317(f9(a899,f906(a899,a895),a895),f319(a899)),x102171))),f317(f317(f9(a899,a899,a895),f225(a899)),f317(a102,x102172)))))) % 112.26/112.09 [10275]P1(f317(f317(f277(a899),x102751),x102752))+~P1(f317(f317(f319(a899),x102752),f285(a899,f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x102751))) % 112.26/112.09 [10276]P1(f317(f317(f277(a899),x102761),x102762))+~P1(f317(f317(f319(a899),x102761),f288(a899,f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x102762))) % 112.26/112.09 [10277]~P1(f317(f317(f277(a899),x102771),x102772))+~P1(f317(f317(f319(a899),x102772),f288(a899,f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x102771))) % 112.26/112.09 [10278]~P1(f317(f317(f277(a899),x102781),x102782))+~P1(f317(f317(f319(a899),x102781),f285(a899,f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x102782))) % 112.26/112.09 [7698]~P94(x76981)+E(f317(f317(f75(x76981),x76982),f317(f94(x76981),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),x76982) % 112.26/112.09 [7962]~P94(x79621)+E(f317(f317(f74(x79621),f317(f94(x79621),x79622)),f72(x79621)),f317(f94(x79621),f317(f317(f74(a1),x79622),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))) % 112.26/112.09 [8106]P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x81062)))+E(f317(f317(f234(a1),x81061),f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),x81062),x81062)),a87))),f72(a1)) % 112.26/112.09 [9532]~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x95322)))+E(f317(f317(f234(a1),x95321),f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),x95322),x95322)),a87))),f317(f317(f80(a1,a1),f317(f317(f234(a1),x95321),f317(f94(a899),x95322))),f317(f317(f20(a1,a1,a1),f317(f317(f10(a1,f906(a1,a1),a1),f75(a1)),f317(f75(a1),x95321))),f7(a1)))) % 112.26/112.09 [9911]~P1(f317(f317(f224(a899),f630(x99112,x99111)),f317(x99111,f630(x99112,x99111))))+P1(f317(f29(a899),f317(f252(a899),f317(f317(f9(a899,a899,a895),f317(f317(f10(a899,f906(a899,a895),a899),f224(a899)),x99111)),x99112)))) % 112.26/112.09 [10046]~P1(f317(f317(f224(a899),f317(f94(a899),x100461)),f317(a102,x100462)))+P1(f317(f317(f80(a1,a895),f317(f94(a1),f317(f317(f74(a1),x100461),a87))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a320),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f9(a1,a899,a895),f317(f317(f10(a899,f906(a899,a895),a1),f224(a899)),a95)),x100462)))) % 112.26/112.09 [10047]~P1(f317(f317(f225(a899),f317(f94(a899),x100471)),f317(a102,x100472)))+P1(f317(f317(f80(a1,a895),f317(f94(a1),f317(f317(f74(a1),x100471),a87))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a320),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f9(a1,a899,a895),f317(f317(f10(a899,f906(a899,a895),a1),f225(a899)),a95)),x100472)))) % 112.26/112.09 [10107]P1(f317(f317(f224(a899),f317(f94(a899),x101071)),f317(a102,x101072)))+~P1(f317(f317(f80(a1,a895),f317(f94(a1),f317(f317(f74(a1),x101071),a87))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a320),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f9(a1,a899,a895),f317(f317(f10(a899,f906(a899,a895),a1),f224(a899)),a95)),x101072)))) % 112.26/112.09 [10108]P1(f317(f317(f225(a899),f317(f94(a899),x101081)),f317(a102,x101082)))+~P1(f317(f317(f80(a1,a895),f317(f94(a1),f317(f317(f74(a1),x101081),a87))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a320),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f9(a1,a899,a895),f317(f317(f10(a899,f906(a899,a895),a1),f225(a899)),a95)),x101082)))) % 112.26/112.09 [10138]~P1(f317(f317(f224(a899),f317(a102,x101382)),f317(f94(a899),x101381)))+P1(f317(f317(f80(a1,a895),f317(f94(a1),f317(f317(f74(a1),x101381),a87))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a320),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f10(a899,a895,a1),f317(f224(a899),x101382)),a95))))) % 112.26/112.09 [10139]~P1(f317(f317(f225(a899),f317(a102,x101392)),f317(f94(a899),x101391)))+P1(f317(f317(f80(a1,a895),f317(f94(a1),f317(f317(f74(a1),x101391),a87))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a320),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f10(a899,a895,a1),f317(f225(a899),x101392)),a95))))) % 112.26/112.09 [10185]P1(f317(f317(f224(a899),f317(a102,x101851)),f317(f94(a899),x101852)))+~P1(f317(f317(f80(a1,a895),f317(f94(a1),f317(f317(f74(a1),x101852),a87))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a320),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f10(a899,a895,a1),f317(f224(a899),x101851)),a95))))) % 112.26/112.09 [10186]P1(f317(f317(f225(a899),f317(a102,x101861)),f317(f94(a899),x101862)))+~P1(f317(f317(f80(a1,a895),f317(f94(a1),f317(f317(f74(a1),x101862),a87))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a320),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f10(a899,a895,a1),f317(f225(a899),x101861)),a95))))) % 112.26/112.09 [10265]~P1(f317(f317(f319(a899),f2(a899)),x102651))+E(f317(a102,f317(f30(a899),f317(f252(a899),f317(f317(f20(a899,a895,a895),f317(f317(f10(a895,f906(a895,a895),a899),a315),f317(f317(f9(a899,f906(a899,a895),a895),f317(f317(f10(a899,f906(f906(a899,a895),a895),a899),f319(a899)),a102)),x102651))),f317(f317(f9(a899,a899,a895),f225(a899)),x102652))))),f317(f30(a899),f317(f252(a899),f317(f317(f20(a899,a895,a895),f317(f317(f10(a895,f906(a895,a895),a899),a315),f317(f317(f9(a899,f906(a899,a895),a895),f319(a899)),x102651))),f317(f317(f9(a899,a899,a895),f225(a899)),f317(a102,x102652)))))) % 112.26/112.09 [8648]~P94(x86481)+E(f317(f317(f75(x86481),f317(f94(x86481),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),x86482),x86482) % 112.26/112.09 [8709]~P94(x87091)+E(f317(f317(f74(x87091),f72(x87091)),f317(f94(x87091),x87092)),f317(f94(x87091),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),x87092))) % 112.26/112.09 [8771]~P94(x87711)+E(f317(f317(f3(x87711),f317(f94(x87711),x87712)),f72(x87711)),f317(f94(x87711),f317(f317(f74(a1),x87712),f317(f73(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))) % 112.26/112.09 [8925]~P1(f317(f317(f225(a899),f317(f94(a899),a77)),x89252))+E(f317(f317(f3(a899),x89251),f317(f317(f3(a899),x89252),f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f3(a899),f317(a102,x89251)),x89252)) % 112.26/112.09 [9575]~P119(x95751)+E(f317(f317(f75(x95751),x95752),x95752),f317(f317(f234(x95751),x95752),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))) % 112.26/112.09 [9576]~P80(x95761)+E(f317(f317(f234(x95761),x95762),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f75(x95761),x95762),x95762)) % 112.26/112.09 [9578]~P94(x95781)+E(f317(f317(f75(x95781),x95782),f317(f94(x95781),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f74(x95781),x95782),x95782)) % 112.26/112.09 [9827]~P112(x98271)+E(f317(f317(f234(x98271),f317(f70(x98271),x98272)),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f234(x98271),x98272),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))) % 112.26/112.09 [9828]~P141(x98281)+E(f317(f317(f234(x98281),f317(f73(x98281),x98282)),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f234(x98281),x98282),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))) % 112.26/112.09 [9824]~P94(x98241)+E(f317(f317(f75(x98241),f317(f94(x98241),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x98242),f317(f317(f74(x98241),x98242),x98242)) % 112.26/112.09 [9944]~P112(x99441)+E(f317(f70(x99441),f317(f317(f234(x99441),x99442),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x99441),x99442),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))) % 112.26/112.09 [10008]~P112(x100081)+P1(f317(f317(f224(x100081),f2(x100081)),f317(f317(f234(x100081),x100082),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))) % 112.26/112.09 [10176]~E(f317(a102,x101762),f317(f94(a899),x101761))+P1(f317(f317(f80(a1,a895),f317(f94(a1),f317(f317(f74(a1),x101761),a87))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a320),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f9(a1,a899,a895),f317(f317(f10(a899,f906(a899,a895),a1),a314),a95)),x101762))))) % 112.26/112.09 [10177]~E(f317(f94(a899),x101771),f317(a102,x101772))+P1(f317(f317(f80(a1,a895),f317(f94(a1),f317(f317(f74(a1),x101771),a87))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a320),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f9(a1,a899,a895),f317(f317(f10(a899,f906(a899,a895),a1),a314),a95)),x101772))))) % 112.26/112.09 [10220]E(f317(a102,x102201),f317(f94(a899),x102202))+~P1(f317(f317(f80(a1,a895),f317(f94(a1),f317(f317(f74(a1),x102202),a87))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a320),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f9(a1,a899,a895),f317(f317(f10(a899,f906(a899,a895),a1),a314),a95)),x102201))))) % 112.26/112.09 [10221]E(f317(f94(a899),x102211),f317(a102,x102212))+~P1(f317(f317(f80(a1,a895),f317(f94(a1),f317(f317(f74(a1),x102211),a87))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a320),f317(f317(f10(a895,a895,a1),a312),a183))),f317(f317(f9(a1,a899,a895),f317(f317(f10(a899,f906(a899,a895),a1),a314),a95)),x102212))))) % 112.26/112.09 [10266]~P15(x102661,x102662)+P1(f317(f317(f319(f906(x102661,a895)),f793(x102662,x102661)),f317(f317(f10(f906(x102661,a895),a895,f906(x102661,a895)),f81(x102661)),f317(f317(f10(f906(x102661,a895),f906(x102661,a895),f906(x102661,a895)),f317(f20(x102661,a895,a895),f317(f317(f10(a895,f906(a895,a895),x102661),a315),f317(f317(f20(x102661,x102661,a895),x102662),f7(x102661))))),f317(f317(f9(f906(x102661,a895),f906(x102661,f906(x102661,a895)),f906(x102661,a895)),f317(f317(f10(f906(f906(x102661,a895),a895),f906(f906(x102661,f906(x102661,a895)),f906(x102661,a895)),f906(x102661,a895)),f10(f906(x102661,a895),a895,x102661)),a314)),x102662))))) % 112.26/112.09 [10006]~P94(x100061)+E(f317(f317(f234(x100061),f317(f94(x100061),a87)),f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100062)),f72(x100061)) % 112.26/112.09 [10007]~P141(x100071)+E(f317(f317(f234(x100071),f317(f73(x100071),f72(x100071))),f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100072)),f72(x100071)) % 112.26/112.09 [10010]~P80(x100101)+E(f317(f317(f234(x100101),x100102),f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),f317(f317(f75(x100101),f317(f317(f75(x100101),x100102),x100102)),x100102)) % 112.26/112.09 [10200]~P1(f317(f317(f224(a1),f2(a1)),x102002))+E(f41(a1,f317(f317(f74(a1),f72(a1)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102001)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102002)),f317(f317(f74(a1),f72(a1)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f41(a1,x102001,x102002)))) % 112.26/112.09 [10223]~P1(f317(f317(f224(a1),f2(a1)),x102232))+E(f317(f317(f31(a1),f317(f317(f74(a1),f72(a1)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102231))),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102232)),f317(f317(f31(a1),x102231),x102232)) % 112.26/112.09 [10225]~P1(f317(f317(f224(a1),x102252),f2(a1)))+E(f317(f317(f31(a1),f317(f317(f74(a1),f72(a1)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102251))),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102252)),f317(f317(f31(a1),f317(f317(f74(a1),x102251),f72(a1))),x102252)) % 112.26/112.09 [10226]~P1(f317(f317(f224(a1),x102262),f2(a1)))+E(f41(a1,f317(f317(f74(a1),f72(a1)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102261)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102262)),f317(f317(f3(a1),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f41(a1,f317(f317(f74(a1),x102261),f72(a1)),x102262))),f72(a1))) % 112.26/112.09 [10098]~P94(x100981)+E(f317(f317(f234(x100981),f317(f94(x100981),a87)),f317(a102,f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100982))),f317(f94(x100981),a87)) % 112.26/112.09 [10100]~P141(x101001)+E(f317(f317(f234(x101001),f317(f73(x101001),f72(x101001))),f317(a102,f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101002))),f317(f73(x101001),f72(x101001))) % 112.26/112.09 [5015]P37(x50151,x50152)+~P8(x50151,x50153,x50152) % 112.26/112.09 [5017]P51(x50171,x50172)+~P8(x50171,x50173,x50172) % 112.26/112.09 [5190]~P8(x51901,x51902,x51903)+P52(x51901,x51902,x51903) % 112.26/112.09 [8172]~E(x81722,x81723)+P33(x81721,x81721,a314,x81722,x81723) % 112.26/112.09 [8722]E(x87221,x87222)+~P33(x87223,x87223,a314,x87221,x87222) % 112.26/112.09 [4819]E(f159(x48191,x48192,x48193),f103(x48191))+~E(x48192,f2(a899)) % 112.26/112.09 [4987]~E(f159(x49872,x49871,x49873),f103(x49872))+E(x49871,f2(a899)) % 112.26/112.09 [5195]~P36(x51951,x51953)+P36(x51951,f311(x51951,x51952,x51953)) % 112.26/112.09 [5304]~P28(x53041,x53042,x53043)+P30(a1,x53041,f168(x53042,x53043)) % 112.26/112.09 [5372]P28(x53721,x53722,x53723)+~P30(a1,x53721,f168(x53722,x53723)) % 112.26/112.09 [5444]~P8(x54441,x54442,x54443)+P8(f900(x54441),f151(x54441,x54442),f148(x54441,x54443)) % 112.26/112.09 [5445]~P52(x54451,x54452,x54453)+P52(f900(x54451),f151(x54451,x54452),f148(x54451,x54453)) % 112.26/112.09 [5558]P55(x55581,x55582,x55583)+~E(f583(x55583,x55582,x55581),f584(x55583,x55582,x55581)) % 112.26/112.09 [5559]P54(x55591,x55592,x55593)+~E(f602(x55593,x55592,x55591),f603(x55593,x55592,x55591)) % 112.26/112.09 [8178]~E(x81782,x81783)+P25(x81781,x81781,f25(x81781),x81782,x81783) % 112.26/112.09 [8730]E(x87301,x87302)+~P25(x87303,x87303,f25(x87303),x87301,x87302) % 112.26/112.09 [4774]~E(f317(f158(x47742),x47741),x47743)+E(x47741,f317(f158(x47742),x47743)) % 112.26/112.09 [4775]~E(x47752,f317(f158(x47751),x47753))+E(f317(f158(x47751),x47752),x47753) % 112.26/112.09 [4825]E(x48251,x48252)+~E(f317(f158(x48253),x48251),f317(f158(x48253),x48252)) % 112.26/112.09 [5041]~P7(x50413,x50411)+P1(f317(f317(x50411,x50412),x50412)) % 112.26/112.09 [5042]~P42(x50423,x50421)+P1(f317(f317(x50421,x50422),x50422)) % 112.26/112.09 [5044]~P59(x50441,x50442)+P1(f317(f305(x50441,x50442),x50443)) % 112.26/112.09 [5110]~P36(x51101,x51102)+P36(f900(x51101),f317(f133(x51101,x51102),x51103)) % 112.26/112.09 [5115]~P1(f317(x51152,x51153))+~E(f317(f252(x51151),x51152),f178(f906(x51151,a895))) % 112.26/112.09 [5116]~P1(f317(x51162,x51163))+~E(f178(f906(x51161,a895)),f317(f252(x51161),x51162)) % 112.26/112.09 [5128]E(x51281,f2(a899))+E(f134(x51282,f159(x51282,x51281,x51283)),x51283) % 112.26/112.09 [5147]~P1(f317(x51471,x51473))+P1(f317(x51471,f84(x51472,x51471))) % 112.26/112.09 [5148]~P1(f317(x51481,x51483))+P1(f317(x51481,f719(x51481,x51482))) % 112.26/112.09 [5160]E(x51601,f2(a899))+E(f317(f131(x51602),f159(x51602,x51601,x51603)),x51603) % 112.26/112.09 [5266]~E(x52662,x52663)+P1(f317(f317(f319(x52661),x52662),f317(a314,x52663))) % 112.26/112.09 [5281]~E(x52812,f2(a899))+E(f317(f162(x52811),f159(x52811,x52812,x52813)),f178(f906(x52811,a895))) % 112.26/112.09 [5326]E(f317(f158(x53261),x53262),f317(f317(f141(x53261),x53263),f103(x53261)))+~E(x53262,f317(f317(f141(x53261),x53263),f103(x53261))) % 112.26/112.09 [5327]~E(x53273,f317(f317(f141(x53271),x53272),f103(x53271)))+E(f317(f317(f141(x53271),x53272),f103(x53271)),f317(f158(x53271),x53273)) % 112.26/112.09 [5368]~P32(x53681,x53682,x53683)+P32(x53681,x53682,f317(f158(x53681),x53683)) % 112.26/112.09 [5369]~P30(x53691,x53692,x53693)+P30(x53691,x53692,f317(f158(x53691),x53693)) % 112.26/112.09 [5373]E(f317(f30(x53731),f720(x53732,x53733,x53731)),x53732)+~E(f317(f30(x53731),x53733),f317(a102,x53732)) % 112.26/112.09 [5380]~P36(x53801,x53803)+P1(f317(f317(f319(x53801),x53802),f306(x53801,x53803))) % 112.26/112.09 [5384]~E(f317(f158(x53842),x53841),f317(f317(f141(x53842),x53843),f103(x53842)))+E(x53841,f317(f317(f141(x53842),x53843),f103(x53842))) % 112.26/112.09 [5385]~E(f317(f317(f141(x53852),x53853),f103(x53852)),f317(f158(x53852),x53851))+E(x53851,f317(f317(f141(x53852),x53853),f103(x53852))) % 112.26/112.09 [5409]E(f79(f905(a899,a899),f44(x54091,x54092)),x54093)+~P1(f317(f44(x54091,x54092),x54093)) % 112.26/112.09 [5448]P32(x54481,x54482,x54483)+~P32(x54481,x54482,f317(f158(x54481),x54483)) % 112.26/112.09 [5449]P30(x54491,x54492,x54493)+~P30(x54491,x54492,f317(f158(x54491),x54493)) % 112.26/112.09 [5488]P1(f317(f317(x54881,x54882),x54882))+~P1(f317(f260(x54883,x54881),x54882)) % 112.26/112.09 [5489]~P1(f317(f317(x54892,x54893),x54893))+P1(f317(f260(x54891,x54892),x54893)) % 112.26/112.09 [5511]~E(x55112,f103(x55111))+P1(f317(f317(f319(f900(x55111)),x55112),f151(x55111,x55113))) % 112.26/112.09 [5521]~P52(x55211,x55212,x55213)+P52(x55211,x55212,f317(f276(x55211,x55211),x55213)) % 112.26/112.09 [5522]~P55(x55221,x55222,x55223)+P55(x55221,x55222,f317(f276(x55221,x55221),x55223)) % 112.26/112.09 [5539]~P3(x55391)+E(f41(x55391,f41(x55391,x55392,x55393),x55393),f41(x55391,x55392,x55393)) % 112.26/112.09 [5641]E(x56411,x56412)+~P1(f317(f317(f319(x56413),x56411),f317(a314,x56412))) % 112.26/112.09 [5688]~P145(x56881)+E(f180(x56881,x56882,f2(a899),x56883),x56883) % 112.26/112.09 [5710]P52(x57101,x57102,x57103)+~P52(x57101,x57102,f317(f276(x57101,x57101),x57103)) % 112.26/112.09 [5711]P55(x57111,x57112,x57113)+~P55(x57111,x57112,f317(f276(x57111,x57111),x57113)) % 112.26/112.09 [5715]~P108(x57152)+E(f140(x57151,x57152,x57153,f103(x57151)),f103(x57151)) % 112.26/112.09 [5727]E(f160(x57271,x57272,f142(x57271,x57273)),f142(x57271,f160(x57271,x57272,x57273)))+~P1(f317(f127(x57271),x57273)) % 112.26/112.09 [5826]~P1(f317(f317(x58263,x58262),x58262))+P1(f317(f317(f319(x58261),x58262),f260(x58261,x58263))) % 112.26/112.09 [5828]E(f317(f126(x58281,x58282),x58283),f103(x58281))+P1(f317(x58282,f655(x58283,x58282,x58281))) % 112.26/112.09 [5896]E(f63(x58961,x58962,x58963),x58962)+P1(f317(x58963,f756(x58962,x58961,x58963))) % 112.26/112.09 [5992]~P1(f317(f127(x59921),x59922))+P1(f317(f127(x59921),f166(x59921,x59922,x59923))) % 112.26/112.09 [5993]~P1(f317(f127(x59931),x59933))+P1(f317(f127(x59931),f160(x59931,x59932,x59933))) % 112.26/112.09 [5994]~P1(f317(f127(x59941),x59943))+P1(f317(f127(x59941),f167(x59941,x59942,x59943))) % 112.26/112.09 [5995]~P1(f317(f127(x59951),x59953))+P1(f317(f127(x59951),f130(x59951,x59952,x59953))) % 112.26/112.09 [5996]~P147(x59961,x59962,x59963)+P1(f317(x59961,f41(a1,x59962,x59963))) % 112.26/112.09 [6013]~P32(x60133,x60131,x60132)+P1(f317(x60131,f732(x60132,x60131,x60133))) % 112.26/112.09 [6014]~P34(x60143,x60141,x60142)+P1(f317(x60141,f739(x60142,x60141,x60143))) % 112.26/112.09 [6015]~P34(x60153,x60151,x60152)+P1(f317(x60151,f749(x60152,x60151,x60153))) % 112.26/112.09 [6016]~P32(x60163,x60161,x60162)+P1(f317(x60161,f776(x60161,x60162,x60163))) % 112.26/112.09 [6017]~P32(x60173,x60171,x60172)+P1(f317(x60171,f777(x60172,x60171,x60173))) % 112.26/112.09 [6022]P1(f317(f317(x60221,x60222),x60222))+~P1(f317(f317(f319(x60223),x60222),f260(x60223,x60221))) % 112.26/112.09 [6037]E(f317(f126(x60371,x60372),x60373),f167(x60371,x60372,x60373))+P1(f317(x60372,f704(x60373,x60372,x60371))) % 112.26/112.09 [6077]~P1(f317(f127(x60771),x60773))+P1(f317(f127(f900(x60771)),f51(x60771,x60772,x60773))) % 112.26/112.09 [6113]~P109(x61131)+E(f317(f317(f92(f906(x61131,a895)),f317(f291(x61131),x61132)),f296(x61131,x61132,x61133)),f178(f906(x61131,a895))) % 112.26/112.09 [6114]~P109(x61141)+E(f317(f317(f92(f906(x61141,a895)),f317(f291(x61141),x61142)),f295(x61141,x61142,x61143)),f178(f906(x61141,a895))) % 112.26/112.09 [6115]~P109(x61151)+E(f317(f317(f92(f906(x61151,a895)),f317(f272(x61151),x61152)),f293(x61151,x61152,x61153)),f178(f906(x61151,a895))) % 112.26/112.09 [6350]E(f317(f126(x63501,x63502),x63503),x63503)+~P1(f317(x63502,f667(x63503,x63502,x63501))) % 112.26/112.09 [6352]E(f317(f317(f299(x63521),f740(x63522,x63523,x63521)),f720(x63522,x63523,x63521)),x63523)+~E(f317(f30(x63521),x63523),f317(a102,x63522)) % 112.26/112.09 [6368]P147(x63681,x63682,x63683)+~P1(f317(x63681,f41(a1,x63682,x63683))) % 112.26/112.09 [6421]P30(x64211,x64212,x64213)+~P1(f317(x64212,f741(x64213,x64212,x64211))) % 112.26/112.09 [6422]P30(x64221,x64222,x64223)+~P1(f317(x64222,f747(x64222,x64223,x64221))) % 112.26/112.09 [6423]P30(x64231,x64232,x64233)+~P1(f317(x64232,f748(x64233,x64232,x64231))) % 112.26/112.09 [6424]P28(x64241,x64242,x64243)+~P1(f317(x64241,f764(x64243,x64242,x64241))) % 112.26/112.09 [6425]P29(x64251,x64252,x64253)+~P1(f317(x64251,f811(x64253,x64252,x64251))) % 112.26/112.09 [6427]E(f167(x64271,x64272,x64273),x64273)+~P1(f317(x64272,f699(x64273,x64272,x64271))) % 112.26/112.09 [6508]~P1(f317(x65082,f558(x65083,x65082,x65081)))+P1(f317(f238(x65081,x65082),x65083)) % 112.26/112.09 [6509]~P1(f317(x65092,f668(x65093,x65092,x65091)))+P1(f317(f150(x65091,x65092),x65093)) % 112.26/112.09 [6765]~P1(f317(f305(x67651,x67652),f442(x67653,x67652,x67651)))+P1(f317(f305(x67651,x67652),x67653)) % 112.26/112.09 [6766]~P1(f317(f305(x67661,x67662),f452(x67663,x67662,x67661)))+P1(f317(f305(x67661,x67662),x67663)) % 112.26/112.09 [7389]~P3(x73891)+E(f317(f317(f74(x73891),f317(f317(f75(x73891),x73892),f317(f317(f31(x73891),x73893),x73892))),f41(x73891,x73893,x73892)),x73893) % 112.26/112.09 [7419]P28(x74191,x74192,x74193)+P1(f317(f317(f319(a1),f764(x74193,x74192,x74191)),f293(a1,x74192,x74193))) % 112.26/112.09 [7852]E(f317(f317(f242(x78521,x78521),f499(x78522,x78523,x78521)),f499(x78522,x78523,x78521)),x78523)+~P1(f317(f317(f319(f905(x78521,x78521)),x78523),f253(x78521,x78522))) % 112.26/112.09 [7970]~P1(f317(f317(f319(x79701),f513(x79703,x79702,x79701)),f306(x79701,x79703)))+P1(f317(f317(f319(x79701),x79702),f306(x79701,x79703))) % 112.26/112.09 [7971]~P1(f317(f317(f319(x79711),f589(x79713,x79712,x79711)),f306(x79711,x79713)))+P1(f317(f317(f319(x79711),x79712),f306(x79711,x79713))) % 112.26/112.09 [7972]~P1(f317(f317(f319(x79721),f591(x79723,x79722,x79721)),f306(x79721,x79723)))+P1(f317(f317(f319(x79721),x79722),f306(x79721,x79723))) % 112.26/112.09 [8065]P32(a1,x80651,f168(x80652,x80653))+P28(f317(f67(a895,a895,a1,a312),x80651),x80652,x80653) % 112.26/112.09 [8153]~P3(x81531)+E(f317(f317(f74(x81531),f317(f317(f75(x81531),f317(f317(f31(x81531),x81532),x81533)),x81533)),f41(x81531,x81532,x81533)),x81532) % 112.26/112.09 [8199]~E(f317(f30(x81991),x81992),f317(a102,x81993))+~P1(f317(f317(f319(x81991),f740(x81993,x81992,x81991)),f720(x81993,x81992,x81991))) % 112.26/112.09 [8640]~P32(a1,x86401,f168(x86402,x86403))+~P28(f317(f67(a895,a895,a1,a312),x86401),x86402,x86403) % 112.26/112.09 [8827]P1(f317(f317(f224(f906(f905(x88271,x88271),a895)),f297(x88271,x88272)),f297(x88271,x88273)))+~P1(f317(f317(f224(f906(f905(x88271,x88271),a895)),x88272),f297(x88271,x88273))) % 112.26/112.09 [9107]E(x91071,f103(x91072))+~P1(f317(f317(f319(f905(f900(x91072),f900(x91072))),f317(f317(f242(f900(x91072),f900(x91072)),x91071),f103(x91072))),f148(x91072,x91073))) % 112.26/112.09 [9131]E(x91311,f103(x91312))+~P1(f317(f317(f319(f905(f900(x91312),f900(x91312))),f317(f317(f242(f900(x91312),f900(x91312)),f103(x91312)),x91311)),f148(x91312,x91313))) % 112.26/112.09 [9256]E(f317(f317(f141(x92561),f673(x92562,x92563,x92561)),f674(x92562,x92563,x92561)),x92563)+~P1(f317(f317(f319(f905(f900(x92561),f900(x92561))),f317(f317(f242(f900(x92561),f900(x92561)),f103(x92561)),x92563)),f137(x92561,x92562))) % 112.26/112.09 [9498]~P128(x94981)+~P1(f317(f317(f225(x94981),f317(f317(f74(x94981),f317(f317(f75(x94981),x94982),x94982)),f317(f317(f75(x94981),x94983),x94983))),f2(x94981))) % 112.26/112.09 [9549]P1(f317(f29(x95491),x95492))+~P1(f317(f317(f319(f905(f906(x95491,a895),f906(x95491,a895))),f317(f317(f242(f906(x95491,a895),f906(x95491,a895)),x95493),x95492)),f304(x95491))) % 112.26/112.09 [9853]~P46(x98531,x98532,x98533)+P1(f317(f317(f224(a1),f317(f317(f67(f905(a1,a1),a1,x98531,f241(a1,a1)),f202(x98531)),f220(x98531,x98532,f217(x98531,x98533)))),f2(a1))) % 112.26/112.09 [9854]~P47(x98541,x98542,x98543)+P1(f317(f317(f225(a1),f317(f317(f67(f905(a1,a1),a1,x98541,f241(a1,a1)),f202(x98541)),f220(x98541,x98542,f217(x98541,x98543)))),f2(a1))) % 112.26/112.09 [9974]P47(x99741,x99742,x99743)+~P1(f317(f317(f225(a1),f317(f317(f67(f905(a1,a1),a1,x99741,f241(a1,a1)),f202(x99741)),f220(x99741,x99742,f217(x99741,x99743)))),f2(a1))) % 112.26/112.09 [9975]P46(x99751,x99752,x99753)+~P1(f317(f317(f224(a1),f317(f317(f67(f905(a1,a1),a1,x99751,f241(a1,a1)),f202(x99751)),f220(x99751,x99752,f217(x99751,x99753)))),f2(a1))) % 112.26/112.09 [10328]~P112(x103281)+~P1(f317(f317(f225(x103281),f317(f317(f74(x103281),f317(f317(f234(x103281),x103282),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x103281),x103283),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f2(x103281))) % 112.26/112.09 [4804]~E(x48043,f103(x48041))+E(f317(f317(f124(x48041),x48042),x48043),x48042) % 112.26/112.09 [4805]~E(x48052,f103(x48051))+E(f317(f317(f124(x48051),x48052),x48053),x48053) % 112.26/112.09 [4811]~E(x48112,f2(a899))+E(f317(f317(f165(x48111),x48112),x48113),f103(x48111)) % 112.26/112.09 [4820]~E(x48203,f103(x48201))+E(f317(f317(f165(x48201),x48202),x48203),f103(x48201)) % 112.26/112.09 [4859]~E(x48591,x48593)+E(x48591,f317(f317(f124(x48592),f103(x48592)),x48593)) % 112.26/112.09 [4950]~P66(x49502)+E(f317(f178(f906(x49501,x49502)),x49503),f178(x49502)) % 112.26/112.09 [4951]~P116(x49512)+E(f317(f232(f906(x49511,x49512)),x49513),f232(x49512)) % 112.26/112.09 [4969]E(x49691,f103(x49692))+~E(f317(f317(f124(x49692),x49693),x49691),x49693) % 112.26/112.09 [4970]E(x49701,f103(x49702))+~E(f317(f317(f124(x49702),x49701),x49703),x49703) % 112.26/112.09 [4978]E(x49781,f103(x49782))+~E(f317(f317(f124(x49782),x49783),x49781),f103(x49782)) % 112.26/112.09 [4979]E(x49791,f103(x49792))+~E(f317(f317(f124(x49792),x49791),x49793),f103(x49792)) % 112.26/112.09 [5008]~E(x50082,f2(a899))+E(f317(f317(f75(a899),x50081),x50082),f317(f317(f75(a899),x50083),x50082)) % 112.26/112.09 [5010]~E(x50101,f2(a899))+E(f317(f317(f75(a899),x50101),x50102),f317(f317(f75(a899),x50101),x50103)) % 112.26/112.09 [5068]~P119(x50681)+E(f317(f317(f74(x50681),x50682),x50683),f317(f317(f74(x50681),x50683),x50682)) % 112.26/112.09 [5069]~P119(x50691)+E(f317(f317(f75(x50691),x50692),x50693),f317(f317(f75(x50691),x50693),x50692)) % 112.26/112.09 [5071]~P108(x50711)+E(f317(f317(f228(x50711),x50712),x50713),f317(f317(f228(x50711),x50713),x50712)) % 112.26/112.09 [5073]~P108(x50731)+E(f317(f317(f223(x50731),x50732),x50733),f317(f317(f223(x50731),x50733),x50732)) % 112.26/112.09 [5075]~P98(x50751)+E(f317(f317(f91(x50751),x50752),x50753),f317(f317(f91(x50751),x50753),x50752)) % 112.26/112.09 [5076]~P99(x50761)+E(f317(f317(f91(x50761),x50762),x50763),f317(f317(f91(x50761),x50763),x50762)) % 112.26/112.09 [5077]~P99(x50771)+E(f317(f317(f92(x50771),x50772),x50773),f317(f317(f92(x50771),x50773),x50772)) % 112.26/112.09 [5079]~P104(x50791)+E(f317(f317(f92(x50791),x50792),x50793),f317(f317(f92(x50791),x50793),x50792)) % 112.26/112.09 [5142]E(f41(a899,x51421,x51422),f2(a899))+~E(x51421,f317(f317(f75(a899),x51422),x51423)) % 112.26/112.09 [5143]E(f41(a1,x51431,x51432),f2(a1))+~E(x51431,f317(f317(f75(a1),x51432),x51433)) % 112.26/112.09 [5207]E(x52071,x52072)+~E(f317(f317(f74(a899),x52073),x52071),f317(f317(f74(a899),x52073),x52072)) % 112.26/112.09 [5208]E(x52081,x52082)+~E(f317(f317(f74(a899),x52081),x52083),f317(f317(f74(a899),x52082),x52083)) % 112.26/112.09 [5218]~P68(x52181)+E(f317(f317(f74(x52181),x52182),f317(f73(x52181),x52183)),f317(f317(f3(x52181),x52182),x52183)) % 112.26/112.09 [5219]~P76(x52191)+E(f317(f317(f74(x52191),x52192),f317(f73(x52191),x52193)),f317(f317(f3(x52191),x52192),x52193)) % 112.26/112.09 [5220]~P114(x52201)+E(f317(f317(f74(x52201),x52202),f317(f73(x52201),x52203)),f317(f317(f3(x52201),x52202),x52203)) % 112.26/112.09 [5221]~P96(x52211)+E(f317(f317(f92(x52211),x52212),f317(f73(x52211),x52213)),f317(f317(f3(x52211),x52212),x52213)) % 112.26/112.09 [5222]~P76(x52221)+E(f317(f317(f3(x52221),x52222),f317(f73(x52221),x52223)),f317(f317(f74(x52221),x52222),x52223)) % 112.26/112.09 [5260]~P1(f317(x52603,x52602))+P1(f317(f317(f319(x52601),x52602),x52603)) % 112.26/112.09 [5262]~P69(x52622)+E(f317(f317(f8(x52621,x52622),x52623),f178(f906(x52621,a895))),f2(x52622)) % 112.26/112.09 [5264]~P75(x52642)+E(f317(f317(f11(x52641,x52642),x52643),f178(f906(x52641,a895))),f72(x52642)) % 112.26/112.09 [5316]~E(x53162,f317(f317(f74(a899),x53161),x53163))+P1(f317(f317(f224(a899),x53161),x53162)) % 112.26/112.09 [5319]~E(x53192,f178(f906(x53191,a895)))+E(f317(f317(f56(x53191),x53192),x53193),f178(f906(f906(x53191,a895),a895))) % 112.26/112.09 [5320]~E(x53202,f178(f906(x53201,a895)))+E(f178(f906(f906(x53201,a895),a895)),f317(f317(f56(x53201),x53202),x53203)) % 112.26/112.09 [5389]~E(f317(f274(x53892,x53893),x53891),f178(f906(x53893,a895)))+E(x53891,f178(f906(f905(x53892,x53893),a895))) % 112.26/112.09 [5390]~E(f317(f254(x53902,x53903),x53901),f178(f906(x53902,a895)))+E(x53901,f178(f906(f905(x53902,x53903),a895))) % 112.26/112.09 [5422]E(f317(f274(x54221,x54222),x54223),f178(f906(x54222,a895)))+~E(x54223,f178(f906(f905(x54221,x54222),a895))) % 112.26/112.09 [5423]E(f317(f254(x54231,x54232),x54233),f178(f906(x54231,a895)))+~E(x54233,f178(f906(f905(x54231,x54232),a895))) % 112.26/112.09 [5426]E(f264(x54261,x54262,x54263),f317(f317(f3(a89),x54262),x54263))+P1(f317(f317(f225(a89),x54262),x54263)) % 112.26/112.09 [5442]P1(f317(x54421,x54422))+~P1(f317(f317(f319(x54423),x54422),x54421)) % 112.26/112.09 [5481]E(x54811,x54812)+~E(f317(f73(f906(x54813,a895)),x54811),f317(f73(f906(x54813,a895)),x54812)) % 112.26/112.09 [5492]~E(x54921,f178(f906(x54922,a895)))+~P1(f317(f317(f319(x54922),x54923),x54921)) % 112.26/112.09 [5523]~E(x55232,f317(f317(f74(a1),x55231),f317(f90(a1),x55233)))+P1(f317(f317(f224(a1),x55231),x55232)) % 112.26/112.09 [5537]E(f317(f317(f299(x55371),x55372),x55373),x55373)+~P1(f317(f317(f319(x55371),x55372),x55373)) % 112.26/112.09 [5548]E(x55481,f178(f906(x55482,a895)))+~E(f317(f317(f56(x55482),x55481),x55483),f178(f906(f906(x55482,a895),a895))) % 112.26/112.09 [5549]E(x55491,f178(f906(x55492,a895)))+~E(f178(f906(f906(x55492,a895),a895)),f317(f317(f56(x55492),x55491),x55493)) % 112.26/112.09 [5556]~P110(x55561)+E(f317(f317(f75(x55561),f317(f73(x55561),x55562)),f317(f73(x55561),x55563)),f317(f317(f75(x55561),x55562),x55563)) % 112.26/112.09 [5557]~P61(x55571)+E(f317(f317(f281(x55571),f317(f73(x55571),x55572)),f317(f73(x55571),x55573)),f317(f317(f281(x55571),x55572),x55573)) % 112.26/112.09 [5588]~P1(f317(x55883,x55882))+P1(f317(f317(f319(x55881),x55882),f317(f252(x55881),x55883))) % 112.26/112.09 [5615]E(x56151,f2(a899))+E(f317(f162(x56152),f159(x56152,x56151,x56153)),f317(f317(f299(x56152),x56153),f178(f906(x56152,a895)))) % 112.26/112.09 [5634]E(f160(x56341,x56342,x56343),x56343)+P1(f317(f317(f319(x56341),x56342),f317(f162(x56341),x56343))) % 112.26/112.09 [5719]~P1(f317(f127(x57191),x57193))+P1(f317(f127(x57191),f317(f126(x57191,x57192),x57193))) % 112.26/112.09 [5762]~P3(x57621)+E(f317(f317(f31(x57621),f41(x57621,x57622,x57623)),x57623),f2(x57621)) % 112.26/112.09 [5781]E(f166(x57811,f317(f317(f141(x57811),x57812),f103(x57811)),x57813),f103(x57811))+P1(f317(f317(f319(a899),f2(a899)),x57813)) % 112.26/112.09 [5787]E(x57871,f2(a899))+E(f317(f161(x57872),f159(x57872,x57871,x57873)),f159(x57872,f317(f317(f3(a899),x57871),f72(a899)),x57873)) % 112.26/112.09 [5838]E(f317(f317(f141(x58381),x58382),x58383),f130(x58381,x58382,x58383))+P1(f317(f317(f319(x58381),x58382),f317(f162(x58381),x58383))) % 112.26/112.09 [5847]E(x58471,x58472)+~E(f317(f317(f75(a899),f317(a102,x58473)),x58471),f317(f317(f75(a899),f317(a102,x58473)),x58472)) % 112.26/112.09 [5848]~E(x58482,f317(f317(f74(a1),x58481),f317(f90(a1),f317(a102,x58483))))+P1(f317(f317(f225(a1),x58481),x58482)) % 112.26/112.09 [5918]~P29(x59181,x59182,x59183)+P30(a899,x59181,f129(a899,f317(f292(a899,x59182),x59183))) % 112.26/112.09 [5971]~E(x59713,f103(x59711))+E(f317(f317(f317(f173(f900(x59711),f900(x59711)),x59712),f157(x59711)),x59713),f103(x59711)) % 112.26/112.09 [5975]P1(f317(x59751,x59752))+~P1(f317(f317(f319(x59753),x59752),f317(f252(x59753),x59751))) % 112.26/112.09 [6008]E(x60081,x60082)+~E(f317(f317(f299(x60083),x60081),f178(f906(x60083,a895))),f317(f317(f299(x60083),x60082),f178(f906(x60083,a895)))) % 112.26/112.09 [6024]~P109(x60241)+E(f317(f317(f92(f906(x60241,a895)),f317(f272(x60241),x60242)),f317(f292(x60241,x60242),x60243)),f178(f906(x60241,a895))) % 112.26/112.09 [6063]E(f130(x60631,x60632,x60633),x60633)+~P1(f317(f317(f319(x60631),x60632),f317(f162(x60631),x60633))) % 112.26/112.09 [6085]~P79(x60851)+E(f317(f300(x60851,x60851,f73(x60851)),f317(f292(x60851,x60852),x60853)),f295(x60851,f317(f73(x60851),x60853),f317(f73(x60851),x60852))) % 112.26/112.09 [6096]E(f317(f179(f900(x60961)),f160(x60961,x60962,x60963)),f317(f179(f900(x60961)),x60963))+P1(f317(f317(f319(x60961),x60962),f317(f162(x60961),x60963))) % 112.26/112.09 [6151]~P109(x61511)+E(f317(f317(f92(f906(x61511,a895)),f317(f292(x61511,x61512),x61513)),f317(f273(x61511),x61513)),f178(f906(x61511,a895))) % 112.26/112.09 [6171]~P79(x61711)+E(f317(f300(x61711,x61711,f73(x61711)),f296(x61711,x61712,x61713)),f296(x61711,f317(f73(x61711),x61713),f317(f73(x61711),x61712))) % 112.26/112.09 [6172]~P79(x61721)+E(f317(f300(x61721,x61721,f73(x61721)),f293(x61721,x61722,x61723)),f293(x61721,f317(f73(x61721),x61723),f317(f73(x61721),x61722))) % 112.26/112.09 [6238]E(f166(x62381,f317(f317(f141(x62381),x62382),f103(x62381)),x62383),f317(f317(f141(x62381),x62382),f103(x62381)))+~P1(f317(f317(f319(a899),f2(a899)),x62383)) % 112.26/112.09 [6243]P29(x62431,x62432,x62433)+~P30(a899,x62431,f129(a899,f317(f292(a899,x62432),x62433))) % 112.26/112.09 [6246]~P79(x62461)+E(f317(f300(x62461,x62461,f73(x62461)),f295(x62461,x62462,x62463)),f317(f292(x62461,f317(f73(x62461),x62463)),f317(f73(x62461),x62462))) % 112.26/112.09 [6268]~P4(x62681)+E(f41(x62681,f317(f73(x62681),f41(x62681,x62682,x62683)),x62683),f41(x62681,f317(f73(x62681),x62682),x62683)) % 112.26/112.09 [6366]~P1(f317(f29(f905(x63662,x63661)),x63663))+P1(f317(f29(x63661),f317(f274(x63662,x63661),x63663))) % 112.26/112.09 [6367]~P1(f317(f29(f905(x63671,x63672)),x63673))+P1(f317(f29(x63671),f317(f254(x63671,x63672),x63673))) % 112.26/112.09 [6372]~P109(x63721)+E(f317(f317(f92(f906(x63721,a895)),f296(x63721,x63722,x63723)),f317(f273(x63721),x63723)),f178(f906(x63721,a895))) % 112.26/112.09 [6373]~P109(x63731)+E(f317(f317(f92(f906(x63731,a895)),f293(x63731,x63732,x63733)),f317(f294(x63731),x63733)),f178(f906(x63731,a895))) % 112.26/112.09 [6374]~P109(x63741)+E(f317(f317(f92(f906(x63741,a895)),f295(x63741,x63742,x63743)),f317(f294(x63741),x63743)),f178(f906(x63741,a895))) % 112.26/112.09 [6447]E(f317(f317(f154(x64471),x64472),f643(x64472,x64473,x64471)),x64473)+~P1(f317(f317(f319(x64471),x64473),f317(f162(x64471),x64472))) % 112.26/112.09 [6595]E(x65951,f103(x65952))+~E(f317(f317(f317(f173(f900(x65952),f900(x65952)),x65953),f157(x65952)),x65951),f103(x65952)) % 112.26/112.09 [6701]~P1(f317(f29(f905(x67012,x67011)),x67013))+P1(f317(f29(f905(x67011,x67012)),f317(f276(x67012,x67011),x67013))) % 112.26/112.09 [6724]E(x67241,x67242)+~E(f280(a899,f277(a899),x67243,x67241),f317(f317(f299(a899),x67242),f178(f906(a899,a895)))) % 112.26/112.09 [6725]E(x67251,x67252)+~E(f280(a899,f277(a899),x67251,x67252),f317(f317(f299(a899),x67253),f178(f906(a899,a895)))) % 112.26/112.09 [6860]P55(x68601,x68602,x68603)+P1(f317(f317(f319(x68601),f584(x68603,x68602,x68601)),x68602)) % 112.26/112.09 [6861]P55(x68611,x68612,x68613)+P1(f317(f317(f319(x68611),f583(x68613,x68612,x68611)),x68612)) % 112.26/112.09 [6871]P1(f317(f305(x68711,x68712),x68713))+P1(f317(f317(x68712,f442(x68713,x68712,x68711)),x68713)) % 112.26/112.09 [6872]P1(f317(f305(x68721,x68722),x68723))+P1(f317(f317(x68722,f452(x68723,x68722,x68721)),x68723)) % 112.26/112.09 [6903]E(f317(f179(f900(x69031)),f160(x69031,x69032,x69033)),f317(f317(f3(a899),f317(f179(f900(x69031)),x69033)),f72(a899)))+~P1(f317(f317(f319(x69031),x69032),f317(f162(x69031),x69033))) % 112.26/112.09 [6942]P1(f317(f238(x69421,x69422),x69423))+P1(f317(f317(f319(x69421),f558(x69423,x69422,x69421)),x69423)) % 112.26/112.09 [6951]~P1(f317(f29(f905(x69512,x69511)),f317(f276(x69511,x69512),x69513)))+P1(f317(f29(f905(x69511,x69512)),x69513)) % 112.26/112.09 [7011]~P1(f317(f317(f319(x70111),x70112),f317(f162(x70111),f104(x70111,x70113))))+P1(f317(f317(f319(x70111),x70112),f317(f162(x70111),x70113))) % 112.26/112.09 [7046]E(f317(f126(x70461,x70462),x70463),x70463)+P1(f317(f317(f319(x70461),f667(x70463,x70462,x70461)),f317(f162(x70461),x70463))) % 112.26/112.09 [7062]E(f317(f126(x70621,x70622),x70623),f103(x70621))+P1(f317(f317(f319(x70621),f655(x70623,x70622,x70621)),f317(f162(x70621),x70623))) % 112.26/112.09 [7087]P30(x70871,x70872,x70873)+P1(f317(f317(f319(x70871),f741(x70873,x70872,x70871)),f317(f162(x70871),x70873))) % 112.26/112.09 [7088]P30(x70881,x70882,x70883)+P1(f317(f317(f319(x70881),f748(x70883,x70882,x70881)),f317(f162(x70881),x70883))) % 112.26/112.09 [7089]P30(x70891,x70892,x70893)+P1(f317(f317(f319(x70891),f747(x70892,x70893,x70891)),f317(f162(x70891),x70893))) % 112.26/112.09 [7092]E(f167(x70921,x70922,x70923),x70923)+P1(f317(f317(f319(x70921),f699(x70923,x70922,x70921)),f317(f162(x70921),x70923))) % 112.26/112.09 [7168]P1(f317(f150(x71681,x71682),x71683))+P1(f317(f317(f319(x71681),f668(x71683,x71682,x71681)),f317(f162(x71681),x71683))) % 112.26/112.09 [7177]~P32(x71771,x71773,x71772)+P1(f317(f317(f319(x71771),f732(x71772,x71773,x71771)),f317(f162(x71771),x71772))) % 112.26/112.09 [7178]~P34(x71781,x71783,x71782)+P1(f317(f317(f319(x71781),f739(x71782,x71783,x71781)),f317(f162(x71781),x71782))) % 112.26/112.09 [7179]~P34(x71791,x71793,x71792)+P1(f317(f317(f319(x71791),f749(x71792,x71793,x71791)),f317(f162(x71791),x71792))) % 112.26/112.09 [7180]~P32(x71801,x71802,x71803)+P1(f317(f317(f319(x71801),f776(x71802,x71803,x71801)),f317(f162(x71801),x71803))) % 112.26/112.09 [7181]~P32(x71811,x71813,x71812)+P1(f317(f317(f319(x71811),f777(x71812,x71813,x71811)),f317(f162(x71811),x71812))) % 112.26/112.09 [7215]P1(f317(f317(f319(x72151),x72152),f435(x72153,x72152,x72151)))+~P1(f317(f317(f319(x72151),x72152),f32(f906(x72151,a895),x72153))) % 112.26/112.09 [7216]~P69(x72161)+E(f317(f317(f74(x72161),f317(f317(f8(a899,x72161),x72162),f317(f272(a899),x72163))),f317(x72162,x72163)),f317(f317(f8(a899,x72161),x72162),f317(f272(a899),f317(a102,x72163)))) % 112.26/112.09 [7228]P29(x72281,x72282,x72283)+P1(f317(f317(f319(a899),f811(x72283,x72282,x72281)),f317(f292(a899,x72282),x72283))) % 112.26/112.09 [7308]~P32(x73082,x73081,x73083)+P1(f317(x73081,f317(f317(f154(x73082),x73083),f735(x73083,x73081,x73082)))) % 112.26/112.09 [7319]~P1(f317(f317(f319(x73191),x73192),f436(x73192,x73193,x73191)))+P1(f317(f317(f319(x73191),x73192),f33(f906(x73191,a895),x73193))) % 112.26/112.09 [7352]~P69(x73521)+E(f317(f317(f74(x73521),f317(f317(f8(a899,x73521),x73522),f317(f291(a899),x73523))),f317(x73522,f317(a102,x73523))),f317(f317(f8(a899,x73521),x73522),f317(f291(a899),f317(a102,x73523)))) % 112.26/112.09 [7493]P1(f317(f317(f319(f900(x74931)),x74932),f151(x74931,x74933)))+P1(f317(f317(f319(x74931),f644(x74933,x74932,x74931)),f317(f162(x74931),x74932))) % 112.26/112.09 [7509]~P1(f317(f317(f319(f900(x75091)),x75092),f151(x75091,f306(x75091,x75093))))+P1(f317(f317(f319(f900(x75091)),x75092),f306(f900(x75091),f147(x75091,x75093)))) % 112.26/112.09 [7533]~P1(f317(f317(f319(f900(x75331)),x75332),f306(f900(x75331),f147(x75331,x75333))))+P1(f317(f317(f319(f900(x75331)),x75332),f151(x75331,f306(x75331,x75333)))) % 112.26/112.09 [7565]E(f317(f317(f317(f173(f900(x75651),f900(x75651)),x75652),f157(x75651)),x75653),x75653)+~P1(f317(f317(f224(a899),f317(f179(f900(x75651)),x75653)),f72(a899))) % 112.26/112.09 [7598]E(f317(f317(f124(x75981),f737(x75982,x75983,x75981)),f317(f317(f141(x75981),x75983),f738(x75982,x75983,x75981))),x75982)+~P1(f317(f317(f319(x75981),x75983),f317(f162(x75981),x75982))) % 112.26/112.09 [7599]E(f317(f317(f124(x75991),f743(x75992,x75993,x75991)),f317(f317(f141(x75991),x75993),f744(x75992,x75993,x75991))),x75992)+~P1(f317(f317(f319(x75991),x75993),f317(f162(x75991),x75992))) % 112.26/112.09 [7600]E(f317(f317(f124(x76001),f745(x76002,x76003,x76001)),f317(f317(f141(x76001),x76003),f746(x76002,x76003,x76001))),x76002)+~P1(f317(f317(f319(x76001),x76003),f317(f162(x76001),x76002))) % 112.26/112.09 [7621]~P24(x76211,x76212,x76213,f232(f906(x76211,a895)))+P24(f900(x76211),f900(x76212),f317(f144(x76211,x76212),x76213),f232(f906(f900(x76211),a895))) % 112.26/112.09 [7774]E(x77741,f317(f317(f74(a899),f317(f317(f75(a899),f317(f241(a899,a899),x77742)),x77743)),f317(f246(a899,a899),x77742)))+~P1(f317(f44(x77741,x77743),x77742)) % 112.26/112.09 [7782]P24(x77821,x77822,x77823,f232(f906(x77821,a895)))+~P24(f900(x77821),f900(x77822),f317(f144(x77821,x77822),x77823),f232(f906(f900(x77821),a895))) % 112.26/112.09 [7827]P1(f317(f317(f319(f906(x78271,a895)),f436(x78272,x78273,x78271)),x78273))+P1(f317(f317(f319(x78271),x78272),f33(f906(x78271,a895),x78273))) % 112.26/112.09 [7918]P1(f317(f317(f319(f900(x79181)),x79182),f151(x79181,x79183)))+~P1(f317(f317(f319(x79181),f644(x79183,x79182,x79181)),x79183)) % 112.26/112.09 [8019]P30(x80191,x80192,x80193)+~P1(f317(x80192,f317(f317(f154(x80191),x80193),f742(x80193,x80192,x80191)))) % 112.26/112.09 [8044]E(x80441,x80442)+~E(f317(f317(f9(x80443,f906(x80443,a895),a895),f319(x80443)),x80441),f317(f317(f9(x80443,f906(x80443,a895),a895),f319(x80443)),x80442)) % 112.26/112.09 [8052]~P1(f317(f317(f319(f905(x80521,x80521)),x80523),f253(x80521,x80522)))+P1(f317(f317(f319(x80521),f499(x80522,x80523,x80521)),x80522)) % 112.26/112.09 [8054]~P1(f317(f317(f319(x80541),x80543),f32(f906(x80541,a895),x80542)))+P1(f317(f317(f319(f906(x80541,a895)),f435(x80542,x80543,x80541)),x80542)) % 112.26/112.09 [8173]P24(x81731,x81732,f85(x81732,x81731,f232(f906(x81732,a895)),x81733),f232(f906(x81731,a895)))+~E(f317(f300(x81732,x81731,x81733),f232(f906(x81732,a895))),f232(f906(x81731,a895))) % 112.26/112.09 [8227]~P1(f317(f317(f319(x82271),x82272),f317(f162(x82271),f743(x82273,x82272,x82271))))+~P1(f317(f317(f319(x82271),x82272),f317(f162(x82271),x82273))) % 112.26/112.09 [8228]~P1(f317(f317(f319(x82281),x82282),f317(f162(x82281),f746(x82283,x82282,x82281))))+~P1(f317(f317(f319(x82281),x82282),f317(f162(x82281),x82283))) % 112.26/112.09 [8257]P29(f317(f67(a895,a895,a899,a312),x82571),x82572,x82573)+P32(a899,x82571,f129(a899,f317(f292(a899,x82572),x82573))) % 112.26/112.09 [8418]E(x84181,f103(x84182))+P1(f317(f317(f319(x84182),f317(f241(x84182,f905(a89,a89)),f317(f265(x84182,x84181),x84183))),f317(f162(x84182),x84181))) % 112.26/112.09 [8518]~P71(x85181)+E(f317(f132(x85181,x85181,f317(f9(x85181,x85181,x85181),f74(x85181)),x85182),f317(f158(x85181),x85183)),f317(f132(x85181,x85181,f74(x85181),x85182),x85183)) % 112.26/112.09 [8710]~P24(x87102,x87101,x87103,f232(f906(x87102,a895)))+E(f317(f300(x87101,x87102,f85(x87102,x87101,f232(f906(x87102,a895)),x87103)),f232(f906(x87101,a895))),f232(f906(x87102,a895))) % 112.26/112.09 [8780]~P29(f317(f67(a895,a895,a899,a312),x87801),x87802,x87803)+~P32(a899,x87801,f129(a899,f317(f292(a899,x87802),x87803))) % 112.26/112.09 [9027]~P108(x90271)+E(f317(f162(x90271),f139(x90271,x90271,f7(x90271),x90272,x90273)),f317(f317(f299(x90271),x90272),f317(f162(x90271),x90273))) % 112.26/112.09 [9036]~E(f317(x90363,f317(f85(x90361,x90362,f232(f906(x90361,a895)),x90363),f792(x90363,x90362,x90361))),f792(x90363,x90362,x90361))+E(f317(f300(x90361,x90362,x90363),f232(f906(x90361,a895))),f232(f906(x90362,a895))) % 112.26/112.09 [9038]P1(f317(f317(f225(a899),f2(a899)),f606(x90381,x90382,x90383)))+~P1(f317(f317(f319(f905(x90383,x90383)),x90382),f317(f317(f279(x90383,x90383,x90383),x90381),f297(x90383,x90381)))) % 112.26/112.09 [9314]~P57(x93141,x93142)+~P1(f317(f317(f319(f905(x93141,x93141)),f317(f317(f242(x93141,x93141),x93143),x93143)),f317(f317(f279(x93141,x93141,x93141),x93142),f297(x93141,x93142)))) % 112.26/112.09 [9453]~E(f317(f317(f92(f906(f905(x94531,x94531),a895)),f317(f276(x94531,x94531),x94532)),f297(x94531,x94532)),f178(f906(f905(x94531,x94531),a895)))+~P1(f317(f317(f319(f905(x94531,x94531)),f317(f317(f242(x94531,x94531),x94533),x94533)),f317(f317(f279(x94531,x94531,x94531),x94532),f297(x94531,x94532)))) % 112.26/112.09 [9644]~P1(f317(f29(x96441),x96442))+P1(f317(f317(f224(a899),f317(f30(x96441),f317(f317(f3(f906(x96441,a895)),x96442),f317(f317(f299(x96441),x96443),f178(f906(x96441,a895)))))),f317(f30(x96441),x96442))) % 112.26/112.09 [5130]~E(x51303,f103(x51301))+E(f134(x51301,f317(f317(f141(x51301),x51302),x51303)),x51302) % 112.26/112.09 [5139]~E(x51393,f103(x51391))+E(f104(x51391,f317(f317(f141(x51391),x51392),x51393)),f103(x51391)) % 112.26/112.09 [5169]E(x51691,f103(x51692))+E(f134(x51692,f317(f317(f141(x51692),x51693),x51691)),f134(x51692,x51691)) % 112.26/112.09 [5171]E(x51711,f103(x51712))+E(f134(x51712,f317(f317(f124(x51712),x51713),x51711)),f134(x51712,x51711)) % 112.26/112.09 [5177]~E(x51773,f103(x51771))+E(f104(x51771,f317(f317(f124(x51771),x51772),x51773)),f104(x51771,x51772)) % 112.26/112.09 [5179]~E(x51793,f103(x51791))+E(f134(x51791,f317(f317(f124(x51791),x51792),x51793)),f134(x51791,x51792)) % 112.26/112.09 [5212]E(x52121,f103(x52122))+E(f317(f131(x52122),f317(f317(f124(x52122),x52121),x52123)),f317(f131(x52122),x52121)) % 112.26/112.09 [5240]~E(x52402,f103(x52401))+E(f317(f131(x52401),f317(f317(f124(x52401),x52402),x52403)),f317(f131(x52401),x52403)) % 112.26/112.09 [5292]~P108(x52921)+E(f317(f317(f228(x52921),x52922),f317(f317(f223(x52921),x52922),x52923)),x52922) % 112.26/112.09 [5293]~P108(x52931)+E(f317(f317(f223(x52931),x52932),f317(f317(f228(x52931),x52932),x52933)),x52932) % 112.26/112.09 [5294]~P99(x52941)+E(f317(f317(f91(x52941),x52942),f317(f317(f92(x52941),x52942),x52943)),x52942) % 112.26/112.09 [5295]~P99(x52951)+E(f317(f317(f92(x52951),x52952),f317(f317(f91(x52951),x52952),x52953)),x52952) % 112.26/112.09 [5314]~P3(x53141)+E(f41(x53141,f317(f317(f75(x53141),x53142),x53143),x53143),f2(x53141)) % 112.26/112.09 [5315]~P3(x53151)+E(f41(x53151,f317(f317(f75(x53151),x53152),x53153),x53152),f2(x53151)) % 112.26/112.09 [5383]~P68(x53831)+E(f317(f73(x53831),f317(f317(f3(x53831),x53832),x53833)),f317(f317(f3(x53831),x53833),x53832)) % 112.26/112.09 [5446]E(x54461,f103(x54462))+E(f104(x54462,f317(f317(f141(x54462),x54463),x54461)),f317(f317(f141(x54462),x54463),f104(x54462,x54461))) % 112.26/112.09 [5447]E(x54471,f103(x54472))+E(f104(x54472,f317(f317(f124(x54472),x54473),x54471)),f317(f317(f124(x54472),x54473),f104(x54472,x54471))) % 112.26/112.09 [5450]~P5(x54501)+E(f32(x54501,f317(f317(f299(x54501),x54502),x54503)),f317(f317(f91(x54501),x54502),f32(x54501,x54503))) % 112.26/112.09 [5451]~P5(x54511)+E(f33(x54511,f317(f317(f299(x54511),x54512),x54513)),f317(f317(f92(x54511),x54512),f33(x54511,x54513))) % 112.26/112.09 [5497]~P97(x54971)+E(f317(f317(f75(x54971),x54972),f317(f317(f75(x54971),x54972),x54973)),f317(f317(f75(x54971),x54972),x54973)) % 112.26/112.09 [5499]~P108(x54991)+E(f317(f317(f228(x54991),x54992),f317(f317(f228(x54991),x54992),x54993)),f317(f317(f228(x54991),x54992),x54993)) % 112.26/112.09 [5501]~P108(x55011)+E(f317(f317(f223(x55011),x55012),f317(f317(f223(x55011),x55012),x55013)),f317(f317(f223(x55011),x55012),x55013)) % 112.26/112.09 [5503]~P98(x55031)+E(f317(f317(f91(x55031),x55032),f317(f317(f91(x55031),x55032),x55033)),f317(f317(f91(x55031),x55032),x55033)) % 112.26/112.09 [5504]~P99(x55041)+E(f317(f317(f91(x55041),x55042),f317(f317(f91(x55041),x55042),x55043)),f317(f317(f91(x55041),x55042),x55043)) % 112.26/112.09 [5505]~P99(x55051)+E(f317(f317(f92(x55051),x55052),f317(f317(f92(x55051),x55052),x55053)),f317(f317(f92(x55051),x55052),x55053)) % 112.26/112.09 [5507]~P104(x55071)+E(f317(f317(f92(x55071),x55072),f317(f317(f92(x55071),x55072),x55073)),f317(f317(f92(x55071),x55072),x55073)) % 112.26/112.09 [5514]~P3(x55141)+E(f41(x55141,f317(f317(f74(x55141),x55142),x55143),x55143),f41(x55141,x55142,x55143)) % 112.26/112.09 [5515]~P3(x55151)+E(f41(x55151,f317(f317(f74(x55151),x55152),x55153),x55152),f41(x55151,x55153,x55152)) % 112.26/112.09 [5524]~P110(x55241)+E(f317(f317(f75(x55241),x55242),f317(f73(x55241),x55243)),f317(f73(x55241),f317(f317(f75(x55241),x55242),x55243))) % 112.26/112.09 [5525]~P61(x55251)+E(f317(f317(f281(x55251),x55252),f317(f73(x55251),x55253)),f317(f73(x55251),f317(f317(f281(x55251),x55252),x55253))) % 112.26/112.09 [5526]~P81(x55261)+E(f317(f317(f74(x55261),x55262),f317(f155(x55261),x55263)),f317(f155(x55261),f317(f317(f141(x55261),x55262),x55263))) % 112.26/112.09 [5554]~P110(x55541)+E(f317(f317(f75(x55541),f317(f73(x55541),x55542)),x55543),f317(f317(f75(x55541),x55542),f317(f73(x55541),x55543))) % 112.26/112.09 [5560]~P8(x55601,x55602,x55603)+E(f32(f906(x55601,a895),f317(f317(f56(x55601),x55602),x55603)),x55602) % 112.26/112.09 [5626]~P115(x56261)+E(f317(f317(f75(x56261),x56262),f317(f317(f234(x56261),x56262),x56263)),f317(f317(f234(x56261),x56262),f317(a102,x56263))) % 112.26/112.09 [5627]~P119(x56271)+E(f317(f317(f75(x56271),x56272),f317(f317(f234(x56271),x56272),x56273)),f317(f317(f234(x56271),x56272),f317(a102,x56273))) % 112.26/112.09 [5637]~P76(x56371)+E(f317(f317(f74(x56371),f317(f73(x56371),x56372)),f317(f317(f74(x56371),x56372),x56373)),x56373) % 112.26/112.09 [5660]~P145(x56601)+E(f317(f317(f234(x56601),f317(f90(x56601),x56602)),x56603),f317(f90(x56601),f317(f317(f234(a899),x56602),x56603))) % 112.26/112.09 [5661]~P141(x56611)+E(f317(f317(f234(x56611),f317(f93(x56611),x56612)),x56613),f317(f93(x56611),f317(f317(f234(a1),x56612),x56613))) % 112.26/112.09 [5667]~P86(x56671)+E(f317(f70(x56671),f317(f317(f3(x56671),x56672),x56673)),f317(f70(x56671),f317(f317(f3(x56671),x56673),x56672))) % 112.26/112.09 [5669]~P112(x56691)+E(f317(f317(f75(x56691),f76(x56691,x56692)),f76(x56691,x56693)),f76(x56691,f317(f317(f75(x56691),x56692),x56693))) % 112.26/112.09 [5673]E(x56731,f103(x56732))+E(f317(f317(f124(x56732),f317(f161(x56732),x56731)),x56733),f317(f161(x56732),f317(f317(f124(x56732),x56731),x56733))) % 112.26/112.09 [5679]~E(x56792,f317(a102,f317(f317(f74(a899),x56791),x56793)))+P1(f317(f317(f225(a899),x56791),x56792)) % 112.26/112.09 [5680]~P112(x56801)+E(f317(f317(f234(x56801),f317(f70(x56801),x56802)),x56803),f317(f70(x56801),f317(f317(f234(x56801),x56802),x56803))) % 112.26/112.09 [5681]~P110(x56811)+E(f317(f317(f75(x56811),f317(f73(x56811),x56812)),x56813),f317(f73(x56811),f317(f317(f75(x56811),x56812),x56813))) % 112.26/112.09 [5682]~P123(x56821)+E(f317(f317(f281(x56821),f317(f73(x56821),x56822)),x56823),f317(f73(x56821),f317(f317(f281(x56821),x56822),x56823))) % 112.26/112.09 [5780]E(f398(x57801,x57802,x57803),f405(x57801,x57802,x57803))+E(f317(f317(f92(f906(x57803,a895)),x57802),x57801),f178(f906(x57803,a895))) % 112.26/112.09 [5795]~P69(x57952)+E(f317(f317(f8(x57951,x57952),f317(f18(x57952,x57951),f2(x57952))),x57953),f2(x57952)) % 112.26/112.09 [5796]~P75(x57962)+E(f317(f317(f11(x57961,x57962),f317(f18(x57962,x57961),f72(x57962))),x57963),f72(x57962)) % 112.26/112.09 [5798]~P94(x57981)+E(f317(f317(f3(x57981),f317(f94(x57981),x57982)),f317(f94(x57981),x57983)),f317(f94(x57981),f317(f317(f3(a1),x57982),x57983))) % 112.26/112.09 [5801]~P145(x58011)+E(f317(f317(f74(x58011),f317(f90(x58011),x58012)),f317(f90(x58011),x58013)),f317(f90(x58011),f317(f317(f74(a899),x58012),x58013))) % 112.26/112.09 [5802]~P145(x58021)+E(f317(f317(f75(x58021),f317(f90(x58021),x58022)),f317(f90(x58021),x58023)),f317(f90(x58021),f317(f317(f75(a899),x58022),x58023))) % 112.26/112.09 [5803]~P141(x58031)+E(f317(f317(f3(x58031),f317(f93(x58031),x58032)),f317(f93(x58031),x58033)),f317(f93(x58031),f317(f317(f3(a1),x58032),x58033))) % 112.26/112.09 [5804]~P141(x58041)+E(f317(f317(f74(x58041),f317(f93(x58041),x58042)),f317(f93(x58041),x58043)),f317(f93(x58041),f317(f317(f74(a1),x58042),x58043))) % 112.26/112.09 [5805]~P141(x58051)+E(f317(f317(f75(x58051),f317(f93(x58051),x58052)),f317(f93(x58051),x58053)),f317(f93(x58051),f317(f317(f75(a1),x58052),x58053))) % 112.26/112.09 [5806]~P94(x58061)+E(f317(f317(f74(x58061),f317(f94(x58061),x58062)),f317(f94(x58061),x58063)),f317(f94(x58061),f317(f317(f74(a1),x58062),x58063))) % 112.26/112.09 [5807]~P94(x58071)+E(f317(f317(f75(x58071),f317(f94(x58071),x58072)),f317(f94(x58071),x58073)),f317(f94(x58071),f317(f317(f75(a1),x58072),x58073))) % 112.26/112.09 [5855]~E(x58553,x58552)+P1(f317(f317(f224(f906(x58551,a895)),x58552),x58553)) % 112.26/112.09 [5861]~E(x58612,x58613)+P1(f317(f317(f224(f906(x58611,a895)),x58612),x58613)) % 112.26/112.09 [5866]~P112(x58661)+E(f317(f317(f75(x58661),f317(f70(x58661),x58662)),f317(f70(x58661),x58663)),f317(f70(x58661),f317(f317(f75(x58661),x58662),x58663))) % 112.26/112.09 [5867]~P63(x58671)+E(f317(f317(f281(x58671),f317(f70(x58671),x58672)),f317(f70(x58671),x58673)),f317(f70(x58671),f317(f317(f281(x58671),x58672),x58673))) % 112.26/112.09 [5868]~P76(x58681)+E(f317(f317(f74(x58681),f317(f73(x58681),x58682)),f317(f73(x58681),x58683)),f317(f73(x58681),f317(f317(f74(x58681),x58683),x58682))) % 112.26/112.09 [5869]~P68(x58691)+E(f317(f317(f74(x58691),f317(f73(x58691),x58692)),f317(f73(x58691),x58693)),f317(f73(x58691),f317(f317(f74(x58691),x58692),x58693))) % 112.26/112.09 [5870]~P77(x58701)+E(f317(f317(f223(x58701),f317(f73(x58701),x58702)),f317(f73(x58701),x58703)),f317(f73(x58701),f317(f317(f228(x58701),x58702),x58703))) % 112.26/112.09 [5871]~P77(x58711)+E(f317(f317(f228(x58711),f317(f73(x58711),x58712)),f317(f73(x58711),x58713)),f317(f73(x58711),f317(f317(f223(x58711),x58712),x58713))) % 112.26/112.09 [5872]~P96(x58721)+E(f317(f317(f92(x58721),f317(f73(x58721),x58722)),f317(f73(x58721),x58723)),f317(f73(x58721),f317(f317(f91(x58721),x58722),x58723))) % 112.26/112.09 [5873]~P96(x58731)+E(f317(f317(f91(x58731),f317(f73(x58731),x58732)),f317(f73(x58731),x58733)),f317(f73(x58731),f317(f317(f92(x58731),x58732),x58733))) % 112.26/112.09 [5874]~P81(x58741)+E(f317(f317(f74(x58741),f317(f155(x58741),x58742)),f317(f155(x58741),x58743)),f317(f155(x58741),f317(f317(f124(x58741),x58742),x58743))) % 112.26/112.09 [5875]E(x58751,f178(f906(x58752,a895)))+~E(f317(f317(f91(f906(x58752,a895)),x58753),x58751),f178(f906(x58752,a895))) % 112.26/112.09 [5876]E(x58761,f178(f906(x58762,a895)))+~E(f317(f317(f91(f906(x58762,a895)),x58761),x58763),f178(f906(x58762,a895))) % 112.26/112.09 [5877]~P148(x58771,x58772,x58773)+P1(f317(x58771,f317(f317(f31(a1),x58772),x58773))) % 112.26/112.09 [5942]~P1(f317(f29(x59421),x59423))+P1(f317(f29(x59421),f317(f317(f299(x59421),x59422),x59423))) % 112.26/112.09 [5943]~P1(f317(f127(x59431),x59433))+P1(f317(f127(x59431),f317(f317(f165(x59431),x59432),x59433))) % 112.26/112.09 [5944]~P1(f317(f127(x59441),x59443))+P1(f317(f127(x59441),f317(f317(f128(x59441),x59442),x59443))) % 112.26/112.09 [5976]~P108(x59761)+P1(f317(f317(f224(x59761),x59762),f317(f317(f223(x59761),x59763),x59762))) % 112.26/112.09 [5977]~P108(x59771)+P1(f317(f317(f224(x59771),x59772),f317(f317(f223(x59771),x59772),x59773))) % 112.26/112.09 [5978]~P98(x59781)+P1(f317(f317(f224(x59781),x59782),f317(f317(f91(x59781),x59783),x59782))) % 112.26/112.09 [5979]~P99(x59791)+P1(f317(f317(f224(x59791),x59792),f317(f317(f91(x59791),x59793),x59792))) % 112.26/112.09 [5980]~P98(x59801)+P1(f317(f317(f224(x59801),x59802),f317(f317(f91(x59801),x59802),x59803))) % 112.26/112.09 [5981]~P99(x59811)+P1(f317(f317(f224(x59811),x59812),f317(f317(f91(x59811),x59812),x59813))) % 112.26/112.09 [5982]~P119(x59821)+P1(f317(f317(f277(x59821),x59822),f317(f317(f75(x59821),x59823),x59822))) % 112.26/112.09 [5983]~P119(x59831)+P1(f317(f317(f277(x59831),x59832),f317(f317(f75(x59831),x59832),x59833))) % 112.26/112.09 [5997]~E(x59971,f2(a899))+E(f317(f317(f31(a899),f317(f317(f75(a899),x59971),x59972)),f317(f317(f75(a899),x59971),x59973)),f2(a899)) % 112.26/112.09 [6079]~P94(x60791)+E(f317(f317(f3(x60791),f317(f94(x60791),x60792)),f317(f94(x60791),x60793)),f317(f94(x60791),f317(f317(f74(a1),x60792),f317(f73(a1),x60793)))) % 112.26/112.09 [6139]E(x61391,f2(a899))+E(f317(f317(f31(a899),f317(f317(f75(a899),x61391),x61392)),f317(f317(f75(a899),x61391),x61393)),f317(f317(f31(a899),x61392),x61393)) % 112.26/112.09 [6169]E(f142(x61691,f317(f317(f141(x61691),x61692),x61693)),f317(f317(f141(x61691),x61692),f142(x61691,x61693)))+P1(f317(f317(f319(x61691),x61692),f317(f162(x61691),x61693))) % 112.26/112.09 [6205]P148(x62051,x62052,x62053)+~P1(f317(x62051,f317(f317(f31(a1),x62052),x62053))) % 112.26/112.09 [6281]E(x62811,f103(x62812))+E(f317(f317(f141(x62812),f317(f131(x62812),x62811)),f317(f317(f165(x62812),x62813),f317(f161(x62812),x62811))),f317(f317(f165(x62812),f317(a102,x62813)),x62811)) % 112.26/112.09 [6289]E(f317(f317(f3(f906(x62891,a895)),x62892),x62893),x62892)+~E(f317(f317(f92(f906(x62891,a895)),x62892),x62893),f178(f906(x62891,a895))) % 112.26/112.09 [6303]E(f142(x63031,f317(f317(f141(x63031),x63032),x63033)),f142(x63031,x63033))+~P1(f317(f317(f319(x63031),x63032),f317(f162(x63031),x63033))) % 112.26/112.09 [6334]~P1(f317(f317(f224(a899),x63341),x63343))+P1(f317(f317(f224(a899),x63341),f317(f317(f74(a899),x63342),x63343))) % 112.26/112.09 [6336]~P1(f317(f317(f224(a899),x63361),x63362))+P1(f317(f317(f224(a899),x63361),f317(f317(f74(a899),x63362),x63363))) % 112.26/112.09 [6338]~P1(f317(f317(f225(a899),x63381),x63383))+P1(f317(f317(f225(a899),x63381),f317(f317(f74(a899),x63382),x63383))) % 112.26/112.09 [6340]~P1(f317(f317(f225(a899),x63401),x63402))+P1(f317(f317(f225(a899),x63401),f317(f317(f74(a899),x63402),x63403))) % 112.26/112.09 [6380]P1(f317(f29(x63801),x63802))+~P1(f317(f29(x63801),f317(f317(f299(x63801),x63803),x63802))) % 112.26/112.09 [6381]P1(f317(f127(x63811),x63812))+~P1(f317(f127(x63811),f317(f317(f141(x63811),x63813),x63812))) % 112.26/112.09 [6382]P1(f317(f127(x63821),x63822))+~P1(f317(f127(x63821),f317(f317(f124(x63821),x63823),x63822))) % 112.26/112.09 [6383]P1(f317(f127(x63831),x63832))+~P1(f317(f127(x63831),f317(f317(f124(x63831),x63832),x63833))) % 112.26/112.09 [6437]~P119(x64371)+E(f317(f317(f74(x64371),x64372),f317(f317(f75(x64371),x64373),x64372)),f317(f317(f75(x64371),f317(f317(f74(x64371),x64373),f72(x64371))),x64372)) % 112.26/112.09 [6484]~E(x64841,x64842)+~P1(f317(f317(f225(f906(x64843,a895)),x64841),x64842)) % 112.26/112.09 [6530]P1(f317(f317(f319(x65301),x65302),x65303))+P1(f317(f317(f319(x65301),x65302),f317(f73(f906(x65301,a895)),x65303))) % 112.26/112.09 [6536]E(f134(x65361,f317(f317(f128(x65361),x65362),x65363)),f134(x65361,x65363))+~P1(f317(f317(f225(a899),x65362),f317(f179(f900(x65361)),x65363))) % 112.26/112.09 [6537]E(f317(f317(f165(x65371),x65372),f104(x65371,x65373)),f317(f317(f165(x65371),x65372),x65373))+~P1(f317(f317(f225(a899),x65372),f317(f179(f900(x65371)),x65373))) % 112.26/112.09 [6597]E(f317(f317(f317(f173(f900(x65971),f900(x65971)),x65972),f157(x65971)),x65973),x65973)+~E(f41(a899,x65972,f317(f179(f900(x65971)),x65973)),f2(a899)) % 112.26/112.09 [6604]~P8(x66041,x66043,x66042)+E(f317(f317(f279(x66041,x66041,x66041),f317(f276(x66041,x66041),x66042)),x66042),x66042) % 112.26/112.09 [6647]~E(f317(f317(f91(f906(x66471,a895)),x66472),x66473),x66473)+P1(f317(f317(f224(f906(x66471,a895)),x66472),x66473)) % 112.26/112.09 [6652]~P54(x66521,x66521,x66523)+P54(x66521,x66521,f317(f317(f173(f905(x66521,x66521),a895),x66522),x66523)) % 112.26/112.09 [6655]~P1(f317(f317(f319(x66551),x66553),f317(f162(x66551),x66552)))+P1(f317(f317(f225(a899),f2(a899)),f317(f179(f900(x66551)),x66552))) % 112.26/112.09 [6683]~P86(x66831)+E(f317(f70(x66831),f317(f317(f74(x66831),f317(f70(x66831),x66832)),f317(f70(x66831),x66833))),f317(f317(f74(x66831),f317(f70(x66831),x66832)),f317(f70(x66831),x66833))) % 112.26/112.09 [6694]E(f317(f317(f31(a899),f317(f317(f75(a899),x66941),x66942)),f317(f317(f75(a899),x66941),x66943)),f317(f317(f31(a899),x66942),x66943))+~P1(f317(f317(f225(a899),f2(a899)),x66941)) % 112.26/112.09 [6837]~P1(f317(f29(x68371),x68373))+E(f317(f317(f59(x68371,f906(x68371,a895),f299(x68371)),x68372),x68373),f317(f317(f91(f906(x68371,a895)),x68373),x68372)) % 112.26/112.09 [6896]E(f317(f317(f91(f906(x68961,a895)),x68962),x68963),x68962)+~P1(f317(f317(f224(f906(x68961,a895)),x68963),x68962)) % 112.26/112.09 [6898]E(f317(f317(f91(f906(x68981,a895)),x68982),x68983),x68983)+~P1(f317(f317(f224(f906(x68981,a895)),x68982),x68983)) % 112.26/112.09 [6899]E(f317(f317(f92(f906(x68991,a895)),x68992),x68993),x68993)+~P1(f317(f317(f224(f906(x68991,a895)),x68993),x68992)) % 112.26/112.09 [6900]E(f317(f317(f92(f906(x69001,a895)),x69002),x69003),x69002)+~P1(f317(f317(f224(f906(x69001,a895)),x69002),x69003)) % 112.26/112.09 [6949]~P1(f317(f127(x69491),x69492))+E(f317(f317(f3(f906(x69491,a895)),f317(f162(x69491),x69492)),f317(f317(f299(x69491),x69493),f178(f906(x69491,a895)))),f317(f162(x69491),f160(x69491,x69493,x69492))) % 112.26/112.09 [7006]P36(x70061,x70062)+~P36(x70061,f317(f317(f173(f905(x70061,x70061),a895),x70063),x70062)) % 112.26/112.09 [7023]~E(x70231,f2(a899))+P1(f317(f317(f277(a899),f317(f317(f75(a899),x70231),x70232)),f317(f317(f75(a899),x70231),x70233))) % 112.26/112.09 [7074]P1(f317(f45(x70741,x70742),f317(a47,x70743)))+~P1(f317(f45(f317(f73(a1),x70741),f317(f73(a1),x70742)),x70743)) % 112.26/112.09 [7079]E(f317(f317(f3(f906(x70791,a895)),f317(f317(f299(x70791),x70792),x70793)),f317(f317(f299(x70791),x70792),f178(f906(x70791,a895)))),x70793)+P1(f317(f317(f319(x70791),x70792),x70793)) % 112.26/112.09 [7101]E(f317(f317(f92(f906(x71011,a895)),f317(f162(x71011),x71012)),f317(f162(x71011),x71013)),f178(f906(x71011,a895)))+~P1(f317(f127(x71011),f317(f317(f124(x71011),x71012),x71013))) % 112.26/112.09 [7116]~P1(f317(f317(f319(x71161),x71162),f317(f162(x71161),x71163)))+~P1(f317(f127(x71161),f317(f317(f141(x71161),x71162),x71163))) % 112.26/112.09 [7187]P30(x71871,x71872,x71873)+P1(f317(f317(f225(a899),f742(x71873,x71872,x71871)),f317(f179(f900(x71871)),x71873))) % 112.26/112.09 [7197]E(f317(f317(f92(f906(x71971,a895)),x71972),x71973),f178(f906(x71971,a895)))+P1(f317(f317(f319(x71971),f398(x71973,x71972,x71971)),x71972)) % 112.26/112.09 [7198]E(f317(f317(f92(f906(x71981,a895)),x71982),x71983),f178(f906(x71981,a895)))+P1(f317(f317(f319(x71981),f405(x71983,x71982,x71981)),x71983)) % 112.26/112.09 [7201]E(f104(x72011,f317(f317(f165(x72011),x72012),x72013)),f317(f317(f165(x72011),f317(f317(f3(a899),x72012),f72(a899))),x72013))+~P1(f317(f317(f224(a899),x72012),f317(f179(f900(x72011)),x72013))) % 112.26/112.09 [7261]~P32(x72613,x72612,x72611)+P1(f317(f317(f225(a899),f735(x72611,x72612,x72613)),f317(f179(f900(x72613)),x72611))) % 112.26/112.09 [7281]P1(f317(f317(f225(a899),f2(a899)),x72811))+P1(f317(f317(f224(a899),f317(f317(f75(a899),x72812),x72811)),f317(f317(f75(a899),x72813),x72811))) % 112.26/112.09 [7282]P1(f317(f317(f225(a899),f2(a899)),x72821))+P1(f317(f317(f224(a899),f317(f317(f75(a899),x72821),x72822)),f317(f317(f75(a899),x72821),x72823))) % 112.26/112.10 [7285]~P1(f317(f317(f319(x72851),x72852),x72853))+~P1(f317(f317(f319(x72851),x72852),f317(f73(f906(x72851,a895)),x72853))) % 112.26/112.10 [7291]~P1(f317(f317(f225(f906(x72911,a895)),x72912),x72913))+P1(f317(f317(f224(f906(x72911,a895)),x72912),x72913)) % 112.26/112.10 [7397]~P1(f317(f317(f224(a899),x73973),x73972))+P1(f317(f317(f224(a899),f317(f317(f3(a899),x73971),x73972)),f317(f317(f3(a899),x73971),x73973))) % 112.26/112.10 [7398]~P1(f317(f317(f224(a899),x73981),x73983))+P1(f317(f317(f224(a899),f317(f317(f3(a899),x73981),x73982)),f317(f317(f3(a899),x73983),x73982))) % 112.26/112.10 [7399]~P1(f317(f317(f224(a899),x73992),x73993))+P1(f317(f317(f224(a899),f317(f317(f74(a899),x73991),x73992)),f317(f317(f74(a899),x73991),x73993))) % 112.26/112.10 [7400]~P1(f317(f317(f224(a899),x74001),x74003))+P1(f317(f317(f224(a899),f317(f317(f74(a899),x74001),x74002)),f317(f317(f74(a899),x74003),x74002))) % 112.26/112.10 [7402]~P1(f317(f317(f224(a899),x74022),x74023))+P1(f317(f317(f224(a899),f317(f317(f75(a899),x74021),x74022)),f317(f317(f75(a899),x74021),x74023))) % 112.26/112.10 [7404]~P1(f317(f317(f224(a899),x74041),x74043))+P1(f317(f317(f224(a899),f317(f317(f75(a899),x74041),x74042)),f317(f317(f75(a899),x74043),x74042))) % 112.26/112.10 [7405]~P1(f317(f317(f224(a899),x74051),x74053))+P1(f317(f317(f224(a899),f317(f317(f31(a899),x74051),x74052)),f317(f317(f31(a899),x74053),x74052))) % 112.26/112.10 [7406]~P1(f317(f317(f224(a1),x74062),x74063))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x74061),x74062)),f317(f317(f74(a1),x74061),x74063))) % 112.26/112.10 [7409]~P1(f317(f317(f225(a899),x74092),x74093))+P1(f317(f317(f225(a899),f317(f317(f74(a899),x74091),x74092)),f317(f317(f74(a899),x74091),x74093))) % 112.26/112.10 [7410]~P1(f317(f317(f225(a899),x74101),x74103))+P1(f317(f317(f225(a899),f317(f317(f74(a899),x74101),x74102)),f317(f317(f74(a899),x74103),x74102))) % 112.26/112.10 [7411]~P1(f317(f317(f225(a1),x74111),x74113))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x74111),x74112)),f317(f317(f74(a1),x74113),x74112))) % 112.26/112.10 [7414]~P1(f317(f317(f277(a899),x74142),x74143))+P1(f317(f317(f277(a899),f317(f317(f75(a899),x74141),x74142)),f317(f317(f75(a899),x74141),x74143))) % 112.26/112.10 [7492]E(x74921,x74922)+~P1(f317(f317(f319(x74923),x74921),f317(f317(f299(x74923),x74922),f178(f906(x74923,a895))))) % 112.26/112.10 [7494]~E(f317(f317(f92(f906(x74941,a895)),x74942),x74943),f178(f906(x74941,a895)))+P1(f317(f317(f224(f906(x74941,a895)),x74942),f317(f73(f906(x74941,a895)),x74943))) % 112.26/112.10 [7499]P1(f317(f317(f319(f906(x74991,a895)),x74992),f317(f298(x74991),x74993)))+~P1(f317(f317(f224(f906(x74991,a895)),x74992),x74993)) % 112.26/112.10 [7550]E(f317(f317(f141(x75501),f317(f317(f154(x75501),x75502),x75503)),f317(f317(f128(x75501),f317(a102,x75503)),x75502)),f317(f317(f128(x75501),x75503),x75502))+~P1(f317(f317(f225(a899),x75503),f317(f179(f900(x75501)),x75502))) % 112.26/112.10 [7575]P1(f317(f317(f319(f905(x75751,x75751)),x75752),f297(x75751,x75753)))+~P1(f317(f317(f319(f905(x75751,x75751)),x75752),x75753)) % 112.26/112.10 [7584]~P1(f317(f317(f319(f906(x75841,a895)),x75842),f317(f298(x75841),x75843)))+P1(f317(f317(f224(f906(x75841,a895)),x75842),x75843)) % 112.26/112.10 [7629]P1(f317(f317(f224(f906(x76291,a895)),x76292),f32(f906(x76291,a895),x76293)))+~P1(f317(f317(f319(f906(x76291,a895)),x76292),x76293)) % 112.26/112.10 [7654]~P141(x76541)+E(f317(f317(f75(x76541),f317(f317(f234(x76541),f317(f73(x76541),f72(x76541))),x76542)),f317(f317(f234(x76541),x76543),x76542)),f317(f317(f234(x76541),f317(f73(x76541),x76543)),x76542)) % 112.26/112.10 [7676]E(f317(f317(f154(x76761),x76762),f317(f317(f3(a899),f317(f179(f900(x76761)),x76762)),f317(a102,x76763))),f317(f317(f154(x76761),f317(f158(x76761),x76762)),x76763))+~P1(f317(f317(f225(a899),x76763),f317(f179(f900(x76761)),x76762))) % 112.26/112.10 [7693]~E(f317(f317(f92(f906(x76931,a895)),f410(x76933,x76932,x76931)),x76933),f178(f906(x76931,a895)))+E(f317(f317(f92(f906(x76931,a895)),f32(f906(x76931,a895),x76932)),x76933),f178(f906(x76931,a895))) % 112.26/112.10 [7757]~P1(f317(f317(f319(x77573),x77572),f317(f162(x77573),x77571)))+P1(f317(f317(f225(a899),f643(x77571,x77572,x77573)),f317(f179(f900(x77573)),x77571))) % 112.26/112.10 [7765]P1(f317(f317(f319(x77651),f317(f317(f154(x77651),x77652),x77653)),f317(f162(x77651),x77652)))+~P1(f317(f317(f225(a899),x77653),f317(f179(f900(x77651)),x77652))) % 112.26/112.10 [7863]~P1(f317(x78632,f701(x78633,x78632,x78631)))+E(f317(f317(f128(x78631),f317(f179(f900(x78631)),f167(x78631,x78632,x78633))),x78633),f103(x78631)) % 112.26/112.10 [7876]P1(f317(f317(f224(f906(f900(x78761),a895)),f151(x78761,x78762)),f151(x78761,x78763)))+~P1(f317(f317(f224(f906(x78761,a895)),x78762),x78763)) % 112.26/112.10 [7877]P1(f317(f317(f224(f906(f900(x78771),a895)),f150(x78771,x78772)),f150(x78771,x78773)))+~P1(f317(f317(f224(f906(x78771,a895)),x78772),x78773)) % 112.26/112.10 [7904]E(f317(f317(f92(f906(x79041,a895)),f32(f906(x79041,a895),x79042)),x79043),f178(f906(x79041,a895)))+P1(f317(f317(f319(f906(x79041,a895)),f410(x79043,x79042,x79041)),x79042)) % 112.26/112.10 [7906]~P1(f317(f317(f319(f906(x79061,a895)),x79063),x79062))+P1(f317(f317(f224(f906(x79061,a895)),f33(f906(x79061,a895),x79062)),x79063)) % 112.26/112.10 [7908]E(f317(f317(f92(f906(x79081,a895)),x79082),x79083),f178(f906(x79081,a895)))+~P1(f317(f317(f224(f906(x79081,a895)),x79082),f317(f73(f906(x79081,a895)),x79083))) % 112.26/112.10 [7957]E(f317(f317(f3(a899),f317(f317(f74(a899),f317(f155(a899),x79571)),x79572)),f317(f317(f154(a899),x79571),x79573)),f317(f155(a899),f317(f317(f149(a899,x79571),x79573),x79572)))+~P1(f317(f317(f225(a899),x79573),f317(f179(f900(a899)),x79571))) % 112.26/112.10 [8008]P1(f317(f317(f224(a899),x80081),x80082))+~P1(f317(f317(f224(a899),f317(f317(f74(a899),x80083),x80081)),f317(f317(f74(a899),x80083),x80082))) % 112.26/112.10 [8011]P1(f317(f317(f225(a899),x80111),x80112))+~P1(f317(f317(f225(a899),f317(f317(f74(a899),x80113),x80111)),f317(f317(f74(a899),x80113),x80112))) % 112.26/112.10 [8012]P1(f317(f317(f225(a899),x80121),x80122))+~P1(f317(f317(f225(a899),f317(f317(f75(a899),x80123),x80121)),f317(f317(f75(a899),x80123),x80122))) % 112.26/112.10 [8013]P1(f317(f317(f225(a899),x80131),x80132))+~P1(f317(f317(f225(a899),f317(f317(f75(a899),x80131),x80133)),f317(f317(f75(a899),x80132),x80133))) % 112.26/112.10 [8042]P1(f317(f317(f225(a899),f2(a899)),x80421))+~P1(f317(f317(f225(a899),f317(f317(f75(a899),x80422),x80421)),f317(f317(f75(a899),x80423),x80421))) % 112.26/112.10 [8043]P1(f317(f317(f225(a899),f2(a899)),x80431))+~P1(f317(f317(f225(a899),f317(f317(f75(a899),x80431),x80432)),f317(f317(f75(a899),x80431),x80433))) % 112.26/112.10 [8116]E(f237(x81161,x81162,x81163),x81162)+~P1(f317(f317(f224(f906(x81161,a895)),x81163),f317(f317(f299(x81161),x81162),f178(f906(x81161,a895))))) % 112.26/112.10 [8166]~P1(f317(f127(x81661),x81663))+E(f317(f126(x81661,f317(f317(f10(a895,a895,x81661),a312),f317(a314,x81662))),x81663),f160(x81661,x81662,x81663)) % 112.26/112.10 [8191]E(f317(f317(f128(x81911),f317(f179(f900(x81911)),f167(x81911,x81912,x81913))),x81913),f103(x81911))+P1(f317(f317(f319(x81911),f701(x81913,x81912,x81911)),f317(f162(x81911),x81913))) % 112.26/112.10 [8195]E(f317(f317(f124(x81951),f317(f317(f165(x81951),x81952),x81953)),f317(f317(f141(x81951),f317(f317(f154(x81951),x81953),x81952)),f103(x81951))),f317(f317(f165(x81951),f317(a102,x81952)),x81953))+~P1(f317(f317(f225(a899),x81952),f317(f179(f900(x81951)),x81953))) % 112.26/112.10 [8262]E(f317(f126(x82621,f317(f317(f10(a895,a895,x82621),a312),f317(a314,x82622))),x82623),x82623)+P1(f317(f317(f319(x82621),x82622),f317(f162(x82621),x82623))) % 112.26/112.10 [8268]P1(f317(f317(f224(f906(f906(x82681,a895),a895)),f238(x82681,x82682)),f238(x82681,x82683)))+~P1(f317(f317(f224(f906(x82681,a895)),x82682),x82683)) % 112.26/112.10 [8307]~P1(f317(f127(x83071),x83073))+P1(f317(f127(x83071),f317(f317(f317(f173(f900(x83071),f900(x83071)),x83072),f157(x83071)),x83073))) % 112.26/112.10 [8313]~P1(f317(f317(f225(a899),x83132),x83133))+P1(f317(f317(f225(a899),f317(f317(f75(a899),f317(a102,x83131)),x83132)),f317(f317(f75(a899),f317(a102,x83131)),x83133))) % 112.26/112.10 [8333]P1(f317(f317(f224(f906(f906(x83331,a895),a895)),f317(f298(x83331),x83332)),f317(f298(x83331),x83333)))+~P1(f317(f317(f224(f906(x83331,a895)),x83332),x83333)) % 112.26/112.10 [8403]~E(f317(f300(x84031,x84032,x84033),f232(f906(x84031,a895))),f232(f906(x84032,a895)))+E(f317(f67(x84031,x84032,x84032,x84033),f85(x84031,x84032,f232(f906(x84031,a895)),x84033)),f25(x84032)) % 112.26/112.10 [8497]~P1(f317(f317(f224(f906(x84971,a895)),x84973),x84972))+P1(f317(f317(f224(f906(x84971,a895)),f317(f73(f906(x84971,a895)),x84972)),f317(f73(f906(x84971,a895)),x84973))) % 112.26/112.10 [8532]E(f317(f300(a899,a899,f317(f317(f9(a899,a899,a899),f3(a899)),x85321)),f317(f292(a899,x85322),x85323)),f317(f292(a899,f317(f317(f3(a899),x85322),x85321)),f317(f317(f3(a899),x85323),x85321)))+~P1(f317(f317(f225(a899),x85321),x85323)) % 112.26/112.10 [8558]~P81(x85581)+E(f317(f317(f74(x85581),x85582),f317(f132(x85581,x85581,f74(x85581),f2(x85581)),x85583)),f317(f132(x85581,x85581,f74(x85581),x85582),x85583)) % 112.26/112.10 [8634]~P86(x86341)+P1(f317(f317(f224(x86341),f317(f70(x86341),f317(f317(f3(x86341),x86342),x86343))),f317(f317(f74(x86341),f317(f70(x86341),x86342)),f317(f70(x86341),x86343)))) % 112.26/112.10 [8635]~P86(x86351)+P1(f317(f317(f224(x86351),f317(f70(x86351),f317(f317(f74(x86351),x86352),x86353))),f317(f317(f74(x86351),f317(f70(x86351),x86352)),f317(f70(x86351),x86353)))) % 112.26/112.10 [8646]E(f317(f317(f74(a1),f317(f317(f75(a1),x86461),f41(a1,f317(f317(f31(a1),x86462),x86461),x86463))),f41(a1,x86462,x86461)),f41(a1,x86462,f317(f317(f75(a1),x86461),x86463)))+~P1(f317(f317(f225(a1),f2(a1)),x86463)) % 112.26/112.10 [8652]E(f317(f317(f124(x86521),f317(f317(f165(x86521),x86522),x86523)),f317(f317(f141(x86521),f317(f131(x86521),f317(f317(f128(x86521),x86522),x86523))),f103(x86521))),f317(f317(f165(x86521),f317(a102,x86522)),x86523))+~P1(f317(f317(f225(a899),x86522),f317(f179(f900(x86521)),x86523))) % 112.26/112.10 [8672]E(f317(f258(x86721,f317(f317(f144(x86721,f905(a89,x86721)),f317(f242(a89,x86721),f72(a89))),x86722)),f317(a5,x86723)),f317(f317(f154(x86721),x86722),x86723))+~P1(f317(f317(f225(a899),x86723),f317(f179(f900(x86721)),x86722))) % 112.26/112.10 [8740]P1(f317(f317(f319(f905(x87401,x87401)),x87402),f317(f317(f279(x87401,x87401,x87401),x87403),f297(x87401,x87403))))+~P1(f317(f317(f319(f905(x87401,x87401)),x87402),x87403)) % 112.26/112.10 [8751]E(f317(f300(x87511,x87512,x87513),f232(f906(x87511,a895))),f232(f906(x87512,a895)))+~E(f317(f67(x87511,x87512,x87512,x87513),f85(x87511,x87512,f232(f906(x87511,a895)),x87513)),f25(x87512)) % 112.26/112.10 [8760]P1(f317(f317(f224(a899),x87601),x87602))+~P1(f317(f317(f224(a899),f317(f317(f75(a899),f317(a102,x87603)),x87601)),f317(f317(f75(a899),f317(a102,x87603)),x87602))) % 112.26/112.10 [8776]P1(f317(f317(f224(f906(x87761,a895)),x87762),x87763))+~P1(f317(f317(f224(f906(x87761,a895)),f317(f73(f906(x87761,a895)),x87763)),f317(f73(f906(x87761,a895)),x87762))) % 112.26/112.10 [8799]P1(f317(f127(x87991),x87992))+~P1(f317(f127(x87991),f317(f317(f317(f173(f900(x87991),f900(x87991)),x87993),f157(x87991)),x87992))) % 112.26/112.10 [8872]E(f317(f275(x88721,x88721,f297(x88721,x88722)),x88723),x88723)+~P1(f317(f317(f224(f906(x88721,a895)),f317(f275(x88721,x88721,x88722),x88723)),x88723)) % 112.26/112.10 [8920]~P108(x89201)+P13(x89201,f317(f126(x89201,f317(f317(f9(x89201,x89201,a895),a314),f317(x89202,x89203))),x89203)) % 112.26/112.10 [8927]~P1(f317(f317(f224(a899),x89271),x89272))+P1(f317(f317(f224(a899),x89271),f317(f132(a899,a899,f74(a899),x89272),x89273))) % 112.26/112.10 [9013]~P1(f317(f317(f319(f905(x90131,x90131)),x90132),f297(x90131,x90133)))+P1(f317(f317(f319(f905(x90131,x90131)),x90132),f317(f317(f173(f905(x90131,x90131),a895),f604(x90133,x90132,x90131)),x90133))) % 112.26/112.10 [9094]~P81(x90941)+E(f317(f317(f74(x90941),x90942),f317(f132(x90941,x90941,f317(f9(x90941,x90941,x90941),f74(x90941)),f2(x90941)),f317(f158(x90941),x90943))),f317(f132(x90941,x90941,f74(x90941),x90942),x90943)) % 112.26/112.10 [9211]~P25(x92112,x92111,x92113,f232(f906(x92112,a895)),f232(f906(x92111,a895)))+E(f85(x92111,x92112,f232(f906(x92111,a895)),f85(x92112,x92111,f232(f906(x92112,a895)),x92113)),x92113) % 112.26/112.10 [9366]P54(x93661,x93662,x93663)+P1(f317(f317(f319(f905(x93661,x93662)),f317(f317(f242(x93661,x93662),f605(x93663,x93662,x93661)),f603(x93663,x93662,x93661))),x93663)) % 112.26/112.10 [9367]P54(x93671,x93672,x93673)+P1(f317(f317(f319(f905(x93671,x93672)),f317(f317(f242(x93671,x93672),f605(x93673,x93672,x93671)),f602(x93673,x93672,x93671))),x93673)) % 112.26/112.10 [9438]~P1(f317(f317(f319(f905(x94381,x94381)),x94382),f317(f317(f279(x94381,x94381,x94381),x94383),f297(x94381,x94383))))+P1(f317(f317(f319(f905(x94381,x94381)),x94382),f317(f317(f173(f905(x94381,x94381),a895),f606(x94383,x94382,x94381)),x94383))) % 112.26/112.10 [9439]~P1(f317(x94391,f317(f317(f154(x94392),x94393),f317(f179(f900(x94392)),f167(x94392,x94391,x94393)))))+~P1(f317(f317(f225(a899),f317(f179(f900(x94392)),f167(x94392,x94391,x94393))),f317(f179(f900(x94392)),x94393))) % 112.26/112.10 [9530]~P1(f317(f317(f224(f906(x95301,a895)),x95302),x95303))+P1(f317(f317(f224(f906(x95301,a895)),f317(f317(f9(x95301,f906(x95301,a895),a895),f319(x95301)),x95302)),f317(f317(f9(x95301,f906(x95301,a895),a895),f319(x95301)),x95303))) % 112.26/112.10 [9592]~P1(f317(f317(f319(f905(f906(x95921,a895),f906(x95921,a895))),f317(f317(f242(f906(x95921,a895),f906(x95921,a895)),x95922),x95923)),f304(x95921)))+P1(f317(f317(f225(f906(x95921,a895)),x95922),x95923)) % 112.26/112.10 [9620]P55(x96201,x96202,x96203)+~P1(f317(f317(f319(f905(x96201,x96201)),f317(f317(f242(x96201,x96201),f584(x96203,x96202,x96201)),f583(x96203,x96202,x96201))),x96203)) % 112.26/112.10 [9621]P55(x96211,x96212,x96213)+~P1(f317(f317(f319(f905(x96211,x96211)),f317(f317(f242(x96211,x96211),f583(x96213,x96212,x96211)),f584(x96213,x96212,x96211))),x96213)) % 112.26/112.10 [9659]~P1(f317(f317(f319(f905(f900(x96591),f900(x96591))),f317(f317(f242(f900(x96591),f900(x96591)),x96592),x96592)),f137(x96591,x96593)))+P1(f317(f317(f319(f905(x96591,x96591)),f317(f317(f242(x96591,x96591),f639(x96592,x96593,x96591)),f639(x96592,x96593,x96591))),x96593)) % 112.26/112.10 [9709]P1(f317(f317(f224(f906(x97091,a895)),x97092),x97093))+~P1(f317(f317(f224(f906(x97091,a895)),f317(f317(f9(x97091,f906(x97091,a895),a895),f319(x97091)),x97092)),f317(f317(f9(x97091,f906(x97091,a895),a895),f319(x97091)),x97093))) % 112.26/112.10 [9790]E(f317(f317(f3(a899),f317(f317(f8(a899,a899),x97901),f317(f272(a899),x97902))),f317(f317(f8(a899,a899),x97903),f317(f272(a899),x97902))),f317(f317(f8(a899,a899),f317(f317(f20(a899,a899,a899),f317(f317(f10(a899,f906(a899,a899),a899),f3(a899)),x97901)),x97903)),f317(f272(a899),x97902)))+~P1(f317(f317(f224(a899),f317(x97903,f461(x97902,x97901,x97903))),f317(x97901,f461(x97902,x97901,x97903)))) % 112.26/112.10 [5716]~P76(x57161)+E(f317(f317(f3(x57161),f317(f317(f74(x57161),x57162),x57163)),x57163),x57162) % 112.26/112.10 [5717]~P76(x57171)+E(f317(f317(f74(x57171),f317(f317(f3(x57171),x57172),x57173)),x57173),x57172) % 112.26/112.10 [5951]~P76(x59511)+E(f317(f317(f74(x59511),x59512),f317(f317(f74(x59511),f317(f73(x59511),x59512)),x59513)),x59513) % 112.26/112.10 [6040]~P80(x60401)+E(f317(f317(f75(x60401),f317(f317(f234(x60401),x60402),x60403)),x60402),f317(f317(f234(x60401),x60402),f317(a102,x60403))) % 112.26/112.10 [6041]~P119(x60411)+E(f317(f317(f75(x60411),f317(f317(f234(x60411),x60412),x60413)),x60412),f317(f317(f234(x60411),x60412),f317(a102,x60413))) % 112.26/112.10 [6265]~P112(x62651)+E(f317(f70(x62651),f317(f317(f234(x62651),f317(f73(x62651),x62652)),x62653)),f317(f70(x62651),f317(f317(f234(x62651),x62652),x62653))) % 112.26/112.10 [6311]~P80(x63111)+E(f317(f317(f75(x63111),f317(f317(f234(x63111),x63112),x63113)),x63112),f317(f317(f75(x63111),x63112),f317(f317(f234(x63111),x63112),x63113))) % 112.26/112.10 [6371]E(f317(f317(f3(a89),f317(f317(f74(a89),x63711),x63712)),x63713),f264(x63711,x63712,x63713))+~P1(f317(f317(f225(a89),x63712),x63713)) % 112.26/112.10 [6396]~E(f317(f317(f128(x63961),x63963),x63962),f103(x63961))+P1(f317(f317(f224(a899),f317(f179(f900(x63961)),x63962)),x63963)) % 112.26/112.10 [6535]E(f317(f317(f75(a899),f317(f94(a899),x65351)),f317(f317(f75(a899),f317(f94(a899),x65352)),x65353)),f2(a899))+~P1(f317(f317(f225(a1),x65351),a77)) % 112.26/112.10 [6551]~P61(x65511)+E(f317(f317(f234(x65511),f317(f317(f281(x65511),f72(x65511)),x65512)),x65513),f317(f317(f281(x65511),f72(x65511)),f317(f317(f234(x65511),x65512),x65513))) % 112.26/112.10 [6633]E(f317(f317(f3(a899),f317(f317(f74(a899),x66331),x66332)),x66333),f317(f317(f3(a899),x66331),f317(f317(f3(a899),x66333),x66332)))+~P1(f317(f317(f224(a899),x66332),x66333)) % 112.26/112.10 [6635]E(f317(f317(f3(a899),f317(f317(f74(a899),x66351),x66352)),x66353),f317(f317(f74(a899),x66351),f317(f317(f3(a899),x66352),x66353)))+~P1(f317(f317(f224(a899),x66353),x66352)) % 112.26/112.10 [6674]~P108(x66741)+P1(f317(f317(f224(x66741),f317(f317(f228(x66741),x66742),x66743)),x66743)) % 112.26/112.10 [6675]~P108(x66751)+P1(f317(f317(f224(x66751),f317(f317(f228(x66751),x66752),x66753)),x66752)) % 112.26/112.10 [6676]~P99(x66761)+P1(f317(f317(f224(x66761),f317(f317(f92(x66761),x66762),x66763)),x66763)) % 112.26/112.10 [6677]~P104(x66771)+P1(f317(f317(f224(x66771),f317(f317(f92(x66771),x66772),x66773)),x66773)) % 112.26/112.10 [6678]~P99(x66781)+P1(f317(f317(f224(x66781),f317(f317(f92(x66781),x66782),x66783)),x66782)) % 112.26/112.10 [6679]~P104(x66791)+P1(f317(f317(f224(x66791),f317(f317(f92(x66791),x66792),x66793)),x66792)) % 112.26/112.10 [6693]E(f317(f317(f31(a1),f317(f317(f31(a1),x66931),x66932)),x66933),f317(f317(f31(a1),x66931),f317(f317(f75(a1),x66932),x66933)))+~P1(f317(f317(f225(a1),f2(a1)),x66933)) % 112.26/112.10 [6747]~P119(x67471)+E(f317(f317(f74(x67471),f317(f317(f75(x67471),x67472),x67473)),x67473),f317(f317(f75(x67471),f317(f317(f74(x67471),x67472),f72(x67471))),x67473)) % 112.26/112.10 [6748]~P94(x67481)+E(f317(f317(f75(x67481),f317(f73(x67481),f317(f94(x67481),x67482))),x67483),f317(f317(f75(x67481),f317(f94(x67481),f317(f73(a1),x67482))),x67483)) % 112.26/112.10 [6821]~P81(x68211)+E(f317(f155(x68211),f317(f317(f144(x68212,x68211),f317(f18(x68211,x68212),f2(x68211))),x68213)),f2(x68211)) % 112.26/112.10 [6839]E(f317(f317(f74(a899),f317(f94(a899),x68391)),f317(f317(f74(a899),f317(f94(a899),x68392)),x68393)),f317(f317(f74(a899),f317(f94(a899),x68392)),x68393))+~P1(f317(a183,f317(f94(a1),x68391))) % 112.26/112.10 [6854]~P5(x68541)+E(f32(x68541,f317(f317(f299(x68541),x68542),f317(f317(f299(x68541),x68543),f178(f906(x68541,a895))))),f317(f317(f91(x68541),x68542),x68543)) % 112.26/112.10 [6855]~P5(x68551)+E(f33(x68551,f317(f317(f299(x68551),x68552),f317(f317(f299(x68551),x68553),f178(f906(x68551,a895))))),f317(f317(f92(x68551),x68552),x68553)) % 112.26/112.10 [6879]E(f317(f317(f165(x68791),x68792),x68793),x68793)+~P1(f317(f317(f224(a899),f317(f179(f900(x68791)),x68793)),x68792)) % 112.26/112.10 [6891]E(f317(f317(f128(x68911),x68912),x68913),f103(x68911))+~P1(f317(f317(f224(a899),f317(f179(f900(x68911)),x68913)),x68912)) % 112.26/112.10 [6902]E(f317(f317(f74(a899),f317(f317(f3(a899),x69021),x69022)),x69023),f317(f317(f3(a899),f317(f317(f74(a899),x69021),x69023)),x69022))+~P1(f317(f317(f224(a899),x69022),x69021)) % 112.26/112.10 [6916]~P1(f317(f317(f225(a899),x69161),x69163))+P1(f317(f317(f225(a899),f317(f317(f3(a899),x69161),x69162)),x69163)) % 112.26/112.10 [6943]~P108(x69431)+E(f160(x69431,x69432,f317(f317(f138(x69431,x69431,f7(x69431)),x69432),x69433)),x69433) % 112.26/112.10 [7036]E(f317(f317(f3(a899),f317(f317(f74(a899),x70361),x70362)),f317(a102,x70363)),f317(f317(f3(a899),x70361),f317(a102,f317(f317(f3(a899),x70363),x70362))))+~P1(f317(f317(f224(a899),x70362),x70363)) % 112.26/112.10 [7037]~P112(x70371)+P1(f317(f317(f224(x70371),f2(x70371)),f317(f317(f234(x70371),f317(f70(x70371),x70372)),x70373))) % 112.26/112.10 [7128]~P1(f317(f29(x71281),x71282))+P1(f317(f29(x71281),f317(f317(f3(f906(x71281,a895)),x71282),x71283))) % 112.26/112.10 [7129]~P1(f317(f29(x71291),x71293))+P1(f317(f29(x71291),f317(f317(f92(f906(x71291,a895)),x71292),x71293))) % 112.26/112.10 [7130]~P1(f317(f29(x71301),x71302))+P1(f317(f29(x71301),f317(f317(f92(f906(x71301,a895)),x71302),x71303))) % 112.26/112.10 [7271]~P36(x72711,x72713)+P36(x72711,f317(f317(f92(f906(f905(x72711,x72711),a895)),x72712),x72713)) % 112.26/112.10 [7272]~P36(x72721,x72722)+P36(x72721,f317(f317(f92(f906(f905(x72721,x72721),a895)),x72722),x72723)) % 112.26/112.10 [7393]~P108(x73931)+E(f16(x73931,f317(f162(x73931),f317(f317(f141(x73931),x73932),x73933))),f317(f132(x73931,x73931,f223(x73931),x73932),x73933)) % 112.26/112.10 [7394]~P108(x73941)+E(f17(x73941,f317(f162(x73941),f317(f317(f141(x73941),x73942),x73943))),f317(f132(x73941,x73941,f228(x73941),x73942),x73943)) % 112.26/112.10 [7395]~P99(x73951)+E(f12(x73951,f317(f162(x73951),f317(f317(f141(x73951),x73952),x73953))),f317(f132(x73951,x73951,f91(x73951),x73952),x73953)) % 112.26/112.10 [7396]~P99(x73961)+E(f13(x73961,f317(f162(x73961),f317(f317(f141(x73961),x73962),x73963))),f317(f132(x73961,x73961,f92(x73961),x73962),x73963)) % 112.26/112.10 [7460]~P1(f317(f29(x74601),x74602))+P1(f317(f317(f224(a899),f317(f30(x74601),x74602)),f317(f30(x74601),f317(f317(f299(x74601),x74603),x74602)))) % 112.26/112.10 [7467]E(f317(f317(f91(f906(a899,a895)),f317(f292(a899,x74671),x74672)),f317(f292(a899,x74672),f317(f317(f74(a899),x74672),x74673))),f317(f292(a899,x74671),f317(f317(f74(a899),x74672),x74673)))+~P1(f317(f317(f224(a899),x74671),x74672)) % 112.26/112.10 [7476]P1(f317(f317(f224(a899),x74761),x74762))+~P1(f317(f317(f224(a899),f317(f317(f74(a899),x74763),x74761)),x74762)) % 112.26/112.10 [7477]P1(f317(f317(f224(a899),x74771),x74772))+~P1(f317(f317(f224(a899),f317(f317(f74(a899),x74771),x74773)),x74772)) % 112.26/112.10 [7478]P1(f317(f317(f225(a899),x74781),x74782))+~P1(f317(f317(f225(a899),f317(f317(f74(a899),x74781),x74783)),x74782)) % 112.26/112.10 [7518]~P108(x75181)+E(f14(x75181,f223(x75181),f317(f162(x75181),f317(f317(f141(x75181),x75182),x75183))),f317(f132(x75181,x75181,f223(x75181),x75182),x75183)) % 112.26/112.10 [7519]~P108(x75191)+E(f15(x75191,f228(x75191),f317(f162(x75191),f317(f317(f141(x75191),x75192),x75193))),f317(f132(x75191,x75191,f228(x75191),x75192),x75193)) % 112.26/112.10 [7523]~E(x75232,f178(f906(f905(x75231,x75231),a895)))+P1(f317(f317(f224(f906(f905(x75231,x75231),a895)),x75232),x75233)) % 112.26/112.10 [7622]E(f317(f317(f91(f906(x76221,a895)),x76222),f317(f317(f3(f906(x76221,a895)),x76223),x76222)),x76223)+~P1(f317(f317(f224(f906(x76221,a895)),x76222),x76223)) % 112.26/112.10 [7625]~P1(f317(f317(f224(a899),x76251),f317(f317(f74(a899),x76253),x76252)))+P1(f317(f317(f224(a899),f317(f317(f3(a899),x76251),x76252)),x76253)) % 112.26/112.10 [7626]~P1(f317(f317(f225(a899),x76261),f317(f317(f3(a899),x76263),x76262)))+P1(f317(f317(f225(a899),f317(f317(f74(a899),x76261),x76262)),x76263)) % 112.26/112.10 [7683]E(x76831,f103(x76832))+E(f317(f131(x76832),f317(f317(f317(f173(f900(x76832),f900(x76832)),x76833),f157(x76832)),x76831)),f317(f317(f154(x76832),x76831),f41(a899,x76833,f317(f179(f900(x76832)),x76831)))) % 112.26/112.10 [7692]E(f317(f317(f299(x76921),x76922),f317(f317(f3(f906(x76921,a895)),x76923),f317(f317(f299(x76921),x76922),f178(f906(x76921,a895))))),x76923)+~P1(f317(f317(f319(x76921),x76922),x76923)) % 112.26/112.10 [7854]P1(f317(f317(f224(a899),x78541),f317(f317(f74(a899),x78542),x78543)))+~P1(f317(f317(f224(a899),f317(f317(f3(a899),x78541),x78543)),x78542)) % 112.26/112.10 [7855]P1(f317(f317(f225(a899),x78551),f317(f317(f3(a899),x78552),x78553)))+~P1(f317(f317(f225(a899),f317(f317(f74(a899),x78551),x78553)),x78552)) % 112.26/112.10 [7881]P1(f317(f29(x78811),x78812))+~P1(f317(f29(x78811),f317(f317(f91(f906(x78811,a895)),x78813),x78812))) % 112.26/112.10 [7882]P1(f317(f29(x78821),x78822))+~P1(f317(f29(x78821),f317(f317(f91(f906(x78821,a895)),x78822),x78823))) % 112.26/112.10 [7956]~P45(x79561,x79563)+P1(f317(f317(f319(f905(x79561,x79561)),f317(f317(f242(x79561,x79561),x79562),x79562)),x79563)) % 112.26/112.10 [8089]E(f317(f317(f154(a899),f129(a899,f317(f292(a899,x80891),x80892))),x80893),f317(f317(f74(a899),x80891),x80893))+~P1(f317(f317(f225(a899),f317(f317(f74(a899),x80891),x80893)),x80892)) % 112.26/112.10 [8155]E(f317(f317(f165(a899),x81551),f129(a899,f317(f292(a899,x81552),x81553))),f129(a899,f317(f292(a899,x81552),f317(f317(f74(a899),x81552),x81551))))+~P1(f317(f317(f224(a899),f317(f317(f74(a899),x81552),x81551)),x81553)) % 112.26/112.10 [8212]~P94(x82121)+E(f317(f317(f234(x82121),x82122),f317(f94(a899),f317(f317(f74(a1),x82123),x82123))),f317(f317(f80(x82121,x82121),f317(f317(f234(x82121),x82122),f317(f94(a899),x82123))),f317(f317(f20(x82121,x82121,x82121),f75(x82121)),f7(x82121)))) % 112.26/112.10 [8478]E(f317(f317(f124(x84781),f317(f317(f165(x84781),x84782),x84783)),f317(f317(f141(x84781),f317(f317(f154(x84781),x84783),x84782)),f317(f317(f128(x84781),f317(a102,x84782)),x84783))),x84783)+~P1(f317(f317(f225(a899),x84782),f317(f179(f900(x84781)),x84783))) % 112.26/112.10 [8485]P1(f317(f317(f224(f906(x84851,a895)),f305(x84851,x84852)),f305(x84851,x84853)))+~P1(f317(f317(f224(f906(x84851,f906(x84851,a895))),x84853),x84852)) % 112.26/112.10 [8486]~P55(x84861,x84862,x84863)+P55(x84861,x84862,f317(f317(f3(f906(f905(x84861,x84861),a895)),x84863),f297(x84861,f178(f906(f905(x84861,x84861),a895))))) % 112.26/112.10 [8505]P1(f317(f317(f224(f906(x85051,a895)),f306(x85051,x85052)),f306(x85051,x85053)))+~P1(f317(f317(f224(f906(f905(x85051,x85051),a895)),x85053),x85052)) % 112.26/112.10 [8511]~P1(f317(f317(f225(f906(x85111,a895)),x85113),x85112))+P1(f317(f317(f319(x85111),f444(x85112,x85113,x85111)),f317(f317(f3(f906(x85111,a895)),x85112),x85113))) % 112.26/112.10 [8513]~P128(x85131)+P1(f317(f317(f224(x85131),f2(x85131)),f317(f317(f74(x85131),f317(f317(f75(x85131),x85132),x85132)),f317(f317(f75(x85131),x85133),x85133)))) % 112.26/112.10 [8547]P1(f317(f317(f224(f906(x85471,a895)),f317(f271(x85471),x85472)),f317(f271(x85471),x85473)))+~P1(f317(f317(f224(f906(f905(x85471,x85471),a895)),x85472),x85473)) % 112.26/112.10 [8576]~P53(x85761,x85762)+~P1(f317(f317(f319(f905(x85761,x85761)),f317(f317(f242(x85761,x85761),x85763),x85763)),x85762)) % 112.26/112.10 [8578]~P36(x85781,x85782)+~P1(f317(f317(f319(f905(x85781,x85781)),f317(f317(f242(x85781,x85781),x85783),x85783)),x85782)) % 112.26/112.10 [8636]P1(f317(f317(f224(f906(x86361,a895)),f32(f906(x86361,a895),x86362)),f32(f906(x86361,a895),x86363)))+~P1(f317(f317(f224(f906(f906(x86361,a895),a895)),x86362),x86363)) % 112.26/112.10 [8637]P1(f317(f317(f224(f906(x86371,a895)),f33(f906(x86371,a895),x86372)),f33(f906(x86371,a895),x86373)))+~P1(f317(f317(f224(f906(f906(x86371,a895),a895)),x86373),x86372)) % 112.26/112.10 [8691]~P8(x86911,x86913,x86912)+P1(f317(f317(f224(f906(f905(x86911,x86911),a895)),x86912),f317(f317(f244(x86911,x86911),x86913),f317(f18(f906(x86911,a895),x86911),x86913)))) % 112.26/112.10 [8692]~P52(x86921,x86923,x86922)+P1(f317(f317(f224(f906(f905(x86921,x86921),a895)),x86922),f317(f317(f244(x86921,x86921),x86923),f317(f18(f906(x86921,a895),x86921),x86923)))) % 112.26/112.10 [8741]~P86(x87411)+P1(f317(f317(f224(x87411),f317(f317(f3(x87411),f317(f70(x87411),x87412)),f317(f70(x87411),x87413))),f317(f70(x87411),f317(f317(f3(x87411),x87413),x87412)))) % 112.26/112.10 [8742]~P86(x87421)+P1(f317(f317(f224(x87421),f317(f317(f3(x87421),f317(f70(x87421),x87422)),f317(f70(x87421),x87423))),f317(f70(x87421),f317(f317(f3(x87421),x87422),x87423)))) % 112.26/112.10 [8774]P1(f317(f317(f224(f906(f905(x87741,x87741),a895)),f297(x87741,x87742)),f297(x87741,x87743)))+~P1(f317(f317(f224(f906(f905(x87741,x87741),a895)),x87742),x87743)) % 112.26/112.10 [8885]~P24(x88852,x88851,x88853,f232(f906(x88852,a895)))+E(f317(f67(x88851,x88852,x88852,f85(x88852,x88851,f232(f906(x88852,a895)),x88853)),x88853),f25(x88852)) % 112.26/112.10 [8945]P55(x89451,x89452,x89453)+~P55(x89451,x89452,f317(f317(f3(f906(f905(x89451,x89451),a895)),x89453),f297(x89451,f178(f906(f905(x89451,x89451),a895))))) % 112.26/112.10 [8965]P1(f317(f317(f224(f906(f905(f900(x89651),f900(x89651)),a895)),f147(x89651,x89652)),f147(x89651,x89653)))+~P1(f317(f317(f224(f906(f905(x89651,x89651),a895)),x89652),x89653)) % 112.26/112.10 [8966]P1(f317(f317(f224(f906(f905(f900(x89661),f900(x89661)),a895)),f148(x89661,x89662)),f148(x89661,x89663)))+~P1(f317(f317(f224(f906(f905(x89661,x89661),a895)),x89662),x89663)) % 112.26/112.10 [8987]~P52(x89871,x89873,x89872)+P1(f317(f317(f224(f906(f905(x89871,x89871),a895)),x89872),f317(f317(f279(x89871,x89871,x89871),f317(f276(x89871,x89871),x89872)),x89872))) % 112.26/112.10 [9039]~P1(f317(f127(x90391),x90392))+E(f317(f126(x90391,f317(f317(f9(x90391,f906(x90391,a895),a895),f319(x90391)),f317(f162(x90391),f166(x90391,x90392,x90393)))),x90392),f166(x90391,x90392,x90393)) % 112.26/112.10 [9092]E(x90921,x90922)+~P1(f317(f317(f319(f905(x90923,x90923)),f317(f317(f242(x90923,x90923),x90921),x90922)),f297(x90923,f178(f906(f905(x90923,x90923),a895))))) % 112.26/112.10 [9174]P1(f317(f317(f319(x91741),x91742),f306(x91741,x91743)))+P1(f317(f317(f319(f905(x91741,x91741)),f317(f317(f242(x91741,x91741),f513(x91743,x91742,x91741)),x91742)),x91743)) % 112.26/112.10 [9175]P1(f317(f317(f319(x91751),x91752),f306(x91751,x91753)))+P1(f317(f317(f319(f905(x91751,x91751)),f317(f317(f242(x91751,x91751),f589(x91753,x91752,x91751)),x91752)),x91753)) % 112.26/112.10 [9176]P1(f317(f317(f319(x91761),x91762),f306(x91761,x91763)))+P1(f317(f317(f319(f905(x91761,x91761)),f317(f317(f242(x91761,x91761),f591(x91763,x91762,x91761)),x91762)),x91763)) % 112.26/112.10 [9212]P24(x92121,x92122,x92123,f232(f906(x92121,a895)))+~E(f317(f67(x92122,x92121,x92121,f85(x92121,x92122,f232(f906(x92121,a895)),x92123)),x92123),f25(x92121)) % 112.26/112.10 [9265]~P1(f317(f317(f319(f900(x92651)),x92653),f151(x92651,x92652)))+P1(f317(f150(x92651,f317(f317(f9(x92651,f906(x92651,a895),a895),f319(x92651)),x92652)),x92653)) % 112.26/112.10 [9288]P1(f317(x92883,x92882))+E(f317(f252(x92881),f317(f317(f20(x92881,a895,a895),f317(f317(f10(a895,f906(a895,a895),x92881),a315),f317(a314,x92882))),x92883)),f178(f906(x92881,a895))) % 112.26/112.10 [9305]~P86(x93051)+P1(f317(f317(f224(x93051),f317(f70(x93051),f317(f317(f3(x93051),f317(f70(x93051),x93052)),f317(f70(x93051),x93053)))),f317(f70(x93051),f317(f317(f3(x93051),x93052),x93053)))) % 112.26/112.10 [9319]~P1(f317(x93193,x93192))+E(f317(f252(x93191),f317(f317(f20(x93191,a895,a895),f317(f317(f10(a895,f906(a895,a895),x93191),a315),f317(a314,x93192))),x93193)),f317(f317(f299(x93191),x93192),f178(f906(x93191,a895)))) % 112.26/112.10 [9328]~P1(f317(f317(f319(f906(x93281,a895)),x93283),f317(f298(x93281),x93282)))+P1(f317(f238(x93281,f317(f317(f9(x93281,f906(x93281,a895),a895),f319(x93281)),x93282)),x93283)) % 112.26/112.10 [9365]P36(x93651,x93652)+P1(f317(f317(f319(f905(x93651,x93651)),f317(f317(f242(x93651,x93651),f317(f550(x93652,x93651),f317(a102,x93653))),f317(f550(x93652,x93651),x93653))),x93652)) % 112.26/112.10 [9507]P1(f317(f317(f319(f900(x95071)),x95072),f151(x95071,x95073)))+~P1(f317(f150(x95071,f317(f317(f9(x95071,f906(x95071,a895),a895),f319(x95071)),x95073)),x95072)) % 112.26/112.10 [9522]P1(f317(f317(f319(f906(x95221,a895)),x95222),f317(f298(x95221),x95223)))+~P1(f317(f238(x95221,f317(f317(f9(x95221,f906(x95221,a895),a895),f319(x95221)),x95223)),x95222)) % 112.26/112.10 [9587]P1(f317(f317(f319(x95871),f317(f258(x95871,x95872),x95873)),f317(f162(x95871),f317(f317(f144(f905(a89,x95871),x95871),f246(a89,x95871)),x95872))))+~P1(f317(f317(f225(a89),x95873),f317(f155(a89),f317(f317(f144(f905(a89,x95871),a89),f241(a89,x95871)),x95872)))) % 112.26/112.10 [9637]P1(f317(f317(f224(f906(f905(f900(x96371),f900(x96371)),a895)),f148(x96371,x96372)),f317(f317(f244(f900(x96371),f900(x96371)),f151(x96371,x96373)),f317(f18(f906(f900(x96371),a895),f900(x96371)),f151(x96371,x96373)))))+~P1(f317(f317(f224(f906(f905(x96371,x96371),a895)),x96372),f317(f317(f244(x96371,x96371),x96373),f317(f18(f906(x96371,a895),x96371),x96373)))) % 112.26/112.10 [9662]P1(f317(f317(f319(x96621),f317(f241(x96621,f905(a89,a89)),f317(f256(x96621,x96622),x96623))),f317(f162(x96621),f317(f317(f144(f905(a89,x96621),x96621),f246(a89,x96621)),x96622))))+~P1(f317(f317(f225(a89),f2(a89)),f317(f155(a89),f317(f317(f144(f905(a89,x96621),a89),f241(a89,x96621)),x96622)))) % 112.26/112.10 [9677]~P1(f317(f317(f224(f906(f905(x96771,x96771),a895)),x96772),f317(f317(f244(x96771,x96771),x96773),f317(f18(f906(x96771,a895),x96771),x96773))))+P1(f317(f317(f224(f906(f905(x96771,x96771),a895)),f317(f317(f279(x96771,x96771,x96771),x96772),f297(x96771,x96772))),f317(f317(f244(x96771,x96771),x96773),f317(f18(f906(x96771,a895),x96771),x96773)))) % 112.26/112.10 [9977]~P36(x99771,x99772)+~P1(f317(f317(f319(f905(x99771,x99771)),f317(f317(f242(x99771,x99771),f317(x99773,f317(a102,f551(x99772,x99771,x99773)))),f317(x99773,f551(x99772,x99771,x99773)))),x99772)) % 112.26/112.10 [9978]~P36(x99781,x99782)+~P1(f317(f317(f319(f905(x99781,x99781)),f317(f317(f242(x99781,x99781),f317(x99783,f317(a102,f594(x99783,x99782,x99781)))),f317(x99783,f594(x99783,x99782,x99781)))),x99782)) % 112.26/112.10 [10234]P1(f317(f317(f224(f906(f905(f906(x102341,a895),f906(x102341,a895)),a895)),f317(f317(f279(f906(x102341,a895),f906(x102341,a895),f906(x102341,a895)),f308(x102341,x102342)),f317(f317(f91(f906(f905(f906(x102341,a895),f906(x102341,a895)),a895)),f308(x102341,x102343)),f317(f317(f299(f905(f906(x102341,a895),f906(x102341,a895))),f317(f317(f242(f906(x102341,a895),f906(x102341,a895)),f178(f906(x102341,a895))),f178(f906(x102341,a895)))),f178(f906(f905(f906(x102341,a895),f906(x102341,a895)),a895)))))),f308(x102341,x102342)))+~P1(f317(f317(f224(f906(f905(x102341,x102341),a895)),f317(f317(f279(x102341,x102341,x102341),x102342),x102343)),x102342)) % 112.26/112.10 [10235]P1(f317(f317(f224(f906(f905(f906(x102351,a895),f906(x102351,a895)),a895)),f317(f317(f279(f906(x102351,a895),f906(x102351,a895),f906(x102351,a895)),f309(x102351,x102352)),f317(f317(f91(f906(f905(f906(x102351,a895),f906(x102351,a895)),a895)),f309(x102351,x102353)),f317(f317(f299(f905(f906(x102351,a895),f906(x102351,a895))),f317(f317(f242(f906(x102351,a895),f906(x102351,a895)),f178(f906(x102351,a895))),f178(f906(x102351,a895)))),f178(f906(f905(f906(x102351,a895),f906(x102351,a895)),a895)))))),f309(x102351,x102352)))+~P1(f317(f317(f224(f906(f905(x102351,x102351),a895)),f317(f317(f279(x102351,x102351,x102351),x102352),x102353)),x102352)) % 112.26/112.10 [7392]~P1(f317(f317(f224(a899),x73922),x73921))+E(f317(f317(f3(a899),f317(a102,f317(f317(f3(a899),x73921),x73922))),x73923),f317(f317(f3(a899),f317(a102,x73921)),f317(f317(f74(a899),x73922),x73923))) % 112.26/112.10 [7432]~P3(x74321)+E(f317(f317(f74(x74321),f41(x74321,x74322,x74323)),f317(f317(f75(x74321),f317(f317(f31(x74321),x74322),x74323)),x74323)),x74322) % 112.26/112.10 [7630]E(f317(f317(f75(a899),f317(f94(a899),x76301)),f317(f317(f75(a899),f317(f94(a899),x76302)),x76303)),f317(f317(f75(a899),f317(f94(a899),f317(f317(f75(a1),x76301),x76302))),x76303))+P1(f317(f317(f225(a1),x76301),a77)) % 112.26/112.10 [8098]~P1(f317(f317(f224(a899),x80983),x80982))+P1(f317(f317(f224(a899),x80981),f317(f317(f3(a899),f317(f317(f74(a899),x80982),x80981)),x80983))) % 112.26/112.10 [8298]~P1(f317(f317(f224(a899),x82981),x82982))+E(f317(f317(f124(a899),f129(a899,f317(f292(a899,x82981),x82982))),f129(a899,f317(f292(a899,x82982),f317(f317(f74(a899),x82982),x82983)))),f129(a899,f317(f292(a899,x82981),f317(f317(f74(a899),x82982),x82983)))) % 112.26/112.10 [8555]~P1(f317(f29(x85551),x85552))+E(f317(a102,f317(f30(x85551),f317(f317(f3(f906(x85551,a895)),x85552),f317(f317(f299(x85551),x85553),f178(f906(x85551,a895)))))),f317(f30(x85551),f317(f317(f299(x85551),x85553),x85552))) % 112.26/112.10 [8594]~P1(f317(f29(x85941),x85942))+E(f317(f317(f74(a899),f72(a899)),f317(f30(x85941),f317(f317(f3(f906(x85941,a895)),x85942),f317(f317(f299(x85941),x85943),f178(f906(x85941,a895)))))),f317(f30(x85941),f317(f317(f299(x85941),x85943),x85942))) % 112.26/112.10 [8783]E(f317(f317(f3(a899),f317(f30(x87831),x87832)),f317(f30(x87831),f317(f317(f92(f906(x87831,a895)),x87832),x87833))),f317(f30(x87831),f317(f317(f3(f906(x87831,a895)),x87832),x87833)))+~P1(f317(f29(x87831),f317(f317(f92(f906(x87831,a895)),x87832),x87833))) % 112.26/112.10 [9034]~P6(f317(x90342,f445(x90342,x90343,x90341)))+E(f317(f90(a1),f317(f317(f8(x90341,a899),f317(f317(f10(a1,a899,x90341),a95),x90342)),x90343)),f317(f317(f8(x90341,a1),x90342),x90343)) % 112.26/112.10 [9035]~P6(f317(x90352,f446(x90352,x90353,x90351)))+E(f317(f90(a1),f317(f317(f11(x90351,a899),f317(f317(f10(a1,a899,x90351),a95),x90352)),x90353)),f317(f317(f11(x90351,a1),x90352),x90353)) % 112.26/112.10 [9075]~P1(f317(f29(x90751),x90753))+P1(f317(f317(f224(a899),f317(f317(f3(a899),f317(f30(x90751),x90752)),f317(f30(x90751),x90753))),f317(f30(x90751),f317(f317(f3(f906(x90751,a895)),x90752),x90753)))) % 112.26/112.10 [9102]P1(f317(f317(f319(x91021),f445(x91022,x91023,x91021)),x91023))+E(f317(f90(a1),f317(f317(f8(x91021,a899),f317(f317(f10(a1,a899,x91021),a95),x91022)),x91023)),f317(f317(f8(x91021,a1),x91022),x91023)) % 112.26/112.10 [9103]P1(f317(f317(f319(x91031),f446(x91032,x91033,x91031)),x91033))+E(f317(f90(a1),f317(f317(f11(x91031,a899),f317(f317(f10(a1,a899,x91031),a95),x91032)),x91033)),f317(f317(f11(x91031,a1),x91032),x91033)) % 112.26/112.10 [9166]E(f79(x91661,f317(f317(f9(x91661,f906(x91661,a895),a895),f319(x91661)),f317(f317(f3(f906(x91661,a895)),x91662),f317(f317(f299(x91661),x91663),f178(f906(x91661,a895)))))),f237(x91661,x91663,x91662))+P1(f317(f317(f224(f906(x91661,a895)),x91662),f317(f317(f299(x91661),x91663),f178(f906(x91661,a895))))) % 112.26/112.10 [9523]E(f317(f317(f144(f900(x95231),x95231),f317(f317(f9(f900(x95231),a899,x95231),f154(x95231)),x95232)),f317(f126(f900(x95231),f317(f317(f10(a899,a895,f900(x95231)),f317(f225(a899),x95232)),f179(f900(x95231)))),x95233)),f317(f317(f154(f900(x95231)),f169(x95231,x95233)),x95232))+~P1(f317(f317(f225(a899),x95232),f317(f179(f900(f900(x95231))),f169(x95231,x95233)))) % 112.26/112.10 [9610]E(f317(f126(x96101,x96102),x96103),f167(x96101,x96102,x96103))+P1(f317(f317(f319(x96101),f704(x96103,x96102,x96101)),f317(f162(x96101),f317(f317(f128(x96101),f317(f179(f900(x96101)),f167(x96101,x96102,x96103))),x96103)))) % 112.26/112.10 [9750]E(f317(f317(f128(x97501),f317(f179(f900(x97501)),f167(x97501,x97502,x97503))),x97503),f103(x97501))+~P1(f317(x97502,f317(f131(x97501),f317(f317(f128(x97501),f317(f179(f900(x97501)),f167(x97501,x97502,x97503))),x97503)))) % 112.26/112.10 [9842]~P1(f317(f317(f319(f905(x98421,x98421)),x98422),f297(x98421,x98423)))+P1(f317(f317(f319(f905(x98421,x98421)),x98422),f317(f317(f36(a899,f906(f905(x98421,x98421),a895)),f232(f906(a899,a895))),f317(f317(f9(a899,f906(f905(x98421,x98421),a895),f906(f905(x98421,x98421),a895)),f173(f905(x98421,x98421),a895)),x98423)))) % 112.26/112.10 [9904]~P1(f317(f317(f224(f906(x99041,a895)),f317(f317(f36(a899,f906(x99041,a895)),f317(f292(a899,f2(a899)),f488(x99043,x99042,x99041))),x99042)),x99043))+P1(f317(f317(f224(f906(x99041,a895)),f317(f317(f36(a899,f906(x99041,a895)),f232(f906(a899,a895))),x99042)),x99043)) % 112.26/112.10 [9950]~P1(f317(f317(f225(a1),f2(a1)),x99503))+P1(f317(f317(f225(a1),x99501),f317(f317(f74(a1),x99502),f317(f317(f75(a1),f317(f317(f74(a1),f317(f70(a1),f317(f317(f3(a1),x99502),x99501))),f72(a1))),x99503)))) % 112.26/112.10 [9964]~P36(x99641,f317(f317(f91(f906(f905(x99641,x99641),a895)),x99642),x99643))+P36(x99641,f317(f317(f91(f906(f905(x99641,x99641),a895)),f317(f317(f91(f906(f905(x99641,x99641),a895)),f317(f317(f279(x99641,x99641,x99641),x99642),x99642)),f317(f317(f279(x99641,x99641,x99641),x99643),x99642))),x99643)) % 112.26/112.10 [10039]P36(x100391,f317(f317(f91(f906(f905(x100391,x100391),a895)),x100392),x100393))+~P36(x100391,f317(f317(f91(f906(f905(x100391,x100391),a895)),f317(f317(f91(f906(f905(x100391,x100391),a895)),f317(f317(f279(x100391,x100391,x100391),x100392),x100392)),f317(f317(f279(x100391,x100391,x100391),x100393),x100392))),x100393)) % 112.26/112.10 [9614]~P141(x96141)+E(f317(f93(x96141),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x96142),x96143)),f178(f906(f905(a899,a899),a895)))))),f317(f317(f3(x96141),f317(f90(x96141),x96142)),f317(f90(x96141),x96143))) % 112.26/112.10 [9697]P1(f317(x96973,x96972))+E(f317(f252(x96971),f317(f317(f20(x96971,a895,a895),f317(f317(f10(a895,f906(a895,a895),x96971),a315),f317(f317(f9(x96971,x96971,a895),a314),x96972))),x96973)),f178(f906(x96971,a895))) % 112.26/112.10 [9699]~P1(f317(x96993,x96992))+E(f317(f252(x96991),f317(f317(f20(x96991,a895,a895),f317(f317(f10(a895,f906(a895,a895),x96991),a315),f317(f317(f9(x96991,x96991,a895),a314),x96992))),x96993)),f317(f317(f299(x96991),x96992),f178(f906(x96991,a895)))) % 112.26/112.10 [9930]E(x99301,x99302)+P1(f317(f317(f233(x99303,x99303,f317(f317(f10(f906(x99303,a895),f906(x99303,a895),x99303),f317(f10(a895,a895,x99303),a312)),a314)),x99301),x99302)) % 112.26/112.10 [10019]~E(x100191,x100192)+~P1(f317(f317(f233(x100193,x100193,f317(f317(f10(f906(x100193,a895),f906(x100193,a895),x100193),f317(f10(a895,a895,x100193),a312)),a314)),x100191),x100192)) % 112.26/112.10 [10031]~P1(f317(f29(x100311),x100313))+E(f317(f317(f59(x100311,f906(x100311,a895),f317(f317(f10(f906(x100311,a895),f906(f906(x100311,a895),f906(x100311,a895)),x100311),f317(f9(f906(x100311,a895),f906(x100311,a895),f906(x100311,a895)),f3(f906(x100311,a895)))),f317(f317(f9(x100311,f906(x100311,a895),f906(x100311,a895)),f299(x100311)),f178(f906(x100311,a895))))),x100312),x100313),f317(f317(f3(f906(x100311,a895)),x100312),x100313)) % 112.26/112.10 [10061]~P1(f317(f317(f225(a1),f2(a1)),x100613))+P1(f317(f317(f225(a1),f317(f317(f3(a1),x100611),f317(f317(f75(a1),f317(f317(f74(a1),f317(f70(a1),f317(f317(f3(a1),x100611),x100612))),f72(a1))),x100613))),x100612)) % 112.26/112.10 [10324]~P1(f317(f317(f319(x103241),x103243),f306(x103241,x103242)))+P1(f317(f305(x103241,f317(f317(f9(x103241,f906(f905(x103241,x103241),a895),f906(x103241,a895)),f317(f317(f10(f906(x103241,f906(f906(f905(x103241,x103241),a895),a895)),f906(f906(f905(x103241,x103241),a895),f906(x103241,a895)),x103241),f9(x103241,f906(f905(x103241,x103241),a895),a895)),f317(f317(f10(f906(x103241,f905(x103241,x103241)),f906(x103241,f906(f906(f905(x103241,x103241),a895),a895)),x103241),f317(f10(f905(x103241,x103241),f906(f906(f905(x103241,x103241),a895),a895),x103241),f319(f905(x103241,x103241)))),f242(x103241,x103241)))),x103242)),x103243)) % 112.26/112.10 [10337]P1(f317(f317(f319(x103371),x103372),f306(x103371,x103373)))+~P1(f317(f305(x103371,f317(f317(f9(x103371,f906(f905(x103371,x103371),a895),f906(x103371,a895)),f317(f317(f10(f906(x103371,f906(f906(f905(x103371,x103371),a895),a895)),f906(f906(f905(x103371,x103371),a895),f906(x103371,a895)),x103371),f9(x103371,f906(f905(x103371,x103371),a895),a895)),f317(f317(f10(f906(x103371,f905(x103371,x103371)),f906(x103371,f906(f906(f905(x103371,x103371),a895),a895)),x103371),f317(f10(f905(x103371,x103371),f906(f906(f905(x103371,x103371),a895),a895),x103371),f319(f905(x103371,x103371)))),f242(x103371,x103371)))),x103373)),x103372)) % 112.26/112.10 [9902]~P1(f317(f29(x99021),f317(f252(x99021),x99023)))+P1(f317(f29(x99021),f317(f252(x99021),f317(f317(f20(x99021,a895,a895),f317(f317(f10(a895,f906(a895,a895),x99021),a315),x99022)),x99023)))) % 112.26/112.10 [9903]~P1(f317(f29(x99031),f317(f252(x99031),x99032)))+P1(f317(f29(x99031),f317(f252(x99031),f317(f317(f20(x99031,a895,a895),f317(f317(f10(a895,f906(a895,a895),x99031),a315),x99032)),x99033)))) % 112.26/112.10 [9998]P1(f317(f29(x99981),f317(f252(x99981),x99982)))+~P1(f317(f29(x99981),f317(f252(x99981),f317(f317(f20(x99981,a895,a895),f317(f317(f10(a895,f906(a895,a895),x99981),a316),x99983)),x99982)))) % 112.26/112.10 [9999]P1(f317(f29(x99991),f317(f252(x99991),x99992)))+~P1(f317(f29(x99991),f317(f252(x99991),f317(f317(f20(x99991,a895,a895),f317(f317(f10(a895,f906(a895,a895),x99991),a316),x99992)),x99993)))) % 112.26/112.10 [10303]~P1(f317(f29(x103031),x103032))+P1(f317(f29(f900(x103031)),f317(f252(f900(x103031)),f317(f317(f20(f900(x103031),a895,a895),f317(f317(f10(a895,f906(a895,a895),f900(x103031)),a315),f317(f317(f9(f900(x103031),f906(x103031,a895),a895),f317(f317(f10(f906(x103031,a895),f906(f906(x103031,a895),a895),f900(x103031)),f224(f906(x103031,a895))),f162(x103031))),x103032))),f317(f317(f9(f900(x103031),a899,a895),f317(f317(f10(a899,f906(a899,a895),f900(x103031)),a314),f179(f900(x103031)))),x103033))))) % 112.26/112.10 [10304]~P1(f317(f29(x103041),x103042))+P1(f317(f29(f900(x103041)),f317(f252(f900(x103041)),f317(f317(f20(f900(x103041),a895,a895),f317(f317(f10(a895,f906(a895,a895),f900(x103041)),a315),f317(f317(f9(f900(x103041),f906(x103041,a895),a895),f317(f317(f10(f906(x103041,a895),f906(f906(x103041,a895),a895),f900(x103041)),f224(f906(x103041,a895))),f162(x103041))),x103042))),f317(f317(f9(f900(x103041),a899,a895),f317(f317(f10(a899,f906(a899,a895),f900(x103041)),f224(a899)),f179(f900(x103041)))),x103043))))) % 112.26/112.10 [10012]~P119(x100121)+E(f317(f317(f234(x100121),x100122),f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100123)),f317(f317(f75(x100121),f317(f317(f234(x100121),x100122),x100123)),f317(f317(f234(x100121),x100122),x100123))) % 112.26/112.10 [10042]~P80(x100421)+E(f317(f317(f234(x100421),f317(f317(f234(x100421),x100422),x100423)),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f234(x100421),x100422),f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100423))) % 112.26/112.10 [10099]~P141(x100991)+E(f317(f317(f234(x100991),f317(f73(x100991),x100992)),f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100993)),f317(f317(f234(x100991),x100992),f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100993))) % 112.26/112.10 [10242]~P112(x102421)+P1(f317(f317(f224(x102421),f2(x102421)),f317(f317(f74(x102421),f317(f317(f234(x102421),x102422),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102421),x102423),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))))) % 112.26/112.10 [10109]~P119(x101091)+E(f317(f317(f234(x101091),x101092),f317(a102,f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101093))),f317(f317(f75(x101091),x101092),f317(f317(f75(x101091),f317(f317(f234(x101091),x101092),x101093)),f317(f317(f234(x101091),x101092),x101093)))) % 112.26/112.10 [10159]~P80(x101591)+E(f317(f317(f75(x101591),x101592),f317(f317(f234(x101591),f317(f317(f234(x101591),x101592),x101593)),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x101591),x101592),f317(a102,f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101593)))) % 112.26/112.10 [10199]~P112(x101991)+P1(f317(f317(f224(x101991),f2(x101991)),f317(f317(f234(x101991),x101992),f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101993)))) % 112.26/112.10 [10279]~P94(x102791)+E(f317(f317(f3(x102791),f317(f317(f74(x102791),f317(f317(f234(x102791),x102792),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102791),x102793),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f317(f317(f75(x102791),f317(f317(f75(x102791),f317(f94(x102791),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102792)),x102793)),f317(f317(f234(x102791),f317(f317(f3(x102791),x102792),x102793)),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))) % 112.26/112.10 [10280]~P94(x102801)+E(f317(f317(f74(x102801),f317(f317(f74(x102801),f317(f317(f234(x102801),x102802),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102801),x102803),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f317(f317(f75(x102801),f317(f317(f75(x102801),f317(f94(x102801),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102802)),x102803)),f317(f317(f234(x102801),f317(f317(f74(x102801),x102802),x102803)),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))) % 112.26/112.10 [7898]P24(x78981,x78982,x78983,x78984)+~E(f506(x78984,x78983,x78982,x78981),f507(x78984,x78983,x78982,x78981)) % 112.26/112.10 [8189]P33(x81891,x81892,x81893,x81894,f103(x81892))+~E(x81894,f103(x81891)) % 112.26/112.10 [8190]P33(x81901,x81902,x81903,f103(x81901),x81904)+~E(x81904,f103(x81902)) % 112.26/112.10 [8731]~P33(x87312,x87313,x87314,x87311,f103(x87313))+E(x87311,f103(x87312)) % 112.26/112.10 [8732]~P33(x87323,x87322,x87324,f103(x87323),x87321)+E(x87321,f103(x87322)) % 112.26/112.10 [5135]~P17(x51353,x51351,x51354)+E(f317(f317(x51351,x51352),x51352),x51352) % 112.26/112.10 [5381]P1(f317(x53812,x53814))+E(f317(f126(x53811,x53812),f159(x53811,x53813,x53814)),f103(x53811)) % 112.26/112.10 [5419]~E(x54194,f178(f906(x54191,a895)))+E(f317(f300(x54191,x54192,x54193),x54194),f178(f906(x54192,a895))) % 112.26/112.10 [5665]~P1(f317(x56652,x56654))+E(f317(f126(x56651,x56652),f159(x56651,x56653,x56654)),f159(x56651,x56653,x56654)) % 112.26/112.10 [5695]~E(f317(f300(x56952,x56953,x56954),x56951),f178(f906(x56953,a895)))+E(x56951,f178(f906(x56952,a895))) % 112.26/112.10 [5882]~P7(x58821,x58823)+E(f261(x58821,x58822,f260(x58821,x58823),x58824),x58824) % 112.26/112.10 [5998]~P108(x59982)+E(f317(f317(f138(x59981,x59982,x59983),x59984),f103(x59981)),f317(f317(f141(x59981),x59984),f103(x59981))) % 112.26/112.10 [6365]~E(x63651,f178(f906(x63652,a895)))+~P1(f317(f57(x63652,x63653,x63651),x63654)) % 112.26/112.10 [6388]~P58(x63881,x63883,x63884,x63882)+P1(f317(f29(x63881),x63882)) % 112.26/112.10 [6390]~P58(x63901,x63903,x63902,x63904)+P1(f317(f29(x63901),x63902)) % 112.26/112.10 [6398]~P58(x63982,x63983,x63984,x63981)+~E(x63981,f178(f906(x63982,a895))) % 112.26/112.10 [6432]~P109(x64321)+E(f317(f317(f92(f906(x64321,a895)),f317(f292(x64321,x64322),x64323)),f293(x64321,x64323,x64324)),f178(f906(x64321,a895))) % 112.26/112.10 [6459]~P1(f317(f317(x64593,x64594),x64592))+P1(f317(f317(f319(x64591),x64592),f284(x64591,x64593,x64594))) % 112.26/112.10 [6460]~P1(f317(f317(x64603,x64604),x64602))+P1(f317(f317(f319(x64601),x64602),f285(x64601,x64603,x64604))) % 112.26/112.10 [6461]~P1(f317(f317(x64613,x64612),x64614))+P1(f317(f317(f319(x64611),x64612),f286(x64611,x64613,x64614))) % 112.26/112.10 [6462]~P1(f317(f317(x64623,x64622),x64624))+P1(f317(f317(f319(x64621),x64622),f288(x64621,x64623,x64624))) % 112.26/112.10 [6608]~P109(x66081)+E(f317(f317(f92(f906(x66081,a895)),f296(x66081,x66082,x66083)),f293(x66081,x66083,x66084)),f178(f906(x66081,a895))) % 112.26/112.10 [6609]~P109(x66091)+E(f317(f317(f92(f906(x66091,a895)),f293(x66091,x66092,x66093)),f296(x66091,x66093,x66094)),f178(f906(x66091,a895))) % 112.26/112.10 [6610]~P109(x66101)+E(f317(f317(f92(f906(x66101,a895)),f293(x66101,x66102,x66103)),f295(x66101,x66103,x66104)),f178(f906(x66101,a895))) % 112.26/112.10 [6611]~P109(x66111)+E(f317(f317(f92(f906(x66111,a895)),f295(x66111,x66112,x66113)),f296(x66111,x66113,x66114)),f178(f906(x66111,a895))) % 112.26/112.10 [6612]~P109(x66121)+E(f317(f317(f92(f906(x66121,a895)),f295(x66121,x66122,x66123)),f295(x66121,x66123,x66124)),f178(f906(x66121,a895))) % 112.26/112.10 [6650]P1(f317(f317(x66501,x66502),f549(x66502,x66501)))+~P1(f317(f239(x66503,x66504,x66501),x66502)) % 112.26/112.10 [6732]~P108(x67322)+E(f317(f162(x67321),f140(x67321,x67322,x67323,x67324)),f317(f162(x67321),x67324)) % 112.26/112.10 [6784]~P145(x67841)+E(f180(x67841,x67842,f317(a102,x67843),x67844),f180(x67841,x67842,x67843,f317(x67842,x67844))) % 112.26/112.10 [6848]~P1(f317(f317(f319(x68484),x68483),f284(x68484,x68481,x68482)))+P1(f317(f317(x68481,x68482),x68483)) % 112.26/112.10 [6849]~P1(f317(f317(f319(x68494),x68493),f285(x68494,x68491,x68492)))+P1(f317(f317(x68491,x68492),x68493)) % 112.26/112.10 [6850]~P1(f317(f317(f319(x68504),x68502),f286(x68504,x68501,x68503)))+P1(f317(f317(x68501,x68502),x68503)) % 112.26/112.10 [6851]~P1(f317(f317(f319(x68514),x68512),f288(x68514,x68511,x68513)))+P1(f317(f317(x68511,x68512),x68513)) % 112.26/112.10 [6928]E(f317(f30(f904(x69281,x69282)),f303(x69281,x69282,x69283,x69284)),f2(a899))+P1(f317(f29(x69282),x69284)) % 112.26/112.10 [6929]E(f317(f30(f904(x69291,x69292)),f303(x69291,x69292,x69293,x69294)),f2(a899))+P1(f317(f29(x69291),x69293)) % 112.26/112.10 [7136]~P14(x71364,x71361,x71362)+E(f317(f67(x71361,x71361,x71361,f317(x71362,x71363)),f317(x71362,x71363)),f317(x71362,x71363)) % 112.26/112.10 [7377]E(f267(x73771,x73772,x73773,x73774),f317(f242(f906(a89,f906(a895,f902(f901(x73771)))),f905(a89,a89)),f37(x73771)))+~P1(f317(f317(f224(a89),x73773),f2(a89))) % 112.26/112.10 [8021]~E(x80212,x80213)+P1(f317(f317(f319(f905(x80211,x80211)),f317(f317(f242(x80211,x80211),x80212),x80213)),f297(x80211,x80214))) % 112.26/112.10 [8050]~P24(x80501,x80502,x80503,f232(f906(x80501,a895)))+E(f317(f71(x80501,x80502,f232(f906(x80501,a895)),x80503),f317(x80503,x80504)),x80504) % 112.26/112.10 [8051]~P24(x80511,x80512,x80513,f232(f906(x80511,a895)))+E(f317(f85(x80511,x80512,f232(f906(x80511,a895)),x80513),f317(x80513,x80514)),x80514) % 112.26/112.10 [8138]~P1(f317(f317(f319(f900(x81381)),f317(f317(f141(x81381),x81384),x81382)),f151(x81381,x81383)))+P1(f317(f317(f319(f900(x81381)),x81382),f151(x81381,x81383))) % 112.26/112.10 [8139]~P1(f317(f317(f319(f900(x81391)),f317(f317(f124(x81391),x81394),x81392)),f151(x81391,x81393)))+P1(f317(f317(f319(f900(x81391)),x81392),f151(x81391,x81393))) % 112.26/112.10 [8140]~P1(f317(f317(f319(f900(x81401)),f317(f317(f124(x81401),x81402),x81404)),f151(x81401,x81403)))+P1(f317(f317(f319(f900(x81401)),x81402),f151(x81401,x81403))) % 112.26/112.10 [8151]~P108(x81511)+P13(x81511,f317(f317(f144(x81512,x81511),x81513),f140(x81512,x81511,x81513,x81514))) % 112.26/112.10 [8256]P24(x82564,x82563,x82561,x82562)+E(f317(x82561,f506(x82562,x82561,x82563,x82564)),f317(x82561,f507(x82562,x82561,x82563,x82564))) % 112.26/112.10 [8363]~P24(x83632,x83631,x83634,x83633)+P24(x83631,x83632,f71(x83632,x83631,x83633,x83634),f317(f300(x83632,x83631,x83634),x83633)) % 112.26/112.10 [8503]P36(f905(x85032,x85034),f270(x85032,x85034,x85031,x85033))+P1(f317(x85031,f555(x85032,x85033,x85034,x85031))) % 112.26/112.10 [8619]E(x86191,x86192)+~P1(f317(f317(f319(f905(x86193,x86193)),f317(f317(f242(x86193,x86193),x86191),x86192)),f253(x86193,x86194))) % 112.26/112.10 [8683]~P1(f317(f29(f904(x86833,x86831)),f303(x86833,x86831,x86834,x86832)))+P1(f317(f29(x86831),x86832)) % 112.26/112.10 [8684]~P1(f317(f29(f904(x86841,x86843)),f303(x86841,x86843,x86842,x86844)))+P1(f317(f29(x86841),x86842)) % 112.26/112.10 [8693]~P24(x86931,x86932,x86933,x86934)+P25(x86931,x86932,x86933,x86934,f317(f300(x86931,x86932,x86933),x86934)) % 112.26/112.10 [8694]P11(x86941,x86942,x86943,x86944)+~E(f317(x86944,f812(x86942,x86944,x86943,x86941)),f317(x86944,f813(x86942,x86944,x86943,x86941))) % 112.26/112.10 [8784]~P25(x87842,x87843,x87844,x87841,f178(f906(x87843,a895)))+E(x87841,f178(f906(x87842,a895))) % 112.26/112.10 [8785]~P25(x87853,x87852,x87854,f178(f906(x87853,a895)),x87851)+E(x87851,f178(f906(x87852,a895))) % 112.26/112.10 [8877]P36(f905(x88771,x88772),f270(x88771,x88772,x88773,x88774))+~P36(x88772,f317(x88774,f555(x88771,x88774,x88772,x88773))) % 112.26/112.10 [9443]E(f317(f317(f149(x94431,x94432),f650(x94433,x94434,x94432,x94431)),f651(x94433,x94434,x94432,x94431)),x94434)+~P1(f317(f317(f319(f905(f900(x94431),f900(x94431))),f317(f317(f242(f900(x94431),f900(x94431)),x94432),x94434)),f147(x94431,x94433))) % 112.26/112.10 [9448]~P1(f317(f317(f319(f905(f900(x94481),f900(x94481))),f317(f317(f242(f900(x94481),f900(x94481)),x94482),x94483)),f135(x94481,x94484)))+P1(f317(f317(f319(f905(f900(x94481),f900(x94481))),f317(f317(f242(f900(x94481),f900(x94481)),x94482),x94483)),f137(x94481,x94484))) % 112.26/112.10 [9560]P1(f317(f29(x95601),x95602))+~P1(f317(f317(f319(f905(f906(x95601,a895),f906(x95601,a895))),f317(f317(f242(f906(x95601,a895),f906(x95601,a895)),x95603),x95602)),f309(x95601,x95604))) % 112.26/112.10 [9561]P1(f317(f29(x95611),x95612))+~P1(f317(f317(f319(f905(f906(x95611,a895),f906(x95611,a895))),f317(f317(f242(f906(x95611,a895),f906(x95611,a895)),x95612),x95613)),f309(x95611,x95614))) % 112.26/112.10 [9564]~E(x95641,f178(f906(x95642,a895)))+~P1(f317(f317(f319(f905(f906(x95642,a895),f906(x95642,a895))),f317(f317(f242(f906(x95642,a895),f906(x95642,a895)),x95643),x95641)),f309(x95642,x95644))) % 112.26/112.10 [10210]P11(x102101,x102102,x102103,x102104)+~P1(f317(f317(f247(x102101,x102101,a895),f317(f317(f9(x102101,f906(x102101,x102102),f906(x102101,a895)),f317(f317(f10(f906(x102102,a895),f906(f906(x102101,x102102),f906(x102101,a895)),x102101),f10(x102102,a895,x102101)),f317(f317(f10(x102102,f906(x102102,a895),x102101),a314),x102104))),x102104)),f562(x102104,x102103,x102102,x102101))) % 112.26/112.10 [5033]~E(x50332,f103(x50331))+E(f317(f317(f149(x50331,x50332),x50333),x50334),f103(x50331)) % 112.26/112.10 [5034]~E(x50344,f103(x50341))+E(f317(f317(f144(x50341,x50342),x50343),x50344),f103(x50342)) % 112.26/112.10 [5268]E(x52681,f103(x52682))+~E(f317(f317(f144(x52682,x52683),x52684),x52681),f103(x52683)) % 112.26/112.10 [5269]E(x52691,f103(x52692))+~E(f317(f317(f149(x52692,x52691),x52693),x52694),f103(x52692)) % 112.26/112.10 [5306]E(x53061,x53062)+~E(f317(f317(f124(x53063),x53064),x53061),f317(f317(f124(x53063),x53064),x53062)) % 112.26/112.10 [5307]E(x53071,x53072)+~E(f317(f317(f124(x53073),x53071),x53074),f317(f317(f124(x53073),x53072),x53074)) % 112.26/112.10 [5456]P1(f317(x54563,x54562))+E(f160(x54561,x54562,f317(f126(x54561,x54563),x54564)),f317(f126(x54561,x54563),x54564)) % 112.26/112.10 [5458]~P1(f317(x54582,x54583))+P32(x54581,x54582,f317(f317(f141(x54581),x54583),x54584)) % 112.26/112.10 [5468]E(x54681,x54682)+~E(f129(a899,f317(f292(a899,x54681),x54683)),f317(f317(f141(a899),x54682),x54684)) % 112.26/112.10 [5517]~P26(x55172,x55173)+P26(x55171,f317(f317(f68(x55172,x55171),x55173),x55174)) % 112.26/112.10 [5518]~P36(x55182,x55183)+P36(x55181,f317(f317(f278(x55182,x55181),x55183),x55184)) % 112.26/112.10 [5519]~P37(x55192,x55193)+P37(x55191,f317(f317(f278(x55192,x55191),x55193),x55194)) % 112.26/112.10 [5520]~P51(x55202,x55203)+P51(x55201,f317(f317(f278(x55202,x55201),x55203),x55204)) % 112.26/112.10 [5649]~P32(x56491,x56492,x56494)+P32(x56491,x56492,f317(f317(f141(x56491),x56493),x56494)) % 112.26/112.10 [5650]~P32(x56501,x56502,x56504)+P32(x56501,x56502,f317(f317(f124(x56501),x56503),x56504)) % 112.26/112.10 [5651]~P32(x56511,x56512,x56513)+P32(x56511,x56512,f317(f317(f124(x56511),x56513),x56514)) % 112.26/112.10 [5738]~E(x57381,f103(x57382))+~E(f317(f317(f124(x57382),x57383),f317(f317(f141(x57382),x57384),f103(x57382))),x57381) % 112.26/112.10 [5763]~P30(x57633,x57631,f317(f317(f141(x57633),x57632),x57634))+P1(f317(x57631,x57632)) % 112.26/112.10 [5773]E(f104(x57731,x57732),x57733)+~E(f317(f317(f124(x57731),x57733),f317(f317(f141(x57731),x57734),f103(x57731))),x57732) % 112.26/112.10 [5774]E(f134(x57741,x57742),x57743)+~E(f317(f317(f124(x57741),x57744),f317(f317(f141(x57741),x57743),f103(x57741))),x57742) % 112.26/112.10 [5884]~E(f129(a899,f317(f292(a899,x58841),x58842)),f317(f317(f141(a899),x58843),x58844))+P1(f317(f317(f225(a899),x58841),x58842)) % 112.26/112.10 [5902]P30(x59021,x59022,x59023)+~P30(x59021,x59022,f317(f317(f141(x59021),x59024),x59023)) % 112.26/112.10 [5903]P30(x59031,x59032,x59033)+~P30(x59031,x59032,f317(f317(f124(x59031),x59034),x59033)) % 112.26/112.10 [5904]P30(x59041,x59042,x59043)+~P30(x59041,x59042,f317(f317(f124(x59041),x59043),x59044)) % 112.26/112.10 [6103]E(x61031,f317(f317(f124(x61032),f317(f158(x61032),x61033)),f317(f317(f141(x61032),x61034),f103(x61032))))+~E(f317(f158(x61032),x61031),f317(f317(f141(x61032),x61034),x61033)) % 112.26/112.10 [6284]~P109(x62841)+E(f317(f317(f92(f906(x62841,a895)),f317(f292(x62841,x62842),x62843)),f317(f292(x62841,x62843),x62844)),f178(f906(x62841,a895))) % 112.26/112.10 [6295]E(f317(f317(f154(x62951),f159(x62951,x62952,x62953)),x62954),x62953)+~P1(f317(f317(f225(a899),x62954),x62952)) % 112.26/112.10 [6322]~P69(x63221)+E(f317(f155(x63221),f317(f317(f144(a1,x63221),x63222),f168(x63223,x63224))),f317(f317(f8(a1,x63221),x63222),f317(f162(a1),f168(x63223,x63224)))) % 112.26/112.10 [6323]~P69(x63231)+E(f317(f317(f8(a1,x63231),x63232),f317(f162(a1),f168(x63233,x63234))),f317(f155(x63231),f317(f317(f144(a1,x63231),x63232),f168(x63233,x63234)))) % 112.26/112.10 [6472]~E(x64722,f317(f317(f124(x64721),f317(f158(x64721),x64724)),f317(f317(f141(x64721),x64723),f103(x64721))))+E(f317(f158(x64721),x64722),f317(f317(f141(x64721),x64723),x64724)) % 112.26/112.10 [6488]~P19(x64882,x64883,x64884,x64881)+E(f317(x64881,f178(f906(x64882,a895))),f25(x64883)) % 112.26/112.10 [6516]~P109(x65161)+E(f317(f317(f92(f906(x65161,a895)),f296(x65161,x65162,x65163)),f317(f292(x65161,x65163),x65164)),f178(f906(x65161,a895))) % 112.26/112.10 [6735]E(x67351,f178(f906(x67352,a895)))+~E(f303(x67353,x67352,x67354,x67351),f178(f906(f904(x67353,x67352),a895))) % 112.26/112.10 [6736]E(x67361,f178(f906(x67362,a895)))+~E(f303(x67362,x67363,x67361,x67364),f178(f906(f904(x67362,x67363),a895))) % 112.26/112.10 [6805]~P108(x68052)+E(f317(f179(f900(x68051)),f140(x68051,x68052,x68053,x68054)),f317(f179(f900(x68051)),x68054)) % 112.26/112.10 [6816]~P1(f317(f240(x68163,x68164,x68161),x68162))+P1(f317(f317(x68161,f545(x68162,x68161)),x68162)) % 112.26/112.10 [6862]~P1(f317(f29(x68622),x68624))+P1(f317(f29(x68621),f317(f300(x68622,x68621,x68623),x68624))) % 112.26/112.10 [7097]~P24(x70972,x70971,x70973,x70974)+E(f317(f30(x70971),f317(f300(x70972,x70971,x70973),x70974)),f317(f30(x70972),x70974)) % 112.26/112.10 [7115]E(f317(f300(x71151,x71152,x71153),f317(f301(x71151,x71152,x71153),x71154)),x71154)+~E(f317(f300(x71151,x71152,x71153),f232(f906(x71151,a895))),f232(f906(x71152,a895))) % 112.26/112.10 [7531]~P24(x75311,x75312,x75313,f232(f906(x75311,a895)))+E(f317(f301(x75311,x75312,x75313),f317(f300(x75311,x75312,x75313),x75314)),x75314) % 112.26/112.10 [7815]E(x78151,x78152)+~P1(f317(f317(f319(x78153),x78151),f317(f162(x78153),f159(x78153,x78154,x78152)))) % 112.26/112.10 [7824]~E(x78241,f2(a899))+~P1(f317(f317(f319(x78242),x78243),f317(f162(x78242),f159(x78242,x78241,x78244)))) % 112.26/112.10 [7857]P1(f317(x78571,x78572))+~P1(f317(f317(f319(x78573),x78572),f317(f162(x78573),f167(x78573,x78571,x78574)))) % 112.26/112.10 [7967]~P1(f317(f317(f319(f900(x79671)),f317(f317(f141(x79671),x79672),x79674)),f151(x79671,x79673)))+P1(f317(f317(f319(x79671),x79672),x79673)) % 112.26/112.10 [8095]~P1(f317(f317(f319(x80951),x80952),f317(f162(x80951),f166(x80951,x80953,x80954))))+P1(f317(f317(f319(x80951),x80952),f317(f162(x80951),x80953))) % 112.26/112.10 [8096]~P1(f317(f317(f319(x80961),x80962),f317(f162(x80961),f160(x80961,x80964,x80963))))+P1(f317(f317(f319(x80961),x80962),f317(f162(x80961),x80963))) % 112.26/112.10 [8097]~P1(f317(f317(f319(x80971),x80972),f317(f162(x80971),f167(x80971,x80974,x80973))))+P1(f317(f317(f319(x80971),x80972),f317(f162(x80971),x80973))) % 112.26/112.10 [8107]E(f317(f179(f900(x81071)),x81072),x81073)+~P1(f317(f317(f319(f900(x81071)),x81072),f317(f162(f900(x81071)),f51(x81071,x81073,x81074)))) % 112.26/112.10 [8202]P1(f317(x82023,x82022))+E(f317(f126(x82021,f317(f317(f10(a895,a895,x82021),a312),f317(a314,x82022))),f317(f126(x82021,x82023),x82024)),f317(f126(x82021,x82023),x82024)) % 112.26/112.10 [8314]E(f317(f317(f154(x83141),f167(x83141,x83142,x83143)),x83144),f317(f317(f154(x83141),x83143),x83144))+~P1(f317(f317(f225(a899),x83144),f317(f179(f900(x83141)),f167(x83141,x83142,x83143)))) % 112.26/112.10 [8401]~P69(x84011)+E(f317(f317(f8(a899,x84011),f317(f317(f10(a899,x84011,a899),x84012),a102)),f317(f292(a899,x84013),x84014)),f317(f317(f8(a899,x84011),x84012),f317(f292(a899,f317(a102,x84013)),f317(a102,x84014)))) % 112.26/112.10 [8410]~P69(x84101)+E(f317(f317(f8(a899,x84101),f317(f317(f10(a899,x84101,a899),x84102),a102)),f293(a899,x84103,x84104)),f317(f317(f8(a899,x84101),x84102),f293(a899,f317(a102,x84103),f317(a102,x84104)))) % 112.26/112.10 [8540]~P24(x85401,x85403,x85404,f232(f906(x85401,a895)))+P24(x85401,f906(x85402,x85403),f317(f317(f10(x85403,f906(x85402,x85403),x85401),f18(x85403,x85402)),x85404),f232(f906(x85401,a895))) % 112.26/112.10 [8625]~P24(x86252,x86251,x86254,x86253)+E(f317(f300(x86251,x86252,f71(x86252,x86251,x86253,x86254)),f317(f300(x86252,x86251,x86254),x86253)),x86253) % 112.26/112.10 [8685]~P1(f317(f317(f319(f905(x86851,x86851)),f317(f317(f242(x86851,x86851),x86852),x86854)),f253(x86851,x86853)))+P1(f317(f317(f319(x86851),x86852),x86853)) % 112.26/112.10 [8808]~P24(x88082,x88081,x88083,f232(f906(x88082,a895)))+E(f317(f300(x88081,x88082,f85(x88082,x88081,f232(f906(x88082,a895)),x88083)),f317(f300(x88082,x88081,x88083),x88084)),x88084) % 112.26/112.10 [8883]~P25(x88831,x88832,x88833,x88834,f232(f906(x88832,a895)))+E(f317(f300(x88831,x88832,x88833),f232(f906(x88831,a895))),f232(f906(x88832,a895))) % 112.26/112.10 [8916]~E(f317(f317(f8(x89161,a899),x89164),x89163),f317(a102,x89162))+P1(f317(f317(f319(x89161),f850(x89162,x89163,x89164,x89161)),x89163)) % 112.26/112.10 [8937]~E(f317(f317(f8(x89374,a899),x89371),x89373),f317(a102,x89372))+P1(f317(f317(f225(a899),f2(a899)),f317(x89371,f850(x89372,x89373,x89371,x89374)))) % 112.26/112.10 [8948]~P1(f317(f29(x89482),x89484))+P1(f317(f317(f224(a899),f317(f30(x89481),f317(f300(x89482,x89481,x89483),x89484))),f317(f30(x89482),x89484))) % 112.26/112.10 [8949]E(f317(f317(f242(x89491,x89492),f623(x89493,x89494,x89492,x89491)),f624(x89493,x89494,x89492,x89491)),x89494)+~P1(f317(f317(f319(f905(x89491,x89492)),x89494),f317(f276(x89492,x89491),x89493))) % 112.26/112.10 [8957]P24(x89571,x89572,x89573,x89574)+P1(f317(f317(f319(x89571),f506(x89574,x89573,x89572,x89571)),x89574)) % 112.26/112.10 [8958]P24(x89581,x89582,x89583,x89584)+P1(f317(f317(f319(x89581),f507(x89584,x89583,x89582,x89581)),x89584)) % 112.26/112.10 [9026]P11(x90261,x90262,x90263,x90264)+P1(f317(f317(f319(f905(x90261,x90261)),f562(x90264,x90263,x90262,x90261)),x90263)) % 112.26/112.10 [9080]P1(f317(x90801,x90802))+~P1(f317(x90801,f317(f317(f242(x90803,x90804),f449(x90804,x90803,x90801)),f450(x90804,x90803,x90801)))) % 112.26/112.10 [9097]E(f317(f179(f900(x90971)),x90972),f317(f179(f900(x90971)),x90973))+~P1(f317(f317(f319(f905(f900(x90971),f900(x90971))),f317(f317(f242(f900(x90971),f900(x90971)),x90972),x90973)),f135(x90971,x90974))) % 112.26/112.10 [9098]E(f317(f179(f900(x90981)),x90982),f317(f179(f900(x90981)),x90983))+~P1(f317(f317(f319(f905(f900(x90981),f900(x90981))),f317(f317(f242(f900(x90981),f900(x90981)),x90982),x90983)),f147(x90981,x90984))) % 112.26/112.10 [9101]E(f317(f179(f900(x91011)),x91012),f317(f179(f900(x91011)),x91013))+~P1(f317(f317(f319(f905(f900(x91011),f900(x91011))),f317(f317(f242(f900(x91011),f900(x91011)),x91012),x91013)),f148(x91011,x91014))) % 112.26/112.10 [9170]P1(f317(f317(f224(a899),f145(x91701,x91702,x91703)),f145(x91701,x91704,x91703)))+P1(f317(f317(f319(x91701),f649(x91704,x91702,x91703,x91701)),f317(f162(x91701),x91703))) % 112.26/112.10 [9173]E(f317(f179(f900(x91731)),x91732),f317(f179(f900(x91731)),x91733))+~P1(f317(f317(f319(f905(f900(x91731),f900(x91731))),f317(f317(f242(f900(x91731),f900(x91731)),x91732),x91733)),f297(f900(x91731),f147(x91731,x91734)))) % 112.26/112.10 [9291]P1(f317(f317(f277(a899),x92911),x92912))+P1(f317(f317(f224(f906(a899,a895)),f280(a899,f277(a899),x92911,x92912)),f280(a899,f277(a899),x92913,x92914))) % 112.26/112.10 [9414]~P24(x94141,x94142,x94143,x94144)+~P1(f317(f317(f225(a899),f317(f30(x94142),f317(f300(x94141,x94142,x94143),x94144))),f317(f30(x94141),x94144))) % 112.26/112.10 [9461]~P1(f317(f317(f319(f905(f900(x94611),f900(x94611))),f317(f317(f242(f900(x94611),f900(x94611)),x94612),x94613)),f147(x94611,x94614)))+P1(f317(f317(f319(f905(f900(x94611),f900(x94611))),f317(f317(f242(f900(x94611),f900(x94611)),x94612),x94613)),f148(x94611,f297(x94611,x94614)))) % 112.26/112.10 [9465]~P1(f317(f317(f319(f905(f900(x94651),f900(x94651))),f317(f317(f242(f900(x94651),f900(x94651)),x94652),x94653)),f148(x94651,x94654)))+P1(f317(f317(f319(f905(f900(x94651),f900(x94651))),f317(f317(f242(f900(x94651),f900(x94651)),x94652),x94653)),f297(f900(x94651),f147(x94651,x94654)))) % 112.26/112.10 [9481]P1(f317(f317(f319(f905(x94811,x94811)),f317(f317(f242(x94811,x94811),x94812),x94813)),f297(x94811,x94814)))+~P1(f317(f317(f319(f905(x94811,x94811)),f317(f317(f242(x94811,x94811),x94812),x94813)),f317(f317(f279(x94811,x94811,x94811),x94814),f297(x94811,x94814)))) % 112.26/112.10 [9555]P1(f317(f317(f277(a899),x95551),x95552))+~P1(f317(f317(f225(f906(a899,a895)),f280(a899,f277(a899),x95553,x95554)),f280(a899,f277(a899),x95551,x95552))) % 112.26/112.10 [9678]E(f317(f317(f124(x96781),f664(x96782,x96783,x96784,x96781)),f317(f317(f141(x96781),f665(x96782,x96783,x96784,x96781)),f670(x96782,x96783,x96784,x96781))),x96784)+~P1(f317(f317(f319(f905(f900(x96781),f900(x96781))),f317(f317(f242(f900(x96781),f900(x96781)),x96784),x96783)),f147(x96781,x96782))) % 112.26/112.10 [9679]E(f317(f317(f124(x96791),f664(x96792,x96793,x96794,x96791)),f317(f317(f141(x96791),f666(x96792,x96793,x96794,x96791)),f670(x96792,x96793,x96794,x96791))),x96793)+~P1(f317(f317(f319(f905(f900(x96791),f900(x96791))),f317(f317(f242(f900(x96791),f900(x96791)),x96794),x96793)),f147(x96791,x96792))) % 112.26/112.10 [9757]P1(f317(f317(f319(f905(x97571,x97571)),f317(f317(f242(x97571,x97571),x97572),f620(x97573,x97574,x97572,x97571))),f297(x97571,x97573)))+~P1(f317(f317(f319(f905(x97571,x97571)),f317(f317(f242(x97571,x97571),x97572),x97574)),f317(f317(f279(x97571,x97571,x97571),x97573),f297(x97571,x97573)))) % 112.26/112.10 [9825]P1(f317(f317(f224(a899),f145(x98251,x98252,x98253)),f145(x98251,x98254,x98253)))+~P1(f317(f317(f225(a899),f317(x98252,f649(x98254,x98252,x98253,x98251))),f317(x98254,f649(x98254,x98252,x98253,x98251)))) % 112.26/112.10 [9898]P1(f317(f317(f319(f905(x98981,x98981)),f317(f317(f242(x98981,x98981),f612(x98982,x98983,x98984,x98981)),x98983)),f297(x98981,x98982)))+~P1(f317(f317(f319(f905(x98981,x98981)),f317(f317(f242(x98981,x98981),x98984),x98983)),f317(f317(f279(x98981,x98981,x98981),x98982),f297(x98981,x98982)))) % 112.26/112.10 [5287]~E(x52872,x52873)+E(f160(x52871,x52872,f317(f317(f141(x52871),x52873),x52874)),x52874) % 112.26/112.10 [5412]P1(f317(x54122,x54123))+E(f167(x54121,x54122,f317(f317(f141(x54121),x54123),x54124)),f103(x54121)) % 112.26/112.10 [5480]~P89(x54802)+E(f317(f317(f73(f906(x54801,x54802)),x54803),x54804),f317(f73(x54802),f317(x54803,x54804))) % 112.26/112.10 [5493]~E(x54932,f2(a899))+E(f317(f317(f128(x54931),x54932),f317(f317(f141(x54931),x54933),x54934)),f317(f317(f141(x54931),x54933),x54934)) % 112.26/112.10 [5494]P1(f317(x54942,x54943))+E(f317(f126(x54941,x54942),f317(f317(f141(x54941),x54943),x54944)),f317(f126(x54941,x54942),x54944)) % 112.26/112.10 [5632]~E(x56322,x56324)+P1(f317(f317(f317(f299(x56321),x56322),x56323),x56324)) % 112.26/112.10 [5640]E(x56401,f103(x56402))+E(f134(x56403,f317(f317(f144(x56402,x56403),x56404),x56401)),f317(x56404,f134(x56402,x56401))) % 112.26/112.10 [5654]~E(x56541,f58(x56542,x56544))+E(f317(x56541,f317(f317(f299(x56542),x56543),f178(f906(x56542,a895)))),x56543) % 112.26/112.10 [5690]E(x56901,f103(x56902))+E(f317(f131(x56903),f317(f317(f144(x56902,x56903),x56904),x56901)),f317(x56904,f317(f131(x56902),x56901))) % 112.26/112.10 [5793]~P1(f317(x57933,x57934))+P1(f317(f317(f317(f299(x57931),x57932),x57933),x57934)) % 112.26/112.10 [5921]~P18(x59212,x59214,x59211)+E(f317(x59211,f317(f317(f299(x59212),x59213),f178(f906(x59212,a895)))),x59213) % 112.26/112.10 [5947]~E(x59472,x59473)+P1(f317(f317(f319(x59471),x59472),f317(f317(f299(x59471),x59473),x59474))) % 112.26/112.10 [5952]~P119(x59521)+E(f317(f317(f74(x59521),x59522),f317(f317(f74(x59521),x59523),x59524)),f317(f317(f74(x59521),x59523),f317(f317(f74(x59521),x59522),x59524))) % 112.26/112.10 [5953]~P119(x59531)+E(f317(f317(f75(x59531),x59532),f317(f317(f75(x59531),x59533),x59534)),f317(f317(f75(x59531),x59533),f317(f317(f75(x59531),x59532),x59534))) % 112.26/112.10 [5955]~P108(x59551)+E(f317(f317(f228(x59551),x59552),f317(f317(f228(x59551),x59553),x59554)),f317(f317(f228(x59551),x59553),f317(f317(f228(x59551),x59552),x59554))) % 112.26/112.10 [5957]~P108(x59571)+E(f317(f317(f223(x59571),x59572),f317(f317(f223(x59571),x59573),x59574)),f317(f317(f223(x59571),x59573),f317(f317(f223(x59571),x59572),x59574))) % 112.26/112.10 [5959]~P98(x59591)+E(f317(f317(f91(x59591),x59592),f317(f317(f91(x59591),x59593),x59594)),f317(f317(f91(x59591),x59593),f317(f317(f91(x59591),x59592),x59594))) % 112.26/112.10 [5960]~P99(x59601)+E(f317(f317(f91(x59601),x59602),f317(f317(f91(x59601),x59603),x59604)),f317(f317(f91(x59601),x59603),f317(f317(f91(x59601),x59602),x59604))) % 112.26/112.10 [5961]~P99(x59611)+E(f317(f317(f92(x59611),x59612),f317(f317(f92(x59611),x59613),x59614)),f317(f317(f92(x59611),x59613),f317(f317(f92(x59611),x59612),x59614))) % 112.26/112.10 [5963]~P104(x59631)+E(f317(f317(f92(x59631),x59632),f317(f317(f92(x59631),x59633),x59634)),f317(f317(f92(x59631),x59633),f317(f317(f92(x59631),x59632),x59634))) % 112.26/112.10 [5970]E(x59701,x59702)+E(f160(x59703,x59701,f317(f317(f141(x59703),x59702),x59704)),f317(f317(f141(x59703),x59702),f160(x59703,x59701,x59704))) % 112.26/112.10 [5985]~P1(f317(x59852,x59853))+E(f317(f126(x59851,x59852),f317(f317(f141(x59851),x59853),x59854)),f317(f317(f141(x59851),x59853),f317(f126(x59851,x59852),x59854))) % 112.26/112.10 [6125]~P1(f317(x61252,x61253))+E(f167(x61251,x61252,f317(f317(f141(x61251),x61253),x61254)),f317(f317(f141(x61251),x61253),f167(x61251,x61252,x61254))) % 112.26/112.10 [6189]E(x61891,f178(f906(x61892,a895)))+E(f317(f317(f35(x61892,f906(x61893,a895)),x61891),f317(f18(f906(x61893,a895),x61892),x61894)),x61894) % 112.26/112.10 [6190]E(x61901,f178(f906(x61902,a895)))+E(f317(f317(f36(x61902,f906(x61903,a895)),x61901),f317(f18(f906(x61903,a895),x61902),x61904)),x61904) % 112.26/112.10 [6199]~E(x61994,f178(f906(x61992,a895)))+E(f317(f317(f244(x61991,x61992),x61993),f317(f18(f906(x61992,a895),x61991),x61994)),f178(f906(f905(x61991,x61992),a895))) % 112.26/112.10 [6200]~E(x62003,f178(f906(x62001,a895)))+E(f317(f317(f244(x62001,x62002),x62003),f317(f18(f906(x62002,a895),x62001),x62004)),f178(f906(f905(x62001,x62002),a895))) % 112.26/112.10 [6256]E(x62561,f2(a899))+E(f317(f317(f128(x62562),x62561),f317(f317(f141(x62562),x62563),x62564)),f317(f317(f128(x62562),f317(f317(f3(a899),x62561),f72(a899))),x62564)) % 112.26/112.10 [6277]E(x62771,f178(f906(x62772,a895)))+E(f317(f300(x62772,x62773,f317(f18(x62773,x62772),x62774)),x62771),f317(f317(f299(x62773),x62774),f178(f906(x62773,a895)))) % 112.26/112.10 [6280]E(f317(f301(x62801,x62802,f317(f18(x62802,x62801),x62803)),x62804),f178(f906(x62801,a895)))+P1(f317(f317(f319(x62802),x62803),x62804)) % 112.26/112.10 [6348]~E(x63483,f178(f906(x63481,a895)))+E(f317(f317(f35(x63481,f906(x63482,a895)),x63483),f317(f18(f906(x63482,a895),x63481),x63484)),f232(f906(x63482,a895))) % 112.26/112.10 [6349]~E(x63493,f178(f906(x63491,a895)))+E(f317(f317(f36(x63491,f906(x63492,a895)),x63493),f317(f18(f906(x63492,a895),x63491),x63494)),f178(f906(x63492,a895))) % 112.26/112.10 [6351]~P3(x63511)+E(f41(x63511,f317(f317(f75(x63511),x63512),x63513),f317(f317(f75(x63511),x63512),x63514)),f317(f317(f75(x63511),x63512),f41(x63511,x63513,x63514))) % 112.26/112.10 [6526]E(f317(f301(x65261,x65262,f317(f18(x65262,x65261),x65263)),x65264),f232(f906(x65261,a895)))+~P1(f317(f317(f319(x65262),x65263),x65264)) % 112.26/112.10 [6549]~P1(f317(f317(f319(x65491),x65492),x65494))+P1(f317(f317(f319(x65491),x65492),f317(f317(f299(x65491),x65493),x65494))) % 112.26/112.10 [6554]P1(f317(x65541,x65542))+~P1(f317(f150(x65543,x65541),f317(f317(f141(x65543),x65542),x65544))) % 112.26/112.10 [6563]~E(x65633,f317(f317(f3(a899),f317(f179(f900(x65631)),x65632)),f72(a899)))+E(f104(x65631,f317(f317(f149(x65631,x65632),x65633),x65634)),f104(x65631,x65632)) % 112.26/112.10 [6586]~P108(x65861)+E(f317(f317(f92(f906(x65861,a895)),f317(f291(x65861),x65862)),f293(x65861,x65863,x65864)),f293(x65861,x65863,f317(f317(f228(x65861),x65862),x65864))) % 112.26/112.10 [6587]~P108(x65871)+E(f317(f317(f92(f906(x65871,a895)),f317(f273(x65871),x65872)),f293(x65871,x65873,x65874)),f293(x65871,f317(f317(f223(x65871),x65872),x65873),x65874)) % 112.26/112.10 [6603]E(f317(f317(f92(f906(x66031,a895)),x66032),f317(f317(f299(x66031),x66033),x66034)),f317(f317(f92(f906(x66031,a895)),x66032),x66034))+P1(f317(f317(f319(x66031),x66033),x66032)) % 112.26/112.10 [6615]E(f160(x66151,x66152,f317(f317(f124(x66151),x66153),x66154)),f317(f317(f124(x66151),x66153),f160(x66151,x66152,x66154)))+P1(f317(f317(f319(x66151),x66152),f317(f162(x66151),x66153))) % 112.26/112.10 [6620]~P80(x66201)+E(f317(f317(f75(x66201),f317(f317(f234(x66201),x66202),x66203)),f317(f317(f234(x66201),x66202),x66204)),f317(f317(f234(x66201),x66202),f317(f317(f74(a899),x66203),x66204))) % 112.26/112.10 [6621]~P119(x66211)+E(f317(f317(f75(x66211),f317(f317(f234(x66211),x66212),x66213)),f317(f317(f234(x66211),x66212),x66214)),f317(f317(f234(x66211),x66212),f317(f317(f74(a899),x66213),x66214))) % 112.26/112.10 [6658]~P119(x66581)+E(f317(f317(f74(x66581),f317(f317(f75(x66581),x66582),x66583)),f317(f317(f75(x66581),x66582),x66584)),f317(f317(f75(x66581),x66582),f317(f317(f74(x66581),x66583),x66584))) % 112.26/112.10 [6659]~P108(x66591)+E(f317(f317(f223(x66591),f317(f317(f228(x66591),x66592),x66593)),f317(f317(f228(x66591),x66592),x66594)),f317(f317(f228(x66591),x66592),f317(f317(f223(x66591),x66593),x66594))) % 112.26/112.10 [6660]~P108(x66601)+E(f317(f317(f228(x66601),f317(f317(f223(x66601),x66602),x66603)),f317(f317(f223(x66601),x66602),x66604)),f317(f317(f223(x66601),x66602),f317(f317(f228(x66601),x66603),x66604))) % 112.26/112.10 [6661]~P103(x66611)+E(f317(f317(f92(x66611),f317(f317(f91(x66611),x66612),x66613)),f317(f317(f91(x66611),x66612),x66614)),f317(f317(f91(x66611),x66612),f317(f317(f92(x66611),x66613),x66614))) % 112.26/112.10 [6662]~P103(x66621)+E(f317(f317(f91(x66621),f317(f317(f92(x66621),x66622),x66623)),f317(f317(f92(x66621),x66622),x66624)),f317(f317(f92(x66621),x66622),f317(f317(f91(x66621),x66623),x66624))) % 112.26/112.10 [6696]~P3(x66961)+E(f41(x66961,f317(f317(f75(x66961),x66962),x66963),f317(f317(f75(x66961),x66964),x66963)),f317(f317(f75(x66961),f41(x66961,x66962,x66964)),x66963)) % 112.26/112.10 [6699]~E(f317(f179(f900(x66991)),x66993),f317(f179(f900(x66992)),x66994))+E(f317(f317(f144(f905(x66991,x66992),x66992),f246(x66991,x66992)),f317(f317(f171(x66991,x66992),x66993),x66994)),x66994) % 112.26/112.10 [6700]~E(f317(f179(f900(x67001)),x67003),f317(f179(f900(x67002)),x67004))+E(f317(f317(f144(f905(x67001,x67002),x67001),f241(x67001,x67002)),f317(f317(f171(x67001,x67002),x67003),x67004)),x67003) % 112.26/112.10 [6705]P1(f317(f150(x67051,x67052),x67053))+~P1(f317(f150(x67051,x67052),f317(f317(f141(x67051),x67054),x67053))) % 112.26/112.10 [6706]P1(f317(f150(x67061,x67062),x67063))+~P1(f317(f150(x67061,x67062),f317(f317(f124(x67061),x67064),x67063))) % 112.26/112.10 [6707]P1(f317(f150(x67071,x67072),x67073))+~P1(f317(f150(x67071,x67072),f317(f317(f124(x67071),x67073),x67074))) % 112.26/112.10 [6712]~P4(x67121)+E(f41(x67121,f317(f317(f3(x67121),x67122),f41(x67121,x67123,x67124)),x67124),f41(x67121,f317(f317(f3(x67121),x67122),x67123),x67124)) % 112.26/112.10 [6714]~P3(x67141)+E(f41(x67141,f317(f317(f75(x67141),x67142),f41(x67141,x67143,x67144)),x67144),f41(x67141,f317(f317(f75(x67141),x67142),x67143),x67144)) % 112.26/112.10 [6715]~P3(x67151)+E(f41(x67151,f317(f317(f74(x67151),x67152),f41(x67151,x67153,x67154)),x67154),f41(x67151,f317(f317(f74(x67151),x67152),x67153),x67154)) % 112.26/112.10 [6797]~P108(x67971)+E(f317(f317(f92(f906(x67971,a895)),f293(x67971,x67972,x67973)),f317(f291(x67971),x67974)),f293(x67971,x67972,f317(f317(f228(x67971),x67973),x67974))) % 112.26/112.10 [6798]~P108(x67981)+E(f317(f317(f92(f906(x67981,a895)),f293(x67981,x67982,x67983)),f317(f273(x67981),x67984)),f293(x67981,f317(f317(f223(x67981),x67982),x67984),x67983)) % 112.26/112.10 [6801]~E(f317(f179(f900(x68011)),x68013),f317(f179(f900(x68012)),x68014))+E(f317(f317(f171(x68011,x68012),f317(f158(x68011),x68013)),f317(f158(x68012),x68014)),f317(f158(f905(x68011,x68012)),f317(f317(f171(x68011,x68012),x68013),x68014))) % 112.26/112.10 [6813]E(x68131,f317(f317(f3(a899),f317(f179(f900(x68132)),x68133)),f72(a899)))+E(f104(x68132,f317(f317(f149(x68132,x68133),x68131),x68134)),f317(f317(f149(x68132,f104(x68132,x68133)),x68131),x68134)) % 112.26/112.10 [6828]~P1(f317(f127(x68282),x68284))+P1(f317(f127(f905(x68281,x68282)),f317(f317(f171(x68281,x68282),x68283),x68284))) % 112.26/112.10 [6829]~P1(f317(f127(x68291),x68293))+P1(f317(f127(f905(x68291,x68292)),f317(f317(f171(x68291,x68292),x68293),x68294))) % 112.26/112.10 [7100]E(f317(f317(f31(a899),x71001),x71002),x71003)+~P1(f317(f44(x71001,x71002),f317(f317(f242(a899,a899),x71003),x71004))) % 112.26/112.10 [7124]E(f41(a899,x71241,x71242),x71243)+~P1(f317(f44(x71241,x71242),f317(f317(f242(a899,a899),x71244),x71243))) % 112.26/112.10 [7127]P1(f317(f127(x71271),x71272))+~P1(f317(f127(x71273),f317(f317(f144(x71271,x71273),x71274),x71272))) % 112.26/112.10 [7210]E(f160(x72101,x72102,f317(f317(f124(x72101),x72103),x72104)),f317(f317(f124(x72101),f160(x72101,x72102,x72103)),x72104))+~P1(f317(f317(f319(x72101),x72102),f317(f162(x72101),x72103))) % 112.26/112.10 [7303]~P4(x73031)+E(f41(x73031,f317(f317(f3(x73031),f41(x73031,x73032,x73033)),x73034),x73033),f41(x73031,f317(f317(f3(x73031),x73032),x73034),x73033)) % 112.26/112.10 [7306]~P3(x73061)+E(f41(x73061,f317(f317(f74(x73061),f41(x73061,x73062,x73063)),x73064),x73063),f41(x73061,f317(f317(f74(x73061),x73062),x73064),x73063)) % 112.26/112.10 [7307]~P3(x73071)+E(f41(x73071,f317(f317(f75(x73071),f41(x73071,x73072,x73073)),x73074),x73073),f41(x73071,f317(f317(f75(x73071),x73072),x73074),x73073)) % 112.26/112.10 [7501]~E(x75011,f317(f317(f141(x75012),x75013),x75014))+~P1(f317(f317(f224(a899),f317(f179(f900(x75012)),x75011)),f317(f179(f900(x75012)),x75014))) % 112.26/112.10 [7705]P24(x77051,x77052,x77053,f317(f162(x77051),x77054))+~P1(f317(f127(x77052),f317(f317(f144(x77051,x77052),x77053),x77054))) % 112.26/112.10 [7780]~P1(f317(f317(f224(f906(x77801,a895)),x77802),x77804))+P1(f317(f317(f224(f906(x77801,a895)),x77802),f317(f317(f299(x77801),x77803),x77804))) % 112.26/112.10 [7816]~P4(x78161)+E(f41(x78161,f317(f317(f3(x78161),f41(x78161,x78162,x78163)),f41(x78161,x78164,x78163)),x78163),f41(x78161,f317(f317(f3(x78161),x78162),x78164),x78163)) % 112.26/112.10 [7817]~P3(x78171)+E(f41(x78171,f317(f317(f74(x78171),f41(x78171,x78172,x78173)),f41(x78171,x78174,x78173)),x78173),f41(x78171,f317(f317(f74(x78171),x78172),x78174),x78173)) % 112.26/112.10 [7818]~P3(x78181)+E(f41(x78181,f317(f317(f75(x78181),f41(x78181,x78182,x78183)),f41(x78181,x78184,x78183)),x78183),f41(x78181,f317(f317(f75(x78181),x78182),x78184),x78183)) % 112.26/112.10 [7922]~E(f317(x79224,f453(x79224,x79223,x79221,x79222)),f178(f906(x79222,a895)))+E(f317(f317(f36(x79221,f906(x79222,a895)),x79223),x79224),f178(f906(x79222,a895))) % 112.26/112.10 [7923]~E(f317(x79234,f464(x79234,x79233,x79231,x79232)),f232(f906(x79232,a895)))+E(f317(f317(f35(x79231,f906(x79232,a895)),x79233),x79234),f232(f906(x79232,a895))) % 112.26/112.10 [7924]~E(f317(x79244,f465(x79244,x79243,x79242,x79241)),f232(f906(x79242,a895)))+E(f317(f317(f35(x79241,f906(x79242,a895)),x79243),x79244),f232(f906(x79242,a895))) % 112.26/112.10 [7925]~E(f317(x79254,f466(x79254,x79253,x79252,x79251)),f178(f906(x79252,a895)))+E(f317(f317(f36(x79251,f906(x79252,a895)),x79253),x79254),f178(f906(x79252,a895))) % 112.26/112.10 [8315]P1(f317(x83151,x83152))+~P1(f317(f317(f319(x83153),x83152),f317(f317(f92(f906(x83153,a895)),x83154),f317(f252(x83153),x83151)))) % 112.26/112.10 [8352]~P1(f317(f317(f224(f906(x83521,a895)),x83523),x83524))+P1(f317(f317(f224(f906(x83521,a895)),f317(f317(f299(x83521),x83522),x83523)),f317(f317(f299(x83521),x83522),x83524))) % 112.26/112.10 [8533]P1(f317(x85332,x85333))+E(f317(f317(f128(x85331),f317(f179(f900(x85331)),f167(x85331,x85332,f317(f317(f141(x85331),x85333),x85334)))),f317(f317(f141(x85331),x85333),x85334)),f317(f317(f141(x85331),x85333),x85334)) % 112.26/112.10 [8639]~P1(f317(f317(f225(a899),f317(x86394,x86392)),f317(x86394,x86393)))+P1(f317(f317(f319(f905(x86391,x86391)),f317(f317(f242(x86391,x86391),x86392),x86393)),f317(f317(f278(a899,x86391),a230),x86394))) % 112.26/112.10 [8735]~P1(f317(x87352,f722(x87354,x87352,x87353,x87351)))+E(f167(x87351,x87352,f317(f317(f124(x87351),x87353),x87354)),f317(f317(f124(x87351),x87353),f167(x87351,x87352,x87354))) % 112.26/112.10 [8812]P24(f900(x88121),f900(x88122),f317(f144(x88121,x88122),x88123),x88124)+~P24(x88121,x88122,x88123,f32(f906(x88121,a895),f317(f300(f900(x88121),f906(x88121,a895),f162(x88121)),x88124))) % 112.26/112.10 [8887]~P1(f317(x88872,x88873))+E(f317(f317(f128(x88871),f317(f179(f900(x88871)),f167(x88871,x88872,f317(f317(f141(x88871),x88873),x88874)))),f317(f317(f141(x88871),x88873),x88874)),f317(f317(f128(x88871),f317(f179(f900(x88871)),f167(x88871,x88872,x88874))),x88874)) % 112.26/112.10 [8928]~E(x89282,x89283)+E(f317(f126(x89281,f317(f317(f10(a895,a895,x89281),a312),f317(a314,x89282))),f317(f317(f141(x89281),x89283),x89284)),f317(f126(x89281,f317(f317(f10(a895,a895,x89281),a312),f317(a314,x89282))),x89284)) % 112.26/112.10 [8938]E(f317(f317(f36(x89381,f906(x89382,a895)),x89383),x89384),f178(f906(x89382,a895)))+P1(f317(f317(f319(x89381),f453(x89384,x89383,x89381,x89382)),x89383)) % 112.26/112.10 [8939]E(f317(f317(f35(x89391,f906(x89392,a895)),x89393),x89394),f232(f906(x89392,a895)))+P1(f317(f317(f319(x89391),f464(x89394,x89393,x89391,x89392)),x89393)) % 112.26/112.10 [8940]E(f317(f317(f35(x89401,f906(x89402,a895)),x89403),x89404),f232(f906(x89402,a895)))+P1(f317(f317(f319(x89401),f465(x89404,x89403,x89402,x89401)),x89403)) % 112.26/112.10 [8941]E(f317(f317(f36(x89411,f906(x89412,a895)),x89413),x89414),f178(f906(x89412,a895)))+P1(f317(f317(f319(x89411),f466(x89414,x89413,x89412,x89411)),x89413)) % 112.26/112.10 [8979]P1(f317(f317(f225(a899),f317(x89791,x89792)),f317(x89791,x89793)))+~P1(f317(f317(f319(f905(x89794,x89794)),f317(f317(f242(x89794,x89794),x89792),x89793)),f317(f317(f278(a899,x89794),a230),x89791))) % 112.26/112.10 [9005]E(f167(x90051,x90052,f317(f317(f124(x90051),x90053),x90054)),f317(f317(f124(x90051),x90053),f167(x90051,x90052,x90054)))+P1(f317(f317(f319(x90051),f722(x90054,x90052,x90053,x90051)),f317(f162(x90051),x90053))) % 112.26/112.10 [9056]~P25(x90561,x90562,x90563,f232(f906(x90561,a895)),f232(f906(x90562,a895)))+E(f317(f300(x90561,x90562,x90563),f317(f73(f906(x90561,a895)),x90564)),f317(f73(f906(x90562,a895)),f317(f300(x90561,x90562,x90563),x90564))) % 112.26/112.10 [9159]P1(f317(f317(f319(x91591),f495(x91592,x91593,x91594,x91591)),x91593))+~P1(f317(f317(f319(f906(x91591,a895)),x91594),f317(f317(f56(x91591),x91593),x91592))) % 112.26/112.10 [9162]E(x91621,x91622)+~P1(f317(f317(f319(f905(x91623,x91623)),f317(f317(f242(x91623,x91623),x91621),x91622)),f317(f317(f173(f905(x91623,x91623),a895),f2(a899)),x91624))) % 112.26/112.10 [9243]E(f317(f275(x92431,x92431,x92432),f317(f317(f299(x92431),f495(x92432,x92433,x92434,x92431)),f178(f906(x92431,a895)))),x92434)+~P1(f317(f317(f319(f906(x92431,a895)),x92434),f317(f317(f56(x92431),x92433),x92432))) % 112.26/112.10 [9248]~P1(f317(f317(f319(f905(x92481,x92481)),f317(f317(f242(x92481,x92481),x92483),x92482)),f297(x92481,x92484)))+P1(f317(f317(f319(f905(x92481,x92481)),f317(f317(f242(x92481,x92481),x92482),x92483)),f297(x92481,f317(f276(x92481,x92481),x92484)))) % 112.26/112.10 [9261]~P3(x92611)+E(f317(f317(f74(x92611),f317(f317(f74(x92611),f317(f317(f75(x92611),x92612),f317(f317(f31(x92611),x92613),x92612))),f41(x92611,x92613,x92612))),x92614),f317(f317(f74(x92611),x92613),x92614)) % 112.26/112.10 [9272]~P1(f317(f317(f319(x92721),x92723),x92724))+P1(f317(f317(f319(f906(x92721,a895)),f317(f275(x92721,x92721,x92722),f317(f317(f299(x92721),x92723),f178(f906(x92721,a895))))),f317(f317(f56(x92721),x92724),x92722))) % 112.26/112.10 [9284]P1(f317(f317(f319(f905(x92841,x92841)),f317(f317(f242(x92841,x92841),x92842),x92843)),f297(x92841,x92844)))+~P1(f317(f317(f319(f905(x92841,x92841)),f317(f317(f242(x92841,x92841),x92843),x92842)),f297(x92841,f317(f276(x92841,x92841),x92844)))) % 112.26/112.10 [9372]E(f317(f317(f149(x93721,f317(f158(x93721),x93722)),f317(f317(f3(a899),f317(f317(f3(a899),f317(f179(f900(x93721)),x93722)),x93723)),f72(a899))),x93724),f317(f158(x93721),f317(f317(f149(x93721,x93722),x93723),x93724)))+~P1(f317(f317(f225(a899),x93723),f317(f179(f900(x93721)),x93722))) % 112.26/112.10 [9375]~P1(f317(x93752,f717(x93754,x93752,x93753,x93751)))+E(f317(f317(f128(x93751),f317(f179(f900(x93751)),f167(x93751,x93752,f317(f317(f124(x93751),x93753),x93754)))),f317(f317(f124(x93751),x93753),x93754)),f317(f317(f128(x93751),f317(f179(f900(x93751)),f167(x93751,x93752,x93754))),x93754)) % 112.26/112.10 [9422]~P24(x94222,x94221,x94223,f232(f906(x94222,a895)))+P1(f317(f317(f224(f906(x94221,a895)),f317(f300(x94222,x94221,x94223),f317(f73(f906(x94222,a895)),x94224))),f317(f73(f906(x94221,a895)),f317(f300(x94222,x94221,x94223),x94224)))) % 112.26/112.10 [9434]~P5(x94341)+E(f317(f132(x94341,x94342,f317(f9(x94342,x94341,x94341),f317(f317(f10(x94341,f906(x94341,x94341),x94342),f92(x94341)),x94343)),f232(x94341)),x94344),f317(f317(f35(x94342,x94341),f317(f162(x94342),x94344)),x94343)) % 112.26/112.10 [9435]~P5(x94351)+E(f317(f132(x94351,x94352,f317(f9(x94352,x94351,x94351),f317(f317(f10(x94351,f906(x94351,x94351),x94352),f91(x94351)),x94353)),f178(x94351)),x94354),f317(f317(f36(x94352,x94351),f317(f162(x94352),x94354)),x94353)) % 112.26/112.10 [9445]E(f317(f317(f128(x94451),f317(f179(f900(x94451)),f167(x94451,x94452,f317(f317(f124(x94451),x94453),x94454)))),f317(f317(f124(x94451),x94453),x94454)),f317(f317(f128(x94451),f317(f179(f900(x94451)),f167(x94451,x94452,x94454))),x94454))+P1(f317(f317(f319(x94451),f717(x94454,x94452,x94453,x94451)),f317(f162(x94451),x94453))) % 112.26/112.10 [9515]~P1(f317(f317(f319(f905(f900(x95154),f900(x95154))),f317(f317(f242(f900(x95154),f900(x95154)),x95153),x95152)),f147(x95154,x95151)))+P1(f317(f317(f225(a899),f650(x95151,x95152,x95153,x95154)),f317(f179(f900(x95154)),x95153))) % 112.26/112.10 [9516]~P3(x95161)+E(f317(f317(f74(x95161),f317(f317(f74(x95161),f317(f317(f75(x95161),f317(f317(f31(x95161),x95162),x95163)),x95163)),f41(x95161,x95162,x95163))),x95164),f317(f317(f74(x95161),x95162),x95164)) % 112.26/112.10 [9545]~P1(f317(f317(f319(f905(f900(x95451),f900(x95451))),f317(f317(f242(f900(x95451),f900(x95451)),x95452),x95453)),f317(f276(f900(x95451),f900(x95451)),f147(x95451,x95454))))+P1(f317(f317(f319(f905(f900(x95451),f900(x95451))),f317(f317(f242(f900(x95451),f900(x95451)),x95452),x95453)),f147(x95451,f317(f276(x95451,x95451),x95454)))) % 112.26/112.10 [9546]P1(f317(f317(f319(f905(f900(x95461),f900(x95461))),f317(f317(f242(f900(x95461),f900(x95461)),x95462),x95463)),f317(f276(f900(x95461),f900(x95461)),f147(x95461,x95464))))+~P1(f317(f317(f319(f905(f900(x95461),f900(x95461))),f317(f317(f242(f900(x95461),f900(x95461)),x95462),x95463)),f147(x95461,f317(f276(x95461,x95461),x95464)))) % 112.26/112.10 [9590]~P1(f317(f317(f319(x95901),x95903),f317(f254(x95901,x95902),x95904)))+P1(f317(f317(f319(f905(x95901,x95902)),f317(f317(f242(x95901,x95902),x95903),f552(x95904,x95902,x95903,x95901))),x95904)) % 112.26/112.10 [9591]~P1(f317(f317(f319(x95911),x95913),f317(f254(x95911,x95912),x95914)))+P1(f317(f317(f319(f905(x95911,x95912)),f317(f317(f242(x95911,x95912),x95913),f556(x95914,x95912,x95913,x95911))),x95914)) % 112.26/112.10 [9752]~P1(f317(f317(f319(f905(x97521,x97521)),f317(f317(f242(x97521,x97521),x97522),x97524)),f317(f317(f279(x97521,x97521,x97521),x97523),f297(x97521,x97523))))+P1(f317(f317(f319(f905(x97521,x97521)),f317(f317(f242(x97521,x97521),x97522),f612(x97523,x97524,x97522,x97521))),x97523)) % 112.26/112.10 [9912]P11(x99121,x99122,x99123,x99124)+P1(f317(f317(f319(f905(x99121,x99121)),f317(f317(f242(x99121,x99121),f813(x99122,x99124,x99123,x99121)),f812(x99122,x99124,x99123,x99121))),x99123)) % 112.26/112.10 [9919]~P1(f317(f317(f319(f905(x99192,x99191)),x99194),f317(f276(x99191,x99192),x99193)))+P1(f317(f317(f319(f905(x99191,x99192)),f317(f317(f242(x99191,x99192),f624(x99193,x99194,x99191,x99192)),f623(x99193,x99194,x99191,x99192))),x99193)) % 112.26/112.10 [9943]~P1(f317(f317(f319(f905(f900(x99431),f900(x99431))),f317(f317(f242(f900(x99431),f900(x99431)),x99434),x99433)),f147(x99431,x99432)))+P1(f317(f317(f319(f905(x99431,x99431)),f317(f317(f242(x99431,x99431),f665(x99432,x99433,x99434,x99431)),f666(x99432,x99433,x99434,x99431))),x99432)) % 112.26/112.10 [10033]~P1(f317(f317(f319(f905(f900(x100331),f900(x100331))),f317(f317(f242(f900(x100331),f900(x100331)),x100332),x100334)),f147(x100331,x100333)))+P1(f317(f317(f319(f905(x100331,x100331)),f317(f317(f242(x100331,x100331),f317(f317(f154(x100331),x100332),f650(x100333,x100334,x100332,x100331))),f651(x100333,x100334,x100332,x100331))),x100333)) % 112.26/112.10 [10053]~P1(f317(f29(x100532),x100534))+E(f317(f317(f317(f60(f906(x100531,a895),x100532,f91(f906(x100531,a895))),f317(f317(f9(x100532,f906(x100531,a895),f906(x100531,a895)),f317(f317(f10(x100531,f906(f906(x100531,a895),f906(x100531,a895)),x100532),f299(x100531)),x100533)),f178(f906(x100531,a895)))),f178(f906(x100531,a895))),x100534),f317(f300(x100532,x100531,x100533),x100534)) % 112.26/112.10 [10165]~P24(x101651,x101652,x101653,f232(f906(x101651,a895)))+P1(f317(f317(f224(f906(x101651,a895)),f317(f301(x101651,x101652,x101653),f317(f317(f299(x101652),x101654),f178(f906(x101652,a895))))),f317(f317(f299(x101651),f79(x101651,f317(f317(f9(x101651,x101652,a895),f317(f317(f10(x101652,f906(x101652,a895),x101651),a314),x101653)),x101654))),f178(f906(x101651,a895))))) % 112.26/112.10 [5701]~E(f317(f317(f124(x57011),x57012),x57014),x57013)+E(f317(f317(f165(x57011),f317(f179(f900(x57011)),x57012)),x57013),x57012) % 112.26/112.10 [5702]~E(f317(f317(f124(x57022),x57023),x57021),x57024)+E(x57021,f317(f317(f128(x57022),f317(f179(f900(x57022)),x57023)),x57024)) % 112.26/112.10 [5713]~E(x57134,f2(a899))+E(f317(f317(f154(x57131),f317(f317(f141(x57131),x57132),x57133)),x57134),x57132) % 112.26/112.10 [6269]~P119(x62691)+E(f317(f317(f234(x62691),f317(f317(f234(x62691),x62692),x62693)),x62694),f317(f317(f234(x62691),x62692),f317(f317(f75(a899),x62693),x62694))) % 112.26/112.10 [6270]~P80(x62701)+E(f317(f317(f234(x62701),f317(f317(f234(x62701),x62702),x62703)),x62704),f317(f317(f234(x62701),x62702),f317(f317(f75(a899),x62703),x62704))) % 112.26/112.10 [6278]E(x62781,f2(a899))+E(f317(f317(f154(x62782),f317(f317(f141(x62782),x62783),x62784)),x62781),f317(f317(f154(x62782),x62784),f317(f317(f3(a899),x62781),f72(a899)))) % 112.26/112.10 [6306]~P123(x63061)+E(f317(f317(f281(x63061),f317(f317(f75(x63061),x63062),x63063)),x63064),f317(f317(f75(x63061),x63062),f317(f317(f281(x63061),x63063),x63064))) % 112.26/112.10 [6307]~P71(x63071)+E(f317(f317(f74(x63071),f317(f317(f74(x63071),x63072),x63073)),x63074),f317(f317(f74(x63071),x63072),f317(f317(f74(x63071),x63073),x63074))) % 112.26/112.10 [6308]~P119(x63081)+E(f317(f317(f74(x63081),f317(f317(f74(x63081),x63082),x63083)),x63084),f317(f317(f74(x63081),x63082),f317(f317(f74(x63081),x63083),x63084))) % 112.26/112.10 [6309]~P70(x63091)+E(f317(f317(f75(x63091),f317(f317(f75(x63091),x63092),x63093)),x63094),f317(f317(f75(x63091),x63092),f317(f317(f75(x63091),x63093),x63094))) % 112.26/112.10 [6310]~P119(x63101)+E(f317(f317(f75(x63101),f317(f317(f75(x63101),x63102),x63103)),x63104),f317(f317(f75(x63101),x63102),f317(f317(f75(x63101),x63103),x63104))) % 112.26/112.10 [6313]~P108(x63131)+E(f317(f317(f228(x63131),f317(f317(f228(x63131),x63132),x63133)),x63134),f317(f317(f228(x63131),x63132),f317(f317(f228(x63131),x63133),x63134))) % 112.26/112.10 [6315]~P108(x63151)+E(f317(f317(f223(x63151),f317(f317(f223(x63151),x63152),x63153)),x63154),f317(f317(f223(x63151),x63152),f317(f317(f223(x63151),x63153),x63154))) % 112.26/112.10 [6317]~P98(x63171)+E(f317(f317(f91(x63171),f317(f317(f91(x63171),x63172),x63173)),x63174),f317(f317(f91(x63171),x63172),f317(f317(f91(x63171),x63173),x63174))) % 112.26/112.10 [6318]~P99(x63181)+E(f317(f317(f91(x63181),f317(f317(f91(x63181),x63182),x63183)),x63184),f317(f317(f91(x63181),x63182),f317(f317(f91(x63181),x63183),x63184))) % 112.26/112.10 [6319]~P99(x63191)+E(f317(f317(f92(x63191),f317(f317(f92(x63191),x63192),x63193)),x63194),f317(f317(f92(x63191),x63192),f317(f317(f92(x63191),x63193),x63194))) % 112.26/112.10 [6321]~P104(x63211)+E(f317(f317(f92(x63211),f317(f317(f92(x63211),x63212),x63213)),x63214),f317(f317(f92(x63211),x63212),f317(f317(f92(x63211),x63213),x63214))) % 112.26/112.10 [6330]~P3(x63301)+E(f41(x63301,f317(f317(f74(x63301),x63302),f317(f317(f75(x63301),x63303),x63304)),x63304),f41(x63301,x63302,x63304)) % 112.26/112.10 [6331]~P3(x63311)+E(f41(x63311,f317(f317(f74(x63311),x63312),f317(f317(f75(x63311),x63313),x63314)),x63313),f41(x63311,x63312,x63313)) % 112.26/112.10 [6473]E(f317(f317(f154(x64731),f317(f317(f165(x64731),x64732),x64733)),x64734),f317(f317(f154(x64731),x64733),x64734))+~P1(f317(f317(f225(a899),x64734),x64732)) % 112.26/112.10 [6654]~E(x66542,x66544)+P1(f317(f317(f162(x66541),f317(f317(f141(x66541),x66542),x66543)),x66544)) % 112.26/112.10 [6656]~P119(x66561)+E(f317(f317(f74(x66561),f317(f317(f74(x66561),x66562),x66563)),x66564),f317(f317(f74(x66561),f317(f317(f74(x66561),x66562),x66564)),x66563)) % 112.26/112.10 [6657]~P119(x66571)+E(f317(f317(f75(x66571),f317(f317(f75(x66571),x66572),x66573)),x66574),f317(f317(f75(x66571),f317(f317(f75(x66571),x66572),x66574)),x66573)) % 112.26/112.10 [6718]~P145(x67182)+E(f317(f317(f8(x67181,x67182),f317(f18(x67182,x67181),x67183)),x67184),f317(f317(f75(x67182),f317(f90(x67182),f317(f30(x67181),x67184))),x67183)) % 112.26/112.10 [6894]E(f317(f317(f92(f906(x68941,a895)),f317(f317(f299(x68941),x68942),x68943)),x68944),f317(f317(f92(f906(x68941,a895)),x68943),x68944))+P1(f317(f317(f319(x68941),x68942),x68944)) % 112.26/112.10 [6963]~P79(x69631)+E(f317(f317(f228(x69631),f317(f317(f3(x69631),x69632),x69633)),f317(f317(f3(x69631),x69634),x69633)),f317(f317(f3(x69631),f317(f317(f228(x69631),x69632),x69634)),x69633)) % 112.26/112.10 [6964]~P79(x69641)+E(f317(f317(f223(x69641),f317(f317(f3(x69641),x69642),x69643)),f317(f317(f3(x69641),x69644),x69643)),f317(f317(f3(x69641),f317(f317(f223(x69641),x69642),x69644)),x69643)) % 112.26/112.10 [6965]~P84(x69651)+E(f317(f317(f228(x69651),f317(f317(f74(x69651),x69652),x69653)),f317(f317(f74(x69651),x69654),x69653)),f317(f317(f74(x69651),f317(f317(f228(x69651),x69652),x69654)),x69653)) % 112.26/112.10 [6966]~P84(x69661)+E(f317(f317(f223(x69661),f317(f317(f74(x69661),x69662),x69663)),f317(f317(f74(x69661),x69664),x69663)),f317(f317(f74(x69661),f317(f317(f223(x69661),x69662),x69664)),x69663)) % 112.26/112.10 [6967]~P113(x69671)+E(f317(f317(f74(x69671),f317(f317(f75(x69671),x69672),x69673)),f317(f317(f75(x69671),x69674),x69673)),f317(f317(f75(x69671),f317(f317(f74(x69671),x69672),x69674)),x69673)) % 112.26/112.10 [6969]~P123(x69691)+E(f317(f317(f3(x69691),f317(f317(f281(x69691),x69692),x69693)),f317(f317(f281(x69691),x69694),x69693)),f317(f317(f281(x69691),f317(f317(f3(x69691),x69692),x69694)),x69693)) % 112.26/112.10 [6970]~P123(x69701)+E(f317(f317(f74(x69701),f317(f317(f281(x69701),x69702),x69703)),f317(f317(f281(x69701),x69704),x69703)),f317(f317(f281(x69701),f317(f317(f74(x69701),x69702),x69704)),x69703)) % 112.26/112.10 [6971]~P108(x69711)+E(f317(f317(f223(x69711),f317(f317(f228(x69711),x69712),x69713)),f317(f317(f228(x69711),x69714),x69713)),f317(f317(f228(x69711),f317(f317(f223(x69711),x69712),x69714)),x69713)) % 112.26/112.10 [6972]~P108(x69721)+E(f317(f317(f228(x69721),f317(f317(f223(x69721),x69722),x69723)),f317(f317(f223(x69721),x69724),x69723)),f317(f317(f223(x69721),f317(f317(f228(x69721),x69722),x69724)),x69723)) % 112.26/112.10 [6973]~P75(x69731)+E(f317(f317(f75(x69731),f317(f317(f234(x69731),x69732),x69733)),f317(f317(f234(x69731),x69734),x69733)),f317(f317(f234(x69731),f317(f317(f75(x69731),x69732),x69734)),x69733)) % 112.26/112.10 [6974]~P119(x69741)+E(f317(f317(f75(x69741),f317(f317(f234(x69741),x69742),x69743)),f317(f317(f234(x69741),x69744),x69743)),f317(f317(f234(x69741),f317(f317(f75(x69741),x69742),x69744)),x69743)) % 112.26/112.10 [6975]~P61(x69751)+E(f317(f317(f281(x69751),f317(f317(f234(x69751),x69752),x69753)),f317(f317(f234(x69751),x69754),x69753)),f317(f317(f234(x69751),f317(f317(f281(x69751),x69752),x69754)),x69753)) % 112.26/112.10 [6976]~P103(x69761)+E(f317(f317(f92(x69761),f317(f317(f91(x69761),x69762),x69763)),f317(f317(f91(x69761),x69764),x69763)),f317(f317(f91(x69761),f317(f317(f92(x69761),x69762),x69764)),x69763)) % 112.26/112.10 [6977]~P103(x69771)+E(f317(f317(f91(x69771),f317(f317(f92(x69771),x69772),x69773)),f317(f317(f92(x69771),x69774),x69773)),f317(f317(f92(x69771),f317(f317(f91(x69771),x69772),x69774)),x69773)) % 112.26/112.10 [6978]~P119(x69781)+E(f317(f317(f74(x69781),f317(f317(f75(x69781),x69782),x69783)),f317(f317(f75(x69781),x69784),x69783)),f317(f317(f75(x69781),f317(f317(f74(x69781),x69782),x69784)),x69783)) % 112.26/112.10 [7012]E(f317(f317(f149(x70121,x70122),x70123),x70124),x70122)+~P1(f317(f317(f224(a899),f317(f179(f900(x70121)),x70122)),x70123)) % 112.26/112.10 [7039]~P1(f317(x70393,x70394))+P1(f317(f317(f317(f91(f906(x70391,a895)),x70392),x70393),x70394)) % 112.26/112.10 [7041]~P1(f317(x70412,x70414))+P1(f317(f317(f317(f91(f906(x70411,a895)),x70412),x70413),x70414)) % 112.26/112.10 [7061]E(f317(f317(f154(x70611),f317(f317(f124(x70611),x70612),x70613)),x70614),f317(f317(f154(x70611),x70612),x70614))+~P1(f317(f317(f225(a899),x70614),f317(f179(f900(x70611)),x70612))) % 112.26/112.10 [7072]E(f317(f317(f3(f906(x70721,a895)),f317(f317(f299(x70721),x70722),x70723)),x70724),f317(f317(f3(f906(x70721,a895)),x70723),x70724))+~P1(f317(f317(f319(x70721),x70722),x70724)) % 112.26/112.10 [7113]~E(f129(a899,f317(f292(a899,x71131),x71132)),f317(f317(f141(a899),x71134),x71133))+E(f129(a899,f317(f292(a899,f317(f317(f74(a899),x71131),f72(a899))),x71132)),x71133) % 112.26/112.10 [7135]~P1(f317(f317(f162(x71351),x71353),x71354))+P1(f317(f317(f162(x71351),f317(f317(f141(x71351),x71352),x71353)),x71354)) % 112.26/112.10 [7185]E(x71851,f2(a899))+E(f317(f317(f141(x71852),x71853),f317(f317(f165(x71852),f317(f317(f3(a899),x71851),f72(a899))),x71854)),f317(f317(f165(x71852),x71851),f317(f317(f141(x71852),x71853),x71854))) % 112.26/112.10 [7287]E(f317(f317(f154(x72871),x72872),f317(f317(f3(a899),x72873),f317(f179(f900(x72871)),x72874))),f317(f317(f154(x72871),f317(f317(f124(x72871),x72874),x72872)),x72873))+P1(f317(f317(f225(a899),x72873),f317(f179(f900(x72871)),x72874))) % 112.26/112.10 [7315]E(f317(f317(f92(f906(x73151,a895)),x73152),f317(f317(f299(x73151),x73153),x73154)),f317(f317(f299(x73151),x73153),f317(f317(f92(f906(x73151,a895)),x73152),x73154)))+~P1(f317(f317(f319(x73151),x73153),x73152)) % 112.26/112.10 [7353]E(f317(f317(f154(x73531),f317(f317(f149(x73531,x73532),x73533),x73534)),x73533),x73534)+~P1(f317(f317(f225(a899),x73533),f317(f179(f900(x73531)),x73532))) % 112.26/112.10 [7375]E(x73751,f178(f906(x73752,a895)))+E(f317(f300(f905(x73753,x73752),x73753,f241(x73753,x73752)),f317(f317(f244(x73753,x73752),x73754),f317(f18(f906(x73752,a895),x73753),x73751))),x73754) % 112.26/112.10 [7376]E(x73761,f178(f906(x73762,a895)))+E(f317(f300(f905(x73762,x73763),x73763,f246(x73762,x73763)),f317(f317(f244(x73762,x73763),x73761),f317(f18(f906(x73763,a895),x73762),x73764))),x73764) % 112.26/112.10 [7451]E(f317(f317(f3(f906(x74511,a895)),f317(f317(f299(x74511),x74512),x74513)),x74514),f317(f317(f299(x74511),x74512),f317(f317(f3(f906(x74511,a895)),x74513),x74514)))+P1(f317(f317(f319(x74511),x74512),x74514)) % 112.26/112.10 [7487]~E(x74874,f178(f906(x74872,a895)))+E(f317(f300(f905(x74871,x74872),x74871,f241(x74871,x74872)),f317(f317(f244(x74871,x74872),x74873),f317(f18(f906(x74872,a895),x74871),x74874))),f178(f906(x74871,a895))) % 112.26/112.10 [7488]~E(x74883,f178(f906(x74881,a895)))+E(f317(f300(f905(x74881,x74882),x74882,f246(x74881,x74882)),f317(f317(f244(x74881,x74882),x74883),f317(f18(f906(x74882,a895),x74881),x74884))),f178(f906(x74882,a895))) % 112.26/112.10 [7540]~P1(f317(f317(f319(x75401),x75402),x75404))+P1(f317(f317(f319(x75401),x75402),f317(f317(f91(f906(x75401,a895)),x75403),x75404))) % 112.26/112.10 [7543]~P1(f317(f317(f319(x75431),x75432),x75433))+P1(f317(f317(f319(x75431),x75432),f317(f317(f91(f906(x75431,a895)),x75433),x75434))) % 112.26/112.10 [7561]E(f317(f317(f92(f906(x75611,a895)),f317(f317(f299(x75611),x75612),x75613)),x75614),f317(f317(f299(x75611),x75612),f317(f317(f92(f906(x75611,a895)),x75613),x75614)))+~P1(f317(f317(f319(x75611),x75612),x75614)) % 112.26/112.10 [7838]P1(f317(x78381,x78382))+~P1(f317(f317(f317(f92(f906(x78383,a895)),x78384),x78381),x78382)) % 112.26/112.10 [7839]P1(f317(x78391,x78392))+~P1(f317(f317(f317(f92(f906(x78393,a895)),x78391),x78394),x78392)) % 112.26/112.10 [7840]E(f317(f317(f8(x78401,a899),x78402),f317(f317(f3(f906(x78401,a895)),x78403),f317(f317(f299(x78401),x78404),f178(f906(x78401,a895))))),f317(f317(f8(x78401,a899),x78402),x78403))+P1(f317(f317(f319(x78401),x78404),x78403)) % 112.26/112.10 [7845]~P69(x78451)+E(f317(f155(x78451),f317(f317(f144(a899,x78451),x78452),f129(a899,f317(f292(a899,x78453),x78454)))),f317(f317(f8(a899,x78451),x78452),f317(f162(a899),f129(a899,f317(f292(a899,x78453),x78454))))) % 112.26/112.10 [7846]~P69(x78461)+E(f317(f317(f8(a899,x78461),x78462),f317(f162(a899),f129(a899,f317(f292(a899,x78463),x78464)))),f317(f155(x78461),f317(f317(f144(a899,x78461),x78462),f129(a899,f317(f292(a899,x78463),x78464))))) % 112.26/112.10 [7960]~E(x79603,x79604)+P1(f317(f57(x79601,x79602,f317(f317(f299(x79601),x79603),f178(f906(x79601,a895)))),x79604)) % 112.26/112.10 [8057]P1(f317(f317(f319(x80571),x80572),f317(f162(x80571),x80573)))+~P1(f317(f317(f319(x80571),x80572),f317(f162(x80571),f317(f317(f165(x80571),x80574),x80573)))) % 112.26/112.10 [8058]P1(f317(f317(f319(x80581),x80582),f317(f162(x80581),x80583)))+~P1(f317(f317(f319(x80581),x80582),f317(f162(x80581),f317(f317(f128(x80581),x80584),x80583)))) % 112.26/112.10 [8128]P1(f317(f317(f319(x81281),x81282),x81283))+~P1(f317(f317(f319(x81281),x81282),f317(f317(f3(f906(x81281,a895)),x81283),x81284))) % 112.26/112.10 [8130]P1(f317(f317(f319(x81301),x81302),x81303))+~P1(f317(f317(f319(x81301),x81302),f317(f317(f92(f906(x81301,a895)),x81304),x81303))) % 112.26/112.10 [8133]P1(f317(f317(f319(x81331),x81332),x81333))+~P1(f317(f317(f319(x81331),x81332),f317(f317(f92(f906(x81331,a895)),x81333),x81334))) % 112.26/112.10 [8148]E(f317(f317(f124(x81481),f317(f317(f165(x81481),x81482),x81483)),f317(f317(f141(x81481),x81484),f317(f317(f128(x81481),f317(a102,x81482)),x81483))),f317(f317(f149(x81481,x81483),x81482),x81484))+~P1(f317(f317(f225(a899),x81482),f317(f179(f900(x81481)),x81483))) % 112.26/112.10 [8171]P1(f317(f317(f319(x81711),x81712),x81713))+~P1(f317(f317(f224(f906(x81711,a895)),f317(f317(f299(x81711),x81712),x81714)),x81713)) % 112.26/112.10 [8208]~P1(f317(f317(f319(x82081),x82082),x82083))+~P1(f317(f317(f319(x82081),x82082),f317(f317(f3(f906(x82081,a895)),x82084),x82083))) % 112.26/112.10 [8241]~P1(f317(f317(f225(a899),x82414),f317(f179(f900(x82411)),x82413)))+P1(f317(f317(f319(x82411),x82412),f317(f162(x82411),f317(f317(f149(x82411,x82413),x82414),x82412)))) % 112.26/112.10 [8294]E(f317(f317(f154(x82941),f317(f317(f128(x82941),x82942),x82943)),x82944),f317(f317(f154(x82941),x82943),f317(f317(f74(a899),x82942),x82944)))+~P1(f317(f317(f224(a899),f317(f317(f74(a899),x82942),x82944)),f317(f179(f900(x82941)),x82943))) % 112.26/112.10 [8303]~P145(x83032)+E(f317(f317(f8(x83031,x83032),f317(f317(f10(a899,x83032,x83031),f90(x83032)),x83033)),x83034),f317(f90(x83032),f317(f317(f8(x83031,a899),x83033),x83034))) % 112.26/112.10 [8304]~P141(x83042)+E(f317(f317(f8(x83041,x83042),f317(f317(f10(a1,x83042,x83041),f93(x83042)),x83043)),x83044),f317(f93(x83042),f317(f317(f8(x83041,a1),x83043),x83044))) % 112.26/112.10 [8354]~P64(x83542)+E(f317(f317(f11(x83541,x83542),f317(f317(f10(x83542,x83542,x83541),f70(x83542)),x83543)),x83544),f317(f70(x83542),f317(f317(f11(x83541,x83542),x83543),x83544))) % 112.26/112.10 [8355]~P68(x83552)+E(f317(f317(f8(x83551,x83552),f317(f317(f10(x83552,x83552,x83551),f73(x83552)),x83553)),x83554),f317(f73(x83552),f317(f317(f8(x83551,x83552),x83553),x83554))) % 112.26/112.10 [8358]E(f317(f317(f8(x83581,a899),x83582),f317(f317(f3(f906(x83581,a895)),x83583),f317(f317(f299(x83581),x83584),f178(f906(x83581,a895))))),f317(f317(f3(a899),f317(f317(f8(x83581,a899),x83582),x83583)),f317(x83582,x83584)))+~P1(f317(f317(f319(x83581),x83584),x83583)) % 112.26/112.10 [8377]P1(f317(f317(f224(f906(x83771,a895)),x83772),x83773))+~P1(f317(f317(f224(f906(x83771,a895)),f317(f317(f299(x83771),x83774),x83772)),x83773)) % 112.26/112.10 [8501]~E(f317(f300(x85012,x85013,x85011),f232(f906(x85012,a895))),f232(f906(x85013,a895)))+E(f317(x85011,f317(f85(x85012,x85013,f232(f906(x85012,a895)),x85011),x85014)),x85014) % 112.26/112.10 [8585]P36(x85851,x85852)+~P36(x85851,f317(f317(f299(f905(x85851,x85851)),f317(f317(f242(x85851,x85851),x85853),x85854)),x85852)) % 112.26/112.10 [8586]P57(x85861,x85862)+~P57(x85861,f317(f317(f299(f905(x85861,x85861)),f317(f317(f242(x85861,x85861),x85863),x85864)),x85862)) % 112.26/112.10 [8591]~P108(x85911)+E(f317(f317(f138(x85911,x85911,f7(x85911)),x85912),f317(f317(f138(x85911,x85911,f7(x85911)),x85913),x85914)),f317(f317(f138(x85911,x85911,f7(x85911)),x85913),f317(f317(f138(x85911,x85911,f7(x85911)),x85912),x85914))) % 112.26/112.10 [8606]E(x86061,x86062)+~P1(f317(f57(x86063,x86064,f317(f317(f299(x86063),x86061),f178(f906(x86063,a895)))),x86062)) % 112.26/112.10 [8615]E(f317(f317(f124(x86151),f317(f317(f165(x86151),x86152),x86153)),f317(f317(f165(x86151),x86154),f317(f317(f128(x86151),x86152),x86153))),f317(f317(f165(x86151),f317(f317(f74(a899),x86152),x86154)),x86153))+~P1(f317(f317(f224(a899),f317(f317(f74(a899),x86152),x86154)),f317(f179(f900(x86151)),x86153))) % 112.26/112.10 [8655]P1(f317(f29(x86551),x86552))+~E(x86552,f317(f300(a899,x86551,x86553),f317(f252(a899),f317(f317(f9(a899,a899,a895),f225(a899)),x86554)))) % 112.26/112.10 [8675]~P91(x86751)+E(f317(f132(x86751,x86751,f74(x86751),f317(f317(f74(x86751),x86752),x86753)),x86754),f317(f317(f74(x86751),x86752),f317(f132(x86751,x86751,f74(x86751),x86753),x86754))) % 112.26/112.10 [8711]P1(f317(f317(f224(f906(x87111,a895)),f317(f254(x87111,x87112),x87113)),f317(f254(x87111,x87112),x87114)))+~P1(f317(f317(f224(f906(f905(x87111,x87112),a895)),x87113),x87114)) % 112.26/112.10 [8723]~P1(f317(f317(f224(a899),x87232),x87234))+P1(f317(f317(f224(f906(x87231,a895)),f317(f162(x87231),f317(f317(f165(x87231),x87232),x87233))),f317(f162(x87231),f317(f317(f165(x87231),x87234),x87233)))) % 112.26/112.10 [8724]~P1(f317(f317(f224(a899),x87244),x87242))+P1(f317(f317(f224(f906(x87241,a895)),f317(f162(x87241),f317(f317(f128(x87241),x87242),x87243))),f317(f162(x87241),f317(f317(f128(x87241),x87244),x87243)))) % 112.26/112.10 [8781]~P1(f317(f29(x87811),f317(f317(f3(f906(x87811,a895)),x87812),x87814)))+P1(f317(f29(x87811),f317(f317(f3(f906(x87811,a895)),x87812),f317(f317(f299(x87811),x87813),x87814)))) % 112.26/112.10 [8823]P1(f317(f317(f319(f905(x88231,x88231)),x88232),f297(x88231,x88233)))+~P1(f317(f317(f319(f905(x88231,x88231)),x88232),f317(f317(f173(f905(x88231,x88231),a895),x88234),x88233))) % 112.26/112.10 [8909]~P1(f317(f29(x89091),f317(f317(f3(f906(x89091,a895)),x89092),f317(f317(f299(x89091),x89094),x89093))))+P1(f317(f29(x89091),f317(f317(f3(f906(x89091,a895)),x89092),x89093))) % 112.26/112.10 [9120]~P108(x91201)+P1(f317(f317(f224(x91201),f317(f317(f223(x91201),x91202),f317(f317(f228(x91201),x91203),x91204))),f317(f317(f228(x91201),f317(f317(f223(x91201),x91202),x91203)),f317(f317(f223(x91201),x91202),x91204)))) % 112.26/112.10 [9121]~P99(x91211)+P1(f317(f317(f224(x91211),f317(f317(f91(x91211),x91212),f317(f317(f92(x91211),x91213),x91214))),f317(f317(f92(x91211),f317(f317(f91(x91211),x91212),x91213)),f317(f317(f91(x91211),x91212),x91214)))) % 112.26/112.10 [9268]E(x92681,x92682)+~P1(f317(f317(f319(f905(x92683,x92683)),f317(f317(f242(x92683,x92683),x92681),x92682)),f317(f162(f905(x92683,x92683)),f317(f317(f171(x92683,x92683),x92684),x92684)))) % 112.26/112.10 [9299]~P1(f317(f317(f319(f905(x92991,x92991)),f317(f317(f242(x92991,x92991),x92993),x92992)),f297(x92991,x92994)))+~P36(x92991,f317(f317(f299(f905(x92991,x92991)),f317(f317(f242(x92991,x92991),x92992),x92993)),x92994)) % 112.26/112.10 [9300]~P1(f317(f317(f319(f905(x93001,x93001)),f317(f317(f242(x93001,x93001),x93003),x93002)),f297(x93001,x93004)))+~P57(x93001,f317(f317(f299(f905(x93001,x93001)),f317(f317(f242(x93001,x93001),x93002),x93003)),x93004)) % 112.26/112.10 [9304]E(x93041,x93042)+E(f317(f126(x93043,f317(f317(f10(a895,a895,x93043),a312),f317(a314,x93041))),f317(f317(f141(x93043),x93042),x93044)),f317(f317(f141(x93043),x93042),f317(f126(x93043,f317(f317(f10(a895,a895,x93043),a312),f317(a314,x93041))),x93044))) % 112.26/112.10 [9335]~P25(x93352,x93351,x93353,f232(f906(x93352,a895)),f232(f906(x93351,a895)))+E(f317(f300(x93351,x93352,f85(x93352,x93351,f232(f906(x93352,a895)),x93353)),x93354),f317(f301(x93352,x93351,x93353),x93354)) % 112.26/112.10 [9351]~P108(x93511)+P1(f317(f317(f224(x93511),f317(f317(f223(x93511),f317(f317(f228(x93511),x93512),x93513)),f317(f317(f228(x93511),x93512),x93514))),f317(f317(f228(x93511),x93512),f317(f317(f223(x93511),x93513),x93514)))) % 112.26/112.10 [9352]~P99(x93521)+P1(f317(f317(f224(x93521),f317(f317(f91(x93521),f317(f317(f92(x93521),x93522),x93523)),f317(f317(f92(x93521),x93522),x93524))),f317(f317(f92(x93521),x93522),f317(f317(f91(x93521),x93523),x93524)))) % 112.26/112.10 [9416]~P25(x94162,x94161,x94164,f232(f906(x94162,a895)),f232(f906(x94161,a895)))+E(f317(f252(x94161),f317(f317(f10(x94162,a895,x94161),x94163),f85(x94162,x94161,f232(f906(x94162,a895)),x94164))),f317(f300(x94162,x94161,x94164),f317(f252(x94162),x94163))) % 112.26/112.10 [9430]~E(f317(f300(x94302,x94301,x94303),f232(f906(x94302,a895))),f232(f906(x94301,a895)))+P1(f317(f317(f224(f906(x94301,a895)),f317(f73(f906(x94301,a895)),f317(f300(x94302,x94301,x94303),x94304))),f317(f300(x94302,x94301,x94303),f317(f73(f906(x94302,a895)),x94304)))) % 112.26/112.10 [9765]P1(f317(f317(f319(f905(x97651,x97651)),f317(f317(f242(x97651,x97651),x97652),x97653)),f317(f276(x97651,x97651),f317(f317(f279(x97651,x97651,x97651),x97654),f297(x97651,x97654)))))+~P1(f317(f317(f319(f905(x97651,x97651)),f317(f317(f242(x97651,x97651),x97652),x97653)),f317(f317(f279(x97651,x97651,x97651),f317(f276(x97651,x97651),x97654)),f297(x97651,f317(f276(x97651,x97651),x97654))))) % 112.26/112.10 [9766]~P1(f317(f317(f319(f905(x97661,x97661)),f317(f317(f242(x97661,x97661),x97662),x97663)),f317(f276(x97661,x97661),f317(f317(f279(x97661,x97661,x97661),x97664),f297(x97661,x97664)))))+P1(f317(f317(f319(f905(x97661,x97661)),f317(f317(f242(x97661,x97661),x97662),x97663)),f317(f317(f279(x97661,x97661,x97661),f317(f276(x97661,x97661),x97664)),f297(x97661,f317(f276(x97661,x97661),x97664))))) % 112.26/112.10 [9787]~P1(f317(f317(f319(x97872),x97874),f317(f274(x97871,x97872),x97873)))+P1(f317(f317(f319(f905(x97871,x97872)),f317(f317(f242(x97871,x97872),f540(x97873,x97871,x97874,x97872)),x97874)),x97873)) % 112.26/112.10 [9788]~P1(f317(f317(f319(x97882),x97884),f317(f274(x97881,x97882),x97883)))+P1(f317(f317(f319(f905(x97881,x97882)),f317(f317(f242(x97881,x97882),f546(x97883,x97881,x97884,x97882)),x97884)),x97883)) % 112.26/112.10 [9813]~P1(f317(f317(f319(x98131),x98134),f317(f317(f91(f906(x98131,a895)),x98132),x98133)))+P1(f317(f317(f317(f91(f906(x98131,a895)),f317(f317(f9(x98131,f906(x98131,a895),a895),f319(x98131)),x98132)),f317(f317(f9(x98131,f906(x98131,a895),a895),f319(x98131)),x98133)),x98134)) % 112.26/112.10 [9814]~P1(f317(f317(f319(x98141),x98144),f317(f317(f92(f906(x98141,a895)),x98142),x98143)))+P1(f317(f317(f317(f92(f906(x98141,a895)),f317(f317(f9(x98141,f906(x98141,a895),a895),f319(x98141)),x98142)),f317(f317(f9(x98141,f906(x98141,a895),a895),f319(x98141)),x98143)),x98144)) % 112.26/112.10 [9896]~P1(f317(f317(f319(f905(x98961,x98961)),f317(f317(f242(x98961,x98961),x98964),x98963)),f317(f317(f279(x98961,x98961,x98961),x98962),f297(x98961,x98962))))+P1(f317(f317(f319(f905(x98961,x98961)),f317(f317(f242(x98961,x98961),f620(x98962,x98963,x98964,x98961)),x98963)),x98962)) % 112.26/112.10 [9931]P1(f317(f317(f319(x99311),x99312),f317(f317(f91(f906(x99311,a895)),x99313),x99314)))+~P1(f317(f317(f317(f91(f906(x99311,a895)),f317(f317(f9(x99311,f906(x99311,a895),a895),f319(x99311)),x99313)),f317(f317(f9(x99311,f906(x99311,a895),a895),f319(x99311)),x99314)),x99312)) % 112.26/112.10 [9932]P1(f317(f317(f319(x99321),x99322),f317(f317(f92(f906(x99321,a895)),x99323),x99324)))+~P1(f317(f317(f317(f92(f906(x99321,a895)),f317(f317(f9(x99321,f906(x99321,a895),a895),f319(x99321)),x99323)),f317(f317(f9(x99321,f906(x99321,a895),a895),f319(x99321)),x99324)),x99322)) % 112.26/112.10 [10215]P31(x102151,f317(f317(f9(x102151,f906(f905(x102151,x102151),a895),f906(x102151,a895)),f317(f317(f10(f906(x102151,f906(f906(f905(x102151,x102151),a895),a895)),f906(f906(f905(x102151,x102151),a895),f906(x102151,a895)),x102151),f9(x102151,f906(f905(x102151,x102151),a895),a895)),f317(f317(f10(f906(x102151,f905(x102151,x102151)),f906(x102151,f906(f906(f905(x102151,x102151),a895),a895)),x102151),f317(f10(f905(x102151,x102151),f906(f906(f905(x102151,x102151),a895),a895),x102151),f319(f905(x102151,x102151)))),f242(x102151,x102151)))),x102152),x102153,x102154)+~P1(f317(f317(f319(f905(f900(x102151),f900(x102151))),f317(f317(f242(f900(x102151),f900(x102151)),x102153),x102154)),f148(x102151,x102152))) % 112.26/112.10 [10219]P58(x102191,f317(f317(f9(x102191,f906(f905(x102191,x102191),a895),f906(x102191,a895)),f317(f317(f10(f906(x102191,f906(f906(f905(x102191,x102191),a895),a895)),f906(f906(f905(x102191,x102191),a895),f906(x102191,a895)),x102191),f9(x102191,f906(f905(x102191,x102191),a895),a895)),f317(f317(f10(f906(x102191,f905(x102191,x102191)),f906(x102191,f906(f906(f905(x102191,x102191),a895),a895)),x102191),f317(f10(f905(x102191,x102191),f906(f906(f905(x102191,x102191),a895),a895),x102191),f319(f905(x102191,x102191)))),f242(x102191,x102191)))),x102192),x102193,x102194)+~P1(f317(f317(f319(f905(f906(x102191,a895),f906(x102191,a895))),f317(f317(f242(f906(x102191,a895),f906(x102191,a895)),x102193),x102194)),f309(x102191,x102192))) % 112.26/112.10 [10254]E(x102541,x102542)+~E(f317(f317(f9(x102543,f906(f905(x102543,x102544),a895),f906(x102544,a895)),f317(f317(f10(f906(x102544,f906(f906(f905(x102543,x102544),a895),a895)),f906(f906(f905(x102543,x102544),a895),f906(x102544,a895)),x102543),f9(x102544,f906(f905(x102543,x102544),a895),a895)),f317(f317(f10(f906(x102544,f905(x102543,x102544)),f906(x102544,f906(f906(f905(x102543,x102544),a895),a895)),x102543),f317(f10(f905(x102543,x102544),f906(f906(f905(x102543,x102544),a895),a895),x102544),f319(f905(x102543,x102544)))),f242(x102543,x102544)))),x102541),f317(f317(f9(x102543,f906(f905(x102543,x102544),a895),f906(x102544,a895)),f317(f317(f10(f906(x102544,f906(f906(f905(x102543,x102544),a895),a895)),f906(f906(f905(x102543,x102544),a895),f906(x102544,a895)),x102543),f9(x102544,f906(f905(x102543,x102544),a895),a895)),f317(f317(f10(f906(x102544,f905(x102543,x102544)),f906(x102544,f906(f906(f905(x102543,x102544),a895),a895)),x102543),f317(f10(f905(x102543,x102544),f906(f906(f905(x102543,x102544),a895),a895),x102544),f319(f905(x102543,x102544)))),f242(x102543,x102544)))),x102542)) % 112.26/112.10 [10257]~P31(x102571,f317(f317(f9(x102571,f906(f905(x102571,x102571),a895),f906(x102571,a895)),f317(f317(f10(f906(x102571,f906(f906(f905(x102571,x102571),a895),a895)),f906(f906(f905(x102571,x102571),a895),f906(x102571,a895)),x102571),f9(x102571,f906(f905(x102571,x102571),a895),a895)),f317(f317(f10(f906(x102571,f905(x102571,x102571)),f906(x102571,f906(f906(f905(x102571,x102571),a895),a895)),x102571),f317(f10(f905(x102571,x102571),f906(f906(f905(x102571,x102571),a895),a895),x102571),f319(f905(x102571,x102571)))),f242(x102571,x102571)))),x102574),x102572,x102573)+P1(f317(f317(f319(f905(f900(x102571),f900(x102571))),f317(f317(f242(f900(x102571),f900(x102571)),x102572),x102573)),f148(x102571,x102574))) % 112.26/112.10 [10258]~P58(x102581,f317(f317(f9(x102581,f906(f905(x102581,x102581),a895),f906(x102581,a895)),f317(f317(f10(f906(x102581,f906(f906(f905(x102581,x102581),a895),a895)),f906(f906(f905(x102581,x102581),a895),f906(x102581,a895)),x102581),f9(x102581,f906(f905(x102581,x102581),a895),a895)),f317(f317(f10(f906(x102581,f905(x102581,x102581)),f906(x102581,f906(f906(f905(x102581,x102581),a895),a895)),x102581),f317(f10(f905(x102581,x102581),f906(f906(f905(x102581,x102581),a895),a895),x102581),f319(f905(x102581,x102581)))),f242(x102581,x102581)))),x102584),x102582,x102583)+P1(f317(f317(f319(f905(f906(x102581,a895),f906(x102581,a895))),f317(f317(f242(f906(x102581,a895),f906(x102581,a895)),x102582),x102583)),f309(x102581,x102584))) % 112.26/112.10 [7610]~P94(x76101)+E(f317(f317(f74(x76101),f317(f94(x76101),x76102)),f317(f317(f3(x76101),f317(f94(x76101),x76103)),x76104)),f317(f317(f3(x76101),f317(f94(x76101),f317(f317(f74(a1),x76102),x76103))),x76104)) % 112.26/112.10 [7611]~P94(x76111)+E(f317(f317(f74(x76111),f317(f94(x76111),x76112)),f317(f317(f74(x76111),f317(f94(x76111),x76113)),x76114)),f317(f317(f74(x76111),f317(f94(x76111),f317(f317(f74(a1),x76112),x76113))),x76114)) % 112.26/112.10 [7612]~P94(x76121)+E(f317(f317(f75(x76121),f317(f94(x76121),x76122)),f317(f317(f75(x76121),f317(f94(x76121),x76123)),x76124)),f317(f317(f75(x76121),f317(f94(x76121),f317(f317(f75(a1),x76122),x76123))),x76124)) % 112.26/112.10 [7655]~P145(x76551)+E(f317(f155(x76551),f317(f317(f144(x76552,x76551),f317(f18(x76551,x76552),x76553)),x76554)),f317(f317(f75(x76551),f317(f90(x76551),f317(f179(f900(x76552)),x76554))),x76553)) % 112.26/112.10 [7895]E(f317(f258(x78951,f317(f317(f141(f905(a89,x78951)),x78952),x78953)),x78954),f317(f246(a89,x78951),x78952))+~P1(f317(f317(f225(a89),x78954),f317(f241(a89,x78951),x78952))) % 112.26/112.10 [7936]~P94(x79361)+E(f317(f317(f74(x79361),f317(f94(x79361),x79362)),f317(f317(f3(x79361),x79363),f317(f94(x79361),x79364))),f317(f317(f74(x79361),f317(f94(x79361),f317(f317(f74(a1),x79362),f317(f73(a1),x79364)))),x79363)) % 112.26/112.10 [8070]E(f317(f258(x80701,x80702),f317(f317(f3(a89),x80703),f317(f241(a89,x80701),x80704))),f317(f258(x80701,f317(f317(f141(f905(a89,x80701)),x80704),x80702)),x80703))+P1(f317(f317(f225(a89),x80703),f317(f241(a89,x80701),x80704))) % 112.26/112.10 [8507]~P1(f317(f317(f319(x85071),x85072),f317(f162(x85071),f104(x85071,x85074))))+P1(f317(f317(f319(x85071),x85072),f317(f162(x85071),f104(x85071,f317(f317(f124(x85071),x85073),x85074))))) % 112.26/112.10 [8508]~P1(f317(f317(f319(x85081),x85082),f317(f162(x85081),f104(x85081,x85083))))+P1(f317(f317(f319(x85081),x85082),f317(f162(x85081),f104(x85081,f317(f317(f124(x85081),x85083),x85084))))) % 112.26/112.10 [8528]E(f317(f317(f91(f906(x85281,a895)),f317(f317(f92(f906(x85281,a895)),x85282),x85283)),x85284),f317(f317(f92(f906(x85281,a895)),x85282),f317(f317(f91(f906(x85281,a895)),x85283),x85284)))+~P1(f317(f317(f224(f906(x85281,a895)),x85284),x85282)) % 112.26/112.10 [8837]~E(f317(f317(f91(f906(x88371,a895)),f317(f317(f92(f906(x88371,a895)),x88373),x88374)),x88372),f317(f317(f92(f906(x88371,a895)),x88373),f317(f317(f91(f906(x88371,a895)),x88374),x88372)))+P1(f317(f317(f224(f906(x88371,a895)),x88372),x88373)) % 112.26/112.10 [9125]~P1(f317(f317(f224(f906(x91251,a895)),x91252),f317(f317(f91(f906(x91251,a895)),x91253),x91254)))+P1(f317(f317(f224(f906(x91251,a895)),f317(f317(f3(f906(x91251,a895)),x91252),x91253)),x91254)) % 112.26/112.10 [9240]~E(f317(f300(x92401,x92402,x92403),f232(f906(x92401,a895))),f232(f906(x92402,a895)))+E(f317(f300(x92401,x92402,x92403),f317(f300(x92402,x92401,f85(x92401,x92402,f232(f906(x92401,a895)),x92403)),x92404)),x92404) % 112.26/112.10 [9245]P1(f317(f317(f224(f906(x92451,a895)),x92452),f317(f317(f91(f906(x92451,a895)),x92453),x92454)))+~P1(f317(f317(f224(f906(x92451,a895)),f317(f317(f3(f906(x92451,a895)),x92452),x92453)),x92454)) % 112.26/112.10 [9330]~P86(x93301)+E(f317(f70(x93301),f317(f317(f8(x93302,x93301),f317(f317(f10(x93301,x93301,x93302),f70(x93301)),x93303)),x93304)),f317(f317(f8(x93302,x93301),f317(f317(f10(x93301,x93301,x93302),f70(x93301)),x93303)),x93304)) % 112.26/112.10 [9506]~P86(x95061)+P1(f317(f317(f224(x95061),f2(x95061)),f317(f317(f8(x95062,x95061),f317(f317(f10(x95061,x95061,x95062),f70(x95061)),x95063)),x95064))) % 112.26/112.10 [9510]~P68(x95101)+E(f317(f155(x95101),f317(f317(f144(x95102,x95101),f317(f67(x95101,x95101,x95102,f73(x95101)),x95103)),x95104)),f317(f73(x95101),f317(f155(x95101),f317(f317(f144(x95102,x95101),x95103),x95104)))) % 112.26/112.10 [9661]~P86(x96611)+P1(f317(f317(f224(x96611),f317(f70(x96611),f317(f317(f8(x96612,x96611),x96613),x96614))),f317(f317(f8(x96612,x96611),f317(f317(f10(x96611,x96611,x96612),f70(x96611)),x96613)),x96614))) % 112.26/112.10 [9690]~E(f317(f317(f74(a899),x96901),x96904),f317(f317(f74(a899),x96903),x96902))+P1(f317(f317(f319(f905(f905(a899,a899),f905(a899,a899))),f317(f317(f242(f905(a899,a899),f905(a899,a899)),f317(f317(f242(a899,a899),x96901),x96902)),f317(f317(f242(a899,a899),x96903),x96904))),a99)) % 112.26/112.10 [9691]~P1(f317(f317(f225(a899),x96911),x96913))+P1(f317(f317(f319(f905(f905(a899,a899),f905(a899,a899))),f317(f317(f242(f905(a899,a899),f905(a899,a899)),f317(f317(f242(a899,a899),x96911),x96912)),f317(f317(f242(a899,a899),x96913),x96914))),a26)) % 112.26/112.10 [9692]~P1(f317(f317(f225(a899),x96921),x96923))+P1(f317(f317(f319(f905(f905(a899,a899),f905(a899,a899))),f317(f317(f242(f905(a899,a899),f905(a899,a899)),f317(f317(f242(a899,a899),x96921),x96922)),f317(f317(f242(a899,a899),x96923),x96924))),a65)) % 112.26/112.10 [9838]E(f317(f317(f74(a899),x98381),x98382),f317(f317(f74(a899),x98383),x98384))+~P1(f317(f317(f319(f905(f905(a899,a899),f905(a899,a899))),f317(f317(f242(f905(a899,a899),f905(a899,a899)),f317(f317(f242(a899,a899),x98381),x98384)),f317(f317(f242(a899,a899),x98383),x98382))),a99)) % 112.26/112.10 [9870]E(f317(f317(f154(x98701),f317(f317(f128(x98701),f317(f179(f900(x98701)),f167(x98701,x98702,x98703))),x98703)),x98704),f317(f317(f154(x98701),x98703),f317(f317(f74(a899),x98704),f317(f179(f900(x98701)),f167(x98701,x98702,x98703)))))+~P1(f317(f317(f225(a899),x98704),f317(f179(f900(x98701)),f317(f317(f128(x98701),f317(f179(f900(x98701)),f167(x98701,x98702,x98703))),x98703)))) % 112.26/112.10 [9887]~P1(f317(f317(f319(x98872),x98874),f317(f317(f35(x98871,f906(x98872,a895)),f232(f906(x98871,a895))),x98873)))+P1(f317(f317(f317(f35(x98871,f906(x98872,a895)),f232(f906(x98871,a895))),f317(f317(f10(f906(x98872,a895),f906(x98872,a895),x98871),f317(f9(x98872,f906(x98872,a895),a895),f319(x98872))),x98873)),x98874)) % 112.26/112.10 [9888]~P1(f317(f317(f319(x98882),x98884),f317(f317(f36(x98881,f906(x98882,a895)),f232(f906(x98881,a895))),x98883)))+P1(f317(f317(f317(f36(x98881,f906(x98882,a895)),f232(f906(x98881,a895))),f317(f317(f10(f906(x98882,a895),f906(x98882,a895),x98881),f317(f9(x98882,f906(x98882,a895),a895),f319(x98882))),x98883)),x98884)) % 112.26/112.10 [9957]~P1(f317(f45(x99571,x99572),f317(f317(f242(a1,a1),x99574),x99573)))+P1(f317(f45(f317(f73(a1),x99571),x99572),f317(f317(f242(a1,a1),f317(f317(f317(f86(a1),f317(f317(a314,x99573),f2(a1))),f317(f73(a1),x99574)),f317(f317(f3(a1),f317(f73(a1),x99574)),f72(a1)))),f317(f317(f317(f86(a1),f317(f317(a314,x99573),f2(a1))),f2(a1)),f317(f317(f3(a1),x99572),x99573))))) % 112.26/112.10 [9969]P1(f317(f317(f319(x99691),x99692),f317(f317(f35(x99693,f906(x99691,a895)),f232(f906(x99693,a895))),x99694)))+~P1(f317(f317(f317(f35(x99693,f906(x99691,a895)),f232(f906(x99693,a895))),f317(f317(f10(f906(x99691,a895),f906(x99691,a895),x99693),f317(f9(x99691,f906(x99691,a895),a895),f319(x99691))),x99694)),x99692)) % 112.26/112.10 [9970]P1(f317(f317(f319(x99701),x99702),f317(f317(f36(x99703,f906(x99701,a895)),f232(f906(x99703,a895))),x99704)))+~P1(f317(f317(f317(f36(x99703,f906(x99701,a895)),f232(f906(x99703,a895))),f317(f317(f10(f906(x99701,a895),f906(x99701,a895),x99703),f317(f9(x99701,f906(x99701,a895),a895),f319(x99701))),x99704)),x99702)) % 112.26/112.10 [9982]E(f317(f317(f36(a899,f906(x99821,a895)),f232(f906(a899,a895))),x99822),f317(f317(f36(a899,f906(x99821,a895)),f232(f906(a899,a895))),x99823))+~E(f317(f317(f36(a899,f906(x99821,a895)),f317(f292(a899,f2(a899)),f489(x99822,x99824,x99823,x99821))),x99823),f317(f317(f36(a899,f906(x99821,a895)),f317(f292(a899,f2(a899)),f317(f317(f74(a899),f489(x99822,x99824,x99823,x99821)),x99824))),x99822)) % 112.26/112.10 [10335]~P1(f317(f317(f224(f906(f905(x103351,x103352),a895)),x103353),x103354))+P1(f317(f317(f224(f906(x103351,f906(x103352,a895))),f317(f317(f9(x103351,f906(f905(x103351,x103352),a895),f906(x103352,a895)),f317(f317(f10(f906(x103352,f906(f906(f905(x103351,x103352),a895),a895)),f906(f906(f905(x103351,x103352),a895),f906(x103352,a895)),x103351),f9(x103352,f906(f905(x103351,x103352),a895),a895)),f317(f317(f10(f906(x103352,f905(x103351,x103352)),f906(x103352,f906(f906(f905(x103351,x103352),a895),a895)),x103351),f317(f10(f905(x103351,x103352),f906(f906(f905(x103351,x103352),a895),a895),x103352),f319(f905(x103351,x103352)))),f242(x103351,x103352)))),x103353)),f317(f317(f9(x103351,f906(f905(x103351,x103352),a895),f906(x103352,a895)),f317(f317(f10(f906(x103352,f906(f906(f905(x103351,x103352),a895),a895)),f906(f906(f905(x103351,x103352),a895),f906(x103352,a895)),x103351),f9(x103352,f906(f905(x103351,x103352),a895),a895)),f317(f317(f10(f906(x103352,f905(x103351,x103352)),f906(x103352,f906(f906(f905(x103351,x103352),a895),a895)),x103351),f317(f10(f905(x103351,x103352),f906(f906(f905(x103351,x103352),a895),a895),x103352),f319(f905(x103351,x103352)))),f242(x103351,x103352)))),x103354))) % 112.26/112.10 [10351]P1(f317(f317(f224(f906(f905(x103511,x103512),a895)),x103513),x103514))+~P1(f317(f317(f224(f906(x103511,f906(x103512,a895))),f317(f317(f9(x103511,f906(f905(x103511,x103512),a895),f906(x103512,a895)),f317(f317(f10(f906(x103512,f906(f906(f905(x103511,x103512),a895),a895)),f906(f906(f905(x103511,x103512),a895),f906(x103512,a895)),x103511),f9(x103512,f906(f905(x103511,x103512),a895),a895)),f317(f317(f10(f906(x103512,f905(x103511,x103512)),f906(x103512,f906(f906(f905(x103511,x103512),a895),a895)),x103511),f317(f10(f905(x103511,x103512),f906(f906(f905(x103511,x103512),a895),a895),x103512),f319(f905(x103511,x103512)))),f242(x103511,x103512)))),x103513)),f317(f317(f9(x103511,f906(f905(x103511,x103512),a895),f906(x103512,a895)),f317(f317(f10(f906(x103512,f906(f906(f905(x103511,x103512),a895),a895)),f906(f906(f905(x103511,x103512),a895),f906(x103512,a895)),x103511),f9(x103512,f906(f905(x103511,x103512),a895),a895)),f317(f317(f10(f906(x103512,f905(x103511,x103512)),f906(x103512,f906(f906(f905(x103511,x103512),a895),a895)),x103511),f317(f10(f905(x103511,x103512),f906(f906(f905(x103511,x103512),a895),a895),x103512),f319(f905(x103511,x103512)))),f242(x103511,x103512)))),x103514))) % 112.26/112.10 [9378]~P1(f317(f317(f319(f905(x93781,x93781)),x93782),f297(x93781,x93784)))+P1(f317(f317(f319(f905(x93781,x93781)),x93782),f297(x93781,f317(f317(f91(f906(f905(x93781,x93781),a895)),x93783),x93784)))) % 112.26/112.10 [9379]~P1(f317(f317(f319(f905(x93791,x93791)),x93792),f297(x93791,x93793)))+P1(f317(f317(f319(f905(x93791,x93791)),x93792),f297(x93791,f317(f317(f91(f906(f905(x93791,x93791),a895)),x93793),x93794)))) % 112.26/112.10 [10069]~P1(f317(f317(f224(a899),f317(f317(f74(a899),x100691),x100694)),f317(f317(f74(a899),x100693),x100692)))+P1(f317(f317(f224(a1),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x100691),x100692)),f178(f906(f905(a899,a899),a895)))))),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x100693),x100694)),f178(f906(f905(a899,a899),a895))))))) % 112.26/112.10 [10070]~P1(f317(f317(f225(a899),f317(f317(f74(a899),x100701),x100704)),f317(f317(f74(a899),x100703),x100702)))+P1(f317(f317(f225(a1),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x100701),x100702)),f178(f906(f905(a899,a899),a895)))))),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x100703),x100704)),f178(f906(f905(a899,a899),a895))))))) % 112.26/112.10 [10157]P1(f317(f317(f224(a899),f317(f317(f74(a899),x101571),x101572)),f317(f317(f74(a899),x101573),x101574)))+~P1(f317(f317(f224(a1),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x101571),x101574)),f178(f906(f905(a899,a899),a895)))))),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x101573),x101572)),f178(f906(f905(a899,a899),a895))))))) % 112.26/112.10 [10158]P1(f317(f317(f225(a899),f317(f317(f74(a899),x101581),x101582)),f317(f317(f74(a899),x101583),x101584)))+~P1(f317(f317(f225(a1),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x101581),x101584)),f178(f906(f905(a899,a899),a895)))))),f317(a83,f317(f275(f905(a899,a899),f905(a899,a899),a99),f317(f317(f299(f905(a899,a899)),f317(f317(f242(a899,a899),x101583),x101582)),f178(f906(f905(a899,a899),a895))))))) % 112.26/112.10 [10201]P1(f317(f317(f224(f906(x102011,a895)),f317(f317(f36(a899,f906(x102011,a895)),f232(f906(a899,a895))),x102012)),f317(f317(f36(a899,f906(x102011,a895)),f232(f906(a899,a895))),x102013)))+~P1(f317(f317(f224(f906(x102011,a895)),f317(f317(f36(a899,f906(x102011,a895)),f317(f292(a899,f2(a899)),f490(x102013,x102014,x102012,x102011))),x102012)),f317(f317(f36(a899,f906(x102011,a895)),f317(f292(a899,f2(a899)),f317(f317(f74(a899),f490(x102013,x102014,x102012,x102011)),x102014))),x102013))) % 112.26/112.10 [10261]P1(f317(f317(f224(a89),x102614),f2(a89)))+E(f317(f317(f249(f905(a89,a89),f905(x102611,f906(a898,a313)),f905(a89,a89),f905(f906(a89,f906(a895,f902(f901(x102611)))),f905(a89,a89))),f317(x102612,x102613)),f317(f317(f10(f906(f906(a89,f906(a895,f902(f901(x102611)))),f906(f905(a89,a89),f905(f906(a89,f906(a895,f902(f901(x102611)))),f905(a89,a89)))),f906(f905(a89,a89),f905(f906(a89,f906(a895,f902(f901(x102611)))),f905(a89,a89))),f905(x102611,f906(a898,a313))),f317(f249(f905(a89,a89),f906(a89,f906(a895,f902(f901(x102611)))),f905(a89,a89),f905(f906(a89,f906(a895,f902(f901(x102611)))),f905(a89,a89))),f267(x102611,x102612,f317(f317(f3(a89),x102614),f72(a89)),x102613))),f317(f317(f10(f906(f906(a89,f906(a895,f902(f901(x102611)))),f906(a89,f906(a895,f902(f901(x102611))))),f906(f906(a89,f906(a895,f902(f901(x102611)))),f906(f905(a89,a89),f905(f906(a89,f906(a895,f902(f901(x102611)))),f905(a89,a89)))),f905(x102611,f906(a898,a313))),f317(f10(f906(a89,f906(a895,f902(f901(x102611)))),f906(f905(a89,a89),f905(f906(a89,f906(a895,f902(f901(x102611)))),f905(a89,a89))),f906(a89,f906(a895,f902(f901(x102611))))),f242(f906(a89,f906(a895,f902(f901(x102611)))),f905(a89,a89)))),f317(f317(f10(f906(a89,f906(a895,f902(f901(x102611)))),f906(f906(a89,f906(a895,f902(f901(x102611)))),f906(a89,f906(a895,f902(f901(x102611))))),f905(x102611,f906(a898,a313))),f40(x102611)),f317(f317(f10(x102611,f906(a89,f906(a895,f902(f901(x102611)))),f905(x102611,f906(a898,a313))),f38(x102611)),f241(x102611,f906(a898,a313))))))),f267(x102611,x102612,x102614,x102613)) % 112.26/112.10 [10325]~P1(f317(f317(f319(x103252),x103254),f317(f274(x103251,x103252),x103253)))+P1(f317(f240(x103251,x103252,f317(f317(f9(x103251,f906(f905(x103251,x103252),a895),f906(x103252,a895)),f317(f317(f10(f906(x103252,f906(f906(f905(x103251,x103252),a895),a895)),f906(f906(f905(x103251,x103252),a895),f906(x103252,a895)),x103251),f9(x103252,f906(f905(x103251,x103252),a895),a895)),f317(f317(f10(f906(x103252,f905(x103251,x103252)),f906(x103252,f906(f906(f905(x103251,x103252),a895),a895)),x103251),f317(f10(f905(x103251,x103252),f906(f906(f905(x103251,x103252),a895),a895),x103252),f319(f905(x103251,x103252)))),f242(x103251,x103252)))),x103253)),x103254)) % 112.26/112.10 [10326]~P1(f317(f317(f319(x103261),x103264),f317(f254(x103261,x103262),x103263)))+P1(f317(f239(x103261,x103262,f317(f317(f9(x103261,f906(f905(x103261,x103262),a895),f906(x103262,a895)),f317(f317(f10(f906(x103262,f906(f906(f905(x103261,x103262),a895),a895)),f906(f906(f905(x103261,x103262),a895),f906(x103262,a895)),x103261),f9(x103262,f906(f905(x103261,x103262),a895),a895)),f317(f317(f10(f906(x103262,f905(x103261,x103262)),f906(x103262,f906(f906(f905(x103261,x103262),a895),a895)),x103261),f317(f10(f905(x103261,x103262),f906(f906(f905(x103261,x103262),a895),a895),x103262),f319(f905(x103261,x103262)))),f242(x103261,x103262)))),x103263)),x103264)) % 112.26/112.10 [10338]P1(f317(f317(f319(x103381),x103382),f317(f274(x103383,x103381),x103384)))+~P1(f317(f240(x103383,x103381,f317(f317(f9(x103383,f906(f905(x103383,x103381),a895),f906(x103381,a895)),f317(f317(f10(f906(x103381,f906(f906(f905(x103383,x103381),a895),a895)),f906(f906(f905(x103383,x103381),a895),f906(x103381,a895)),x103383),f9(x103381,f906(f905(x103383,x103381),a895),a895)),f317(f317(f10(f906(x103381,f905(x103383,x103381)),f906(x103381,f906(f906(f905(x103383,x103381),a895),a895)),x103383),f317(f10(f905(x103383,x103381),f906(f906(f905(x103383,x103381),a895),a895),x103381),f319(f905(x103383,x103381)))),f242(x103383,x103381)))),x103384)),x103382)) % 112.26/112.10 [10339]P1(f317(f317(f319(x103391),x103392),f317(f254(x103391,x103393),x103394)))+~P1(f317(f239(x103391,x103393,f317(f317(f9(x103391,f906(f905(x103391,x103393),a895),f906(x103393,a895)),f317(f317(f10(f906(x103393,f906(f906(f905(x103391,x103393),a895),a895)),f906(f906(f905(x103391,x103393),a895),f906(x103393,a895)),x103391),f9(x103393,f906(f905(x103391,x103393),a895),a895)),f317(f317(f10(f906(x103393,f905(x103391,x103393)),f906(x103393,f906(f906(f905(x103391,x103393),a895),a895)),x103391),f317(f10(f905(x103391,x103393),f906(f906(f905(x103391,x103393),a895),a895),x103393),f319(f905(x103391,x103393)))),f242(x103391,x103393)))),x103394)),x103392)) % 112.26/112.10 [9993]P1(f317(f150(x99931,x99932),x99933))+~P1(f317(f150(x99931,f317(f317(f20(x99931,a895,a895),f317(f317(f10(a895,f906(a895,a895),x99931),a315),x99934)),x99932)),x99933)) % 112.26/112.10 [9994]P1(f317(f150(x99941,x99942),x99943))+~P1(f317(f150(x99941,f317(f317(f20(x99941,a895,a895),f317(f317(f10(a895,f906(a895,a895),x99941),a315),x99942)),x99944)),x99943)) % 112.26/112.10 [10081]~P119(x100811)+E(f317(f317(f75(x100811),f317(f317(f74(x100811),f72(x100811)),f72(x100811))),f317(f317(f8(a899,x100811),f317(f317(f10(x100811,x100811,a899),f317(f74(x100811),x100812)),f317(f317(f9(a899,x100811,x100811),f317(f317(f10(x100811,f906(x100811,x100811),a899),f75(x100811)),f90(x100811))),x100813))),f317(f272(a899),x100814))),f317(f317(f75(x100811),f317(f90(x100811),x100814)),f317(f317(f74(x100811),x100812),f317(f317(f74(x100811),x100812),f317(f317(f75(x100811),f317(f90(x100811),f317(f317(f3(a899),x100814),f72(a899)))),x100813))))) % 112.26/112.10 [10222]P1(f317(x102221,f557(x102222,x102223,x102224,x102221)))+P36(x102222,f317(f252(f905(x102222,x102222)),f317(f247(x102222,x102222,a895),f317(f317(f10(f906(x102222,a895),f906(x102222,a895),x102222),f317(f20(x102222,a895,a895),f317(f317(f10(a895,f906(a895,a895),x102222),a315),x102221))),f317(f317(f9(x102222,f906(x102222,x102222),f906(x102222,a895)),f317(f317(f10(f906(x102222,a895),f906(f906(x102222,x102222),f906(x102222,a895)),x102222),f10(x102222,a895,x102222)),a314)),x102223))))) % 112.26/112.10 [10236]~P1(f317(f317(f225(a899),f317(x102364,f317(x102363,f557(x102361,x102363,x102364,x102362)))),f317(x102364,f557(x102361,x102363,x102364,x102362))))+P36(x102361,f317(f252(f905(x102361,x102361)),f317(f247(x102361,x102361,a895),f317(f317(f10(f906(x102361,a895),f906(x102361,a895),x102361),f317(f20(x102361,a895,a895),f317(f317(f10(a895,f906(a895,a895),x102361),a315),x102362))),f317(f317(f9(x102361,f906(x102361,x102361),f906(x102361,a895)),f317(f317(f10(f906(x102361,a895),f906(f906(x102361,x102361),f906(x102361,a895)),x102361),f10(x102361,a895,x102361)),a314)),x102363))))) % 112.26/112.10 [10312]~P5(x103121)+E(f32(x103121,f317(f252(x103121),f317(f317(f10(f906(f906(x103122,x103121),a895),a895,x103121),f81(f906(x103122,x103121))),f317(f317(f10(f906(f906(x103122,x103121),a895),f906(f906(x103122,x103121),a895),x103121),f317(f20(f906(x103122,x103121),a895,a895),f317(f317(f10(a895,f906(a895,a895),f906(x103122,x103121)),a315),f317(f317(f9(f906(x103122,x103121),f906(f906(x103122,x103121),a895),a895),f319(f906(x103122,x103121))),x103123)))),f317(f317(f9(x103121,f906(f906(x103122,x103121),x103121),f906(f906(x103122,x103121),a895)),f317(f317(f10(f906(x103121,a895),f906(f906(f906(x103122,x103121),x103121),f906(f906(x103122,x103121),a895)),x103121),f10(x103121,a895,f906(x103122,x103121))),a314)),f317(f317(f9(f906(x103122,x103121),x103122,x103121),f7(f906(x103122,x103121))),x103124)))))),f317(f32(f906(x103122,x103121),x103123),x103124)) % 112.26/112.10 [10313]~P5(x103131)+E(f32(x103131,f317(f252(x103131),f317(f317(f10(f906(f906(x103132,x103131),a895),a895,x103131),f81(f906(x103132,x103131))),f317(f317(f10(f906(f906(x103132,x103131),a895),f906(f906(x103132,x103131),a895),x103131),f317(f20(f906(x103132,x103131),a895,a895),f317(f317(f10(a895,f906(a895,a895),f906(x103132,x103131)),a315),f317(f317(f9(f906(x103132,x103131),f906(f906(x103132,x103131),a895),a895),f319(f906(x103132,x103131))),x103133)))),f317(f317(f9(x103131,f906(f906(x103132,x103131),x103131),f906(f906(x103132,x103131),a895)),f317(f317(f10(f906(x103131,a895),f906(f906(f906(x103132,x103131),x103131),f906(f906(x103132,x103131),a895)),x103131),f10(x103131,a895,f906(x103132,x103131))),a314)),f317(f317(f9(f906(x103132,x103131),x103132,x103131),f7(f906(x103132,x103131))),x103134)))))),f317(f32(f906(x103132,x103131),x103133),x103134)) % 112.26/112.10 [10314]~P5(x103141)+E(f33(x103141,f317(f252(x103141),f317(f317(f10(f906(f906(x103142,x103141),a895),a895,x103141),f81(f906(x103142,x103141))),f317(f317(f10(f906(f906(x103142,x103141),a895),f906(f906(x103142,x103141),a895),x103141),f317(f20(f906(x103142,x103141),a895,a895),f317(f317(f10(a895,f906(a895,a895),f906(x103142,x103141)),a315),f317(f317(f9(f906(x103142,x103141),f906(f906(x103142,x103141),a895),a895),f319(f906(x103142,x103141))),x103143)))),f317(f317(f9(x103141,f906(f906(x103142,x103141),x103141),f906(f906(x103142,x103141),a895)),f317(f317(f10(f906(x103141,a895),f906(f906(f906(x103142,x103141),x103141),f906(f906(x103142,x103141),a895)),x103141),f10(x103141,a895,f906(x103142,x103141))),a314)),f317(f317(f9(f906(x103142,x103141),x103142,x103141),f7(f906(x103142,x103141))),x103144)))))),f317(f33(f906(x103142,x103141),x103143),x103144)) % 112.26/112.10 [10315]~P5(x103151)+E(f33(x103151,f317(f252(x103151),f317(f317(f10(f906(f906(x103152,x103151),a895),a895,x103151),f81(f906(x103152,x103151))),f317(f317(f10(f906(f906(x103152,x103151),a895),f906(f906(x103152,x103151),a895),x103151),f317(f20(f906(x103152,x103151),a895,a895),f317(f317(f10(a895,f906(a895,a895),f906(x103152,x103151)),a315),f317(f317(f9(f906(x103152,x103151),f906(f906(x103152,x103151),a895),a895),f319(f906(x103152,x103151))),x103153)))),f317(f317(f9(x103151,f906(f906(x103152,x103151),x103151),f906(f906(x103152,x103151),a895)),f317(f317(f10(f906(x103151,a895),f906(f906(f906(x103152,x103151),x103151),f906(f906(x103152,x103151),a895)),x103151),f10(x103151,a895,f906(x103152,x103151))),a314)),f317(f317(f9(f906(x103152,x103151),x103152,x103151),f7(f906(x103152,x103151))),x103154)))))),f317(f33(f906(x103152,x103151),x103153),x103154)) % 112.26/112.10 [10364]~P1(f317(f317(f319(f905(x103641,x103641)),f317(f317(f242(x103641,x103641),x103643),x103644)),f317(f317(f91(f906(f905(x103641,x103641),a895)),x103642),f297(x103641,f178(f906(f905(x103641,x103641),a895))))))+P1(f317(f317(f317(f317(f91(f906(x103641,f906(x103641,a895))),f317(f317(f9(x103641,f906(f905(x103641,x103641),a895),f906(x103641,a895)),f317(f317(f10(f906(x103641,f906(f906(f905(x103641,x103641),a895),a895)),f906(f906(f905(x103641,x103641),a895),f906(x103641,a895)),x103641),f9(x103641,f906(f905(x103641,x103641),a895),a895)),f317(f317(f10(f906(x103641,f905(x103641,x103641)),f906(x103641,f906(f906(f905(x103641,x103641),a895),a895)),x103641),f317(f10(f905(x103641,x103641),f906(f906(f905(x103641,x103641),a895),a895),x103641),f319(f905(x103641,x103641)))),f242(x103641,x103641)))),x103642)),a314),x103643),x103644)) % 112.26/112.10 [10374]P1(f317(f317(f319(f905(x103741,x103741)),f317(f317(f242(x103741,x103741),x103742),x103743)),f317(f317(f91(f906(f905(x103741,x103741),a895)),x103744),f297(x103741,f178(f906(f905(x103741,x103741),a895))))))+~P1(f317(f317(f317(f317(f91(f906(x103741,f906(x103741,a895))),f317(f317(f9(x103741,f906(f905(x103741,x103741),a895),f906(x103741,a895)),f317(f317(f10(f906(x103741,f906(f906(f905(x103741,x103741),a895),a895)),f906(f906(f905(x103741,x103741),a895),f906(x103741,a895)),x103741),f9(x103741,f906(f905(x103741,x103741),a895),a895)),f317(f317(f10(f906(x103741,f905(x103741,x103741)),f906(x103741,f906(f906(f905(x103741,x103741),a895),a895)),x103741),f317(f10(f905(x103741,x103741),f906(f906(f905(x103741,x103741),a895),a895),x103741),f319(f905(x103741,x103741)))),f242(x103741,x103741)))),x103744)),a314),x103742),x103743)) % 112.26/112.10 [10322]E(f317(f317(f141(f900(x103221)),f317(f317(f141(x103221),x103222),f317(f132(f900(x103221),f900(x103221),f124(x103221),f103(x103221)),f317(f317(f144(f900(x103221),f900(x103221)),f146(f900(x103221),x103221,f103(x103221),f317(f317(f10(f900(x103221),f906(f900(x103221),f900(x103221)),x103221),f18(f900(x103221),f900(x103221))),f317(f317(f9(x103221,f900(x103221),f900(x103221)),f141(x103221)),f103(x103221))))),x103223)))),f169(x103221,f317(f317(f141(f900(x103221)),x103224),f317(f132(f900(f900(x103221)),f900(f900(x103221)),f124(f900(x103221)),f103(f900(x103221))),f317(f317(f144(f900(x103221),f900(f900(x103221))),f146(f900(f900(x103221)),x103221,f103(f900(x103221)),f317(f18(f906(f900(x103221),f900(f900(x103221))),x103221),f317(f317(f9(f900(x103221),f900(f900(x103221)),f900(f900(x103221))),f141(f900(x103221))),f103(f900(x103221)))))),x103223))))),f169(x103221,f317(f317(f141(f900(x103221)),f317(f317(f141(x103221),x103222),x103224)),x103223)))+~P1(f317(f305(f900(f900(x103221)),f170(x103221)),f317(f317(f141(f900(x103221)),f317(f317(f141(x103221),x103222),x103224)),x103223))) % 112.26/112.10 [10363]~P1(f317(f29(x103632),f317(f252(x103632),x103634)))+P1(f317(f29(x103631),f317(f252(x103631),f317(f317(f10(f906(x103632,a895),a895,x103631),f81(x103632)),f317(f317(f9(x103631,f906(x103632,a895),f906(x103632,a895)),f317(f317(f10(f906(x103632,f906(a895,a895)),f906(f906(x103632,a895),f906(x103632,a895)),x103631),f20(x103632,a895,a895)),f317(f317(f10(f906(x103632,a895),f906(x103632,f906(a895,a895)),x103631),f317(f10(a895,f906(a895,a895),x103632),a315)),f317(f317(f9(x103631,f906(x103632,x103631),f906(x103632,a895)),f317(f317(f10(f906(x103631,a895),f906(f906(x103632,x103631),f906(x103632,a895)),x103631),f10(x103631,a895,x103632)),a314)),x103633)))),x103634))))) % 112.26/112.10 [8875]P24(x88751,x88752,x88753,x88754)+~P25(x88751,x88752,x88753,x88754,x88755) % 112.26/112.10 [5334]E(x53341,x53342)+~E(f159(x53343,x53341,x53344),f159(x53343,x53342,x53345)) % 112.26/112.10 [5335]E(x53351,x53352)+~E(f116(x53353,x53354,x53351),f116(x53353,x53355,x53352)) % 112.26/112.10 [5336]E(x53361,x53362)+~E(f116(x53363,x53361,x53364),f116(x53363,x53362,x53365)) % 112.26/112.10 [8201]~E(f317(x82013,x82014),x82015)+E(f69(x82011,x82012,x82013,x82014,x82015),x82013) % 112.26/112.10 [8733]~E(f69(x87334,x87335,x87331,x87332,x87333),x87331)+E(f317(x87331,x87332),x87333) % 112.26/112.10 [9349]~P25(x93492,x93491,x93494,x93493,x93495)+P25(x93491,x93492,f71(x93492,x93491,x93493,x93494),x93495,x93493) % 112.26/112.10 [9350]~P25(x93502,x93501,x93504,x93503,x93505)+P25(x93501,x93502,f85(x93502,x93501,x93503,x93504),x93505,x93503) % 112.26/112.10 [6155]P1(f317(f240(x61551,x61552,x61553),x61554))+~P1(f317(f317(x61553,x61555),x61554)) % 112.26/112.10 [6157]P1(f317(f239(x61571,x61572,x61573),x61574))+~P1(f317(f317(x61573,x61574),x61575)) % 112.26/112.10 [6645]~E(x66455,f2(a89))+E(f317(f186(x66451,x66452,x66453,x66454),x66455),f114(x66452)) % 112.26/112.10 [6646]~E(x66465,f2(a89))+E(f317(f188(x66461,x66462,x66463,x66464),x66465),f105(x66462)) % 112.26/112.10 [6786]~E(x67863,f2(a89))+E(f317(f263(x67861,x67862,x67863,x67864),x67865),f317(f242(x67861,x67862),x67865)) % 112.26/112.10 [7850]~P20(x78504,x78501,x78502,x78505)+E(f317(f67(x78501,x78501,x78501,f317(x78502,x78503)),f317(x78502,x78503)),f317(x78502,x78503)) % 112.26/112.10 [8242]~P16(x82425,x82421,x82422)+E(f317(f67(x82421,x82421,x82421,f317(x82422,x82423)),f317(x82422,x82424)),f317(f67(x82421,x82421,x82421,f317(x82422,x82424)),f317(x82422,x82423))) % 112.26/112.10 [8568]P1(f317(f317(f319(f905(x85681,x85681)),f317(f317(f242(x85681,x85681),x85682),x85683)),f311(x85681,x85684,x85685)))+~P1(f317(f317(f225(a899),f317(x85684,x85682)),f317(x85684,x85683))) % 112.26/112.10 [8661]~P1(f317(f317(f319(x86614),x86613),f280(x86614,x86611,x86612,x86615)))+P1(f317(f317(x86611,x86612),x86613)) % 112.26/112.10 [8662]~P1(f317(f317(f319(x86624),x86623),f289(x86624,x86621,x86622,x86625)))+P1(f317(f317(x86621,x86622),x86623)) % 112.26/112.10 [8663]~P1(f317(f317(f319(x86634),x86632),f280(x86634,x86631,x86635,x86633)))+P1(f317(f317(x86631,x86632),x86633)) % 112.26/112.10 [8664]~P1(f317(f317(f319(x86644),x86642),f289(x86644,x86641,x86645,x86643)))+P1(f317(f317(x86641,x86642),x86643)) % 112.26/112.10 [8745]~P25(x87451,x87453,x87455,x87452,x87454)+E(f317(f30(x87451),x87452),f317(f30(x87453),x87454)) % 112.26/112.10 [8793]~P25(x87931,x87932,x87933,x87934,x87935)+E(f317(f300(x87931,x87932,x87933),x87934),x87935) % 112.26/112.10 [8813]~P56(x88132,x88131,x88135,x88133,x88134)+E(f317(f300(x88131,x88132,x88133),x88134),f232(f906(x88132,a895))) % 112.26/112.10 [9257]~P33(x92571,x92572,x92573,x92574,x92575)+P33(x92571,x92572,x92573,f317(f158(x92571),x92574),f317(f158(x92572),x92575)) % 112.26/112.10 [9259]~P33(x92591,x92592,x92593,f317(f158(x92591),x92594),x92595)+P33(x92591,x92592,x92593,x92594,f317(f158(x92592),x92595)) % 112.26/112.10 [9260]~P33(x92601,x92602,x92603,x92604,f317(f158(x92602),x92605))+P33(x92601,x92602,x92603,f317(f158(x92601),x92604),x92605) % 112.26/112.10 [9266]P33(x92661,x92662,x92663,x92664,x92665)+~P33(x92661,x92662,x92663,f317(f158(x92661),x92664),f317(f158(x92662),x92665)) % 112.26/112.10 [9680]P1(f317(f317(f319(f905(f900(x96801),f900(x96801))),f317(f317(f242(f900(x96801),f900(x96801)),f317(f317(f141(x96801),x96802),x96803)),f317(f317(f141(x96801),x96802),x96804))),f147(x96801,x96805)))+~P1(f317(f317(f319(f905(f900(x96801),f900(x96801))),f317(f317(f242(f900(x96801),f900(x96801)),x96803),x96804)),f147(x96801,x96805))) % 112.26/112.10 [9681]P1(f317(f317(f319(f905(f900(x96811),f900(x96811))),f317(f317(f242(f900(x96811),f900(x96811)),f317(f317(f124(x96811),x96812),x96813)),f317(f317(f124(x96811),x96812),x96814))),f137(x96811,x96815)))+~P1(f317(f317(f319(f905(f900(x96811),f900(x96811))),f317(f317(f242(f900(x96811),f900(x96811)),x96813),x96814)),f137(x96811,x96815))) % 112.26/112.10 [9878]E(f317(f317(f141(x98781),f635(x98782,x98783,x98784,x98785,x98781)),f638(x98782,x98783,x98784,x98785,x98781)),x98785)+~P1(f317(f317(f319(f905(f900(x98781),f900(x98781))),f317(f317(f242(f900(x98781),f900(x98781)),x98785),f317(f317(f141(x98781),x98784),x98783))),f148(x98781,x98782))) % 112.26/112.10 [9899]E(f317(f317(f141(x98991),f636(x98992,x98993,x98994,x98995,x98991)),f637(x98992,x98993,x98994,x98995,x98991)),x98993)+~P1(f317(f317(f319(f905(f900(x98991),f900(x98991))),f317(f317(f242(f900(x98991),f900(x98991)),f317(f317(f141(x98991),x98995),x98994)),x98993)),f148(x98991,x98992))) % 112.26/112.10 [10043]~P1(f317(f317(f319(f905(f900(x100431),f900(x100431))),f317(f317(f242(f900(x100431),f900(x100431)),f317(f317(f141(x100431),x100435),x100432)),x100434)),f148(x100431,x100433)))+P1(f317(f317(f319(f905(f900(x100431),f900(x100431))),f317(f317(f242(f900(x100431),f900(x100431)),x100432),f637(x100433,x100434,x100432,x100435,x100431))),f148(x100431,x100433))) % 112.26/112.10 [10124]~P1(f317(f317(f319(f905(f900(x101241),f900(x101241))),f317(f317(f242(f900(x101241),f900(x101241)),x101245),f317(f317(f141(x101241),x101244),x101243))),f148(x101241,x101242)))+P1(f317(f317(f319(f905(f900(x101241),f900(x101241))),f317(f317(f242(f900(x101241),f900(x101241)),f638(x101242,x101243,x101244,x101245,x101241)),x101243)),f148(x101241,x101242))) % 112.26/112.10 [10316]P1(f317(f317(f319(f905(x103161,x103161)),f317(f317(f242(x103161,x103161),f317(x103162,f317(f317(f74(a899),x103163),x103164))),f317(x103162,x103163))),f297(x103161,x103165)))+~P1(f317(f317(f319(f905(x103161,x103161)),f317(f317(f242(x103161,x103161),f317(x103162,f317(a102,f601(x103164,x103163,x103165,x103162,x103161)))),f317(x103162,f601(x103164,x103163,x103165,x103162,x103161)))),f297(x103161,x103165))) % 112.26/112.10 [5308]E(x53081,x53082)+~E(f317(f317(f141(x53083),x53084),x53081),f317(f317(f141(x53083),x53085),x53082)) % 112.26/112.10 [5309]E(x53091,x53092)+~E(f317(f317(f141(x53093),x53091),x53094),f317(f317(f141(x53093),x53092),x53095)) % 112.26/112.10 [5351]P1(f317(x53511,x53512))+~E(f317(f126(x53513,x53511),x53514),f317(f317(f141(x53513),x53512),x53515)) % 112.26/112.10 [5352]P1(f317(x53521,x53522))+~E(f317(f317(f141(x53523),x53522),x53524),f317(f126(x53523,x53521),x53525)) % 112.26/112.10 [5513]~E(f317(f317(f128(x55131),x55133),x55132),f317(f317(f141(x55131),x55134),x55135))+E(f317(f317(f154(x55131),x55132),x55133),x55134) % 112.26/112.10 [5653]~P14(x56534,x56535,x56531)+E(f317(f317(x56531,x56532),f317(f317(x56531,x56532),x56533)),f317(f317(x56531,x56532),x56533)) % 112.26/112.10 [6214]~E(x62144,f2(a89))+E(f317(f317(f107(x62141,x62142,x62143),x62144),x62145),f317(f317(f242(f900(x62142),x62141),f103(x62142)),x62145)) % 112.26/112.10 [6288]~P108(x62882)+~E(f317(f317(f138(x62881,x62882,x62883),x62884),x62885),f103(x62881)) % 112.26/112.10 [6686]E(x66861,x66862)+~E(f317(f317(f124(x66863),x66864),f317(f317(f141(x66863),x66861),f103(x66863))),f317(f317(f124(x66863),x66865),f317(f317(f141(x66863),x66862),f103(x66863)))) % 112.26/112.10 [6687]E(x66871,x66872)+~E(f317(f317(f124(x66873),x66871),f317(f317(f141(x66873),x66874),f103(x66873))),f317(f317(f124(x66873),x66872),f317(f317(f141(x66873),x66875),f103(x66873)))) % 112.26/112.10 [7010]E(f317(f317(f299(x70101),f317(x70102,x70103)),f317(f300(x70104,x70101,x70102),x70105)),f317(f300(x70104,x70101,x70102),x70105))+~P1(f317(f317(f319(x70104),x70103),x70105)) % 112.26/112.10 [7017]~P1(f317(x70174,f317(x70173,x70175)))+P1(f317(f317(f301(x70171,x70172,x70173),x70174),x70175)) % 112.26/112.10 [7020]~P1(f317(f317(x70203,x70205),x70204))+P1(f317(f317(f233(x70201,x70202,x70203),x70204),x70205)) % 112.26/112.10 [7117]~E(f317(f300(x71171,x71172,x71173),x71174),x71175)+E(f317(f300(f906(x71171,a895),f906(x71172,a895),f300(x71171,x71172,x71173)),f317(f298(x71171),x71174)),f317(f298(x71172),x71175)) % 112.26/112.10 [7145]E(f317(f261(x71451,x71452,x71453,x71454),x71455),f317(x71454,x71455))+~P1(f317(f317(f319(x71451),x71455),x71453)) % 112.26/112.10 [7459]P24(x74591,x74592,x74593,x74594)+~P24(x74591,x74592,x74593,f317(f317(f299(x74591),x74595),x74594)) % 112.26/112.10 [7564]~P1(f317(f317(f319(x75644),x75643),x75645))+P1(f317(f317(f319(x75641),f317(x75642,x75643)),f317(f300(x75644,x75641,x75642),x75645))) % 112.26/112.10 [7585]~P108(x75852)+E(f140(x75851,x75852,x75853,f317(f126(x75851,x75854),x75855)),f317(f126(x75851,x75854),f140(x75851,x75852,x75853,x75855))) % 112.26/112.10 [7616]P1(f317(x76161,f317(x76162,x76163)))+~P1(f317(f317(f301(x76164,x76165,x76162),x76161),x76163)) % 112.26/112.10 [7619]P1(f317(f317(x76191,x76192),x76193))+~P1(f317(f317(f233(x76194,x76195,x76191),x76193),x76192)) % 112.26/112.10 [7685]~P1(f317(f317(f319(x76853),f317(x76854,x76852)),x76855))+P1(f317(f317(f319(x76851),x76852),f317(f301(x76851,x76853,x76854),x76855))) % 112.26/112.10 [8083]~P1(f317(f317(f319(x80835),x80833),f317(f301(x80835,x80831,x80832),x80834)))+P1(f317(f317(f319(x80831),f317(x80832,x80833)),x80834)) % 112.26/112.10 [8382]~P16(x83822,x83821,x83823)+E(f317(f132(x83821,x83822,f317(f9(x83822,x83821,x83821),x83823),x83824),f142(x83822,x83825)),f317(f317(f59(x83822,x83821,x83823),x83824),f317(f162(x83822),x83825))) % 112.26/112.10 [8404]E(f317(x84041,f768(x84042,x84041,x84043,x84044)),x84044)+~P1(f317(f317(f319(x84045),x84044),f317(f300(x84043,x84045,x84041),x84042))) % 112.26/112.10 [8708]~E(x87082,f317(f317(f141(x87081),x87084),x87085))+P1(f317(f317(f319(f905(f900(x87081),f900(x87081))),f317(f317(f242(f900(x87081),f900(x87081)),f103(x87081)),x87082)),f137(x87081,x87083))) % 112.26/112.10 [8754]E(f317(x87541,f317(f85(x87542,x87543,x87544,x87541),x87545)),x87545)+~P1(f317(f317(f319(x87543),x87545),f317(f300(x87542,x87543,x87541),x87544))) % 112.26/112.10 [8757]P24(x87571,x87572,f85(x87572,x87571,x87573,x87574),x87575)+~P1(f317(f317(f224(f906(x87571,a895)),x87575),f317(f300(x87572,x87571,x87574),x87573))) % 112.26/112.10 [8764]~P33(x87641,x87643,x87645,x87642,x87644)+E(f317(f179(f900(x87641)),x87642),f317(f179(f900(x87643)),x87644)) % 112.26/112.10 [8775]P1(f317(f317(f224(f906(x87751,a895)),f317(f317(f35(x87752,f906(x87751,a895)),x87753),x87754)),f317(x87754,x87755)))+~P1(f317(f317(f319(x87752),x87755),x87753)) % 112.26/112.10 [8829]~P56(x88291,x88292,x88293,x88295,x88294)+E(f317(f300(x88291,x88292,x88293),f232(f906(x88291,a895))),x88294) % 112.26/112.10 [9054]E(f317(f126(x90541,x90542),f723(x90543,x90544,x90545,x90542,x90541)),x90543)+~E(f317(f126(x90541,x90542),x90545),f317(f317(f141(x90541),x90544),x90543)) % 112.26/112.10 [9055]E(f317(f126(x90551,x90552),f727(x90553,x90552,x90554,x90555,x90551)),x90554)+~E(f317(f317(f141(x90551),x90555),x90554),f317(f126(x90551,x90552),x90553)) % 112.26/112.10 [9146]E(f317(f179(f900(x91461)),x91462),x91463)+~P1(f317(f317(f319(f905(f900(x91461),f900(x91461))),f317(f317(f242(f900(x91461),f900(x91461)),x91464),x91462)),f317(f133(x91461,x91465),x91463))) % 112.26/112.10 [9147]E(f317(f179(f900(x91471)),x91472),x91473)+~P1(f317(f317(f319(f905(f900(x91471),f900(x91471))),f317(f317(f242(f900(x91471),f900(x91471)),x91472),x91474)),f317(f133(x91471,x91475),x91473))) % 112.26/112.10 [9216]P1(f317(f317(f319(x92161),f768(x92162,x92163,x92161,x92164)),x92162))+~P1(f317(f317(f319(x92165),x92164),f317(f300(x92161,x92165,x92163),x92162))) % 112.26/112.10 [9376]E(f317(f300(x93761,x93762,x93763),f851(x93764,x93763,x93761,x93765,x93762)),x93765)+~P1(f317(f317(f224(f906(x93762,a895)),x93765),f317(f300(x93761,x93762,x93763),x93764))) % 112.26/112.10 [9698]P1(f317(f317(f319(f905(f900(x96981),f900(x96981))),f317(f317(f242(f900(x96981),f900(x96981)),f317(f317(f141(x96981),x96982),x96983)),f317(f317(f141(x96981),x96982),x96984))),f297(f900(x96981),f147(x96981,x96985))))+~P1(f317(f317(f319(f905(f900(x96981),f900(x96981))),f317(f317(f242(f900(x96981),f900(x96981)),x96983),x96984)),f297(f900(x96981),f147(x96981,x96985)))) % 112.26/112.10 [9729]~E(f317(x97293,f676(x97295,x97294,x97293,x97292,x97291)),f317(x97295,f676(x97295,x97294,x97293,x97292,x97291)))+E(f317(f317(f144(x97291,x97292),x97293),x97294),f317(f317(f144(x97291,x97292),x97295),x97294)) % 112.26/112.10 [9804]~E(f317(f126(x98041,x98045),x98044),f317(f317(f141(x98041),x98043),x98042))+E(f317(f317(f124(x98041),f726(x98042,x98043,x98044,x98045,x98041)),f317(f317(f141(x98041),x98043),f723(x98042,x98043,x98044,x98045,x98041))),x98044) % 112.26/112.10 [9805]~E(f317(f317(f141(x98051),x98055),x98054),f317(f126(x98051,x98053),x98052))+E(f317(f317(f124(x98051),f728(x98052,x98053,x98054,x98055,x98051)),f317(f317(f141(x98051),x98055),f727(x98052,x98053,x98054,x98055,x98051))),x98052) % 112.26/112.10 [9809]E(f317(f317(f144(x98091,x98092),x98093),x98094),f317(f317(f144(x98091,x98092),x98095),x98094))+P1(f317(f317(f319(x98091),f676(x98093,x98094,x98095,x98092,x98091)),f317(f162(x98091),x98094))) % 112.26/112.10 [9839]~P1(f317(f317(f319(x98395),x98394),f317(f275(x98391,x98395,x98393),x98392)))+P1(f317(f317(f319(x98391),f491(x98392,x98393,x98391,x98394,x98395)),x98392)) % 112.26/112.10 [9840]~P1(f317(f317(f319(x98405),x98404),f317(f275(x98401,x98405,x98403),x98402)))+P1(f317(f317(f319(x98401),f496(x98402,x98403,x98401,x98404,x98405)),x98402)) % 112.26/112.10 [9871]~P1(f317(f317(f224(f906(x98715,a895)),x98714),f317(f300(x98711,x98715,x98713),x98712)))+P1(f317(f317(f224(f906(x98711,a895)),f851(x98712,x98713,x98711,x98714,x98715)),x98712)) % 112.26/112.10 [10317]E(x103171,f2(a89))+E(f213(f905(f900(x103172),x103173),f905(x103172,x103173),f317(f317(f242(f900(x103172),x103173),f103(x103172)),x103174),f317(f247(x103172,x103173,f905(f900(x103172),x103173)),f317(f317(f9(x103172,f906(x103173,f905(f900(x103172),x103173)),f906(x103173,f905(f900(x103172),x103173))),f317(f317(f10(f906(f905(f900(x103172),x103173),f905(f900(x103172),x103173)),f906(f906(x103173,f905(f900(x103172),x103173)),f906(x103173,f905(f900(x103172),x103173))),x103172),f10(f905(f900(x103172),x103173),f905(f900(x103172),x103173),x103173)),f317(f317(f10(f906(f900(x103172),f906(x103173,f905(f900(x103172),x103173))),f906(f905(f900(x103172),x103173),f905(f900(x103172),x103173)),x103172),f247(f900(x103172),x103173,f905(f900(x103172),x103173))),f317(f317(f10(f906(f900(x103172),f900(x103172)),f906(f900(x103172),f906(x103173,f905(f900(x103172),x103173))),x103172),f317(f10(f900(x103172),f906(x103173,f905(f900(x103172),x103173)),f900(x103172)),f242(f900(x103172),x103173))),f141(x103172))))),f317(f107(x103173,x103172,x103175),f317(f317(f3(a89),x103171),f72(a89))))),f317(x103175,x103174)),f317(f317(f107(x103173,x103172,x103175),x103171),x103174)) % 112.26/112.10 [6092]E(x60921,x60922)+~E(f317(f246(x60923,x60924),f317(f317(f242(x60923,x60924),x60925),x60921)),x60922) % 112.26/112.10 [6093]E(x60931,x60932)+~E(f317(f241(x60933,x60934),f317(f317(f242(x60933,x60934),x60931),x60935)),x60932) % 112.26/112.10 [6364]~E(x63643,f317(f317(f124(x63641),x63644),f317(f317(f141(x63641),x63642),x63645)))+P1(f317(f317(f319(x63641),x63642),f317(f162(x63641),x63643))) % 112.26/112.10 [6773]E(f317(f300(x67731,x67732,f317(f18(x67732,x67731),x67733)),x67734),f317(f317(f299(x67732),x67733),f178(f906(x67732,a895))))+~P1(f317(f317(f319(x67731),x67735),x67734)) % 112.26/112.10 [6847]E(f317(f317(f91(f906(x68471,a895)),f317(f162(x68471),x68472)),f317(f162(x68471),x68473)),f317(f162(x68471),x68474))+~E(f156(x68471,x68475,x68474),f317(f317(f242(f900(x68471),f900(x68471)),x68472),x68473)) % 112.26/112.10 [6948]~P108(x69482)+E(f317(f179(f900(x69481)),f317(f317(f138(x69481,x69482,x69483),x69484),x69485)),f317(a102,f317(f179(f900(x69481)),x69485))) % 112.26/112.10 [6962]~P108(x69622)+E(f317(f162(x69621),f317(f317(f138(x69621,x69622,x69623),x69624),x69625)),f317(f317(f299(x69621),x69624),f317(f162(x69621),x69625))) % 112.26/112.10 [7239]~P119(x72391)+E(f317(f317(f74(x72391),f317(f317(f74(x72391),x72392),x72393)),f317(f317(f74(x72391),x72394),x72395)),f317(f317(f74(x72391),f317(f317(f74(x72391),x72392),x72394)),f317(f317(f74(x72391),x72393),x72395))) % 112.26/112.10 [7240]~P119(x72401)+E(f317(f317(f75(x72401),f317(f317(f75(x72401),x72402),x72403)),f317(f317(f75(x72401),x72404),x72405)),f317(f317(f75(x72401),f317(f317(f75(x72401),x72402),x72404)),f317(f317(f75(x72401),x72403),x72405))) % 112.26/112.10 [7241]~P61(x72411)+E(f317(f317(f281(x72411),f317(f317(f75(x72411),x72412),x72413)),f317(f317(f75(x72411),x72414),x72415)),f317(f317(f75(x72411),f317(f317(f281(x72411),x72412),x72414)),f317(f317(f281(x72411),x72413),x72415))) % 112.26/112.10 [7255]~P108(x72551)+E(f296(x72551,f317(f317(f223(x72551),x72552),x72553),f317(f317(f228(x72551),x72554),x72555)),f317(f317(f92(f906(x72551,a895)),f296(x72551,x72552,x72554)),f296(x72551,x72553,x72555))) % 112.26/112.10 [7256]~P108(x72561)+E(f293(x72561,f317(f317(f223(x72561),x72562),x72563),f317(f317(f228(x72561),x72564),x72565)),f317(f317(f92(f906(x72561,a895)),f293(x72561,x72562,x72564)),f293(x72561,x72563,x72565))) % 112.26/112.10 [7257]~P108(x72571)+E(f295(x72571,f317(f317(f223(x72571),x72572),x72573),f317(f317(f228(x72571),x72574),x72575)),f317(f317(f92(f906(x72571,a895)),f295(x72571,x72572,x72574)),f295(x72571,x72573,x72575))) % 112.26/112.10 [7258]~P108(x72581)+E(f317(f317(f92(f906(x72581,a895)),f317(f292(x72581,x72582),x72583)),f317(f292(x72581,x72584),x72585)),f317(f292(x72581,f317(f317(f223(x72581),x72582),x72584)),f317(f317(f228(x72581),x72583),x72585))) % 112.26/112.10 [7378]~P1(f317(x73781,f443(x73783,x73782,x73781)))+P1(f317(x73781,f317(f317(f242(x73782,x73783),x73784),x73785))) % 112.26/112.10 [7490]~E(x74902,f317(x74904,x74905))+P1(f317(f317(f319(x74901),x74902),f317(f300(x74903,x74901,x74904),f232(f906(x74903,a895))))) % 112.26/112.10 [7562]~P16(x75623,x75622,x75624)+P16(x75621,x75622,f317(f317(f10(x75623,f906(x75622,x75622),x75621),x75624),x75625)) % 112.26/112.10 [7563]~P14(x75633,x75632,x75634)+P14(x75631,x75632,f317(f317(f10(x75633,f906(x75632,x75632),x75631),x75634),x75635)) % 112.26/112.10 [7702]~P24(x77021,x77022,x77023,x77024)+P24(x77021,x77022,x77023,f317(f317(f3(f906(x77021,a895)),x77024),x77025)) % 112.26/112.10 [7859]~P1(f317(f317(x78593,x78594),x78595))+P1(f317(f317(f247(x78591,x78592,a895),x78593),f317(f317(f242(x78591,x78592),x78594),x78595))) % 112.26/112.10 [7973]~P1(f317(x79732,x79734))+~E(f317(f317(f128(x79731),f317(f179(f900(x79731)),f167(x79731,x79732,x79733))),x79733),f317(f317(f141(x79731),x79734),x79735)) % 112.26/112.10 [7993]P24(x79931,x79932,x79933,x79934)+~P24(x79931,x79932,x79933,f317(f317(f91(f906(x79931,a895)),x79935),x79934)) % 112.26/112.10 [7994]P24(x79941,x79942,x79943,x79944)+~P24(x79941,x79942,x79943,f317(f317(f91(f906(x79941,a895)),x79944),x79945)) % 112.26/112.10 [8041]~P108(x80412)+E(f317(f317(f138(x80411,x80412,x80413),x80414),f140(x80411,x80412,x80413,x80415)),f140(x80411,x80412,x80413,f317(f317(f141(x80411),x80414),x80415))) % 112.26/112.10 [8359]~P14(x83592,x83591,x83593)+E(f317(f132(x83591,x83592,f317(f9(x83592,x83591,x83591),x83593),x83594),x83595),f317(f317(f59(x83592,x83591,x83593),x83594),f317(f162(x83592),x83595))) % 112.26/112.10 [8387]~E(f317(f317(f128(x83871),f317(f179(f900(x83871)),f167(x83871,x83872,x83873))),x83873),f317(f317(f141(x83871),x83874),x83875))+E(f317(f317(f124(x83871),f167(x83871,x83872,x83873)),f317(f317(f141(x83871),x83874),x83875)),x83873) % 112.26/112.10 [8414]P1(f317(f317(x84141,x84142),x84143))+~P1(f317(f317(f247(x84144,x84145,a895),x84141),f317(f317(f242(x84144,x84145),x84142),x84143))) % 112.26/112.10 [8892]P1(f317(f317(f224(f906(x88921,a895)),f317(f300(x88922,x88921,x88923),x88924)),f317(f300(x88922,x88921,x88923),x88925)))+~P1(f317(f317(f224(f906(x88922,a895)),x88924),x88925)) % 112.26/112.10 [8893]P1(f317(f317(f224(f906(x88931,a895)),f317(f301(x88931,x88932,x88933),x88934)),f317(f301(x88931,x88932,x88933),x88935)))+~P1(f317(f317(f224(f906(x88932,a895)),x88934),x88935)) % 112.26/112.10 [8972]E(x89721,f2(a89))+E(f317(f317(f249(x89722,x89723,x89722,f905(x89723,x89722)),f317(x89724,x89725)),f263(x89723,x89722,f317(f317(f3(a89),x89721),f72(a89)),x89724)),f317(f263(x89723,x89722,x89721,x89724),x89725)) % 112.26/112.10 [9079]P1(f317(f317(f245(x90791,x90792,a895,x90793),x90794),x90795))+~P1(f317(x90793,f317(f317(f242(x90791,x90792),x90794),x90795))) % 112.26/112.10 [9355]~P1(f317(f317(f245(x93552,x93553,a895,x93551),x93554),x93555))+P1(f317(x93551,f317(f317(f242(x93552,x93553),x93554),x93555))) % 112.26/112.10 [9540]~P1(f317(f317(f319(x95402),x95405),f317(f300(x95401,x95402,x95404),x95403)))+P1(f317(f317(f319(x95401),f317(f85(x95401,x95402,x95403,x95404),x95405)),x95403)) % 112.26/112.10 [9639]~P1(f317(f29(x96393),f317(f300(x96392,x96393,x96395),f232(f906(x96392,a895)))))+P1(f317(f29(x96391),f317(f300(x96392,x96391,f317(f317(f10(x96393,x96391,x96392),x96394),x96395)),f232(f906(x96392,a895))))) % 112.26/112.10 [9665]P1(f317(f317(f224(f906(f906(x96651,a895),a895)),f317(f300(f906(x96652,a895),f906(x96651,a895),f300(x96652,x96651,x96653)),f317(f298(x96652),x96654))),f317(f298(x96651),x96655)))+~P1(f317(f317(f224(f906(x96651,a895)),f317(f300(x96652,x96651,x96653),x96654)),x96655)) % 112.26/112.10 [9737]E(x97371,x97372)+~P1(f317(f61(x97373,x97374,x97375,x97371,f178(f906(x97373,a895))),x97372)) % 112.26/112.10 [9753]E(f317(f317(f242(x97531,x97532),f537(x97533,x97534,x97535,x97532,x97531)),f539(x97533,x97534,x97535,x97532,x97531)),x97535)+~P1(f317(f317(f319(f905(x97531,x97532)),x97535),f317(f317(f244(x97531,x97532),x97534),x97533))) % 112.26/112.10 [9845]P1(f317(f317(f319(x98451),f537(x98452,x98453,x98454,x98455,x98451)),x98453))+~P1(f317(f317(f319(f905(x98451,x98455)),x98454),f317(f317(f244(x98451,x98455),x98453),x98452))) % 112.26/112.10 [9855]P1(f317(f317(f319(x98551),f468(x98552,x98553,x98554,x98555,x98551)),x98555))+P1(f317(f317(f224(f906(x98554,a895)),f317(f300(x98551,x98554,x98553),x98555)),x98552)) % 112.26/112.10 [10002]P1(f317(f317(f319(x100021),f539(x100022,x100023,x100024,x100021,x100025)),f317(x100022,f537(x100022,x100023,x100024,x100021,x100025))))+~P1(f317(f317(f319(f905(x100025,x100021)),x100024),f317(f317(f244(x100025,x100021),x100023),x100022))) % 112.26/112.10 [10022]P1(f317(f317(f319(f905(x100221,x100221)),f317(f317(f242(x100221,x100221),x100222),f617(x100223,x100224,x100225,x100222,x100221))),x100223))+~P1(f317(f317(f319(f905(x100221,x100221)),f317(f317(f242(x100221,x100221),x100222),x100225)),f317(f317(f173(f905(x100221,x100221),a895),f317(a102,x100224)),x100223))) % 112.26/112.10 [10023]P1(f317(f317(f319(f905(x100231,x100231)),f317(f317(f242(x100231,x100231),x100232),f618(x100233,x100234,x100235,x100232,x100231))),x100233))+~P1(f317(f317(f319(f905(x100231,x100231)),f317(f317(f242(x100231,x100231),x100232),x100235)),f317(f317(f173(f905(x100231,x100231),a895),f317(a102,x100234)),x100233))) % 112.26/112.10 [10040]~P1(f317(f317(f319(f905(f900(x100401),f900(x100401))),f317(f317(f242(f900(x100401),f900(x100401)),f317(f317(f141(x100401),x100402),x100405)),x100404)),f148(x100401,x100403)))+P1(f317(f317(f319(f905(x100401,x100401)),f317(f317(f242(x100401,x100401),x100402),f636(x100403,x100404,x100405,x100402,x100401))),x100403)) % 112.26/112.10 [10062]~P1(f317(f317(f319(x100621),f317(x100623,f468(x100625,x100623,x100621,x100624,x100622))),x100625))+P1(f317(f317(f224(f906(x100621,a895)),f317(f300(x100622,x100621,x100623),x100624)),x100625)) % 112.26/112.10 [6444]P1(f317(x64442,x64444))+E(f167(x64441,x64442,f317(f317(f124(x64441),x64443),f317(f317(f141(x64441),x64444),x64445))),f167(x64441,x64442,x64443)) % 112.26/112.10 [6493]~P67(x64932)+E(f317(f317(f317(f3(f906(x64931,x64932)),x64933),x64934),x64935),f317(f317(f3(x64932),f317(x64933,x64935)),f317(x64934,x64935))) % 112.26/112.10 [6495]~P99(x64952)+E(f317(f317(f317(f91(f906(x64951,x64952)),x64953),x64954),x64955),f317(f317(f91(x64952),f317(x64953,x64955)),f317(x64954,x64955))) % 112.26/112.10 [6497]~P99(x64972)+E(f317(f317(f317(f92(f906(x64971,x64972)),x64973),x64974),x64975),f317(f317(f92(x64972),f317(x64973,x64975)),f317(x64974,x64975))) % 112.26/112.10 [6517]E(x65171,x65172)+E(f317(f317(f154(x65173),f317(f317(f149(x65173,x65174),x65171),x65175)),x65172),f317(f317(f154(x65173),x65174),x65172)) % 112.26/112.10 [6791]~E(x67914,f178(f906(x67913,a895)))+E(f317(f317(f3(f906(x67911,a895)),x67912),f317(f317(f36(x67913,f906(x67911,a895)),x67914),x67915)),x67912) % 112.26/112.10 [6792]~E(x67924,f178(f906(x67923,a895)))+E(f317(f317(f91(f906(x67921,a895)),x67922),f317(f317(f36(x67923,f906(x67921,a895)),x67924),x67925)),x67922) % 112.26/112.10 [6793]~E(x67934,f178(f906(x67933,a895)))+E(f317(f317(f92(f906(x67931,a895)),x67932),f317(f317(f35(x67933,f906(x67931,a895)),x67934),x67935)),x67932) % 112.26/112.10 [6809]~E(x68094,f178(f906(x68093,a895)))+E(f317(f317(f299(x68091),x68092),f317(f317(f36(x68093,f906(x68091,a895)),x68094),x68095)),f317(f317(f299(x68091),x68092),f178(f906(x68091,a895)))) % 112.26/112.10 [7608]E(f317(f317(f154(x76081),f317(f317(f144(x76082,x76081),x76083),x76084)),x76085),f317(x76083,f317(f317(f154(x76082),x76084),x76085)))+~P1(f317(f317(f225(a899),x76085),f317(f179(f900(x76082)),x76084))) % 112.26/112.10 [7673]E(f317(f317(f91(f906(x76731,a895)),f317(x76732,x76733)),f317(f317(f36(x76734,f906(x76731,a895)),x76735),x76732)),f317(f317(f36(x76734,f906(x76731,a895)),x76735),x76732))+~P1(f317(f317(f319(x76734),x76733),x76735)) % 112.26/112.10 [7674]E(f317(f317(f92(f906(x76741,a895)),f317(x76742,x76743)),f317(f317(f35(x76744,f906(x76741,a895)),x76745),x76742)),f317(f317(f35(x76744,f906(x76741,a895)),x76745),x76742))+~P1(f317(f317(f319(x76744),x76743),x76745)) % 112.26/112.10 [8281]~E(x82813,f178(f906(x82811,a895)))+E(f317(f317(f36(x82811,f906(x82812,a895)),x82813),f317(f317(f10(f906(x82812,a895),f906(x82812,a895),x82811),f317(f299(x82812),x82814)),x82815)),f178(f906(x82812,a895))) % 112.26/112.10 [8286]~P1(f317(f317(f319(x82864),x82863),x82865))+P1(f317(f317(f224(f906(x82861,a895)),f317(x82862,x82863)),f317(f317(f36(x82864,f906(x82861,a895)),x82865),x82862))) % 112.26/112.10 [8413]~E(f317(x84134,x84132),x84135)+P1(f317(f317(f319(x84131),x84132),f317(f301(x84131,x84133,x84134),f317(f317(f299(x84133),x84135),f178(f906(x84133,a895)))))) % 112.26/112.10 [8460]~P54(x84601,x84602,f317(f276(x84602,x84601),x84603))+E(f317(f317(f92(f906(x84601,a895)),f317(f275(x84602,x84601,x84603),x84604)),f317(f275(x84602,x84601,x84603),x84605)),f317(f275(x84602,x84601,x84603),f317(f317(f92(f906(x84602,a895)),x84604),x84605))) % 112.26/112.10 [8537]E(x85371,f2(a89))+E(f317(f108(x85372,x85373,f317(x85374,f317(f317(f3(a89),x85371),f72(a89)))),f317(f317(f9(x85372,a89,f901(x85373)),x85375),x85371)),f317(f188(x85372,x85373,x85374,x85375),x85371)) % 112.26/112.10 [8575]E(x85751,f178(f906(x85752,a895)))+E(f317(f317(f36(x85752,f906(x85753,a895)),x85751),f317(f317(f10(f906(x85753,a895),f906(x85753,a895),x85752),f317(f299(x85753),x85754)),x85755)),f317(f317(f299(x85753),x85754),f317(f317(f36(x85752,f906(x85753,a895)),x85751),x85755))) % 112.26/112.10 [8626]~P24(x86262,x86261,x86263,f232(f906(x86262,a895)))+E(f317(f317(f3(f906(x86261,a895)),f317(f300(x86262,x86261,x86263),x86264)),f317(f300(x86262,x86261,x86263),x86265)),f317(f300(x86262,x86261,x86263),f317(f317(f3(f906(x86262,a895)),x86264),x86265))) % 112.26/112.10 [8627]~P24(x86272,x86271,x86273,f232(f906(x86272,a895)))+E(f317(f317(f92(f906(x86271,a895)),f317(f300(x86272,x86271,x86273),x86274)),f317(f300(x86272,x86271,x86273),x86275)),f317(f300(x86272,x86271,x86273),f317(f317(f92(f906(x86272,a895)),x86274),x86275))) % 112.26/112.10 [8695]~P1(f317(f317(f62(x86951,x86952,x86955),x86953),x86954))+P1(f317(f317(f319(f905(x86951,x86952)),f317(f317(f242(x86951,x86952),x86953),x86954)),x86955)) % 112.26/112.10 [8727]P1(f317(f317(f319(x87271),x87272),f317(f274(x87273,x87271),x87274)))+~P1(f317(f317(f319(f905(x87273,x87271)),f317(f317(f242(x87273,x87271),x87275),x87272)),x87274)) % 112.26/112.10 [8729]P1(f317(f317(f319(x87291),x87292),f317(f254(x87291,x87293),x87294)))+~P1(f317(f317(f319(f905(x87291,x87293)),f317(f317(f242(x87291,x87293),x87292),x87295)),x87294)) % 112.26/112.10 [8876]P1(f317(f317(f62(x88761,x88762,x88763),x88764),x88765))+~P1(f317(f317(f319(f905(x88761,x88762)),f317(f317(f242(x88761,x88762),x88764),x88765)),x88763)) % 112.26/112.10 [8915]E(f317(x89151,x89152),x89153)+~P1(f317(f317(f319(x89154),x89152),f317(f301(x89154,x89155,x89151),f317(f317(f299(x89155),x89153),f178(f906(x89155,a895)))))) % 112.26/112.10 [9143]P1(f317(f317(f319(f905(x91431,x91432)),f317(f317(f242(x91431,x91432),x91433),x91434)),f317(f276(x91432,x91431),x91435)))+~P1(f317(f317(f319(f905(x91432,x91431)),f317(f317(f242(x91432,x91431),x91434),x91433)),x91435)) % 112.26/112.10 [9161]~P1(f317(f317(x91611,x91615),x91614))+P1(f317(f317(x91611,f317(f246(x91612,x91613),f317(f317(f242(x91612,x91613),x91614),x91615))),f317(f241(x91612,x91613),f317(f317(f242(x91612,x91613),x91614),x91615)))) % 112.26/112.10 [9191]~P1(f317(f317(f319(f905(x91912,x91911)),f317(f317(f242(x91912,x91911),x91914),x91913)),f317(f276(x91911,x91912),x91915)))+P1(f317(f317(f319(f905(x91911,x91912)),f317(f317(f242(x91911,x91912),x91913),x91914)),x91915)) % 112.26/112.10 [9223]~P1(f317(f317(f319(f905(x92233,x92231)),f317(f317(f242(x92233,x92231),x92235),x92232)),x92234))+P1(f317(f317(f319(x92231),x92232),f317(f275(x92233,x92231,x92234),f317(f317(f299(x92233),x92235),f178(f906(x92233,a895)))))) % 112.26/112.10 [9270]P1(f317(f317(f319(f905(x92701,x92702)),f317(f317(f242(x92701,x92702),x92703),x92704)),x92705))+~P1(f317(f317(f319(x92702),x92704),f317(f275(x92701,x92702,x92705),f317(f317(f299(x92701),x92703),f178(f906(x92701,a895)))))) % 112.26/112.10 [9362]~P69(x93621)+E(f317(f317(f8(a899,x93621),x93622),f293(a899,f317(f317(f74(a899),x93623),x93624),f317(f317(f74(a899),x93625),x93624))),f317(f317(f8(a899,x93621),f317(f317(f10(a899,x93621,a899),x93622),f317(f317(f9(a899,a899,a899),f74(a899)),x93624))),f293(a899,x93623,x93625))) % 112.26/112.10 [9381]~P69(x93811)+E(f317(f317(f8(a899,x93811),x93812),f317(f292(a899,f317(f317(f74(a899),x93813),x93814)),f317(f317(f74(a899),x93815),x93814))),f317(f317(f8(a899,x93811),f317(f317(f10(a899,x93811,a899),x93812),f317(f317(f9(a899,a899,a899),f74(a899)),x93814))),f317(f292(a899,x93813),x93815))) % 112.26/112.10 [9440]~P24(x94401,x94402,x94403,f232(f906(x94401,a895)))+E(f317(f317(f144(x94401,x94402),x94403),f317(f126(x94401,f317(f317(f10(a895,a895,x94401),a312),f317(a314,x94404))),x94405)),f317(f126(x94402,f317(f317(f10(a895,a895,x94402),a312),f317(a314,f317(x94403,x94404)))),f317(f317(f144(x94401,x94402),x94403),x94405))) % 112.26/112.10 [9458]~P24(x94581,x94582,x94583,f317(f317(f299(x94581),x94584),f317(f162(x94581),x94585)))+E(f317(f317(f144(x94581,x94582),x94583),f317(f126(x94581,f317(f317(f10(a895,a895,x94581),a312),f317(a314,x94584))),x94585)),f317(f126(x94582,f317(f317(f10(a895,a895,x94582),a312),f317(a314,f317(x94583,x94584)))),f317(f317(f144(x94581,x94582),x94583),x94585))) % 112.26/112.10 [9627]P1(f317(f317(f319(f905(f900(x96271),f900(x96271))),f317(f317(f242(f900(x96271),f900(x96271)),f317(f317(f141(x96271),x96272),x96273)),f317(f317(f141(x96271),x96274),x96273))),f147(x96271,x96275)))+~P1(f317(f317(f319(f905(x96271,x96271)),f317(f317(f242(x96271,x96271),x96272),x96274)),x96275)) % 112.26/112.10 [9748]E(f317(f317(f299(x97481),f500(x97482,x97483,x97484,x97485,x97481)),f511(x97482,x97483,x97484,x97485,x97481)),f317(f317(f299(x97481),x97484),x97483))+~P1(f317(f57(x97481,x97485,f317(f317(f299(x97481),x97484),x97483)),x97482)) % 112.26/112.10 [9749]E(f317(f317(f299(x97491),f522(x97492,x97493,x97494,x97495,x97491)),f535(x97492,x97493,x97494,x97495,x97491)),f317(f317(f299(x97491),x97494),x97493))+~P1(f317(f57(x97491,x97495,f317(f317(f299(x97491),x97494),x97493)),x97492)) % 112.26/112.10 [9830]P1(f317(f317(f319(x98301),f479(x98302,x98303,x98304,x98305,x98301)),x98304))+P1(f317(f317(f317(f35(x98301,f906(x98305,a895)),x98304),x98303),x98302)) % 112.26/112.10 [9835]P1(f317(f317(f319(x98351),f475(x98352,x98353,x98351,x98354,x98355)),x98353))+P1(f317(f317(f319(x98355),x98354),f317(f317(f35(x98351,f906(x98355,a895)),x98353),x98352))) % 112.26/112.10 [9843]P1(f317(f317(f319(x98431),f467(x98432,x98433,x98431,x98434,x98435)),x98433))+P1(f317(f317(f224(f906(x98435,a895)),x98434),f317(f317(f35(x98431,f906(x98435,a895)),x98433),x98432))) % 112.26/112.10 [9844]P1(f317(f317(f319(x98441),f818(x98442,x98443,x98444,x98445,x98441)),x98445))+P1(f317(f317(f224(f906(x98444,a895)),x98443),f317(f317(f35(x98441,f906(x98444,a895)),x98445),x98442))) % 112.26/112.10 [9846]P1(f317(f317(x98461,f482(x98462,x98461,x98463,x98464,x98465)),x98462))+~P1(f317(f317(f317(f36(x98465,f906(x98464,a895)),x98463),x98461),x98462)) % 112.26/112.10 [9850]P1(f317(f317(f319(x98501),f482(x98502,x98503,x98504,x98505,x98501)),x98504))+~P1(f317(f317(f317(f36(x98501,f906(x98505,a895)),x98504),x98503),x98502)) % 112.26/112.10 [9851]P52(x98514,f317(f317(f35(x98511,f906(x98514,a895)),x98515),x98513),f317(f317(f35(x98511,f906(f905(x98514,x98514),a895)),x98515),x98512))+P1(f317(f317(f319(x98511),f755(x98512,x98513,x98514,x98515,x98511)),x98515)) % 112.26/112.10 [9852]P52(x98524,f317(f317(f36(x98521,f906(x98524,a895)),x98525),x98523),f317(f317(f36(x98521,f906(f905(x98524,x98524),a895)),x98525),x98522))+P1(f317(f317(f319(x98521),f809(x98522,x98523,x98524,x98525,x98521)),x98525)) % 112.26/112.10 [9863]P1(f317(f317(f319(x98631),f477(x98632,x98633,x98631,x98634,x98635)),x98633))+~P1(f317(f317(f319(x98635),x98634),f317(f317(f36(x98631,f906(x98635,a895)),x98633),x98632))) % 112.26/112.10 [9869]P1(f317(f317(f319(x98691),x98692),f317(x98693,f477(x98693,x98694,x98695,x98692,x98691))))+~P1(f317(f317(f319(x98691),x98692),f317(f317(f36(x98695,f906(x98691,a895)),x98694),x98693))) % 112.26/112.10 [9951]~P1(f317(f317(x99514,f479(x99515,x99514,x99513,x99512,x99511)),x99515))+P1(f317(f317(f317(f35(x99511,f906(x99512,a895)),x99513),x99514),x99515)) % 112.26/112.10 [9954]~P1(f317(f317(f319(x99541),x99542),f317(x99545,f475(x99545,x99544,x99543,x99542,x99541))))+P1(f317(f317(f319(x99541),x99542),f317(f317(f35(x99543,f906(x99541,a895)),x99544),x99545))) % 112.26/112.10 [9958]~P52(x99581,f317(x99584,f755(x99585,x99584,x99581,x99583,x99582)),f317(x99585,f755(x99585,x99584,x99581,x99583,x99582)))+P52(x99581,f317(f317(f35(x99582,f906(x99581,a895)),x99583),x99584),f317(f317(f35(x99582,f906(f905(x99581,x99581),a895)),x99583),x99585)) % 112.26/112.10 [9959]~P52(x99591,f317(x99594,f809(x99595,x99594,x99591,x99593,x99592)),f317(x99595,f809(x99595,x99594,x99591,x99593,x99592)))+P52(x99591,f317(f317(f36(x99592,f906(x99591,a895)),x99593),x99594),f317(f317(f36(x99592,f906(f905(x99591,x99591),a895)),x99593),x99595)) % 112.26/112.10 [9960]~P1(f317(f317(f224(f906(x99601,a895)),x99602),f317(x99605,f467(x99605,x99604,x99603,x99602,x99601))))+P1(f317(f317(f224(f906(x99601,a895)),x99602),f317(f317(f35(x99603,f906(x99601,a895)),x99604),x99605))) % 112.26/112.10 [9961]~P1(f317(f317(f224(f906(x99611,a895)),x99612),f317(x99615,f818(x99615,x99612,x99611,x99614,x99613))))+P1(f317(f317(f224(f906(x99611,a895)),x99612),f317(f317(f35(x99613,f906(x99611,a895)),x99614),x99615))) % 112.26/112.10 [10026]~P1(f317(f317(f319(x100261),f500(x100265,x100264,x100263,x100262,x100261)),f511(x100265,x100264,x100263,x100262,x100261)))+~P1(f317(f57(x100261,x100262,f317(f317(f299(x100261),x100263),x100264)),x100265)) % 112.26/112.10 [10027]~P1(f317(f317(f319(x100271),f522(x100275,x100274,x100273,x100272,x100271)),f535(x100275,x100274,x100273,x100272,x100271)))+~P1(f317(f57(x100271,x100272,f317(f317(f299(x100271),x100273),x100274)),x100275)) % 112.26/112.10 [10028]~P1(f317(f317(f319(f905(x100281,x100281)),f317(f317(f242(x100281,x100281),x100282),x100285)),f317(f317(f173(f905(x100281,x100281),a895),f317(a102,x100284)),x100283)))+P1(f317(f317(f319(f905(x100281,x100281)),f317(f317(f242(x100281,x100281),x100282),f619(x100283,x100284,x100285,x100282,x100281))),f317(f317(f173(f905(x100281,x100281),a895),x100284),x100283))) % 112.26/112.10 [10034]P1(f317(f61(x100341,x100341,x100342,f500(x100343,x100344,x100345,x100342,x100341),f511(x100343,x100344,x100345,x100342,x100341)),x100343))+~P1(f317(f57(x100341,x100342,f317(f317(f299(x100341),x100345),x100344)),x100343)) % 112.26/112.10 [10035]P1(f317(f61(x100351,x100351,x100352,f522(x100353,x100354,x100355,x100352,x100351),f535(x100353,x100354,x100355,x100352,x100351)),x100353))+~P1(f317(f57(x100351,x100352,f317(f317(f299(x100351),x100355),x100354)),x100353)) % 112.26/112.10 [10045]~P108(x100451)+P13(x100451,f317(f317(f144(x100452,x100451),x100453),f317(f126(x100452,f317(f317(f9(x100452,x100451,a895),f317(f317(f10(x100451,f906(x100451,a895),x100452),a314),x100453)),f317(x100454,x100455))),x100455))) % 112.26/112.10 [10096]~P1(f317(f317(f319(x100962),x100965),f317(f275(x100961,x100962,x100964),x100963)))+P1(f317(f317(f319(f905(x100961,x100962)),f317(f317(f242(x100961,x100962),f491(x100963,x100964,x100961,x100965,x100962)),x100965)),x100964)) % 112.26/112.10 [10097]~P1(f317(f317(f319(x100972),x100975),f317(f275(x100971,x100972,x100974),x100973)))+P1(f317(f317(f319(f905(x100971,x100972)),f317(f317(f242(x100971,x100972),f496(x100973,x100974,x100971,x100975,x100972)),x100975)),x100974)) % 112.26/112.10 [10117]~P1(f317(f317(f319(f905(x101171,x101171)),f317(f317(f242(x101171,x101171),x101175),x101174)),f317(f317(f173(f905(x101171,x101171),a895),f317(a102,x101173)),x101172)))+P1(f317(f317(f319(f905(x101171,x101171)),f317(f317(f242(x101171,x101171),f619(x101172,x101173,x101174,x101175,x101171)),x101174)),x101172)) % 112.26/112.10 [10120]~P1(f317(f317(f319(f905(x101201,x101201)),f317(f317(f242(x101201,x101201),x101205),x101204)),f317(f317(f173(f905(x101201,x101201),a895),f317(a102,x101203)),x101202)))+P1(f317(f317(f319(f905(x101201,x101201)),f317(f317(f242(x101201,x101201),f617(x101202,x101203,x101204,x101205,x101201)),x101204)),f317(f317(f173(f905(x101201,x101201),a895),x101203),x101202))) % 112.26/112.10 [10121]~P1(f317(f317(f319(f905(x101211,x101211)),f317(f317(f242(x101211,x101211),x101215),x101214)),f317(f317(f173(f905(x101211,x101211),a895),f317(a102,x101213)),x101212)))+P1(f317(f317(f319(f905(x101211,x101211)),f317(f317(f242(x101211,x101211),f618(x101212,x101213,x101214,x101215,x101211)),x101214)),f317(f317(f173(f905(x101211,x101211),a895),x101213),x101212))) % 112.26/112.10 [10122]~P1(f317(f317(f319(f905(f900(x101221),f900(x101221))),f317(f317(f242(f900(x101221),f900(x101221)),x101225),f317(f317(f141(x101221),x101224),x101223))),f148(x101221,x101222)))+P1(f317(f317(f319(f905(x101221,x101221)),f317(f317(f242(x101221,x101221),f635(x101222,x101223,x101224,x101225,x101221)),x101224)),x101222)) % 112.26/112.10 [7694]~E(x76943,f178(f906(x76942,a895)))+E(f317(f317(f91(f906(x76941,a895)),f317(f317(f36(x76942,f906(x76941,a895)),x76943),x76944)),x76945),x76945) % 112.26/112.10 [7695]~E(x76953,f178(f906(x76952,a895)))+E(f317(f317(f92(f906(x76951,a895)),f317(f317(f35(x76952,f906(x76951,a895)),x76953),x76954)),x76955),x76955) % 112.26/112.10 [8122]~E(x81223,f178(f906(x81222,a895)))+E(f317(f317(f3(f906(x81221,a895)),f317(f317(f35(x81222,f906(x81221,a895)),x81223),x81224)),x81225),f317(f317(f3(f906(x81221,a895)),f232(f906(x81221,a895))),x81225)) % 112.26/112.10 [8255]E(f317(f317(f149(x82551,f317(f317(f124(x82551),x82552),x82553)),x82554),x82555),f317(f317(f124(x82551),f317(f317(f149(x82551,x82552),x82554),x82555)),x82553))+~P1(f317(f317(f225(a899),x82554),f317(f179(f900(x82551)),x82552))) % 112.26/112.10 [8527]E(f317(f317(f154(x85271),f317(f317(f144(a899,x85271),x85272),f129(a899,f317(f292(a899,x85273),x85274)))),x85275),f317(x85272,f317(f317(f74(a899),x85273),x85275)))+~P1(f317(f317(f225(a899),x85275),f317(f317(f3(a899),x85274),x85273))) % 112.26/112.10 [8541]E(x85411,f2(a89))+E(f112(x85412,x85413,f317(x85414,f317(f317(f3(a89),x85411),f72(a89))),f317(f317(f9(x85412,a89,f901(f902(x85413))),x85415),x85411)),f317(f186(x85412,x85413,x85414,x85415),x85411)) % 112.26/112.10 [8565]~E(x85653,f178(f906(x85651,a895)))+E(f317(f317(f35(x85651,f906(x85652,a895)),x85653),f317(f317(f10(f906(x85652,a895),f906(x85652,a895),x85651),f317(f3(f906(x85652,a895)),x85654)),x85655)),f232(f906(x85652,a895))) % 112.26/112.10 [8566]~E(x85663,f178(f906(x85661,a895)))+E(f317(f317(f35(x85661,f906(x85662,a895)),x85663),f317(f317(f10(f906(x85662,a895),f906(x85662,a895),x85661),f317(f92(f906(x85662,a895)),x85664)),x85665)),f232(f906(x85662,a895))) % 112.26/112.10 [8567]~E(x85673,f178(f906(x85671,a895)))+E(f317(f317(f36(x85671,f906(x85672,a895)),x85673),f317(f317(f10(f906(x85672,a895),f906(x85672,a895),x85671),f317(f91(f906(x85672,a895)),x85674)),x85675)),f178(f906(x85672,a895))) % 112.26/112.10 [8569]~P146(x85692)+E(f317(f317(f8(x85691,x85692),f317(f317(f10(x85692,x85692,x85691),f317(f75(x85692),x85693)),x85694)),x85695),f317(f317(f75(x85692),x85693),f317(f317(f8(x85691,x85692),x85694),x85695))) % 112.26/112.10 [8860]E(x88601,f178(f906(x88602,a895)))+E(f317(f317(f35(x88602,f906(x88603,a895)),x88601),f317(f317(f10(f906(x88603,a895),f906(x88603,a895),x88602),f317(f3(f906(x88603,a895)),x88604)),x88605)),f317(f317(f3(f906(x88603,a895)),x88604),f317(f317(f36(x88602,f906(x88603,a895)),x88601),x88605))) % 112.26/112.10 [8861]E(x88611,f178(f906(x88612,a895)))+E(f317(f317(f35(x88612,f906(x88613,a895)),x88611),f317(f317(f10(f906(x88613,a895),f906(x88613,a895),x88612),f317(f92(f906(x88613,a895)),x88614)),x88615)),f317(f317(f92(f906(x88613,a895)),x88614),f317(f317(f35(x88612,f906(x88613,a895)),x88611),x88615))) % 112.26/112.10 [8862]E(x88621,f178(f906(x88622,a895)))+E(f317(f317(f36(x88622,f906(x88623,a895)),x88621),f317(f317(f10(f906(x88623,a895),f906(x88623,a895),x88622),f317(f91(f906(x88623,a895)),x88624)),x88625)),f317(f317(f91(f906(x88623,a895)),x88624),f317(f317(f36(x88622,f906(x88623,a895)),x88621),x88625))) % 112.26/112.10 [9061]~P1(f317(f317(f225(a899),f317(x90614,x90612)),f317(x90614,x90613)))+P1(f317(f317(f319(f905(x90611,x90611)),f317(f317(f242(x90611,x90611),x90612),x90613)),f143(x90611,f317(f317(f141(f906(x90611,a899)),x90614),x90615)))) % 112.26/112.10 [9326]~P24(x93262,x93261,x93263,f317(f317(f91(f906(x93262,a895)),x93264),x93265))+E(f317(f317(f92(f906(x93261,a895)),f317(f300(x93262,x93261,x93263),f317(f317(f3(f906(x93262,a895)),x93264),x93265))),f317(f300(x93262,x93261,x93263),f317(f317(f3(f906(x93262,a895)),x93265),x93264))),f178(f906(x93261,a895))) % 112.26/112.10 [9589]~P24(x95893,x95891,x95895,f232(f906(x95893,a895)))+E(f317(f67(x95891,x95892,x95893,f317(f67(x95893,x95892,x95891,x95894),f85(x95893,x95891,f232(f906(x95893,a895)),x95895))),x95895),x95894) % 112.26/112.10 [9623]~P1(f317(f317(f224(f906(x96233,a895)),f317(f275(x96231,x96233,x96234),x96232)),x96235))+P1(f317(f317(f224(f906(x96231,a895)),x96232),f317(f73(f906(x96231,a895)),f317(f275(x96233,x96231,f317(f276(x96231,x96233),x96234)),f317(f73(f906(x96233,a895)),x96235))))) % 112.26/112.10 [9648]~P24(x96481,x96482,x96483,f317(f317(f299(x96481),x96484),x96485))+~P1(f317(f317(f319(x96482),f317(x96483,x96484)),f317(f300(x96481,x96482,x96483),f317(f317(f3(f906(x96481,a895)),x96485),f317(f317(f299(x96481),x96484),f178(f906(x96481,a895))))))) % 112.26/112.10 [9702]P1(f317(f317(f224(f906(x97021,a895)),f317(f275(x97022,x97021,x97023),x97024)),x97025))+~P1(f317(f317(f224(f906(x97022,a895)),x97024),f317(f73(f906(x97022,a895)),f317(f275(x97021,x97022,f317(f276(x97022,x97021),x97023)),f317(f73(f906(x97021,a895)),x97025))))) % 112.26/112.10 [9775]~P86(x97751)+P1(f317(f317(f224(x97751),f317(f70(x97751),f317(f317(f3(x97751),f317(f317(f74(x97751),x97752),x97753)),f317(f317(f74(x97751),x97754),x97755)))),f317(f317(f74(x97751),f317(f70(x97751),f317(f317(f3(x97751),x97752),x97754))),f317(f70(x97751),f317(f317(f3(x97751),x97753),x97755))))) % 112.26/112.10 [9885]P1(f317(f317(f319(x98851),f469(x98852,x98853,x98854,x98851,x98855)),x98854))+P1(f317(f317(f224(f906(x98855,a895)),f317(f317(f36(x98851,f906(x98855,a895)),x98854),x98853)),x98852)) % 112.26/112.10 [10064]~P1(f317(f317(f224(f906(x100641,a895)),f317(x100644,f469(x100645,x100644,x100643,x100642,x100641))),x100645))+P1(f317(f317(f224(f906(x100641,a895)),f317(f317(f36(x100642,f906(x100641,a895)),x100643),x100644)),x100645)) % 112.26/112.10 [8674]E(f317(f317(f124(x86741),x86742),f317(f317(f149(x86741,x86743),f317(f317(f3(a899),x86744),f317(f179(f900(x86741)),x86742))),x86745)),f317(f317(f149(x86741,f317(f317(f124(x86741),x86742),x86743)),x86744),x86745))+P1(f317(f317(f225(a899),x86744),f317(f179(f900(x86741)),x86742))) % 112.26/112.10 [8702]~P139(x87021)+E(f317(f317(f74(x87021),f317(f317(f75(x87021),x87022),x87023)),f317(f317(f74(x87021),f317(f317(f75(x87021),x87024),x87023)),x87025)),f317(f317(f74(x87021),f317(f317(f75(x87021),f317(f317(f74(x87021),x87022),x87024)),x87023)),x87025)) % 112.26/112.10 [9279]~P146(x92791)+E(f317(f155(x92791),f317(f317(f144(x92792,x92791),f317(f317(f10(x92791,x92791,x92792),f317(f75(x92791),x92793)),x92794)),x92795)),f317(f317(f75(x92791),x92793),f317(f155(x92791),f317(f317(f144(x92792,x92791),x92794),x92795)))) % 112.26/112.10 [9457]E(f317(f179(f900(x94571)),f317(f317(f165(x94571),f317(f317(f228(a899),f317(f179(f900(x94571)),x94572)),f317(f179(f900(x94573)),x94574))),x94572)),f317(f179(f900(x94573)),f317(f317(f165(x94573),f317(f317(f228(a899),f317(f179(f900(x94571)),x94572)),f317(f179(f900(x94573)),x94574))),x94574)))+P1(f317(x94575,f317(f317(f171(x94571,x94573),x94572),x94574))) % 112.26/112.10 [9712]~P146(x97122)+E(f317(f317(f8(x97121,x97122),f317(f317(f9(x97121,x97122,x97122),f317(f317(f10(x97122,f906(x97122,x97122),x97121),f75(x97122)),x97123)),x97124)),x97125),f317(f317(f75(x97122),f317(f317(f8(x97121,x97122),x97123),x97125)),x97124)) % 112.26/112.10 [9713]~P62(x97132)+E(f317(f317(f8(x97131,x97132),f317(f317(f9(x97131,x97132,x97132),f317(f317(f10(x97132,f906(x97132,x97132),x97131),f281(x97132)),x97133)),x97134)),x97135),f317(f317(f281(x97132),f317(f317(f8(x97131,x97132),x97133),x97135)),x97134)) % 112.26/112.10 [9720]~P68(x97202)+E(f317(f317(f8(x97201,x97202),f317(f317(f20(x97201,x97202,x97202),f317(f317(f10(x97202,f906(x97202,x97202),x97201),f3(x97202)),x97203)),x97204)),x97205),f317(f317(f3(x97202),f317(f317(f8(x97201,x97202),x97203),x97205)),f317(f317(f8(x97201,x97202),x97204),x97205))) % 112.26/112.10 [9721]~P69(x97212)+E(f317(f317(f8(x97211,x97212),f317(f317(f20(x97211,x97212,x97212),f317(f317(f10(x97212,f906(x97212,x97212),x97211),f74(x97212)),x97213)),x97214)),x97215),f317(f317(f74(x97212),f317(f317(f8(x97211,x97212),x97213),x97215)),f317(f317(f8(x97211,x97212),x97214),x97215))) % 112.26/112.10 [9722]~P75(x97222)+E(f317(f317(f11(x97221,x97222),f317(f317(f20(x97221,x97222,x97222),f317(f317(f10(x97222,f906(x97222,x97222),x97221),f75(x97222)),x97223)),x97224)),x97225),f317(f317(f75(x97222),f317(f317(f11(x97221,x97222),x97223),x97225)),f317(f317(f11(x97221,x97222),x97224),x97225))) % 112.26/112.10 [9760]~E(x97603,f178(f906(x97601,a895)))+E(f317(f317(f35(x97601,f906(x97602,a895)),x97603),f317(f317(f9(x97601,f906(x97602,a895),f906(x97602,a895)),f317(f317(f10(f906(x97602,a895),f906(f906(x97602,a895),f906(x97602,a895)),x97601),f3(f906(x97602,a895))),x97604)),x97605)),f232(f906(x97602,a895))) % 112.26/112.10 [9761]~E(x97613,f178(f906(x97611,a895)))+E(f317(f317(f35(x97611,f906(x97612,a895)),x97613),f317(f317(f9(x97611,f906(x97612,a895),f906(x97612,a895)),f317(f317(f10(f906(x97612,a895),f906(f906(x97612,a895),f906(x97612,a895)),x97611),f92(f906(x97612,a895))),x97614)),x97615)),f232(f906(x97612,a895))) % 112.26/112.10 [9762]~E(x97623,f178(f906(x97621,a895)))+E(f317(f317(f36(x97621,f906(x97622,a895)),x97623),f317(f317(f9(x97621,f906(x97622,a895),f906(x97622,a895)),f317(f317(f10(f906(x97622,a895),f906(f906(x97622,a895),f906(x97622,a895)),x97621),f91(f906(x97622,a895))),x97624)),x97625)),f178(f906(x97622,a895))) % 112.26/112.10 [9783]E(x97831,f178(f906(x97832,a895)))+E(f317(f317(f35(x97832,f906(x97833,a895)),x97831),f317(f317(f9(x97832,f906(x97833,a895),f906(x97833,a895)),f317(f317(f10(f906(x97833,a895),f906(f906(x97833,a895),f906(x97833,a895)),x97832),f3(f906(x97833,a895))),x97834)),x97835)),f317(f317(f3(f906(x97833,a895)),f317(f317(f35(x97832,f906(x97833,a895)),x97831),x97834)),x97835)) % 112.26/112.10 [9784]E(x97841,f178(f906(x97842,a895)))+E(f317(f317(f35(x97842,f906(x97843,a895)),x97841),f317(f317(f9(x97842,f906(x97843,a895),f906(x97843,a895)),f317(f317(f10(f906(x97843,a895),f906(f906(x97843,a895),f906(x97843,a895)),x97842),f92(f906(x97843,a895))),x97844)),x97845)),f317(f317(f92(f906(x97843,a895)),f317(f317(f35(x97842,f906(x97843,a895)),x97841),x97844)),x97845)) % 112.26/112.10 [9785]E(x97851,f178(f906(x97852,a895)))+E(f317(f317(f36(x97852,f906(x97853,a895)),x97851),f317(f317(f9(x97852,f906(x97853,a895),f906(x97853,a895)),f317(f317(f10(f906(x97853,a895),f906(f906(x97853,a895),f906(x97853,a895)),x97852),f91(f906(x97853,a895))),x97854)),x97855)),f317(f317(f91(f906(x97853,a895)),f317(f317(f36(x97852,f906(x97853,a895)),x97851),x97854)),x97855)) % 112.26/112.10 [9331]~P1(f317(f317(f224(a899),x93311),x93314))+E(f317(f317(f3(a899),f317(f317(f74(a899),f317(f317(f75(a899),x93311),x93312)),x93313)),f317(f317(f74(a899),f317(f317(f75(a899),x93314),x93312)),x93315)),f317(f317(f3(a899),x93313),f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x93314),x93311)),x93312)),x93315))) % 112.26/112.10 [9934]~P146(x99341)+E(f317(f155(x99341),f317(f317(f144(x99342,x99341),f317(f317(f9(x99342,x99341,x99341),f317(f317(f10(x99341,f906(x99341,x99341),x99342),f75(x99341)),x99343)),x99344)),x99345)),f317(f317(f75(x99341),f317(f155(x99341),f317(f317(f144(x99342,x99341),x99343),x99345))),x99344)) % 112.26/112.10 [9940]~P68(x99401)+E(f317(f155(x99401),f317(f317(f144(x99402,x99401),f317(f317(f20(x99402,x99401,x99401),f317(f317(f10(x99401,f906(x99401,x99401),x99402),f3(x99401)),x99403)),x99404)),x99405)),f317(f317(f3(x99401),f317(f155(x99401),f317(f317(f144(x99402,x99401),x99403),x99405))),f317(f155(x99401),f317(f317(f144(x99402,x99401),x99404),x99405)))) % 112.26/112.10 [9941]~P69(x99411)+E(f317(f155(x99411),f317(f317(f144(x99412,x99411),f317(f317(f20(x99412,x99411,x99411),f317(f317(f10(x99411,f906(x99411,x99411),x99412),f74(x99411)),x99413)),x99414)),x99415)),f317(f317(f74(x99411),f317(f155(x99411),f317(f317(f144(x99412,x99411),x99413),x99415))),f317(f155(x99411),f317(f317(f144(x99412,x99411),x99414),x99415)))) % 112.26/112.10 [10088]P1(f317(x100881,f317(f317(f171(x100882,x100883),x100884),x100885)))+~P1(f317(x100881,f317(f317(f171(x100882,x100883),f317(f317(f165(x100882),f317(f317(f228(a899),f317(f179(f900(x100882)),x100884)),f317(f179(f900(x100883)),x100885))),x100884)),f317(f317(f165(x100883),f317(f317(f228(a899),f317(f179(f900(x100882)),x100884)),f317(f179(f900(x100883)),x100885))),x100885)))) % 112.26/112.10 [10350]~P1(f317(f317(f319(f905(x103502,x103501)),f317(f317(f242(x103502,x103501),x103504),x103505)),f317(f276(x103501,x103502),x103503)))+P1(f317(f317(f233(x103501,x103502,f317(f317(f9(x103501,f906(f905(x103501,x103502),a895),f906(x103502,a895)),f317(f317(f10(f906(x103502,f906(f906(f905(x103501,x103502),a895),a895)),f906(f906(f905(x103501,x103502),a895),f906(x103502,a895)),x103501),f9(x103502,f906(f905(x103501,x103502),a895),a895)),f317(f317(f10(f906(x103502,f905(x103501,x103502)),f906(x103502,f906(f906(f905(x103501,x103502),a895),a895)),x103501),f317(f10(f905(x103501,x103502),f906(f906(f905(x103501,x103502),a895),a895),x103502),f319(f905(x103501,x103502)))),f242(x103501,x103502)))),x103503)),x103504),x103505)) % 112.26/112.10 [10360]P1(f317(f317(f319(f905(x103601,x103602)),f317(f317(f242(x103601,x103602),x103603),x103604)),f317(f276(x103602,x103601),x103605)))+~P1(f317(f317(f233(x103602,x103601,f317(f317(f9(x103602,f906(f905(x103602,x103601),a895),f906(x103601,a895)),f317(f317(f10(f906(x103601,f906(f906(f905(x103602,x103601),a895),a895)),f906(f906(f905(x103602,x103601),a895),f906(x103601,a895)),x103602),f9(x103601,f906(f905(x103602,x103601),a895),a895)),f317(f317(f10(f906(x103601,f905(x103602,x103601)),f906(x103601,f906(f906(f905(x103602,x103601),a895),a895)),x103602),f317(f10(f905(x103602,x103601),f906(f906(f905(x103602,x103601),a895),a895),x103601),f319(f905(x103602,x103601)))),f242(x103602,x103601)))),x103605)),x103603),x103604)) % 112.26/112.10 [9588]~P1(f317(f317(f224(a899),x95884),x95881))+E(f317(f317(f3(a899),f317(f317(f74(a899),f317(f317(f75(a899),x95881),x95882)),x95883)),f317(f317(f74(a899),f317(f317(f75(a899),x95884),x95882)),x95885)),f317(f317(f3(a899),f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x95881),x95884)),x95882)),x95883)),x95885)) % 112.26/112.10 [7386]E(x73861,x73862)+~E(f210(x73863,x73864,x73865,x73861),f210(x73863,x73864,x73866,x73862)) % 112.26/112.10 [7387]E(x73871,x73872)+~E(f210(x73873,x73874,x73871,x73875),f210(x73873,x73874,x73872,x73876)) % 112.26/112.10 [8510]~P19(x85105,x85101,x85102,x85106)+E(f317(f67(x85101,x85101,x85101,f317(x85102,x85103)),f317(x85102,x85104)),f317(f67(x85101,x85101,x85101,f317(x85102,x85104)),f317(x85102,x85103))) % 112.26/112.10 [8746]~P56(x87464,x87465,x87462,x87461,x87466)+E(f317(x87461,f317(x87462,x87463)),x87463) % 112.26/112.10 [8913]P24(x89131,x89132,x89133,x89134)+~P24(x89131,x89135,f317(f67(x89132,x89135,x89131,x89136),x89133),x89134) % 112.26/112.10 [8986]~E(x89866,x89864)+E(f317(f69(x89861,x89862,x89863,x89864,x89865),x89866),x89865) % 112.26/112.10 [8992]E(x89921,x89922)+E(f317(f69(x89923,x89924,x89925,x89922,x89926),x89921),f317(x89925,x89921)) % 112.26/112.10 [9004]~P24(x90044,x90042,f317(f67(x90041,x90042,x90044,x90043),x90045),x90046)+P24(x90041,x90042,x90043,f317(f300(x90044,x90041,x90045),x90046)) % 112.26/112.10 [9723]P1(f317(f29(x97231),x97232))+~P1(f317(f61(x97231,x97233,x97234,x97235,x97232),x97236)) % 112.26/112.10 [9732]~P1(f317(f317(f319(x97324),x97323),f287(x97324,x97321,x97325,x97322,x97326)))+P1(f317(f317(x97321,x97322),x97323)) % 112.26/112.10 [9733]~P1(f317(f317(f319(x97334),x97333),f290(x97334,x97335,x97331,x97332,x97336)))+P1(f317(f317(x97331,x97332),x97333)) % 112.26/112.10 [9734]~P1(f317(f317(f319(x97344),x97342),f287(x97344,x97345,x97341,x97346,x97343)))+P1(f317(f317(x97341,x97342),x97343)) % 112.26/112.10 [9735]~P1(f317(f317(f319(x97354),x97352),f290(x97354,x97351,x97355,x97356,x97353)))+P1(f317(f317(x97351,x97352),x97353)) % 112.26/112.10 [10237]P12(x102371,x102372,x102373,x102374,x102375,x102376)+~E(f317(f317(x102376,f825(x102373,x102376,x102375,x102372,x102374,x102371)),f835(x102373,x102376,x102375,x102372,x102374,x102371)),f317(f317(x102376,f826(x102373,x102376,x102375,x102372,x102374,x102371)),f834(x102373,x102376,x102375,x102372,x102374,x102371))) % 112.26/112.10 [5844]E(x58441,x58442)+~E(f317(f317(f242(x58443,x58444),x58445),x58441),f317(f317(f242(x58443,x58444),x58446),x58442)) % 112.26/112.10 [5846]E(x58461,x58462)+~E(f317(f317(f242(x58463,x58464),x58461),x58465),f317(f317(f242(x58463,x58464),x58462),x58466)) % 112.26/112.10 [5991]~P16(x59915,x59916,x59911)+E(f317(f317(x59911,x59912),f317(f317(x59911,x59913),x59914)),f317(f317(x59911,x59913),f317(f317(x59911,x59912),x59914))) % 112.26/112.10 [7453]~P31(x74534,x74531,f317(f317(f141(x74534),x74532),x74535),f317(f317(f141(x74534),x74533),x74536))+P1(f317(f317(x74531,x74532),x74533)) % 112.26/112.10 [7812]P31(x78121,x78122,x78123,x78124)+~P31(x78121,x78122,f317(f317(f141(x78121),x78125),x78123),f317(f317(f141(x78121),x78126),x78124)) % 112.26/112.10 [8850]~P56(x88505,x88501,x88502,x88506,x88504)+P1(f317(f317(f319(x88501),f317(x88502,x88503)),x88504)) % 112.26/112.10 [9052]~E(x90523,f317(f317(f141(x90521),x90525),x90526))+P1(f317(f317(f319(f905(f900(x90521),f900(x90521))),f317(f317(f242(f900(x90521),f900(x90521)),x90522),f317(f317(f124(x90521),x90522),x90523))),f137(x90521,x90524))) % 112.26/112.10 [9285]~P33(x92851,x92852,x92853,x92855,x92856)+P33(x92851,x92852,x92853,f317(f317(f165(x92851),x92854),x92855),f317(f317(f165(x92852),x92854),x92856)) % 112.26/112.10 [9286]~P33(x92861,x92862,x92863,x92865,x92866)+P33(x92861,x92862,x92863,f317(f317(f128(x92861),x92864),x92865),f317(f317(f128(x92862),x92864),x92866)) % 112.26/112.10 [9550]E(f317(f300(x95501,x95502,f69(x95501,x95502,x95503,x95504,x95505)),x95506),f317(f300(x95501,x95502,x95503),x95506))+P1(f317(f317(f319(x95501),x95504),x95506)) % 112.26/112.10 [9553]E(f317(f317(f144(x95531,x95532),f69(x95531,x95532,x95533,x95534,x95535)),x95536),f317(f317(f144(x95531,x95532),x95533),x95536))+P1(f317(f317(f319(x95531),x95534),f317(f162(x95531),x95536))) % 112.26/112.10 [9795]~P23(x97954,x97952,x97955,x97953,x97956,x97951)+E(f317(x97951,f178(f906(x97952,a895))),x97953) % 112.26/112.10 [10029]~E(f317(x100294,f317(f241(x100291,x100293),x100295)),f317(x100296,f317(f241(x100291,x100293),x100295)))+E(f317(f248(x100291,x100292,x100293,x100293,x100294,f25(x100293)),x100295),f317(f248(x100291,x100292,x100293,x100293,x100296,f25(x100293)),x100295)) % 112.26/112.10 [10030]~E(f317(x100304,f317(f246(x100301,x100302),x100305)),f317(x100306,f317(f246(x100301,x100302),x100305)))+E(f317(f248(x100301,x100301,x100302,x100303,f25(x100301),x100304),x100305),f317(f248(x100301,x100301,x100302,x100303,f25(x100301),x100306),x100305)) % 112.26/112.10 [10084]~E(f317(f248(x100842,x100846,x100843,x100843,x100841,f25(x100843)),x100844),f317(f248(x100842,x100846,x100843,x100843,x100845,f25(x100843)),x100844))+E(f317(x100841,f317(f241(x100842,x100843),x100844)),f317(x100845,f317(f241(x100842,x100843),x100844))) % 112.26/112.10 [10085]~E(f317(f248(x100852,x100852,x100853,x100856,f25(x100852),x100851),x100854),f317(f248(x100852,x100852,x100853,x100856,f25(x100852),x100855),x100854))+E(f317(x100851,f317(f246(x100852,x100853),x100854)),f317(x100855,f317(f246(x100852,x100853),x100854))) % 112.26/112.10 [8953]P1(f317(f317(f319(x89531),x89532),x89533))+~P1(f317(f317(f319(f905(x89531,x89534)),f317(f317(f242(x89531,x89534),x89532),x89535)),f317(f317(f244(x89531,x89534),x89533),x89536))) % 112.26/112.10 [8969]P1(f317(f317(f319(x89691),x89692),f317(x89693,x89694)))+~P1(f317(f317(f319(f905(x89695,x89691)),f317(f317(f242(x89695,x89691),x89694),x89692)),f317(f317(f244(x89695,x89691),x89696),x89693))) % 112.26/112.10 [9407]P1(f317(f317(f319(f905(x94071,x94071)),f317(f317(f242(x94071,x94071),f317(x94072,x94073)),f317(x94072,x94074))),x94075))+~P1(f317(f317(f319(f905(x94076,x94076)),f317(f317(f242(x94076,x94076),x94073),x94074)),f317(f317(f278(x94071,x94076),x94075),x94072))) % 112.26/112.10 [9427]~P1(f317(f317(f319(f905(x94274,x94274)),f317(f317(f242(x94274,x94274),f317(x94276,x94272)),f317(x94276,x94273))),x94275))+P1(f317(f317(f319(f905(x94271,x94271)),f317(f317(f242(x94271,x94271),x94272),x94273)),f317(f317(f278(x94274,x94271),x94275),x94276))) % 112.26/112.10 [10087]E(f317(f317(f242(x100871,x100872),f626(x100873,x100874,x100875,x100876,x100872,x100871)),f627(x100873,x100874,x100875,x100876,x100872,x100871)),x100876)+~P1(f317(f317(f319(f905(x100871,x100872)),x100876),f317(f317(f279(x100871,x100875,x100872),x100874),x100873))) % 112.26/112.10 [10308]~P1(f317(f317(f319(f905(x103081,x103086)),x103085),f317(f317(f279(x103081,x103082,x103086),x103084),x103083)))+P1(f317(f317(f319(f905(x103081,x103082)),f317(f317(f242(x103081,x103082),f626(x103083,x103084,x103082,x103085,x103086,x103081)),f628(x103083,x103084,x103082,x103085,x103086,x103081))),x103084)) % 112.26/112.10 [10309]~P1(f317(f317(f319(f905(x103096,x103092)),x103095),f317(f317(f279(x103096,x103091,x103092),x103094),x103093)))+P1(f317(f317(f319(f905(x103091,x103092)),f317(f317(f242(x103091,x103092),f628(x103093,x103094,x103091,x103095,x103092,x103096)),f627(x103093,x103094,x103091,x103095,x103092,x103096))),x103093)) % 112.26/112.10 [10310]P12(x103101,x103102,x103103,x103104,x103105,x103106)+P1(f317(f317(f319(f905(x103102,x103102)),f317(f317(f242(x103102,x103102),f834(x103103,x103106,x103105,x103102,x103104,x103101)),f835(x103103,x103106,x103105,x103102,x103104,x103101))),x103105)) % 112.26/112.10 [10311]P12(x103111,x103112,x103113,x103114,x103115,x103116)+P1(f317(f317(f319(f905(x103111,x103111)),f317(f317(f242(x103111,x103111),f826(x103113,x103116,x103115,x103112,x103114,x103111)),f825(x103113,x103116,x103115,x103112,x103114,x103111))),x103114)) % 112.26/112.10 [7883]~P5(x78832)+E(f317(f317(f35(x78831,x78832),x78833),f317(f317(f9(x78831,x78834,x78832),x78835),x78836)),f317(f317(f317(f35(x78831,f906(x78834,x78832)),x78833),x78835),x78836)) % 112.26/112.10 [7884]~P5(x78842)+E(f317(f317(f36(x78841,x78842),x78843),f317(f317(f9(x78841,x78844,x78842),x78845),x78846)),f317(f317(f317(f36(x78841,f906(x78844,x78842)),x78843),x78845),x78846)) % 112.26/112.10 [8657]E(f317(f317(f36(x86571,f906(x86572,a895)),x86573),f317(f317(f10(f906(x86572,a895),f906(x86572,a895),x86571),f317(f299(x86572),x86574)),x86575)),f317(f317(f299(x86572),x86574),f317(f317(f36(x86571,f906(x86572,a895)),x86573),x86575)))+~P1(f317(f317(f319(x86571),x86576),x86573)) % 112.26/112.10 [9105]~P5(x91052)+E(f317(f317(f35(x91051,x91052),x91053),f317(f317(f10(f906(x91054,x91052),x91052,x91051),f317(f35(x91054,x91052),x91055)),f317(f9(x91054,x91051,x91052),x91056))),f317(f317(f35(x91054,x91052),x91055),f317(f317(f10(f906(x91051,x91052),x91052,x91054),f317(f35(x91051,x91052),x91053)),x91056))) % 112.26/112.10 [9106]~P5(x91062)+E(f317(f317(f36(x91061,x91062),x91063),f317(f317(f10(f906(x91064,x91062),x91062,x91061),f317(f36(x91064,x91062),x91065)),f317(f9(x91064,x91061,x91062),x91066))),f317(f317(f36(x91064,x91062),x91065),f317(f317(f10(f906(x91061,x91062),x91062,x91064),f317(f36(x91061,x91062),x91063)),x91066))) % 112.26/112.10 [9311]P1(f317(f317(f319(x93111),x93112),f317(f162(x93111),x93113)))+~P1(f317(f317(f319(f905(x93114,x93111)),f317(f317(f242(x93114,x93111),x93115),x93112)),f317(f162(f905(x93114,x93111)),f317(f317(f171(x93114,x93111),x93116),x93113)))) % 112.26/112.10 [9312]P1(f317(f317(f319(x93121),x93122),f317(f162(x93121),x93123)))+~P1(f317(f317(f319(f905(x93121,x93124)),f317(f317(f242(x93121,x93124),x93122),x93125)),f317(f162(f905(x93121,x93124)),f317(f317(f171(x93121,x93124),x93123),x93126)))) % 112.26/112.10 [9423]P1(f317(f317(f224(f906(x94231,a895)),f317(f275(x94232,x94231,x94233),x94234)),x94235))+~P1(f317(f317(f224(f906(f905(x94232,x94231),a895)),x94233),f317(f317(f244(x94232,x94231),x94236),f317(f18(f906(x94231,a895),x94232),x94235)))) % 112.26/112.10 [9428]~P25(x94284,x94282,x94285,f232(f906(x94284,a895)),f232(f906(x94282,a895)))+E(f317(f317(f35(x94281,f906(x94282,a895)),x94283),f317(f317(f10(f906(x94284,a895),f906(x94282,a895),x94281),f300(x94284,x94282,x94285)),x94286)),f317(f300(x94284,x94282,x94285),f317(f317(f35(x94281,f906(x94284,a895)),x94283),x94286))) % 112.26/112.10 [9626]P1(f317(f317(f319(f905(f900(x96261),f900(x96261))),f317(f317(f242(f900(x96261),f900(x96261)),f317(f317(f141(x96261),x96262),x96263)),f317(f317(f141(x96261),x96264),x96265))),f137(x96261,x96266)))+~P1(f317(f317(f319(f905(x96261,x96261)),f317(f317(f242(x96261,x96261),x96262),x96264)),x96266)) % 112.26/112.10 [10083]E(f317(f317(f242(x100831,x100832),f575(x100833,x100834,x100835,x100832,x100831,x100836)),f578(x100833,x100834,x100835,x100832,x100831,x100836)),x100836)+P1(f317(f317(f319(x100835),x100834),f317(f317(f247(x100831,x100832,f906(x100835,a895)),x100833),x100836))) % 112.26/112.10 [10089]E(f317(f317(f242(x100891,x100892),f576(x100893,x100894,x100892,x100891,x100895,x100896)),f577(x100893,x100894,x100892,x100891,x100895,x100896)),x100893)+~P1(f317(f317(f319(x100896),x100895),f317(f317(f247(x100891,x100892,f906(x100896,a895)),x100894),x100893))) % 112.26/112.10 [10252]P1(f317(f317(f319(x102521),x102522),f317(f317(x102523,f576(x102524,x102523,x102525,x102526,x102522,x102521)),f577(x102524,x102523,x102525,x102526,x102522,x102521))))+~P1(f317(f317(f319(x102521),x102522),f317(f317(f247(x102526,x102525,f906(x102521,a895)),x102523),x102524))) % 112.26/112.10 [10281]~P1(f317(f317(f319(x102811),x102812),f317(f317(x102815,f575(x102815,x102812,x102811,x102814,x102813,x102816)),f578(x102815,x102812,x102811,x102814,x102813,x102816))))+P1(f317(f317(f319(x102811),x102812),f317(f317(f247(x102813,x102814,f906(x102811,a895)),x102815),x102816))) % 112.26/112.10 [8557]E(x85571,x85572)+E(f317(f317(f149(x85573,f317(f317(f149(x85573,x85574),x85571),x85575)),x85572),x85576),f317(f317(f149(x85573,f317(f317(f149(x85573,x85574),x85572),x85576)),x85571),x85575)) % 112.26/112.10 [9687]~P1(f317(f317(f319(x96873),x96876),x96875))+E(f317(f317(f299(x96871),x96872),f317(f300(x96873,x96871,x96874),f317(f317(f3(f906(x96873,a895)),x96875),f317(f317(f299(x96873),x96876),f178(f906(x96873,a895)))))),f317(f300(x96873,x96871,f69(x96873,x96871,x96874,x96876,x96872)),x96875)) % 112.26/112.10 [9184]~P1(f317(f317(x91844,x91845),x91846))+P1(f317(f317(f317(f317(f91(f906(x91841,f906(x91842,a895))),x91843),x91844),x91845),x91846)) % 112.26/112.10 [9186]~P1(f317(f317(x91863,x91865),x91866))+P1(f317(f317(f317(f317(f91(f906(x91861,f906(x91862,a895))),x91863),x91864),x91865),x91866)) % 112.26/112.10 [9478]P1(f317(f317(x94781,x94782),x94783))+~P1(f317(f317(f317(f317(f92(f906(x94784,f906(x94785,a895))),x94786),x94781),x94782),x94783)) % 112.26/112.10 [9479]P1(f317(f317(x94791,x94792),x94793))+~P1(f317(f317(f317(f317(f92(f906(x94794,f906(x94795,a895))),x94791),x94796),x94792),x94793)) % 112.26/112.10 [9922]~P69(x99222)+E(f317(f317(f8(x99221,x99222),f317(f317(f9(x99221,f906(x99223,a895),x99222),f317(f317(f10(f906(x99223,x99222),f906(f906(x99223,a895),x99222),x99221),f8(x99223,x99222)),x99224)),x99225)),x99226),f317(f317(f8(f905(x99221,x99223),x99222),f317(f247(x99221,x99223,x99222),x99224)),f317(f317(f244(x99221,x99223),x99226),f317(f18(f906(x99223,a895),x99221),x99225)))) % 112.26/112.10 [9923]~P75(x99232)+E(f317(f317(f11(x99231,x99232),f317(f317(f9(x99231,f906(x99233,a895),x99232),f317(f317(f10(f906(x99233,x99232),f906(f906(x99233,a895),x99232),x99231),f11(x99233,x99232)),x99234)),x99235)),x99236),f317(f317(f11(f905(x99231,x99233),x99232),f317(f247(x99231,x99233,x99232),x99234)),f317(f317(f244(x99231,x99233),x99236),f317(f18(f906(x99233,a895),x99231),x99235)))) % 112.26/112.10 [10054]~P69(x100542)+E(f317(f317(f8(x100541,x100542),f317(f317(f9(x100541,f906(x100543,a895),x100542),f317(f317(f10(f906(x100543,x100542),f906(f906(x100543,a895),x100542),x100541),f8(x100543,x100542)),f317(f9(x100543,x100541,x100542),x100544))),x100545)),x100546),f317(f317(f8(x100543,x100542),f317(f317(f9(x100543,f906(x100541,a895),x100542),f317(f317(f10(f906(x100541,x100542),f906(f906(x100541,a895),x100542),x100543),f8(x100541,x100542)),x100544)),x100546)),x100545)) % 112.26/112.10 [10372]~P1(f317(f317(f319(f905(x103721,x103722)),f317(f317(f242(x103721,x103722),x103725),x103726)),f317(f317(f91(f906(f905(x103721,x103722),a895)),x103723),x103724)))+P1(f317(f317(f317(f317(f91(f906(x103721,f906(x103722,a895))),f317(f317(f9(x103721,f906(f905(x103721,x103722),a895),f906(x103722,a895)),f317(f317(f10(f906(x103722,f906(f906(f905(x103721,x103722),a895),a895)),f906(f906(f905(x103721,x103722),a895),f906(x103722,a895)),x103721),f9(x103722,f906(f905(x103721,x103722),a895),a895)),f317(f317(f10(f906(x103722,f905(x103721,x103722)),f906(x103722,f906(f906(f905(x103721,x103722),a895),a895)),x103721),f317(f10(f905(x103721,x103722),f906(f906(f905(x103721,x103722),a895),a895),x103722),f319(f905(x103721,x103722)))),f242(x103721,x103722)))),x103723)),f317(f317(f9(x103721,f906(f905(x103721,x103722),a895),f906(x103722,a895)),f317(f317(f10(f906(x103722,f906(f906(f905(x103721,x103722),a895),a895)),f906(f906(f905(x103721,x103722),a895),f906(x103722,a895)),x103721),f9(x103722,f906(f905(x103721,x103722),a895),a895)),f317(f317(f10(f906(x103722,f905(x103721,x103722)),f906(x103722,f906(f906(f905(x103721,x103722),a895),a895)),x103721),f317(f10(f905(x103721,x103722),f906(f906(f905(x103721,x103722),a895),a895),x103722),f319(f905(x103721,x103722)))),f242(x103721,x103722)))),x103724)),x103725),x103726)) % 112.26/112.10 [10373]~P1(f317(f317(f319(f905(x103731,x103732)),f317(f317(f242(x103731,x103732),x103735),x103736)),f317(f317(f92(f906(f905(x103731,x103732),a895)),x103733),x103734)))+P1(f317(f317(f317(f317(f92(f906(x103731,f906(x103732,a895))),f317(f317(f9(x103731,f906(f905(x103731,x103732),a895),f906(x103732,a895)),f317(f317(f10(f906(x103732,f906(f906(f905(x103731,x103732),a895),a895)),f906(f906(f905(x103731,x103732),a895),f906(x103732,a895)),x103731),f9(x103732,f906(f905(x103731,x103732),a895),a895)),f317(f317(f10(f906(x103732,f905(x103731,x103732)),f906(x103732,f906(f906(f905(x103731,x103732),a895),a895)),x103731),f317(f10(f905(x103731,x103732),f906(f906(f905(x103731,x103732),a895),a895),x103732),f319(f905(x103731,x103732)))),f242(x103731,x103732)))),x103733)),f317(f317(f9(x103731,f906(f905(x103731,x103732),a895),f906(x103732,a895)),f317(f317(f10(f906(x103732,f906(f906(f905(x103731,x103732),a895),a895)),f906(f906(f905(x103731,x103732),a895),f906(x103732,a895)),x103731),f9(x103732,f906(f905(x103731,x103732),a895),a895)),f317(f317(f10(f906(x103732,f905(x103731,x103732)),f906(x103732,f906(f906(f905(x103731,x103732),a895),a895)),x103731),f317(f10(f905(x103731,x103732),f906(f906(f905(x103731,x103732),a895),a895),x103732),f319(f905(x103731,x103732)))),f242(x103731,x103732)))),x103734)),x103735),x103736)) % 112.26/112.10 [10382]P1(f317(f317(f319(f905(x103821,x103822)),f317(f317(f242(x103821,x103822),x103823),x103824)),f317(f317(f91(f906(f905(x103821,x103822),a895)),x103825),x103826)))+~P1(f317(f317(f317(f317(f91(f906(x103821,f906(x103822,a895))),f317(f317(f9(x103821,f906(f905(x103821,x103822),a895),f906(x103822,a895)),f317(f317(f10(f906(x103822,f906(f906(f905(x103821,x103822),a895),a895)),f906(f906(f905(x103821,x103822),a895),f906(x103822,a895)),x103821),f9(x103822,f906(f905(x103821,x103822),a895),a895)),f317(f317(f10(f906(x103822,f905(x103821,x103822)),f906(x103822,f906(f906(f905(x103821,x103822),a895),a895)),x103821),f317(f10(f905(x103821,x103822),f906(f906(f905(x103821,x103822),a895),a895),x103822),f319(f905(x103821,x103822)))),f242(x103821,x103822)))),x103825)),f317(f317(f9(x103821,f906(f905(x103821,x103822),a895),f906(x103822,a895)),f317(f317(f10(f906(x103822,f906(f906(f905(x103821,x103822),a895),a895)),f906(f906(f905(x103821,x103822),a895),f906(x103822,a895)),x103821),f9(x103822,f906(f905(x103821,x103822),a895),a895)),f317(f317(f10(f906(x103822,f905(x103821,x103822)),f906(x103822,f906(f906(f905(x103821,x103822),a895),a895)),x103821),f317(f10(f905(x103821,x103822),f906(f906(f905(x103821,x103822),a895),a895),x103822),f319(f905(x103821,x103822)))),f242(x103821,x103822)))),x103826)),x103823),x103824)) % 112.26/112.10 [10383]P1(f317(f317(f319(f905(x103831,x103832)),f317(f317(f242(x103831,x103832),x103833),x103834)),f317(f317(f92(f906(f905(x103831,x103832),a895)),x103835),x103836)))+~P1(f317(f317(f317(f317(f92(f906(x103831,f906(x103832,a895))),f317(f317(f9(x103831,f906(f905(x103831,x103832),a895),f906(x103832,a895)),f317(f317(f10(f906(x103832,f906(f906(f905(x103831,x103832),a895),a895)),f906(f906(f905(x103831,x103832),a895),f906(x103832,a895)),x103831),f9(x103832,f906(f905(x103831,x103832),a895),a895)),f317(f317(f10(f906(x103832,f905(x103831,x103832)),f906(x103832,f906(f906(f905(x103831,x103832),a895),a895)),x103831),f317(f10(f905(x103831,x103832),f906(f906(f905(x103831,x103832),a895),a895),x103832),f319(f905(x103831,x103832)))),f242(x103831,x103832)))),x103835)),f317(f317(f9(x103831,f906(f905(x103831,x103832),a895),f906(x103832,a895)),f317(f317(f10(f906(x103832,f906(f906(f905(x103831,x103832),a895),a895)),f906(f906(f905(x103831,x103832),a895),f906(x103832,a895)),x103831),f9(x103832,f906(f905(x103831,x103832),a895),a895)),f317(f317(f10(f906(x103832,f905(x103831,x103832)),f906(x103832,f906(f906(f905(x103831,x103832),a895),a895)),x103831),f317(f10(f905(x103831,x103832),f906(f906(f905(x103831,x103832),a895),a895),x103832),f319(f905(x103831,x103832)))),f242(x103831,x103832)))),x103836)),x103833),x103834)) % 112.26/112.10 [10366]~P1(f317(f317(f319(f905(x103662,x103663)),f317(f317(f242(x103662,x103663),x103665),x103666)),f317(f317(f35(x103661,f906(f905(x103662,x103663),a895)),f232(f906(x103661,a895))),x103664)))+P1(f317(f317(f317(f317(f35(x103661,f906(x103662,f906(x103663,a895))),f232(f906(x103661,a895))),f317(f317(f10(f906(f905(x103662,x103663),a895),f906(x103662,f906(x103663,a895)),x103661),f317(f9(x103662,f906(f905(x103662,x103663),a895),f906(x103663,a895)),f317(f317(f10(f906(x103663,f906(f906(f905(x103662,x103663),a895),a895)),f906(f906(f905(x103662,x103663),a895),f906(x103663,a895)),x103662),f9(x103663,f906(f905(x103662,x103663),a895),a895)),f317(f317(f10(f906(x103663,f905(x103662,x103663)),f906(x103663,f906(f906(f905(x103662,x103663),a895),a895)),x103662),f317(f10(f905(x103662,x103663),f906(f906(f905(x103662,x103663),a895),a895),x103663),f319(f905(x103662,x103663)))),f242(x103662,x103663))))),x103664)),x103665),x103666)) % 112.26/112.10 [10367]~P1(f317(f317(f319(f905(x103672,x103673)),f317(f317(f242(x103672,x103673),x103675),x103676)),f317(f317(f36(x103671,f906(f905(x103672,x103673),a895)),f232(f906(x103671,a895))),x103674)))+P1(f317(f317(f317(f317(f36(x103671,f906(x103672,f906(x103673,a895))),f232(f906(x103671,a895))),f317(f317(f10(f906(f905(x103672,x103673),a895),f906(x103672,f906(x103673,a895)),x103671),f317(f9(x103672,f906(f905(x103672,x103673),a895),f906(x103673,a895)),f317(f317(f10(f906(x103673,f906(f906(f905(x103672,x103673),a895),a895)),f906(f906(f905(x103672,x103673),a895),f906(x103673,a895)),x103672),f9(x103673,f906(f905(x103672,x103673),a895),a895)),f317(f317(f10(f906(x103673,f905(x103672,x103673)),f906(x103673,f906(f906(f905(x103672,x103673),a895),a895)),x103672),f317(f10(f905(x103672,x103673),f906(f906(f905(x103672,x103673),a895),a895),x103673),f319(f905(x103672,x103673)))),f242(x103672,x103673))))),x103674)),x103675),x103676)) % 112.26/112.10 [10376]P1(f317(f317(f319(f905(x103761,x103762)),f317(f317(f242(x103761,x103762),x103763),x103764)),f317(f317(f35(x103765,f906(f905(x103761,x103762),a895)),f232(f906(x103765,a895))),x103766)))+~P1(f317(f317(f317(f317(f35(x103765,f906(x103761,f906(x103762,a895))),f232(f906(x103765,a895))),f317(f317(f10(f906(f905(x103761,x103762),a895),f906(x103761,f906(x103762,a895)),x103765),f317(f9(x103761,f906(f905(x103761,x103762),a895),f906(x103762,a895)),f317(f317(f10(f906(x103762,f906(f906(f905(x103761,x103762),a895),a895)),f906(f906(f905(x103761,x103762),a895),f906(x103762,a895)),x103761),f9(x103762,f906(f905(x103761,x103762),a895),a895)),f317(f317(f10(f906(x103762,f905(x103761,x103762)),f906(x103762,f906(f906(f905(x103761,x103762),a895),a895)),x103761),f317(f10(f905(x103761,x103762),f906(f906(f905(x103761,x103762),a895),a895),x103762),f319(f905(x103761,x103762)))),f242(x103761,x103762))))),x103766)),x103763),x103764)) % 112.26/112.10 [10377]P1(f317(f317(f319(f905(x103771,x103772)),f317(f317(f242(x103771,x103772),x103773),x103774)),f317(f317(f36(x103775,f906(f905(x103771,x103772),a895)),f232(f906(x103775,a895))),x103776)))+~P1(f317(f317(f317(f317(f36(x103775,f906(x103771,f906(x103772,a895))),f232(f906(x103775,a895))),f317(f317(f10(f906(f905(x103771,x103772),a895),f906(x103771,f906(x103772,a895)),x103775),f317(f9(x103771,f906(f905(x103771,x103772),a895),f906(x103772,a895)),f317(f317(f10(f906(x103772,f906(f906(f905(x103771,x103772),a895),a895)),f906(f906(f905(x103771,x103772),a895),f906(x103772,a895)),x103771),f9(x103772,f906(f905(x103771,x103772),a895),a895)),f317(f317(f10(f906(x103772,f905(x103771,x103772)),f906(x103772,f906(f906(f905(x103771,x103772),a895),a895)),x103771),f317(f10(f905(x103771,x103772),f906(f906(f905(x103771,x103772),a895),a895),x103772),f319(f905(x103771,x103772)))),f242(x103771,x103772))))),x103776)),x103773),x103774)) % 112.26/112.10 [7558]E(f317(x75581,f317(x75582,x75583)),f317(x75584,x75583))+~E(f317(f67(x75585,x75586,x75587,x75581),x75582),x75584) % 112.26/112.10 [9703]E(x97031,x97032)+E(f69(x97033,x97034,f69(x97033,x97034,x97035,x97031,x97036),x97032,x97037),f69(x97033,x97034,f69(x97033,x97034,x97035,x97032,x97037),x97031,x97036)) % 112.26/112.10 [9794]~P22(x97943,x97944,x97941,x97945,x97946,x97947)+E(f317(f317(x97941,x97942),x97942),x97942) % 112.26/112.10 [6094]~E(f317(f317(f144(x60941,x60945),x60946),x60942),f317(f317(f144(x60943,x60945),x60947),x60944))+E(f317(f179(f900(x60941)),x60942),f317(f179(f900(x60943)),x60944)) % 112.26/112.10 [8588]E(f317(x85881,f317(x85882,x85883)),f317(x85884,x85883))+~E(f317(f67(x85885,x85886,x85887,x85881),x85882),f317(f67(x85886,x85886,x85887,f25(x85886)),x85884)) % 112.26/112.10 [8942]~P33(x89424,x89425,x89421,f317(f317(f141(x89424),x89422),x89426),f317(f317(f141(x89425),x89423),x89427))+P1(f317(f317(x89421,x89422),x89423)) % 112.26/112.10 [9318]P33(x93181,x93182,x93183,x93184,x93185)+~P33(x93181,x93182,x93183,f317(f317(f141(x93181),x93186),x93184),f317(f317(f141(x93182),x93187),x93185)) % 112.26/112.10 [9955]P1(f317(f317(x99551,x99552),f548(x99553,x99552,x99554,x99551)))+~P1(f317(f317(f243(x99555,x99556,x99557,x99551,x99554),x99552),x99553)) % 112.26/112.10 [9979]P1(f317(f317(x99791,f548(x99792,x99793,x99791,x99794)),x99792))+~P1(f317(f317(f243(x99795,x99796,x99797,x99794,x99791),x99793),x99792)) % 112.26/112.10 [9059]~P20(x90596,x90591,x90593,x90597)+E(f317(f67(x90591,x90591,x90592,f317(x90593,x90594)),f317(f67(x90591,x90591,x90592,f317(x90593,x90594)),x90595)),f317(f67(x90591,x90591,x90592,f317(x90593,x90594)),x90595)) % 112.26/112.10 [9431]~P33(x94313,x94312,x94314,f317(f317(f144(x94311,x94313),x94315),x94316),x94317)+P33(x94311,x94312,f317(f317(f10(x94313,f906(x94312,a895),x94311),x94314),x94315),x94316,x94317) % 112.26/112.10 [9454]P33(x94541,x94542,x94543,f317(f317(f144(x94544,x94541),x94545),x94546),x94547)+~P33(x94544,x94542,f317(f317(f10(x94541,f906(x94542,a895),x94544),x94543),x94545),x94546,x94547) % 112.26/112.10 [9058]~P1(f317(f317(f319(x90581),x90582),f317(f317(x90585,x90586),x90587)))+P1(f317(f317(f319(x90581),x90582),f317(f317(f247(x90583,x90584,f906(x90581,a895)),x90585),f317(f317(f242(x90583,x90584),x90586),x90587)))) % 112.26/112.10 [9344]P1(f317(f317(f317(x93441,x93442),x93443),x93444))+~P1(f317(f317(f317(f247(x93445,x93446,f906(x93447,a895)),x93441),f317(f317(f242(x93445,x93446),x93442),x93443)),x93444)) % 112.26/112.10 [9493]P1(f317(f317(f319(x94931),f317(f317(x94932,x94933),x94934)),f317(f300(f905(x94935,x94936),x94931,f317(f247(x94935,x94936,x94931),x94932)),x94937)))+~P1(f317(f317(f319(f905(x94935,x94936)),f317(f317(f242(x94935,x94936),x94933),x94934)),x94937)) % 112.26/112.10 [9841]P1(f317(f317(f319(f905(f900(x98411),f900(x98411))),f317(f317(f242(f900(x98411),f900(x98411)),f317(f317(f124(x98411),x98412),f317(f317(f141(x98411),x98413),x98414))),f317(f317(f124(x98411),x98412),f317(f317(f141(x98411),x98415),x98416)))),f137(x98411,x98417)))+~P1(f317(f317(f319(f905(x98411,x98411)),f317(f317(f242(x98411,x98411),x98413),x98415)),x98417)) % 112.26/112.10 [9907]~P33(x99071,x99073,x99074,x99076,f317(f317(f144(x99072,x99073),x99075),x99077))+P33(x99071,x99072,f317(f317(f9(x99071,f906(x99072,x99073),f906(x99072,a895)),f317(f317(f10(f906(x99073,a895),f906(f906(x99072,x99073),f906(x99072,a895)),x99071),f10(x99073,a895,x99072)),x99074)),x99075),x99076,x99077) % 112.26/112.10 [9983]P33(x99831,x99832,x99833,x99834,f317(f317(f144(x99835,x99832),x99836),x99837))+~P33(x99831,x99835,f317(f317(f9(x99831,f906(x99835,x99832),f906(x99835,a895)),f317(f317(f10(f906(x99832,a895),f906(f906(x99835,x99832),f906(x99835,a895)),x99831),f10(x99832,a895,x99835)),x99833)),x99836),x99834,x99837) % 112.26/112.10 [10295]P1(f317(f317(f319(x102951),f483(x102952,x102953,x102954,x102955,x102956,x102957,x102951)),x102955))+P1(f317(f317(f317(f317(f35(x102951,f906(x102957,f906(x102956,a895))),x102955),x102954),x102953),x102952)) % 112.26/112.10 [10296]P1(f317(f317(f319(x102961),f766(x102962,x102963,x102964,x102965,x102966,x102967,x102961)),x102967))+P1(f317(f317(f317(f317(f35(x102961,f906(x102963,f906(x102962,a895))),x102967),x102966),x102965),x102964)) % 112.26/112.10 [10297]P1(f317(f317(f319(x102971),f484(x102972,x102973,x102974,x102975,x102976,x102977,x102971)),x102975))+~P1(f317(f317(f317(f317(f36(x102971,f906(x102977,f906(x102976,a895))),x102975),x102974),x102973),x102972)) % 112.26/112.10 [10298]P1(f317(f317(f319(x102981),f767(x102982,x102983,x102984,x102985,x102986,x102987,x102981)),x102985))+~P1(f317(f317(f317(f317(f36(x102981,f906(x102987,f906(x102986,a895))),x102985),x102984),x102983),x102982)) % 112.26/112.10 [10331]P1(f317(f317(f317(x103311,f484(x103312,x103313,x103311,x103314,x103315,x103316,x103317)),x103313),x103312))+~P1(f317(f317(f317(f317(f36(x103317,f906(x103316,f906(x103315,a895))),x103314),x103311),x103313),x103312)) % 112.26/112.10 [10332]P1(f317(f317(f317(x103321,f767(x103322,x103323,x103321,x103324,x103325,x103326,x103327)),x103323),x103322))+~P1(f317(f317(f317(f317(f36(x103327,f906(x103326,f906(x103325,a895))),x103324),x103321),x103323),x103322)) % 112.26/112.10 [10347]~P1(f317(f317(f317(x103475,f483(x103477,x103476,x103475,x103474,x103473,x103472,x103471)),x103476),x103477))+P1(f317(f317(f317(f317(f35(x103471,f906(x103472,f906(x103473,a895))),x103474),x103475),x103476),x103477)) % 112.26/112.10 [10348]~P1(f317(f317(f317(x103485,f766(x103483,x103482,x103487,x103486,x103485,x103484,x103481)),x103486),x103487))+P1(f317(f317(f317(f317(f35(x103481,f906(x103482,f906(x103483,a895))),x103484),x103485),x103486),x103487)) % 112.26/112.10 [10365]~P1(f317(f317(f319(f905(x103651,x103653)),f317(f317(f242(x103651,x103653),x103656),x103657)),f317(f317(f279(x103651,x103652,x103653),x103654),x103655)))+P1(f317(f317(f243(x103651,x103652,x103653,f317(f317(f9(x103651,f906(f905(x103651,x103652),a895),f906(x103652,a895)),f317(f317(f10(f906(x103652,f906(f906(f905(x103651,x103652),a895),a895)),f906(f906(f905(x103651,x103652),a895),f906(x103652,a895)),x103651),f9(x103652,f906(f905(x103651,x103652),a895),a895)),f317(f317(f10(f906(x103652,f905(x103651,x103652)),f906(x103652,f906(f906(f905(x103651,x103652),a895),a895)),x103651),f317(f10(f905(x103651,x103652),f906(f906(f905(x103651,x103652),a895),a895),x103652),f319(f905(x103651,x103652)))),f242(x103651,x103652)))),x103654),f317(f317(f9(x103652,f906(f905(x103652,x103653),a895),f906(x103653,a895)),f317(f317(f10(f906(x103653,f906(f906(f905(x103652,x103653),a895),a895)),f906(f906(f905(x103652,x103653),a895),f906(x103653,a895)),x103652),f9(x103653,f906(f905(x103652,x103653),a895),a895)),f317(f317(f10(f906(x103653,f905(x103652,x103653)),f906(x103653,f906(f906(f905(x103652,x103653),a895),a895)),x103652),f317(f10(f905(x103652,x103653),f906(f906(f905(x103652,x103653),a895),a895),x103653),f319(f905(x103652,x103653)))),f242(x103652,x103653)))),x103655)),x103656),x103657)) % 112.26/112.10 [10375]P1(f317(f317(f319(f905(x103751,x103752)),f317(f317(f242(x103751,x103752),x103753),x103754)),f317(f317(f279(x103751,x103755,x103752),x103756),x103757)))+~P1(f317(f317(f243(x103751,x103755,x103752,f317(f317(f9(x103751,f906(f905(x103751,x103755),a895),f906(x103755,a895)),f317(f317(f10(f906(x103755,f906(f906(f905(x103751,x103755),a895),a895)),f906(f906(f905(x103751,x103755),a895),f906(x103755,a895)),x103751),f9(x103755,f906(f905(x103751,x103755),a895),a895)),f317(f317(f10(f906(x103755,f905(x103751,x103755)),f906(x103755,f906(f906(f905(x103751,x103755),a895),a895)),x103751),f317(f10(f905(x103751,x103755),f906(f906(f905(x103751,x103755),a895),a895),x103755),f319(f905(x103751,x103755)))),f242(x103751,x103755)))),x103756),f317(f317(f9(x103755,f906(f905(x103755,x103752),a895),f906(x103752,a895)),f317(f317(f10(f906(x103752,f906(f906(f905(x103755,x103752),a895),a895)),f906(f906(f905(x103755,x103752),a895),f906(x103752,a895)),x103755),f9(x103752,f906(f905(x103755,x103752),a895),a895)),f317(f317(f10(f906(x103752,f905(x103755,x103752)),f906(x103752,f906(f906(f905(x103755,x103752),a895),a895)),x103755),f317(f10(f905(x103755,x103752),f906(f906(f905(x103755,x103752),a895),a895),x103752),f319(f905(x103755,x103752)))),f242(x103755,x103752)))),x103757)),x103753),x103754)) % 112.26/112.10 [10307]~P146(x103072)+E(f317(f317(f8(x103071,x103072),f317(f317(f9(x103071,f906(x103073,a895),x103072),f317(f317(f10(f906(x103073,x103072),f906(f906(x103073,a895),x103072),x103071),f8(x103073,x103072)),f317(f317(f9(x103071,f906(x103073,x103072),f906(x103073,x103072)),f317(f317(f10(f906(x103072,x103072),f906(f906(x103073,x103072),f906(x103073,x103072)),x103071),f10(x103072,x103072,x103073)),f317(f317(f10(x103072,f906(x103072,x103072),x103071),f75(x103072)),x103074))),x103075))),x103076)),x103077),f317(f317(f75(x103072),f317(f317(f8(x103071,x103072),x103074),x103077)),f317(f317(f8(x103073,x103072),x103075),x103076))) % 112.26/112.10 [9377]~P19(x93777,x93771,x93773,x93778)+E(f317(f67(x93771,x93771,x93772,f317(x93773,x93774)),f317(f67(x93771,x93771,x93772,f317(x93773,x93775)),x93776)),f317(f67(x93771,x93771,x93772,f317(x93773,x93775)),f317(f67(x93771,x93771,x93772,f317(x93773,x93774)),x93776))) % 112.26/112.10 [10370]E(f317(f317(f242(x103701,x103702),f317(x103703,f541(x103704,x103705,x103703,x103706,x103707,x103708,x103702,x103701))),f317(x103705,f542(x103704,x103705,x103703,x103706,x103707,x103708,x103702,x103701))),x103708)+~P1(f317(f317(f319(f905(x103701,x103702)),x103708),f317(f300(f905(x103707,x103706),f905(x103701,x103702),f248(x103707,x103701,x103706,x103702,x103703,x103705)),x103704))) % 112.26/112.10 [10388]~P1(f317(f317(f319(f905(x103888,x103887)),x103886),f317(f300(f905(x103881,x103882),f905(x103888,x103887),f248(x103881,x103888,x103882,x103887,x103885,x103884)),x103883)))+P1(f317(f317(f319(f905(x103881,x103882)),f317(f317(f242(x103881,x103882),f541(x103883,x103884,x103885,x103882,x103881,x103886,x103887,x103888)),f542(x103883,x103884,x103885,x103882,x103881,x103886,x103887,x103888))),x103883)) % 112.26/112.10 [9831]P1(f317(f317(f319(f905(f905(x98311,x98312),f905(x98311,x98312))),f317(f317(f242(f905(x98311,x98312),f905(x98311,x98312)),f317(f317(f242(x98311,x98312),x98313),x98314)),f317(f317(f242(x98311,x98312),x98315),x98316))),f310(x98311,x98312,x98317,x98318)))+~P1(f317(f317(f319(f905(x98311,x98311)),f317(f317(f242(x98311,x98311),x98313),x98315)),x98317)) % 112.26/112.10 [10359]E(f317(f132(x103591,x103592,f317(f9(x103592,x103591,x103591),x103593),f317(x103594,x103595)),x103596),f317(x103594,f317(f132(x103597,x103592,f317(f9(x103592,x103597,x103597),x103598),x103595),x103596)))+P1(f317(f317(f319(x103592),f715(x103595,x103598,x103594,x103593,x103597,x103591,x103596,x103592)),f317(f162(x103592),x103596))) % 112.26/112.10 [10378]~E(f317(f67(x103781,x103781,x103787,f317(x103783,f715(x103785,x103788,x103784,x103783,x103787,x103781,x103786,x103782))),x103784),f317(f67(x103787,x103781,x103787,x103784),f317(x103788,f715(x103785,x103788,x103784,x103783,x103787,x103781,x103786,x103782))))+E(f317(f132(x103781,x103782,f317(f9(x103782,x103781,x103781),x103783),f317(x103784,x103785)),x103786),f317(x103784,f317(f132(x103787,x103782,f317(f9(x103782,x103787,x103787),x103788),x103785),x103786))) % 112.26/112.10 [8593]E(f317(x85931,f317(x85932,x85933)),f317(x85934,f317(x85935,x85933)))+~E(f317(f67(x85936,x85937,x85938,x85931),x85932),f317(f67(x85939,x85937,x85938,x85934),x85935)) % 112.26/112.10 [10216]P1(f317(f317(f319(f905(x102161,x102162)),f317(f317(f242(x102161,x102162),f317(x102163,x102164)),f317(x102165,x102166))),f317(f300(f905(x102167,x102168),f905(x102161,x102162),f248(x102167,x102161,x102168,x102162,x102163,x102165)),x102169)))+~P1(f317(f317(f319(f905(x102167,x102168)),f317(f317(f242(x102167,x102168),x102164),x102166)),x102169)) % 112.26/112.10 [8888]~E(f317(x88884,f317(x88885,x88886)),f317(x88889,f317(x888810,x888811)))+E(f317(f317(f67(x88881,x88882,x88883,x88884),x88885),x88886),f317(f317(f67(x88887,x88882,x88888,x88889),x888810),x888811)) % 112.26/112.10 [4653]~P108(x46531)+~P98(x46531)+E(f223(x46531),f91(x46531)) % 112.26/112.10 [4654]~P108(x46541)+~P104(x46541)+E(f228(x46541),f92(x46541)) % 112.26/112.10 [4899]~P112(x48991)+~P94(x48991)+E(f317(f70(x48991),f317(f94(x48991),a87)),f72(x48991)) % 112.26/112.10 [5192]E(x51921,f2(a1))+E(f76(a1,x51921),f317(f73(a1),f72(a1)))+P1(f317(f317(f225(a1),f2(a1)),x51921)) % 112.26/112.10 [5397]E(x53971,f2(a1))+E(f76(a1,x53971),f72(a1))+~P1(f317(f317(f225(a1),f2(a1)),x53971)) % 112.26/112.10 [7457]~P39(x74571)+P1(f317(f29(a1),x74571))+~P1(f317(f29(a899),f317(f300(a1,a899,a95),x74571))) % 112.26/112.10 [9793]E(x97931,f178(f906(f905(a899,a899),a895)))+~P1(f317(f29(f905(a899,a899)),x97931))+P1(f317(f317(f319(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),f178(f906(f905(a899,a899),a895))),x97931)),a28)) % 112.26/112.10 [9956]E(x99561,f2(a899))+E(x99561,f317(a102,f2(a899)))+~P1(f317(f317(f225(a899),x99561),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))) % 112.26/112.10 [10245]E(x102451,f2(a89))+E(f317(f317(f74(a1),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(a24,f317(f317(f31(a89),x102451),f317(f94(a89),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))))),f72(a1)),f317(a24,x102451))+E(f41(a89,x102451,f317(f94(a89),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f2(a89)) % 112.26/112.10 [10093]E(x100931,f2(a89))+~E(f41(a89,x100931,f317(f94(a89),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f2(a89))+E(f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(a24,f317(f317(f31(a89),x100931),f317(f94(a89),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f317(a24,x100931)) % 112.26/112.10 [4734]~P57(x47341,x47342)+P43(x47341,x47342)+~P44(a895) % 112.26/112.10 [4663]~P145(x46631)+P27(x46631,x46632)+~E(x46632,f2(x46631)) % 112.26/112.10 [4664]~P108(x46641)+P13(x46641,x46642)+~E(x46642,f103(x46641)) % 112.26/112.10 [4673]~P112(x46731)+~E(x46732,f2(x46731))+E(f76(x46731,x46732),f2(x46731)) % 112.26/112.10 [4674]~P90(x46741)+~E(x46742,f2(x46741))+E(f76(x46741,x46742),f2(x46741)) % 112.26/112.10 [4682]~P145(x46822)+~P27(x46822,x46821)+E(x46821,f2(x46822)) % 112.26/112.10 [4727]~P112(x47272)+~E(f76(x47272,x47271),f2(x47272))+E(x47271,f2(x47272)) % 112.26/112.10 [4741]~P2(x47412)+~P2(x47411)+P2(f906(x47411,x47412)) % 112.26/112.10 [4742]~P2(x47422)+~P2(x47421)+P2(f904(x47421,x47422)) % 112.26/112.10 [4743]~P2(x47432)+~P2(x47431)+P2(f905(x47431,x47432)) % 112.26/112.10 [4744]~P6(x47442)+~P6(x47441)+P6(f184(x47441,x47442)) % 112.26/112.10 [4745]~P60(x47452)+~P60(x47451)+P60(f906(x47451,x47452)) % 112.26/112.10 [4746]~P60(x47462)+~P60(x47461)+P60(f904(x47461,x47462)) % 112.26/112.10 [4747]~P60(x47472)+~P60(x47471)+P60(f905(x47471,x47472)) % 112.26/112.10 [4748]~P105(x47482)+~P105(x47481)+P105(f905(x47481,x47482)) % 112.26/112.10 [4871]~P108(x48711)+~P13(x48711,x48712)+P13(x48711,f142(x48711,x48712)) % 112.26/112.10 [5119]~P6(x51192)+~P6(x51191)+P6(f41(a1,x51191,x51192)) % 112.26/112.10 [4684]~P77(x46841)+~E(x46842,f2(x46841))+E(f317(f73(x46841),x46842),x46842) % 112.26/112.10 [4699]~P141(x46991)+~E(x46992,f2(a1))+E(f317(f93(x46991),x46992),f2(x46991)) % 112.26/112.10 [4700]~P92(x47001)+~E(x47002,f2(a1))+E(f317(f93(x47001),x47002),f2(x47001)) % 112.26/112.10 [4724]~P76(x47241)+~E(f2(x47241),x47242)+E(f317(f73(x47241),x47242),f2(x47241)) % 112.26/112.10 [4725]~P86(x47251)+~E(x47252,f2(x47251))+E(f317(f70(x47251),x47252),f2(x47251)) % 112.26/112.10 [4726]~P76(x47261)+~E(x47262,f2(x47261))+E(f317(f73(x47261),x47262),f2(x47261)) % 112.26/112.10 [4750]~P77(x47502)+E(x47501,f2(x47502))+~E(f317(f73(x47502),x47501),x47501) % 112.26/112.10 [4752]E(x47521,f317(a95,x47522))+~E(x47521,f2(a899))+~E(x47522,f317(f90(a1),x47521)) % 112.26/112.10 [4753]E(f317(a95,x47531),x47532)+~E(x47532,f2(a899))+~E(x47531,f317(f90(a1),x47532)) % 112.26/112.10 [4757]~P92(x47572)+E(x47571,f2(a1))+~E(f317(f93(x47572),x47571),f2(x47572)) % 112.26/112.10 [4761]~P86(x47612)+E(x47611,f2(x47612))+~E(f317(f70(x47612),x47611),f2(x47612)) % 112.26/112.10 [4762]~P76(x47622)+E(x47621,f2(x47622))+~E(f317(f73(x47622),x47621),f2(x47622)) % 112.26/112.10 [4763]~P76(x47631)+E(f2(x47631),x47632)+~E(f317(f73(x47631),x47632),f2(x47631)) % 112.26/112.10 [4946]~P108(x49461)+~P13(x49461,x49462)+P13(x49461,f317(f161(x49461),x49462)) % 112.26/112.10 [4973]~P1(x49732)+~P1(x49731)+P1(f317(f317(a315,x49731),x49732)) % 112.26/112.10 [5011]~E(f72(a899),f2(a899))+E(f317(f30(x50111),x50112),f2(a899))+~P1(f317(f29(x50111),x50112)) % 112.26/112.10 [5047]~P115(x50471)+~P146(x50471)+E(f317(f317(f234(x50471),f2(x50471)),f317(a102,x50472)),f2(x50471)) % 112.26/112.10 [5087]~P108(x50871)+P13(x50871,f129(x50871,x50872))+~P1(f317(f29(x50871),x50872)) % 112.26/112.10 [5088]~P108(x50881)+P13(x50881,f707(x50882,x50881))+~P1(f317(f29(x50881),x50882)) % 112.26/112.10 [5111]~P108(x51111)+E(f317(f162(x51111),f129(x51111,x51112)),x51112)+~P1(f317(f29(x51111),x51112)) % 112.26/112.10 [5112]~P108(x51121)+E(f317(f162(x51121),f707(x51122,x51121)),x51122)+~P1(f317(f29(x51121),x51122)) % 112.26/112.10 [5141]P1(x51411)+P1(x51412)+~P1(f317(f317(a316,x51412),x51411)) % 112.26/112.10 [5154]E(x51541,f178(f906(x51542,a895)))+~E(f317(f30(x51542),x51541),f2(a899))+~P1(f317(f29(x51542),x51541)) % 112.26/112.10 [5159]P1(x51591)+~P1(x51592)+~P1(f317(f317(a320,x51592),x51591)) % 112.26/112.10 [5210]~P74(x52101)+E(f317(f70(x52101),x52102),x52102)+P1(f317(f317(f225(x52101),x52102),f2(x52101))) % 112.26/112.10 [5270]~P60(x52702)+~P1(f317(f52(x52702),x52701))+P1(f317(x52701,f708(x52701,x52702))) % 112.26/112.10 [5271]~P60(x52712)+~P1(f317(f52(x52712),x52711))+P1(f317(x52711,f716(x52711,x52712))) % 112.26/112.10 [5312]E(x53121,f103(x53122))+P1(f317(f127(x53122),f104(x53122,x53121)))+~P1(f317(f127(x53122),x53121)) % 112.26/112.10 [5317]~P108(x53171)+~P1(f317(f29(x53171),x53172))+P1(f317(f127(x53171),f129(x53171,x53172))) % 112.26/112.10 [5318]~P108(x53181)+~P1(f317(f29(x53181),x53182))+P1(f317(f127(x53181),f707(x53182,x53181))) % 112.26/112.10 [5323]~P141(x53231)+E(f317(f90(x53231),f317(a95,x53232)),f317(f93(x53231),x53232))+P1(f317(f317(f225(a1),x53232),f2(a1))) % 112.26/112.10 [5344]P7(x53442,x53441)+E(f317(x53441,f494(x53441)),f317(x53441,f497(x53441)))+P1(f317(f317(x53441,f494(x53441)),f497(x53441))) % 112.26/112.10 [5357]E(f317(f90(a1),f339(x53571,x53572)),x53571)+P1(f317(x53572,f317(a95,x53571)))+~P1(f317(x53572,f2(a899))) % 112.26/112.10 [5370]~P60(x53701)+~P1(f317(x53702,f721(x53702,x53701)))+P1(f317(f53(x53701),x53702)) % 112.26/112.10 [5371]~P60(x53711)+~P1(f317(x53712,f731(x53712,x53711)))+P1(f317(f53(x53711),x53712)) % 112.26/112.10 [5407]~P112(x54071)+~E(f76(x54071,x54072),f317(f73(x54071),f72(x54071)))+P1(f317(f317(f225(x54071),x54072),f2(x54071))) % 112.26/112.10 [5482]~E(x54822,f2(a1))+E(f205(x54821,x54822),f317(f317(f242(a1,a1),f2(a1)),f72(a1)))+P1(f317(f317(f225(a1),x54822),f2(a1))) % 112.26/112.10 [5483]~E(x54831,f2(a1))+E(f205(x54831,x54832),f317(f317(f242(a1,a1),f2(a1)),f72(a1)))+P1(f317(f317(f225(a1),x54832),f2(a1))) % 112.26/112.10 [5536]E(f317(f90(a1),f339(x55361,x55362)),x55361)+P1(f317(x55362,f317(a95,x55361)))+P1(f317(f317(f225(a1),x55361),f2(a1))) % 112.26/112.10 [5604]~P112(x56041)+E(f76(x56041,x56042),f317(f73(x56041),f72(x56041)))+~P1(f317(f317(f225(x56041),x56042),f2(x56041))) % 112.26/112.10 [5605]~P86(x56051)+E(f317(f70(x56051),x56052),f317(f73(x56051),x56052))+~P1(f317(f317(f224(x56051),x56052),f2(x56051))) % 112.26/112.10 [5606]~P86(x56061)+E(f317(f70(x56061),x56062),f317(f73(x56061),x56062))+~P1(f317(f317(f225(x56061),x56062),f2(x56061))) % 112.26/112.10 [5607]~P74(x56071)+E(f317(f70(x56071),x56072),f317(f73(x56071),x56072))+~P1(f317(f317(f225(x56071),x56072),f2(x56071))) % 112.26/112.10 [5707]~P1(f317(x57071,f339(x57072,x57071)))+P1(f317(x57071,f317(a95,x57072)))+~P1(f317(x57071,f2(a899))) % 112.26/112.10 [5714]E(x57141,f2(a899))+E(f317(a102,f610(x57142,x57141)),x57141)+~P1(f317(f317(f225(a899),x57141),f317(a102,x57142))) % 112.26/112.10 [5718]P7(x57181,x57182)+~E(f317(x57182,f494(x57182)),f317(x57182,f497(x57182)))+~P1(f317(f317(x57182,f494(x57182)),f497(x57182))) % 112.26/112.10 [5736]~P108(x57361)+P13(x57361,x57362)+P1(f317(f317(f224(a899),f691(x57362,x57361)),f692(x57362,x57361))) % 112.26/112.10 [5737]~P108(x57371)+P13(x57371,x57372)+P1(f317(f317(f224(a899),f698(x57372,x57371)),f703(x57372,x57371))) % 112.26/112.10 [5823]~P86(x58231)+~E(x58232,f2(x58231))+P1(f317(f317(f224(x58231),f317(f70(x58231),x58232)),f2(x58231))) % 112.26/112.10 [5920]~P1(f317(x59201,f339(x59202,x59201)))+P1(f317(x59201,f317(a95,x59202)))+P1(f317(f317(f225(a1),x59202),f2(a1))) % 112.26/112.10 [5945]~P1(f317(x59451,f317(a95,x59452)))+P1(f317(x59451,f2(a899)))+~P1(f317(f317(f225(a1),x59452),f2(a1))) % 112.26/112.10 [6298]~P112(x62981)+~P1(f317(f317(f225(x62981),x62982),f2(x62981)))+P1(f317(f317(f225(x62981),f76(x62981,x62982)),f2(x62981))) % 112.26/112.10 [6418]~P112(x64181)+P1(f317(f317(f224(x64181),f317(f93(x64181),x64182)),f2(x64181)))+~P1(f317(f317(f224(a1),x64182),f2(a1))) % 112.26/112.10 [6419]~P112(x64191)+P1(f317(f317(f225(x64191),f317(f93(x64191),x64192)),f2(x64191)))+~P1(f317(f317(f225(a1),x64192),f2(a1))) % 112.26/112.10 [6428]~P86(x64282)+E(x64281,f2(x64282))+~P1(f317(f317(f224(x64282),f317(f70(x64282),x64281)),f2(x64282))) % 112.26/112.10 [6506]~P141(x65061)+~P1(f317(f317(f319(x65061),x65062),f100(x65061)))+P1(f317(f317(f319(x65061),f317(f73(x65061),x65062)),f100(x65061))) % 112.26/112.10 [6538]~P112(x65381)+~P1(f317(f317(f225(x65381),f76(x65381,x65382)),f2(x65381)))+P1(f317(f317(f225(x65381),x65382),f2(x65381))) % 112.26/112.10 [6716]~P112(x67162)+~P1(f317(f317(f224(x67162),f317(f93(x67162),x67161)),f2(x67162)))+P1(f317(f317(f224(a1),x67161),f2(a1))) % 112.26/112.10 [6717]~P112(x67172)+~P1(f317(f317(f225(x67172),f317(f93(x67172),x67171)),f2(x67172)))+P1(f317(f317(f225(a1),x67171),f2(a1))) % 112.26/112.10 [7231]~P77(x72311)+~P1(f317(f317(f224(x72311),x72312),f2(x72311)))+P1(f317(f317(f224(x72311),f317(f317(f74(x72311),x72312),x72312)),f2(x72311))) % 112.26/112.10 [7233]~P112(x72331)+~P1(f317(f317(f225(x72331),x72332),f2(x72331)))+P1(f317(f317(f225(x72331),f317(f317(f74(x72331),x72332),x72332)),f2(x72331))) % 112.26/112.10 [7234]~P77(x72341)+~P1(f317(f317(f225(x72341),x72342),f2(x72341)))+P1(f317(f317(f225(x72341),f317(f317(f74(x72341),x72342),x72342)),f2(x72341))) % 112.26/112.10 [7805]~P77(x78051)+~P1(f317(f317(f224(x78051),f317(f317(f74(x78051),x78052),x78052)),f2(x78051)))+P1(f317(f317(f224(x78051),x78052),f2(x78051))) % 112.26/112.10 [7806]~P112(x78061)+~P1(f317(f317(f225(x78061),f317(f317(f74(x78061),x78062),x78062)),f2(x78061)))+P1(f317(f317(f225(x78061),x78062),f2(x78061))) % 112.26/112.10 [7807]~P77(x78071)+~P1(f317(f317(f225(x78071),f317(f317(f74(x78071),x78072),x78072)),f2(x78071)))+P1(f317(f317(f225(x78071),x78072),f2(x78071))) % 112.26/112.10 [4798]~E(x47982,f2(a899))+~E(x47981,f2(a899))+E(f317(f317(f74(a899),x47981),x47982),f2(a899)) % 112.26/112.10 [4799]~E(x47992,f72(a899))+~E(x47991,f72(a899))+E(f317(f317(f75(a899),x47991),x47992),f72(a899)) % 112.26/112.10 [4800]~E(x48002,f72(a1))+~E(x48001,f72(a1))+E(f317(f317(f75(a1),x48001),x48002),f72(a1)) % 112.26/112.10 [4855]~P123(x48552)+E(x48551,f2(x48552))+E(f317(f317(f281(x48552),x48551),x48551),f72(x48552)) % 112.26/112.10 [4856]~P3(x48562)+E(x48561,f2(x48562))+E(f317(f317(f31(x48562),x48561),x48561),f72(x48562)) % 112.26/112.10 [4857]~P124(x48572)+E(x48571,f2(x48572))+E(f317(f317(f281(x48572),x48571),x48571),f72(x48572)) % 112.26/112.10 [4875]~P77(x48751)+~E(x48752,f2(x48751))+E(f317(f317(f74(x48751),x48752),x48752),f2(x48751)) % 112.26/112.10 [4878]~P142(x48781)+~E(x48782,f72(x48781))+E(f317(f317(f75(x48781),x48782),x48782),f72(x48781)) % 112.26/112.10 [4879]~P124(x48791)+~E(x48792,f2(x48791))+E(f317(f317(f281(x48791),x48792),x48792),f2(x48791)) % 112.26/112.10 [4924]~E(x49242,f2(a899))+~E(x49241,f2(a899))+E(f317(f73(a1),f317(f90(a1),x49241)),f317(f90(a1),x49242)) % 112.26/112.10 [4943]E(x49431,f72(a899))+E(x49432,f2(a899))+~E(f317(f317(f75(a899),x49432),x49431),x49432) % 112.26/112.10 [4955]E(x49551,f2(a899))+E(x49552,f2(a899))+~E(f317(f317(f75(a899),x49552),x49551),f2(a899)) % 112.26/112.10 [4982]~E(x49822,f2(a899))+~E(x49821,f317(a102,f2(a899)))+E(f317(f317(f74(a899),x49821),x49822),f317(a102,f2(a899))) % 112.26/112.10 [4983]~E(x49831,f2(a899))+~E(x49832,f317(a102,f2(a899)))+E(f317(f317(f74(a899),x49831),x49832),f317(a102,f2(a899))) % 112.26/112.10 [4990]E(x49901,f72(a1))+E(x49902,f317(f94(a1),a87))+~E(f317(f317(f75(a1),x49901),x49902),f72(a1)) % 112.26/112.10 [4991]E(x49911,f72(a1))+E(x49912,f317(f94(a1),a87))+~E(f317(f317(f75(a1),x49912),x49911),f72(a1)) % 112.26/112.10 [4992]E(x49921,f72(a1))+E(x49921,f317(f94(a1),a87))+~E(f317(f317(f75(a1),x49922),x49921),f72(a1)) % 112.26/112.10 [4994]E(x49941,f72(a1))+E(x49941,f317(f94(a1),a87))+~E(f317(f317(f75(a1),x49941),x49942),f72(a1)) % 112.26/112.10 [5019]~P77(x50192)+E(x50191,f2(x50192))+~E(f317(f317(f74(x50192),x50191),x50191),f2(x50192)) % 112.26/112.10 [5025]~E(x50251,f317(f94(a1),a87))+~E(x50252,f317(f94(a1),a87))+E(f317(f317(f75(a1),x50251),x50252),f72(a1)) % 112.26/112.10 [5036]E(x50361,f2(a899))+E(x50362,f2(a899))+~E(f317(f317(f74(a899),x50362),x50361),f317(a102,f2(a899))) % 112.26/112.10 [5046]~P61(x50461)+~P94(x50461)+E(f317(f317(f281(x50461),x50462),f317(f94(x50461),a77)),f2(x50461)) % 112.26/112.10 [5053]~P142(x50531)+~E(x50532,f317(f73(x50531),f72(x50531)))+E(f317(f317(f75(x50531),x50532),x50532),f72(x50531)) % 112.26/112.10 [5058]~P6(x50582)+~P6(x50581)+P6(f317(f317(f74(a1),x50581),x50582)) % 112.26/112.10 [5059]~P6(x50592)+~P6(x50591)+P6(f317(f317(f75(a1),x50591),x50592)) % 112.26/112.10 [5060]~P6(x50602)+~P6(x50601)+P6(f317(f317(f31(a1),x50601),x50602)) % 112.26/112.10 [5062]~E(x50622,f2(a1))+E(x50621,f2(a1))+E(f42(x50621,x50622),f317(f317(f242(a1,a1),f2(a1)),x50621)) % 112.26/112.10 [5085]~E(x50852,f317(a102,f2(a899)))+~E(x50851,f317(a102,f2(a899)))+E(f317(f317(f75(a899),x50851),x50852),f317(a102,f2(a899))) % 112.26/112.10 [5102]E(x51021,f2(a899))+E(x51022,f317(a102,f2(a899)))+~E(f317(f317(f234(a899),x51022),x51021),f317(a102,f2(a899))) % 112.26/112.10 [5103]E(x51031,f2(a899))+E(x51031,f317(a102,f2(a899)))+~E(f317(f317(f74(a899),x51032),x51031),f317(a102,f2(a899))) % 112.26/112.10 [5104]E(x51041,f2(a899))+E(x51041,f317(a102,f2(a899)))+~E(f317(f317(f74(a899),x51041),x51042),f317(a102,f2(a899))) % 112.26/112.10 [5113]~P61(x51131)+~P94(x51131)+E(f317(f317(f281(x51131),x51132),f317(f94(x51131),a87)),f317(f73(x51131),x51132)) % 112.26/112.10 [5133]E(x51331,f317(a95,x51332))+~E(x51331,f2(a899))+P1(f317(f317(f224(a1),f2(a1)),x51332)) % 112.26/112.10 [5134]E(f317(a95,x51341),x51342)+~E(x51342,f2(a899))+P1(f317(f317(f224(a1),f2(a1)),x51341)) % 112.26/112.10 [5150]E(x51501,f317(a102,f2(a899)))+E(x51502,f317(a102,f2(a899)))+~E(f317(f317(f74(a899),x51501),x51502),f317(a102,f2(a899))) % 112.26/112.10 [5161]~E(x51611,f317(a95,x51612))+E(x51611,f2(a899))+P1(f317(f317(f224(a1),f2(a1)),x51612)) % 112.26/112.10 [5162]~E(f317(a95,x51622),x51621)+E(x51621,f2(a899))+P1(f317(f317(f224(a1),f2(a1)),x51622)) % 112.26/112.10 [5185]~P108(x51851)+E(f317(f58(x51851,f223(x51851)),x51852),f16(x51851,x51852))+~P1(f317(f29(x51851),x51852)) % 112.26/112.10 [5186]~P108(x51861)+E(f317(f58(x51861,f228(x51861)),x51862),f17(x51861,x51862))+~P1(f317(f29(x51861),x51862)) % 112.26/112.10 [5187]~P99(x51871)+E(f317(f58(x51871,f91(x51871)),x51872),f12(x51871,x51872))+~P1(f317(f29(x51871),x51872)) % 112.26/112.10 [5188]~P99(x51881)+E(f317(f58(x51881,f92(x51881)),x51882),f13(x51881,x51882))+~P1(f317(f29(x51881),x51882)) % 112.26/112.10 [5265]E(x52651,x52652)+~E(f317(f317(f3(a899),x52652),x52651),f2(a899))+~E(f317(f317(f3(a899),x52651),x52652),f2(a899)) % 112.26/112.10 [5282]P6(x52821)+~P39(x52822)+~P1(f317(f317(f319(a1),x52821),x52822)) % 112.26/112.10 [5313]~P112(x53131)+~E(f76(x53131,x53132),f72(x53131))+P1(f317(f317(f225(x53131),f2(x53131)),x53132)) % 112.26/112.10 [5324]~P94(x53241)+E(f317(f90(x53241),f317(f94(a899),x53242)),f317(f94(x53241),x53242))+P1(f317(a183,f317(f94(a1),x53242))) % 112.26/112.10 [5329]~P43(x53291,x53292)+P44(a895)+P1(f317(f29(f905(x53291,x53291)),x53292)) % 112.26/112.10 [5399]~P108(x53991)+E(f317(f58(x53991,f223(x53991)),x53992),f14(x53991,f223(x53991),x53992))+~P1(f317(f29(x53991),x53992)) % 112.26/112.10 [5400]~P108(x54001)+E(f317(f58(x54001,f228(x54001)),x54002),f15(x54001,f228(x54001),x54002))+~P1(f317(f29(x54001),x54002)) % 112.26/112.10 [5414]E(x54141,x54142)+P1(f317(f317(f225(a899),x54142),x54141))+P1(f317(f317(f225(a899),x54141),x54142)) % 112.26/112.10 [5415]E(x54151,x54152)+P1(f317(f317(f225(a1),x54152),x54151))+P1(f317(f317(f225(a1),x54151),x54152)) % 112.26/112.10 [5469]~P94(x54691)+E(f317(f90(x54691),f317(f94(a899),x54692)),f2(x54691))+~P1(f317(a183,f317(f94(a1),x54692))) % 112.26/112.10 [5472]~E(x54722,f317(a95,x54721))+E(x54721,f317(f90(a1),x54722))+~P1(f317(f317(f224(a1),f2(a1)),x54721)) % 112.26/112.10 [5473]~E(f317(a95,x54731),x54732)+E(x54731,f317(f90(a1),x54732))+~P1(f317(f317(f224(a1),f2(a1)),x54731)) % 112.26/112.10 [5474]~E(x54741,f317(a95,x54742))+E(f317(f90(a1),x54741),x54742)+~P1(f317(f317(f224(a1),f2(a1)),x54742)) % 112.26/112.10 [5484]E(x54841,f317(a95,x54842))+~E(x54842,f317(f90(a1),x54841))+~P1(f317(f317(f224(a1),f2(a1)),x54842)) % 112.26/112.10 [5485]E(f317(a95,x54851),x54852)+~E(x54851,f317(f90(a1),x54852))+~P1(f317(f317(f224(a1),f2(a1)),x54851)) % 112.26/112.10 [5516]~P119(x55162)+E(x55161,f2(x55162))+~P1(f317(f317(f277(x55162),f2(x55162)),x55161)) % 112.26/112.10 [5527]~P86(x55272)+E(x55271,f2(x55272))+P1(f317(f317(f225(x55272),f2(x55272)),f317(f70(x55272),x55271))) % 112.26/112.10 [5591]~P112(x55911)+E(f76(x55911,x55912),f72(x55911))+~P1(f317(f317(f225(x55911),f2(x55911)),x55912)) % 112.26/112.10 [5597]~P94(x55971)+E(f317(f90(x55971),f317(f94(a899),x55972)),f2(x55971))+P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x55972))) % 112.26/112.10 [5608]~P86(x56081)+E(f317(f70(x56081),x56082),x56082)+~P1(f317(f317(f224(x56081),f2(x56081)),x56082)) % 112.26/112.10 [5609]~P86(x56091)+E(f317(f70(x56091),x56092),x56092)+~P1(f317(f317(f225(x56091),f2(x56091)),x56092)) % 112.26/112.10 [5618]E(x56181,f2(a899))+~E(f129(a899,f317(f292(a899,x56182),x56181)),f103(a899))+P1(f317(f317(f224(a899),x56181),x56182)) % 112.26/112.10 [5628]~P69(x56281)+E(f317(f317(f8(x56281,x56281),f7(x56281)),f317(f162(x56281),x56282)),f317(f155(x56281),x56282))+~P1(f317(f127(x56281),x56282)) % 112.26/112.10 [5631]~P141(x56311)+E(f317(f90(x56311),f317(a95,x56312)),f317(f93(x56311),x56312))+~P1(f317(f317(f224(a1),f2(a1)),x56312)) % 112.26/112.10 [5658]E(x56581,x56582)+P1(f317(f317(f225(a899),x56581),x56582))+~P1(f317(f317(f224(a899),x56581),x56582)) % 112.26/112.10 [5659]E(x56591,x56592)+P1(f317(f317(f225(a1),x56591),x56592))+~P1(f317(f317(f224(a1),x56591),x56592)) % 112.26/112.10 [5662]E(x56621,f72(a1))+~E(f317(f317(f75(a1),x56622),x56621),f72(a1))+~P1(f317(f317(f225(a1),f2(a1)),x56622)) % 112.26/112.10 [5663]E(x56631,f72(a1))+~E(f317(f317(f75(a1),x56631),x56632),f72(a1))+~P1(f317(f317(f225(a1),f2(a1)),x56631)) % 112.26/112.10 [5704]~P39(x57042)+P1(f317(f317(f224(a1),f2(a1)),x57041))+~P1(f317(f317(f319(a1),x57041),x57042)) % 112.26/112.10 [5723]~P57(x57231,x57232)+P36(x57231,x57232)+~P1(f317(f29(f905(x57231,x57231)),x57232)) % 112.26/112.10 [5725]~P57(x57251,x57252)+P43(x57251,x57252)+~P1(f317(f29(f905(x57251,x57251)),x57252)) % 112.26/112.10 [5767]E(x57671,f178(f906(x57672,a895)))+~P1(f317(f29(x57672),x57671))+P1(f317(f317(f225(a899),f2(a899)),f317(f30(x57672),x57671))) % 112.26/112.10 [5794]~P1(f317(x57941,x57942))+P1(f317(x57941,f2(a899)))+P1(f317(f317(f225(a899),f790(x57942,x57941)),x57942)) % 112.26/112.10 [5817]E(x58171,f2(a899))+~E(f317(f155(a899),x58172),f2(a899))+~P1(f317(f317(f319(a899),x58171),f317(f162(a899),x58172))) % 112.26/112.10 [5885]E(x58851,x58852)+~P1(f317(f317(f224(a899),x58852),x58851))+~P1(f317(f317(f224(a899),x58851),x58852)) % 112.26/112.10 [5886]E(x58861,x58862)+~P1(f317(f317(f224(a1),x58862),x58861))+~P1(f317(f317(f224(a1),x58861),x58862)) % 112.26/112.10 [5895]E(x58951,x58952)+~P1(f317(f317(f277(a899),x58952),x58951))+~P1(f317(f317(f277(a899),x58951),x58952)) % 112.26/112.10 [5897]E(f317(f30(x58971),x58972),f2(a899))+~P1(f317(f29(x58971),x58972))+P1(f317(f317(f319(x58971),f800(x58972,x58971)),x58972)) % 112.26/112.10 [5906]E(f46(x59061,x59062),f42(x59061,x59062))+P1(f317(f317(f224(a1),f2(a1)),x59061))+~P1(f317(f317(f225(a1),f2(a1)),x59062)) % 112.26/112.10 [5932]~P1(f317(x59321,f332(x59321)))+P1(f317(x59321,f317(a95,x59322)))+~P1(f317(f317(f224(a1),f2(a1)),x59322)) % 112.26/112.10 [5935]P1(f317(f317(f224(a899),x59351),f889(x59352)))+~P1(f317(f29(a899),x59352))+~P1(f317(f317(f319(a899),x59351),x59352)) % 112.26/112.10 [5936]P1(f317(f317(f225(a899),x59361),f891(x59362)))+~P1(f317(f29(a899),x59362))+~P1(f317(f317(f319(a899),x59361),x59362)) % 112.26/112.10 [5967]E(x59671,x59672)+~P1(f317(f317(f225(a899),x59671),f317(a102,x59672)))+P1(f317(f317(f225(a899),x59671),x59672)) % 112.26/112.10 [6004]E(x60041,f317(a102,x60042))+~P1(f317(f317(f224(a899),x60041),f317(a102,x60042)))+P1(f317(f317(f224(a899),x60041),x60042)) % 112.26/112.10 [6020]P1(f317(x60201,f338(x60201)))+~P1(f317(x60201,f317(a95,x60202)))+~P1(f317(f317(f224(a1),f2(a1)),x60202)) % 112.26/112.10 [6036]~P1(f317(x60361,x60362))+~P1(f317(f317(f224(a1),f2(a1)),x60362))+P1(f317(x60361,f317(f90(a1),f879(x60361)))) % 112.26/112.10 [6047]~P86(x60472)+~E(x60471,f2(x60472))+~P1(f317(f317(f225(x60472),f2(x60472)),f317(f70(x60472),x60471))) % 112.26/112.10 [6072]~P57(x60721,x60722)+P36(x60721,f317(f276(x60721,x60721),x60722))+~P1(f317(f29(f905(x60721,x60721)),x60722)) % 112.26/112.10 [6081]~P94(x60811)+E(f317(f90(x60811),f317(f94(a899),x60812)),f317(f94(x60811),x60812))+~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x60812))) % 112.26/112.10 [6084]E(f317(a102,x60841),x60842)+~P1(f317(f317(f225(a899),x60841),x60842))+P1(f317(f317(f225(a899),f317(a102,x60841)),x60842)) % 112.26/112.10 [6100]E(f317(f317(f31(a1),x61001),x61002),f2(a1))+~P1(f317(f317(f224(a1),x61001),f2(a1)))+~P1(f317(f317(f225(a1),x61002),x61001)) % 112.26/112.10 [6112]E(f41(a1,x61121,x61122),x61121)+~P1(f317(f317(f224(a1),x61121),f2(a1)))+~P1(f317(f317(f225(a1),x61122),x61121)) % 112.26/112.10 [6126]E(f43(x61261,x61262),f42(x61261,x61262))+~P1(f317(f317(f224(a1),f2(a1)),x61261))+~P1(f317(f317(f224(a1),f2(a1)),x61262)) % 112.26/112.10 [6136]E(f317(f317(f31(a1),x61361),x61362),f2(a1))+~P1(f317(f317(f224(a1),f2(a1)),x61361))+~P1(f317(f317(f225(a1),x61361),x61362)) % 112.26/112.10 [6147]E(f41(a899,f317(f94(a899),x61471),f317(f94(a899),x61472)),f317(f94(a899),x61471))+P1(f317(a183,f317(f94(a1),x61471)))+~P1(f317(a183,f317(f94(a1),x61472))) % 112.26/112.10 [6149]E(f41(a1,x61491,x61492),x61491)+~P1(f317(f317(f224(a1),f2(a1)),x61491))+~P1(f317(f317(f225(a1),x61491),x61492)) % 112.26/112.10 [6150]E(x61501,x61502)+~P1(f317(f317(f225(a899),x61501),f317(a102,x61502)))+~P1(f317(f317(f224(a899),x61502),x61501)) % 112.26/112.10 [6164]~P77(x61641)+~P1(f317(f317(f224(x61641),x61642),f2(x61641)))+P1(f317(f317(f224(x61641),x61642),f317(f73(x61641),x61642))) % 112.26/112.10 [6165]~P112(x61651)+~P1(f317(f317(f225(x61651),x61652),f2(x61651)))+P1(f317(f317(f225(x61651),x61652),f317(f73(x61651),x61652))) % 112.26/112.10 [6174]~P5(x61741)+E(f317(f317(f59(x61741,x61741,f91(x61741)),f178(x61741)),x61742),f32(x61741,x61742))+~P1(f317(f29(x61741),x61742)) % 112.26/112.10 [6175]~P5(x61751)+E(f317(f317(f59(x61751,x61751,f92(x61751)),f232(x61751)),x61752),f33(x61751,x61752))+~P1(f317(f29(x61751),x61752)) % 112.26/112.10 [6192]~P112(x61921)+~P1(f317(f317(f224(a1),f2(a1)),x61922))+P1(f317(f317(f224(x61921),f2(x61921)),f317(f93(x61921),x61922))) % 112.26/112.10 [6193]~P126(x61931)+~P1(f317(f317(f225(a899),f2(a899)),x61932))+P1(f317(f317(f225(x61931),f2(x61931)),f317(f90(x61931),x61932))) % 112.26/112.10 [6194]~P112(x61941)+~P1(f317(f317(f225(a1),f2(a1)),x61942))+P1(f317(f317(f225(x61941),f2(x61941)),f317(f93(x61941),x61942))) % 112.26/112.10 [6197]~P6(x61972)+~P6(x61971)+E(f317(f300(a899,a1,f90(a1)),f293(a899,f317(a95,x61971),f317(a95,x61972))),f293(a1,x61971,x61972)) % 112.26/112.10 [6203]P1(f317(x62031,x62032))+~P1(f317(f317(f224(a1),f2(a1)),x62032))+~P1(f317(x62031,f317(f90(a1),f880(x62031)))) % 112.26/112.10 [6235]E(f317(f317(f74(a899),f317(f94(a899),x62351)),f317(f94(a899),x62352)),f317(f94(a899),x62351))+P1(f317(f317(f225(a1),x62351),a77))+~P1(f317(f317(f225(a1),x62352),a77)) % 112.26/112.10 [6239]~P112(x62391)+P1(f317(f317(f225(x62391),f2(x62391)),f76(x62391,x62392)))+~P1(f317(f317(f225(x62391),f2(x62391)),x62392)) % 112.26/112.10 [6253]~P79(x62531)+~P1(f317(f317(f224(x62531),x62532),f2(x62531)))+P1(f317(f317(f224(x62531),f2(x62531)),f317(f73(x62531),x62532))) % 112.26/112.10 [6254]~P79(x62541)+~P1(f317(f317(f225(x62541),x62542),f2(x62541)))+P1(f317(f317(f225(x62541),f2(x62541)),f317(f73(x62541),x62542))) % 112.26/112.10 [6257]E(x62571,f232(f906(x62572,a895)))+~E(f317(f30(x62572),x62571),f317(f30(x62572),f232(f906(x62572,a895))))+~P1(f317(f29(x62572),f232(f906(x62572,a895)))) % 112.26/112.10 [6283]~P1(f317(f317(f225(a899),f2(a899)),x62832))+~P1(f317(f317(f277(a899),x62831),x62832))+P1(f317(f317(f224(a899),x62831),x62832)) % 112.26/112.10 [6290]~P77(x62901)+P1(f317(f317(f224(x62901),x62902),f2(x62901)))+~P1(f317(f317(f224(x62901),x62902),f317(f73(x62901),x62902))) % 112.26/112.10 [6291]~P112(x62911)+P1(f317(f317(f225(x62911),x62912),f2(x62911)))+~P1(f317(f317(f225(x62911),x62912),f317(f73(x62911),x62912))) % 112.26/112.10 [6300]~P94(x63001)+P1(f317(f317(f319(x63001),f317(f94(x63001),x63002)),f176(x63001)))+~P1(f317(f317(f224(a1),a77),x63002)) % 112.26/112.10 [6329]E(x63291,f2(a899))+~P1(f317(f317(f225(a899),x63291),f317(a102,x63292)))+P1(f317(f317(f225(a899),f610(x63292,x63291)),x63292)) % 112.26/112.10 [6332]~P149(x63322)+P150(x63321,f317(f317(f299(a894),f911(x63322)),f178(f906(a894,a895))))+P1(f317(f317(f319(a897),f852(x63321,x63322)),a907)) % 112.26/112.10 [6354]~P112(x63541)+~P1(f317(f317(f225(x63541),f2(x63541)),f76(x63541,x63542)))+P1(f317(f317(f225(x63541),f2(x63541)),x63542)) % 112.26/112.10 [6356]~E(f317(f94(a899),x63562),f317(f94(a899),x63561))+P1(f317(f317(f224(a1),f317(f94(a1),x63561)),f2(a1)))+~P1(f317(a183,f317(f94(a1),x63562))) % 112.26/112.10 [6386]E(f317(f241(a1,a1),f46(x63861,x63862)),f317(f317(f31(a1),x63861),x63862))+~P1(f317(f317(f225(a1),x63861),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x63862)) % 112.26/112.10 [6426]E(f317(f246(a1,a1),f46(x64261,x64262)),f41(a1,x64261,x64262))+~P1(f317(f317(f225(a1),x64261),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x64262)) % 112.26/112.10 [6429]~P112(x64292)+~P1(f317(f317(f224(x64292),f2(x64292)),f317(f93(x64292),x64291)))+P1(f317(f317(f224(a1),f2(a1)),x64291)) % 112.26/112.10 [6430]~P126(x64302)+~P1(f317(f317(f225(x64302),f2(x64302)),f317(f90(x64302),x64301)))+P1(f317(f317(f225(a899),f2(a899)),x64301)) % 112.26/112.10 [6431]~P112(x64312)+~P1(f317(f317(f225(x64312),f2(x64312)),f317(f93(x64312),x64311)))+P1(f317(f317(f225(a1),f2(a1)),x64311)) % 112.26/112.10 [6434]E(f317(f241(a1,a1),f43(x64341,x64342)),f317(f317(f31(a1),x64341),x64342))+~P1(f317(f317(f224(a1),f2(a1)),x64342))+~P1(f317(f317(f225(a1),f2(a1)),x64341)) % 112.26/112.10 [6448]E(f317(f246(a1,a1),f43(x64481,x64482)),f41(a1,x64481,x64482))+~P1(f317(f317(f224(a1),f2(a1)),x64482))+~P1(f317(f317(f225(a1),f2(a1)),x64481)) % 112.26/112.10 [6464]~P79(x64641)+P1(f317(f317(f224(x64641),x64642),f2(x64641)))+~P1(f317(f317(f224(x64641),f2(x64641)),f317(f73(x64641),x64642))) % 112.26/112.10 [6465]~P79(x64651)+P1(f317(f317(f225(x64651),x64652),f2(x64651)))+~P1(f317(f317(f225(x64651),f2(x64651)),f317(f73(x64651),x64652))) % 112.26/112.10 [6491]P1(f317(f45(x64911,x64912),f46(x64911,x64912)))+~P1(f317(f317(f225(a1),x64911),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x64912)) % 112.26/112.10 [6505]~P1(f317(f317(f225(a899),f2(a899)),x65051))+~P1(f317(f317(f277(a899),x65052),x65051))+~P1(f317(f317(f225(a899),x65051),x65052)) % 112.26/112.10 [6518]P1(f317(f45(x65181,x65182),f43(x65181,x65182)))+~P1(f317(f317(f224(a1),f2(a1)),x65181))+~P1(f317(f317(f225(a1),f2(a1)),x65182)) % 112.26/112.10 [6561]~P79(x65611)+P1(f317(f317(f224(x65611),f317(f73(x65611),x65612)),f2(x65611)))+~P1(f317(f317(f224(x65611),f2(x65611)),x65612)) % 112.26/112.10 [6562]~P79(x65621)+P1(f317(f317(f225(x65621),f317(f73(x65621),x65622)),f2(x65621)))+~P1(f317(f317(f225(x65621),f2(x65621)),x65622)) % 112.26/112.10 [6583]E(f317(f317(f3(a899),f317(a95,x65831)),f317(a95,x65832)),f317(a95,f184(x65831,x65832)))+~P1(f317(f317(f224(a1),f2(a1)),x65832))+~P1(f317(f317(f224(a1),f2(a1)),x65831)) % 112.26/112.10 [6601]P1(f317(f317(f224(a1),f2(a1)),f184(x66011,x66012)))+~P1(f317(f317(f224(a1),f2(a1)),x66012))+~P1(f317(f317(f224(a1),f2(a1)),x66011)) % 112.26/112.10 [6638]~P1(f317(x66381,x66382))+P1(f317(x66381,f2(a899)))+P1(f317(x66381,f317(f317(f74(a899),f790(x66382,x66381)),f72(a899)))) % 112.26/112.10 [6723]E(f317(f94(a899),x67231),f317(f94(a899),x67232))+~P1(f317(f317(f224(a1),f317(f94(a1),x67232)),f2(a1)))+~P1(f317(a183,f317(f94(a1),x67231))) % 112.26/112.10 [6737]~E(x67371,f2(a899))+~E(f669(x67372,x67371),f2(a899))+E(f317(f132(a899,a899,f74(a899),x67371),x67372),f2(a899)) % 112.26/112.10 [6761]~P1(f317(f29(x67611),f412(x67612,x67611)))+~P1(f317(f29(f906(x67611,a895)),x67612))+P1(f317(f29(x67611),f32(f906(x67611,a895),x67612))) % 112.26/112.10 [6767]E(x67671,x67672)+P1(f317(f317(f225(a1),x67671),x67672))+~P1(f317(f317(f225(a1),x67671),f317(f317(f74(a1),x67672),f72(a1)))) % 112.26/112.10 [6768]P1(f317(f317(f224(a899),f317(a95,x67681)),f317(a95,x67682)))+~P1(f317(f317(f224(a1),f2(a1)),x67682))+~P1(f317(f317(f224(a1),x67681),x67682)) % 112.26/112.10 [6769]P1(f317(f317(f224(a899),f317(a95,x67691)),f317(a95,x67692)))+~P1(f317(f317(f225(a1),f2(a1)),x67691))+~P1(f317(f317(f224(a1),x67691),x67692)) % 112.26/112.10 [6771]P1(f317(f317(f225(a899),f317(a95,x67711)),f317(a95,x67712)))+~P1(f317(f317(f224(a1),f2(a1)),x67711))+~P1(f317(f317(f225(a1),x67711),x67712)) % 112.26/112.10 [6772]P1(f317(f317(f225(a899),f317(a95,x67721)),f317(a95,x67722)))+~P1(f317(f317(f225(a1),f2(a1)),x67722))+~P1(f317(f317(f225(a1),x67721),x67722)) % 112.26/112.10 [6783]E(f41(a899,f317(a95,x67831),f317(a95,x67832)),f317(a95,f41(a1,x67831,x67832)))+~P1(f317(f317(f224(a1),f2(a1)),x67832))+~P1(f317(f317(f224(a1),f2(a1)),x67831)) % 112.26/112.10 [6807]~P79(x68071)+~P1(f317(f317(f224(x68071),f317(f73(x68071),x68072)),f2(x68071)))+P1(f317(f317(f224(x68071),f2(x68071)),x68072)) % 112.26/112.10 [6808]~P79(x68081)+~P1(f317(f317(f225(x68081),f317(f73(x68081),x68082)),f2(x68081)))+P1(f317(f317(f225(x68081),f2(x68081)),x68082)) % 112.26/112.10 [6823]~P1(f317(f317(f225(a1),a77),x68232))+~P1(f317(f317(f225(a1),x68231),x68232))+P1(f317(f317(f225(a899),f317(f94(a899),x68231)),f317(f94(a899),x68232))) % 112.26/112.10 [6917]~P1(f317(f317(f224(a1),f2(a1)),x69171))+P1(f317(f317(f225(a899),f317(a95,x69171)),x69172))+~P1(f317(f317(f225(a1),x69171),f317(f90(a1),x69172))) % 112.26/112.10 [6922]P1(f317(x69221,x69222))+~P1(f317(x69221,f317(a22,f798(x69221,x69222))))+~P1(f317(f317(f319(a899),x69222),f232(f906(a899,a895)))) % 112.26/112.10 [6933]E(x69331,f2(a1))+E(f41(a1,x69332,x69331),f2(a1))+E(f317(f317(f3(a1),f317(f73(a1),f317(f317(f31(a1),x69332),x69331))),f72(a1)),f317(f317(f31(a1),x69332),f317(f73(a1),x69331))) % 112.26/112.10 [6947]~P1(f317(f317(f224(a1),f2(a1)),x69471))+~P1(f317(f317(f225(a899),f317(a95,x69471)),x69472))+P1(f317(f317(f225(a1),x69471),f317(f90(a1),x69472))) % 112.26/112.10 [6983]~P1(f317(f317(f224(a899),f317(a95,x69831)),f317(a95,x69832)))+~P1(f317(f317(f224(a1),f2(a1)),x69832))+P1(f317(f317(f224(a1),x69831),x69832)) % 112.26/112.10 [6984]~P1(f317(f317(f224(a899),f317(a95,x69841)),f317(a95,x69842)))+~P1(f317(f317(f225(a1),f2(a1)),x69841))+P1(f317(f317(f224(a1),x69841),x69842)) % 112.26/112.10 [7016]P1(f317(f317(f224(a1),x70161),x70162))+~P1(f317(f317(f224(a899),f317(f94(a899),x70161)),f317(f94(a899),x70162)))+P1(f317(f317(f224(a1),x70161),a77)) % 112.26/112.10 [7042]P1(f317(f317(f224(a1),f2(a1)),f41(a1,x70421,x70422)))+~P1(f317(f317(f224(a1),f2(a1)),x70422))+~P1(f317(f317(f224(a1),f2(a1)),x70421)) % 112.26/112.10 [7140]P1(f317(f317(f225(a1),a77),x71401))+~P1(f317(f317(f225(a1),x71402),x71401))+~P1(f317(f317(f225(a899),f317(f94(a899),x71402)),f317(f94(a899),x71401))) % 112.26/112.10 [7194]E(f317(f317(f242(a1,a1),f317(f317(f31(a1),x71941),x71942)),f41(a1,x71941,x71942)),f46(x71941,x71942))+~P1(f317(f317(f225(a1),x71941),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x71942)) % 112.26/112.10 [7214]E(f317(f317(f242(a1,a1),f317(f317(f31(a1),x72141),x72142)),f41(a1,x72141,x72142)),f43(x72141,x72142))+~P1(f317(f317(f224(a1),f2(a1)),x72142))+~P1(f317(f317(f224(a1),f2(a1)),x72141)) % 112.26/112.10 [7268]~P97(x72682)+E(x72681,f103(x72682))+E(f317(f132(x72682,x72682,f75(x72682),f317(f131(x72682),x72681)),f317(f161(x72682),x72681)),f317(f58(x72682,f75(x72682)),f317(f162(x72682),x72681))) % 112.26/112.10 [7383]~E(x73831,f2(a899))+E(f317(f132(a899,a899,f74(a899),x73831),x73832),f2(a899))+P1(f317(f317(f319(a899),f669(x73832,x73831)),f317(f162(a899),x73832))) % 112.26/112.10 [7436]~P1(f317(f317(f224(a1),x74361),f2(a1)))+P1(f317(f317(f224(a1),f317(f317(f31(a1),x74361),x74362)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x74362)) % 112.26/112.10 [7437]~P1(f317(f317(f225(a1),x74372),f2(a1)))+P1(f317(f317(f224(a1),f317(f317(f31(a1),x74371),x74372)),f2(a1)))+~P1(f317(f317(f224(a1),f2(a1)),x74371)) % 112.26/112.10 [7438]~P1(f317(f317(f225(a1),x74382),f2(a1)))+P1(f317(f317(f225(a1),f317(f317(f31(a1),x74381),x74382)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x74381)) % 112.26/112.10 [7440]~P1(f317(f317(f225(a1),x74401),f2(a1)))+P1(f317(f317(f225(a1),f317(f317(f31(a1),x74401),x74402)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x74402)) % 112.26/112.10 [7447]P1(f317(f317(f319(f906(x74471,a895)),f412(x74472,x74471)),x74472))+~P1(f317(f29(f906(x74471,a895)),x74472))+P1(f317(f29(x74471),f32(f906(x74471,a895),x74472))) % 112.26/112.10 [7537]P24(x75371,x75371,x75372,f232(f906(x75371,a895)))+~E(f317(f300(x75371,x75371,x75372),f232(f906(x75371,a895))),f232(f906(x75371,a895)))+~P1(f317(f29(x75371),f232(f906(x75371,a895)))) % 112.26/112.10 [7659]~P24(x76591,x76591,x76592,f232(f906(x76591,a895)))+E(f317(f300(x76591,x76591,x76592),f232(f906(x76591,a895))),f232(f906(x76591,a895)))+~P1(f317(f29(x76591),f232(f906(x76591,a895)))) % 112.26/112.10 [7799]E(f317(f317(f31(a1),x77991),x77992),f317(f94(a1),a87))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x77991),x77992)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x77991)) % 112.26/112.10 [7856]~P1(f317(f317(f225(a1),x78562),f2(a1)))+~P1(f317(f317(f225(a1),f317(f317(f31(a1),x78561),x78562)),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x78561)) % 112.26/112.10 [7861]E(f317(f317(f74(a1),x78611),x78612),f41(a1,x78611,x78612))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x78611),x78612)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x78611)) % 112.26/112.10 [7864]P1(f317(f317(f225(a1),x78641),f2(a1)))+~P1(f317(f317(f225(a1),f317(f317(f31(a1),x78641),x78642)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x78642)) % 112.26/112.10 [7880]~P149(x78802)+P150(x78801,f317(f317(f299(a894),f911(x78802)),f178(f906(a894,a895))))+~P150(x78801,f317(f317(f299(a894),f317(a910,f852(x78801,x78802))),f178(f906(a894,a895)))) % 112.26/112.10 [8562]~P108(x85621)+P13(x85621,x85622)+~P1(f317(f317(f224(x85621),f317(f317(f154(x85621),x85622),f691(x85622,x85621))),f317(f317(f154(x85621),x85622),f692(x85622,x85621)))) % 112.26/112.10 [8563]~P108(x85631)+P13(x85631,x85632)+~P1(f317(f317(f224(x85631),f317(f317(f154(x85631),x85632),f698(x85632,x85631))),f317(f317(f154(x85631),x85632),f703(x85632,x85631)))) % 112.26/112.10 [5760]E(x57601,f2(a1))+~E(f41(a1,x57602,x57601),f2(a1))+E(f317(f317(f31(a1),x57602),f317(f73(a1),x57601)),f317(f73(a1),f317(f317(f31(a1),x57602),x57601))) % 112.26/112.10 [5778]~P39(x57782)+~P39(x57781)+P39(f317(f317(f91(f906(a1,a895)),x57781),x57782)) % 112.26/112.10 [5779]~P39(x57792)+~P39(x57791)+P39(f317(f317(f92(f906(a1,a895)),x57791),x57792)) % 112.26/112.10 [5797]~P61(x57971)+~P94(x57971)+E(f317(f73(x57971),f317(f317(f281(x57971),f72(x57971)),x57972)),f317(f317(f281(x57971),f317(f94(x57971),a87)),x57972)) % 112.26/112.10 [5924]E(x59241,f2(a1))+~E(f41(a1,x59242,x59241),f2(a1))+E(f317(f317(f31(a1),f317(f73(a1),x59242)),x59241),f317(f73(a1),f317(f317(f31(a1),x59242),x59241))) % 112.26/112.10 [6066]~P108(x60661)+P13(x60661,x60662)+P1(f317(f317(f225(a899),f692(x60662,x60661)),f317(f179(f900(x60661)),x60662))) % 112.26/112.10 [6067]~P108(x60671)+P13(x60671,x60672)+P1(f317(f317(f225(a899),f703(x60672,x60671)),f317(f179(f900(x60671)),x60672))) % 112.26/112.10 [6229]~P94(x62291)+~E(f317(f94(x62291),x62292),f2(x62291))+P27(x62291,f317(f94(x62291),f317(f317(f74(a1),x62292),f317(f73(a1),a77)))) % 112.26/112.10 [6230]~P94(x62301)+~E(f317(f94(x62301),x62302),f2(x62301))+P27(x62301,f317(f94(x62301),f317(f317(f74(a1),a77),f317(f73(a1),x62302)))) % 112.26/112.10 [6232]E(f317(a47,f43(f317(f73(a1),x62321),f317(f73(a1),x62322))),f42(x62321,x62322))+P1(f317(f317(f224(a1),f2(a1)),x62321))+P1(f317(f317(f225(a1),f2(a1)),x62322)) % 112.26/112.10 [6362]~E(x63622,f2(a899))+~E(x63621,f2(a899))+P1(f317(f317(f224(a1),f317(f90(a1),x63621)),f317(f73(a1),f317(f90(a1),x63622)))) % 112.26/112.10 [6392]E(f317(f317(f74(a899),f317(f94(a899),x63921)),f317(f94(a899),x63922)),f317(f94(a899),f317(f317(f74(a1),x63921),x63922)))+P1(f317(f317(f225(a1),x63921),a77))+P1(f317(f317(f225(a1),x63922),a77)) % 112.26/112.10 [6527]~P77(x65271)+~P1(f317(f317(f224(x65271),f2(x65271)),x65272))+P1(f317(f317(f224(x65271),f317(f73(x65271),x65272)),x65272)) % 112.26/112.10 [6528]~P77(x65281)+~P1(f317(f317(f225(x65281),f2(x65281)),x65282))+P1(f317(f317(f225(x65281),f317(f73(x65281),x65282)),x65282)) % 112.26/112.10 [6709]E(f317(f317(f3(a899),f317(a95,x67091)),f317(a95,x67092)),f317(a95,f317(f317(f3(a1),x67091),x67092)))+~P1(f317(f317(f224(a1),f2(a1)),x67092))+~P1(f317(f317(f224(a1),x67092),x67091)) % 112.26/112.10 [6745]E(f317(a95,f41(a1,f317(f94(a1),x67451),f317(f94(a1),x67452))),f41(a899,f317(f94(a899),x67451),f317(f94(a899),x67452)))+P1(f317(a183,f317(f94(a1),x67451)))+P1(f317(a183,f317(f94(a1),x67452))) % 112.26/112.10 [6762]~P77(x67621)+P1(f317(f317(f224(x67621),f2(x67621)),x67622))+~P1(f317(f317(f224(x67621),f317(f73(x67621),x67622)),x67622)) % 112.26/112.10 [6763]~P77(x67631)+P1(f317(f317(f225(x67631),f2(x67631)),x67632))+~P1(f317(f317(f225(x67631),f317(f73(x67631),x67632)),x67632)) % 112.26/112.10 [6775]~P77(x67751)+~P1(f317(f317(f224(x67751),f2(x67751)),x67752))+P1(f317(f317(f224(x67751),f2(x67751)),f317(f317(f74(x67751),x67752),x67752))) % 112.26/112.10 [6777]~P77(x67771)+~P1(f317(f317(f225(x67771),f2(x67771)),x67772))+P1(f317(f317(f225(x67771),f2(x67771)),f317(f317(f74(x67771),x67772),x67772))) % 112.26/112.10 [6788]E(f317(f317(f74(a899),f317(a95,x67881)),f317(a95,x67882)),f317(a95,f317(f317(f74(a1),x67881),x67882)))+~P1(f317(f317(f224(a1),f2(a1)),x67882))+~P1(f317(f317(f224(a1),f2(a1)),x67881)) % 112.26/112.10 [6800]E(x68001,f2(a899))+P1(f317(f317(f225(a899),f2(a899)),x68002))+~P1(f317(f317(f225(a899),f2(a899)),f317(f317(f234(a899),x68002),x68001))) % 112.26/112.10 [6835]~P94(x68351)+E(f317(f94(x68351),x68352),f2(x68351))+~P27(x68351,f317(f94(x68351),f317(f317(f74(a1),a77),f317(f73(a1),x68352)))) % 112.26/112.10 [6836]~P94(x68361)+E(f317(f94(x68361),x68362),f2(x68361))+~P27(x68361,f317(f94(x68361),f317(f317(f74(a1),x68362),f317(f73(a1),a77)))) % 112.26/112.10 [6895]~P1(f317(f29(x68951),x68952))+~P1(f317(f29(x68951),f232(f906(x68951,a895))))+P1(f317(f29(x68951),f317(f73(f906(x68951,a895)),x68952))) % 112.26/112.10 [6918]~P1(f317(f317(f225(a1),f2(a1)),x69182))+~P1(f317(f317(f224(a1),x69182),x69181))+P1(f317(f317(f225(a1),f2(a1)),f317(f317(f31(a1),x69181),x69182))) % 112.26/112.10 [6919]~P1(f317(f317(f224(a1),x69191),f2(a1)))+~P1(f317(f317(f225(a1),x69192),f2(a1)))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f31(a1),x69191),x69192))) % 112.26/112.10 [6957]~P1(f317(f317(f224(a1),f2(a1)),x69572))+~P1(f317(f317(f224(a1),f2(a1)),x69571))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),x69571),x69572))) % 112.26/112.10 [6958]~P1(f317(f317(f224(a1),f2(a1)),x69582))+~P1(f317(f317(f224(a1),f2(a1)),x69581))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f75(a1),x69581),x69582))) % 112.26/112.10 [6959]~P1(f317(f317(f224(a1),f2(a1)),x69592))+~P1(f317(f317(f224(a1),f2(a1)),x69591))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f31(a1),x69591),x69592))) % 112.26/112.10 [6960]~P1(f317(f317(f224(a1),f2(a1)),x69601))+~P1(f317(f317(f225(a1),f2(a1)),x69602))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f31(a1),x69601),x69602))) % 112.26/112.10 [6961]~P1(f317(f317(f225(a899),f2(a899)),x69612))+~P1(f317(f317(f225(a899),f2(a899)),x69611))+P1(f317(f317(f225(a899),f2(a899)),f317(f317(f75(a899),x69611),x69612))) % 112.26/112.10 [7029]E(x70291,f2(a1))+E(f41(a1,x70292,x70291),f2(a1))+E(f317(f317(f3(a1),f317(f73(a1),f317(f317(f31(a1),x70292),x70291))),f72(a1)),f317(f317(f31(a1),f317(f73(a1),x70292)),x70291)) % 112.26/112.10 [7086]P1(f317(f317(f225(a899),f2(a899)),x70861))+P1(f317(f317(f225(a899),f2(a899)),x70862))+~P1(f317(f317(f225(a899),f2(a899)),f317(f317(f74(a899),x70862),x70861))) % 112.26/112.10 [7090]~P77(x70901)+P1(f317(f317(f224(x70901),f2(x70901)),x70902))+~P1(f317(f317(f224(x70901),f2(x70901)),f317(f317(f74(x70901),x70902),x70902))) % 112.26/112.10 [7091]~P77(x70911)+P1(f317(f317(f225(x70911),f2(x70911)),x70912))+~P1(f317(f317(f225(x70911),f2(x70911)),f317(f317(f74(x70911),x70912),x70912))) % 112.26/112.10 [7141]~P1(f317(f29(x71411),x71412))+P1(f317(f29(x71411),f232(f906(x71411,a895))))+~P1(f317(f29(x71411),f317(f73(f906(x71411,a895)),x71412))) % 112.26/112.10 [7206]P1(f317(f317(f224(a1),x72061),f2(a1)))+~P1(f317(f317(f225(a1),x72062),f2(a1)))+~P1(f317(f317(f224(a1),f2(a1)),f317(f317(f31(a1),x72061),x72062))) % 112.26/112.10 [7212]~P1(f317(f317(f225(a1),f2(a1)),x72121))+P1(f317(f317(f224(a1),x72121),x72122))+~P1(f317(f317(f225(a1),f2(a1)),f317(f317(f31(a1),x72122),x72121))) % 112.26/112.10 [7213]~P1(f317(f317(f224(a1),f2(a1)),x72132))+P1(f317(f317(f224(a1),x72131),x72132))+~P1(f317(f317(f225(a1),f2(a1)),f317(f317(f31(a1),x72132),x72131))) % 112.26/112.10 [7243]P1(f317(f317(f224(a1),f2(a1)),x72431))+~P1(f317(f317(f225(a1),f2(a1)),x72432))+~P1(f317(f317(f224(a1),f2(a1)),f317(f317(f31(a1),x72431),x72432))) % 112.26/112.10 [7244]P1(f317(f317(f225(a1),f2(a1)),x72441))+~P1(f317(f317(f224(a1),f2(a1)),x72442))+~P1(f317(f317(f225(a1),f2(a1)),f317(f317(f31(a1),x72442),x72441))) % 112.26/112.10 [7690]~P1(f317(f29(x76902),f232(f906(x76902,a895))))+~P1(f317(f29(x76901),f232(f906(x76901,a895))))+P1(f317(f29(f904(x76901,x76902)),f232(f906(f904(x76901,x76902),a895)))) % 112.26/112.10 [7691]~P1(f317(f29(x76912),f232(f906(x76912,a895))))+~P1(f317(f29(x76911),f232(f906(x76911,a895))))+P1(f317(f29(f905(x76911,x76912)),f232(f906(f905(x76911,x76912),a895)))) % 112.26/112.10 [7763]~P1(f317(f317(f225(a899),f317(a102,f2(a899))),x77631))+~P1(f317(f317(f225(a899),f317(a102,f2(a899))),x77632))+P1(f317(f317(f225(a899),x77631),f317(f317(f75(a899),x77632),x77631))) % 112.26/112.10 [7764]~P1(f317(f317(f225(a899),f317(a102,f2(a899))),x77641))+~P1(f317(f317(f225(a899),f317(a102,f2(a899))),x77642))+P1(f317(f317(f225(a899),x77641),f317(f317(f75(a899),x77641),x77642))) % 112.26/112.10 [7798]E(f317(f30(x77981),f232(f906(x77981,a895))),f317(a102,f2(a899)))+P1(f317(f29(x77982),f232(f906(x77982,a895))))+~P1(f317(f29(f906(x77982,x77981)),f232(f906(f906(x77982,x77981),a895)))) % 112.26/112.10 [7926]~P1(f317(f317(f224(a899),f317(a102,f2(a899))),x79261))+~P1(f317(f317(f224(a899),f317(a102,f2(a899))),x79262))+P1(f317(f317(f224(a899),f317(a102,f2(a899))),f317(f317(f75(a899),x79261),x79262))) % 112.26/112.10 [7927]~P1(f317(f317(f225(a899),f317(a102,f2(a899))),x79272))+~P1(f317(f317(f225(a899),f317(a102,f2(a899))),x79271))+P1(f317(f317(f225(a899),f317(a102,f2(a899))),f317(f317(f75(a899),x79271),x79272))) % 112.26/112.10 [8609]E(x86091,f103(x86092))+~P1(f317(f127(x86092),x86091))+E(f167(x86092,f317(f317(f10(a895,a895,x86092),a312),f317(f317(f9(x86092,x86092,a895),a314),f134(x86092,x86091))),x86091),f104(x86092,x86091)) % 112.26/112.10 [8704]~P39(x87042)+~P39(x87041)+E(f317(f300(a899,a1,f90(a1)),f317(f317(f91(f906(a899,a895)),f317(f300(a1,a899,a95),x87041)),f317(f300(a1,a899,a95),x87042))),f317(f317(f91(f906(a1,a895)),x87041),x87042)) % 112.26/112.10 [8705]~P39(x87052)+~P39(x87051)+E(f317(f300(a899,a1,f90(a1)),f317(f317(f92(f906(a899,a895)),f317(f300(a1,a899,a95),x87051)),f317(f300(a1,a899,a95),x87052))),f317(f317(f92(f906(a1,a895)),x87051),x87052)) % 112.26/112.10 [9371]~P94(x93711)+~E(f317(f94(x93711),x93712),f72(x93711))+P27(x93711,f317(f94(x93711),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f73(a1),x93712)))) % 112.26/112.10 [9624]~P94(x96241)+E(f317(f94(x96241),x96242),f72(x96241))+~P27(x96241,f317(f94(x96241),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f73(a1),x96242)))) % 112.26/112.10 [10385]E(x103851,f2(a1))+E(x103852,f2(a1))+E(f317(f248(a1,a1,a1,a1,f25(a1),f317(f75(a1),f76(a1,x103852))),f317(f317(f317(f86(f905(a1,a1)),f317(f317(a314,f76(a1,x103851)),f76(a1,x103852))),f49(x103851,x103852)),f317(f317(f247(a1,a1,f905(a1,a1)),f317(f317(f20(a1,f906(a1,f905(a1,a1)),f906(a1,f905(a1,a1))),f317(f317(f10(f906(a1,f906(f905(a1,a1),f905(a1,a1))),f906(f906(a1,f905(a1,a1)),f906(a1,f905(a1,a1))),a1),f20(a1,f905(a1,a1),f905(a1,a1))),f317(f317(f10(f905(a1,a1),f906(a1,f906(f905(a1,a1),f905(a1,a1))),a1),f317(f9(a1,f905(a1,a1),f906(f905(a1,a1),f905(a1,a1))),f317(f317(f10(a895,f906(f905(a1,a1),f906(f905(a1,a1),f905(a1,a1))),a1),f86(f905(a1,a1))),f317(f317(f9(a1,a1,a895),a314),f2(a1))))),f317(f317(f9(a1,a1,f905(a1,a1)),f317(f317(f10(a1,f906(a1,f905(a1,a1)),a1),f242(a1,a1)),f73(a1))),f2(a1))))),f317(f317(f9(a1,f906(a1,a1),f906(a1,f905(a1,a1))),f317(f317(f10(f906(a1,f905(a1,a1)),f906(f906(a1,a1),f906(a1,f905(a1,a1))),a1),f10(a1,f905(a1,a1),a1)),f317(f317(f10(a1,f906(a1,f905(a1,a1)),a1),f242(a1,a1)),f317(f317(f9(a1,a1,a1),f317(f317(f10(a1,f906(a1,a1),a1),f3(a1)),f73(a1))),f72(a1))))),f317(f3(a1),f317(f70(a1),x103852))))),f49(x103851,x103852)))),f42(x103851,x103852)) % 112.26/112.10 [10386]E(x103861,f2(a1))+E(x103862,f2(a1))+E(f317(f248(a1,a1,a1,a1,f25(a1),f317(f75(a1),f76(a1,x103862))),f317(f317(f317(f86(f905(a1,a1)),f317(f317(a316,f317(f317(a315,f317(f317(f225(a1),f2(a1)),x103862)),f317(f317(f224(a1),f2(a1)),x103861))),f317(f317(a315,f317(f317(f225(a1),x103862),f2(a1))),f317(f317(f225(a1),x103861),f2(a1))))),f49(x103861,x103862)),f317(f317(f247(a1,a1,f905(a1,a1)),f317(f317(f20(a1,f906(a1,f905(a1,a1)),f906(a1,f905(a1,a1))),f317(f317(f10(f906(a1,f906(f905(a1,a1),f905(a1,a1))),f906(f906(a1,f905(a1,a1)),f906(a1,f905(a1,a1))),a1),f20(a1,f905(a1,a1),f905(a1,a1))),f317(f317(f10(f905(a1,a1),f906(a1,f906(f905(a1,a1),f905(a1,a1))),a1),f317(f9(a1,f905(a1,a1),f906(f905(a1,a1),f905(a1,a1))),f317(f317(f10(a895,f906(f905(a1,a1),f906(f905(a1,a1),f905(a1,a1))),a1),f86(f905(a1,a1))),f317(f317(f9(a1,a1,a895),a314),f2(a1))))),f317(f317(f9(a1,a1,f905(a1,a1)),f317(f317(f10(a1,f906(a1,f905(a1,a1)),a1),f242(a1,a1)),f73(a1))),f2(a1))))),f317(f317(f9(a1,f906(a1,a1),f906(a1,f905(a1,a1))),f317(f317(f10(f906(a1,f905(a1,a1)),f906(f906(a1,a1),f906(a1,f905(a1,a1))),a1),f10(a1,f905(a1,a1),a1)),f317(f317(f10(a1,f906(a1,f905(a1,a1)),a1),f242(a1,a1)),f317(f317(f9(a1,a1,a1),f317(f317(f10(a1,f906(a1,a1),a1),f3(a1)),f73(a1))),f72(a1))))),f317(f3(a1),f317(f70(a1),x103862))))),f49(x103861,x103862)))),f42(x103861,x103862)) % 112.26/112.10 [5786]~P112(x57861)+~P94(x57861)+E(f317(f70(x57861),f317(f317(f234(x57861),f317(f94(x57861),a87)),x57862)),f72(x57861)) % 112.26/112.10 [6301]~P141(x63011)+~P1(f317(f317(f225(a1),x63012),f2(a1)))+E(f317(f73(x63011),f317(f90(x63011),f317(a95,f317(f73(a1),x63012)))),f317(f93(x63011),x63012)) % 112.26/112.10 [6511]P1(f317(f317(f224(a89),x65111),f72(a89)))+E(f317(f317(f74(a89),f72(a89)),f262(x65111,f317(f317(f31(a89),x65112),x65111))),f262(x65111,x65112))+P1(f317(f317(f225(a89),x65112),x65111)) % 112.26/112.10 [6998]~E(x69982,f72(a899))+~P1(f317(f317(f225(a899),f2(a899)),x69981))+P1(f317(f317(f277(a899),f317(f317(f75(a899),x69981),x69982)),x69981)) % 112.26/112.10 [6999]~E(x69991,f72(a899))+~P1(f317(f317(f225(a899),f2(a899)),x69992))+P1(f317(f317(f277(a899),f317(f317(f75(a899),x69991),x69992)),x69992)) % 112.26/112.10 [7131]~P92(x71311)+~P1(f317(f317(f319(x71311),x71312),f100(x71311)))+~E(f317(f317(f74(x71311),f317(f317(f74(x71311),f72(x71311)),x71312)),x71312),f2(x71311)) % 112.26/112.10 [7245]~P1(f317(f317(f224(a1),x72452),f2(a1)))+~P1(f317(f317(f225(a1),x72451),f2(a1)))+E(f317(f241(a1,a1),f317(a47,f43(f317(f73(a1),x72451),f317(f73(a1),x72452)))),f317(f317(f31(a1),x72451),x72452)) % 112.26/112.10 [7262]~P1(f317(f317(f224(a1),x72622),f2(a1)))+~P1(f317(f317(f225(a1),x72621),f2(a1)))+E(f317(f246(a1,a1),f317(a47,f43(f317(f73(a1),x72621),f317(f73(a1),x72622)))),f41(a1,x72621,x72622)) % 112.26/112.10 [7270]~P1(f317(f317(f225(a1),x72702),f2(a1)))+E(f317(f241(a1,a1),f317(a47,f46(f317(f73(a1),x72701),f317(f73(a1),x72702)))),f317(f317(f31(a1),x72701),x72702))+~P1(f317(f317(f225(a1),f2(a1)),x72701)) % 112.26/112.10 [7288]~P1(f317(f317(f225(a1),x72882),f2(a1)))+E(f317(f246(a1,a1),f317(a47,f46(f317(f73(a1),x72881),f317(f73(a1),x72882)))),f41(a1,x72881,x72882))+~P1(f317(f317(f225(a1),f2(a1)),x72881)) % 112.26/112.10 [7339]E(f317(f317(f31(a1),f317(f317(f234(a1),x73391),x73392)),x73391),f317(f317(f234(a1),x73391),f317(f317(f3(a899),x73392),f317(a102,f2(a899)))))+~P1(f317(f317(f225(a899),f2(a899)),x73392))+~P1(f317(f317(f225(a1),f2(a1)),x73391)) % 112.26/112.10 [7443]~P1(f317(f317(f225(a899),f2(a899)),x74431))+~P1(f317(f317(f225(a899),f2(a899)),x74432))+P1(f317(f317(f225(a899),f317(f317(f3(a899),x74431),x74432)),x74431)) % 112.26/112.10 [7444]~P1(f317(f317(f225(a899),f2(a899)),x74441))+~P1(f317(f317(f225(a899),f72(a899)),x74442))+P1(f317(f317(f225(a899),f317(f317(f31(a899),x74441),x74442)),x74441)) % 112.26/112.10 [7445]~P1(f317(f317(f225(a1),f2(a1)),x74451))+~P1(f317(f317(f225(a1),f72(a1)),x74452))+P1(f317(f317(f225(a1),f317(f317(f31(a1),x74451),x74452)),x74451)) % 112.26/112.10 [7582]E(x75821,f2(a899))+~E(x75822,f2(a1))+~P1(f317(f317(f225(a1),f2(a1)),f317(f317(f234(a1),f317(f70(a1),x75822)),x75821))) % 112.26/112.10 [7623]E(x76231,f72(a899))+~P1(f317(f317(f225(a899),f2(a899)),x76232))+~P1(f317(f317(f277(a899),f317(f317(f75(a899),x76232),x76231)),x76232)) % 112.26/112.10 [7624]E(x76241,f72(a899))+~P1(f317(f317(f225(a899),f2(a899)),x76242))+~P1(f317(f317(f277(a899),f317(f317(f75(a899),x76241),x76242)),x76242)) % 112.26/112.10 [8005]~E(x80052,f103(f900(x80051)))+E(f317(f179(f900(f900(x80051))),f169(x80051,x80052)),f2(a899))+~P13(a899,f317(f158(a899),f317(f317(f144(f900(x80051),a899),f179(f900(x80051))),x80052))) % 112.26/112.10 [8258]P1(f317(x82581,x82582))+~P1(f317(x82581,f317(a98,f519(x82581,x82582))))+~P1(f317(f317(f319(f906(f905(a899,a899),a895)),x82582),a88)) % 112.26/112.10 [8274]E(x82741,f103(f900(x82742)))+E(f317(f179(f900(x82742)),f317(f317(f154(f900(x82742)),x82741),f2(a899))),f317(f179(f900(f900(x82742))),f169(x82742,x82741)))+~P13(a899,f317(f158(a899),f317(f317(f144(f900(x82742),a899),f179(f900(x82742))),x82741))) % 112.26/112.10 [8415]~P37(x84151,x84152)+~P38(x84151,x84152)+P37(x84151,f317(f317(f3(f906(f905(x84151,x84151),a895)),x84152),f297(x84151,f178(f906(f905(x84151,x84151),a895))))) % 112.26/112.10 [8989]~P1(f317(f29(x89891),f317(f252(x89891),x89892)))+~P1(f317(f29(x89891),f232(f906(x89891,a895))))+P1(f317(f29(x89891),f317(f252(x89891),f317(f317(f10(a895,a895,x89891),a312),x89892)))) % 112.26/112.10 [9053]E(f317(f317(f242(a899,a899),f317(a102,f317(f317(f31(a899),f317(f317(f3(a899),x90531),x90532)),x90532))),f41(a899,f317(f317(f3(a899),x90531),x90532),x90532)),f79(f905(a899,a899),f44(x90531,x90532)))+~P1(f317(f317(f225(a899),f2(a899)),x90532))+~P1(f317(f317(f224(a899),x90532),x90531)) % 112.26/112.10 [9336]~P1(f317(f29(x93361),f317(f252(x93361),x93362)))+P1(f317(f29(x93361),f232(f906(x93361,a895))))+~P1(f317(f29(x93361),f317(f252(x93361),f317(f317(f10(a895,a895,x93361),a312),x93362)))) % 112.26/112.10 [10066]P26(x100661,x100662)+~P36(x100661,f317(f241(f906(f905(x100661,x100661),a895),f906(f905(x100661,x100661),a895)),x100662))+~P1(f317(f317(f224(f906(f905(x100661,x100661),a895)),f317(f317(f279(x100661,x100661,x100661),f317(f241(f906(f905(x100661,x100661),a895),f906(f905(x100661,x100661),a895)),x100662)),f317(f246(f906(f905(x100661,x100661),a895),f906(f905(x100661,x100661),a895)),x100662))),f317(f241(f906(f905(x100661,x100661),a895),f906(f905(x100661,x100661),a895)),x100662))) % 112.26/112.10 [10163]~E(f287(a899,f277(a899),f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x101632,x101631),f178(f906(a899,a895)))+~P1(f317(f317(f277(a899),x101632),x101631))+P1(f317(f317(f277(a899),x101631),x101632)) % 112.26/112.10 [10164]~E(f290(a899,f277(a899),f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x101642,x101641),f178(f906(a899,a895)))+~P1(f317(f317(f277(a899),x101642),x101641))+P1(f317(f317(f277(a899),x101641),x101642)) % 112.26/112.10 [7369]~P1(f317(f317(f225(a899),f2(a899)),x73692))+P1(f317(f317(f225(a899),x73691),x73692))+E(f317(a102,f317(f317(f31(a899),f317(f317(f3(a899),x73691),x73692)),x73692)),f317(f317(f31(a899),x73691),x73692)) % 112.26/112.10 [7510]~P1(f317(f317(f225(a899),f2(a899)),x75102))+~P1(f317(f317(f224(a899),x75102),x75101))+E(f317(a102,f317(f317(f31(a899),f317(f317(f3(a899),x75101),x75102)),x75102)),f317(f317(f31(a899),x75101),x75102)) % 112.26/112.10 [8479]~P94(x84791)+~P92(x84791)+~P27(x84791,f317(f94(x84791),f317(f317(f3(a1),f317(f317(f74(a1),x84792),x84792)),a87))) % 112.26/112.10 [9242]E(x92421,f2(a899))+E(f317(f317(f247(a899,a899,f905(a899,a899)),f317(f317(f10(a899,f906(a899,f905(a899,a899)),a899),f242(a899,a899)),a102)),f79(f905(a899,a899),f44(f317(f317(f3(a899),x92422),x92421),x92421))),f79(f905(a899,a899),f44(x92422,x92421)))+P1(f317(f317(f225(a899),x92422),x92421)) % 112.26/112.10 [9426]~P37(x94261,x94262)+~P51(x94261,x94262)+P1(f317(f317(f224(f906(f905(x94261,x94261),a895)),f317(f317(f279(x94261,x94261,x94261),f317(f276(x94261,x94261),x94262)),x94262)),x94262)) % 112.26/112.10 [9689]P1(f317(x96892,f599(x96892,x96891)))+P1(f317(x96891,f599(x96892,x96891)))+E(f317(f252(a1),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f224(a1),f2(a1)))),x96891)),f317(f252(a1),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f224(a1),f2(a1)))),x96892))) % 112.26/112.10 [9693]~P1(f317(x96932,f599(x96932,x96931)))+~P1(f317(x96931,f599(x96932,x96931)))+E(f317(f252(a1),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f224(a1),f2(a1)))),x96931)),f317(f252(a1),f317(f317(f20(a1,a895,a895),f317(f317(f10(a895,f906(a895,a895),a1),a315),f317(f224(a1),f2(a1)))),x96932))) % 112.26/112.10 [10246]~P1(f317(f317(f277(a899),x102462),x102461))+P1(f317(f317(f277(a899),x102461),x102462))+P1(f317(f317(f319(a899),x102461),f285(a899,f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x102462))) % 112.26/112.10 [10247]~P1(f317(f317(f277(a899),x102472),x102471))+P1(f317(f317(f277(a899),x102471),x102472))+P1(f317(f317(f319(a899),x102472),f288(a899,f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x102471))) % 112.26/112.10 [7721]~P62(x77211)+~P94(x77211)+E(f317(f317(f281(x77211),x77212),f317(f94(x77211),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))),x77212) % 112.26/112.10 [9370]~P94(x93701)+~E(f317(f94(x93701),x93702),f72(x93701))+P27(x93701,f317(f94(x93701),f317(f317(f74(a1),x93702),f317(f73(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))) % 112.26/112.10 [9558]~P142(x95581)+~E(x95582,f72(x95581))+E(f317(f317(f234(x95581),x95582),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f72(x95581)) % 112.26/112.10 [9559]~P142(x95591)+~E(x95592,f2(x95591))+E(f317(f317(f234(x95591),x95592),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f2(x95591)) % 112.26/112.10 [9574]~P142(x95741)+~E(x95742,f317(f73(x95741),f72(x95741)))+E(f317(f317(f234(x95741),x95742),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f72(x95741)) % 112.26/112.10 [9625]~P94(x96251)+E(f317(f94(x96251),x96252),f72(x96251))+~P27(x96251,f317(f94(x96251),f317(f317(f74(a1),x96252),f317(f73(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))) % 112.26/112.10 [10009]~P112(x100092)+E(x100091,f2(x100092))+P1(f317(f317(f225(x100092),f2(x100092)),f317(f317(f234(x100092),x100091),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))) % 112.26/112.10 [10065]~P112(x100652)+~E(x100651,f2(x100652))+~P1(f317(f317(f225(x100652),f2(x100652)),f317(f317(f234(x100652),x100651),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))) % 112.26/112.10 [10101]P1(f317(f317(f224(a1),x101011),f2(a1)))+P1(f317(f317(f225(a1),x101012),x101011))+E(f317(f39(x101011),f43(x101012,f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101011))),f43(x101012,x101011)) % 112.26/112.10 [10102]~P1(f317(f317(f225(a1),f2(a1)),x101021))+P1(f317(f317(f225(a1),x101022),x101021))+E(f317(f39(x101021),f43(x101022,f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101021))),f43(x101022,x101021)) % 112.26/112.10 [10103]P1(f317(f317(f224(a1),x101031),f2(a1)))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),x101032),x101031)))+E(f317(f39(x101031),f46(x101032,f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101031))),f46(x101032,x101031)) % 112.26/112.10 [10104]~P1(f317(f317(f225(a1),f2(a1)),x101041))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),x101042),x101041)))+E(f317(f39(x101041),f46(x101042,f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101041))),f46(x101042,x101041)) % 112.26/112.10 [10105]~P145(x101051)+~P1(f317(f317(f224(a1),f2(a1)),x101052))+E(f317(f90(x101051),f317(a95,f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101052))),f317(f317(f74(x101051),f317(f90(x101051),f317(a95,x101052))),f317(f90(x101051),f317(a95,x101052)))) % 112.26/112.10 [5120]~P147(x51201,x51202,x51203)+~E(x51203,f2(a1))+P1(f317(x51201,x51202)) % 112.26/112.10 [5244]~P108(x52441)+~P13(x52441,x52443)+P13(x52441,f160(x52441,x52442,x52443)) % 112.26/112.10 [5245]~P108(x52451)+~P13(x52451,x52453)+P13(x52451,f167(x52451,x52452,x52453)) % 112.26/112.10 [4808]~P76(x48082)+~E(x48083,f317(f73(x48082),x48081))+E(x48081,f317(f73(x48082),x48083)) % 112.26/112.10 [4810]~P76(x48101)+~E(f317(f73(x48101),x48103),x48102)+E(f317(f73(x48101),x48102),x48103) % 112.26/112.10 [4889]~P95(x48893)+E(x48891,x48892)+~E(f317(f90(x48893),x48891),f317(f90(x48893),x48892)) % 112.26/112.10 [4890]~P76(x48903)+E(x48901,x48902)+~E(f317(f73(x48903),x48901),f317(f73(x48903),x48902)) % 112.26/112.10 [4891]~P96(x48913)+E(x48911,x48912)+~E(f317(f73(x48913),x48911),f317(f73(x48913),x48912)) % 112.26/112.10 [4892]~P92(x48923)+E(x48921,x48922)+~E(f317(f93(x48923),x48921),f317(f93(x48923),x48922)) % 112.26/112.10 [4893]~P108(x48933)+E(x48931,x48932)+~E(f317(f291(x48933),x48931),f317(f291(x48933),x48932)) % 112.26/112.10 [4894]~P108(x48943)+E(x48941,x48942)+~E(f317(f272(x48943),x48941),f317(f272(x48943),x48942)) % 112.26/112.10 [4895]~P108(x48953)+E(x48951,x48952)+~E(f317(f294(x48953),x48951),f317(f294(x48953),x48952)) % 112.26/112.10 [4896]~P108(x48963)+E(x48961,x48962)+~E(f317(f273(x48963),x48961),f317(f273(x48963),x48962)) % 112.26/112.10 [4998]~P60(x49981)+~P1(f317(x49982,x49983))+P1(f317(f52(x49981),x49982)) % 112.26/112.10 [5038]~P60(x50383)+P1(f317(x50381,x50382))+~P1(f317(f53(x50383),x50381)) % 112.26/112.10 [5140]~P148(x51401,x51403,x51402)+~E(x51402,f2(a1))+P1(f317(x51401,f2(a1))) % 112.26/112.10 [5180]~E(x51801,f2(a899))+E(f720(x51801,x51802,x51803),f178(f906(x51803,a895)))+~E(f317(f30(x51803),x51802),f317(a102,x51801)) % 112.26/112.10 [5328]~E(x53282,f2(a899))+E(f317(f241(a899,a899),x53281),f2(a899))+~P1(f317(f44(x53283,x53282),x53281)) % 112.26/112.10 [5367]P1(f317(x53671,x53672))+~E(x53673,f317(f90(a1),x53672))+~P1(f317(x53671,f317(a95,x53673))) % 112.26/112.10 [5850]~E(x58503,f2(a899))+~P1(f317(x58501,x58502))+P1(f317(x58501,f41(a899,x58502,x58503))) % 112.26/112.10 [6095]~P105(x60952)+~P105(x60951)+E(f121(x60951,x60952,f122(x60951,x60953),f122(x60952,x60953)),f122(f905(x60951,x60952),x60953)) % 112.26/112.10 [6282]~E(x62823,f2(a899))+P1(f317(x62821,x62822))+~P1(f317(x62821,f41(a899,x62822,x62823))) % 112.26/112.10 [6982]E(x69821,f2(a899))+~P1(f317(x69822,f346(x69821,x69823,x69822)))+P1(f317(x69822,f41(a899,x69823,x69821))) % 112.26/112.10 [7096]~P5(x70961)+~P1(f317(f317(f224(x70961),x70962),f418(x70963,x70962,x70961)))+P1(f317(f317(f224(x70961),x70962),f33(x70961,x70963))) % 112.26/112.10 [7098]~P1(f317(x70981,x70982))+~P1(f317(x70981,f346(x70983,x70982,x70981)))+P1(f317(x70981,f41(a899,x70982,x70983))) % 112.26/112.10 [7200]E(x72001,f103(x72002))+E(f317(f317(f141(x72002),f672(x72003,x72001,x72002)),f675(x72003,x72001,x72002)),x72001)+~P1(f317(f317(f319(f900(x72002)),x72001),f151(x72002,x72003))) % 112.26/112.10 [7232]~P141(x72321)+~P1(f317(f317(f319(x72321),x72322),f100(x72321)))+P1(f317(f317(f319(x72321),f317(f317(f234(x72321),x72322),x72323)),f100(x72321))) % 112.26/112.10 [7555]P36(x75551,x75552)+~P1(f317(f317(f319(x75551),x75553),f586(x75552,x75551)))+P1(f317(f317(f319(x75551),f597(x75552,x75551,x75553)),f586(x75552,x75551))) % 112.26/112.10 [7826]E(x78261,f103(x78262))+~P1(f317(f317(f319(f900(x78262)),x78261),f151(x78262,x78263)))+P1(f317(f317(f319(f900(x78262)),f675(x78263,x78261,x78262)),f151(x78262,x78263))) % 112.26/112.10 [7878]E(x78781,f2(a899))+E(f317(f317(f74(a899),f317(f317(f75(a899),x78781),f349(x78781,x78782,x78783))),f346(x78781,x78782,x78783)),x78782)+P1(f317(x78783,f41(a899,x78782,x78781))) % 112.26/112.10 [7921]~P1(f317(x79213,x79212))+E(f317(f317(f74(a899),f317(f317(f75(a899),x79211),f349(x79211,x79212,x79213))),f346(x79211,x79212,x79213)),x79212)+P1(f317(x79213,f41(a899,x79212,x79211))) % 112.26/112.10 [8061]P1(f317(f317(f225(a1),x80611),f340(x80612,x80613,x80611)))+P1(f317(f317(x80613,f317(f317(f31(a1),x80612),x80611)),f41(a1,x80612,x80611)))+~P1(f317(f317(f225(a1),x80611),f2(a1))) % 112.26/112.10 [8329]P1(f317(f317(x83292,f317(f317(f31(a1),x83291),x83293)),f41(a1,x83291,x83293)))+~P1(f317(f317(f225(a1),x83293),f2(a1)))+P1(f317(f317(f224(a1),f340(x83291,x83292,x83293)),f2(a1))) % 112.26/112.10 [8514]E(f317(f317(f74(a1),f317(f317(f75(a1),x85141),f341(x85142,x85143,x85141))),f340(x85142,x85143,x85141)),x85142)+P1(f317(f317(x85143,f317(f317(f31(a1),x85142),x85141)),f41(a1,x85142,x85141)))+~P1(f317(f317(f225(a1),x85141),f2(a1))) % 112.26/112.10 [8752]~P1(f317(f317(x87521,f341(x87522,x87521,x87523)),f340(x87522,x87521,x87523)))+P1(f317(f317(x87521,f317(f317(f31(a1),x87522),x87523)),f41(a1,x87522,x87523)))+~P1(f317(f317(f225(a1),x87523),f2(a1))) % 112.26/112.10 [9002]~P108(x90021)+~P13(x90021,x90023)+P13(x90021,f139(x90021,x90021,f7(x90021),x90022,x90023)) % 112.26/112.10 [9503]~P127(x95032)+E(x95031,f2(x95032))+~P1(f317(f317(f224(x95032),f317(f317(f74(x95032),f317(f317(f75(x95032),x95033),x95033)),f317(f317(f75(x95032),x95031),x95031))),f2(x95032))) % 112.26/112.10 [9504]~P127(x95042)+E(x95041,f2(x95042))+~P1(f317(f317(f224(x95042),f317(f317(f74(x95042),f317(f317(f75(x95042),x95041),x95041)),f317(f317(f75(x95042),x95043),x95043))),f2(x95042))) % 112.26/112.10 [10320]~P112(x103201)+~P1(f317(f317(f225(x103201),x103202),f2(x103201)))+P1(f317(f317(f225(x103201),f317(f317(f234(x103201),x103202),f317(a102,f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x103203)))),f2(x103201))) % 112.26/112.10 [10329]~P112(x103292)+E(x103291,f2(x103292))+~P1(f317(f317(f224(x103292),f317(f317(f74(x103292),f317(f317(f234(x103292),x103293),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x103292),x103291),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f2(x103292))) % 112.26/112.10 [10330]~P112(x103302)+E(x103301,f2(x103302))+~P1(f317(f317(f224(x103302),f317(f317(f74(x103302),f317(f317(f234(x103302),x103301),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x103302),x103303),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f2(x103302))) % 112.26/112.10 [4844]~E(x48442,x48443)+~P68(x48441)+E(f317(f317(f3(x48441),x48442),x48443),f2(x48441)) % 112.26/112.10 [4845]~E(x48452,x48453)+~P76(x48451)+E(f317(f317(f3(x48451),x48452),x48453),f2(x48451)) % 112.26/112.10 [4858]~P143(x48581)+~E(x48583,f2(x48581))+E(f317(f317(f74(x48581),x48582),x48583),x48582) % 112.26/112.10 [4876]~P140(x48761)+~E(x48763,f2(x48761))+E(f317(f317(f75(x48761),x48762),x48763),f2(x48761)) % 112.26/112.10 [4877]~P140(x48771)+~E(x48772,f2(x48771))+E(f317(f317(f75(x48771),x48772),x48773),f2(x48771)) % 112.26/112.10 [4898]~E(x48983,f103(x48981))+~E(x48982,f103(x48981))+E(f317(f317(f124(x48981),x48982),x48983),f103(x48981)) % 112.26/112.10 [4988]~P143(x49882)+E(x49881,f2(x49882))+~E(f317(f317(f74(x49882),x49883),x49881),x49883) % 112.26/112.10 [4989]~P76(x49891)+~E(x49892,f317(f73(x49891),x49893))+E(f317(f317(f74(x49891),x49892),x49893),f2(x49891)) % 112.26/112.10 [4996]E(x49961,f103(x49962))+E(x49963,f2(a899))+~E(f317(f317(f165(x49962),x49963),x49961),f103(x49962)) % 112.26/112.10 [5006]~P68(x50063)+E(x50061,x50062)+~E(f317(f317(f3(x50063),x50061),x50062),f2(x50063)) % 112.26/112.10 [5007]~P76(x50073)+E(x50071,x50072)+~E(f317(f317(f3(x50073),x50071),x50072),f2(x50073)) % 112.26/112.10 [5020]~P142(x50202)+E(x50201,f2(x50202))+~E(f317(f317(f234(x50202),x50201),x50203),f2(x50202)) % 112.26/112.10 [5021]~P100(x50212)+E(x50211,f178(x50212))+~E(f317(f317(f91(x50212),x50213),x50211),f178(x50212)) % 112.26/112.10 [5022]~P100(x50222)+E(x50221,f178(x50222))+~E(f317(f317(f91(x50222),x50221),x50223),f178(x50222)) % 112.26/112.10 [5023]~P102(x50232)+E(x50231,f232(x50232))+~E(f317(f317(f92(x50232),x50233),x50231),f232(x50232)) % 112.26/112.10 [5024]~P102(x50242)+E(x50241,f232(x50242))+~E(f317(f317(f92(x50242),x50241),x50243),f232(x50242)) % 112.26/112.10 [5094]~P76(x50942)+E(x50941,f317(f73(x50942),x50943))+~E(f317(f317(f74(x50942),x50941),x50943),f2(x50942)) % 112.26/112.10 [5095]~P76(x50951)+E(f317(f73(x50951),x50952),x50953)+~E(f317(f317(f74(x50951),x50952),x50953),f2(x50951)) % 112.26/112.10 [5097]~E(x50972,x50973)+~P65(x50971)+P1(f317(f317(f224(x50971),x50972),x50973)) % 112.26/112.10 [5099]~E(x50992,x50993)+~P109(x50991)+P1(f317(f317(f224(x50991),x50992),x50993)) % 112.26/112.10 [5197]~P121(x51971)+~E(x51972,f317(f73(x51971),x51973))+E(f317(f317(f75(x51971),x51972),x51972),f317(f317(f75(x51971),x51973),x51973)) % 112.26/112.10 [5205]~P108(x52051)+~P13(x52051,x52053)+P13(x52051,f317(f317(f165(x52051),x52052),x52053)) % 112.26/112.10 [5206]~P108(x52061)+~P13(x52061,x52063)+P13(x52061,f317(f317(f128(x52061),x52062),x52063)) % 112.26/112.10 [5242]E(x52421,x52422)+E(x52423,f2(a899))+~E(f317(f317(f75(a899),x52423),x52421),f317(f317(f75(a899),x52423),x52422)) % 112.26/112.10 [5243]E(x52431,x52432)+E(x52433,f2(a899))+~E(f317(f317(f75(a899),x52431),x52433),f317(f317(f75(a899),x52432),x52433)) % 112.26/112.10 [5321]~E(x53212,x53213)+~P109(x53211)+E(f293(x53211,x53212,x53213),f317(f317(f299(x53211),x53212),f178(f906(x53211,a895)))) % 112.26/112.10 [5356]~P112(x53561)+~E(f317(f70(x53561),x53562),f317(f70(x53561),x53563))+P1(f317(f317(f277(x53561),x53562),x53563)) % 112.26/112.10 [5364]~E(x53641,x53642)+~P108(x53643)+~P1(f317(f317(f225(x53643),x53641),x53642)) % 112.26/112.10 [5365]~E(x53651,x53652)+~P109(x53653)+~P1(f317(f317(f225(x53653),x53651),x53652)) % 112.26/112.10 [5378]~P109(x53781)+E(f317(f292(x53781,x53782),x53783),f178(f906(x53781,a895)))+P1(f317(f317(f225(x53781),x53782),x53783)) % 112.26/112.10 [5427]~P109(x54271)+E(f293(x54271,x54272,x54273),f178(f906(x54271,a895)))+P1(f317(f317(f224(x54271),x54272),x54273)) % 112.26/112.10 [5428]~P109(x54281)+E(f295(x54281,x54282,x54283),f178(f906(x54281,a895)))+P1(f317(f317(f225(x54281),x54282),x54283)) % 112.26/112.10 [5429]~P109(x54291)+E(f178(f906(x54291,a895)),f293(x54291,x54292,x54293))+P1(f317(f317(f224(x54291),x54292),x54293)) % 112.26/112.10 [5430]~P109(x54301)+E(f178(f906(x54301,a895)),f295(x54301,x54302,x54303))+P1(f317(f317(f225(x54301),x54302),x54303)) % 112.26/112.10 [5438]~P108(x54381)+~E(f317(f317(f228(x54381),x54382),x54383),x54382)+P1(f317(f317(f224(x54381),x54382),x54383)) % 112.26/112.10 [5439]~P108(x54391)+~E(f317(f317(f223(x54391),x54392),x54393),x54393)+P1(f317(f317(f224(x54391),x54392),x54393)) % 112.26/112.10 [5440]~P98(x54401)+~E(f317(f317(f91(x54401),x54402),x54403),x54403)+P1(f317(f317(f224(x54401),x54402),x54403)) % 112.26/112.10 [5441]~P104(x54411)+~E(f317(f317(f92(x54411),x54412),x54413),x54412)+P1(f317(f317(f224(x54411),x54412),x54413)) % 112.26/112.10 [5460]~P108(x54601)+P13(x54601,x54602)+~P13(x54601,f317(f317(f141(x54601),x54603),x54602)) % 112.26/112.10 [5461]~P108(x54611)+P13(x54611,x54612)+~P13(x54611,f317(f317(f124(x54611),x54613),x54612)) % 112.26/112.10 [5462]~P108(x54621)+P13(x54621,x54622)+~P13(x54621,f317(f317(f124(x54621),x54622),x54623)) % 112.26/112.10 [5467]~P3(x54671)+~E(f41(x54671,x54673,x54672),f2(x54671))+P1(f317(f317(f277(x54671),x54672),x54673)) % 112.26/112.10 [5529]~P108(x55291)+P1(f317(f317(f224(x55291),x55293),x55292))+P1(f317(f317(f224(x55291),x55292),x55293)) % 112.26/112.10 [5534]~P108(x55341)+P1(f317(f317(f225(x55341),x55343),x55342))+P1(f317(f317(f224(x55341),x55342),x55343)) % 112.26/112.10 [5571]~P108(x55711)+E(f317(f317(f228(x55711),x55712),x55713),x55713)+~P1(f317(f317(f224(x55711),x55713),x55712)) % 112.26/112.10 [5573]~P108(x55731)+E(f317(f317(f228(x55731),x55732),x55733),x55732)+~P1(f317(f317(f224(x55731),x55732),x55733)) % 112.26/112.10 [5574]~P108(x55741)+E(f317(f317(f223(x55741),x55742),x55743),x55742)+~P1(f317(f317(f224(x55741),x55743),x55742)) % 112.26/112.10 [5576]~P108(x55761)+E(f317(f317(f223(x55761),x55762),x55763),x55763)+~P1(f317(f317(f224(x55761),x55762),x55763)) % 112.26/112.10 [5577]~P98(x55771)+E(f317(f317(f91(x55771),x55772),x55773),x55772)+~P1(f317(f317(f224(x55771),x55773),x55772)) % 112.26/112.10 [5579]~P98(x55791)+E(f317(f317(f91(x55791),x55792),x55793),x55793)+~P1(f317(f317(f224(x55791),x55792),x55793)) % 112.26/112.10 [5580]~P104(x55801)+E(f317(f317(f92(x55801),x55802),x55803),x55803)+~P1(f317(f317(f224(x55801),x55803),x55802)) % 112.26/112.10 [5582]~P104(x55821)+E(f317(f317(f92(x55821),x55822),x55823),x55822)+~P1(f317(f317(f224(x55821),x55822),x55823)) % 112.26/112.10 [5589]~P123(x55892)+E(x55891,f2(x55892))+E(f317(f317(f281(x55892),f317(f73(x55892),x55893)),f317(f73(x55892),x55891)),f317(f317(f281(x55892),x55893),x55891)) % 112.26/112.10 [5596]~P3(x55961)+E(f41(x55961,x55962,x55963),f2(x55961))+~P1(f317(f317(f277(x55961),x55963),x55962)) % 112.26/112.10 [5642]~P109(x56421)+E(f317(f292(x56421,x56422),x56423),f178(f906(x56421,a895)))+~P1(f317(f317(f224(x56421),x56423),x56422)) % 112.26/112.10 [5675]~P109(x56751)+E(f296(x56751,x56752,x56753),f178(f906(x56751,a895)))+~P1(f317(f317(f224(x56751),x56753),x56752)) % 112.26/112.10 [5676]~P109(x56761)+E(f293(x56761,x56762,x56763),f178(f906(x56761,a895)))+~P1(f317(f317(f225(x56761),x56763),x56762)) % 112.26/112.10 [5677]~P109(x56771)+E(f295(x56771,x56772,x56773),f178(f906(x56771,a895)))+~P1(f317(f317(f224(x56771),x56773),x56772)) % 112.26/112.10 [5729]~E(f317(f317(f3(a899),x57291),x57293),x57292)+E(x57291,f317(f317(f74(a899),x57292),x57293))+~P1(f317(f317(f224(a899),x57293),x57291)) % 112.26/112.10 [5730]~E(x57301,f317(f317(f74(a899),x57303),x57302))+E(f317(f317(f3(a899),x57301),x57302),x57303)+~P1(f317(f317(f224(a899),x57302),x57301)) % 112.26/112.10 [5775]~P1(f317(x57751,x57753))+P1(f317(x57751,f351(x57751,x57752)))+~P1(f317(f317(f224(a899),x57753),x57752)) % 112.26/112.10 [5776]~P1(f317(x57761,x57763))+P1(f317(x57761,f374(x57761,x57762)))+~P1(f317(f317(f225(a899),x57763),x57762)) % 112.26/112.10 [5784]~P109(x57841)+~E(f317(f292(x57841,x57842),x57843),f178(f906(x57841,a895)))+~P1(f317(f317(f225(x57841),x57842),x57843)) % 112.26/112.10 [5789]~P65(x57891)+~P1(f317(f317(f225(x57891),x57892),x57893))+P1(f317(f317(f224(x57891),x57892),x57893)) % 112.26/112.10 [5791]~P109(x57911)+~P1(f317(f317(f225(x57911),x57912),x57913))+P1(f317(f317(f224(x57911),x57912),x57913)) % 112.26/112.10 [5909]~P109(x59091)+~E(f293(x59091,x59092,x59093),f178(f906(x59091,a895)))+~P1(f317(f317(f224(x59091),x59092),x59093)) % 112.26/112.10 [5910]~P109(x59101)+~E(f295(x59101,x59102,x59103),f178(f906(x59101,a895)))+~P1(f317(f317(f225(x59101),x59102),x59103)) % 112.26/112.10 [5911]~P109(x59111)+~E(f178(f906(x59111,a895)),f293(x59111,x59112,x59113))+~P1(f317(f317(f224(x59111),x59112),x59113)) % 112.26/112.10 [5912]~P109(x59121)+~E(f178(f906(x59121,a895)),f295(x59121,x59122,x59123))+~P1(f317(f317(f225(x59121),x59122),x59123)) % 112.26/112.10 [5922]P1(f317(x59221,x59222))+~P1(f317(x59221,f352(x59221,x59223)))+~P1(f317(f317(f224(a899),x59222),x59223)) % 112.26/112.10 [5923]P1(f317(x59231,x59232))+~P1(f317(x59231,f375(x59231,x59233)))+~P1(f317(f317(f225(a899),x59232),x59233)) % 112.26/112.10 [5931]~E(x59311,f317(a102,x59313))+P1(f317(f317(f225(a899),x59311),f317(a102,x59312)))+~P1(f317(f317(f225(a899),x59313),x59312)) % 112.26/112.10 [5950]E(x59501,x59502)+~E(f317(f317(f75(a899),x59503),x59501),f317(f317(f75(a899),x59503),x59502))+~P1(f317(f317(f225(a899),f2(a899)),x59503)) % 112.26/112.10 [6011]E(f317(x60111,f687(x60111,x60112,x60113)),f72(a899))+~E(f317(f317(f8(x60113,a899),x60111),x60112),f72(a899))+~P1(f317(f29(x60113),x60112)) % 112.26/112.10 [6028]~P5(x60281)+P1(f317(f317(f224(x60281),x60282),f32(x60281,x60283)))+~P1(f317(f317(f319(x60281),x60282),x60283)) % 112.26/112.10 [6051]~P65(x60511)+~P1(f317(f317(f225(x60511),x60513),x60512))+~P1(f317(f317(f224(x60511),x60512),x60513)) % 112.26/112.10 [6055]~P65(x60551)+~P1(f317(f317(f225(x60551),x60553),x60552))+~P1(f317(f317(f225(x60551),x60552),x60553)) % 112.26/112.10 [6058]~P108(x60581)+~P1(f317(f317(f225(x60581),x60583),x60582))+~P1(f317(f317(f224(x60581),x60582),x60583)) % 112.26/112.10 [6059]~P108(x60591)+~P1(f317(f317(f225(x60591),x60593),x60592))+~P1(f317(f317(f225(x60591),x60592),x60593)) % 112.26/112.10 [6060]~P109(x60601)+~P1(f317(f317(f225(x60601),x60603),x60602))+~P1(f317(f317(f225(x60601),x60602),x60603)) % 112.26/112.10 [6080]~E(x60802,x60803)+~E(x60801,x60802)+E(f280(a899,f277(a899),x60801,x60802),f317(f317(f299(a899),x60803),f178(f906(a899,a895)))) % 112.26/112.10 [6087]~E(f317(x60872,f621(x60872,x60873,x60871)),f2(a899))+E(f317(f317(f8(x60871,a899),x60872),x60873),f2(a899))+~P1(f317(f29(x60871),x60873)) % 112.26/112.10 [6088]~E(f317(x60882,f596(x60882,x60883,x60881)),f72(a899))+E(f317(f317(f11(x60881,a899),x60882),x60883),f72(a899))+~P1(f317(f29(x60881),x60883)) % 112.26/112.10 [6104]~P107(x61041)+~P1(f317(f317(f225(x61041),x61043),x61042))+P1(f317(f317(f319(x61041),x61042),f317(f294(x61041),x61043))) % 112.26/112.10 [6105]~P107(x61051)+~P1(f317(f317(f224(x61051),x61053),x61052))+P1(f317(f317(f319(x61051),x61052),f317(f273(x61051),x61053))) % 112.26/112.10 [6106]~P107(x61061)+~P1(f317(f317(f224(x61061),x61062),x61063))+P1(f317(f317(f319(x61061),x61062),f317(f291(x61061),x61063))) % 112.26/112.10 [6107]~P107(x61071)+~P1(f317(f317(f225(x61071),x61072),x61073))+P1(f317(f317(f319(x61071),x61072),f317(f272(x61071),x61073))) % 112.26/112.10 [6108]~P112(x61081)+~P1(f317(f317(f277(x61081),x61082),x61083))+P1(f317(f317(f277(x61081),x61082),f317(f70(x61081),x61083))) % 112.26/112.10 [6109]~P114(x61091)+~P1(f317(f317(f277(x61091),x61092),x61093))+P1(f317(f317(f277(x61091),x61092),f317(f73(x61091),x61093))) % 112.26/112.10 [6121]E(f317(x61211,f656(x61211,x61212,x61213)),f317(a102,f2(a899)))+~E(f317(f317(f8(x61213,a899),x61211),x61212),f317(a102,f2(a899)))+~P1(f317(f29(x61213),x61212)) % 112.26/112.10 [6204]~P5(x62041)+~P1(f317(f317(f319(x62041),x62043),x62042))+P1(f317(f317(f224(x62041),f33(x62041,x62042)),x62043)) % 112.26/112.10 [6225]~P1(f317(f317(f224(a899),x62251),x62253))+P1(f317(f317(f224(a899),x62251),x62252))+~P1(f317(f317(f224(a899),x62253),x62252)) % 112.26/112.10 [6226]~P1(f317(f317(f224(a1),x62261),x62263))+P1(f317(f317(f224(a1),x62261),x62262))+~P1(f317(f317(f224(a1),x62263),x62262)) % 112.26/112.10 [6227]~P1(f317(f317(f277(a899),x62271),x62273))+P1(f317(f317(f277(a899),x62271),x62272))+~P1(f317(f317(f277(a899),x62273),x62272)) % 112.26/112.10 [6247]~P107(x62471)+~P1(f317(f317(f319(x62471),x62473),f317(f273(x62471),x62472)))+P1(f317(f317(f224(x62471),x62472),x62473)) % 112.26/112.10 [6248]~P107(x62481)+~P1(f317(f317(f319(x62481),x62482),f317(f291(x62481),x62483)))+P1(f317(f317(f224(x62481),x62482),x62483)) % 112.26/112.10 [6249]~P107(x62491)+~P1(f317(f317(f319(x62491),x62493),f317(f294(x62491),x62492)))+P1(f317(f317(f225(x62491),x62492),x62493)) % 112.26/112.10 [6250]~P107(x62501)+~P1(f317(f317(f319(x62501),x62502),f317(f272(x62501),x62503)))+P1(f317(f317(f225(x62501),x62502),x62503)) % 112.26/112.10 [6251]~P112(x62511)+~P1(f317(f317(f277(x62511),x62512),f317(f70(x62511),x62513)))+P1(f317(f317(f277(x62511),x62512),x62513)) % 112.26/112.10 [6252]~P114(x62521)+~P1(f317(f317(f277(x62521),x62522),f317(f73(x62521),x62523)))+P1(f317(f317(f277(x62521),x62522),x62523)) % 112.26/112.10 [6326]~P1(f317(x63261,x63262))+P1(f317(x63261,f763(x63261)))+~P1(f317(f317(f319(x63263),x63262),f232(f906(x63263,a895)))) % 112.26/112.10 [6474]~P63(x64741)+P1(f317(f317(f225(x64741),f2(x64741)),f836(x64743,x64742,x64741)))+P1(f317(f317(f224(x64741),x64742),x64743)) % 112.26/112.10 [6475]~P64(x64751)+P1(f317(f317(f225(x64751),f2(x64751)),f434(x64753,x64752,x64751)))+P1(f317(f317(f224(x64751),x64752),x64753)) % 112.26/112.10 [6544]~P79(x65441)+~P1(f317(f317(f224(x65441),x65443),f317(f73(x65441),x65442)))+P1(f317(f317(f224(x65441),x65442),f317(f73(x65441),x65443))) % 112.26/112.10 [6546]~P79(x65461)+~P1(f317(f317(f225(x65461),x65463),f317(f73(x65461),x65462)))+P1(f317(f317(f225(x65461),x65462),f317(f73(x65461),x65463))) % 112.26/112.10 [6558]~P1(f317(f317(f225(a899),x65581),x65583))+~P1(f317(f317(f225(a899),x65583),x65582))+P1(f317(f317(f225(a899),f317(a102,x65581)),x65582)) % 112.26/112.10 [6589]~P126(x65891)+P1(f317(f317(f224(x65891),f317(f90(x65891),x65892)),f317(f90(x65891),x65893)))+~P1(f317(f317(f224(a899),x65892),x65893)) % 112.26/112.10 [6590]~P112(x65901)+P1(f317(f317(f224(x65901),f317(f93(x65901),x65902)),f317(f93(x65901),x65903)))+~P1(f317(f317(f224(a1),x65902),x65903)) % 112.26/112.10 [6592]~P112(x65921)+P1(f317(f317(f225(x65921),f317(f93(x65921),x65922)),f317(f93(x65921),x65923)))+~P1(f317(f317(f225(a1),x65922),x65923)) % 112.26/112.10 [6593]~P126(x65931)+P1(f317(f317(f225(x65931),f317(f90(x65931),x65932)),f317(f90(x65931),x65933)))+~P1(f317(f317(f225(a899),x65932),x65933)) % 112.26/112.10 [6599]~P108(x65991)+E(f317(f317(f91(f906(x65991,a895)),f317(f272(x65991),x65992)),f317(f292(x65991,x65992),x65993)),f317(f272(x65991),x65993))+~P1(f317(f317(f224(x65991),x65992),x65993)) % 112.26/112.10 [6629]~P79(x66291)+~P1(f317(f317(f224(x66291),x66293),x66292))+P1(f317(f317(f224(x66291),f317(f73(x66291),x66292)),f317(f73(x66291),x66293))) % 112.26/112.10 [6631]~P96(x66311)+~P1(f317(f317(f224(x66311),x66313),x66312))+P1(f317(f317(f224(x66311),f317(f73(x66311),x66312)),f317(f73(x66311),x66313))) % 112.26/112.10 [6632]~P79(x66321)+~P1(f317(f317(f225(x66321),x66323),x66322))+P1(f317(f317(f225(x66321),f317(f73(x66321),x66322)),f317(f73(x66321),x66323))) % 112.26/112.10 [6668]~P108(x66681)+E(f317(f317(f91(f906(x66681,a895)),f317(f291(x66681),x66682)),f296(x66681,x66682,x66683)),f317(f272(x66681),x66683))+~P1(f317(f317(f225(x66681),x66682),x66683)) % 112.26/112.10 [6669]~P108(x66691)+E(f317(f317(f91(f906(x66691,a895)),f317(f291(x66691),x66692)),f295(x66691,x66692,x66693)),f317(f291(x66691),x66693))+~P1(f317(f317(f224(x66691),x66692),x66693)) % 112.26/112.10 [6670]~P108(x66701)+E(f317(f317(f91(f906(x66701,a895)),f317(f272(x66701),x66702)),f293(x66701,x66702,x66703)),f317(f291(x66701),x66703))+~P1(f317(f317(f224(x66701),x66702),x66703)) % 112.26/112.10 [6704]~P108(x67041)+E(f317(f317(f91(f906(x67041,a895)),f317(f292(x67041,x67042),x67043)),f317(f273(x67041),x67043)),f317(f273(x67041),x67042))+~P1(f317(f317(f224(x67041),x67042),x67043)) % 112.26/112.10 [6865]~P108(x68651)+E(f317(f317(f91(f906(x68651,a895)),f296(x68651,x68652,x68653)),f317(f273(x68651),x68653)),f317(f294(x68651),x68652))+~P1(f317(f317(f225(x68651),x68652),x68653)) % 112.26/112.10 [6866]~P108(x68661)+E(f317(f317(f91(f906(x68661,a895)),f293(x68661,x68662,x68663)),f317(f294(x68661),x68663)),f317(f273(x68661),x68662))+~P1(f317(f317(f224(x68661),x68662),x68663)) % 112.26/112.10 [6867]~P108(x68671)+E(f317(f317(f91(f906(x68671,a895)),f295(x68671,x68672,x68673)),f317(f294(x68671),x68673)),f317(f294(x68671),x68672))+~P1(f317(f317(f224(x68671),x68672),x68673)) % 112.26/112.10 [6886]P1(f317(x68861,x68862))+~P1(f317(f317(f224(a899),x68862),x68863))+P1(f317(f317(f319(a899),f352(x68861,x68863)),f293(a899,f2(a899),x68863))) % 112.26/112.10 [6920]E(x69201,x69202)+~E(f317(f317(f154(x69203),x69201),f633(x69203,x69202,x69201)),f317(f317(f154(x69203),x69202),f633(x69203,x69202,x69201)))+~E(f317(f179(f900(x69203)),x69201),f317(f179(f900(x69203)),x69202)) % 112.26/112.10 [6925]~E(x69253,f317(f317(f31(a899),x69251),x69252))+~P1(f317(f317(f225(a899),f2(a899)),x69252))+P1(f317(f317(f225(a899),x69251),f317(f317(f75(a899),x69252),f317(a102,x69253)))) % 112.26/112.10 [6941]~P1(f317(x69411,x69413))+~P1(f317(f317(f224(a899),x69413),x69412))+P1(f317(f317(f319(a899),f351(x69411,x69412)),f293(a899,f2(a899),x69412))) % 112.26/112.10 [6980]~P1(f317(x69801,x69803))+P1(f317(x69801,f377(x69801,x69802)))+~P1(f317(f317(f319(a899),x69803),f293(a899,f2(a899),x69802))) % 112.26/112.10 [7001]~P126(x70013)+~P1(f317(f317(f224(x70013),f317(f90(x70013),x70011)),f317(f90(x70013),x70012)))+P1(f317(f317(f224(a899),x70011),x70012)) % 112.26/112.10 [7002]~P112(x70023)+~P1(f317(f317(f224(x70023),f317(f93(x70023),x70021)),f317(f93(x70023),x70022)))+P1(f317(f317(f224(a1),x70021),x70022)) % 112.26/112.10 [7004]~P126(x70043)+~P1(f317(f317(f225(x70043),f317(f90(x70043),x70041)),f317(f90(x70043),x70042)))+P1(f317(f317(f225(a899),x70041),x70042)) % 112.26/112.10 [7005]~P112(x70053)+~P1(f317(f317(f225(x70053),f317(f93(x70053),x70051)),f317(f93(x70053),x70052)))+P1(f317(f317(f225(a1),x70051),x70052)) % 112.26/112.10 [7022]~P126(x70221)+~P1(f317(f317(f225(x70221),f72(x70221)),x70222))+P1(f317(f317(f225(x70221),f72(x70221)),f317(f317(f234(x70221),x70222),f317(a102,x70223)))) % 112.26/112.10 [7025]~P79(x70251)+~P1(f317(f317(f224(x70251),f317(f73(x70251),x70253)),f317(f73(x70251),x70252)))+P1(f317(f317(f224(x70251),x70252),x70253)) % 112.26/112.10 [7026]~P96(x70261)+~P1(f317(f317(f224(x70261),f317(f73(x70261),x70263)),f317(f73(x70261),x70262)))+P1(f317(f317(f224(x70261),x70262),x70263)) % 112.26/112.10 [7027]~P79(x70271)+~P1(f317(f317(f225(x70271),f317(f73(x70271),x70273)),f317(f73(x70271),x70272)))+P1(f317(f317(f225(x70271),x70272),x70273)) % 112.26/112.10 [7051]P1(f317(x70511,x70512))+~P1(f317(x70511,f353(x70511,x70513)))+~P1(f317(f317(f319(a899),x70512),f293(a899,f2(a899),x70513))) % 112.26/112.10 [7073]~P63(x70731)+P1(f317(f317(f225(x70731),f836(x70733,x70732,x70731)),f72(x70731)))+P1(f317(f317(f224(x70731),x70732),x70733)) % 112.26/112.10 [7093]~E(f41(a899,x70933,x70932),f41(a899,x70931,x70932))+E(f317(f317(f74(a899),x70931),f317(f317(f75(a899),x70932),f378(x70931,x70932,x70933))),x70933)+~P1(f317(f317(f224(a899),x70931),x70933)) % 112.26/112.10 [7148]E(f317(f317(f8(x71481,a899),x71482),x71483),f2(a899))+~P1(f317(f29(x71481),x71483))+P1(f317(f317(f319(x71481),f621(x71482,x71483,x71481)),x71483)) % 112.26/112.10 [7149]E(f317(f317(f11(x71491,a899),x71492),x71493),f72(a899))+~P1(f317(f29(x71491),x71493))+P1(f317(f317(f319(x71491),f596(x71492,x71493,x71491)),x71493)) % 112.26/112.10 [7171]~P109(x71711)+~P1(f317(f317(f224(x71711),x71712),x71713))+P1(f317(f317(f224(f906(x71711,a895)),f317(f291(x71711),x71712)),f317(f291(x71711),x71713))) % 112.26/112.10 [7172]~P108(x71721)+~P1(f317(f317(f224(x71721),x71722),x71723))+P1(f317(f317(f224(f906(x71721,a895)),f317(f272(x71721),x71722)),f317(f272(x71721),x71723))) % 112.26/112.10 [7173]~P108(x71731)+~P1(f317(f317(f224(x71731),x71733),x71732))+P1(f317(f317(f224(f906(x71731,a895)),f317(f294(x71731),x71732)),f317(f294(x71731),x71733))) % 112.26/112.10 [7174]~P109(x71741)+~P1(f317(f317(f224(x71741),x71743),x71742))+P1(f317(f317(f224(f906(x71741,a895)),f317(f273(x71741),x71742)),f317(f273(x71741),x71743))) % 112.26/112.10 [7175]~P108(x71751)+~P1(f317(f317(f225(x71751),x71752),x71753))+P1(f317(f317(f225(f906(x71751,a895)),f317(f272(x71751),x71752)),f317(f272(x71751),x71753))) % 112.26/112.10 [7186]~P5(x71861)+P1(f317(f317(f224(x71861),x71862),f33(x71861,x71863)))+P1(f317(f317(f319(x71861),f418(x71863,x71862,x71861)),x71863)) % 112.26/112.10 [7192]~P79(x71921)+P1(f317(f317(f224(x71921),f317(f317(f3(x71921),x71922),x71923)),f2(x71921)))+~P1(f317(f317(f224(x71921),x71922),x71923)) % 112.26/112.10 [7193]~P79(x71931)+P1(f317(f317(f225(x71931),f317(f317(f3(x71931),x71932),x71933)),f2(x71931)))+~P1(f317(f317(f225(x71931),x71932),x71933)) % 112.26/112.10 [7235]P1(f317(x72351,x72352))+P1(f317(f317(f224(a899),f353(x72351,x72353)),x72353))+~P1(f317(f317(f319(a899),x72352),f293(a899,f2(a899),x72353))) % 112.26/112.10 [7277]~E(f317(f317(f8(x72771,a899),x72772),x72773),f72(a899))+~P1(f317(f29(x72771),x72773))+P1(f317(f317(f319(x72771),f687(x72772,x72773,x72771)),x72773)) % 112.26/112.10 [7278]~P1(f317(x72781,x72783))+P1(f317(f317(f224(a899),f377(x72781,x72782)),x72782))+~P1(f317(f317(f319(a899),x72783),f293(a899,f2(a899),x72782))) % 112.26/112.10 [7316]~P5(x73161)+P1(f317(f317(f319(x73161),f408(x73163,x73162,x73161)),x73162))+P1(f317(f317(f224(x73161),f32(x73161,x73162)),x73163)) % 112.26/112.10 [7350]~E(f317(f317(f8(x73501,a899),x73502),x73503),f317(a102,f2(a899)))+~P1(f317(f29(x73501),x73503))+P1(f317(f317(f319(x73501),f656(x73502,x73503,x73501)),x73503)) % 112.26/112.10 [7361]E(x73611,f2(a899))+P1(f317(x73612,f41(a899,x73613,x73611)))+P1(f317(f317(f225(a899),f346(x73611,x73613,x73612)),x73611)) % 112.26/112.10 [7473]~P1(f317(x74731,x74732))+P1(f317(x74731,f41(a899,x74732,x74733)))+P1(f317(f317(f225(a899),f346(x74733,x74732,x74731)),x74733)) % 112.26/112.10 [7586]E(x75861,f103(x75862))+~P1(f317(f317(f319(f900(x75862)),x75861),f151(x75862,x75863)))+P1(f317(f317(f319(x75862),f672(x75863,x75861,x75862)),x75863)) % 112.26/112.10 [7609]~P108(x76091)+E(f317(f317(f91(f906(x76091,a895)),f317(f317(f299(x76091),x76092),f178(f906(x76091,a895)))),f296(x76091,x76092,x76093)),f317(f292(x76091,x76092),x76093))+~P1(f317(f317(f225(x76091),x76092),x76093)) % 112.26/112.10 [7632]~P108(x76321)+E(f317(f317(f91(f906(x76321,a895)),f317(f317(f299(x76321),x76322),f178(f906(x76321,a895)))),f295(x76321,x76322,x76323)),f293(x76321,x76322,x76323))+~P1(f317(f317(f224(x76321),x76322),x76323)) % 112.26/112.10 [7743]~P108(x77431)+P1(f317(f317(f224(x77431),x77432),x77433))+~P1(f317(f317(f224(f906(x77431,a895)),f317(f294(x77431),x77433)),f317(f294(x77431),x77432))) % 112.26/112.10 [7744]~P109(x77441)+P1(f317(f317(f224(x77441),x77442),x77443))+~P1(f317(f317(f224(f906(x77441,a895)),f317(f273(x77441),x77443)),f317(f273(x77441),x77442))) % 112.26/112.10 [7745]~P108(x77451)+P1(f317(f317(f224(x77451),x77452),x77453))+~P1(f317(f317(f224(f906(x77451,a895)),f317(f272(x77451),x77452)),f317(f272(x77451),x77453))) % 112.26/112.10 [7746]~P109(x77461)+P1(f317(f317(f224(x77461),x77462),x77463))+~P1(f317(f317(f224(f906(x77461,a895)),f317(f291(x77461),x77462)),f317(f291(x77461),x77463))) % 112.26/112.10 [7747]~P108(x77471)+P1(f317(f317(f225(x77471),x77472),x77473))+~P1(f317(f317(f225(f906(x77471,a895)),f317(f272(x77471),x77472)),f317(f272(x77471),x77473))) % 112.26/112.10 [7770]~P79(x77701)+~P1(f317(f317(f224(x77701),f317(f317(f3(x77701),x77702),x77703)),f2(x77701)))+P1(f317(f317(f224(x77701),x77702),x77703)) % 112.26/112.10 [7771]~P79(x77711)+~P1(f317(f317(f225(x77711),f317(f317(f3(x77711),x77712),x77713)),f2(x77711)))+P1(f317(f317(f225(x77711),x77712),x77713)) % 112.26/112.10 [7928]E(x79281,f2(a899))+~E(f317(f132(a899,a899,f74(a899),x79282),x79283),f2(a899))+~P1(f317(f317(f319(a899),x79281),f317(f162(a899),x79283))) % 112.26/112.10 [7932]~P5(x79321)+~P1(f317(f317(f224(x79321),f408(x79323,x79322,x79321)),x79323))+P1(f317(f317(f224(x79321),f32(x79321,x79322)),x79323)) % 112.26/112.10 [8086]P1(f317(f317(f224(a1),f2(a1)),f342(x80861,x80862,x80863)))+P1(f317(f317(x80862,f317(f317(f31(a1),x80861),x80863)),f41(a1,x80861,x80863)))+~P1(f317(f317(f225(a1),f2(a1)),x80863)) % 112.26/112.10 [8174]E(x81741,x81742)+~E(f317(f179(f900(x81743)),x81741),f317(f179(f900(x81743)),x81742))+~P1(f317(f317(f247(x81743,x81743,a895),a314),f645(x81743,x81741,x81742))) % 112.26/112.10 [8245]~P36(x82452,x82453)+E(x82451,f178(f906(x82452,a895)))+~P1(f317(f317(f224(f906(x82452,a895)),x82451),f317(f275(x82452,x82452,x82453),x82451))) % 112.26/112.10 [8276]~P64(x82761)+~P1(f317(f317(f224(x82761),x82762),f317(f317(f74(x82761),x82763),f434(x82763,x82762,x82761))))+P1(f317(f317(f224(x82761),x82762),x82763)) % 112.26/112.10 [8311]P52(x83111,x83112,x83113)+P1(f317(f317(f319(x83111),f559(x83113,x83112,x83111)),x83112))+P1(f317(f317(f319(f905(x83111,x83111)),f560(x83113,x83112,x83111)),x83113)) % 112.26/112.10 [8332]P1(f317(f317(x83322,f317(f317(f31(a1),x83321),x83323)),f41(a1,x83321,x83323)))+~P1(f317(f317(f225(a1),f2(a1)),x83323))+P1(f317(f317(f225(a1),f342(x83321,x83322,x83323)),x83323)) % 112.26/112.10 [8357]E(f317(f300(a899,a899,f317(f317(f9(a899,a899,a899),f3(a899)),x83571)),f317(f292(a899,x83572),x83573)),f178(f906(a899,a895)))+P1(f317(f317(f225(a899),x83571),x83573))+P1(f317(f317(f225(a899),x83572),x83573)) % 112.26/112.10 [8468]E(f317(f300(a899,a899,f317(f317(f9(a899,a899,a899),f3(a899)),x84681)),f317(f292(a899,x84682),x84683)),f317(f317(f299(a899),f2(a899)),f178(f906(a899,a895))))+P1(f317(f317(f225(a899),x84681),x84683))+~P1(f317(f317(f225(a899),x84682),x84683)) % 112.26/112.10 [8482]~P108(x84821)+E(f139(x84821,x84821,f7(x84821),x84822,x84823),x84823)+~P1(f317(f317(f319(x84821),x84822),f317(f162(x84821),x84823))) % 112.26/112.10 [8495]P24(x84951,x84951,x84952,x84953)+~P1(f317(f29(x84951),x84953))+~P1(f317(f317(f224(f906(x84951,a895)),x84953),f317(f300(x84951,x84951,x84952),x84953))) % 112.26/112.10 [8522]E(f317(f317(f74(a1),f317(f317(f75(a1),x85221),f343(x85222,x85223,x85221))),f342(x85222,x85223,x85221)),x85222)+P1(f317(f317(x85223,f317(f317(f31(a1),x85222),x85221)),f41(a1,x85222,x85221)))+~P1(f317(f317(f225(a1),f2(a1)),x85221)) % 112.26/112.10 [8759]~P1(f317(f317(x87591,f343(x87592,x87591,x87593)),f342(x87592,x87591,x87593)))+P1(f317(f317(x87591,f317(f317(f31(a1),x87592),x87593)),f41(a1,x87592,x87593)))+~P1(f317(f317(f225(a1),f2(a1)),x87593)) % 112.26/112.10 [9657]~P1(f317(f29(x96571),x96572))+~P1(f317(f317(f319(x96571),x96573),x96572))+P1(f317(f317(f225(a899),f317(f30(x96571),f317(f317(f3(f906(x96571,a895)),x96572),f317(f317(f299(x96571),x96573),f178(f906(x96571,a895)))))),f317(f30(x96571),x96572))) % 112.26/112.10 [10260]P52(x102601,x102602,x102603)+~P1(f317(f317(f247(x102601,x102601,a895),f317(f317(f9(x102601,f906(x102601,a895),f906(x102601,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x102601,a895),f906(x102601,a895)),x102601),f10(a895,a895,x102601)),f317(f317(f10(a895,f906(a895,a895),x102601),a315),f317(f317(f9(x102601,f906(x102601,a895),a895),f319(x102601)),x102602)))),f317(f317(f9(x102601,f906(x102601,a895),a895),f319(x102601)),x102602))),f560(x102603,x102602,x102601)))+P1(f317(f317(f319(x102601),f559(x102603,x102602,x102601)),x102602)) % 112.26/112.10 [5551]~P123(x55512)+E(x55511,f2(x55512))+E(f317(f317(f281(x55512),x55513),f317(f73(x55512),x55511)),f317(f73(x55512),f317(f317(f281(x55512),x55513),x55511))) % 112.26/112.10 [5691]~E(x56913,f178(f906(x56911,a895)))+~E(x56912,f178(f906(x56911,a895)))+E(f317(f317(f91(f906(x56911,a895)),x56912),x56913),f178(f906(x56911,a895))) % 112.26/112.10 [5749]~E(x57493,f2(a899))+~P1(f317(x57491,f2(a899)))+P1(f317(x57491,f317(f317(f31(a899),x57492),x57493))) % 112.26/112.10 [5901]~P64(x59012)+E(x59011,f2(x59012))+E(f317(f317(f281(x59012),f317(f70(x59012),x59013)),f317(f70(x59012),x59011)),f317(f70(x59012),f317(f317(f281(x59012),x59013),x59011))) % 112.26/112.10 [6000]~P119(x60001)+~E(x60002,f72(x60001))+P1(f317(f317(f277(x60001),x60002),f317(f317(f234(x60001),x60002),x60003))) % 112.26/112.10 [6021]~P3(x60211)+E(f317(f317(f75(x60211),x60212),f317(f317(f31(x60211),x60213),x60212)),x60213)+~P1(f317(f317(f277(x60211),x60212),x60213)) % 112.26/112.10 [6076]~P1(f317(f29(x60761),x60763))+E(f317(f30(x60761),f317(f317(f299(x60761),x60762),x60763)),f317(a102,f317(f30(x60761),x60763)))+P1(f317(f317(f319(x60761),x60762),x60763)) % 112.26/112.10 [6153]~E(x61532,f2(a899))+P1(f317(x61531,f2(a899)))+~P1(f317(x61531,f317(f317(f31(a899),x61533),x61532))) % 112.26/112.10 [6170]~P1(f317(f29(x61701),x61703))+E(f317(f30(x61701),f317(f317(f299(x61701),x61702),x61703)),f317(f30(x61701),x61703))+~P1(f317(f317(f319(x61701),x61702),x61703)) % 112.26/112.10 [6206]~P1(f317(f29(x62061),x62063))+E(f317(f30(x62061),f317(f317(f299(x62061),x62062),x62063)),f317(f317(f74(a899),f72(a899)),f317(f30(x62061),x62063)))+P1(f317(f317(f319(x62061),x62062),x62063)) % 112.26/112.10 [6213]~P4(x62131)+E(f317(f317(f31(x62131),x62132),f317(f73(x62131),x62133)),f317(f73(x62131),f317(f317(f31(x62131),x62132),x62133)))+~P1(f317(f317(f277(x62131),x62133),x62132)) % 112.26/112.10 [6327]E(f317(f317(f74(a899),x63271),f632(x63271,x63272,x63273)),x63272)+~P1(f317(x63273,f2(a899)))+P1(f317(x63273,f317(f317(f3(a899),x63272),x63271))) % 112.26/112.10 [6328]E(f317(f317(f74(a899),x63281),f654(x63281,x63282,x63283)),x63282)+~P1(f317(x63283,f2(a899)))+P1(f317(x63283,f317(f317(f3(a899),x63282),x63281))) % 112.26/112.10 [6353]~P4(x63531)+E(f317(f317(f31(x63531),f317(f73(x63531),x63532)),x63533),f317(f73(x63531),f317(f317(f31(x63531),x63532),x63533)))+~P1(f317(f317(f277(x63531),x63533),x63532)) % 112.26/112.10 [6377]~P5(x63771)+~P1(f317(f29(x63771),x63773))+E(f317(f317(f59(x63771,x63771,f91(x63771)),x63772),x63773),f317(f317(f91(x63771),x63772),f32(x63771,x63773))) % 112.26/112.10 [6378]~P5(x63781)+~P1(f317(f29(x63781),x63783))+E(f317(f317(f59(x63781,x63781,f92(x63781)),x63782),x63783),f317(f317(f92(x63781),x63782),f33(x63781,x63783))) % 112.26/112.10 [6384]~P94(x63841)+~E(f317(f94(x63841),x63842),f317(f94(x63841),x63843))+P27(x63841,f317(f94(x63841),f317(f317(f74(a1),x63842),f317(f73(a1),x63843)))) % 112.26/112.10 [6394]~P141(x63941)+E(f317(f317(f3(x63941),f317(f90(x63941),x63942)),f317(f90(x63941),x63943)),f317(f90(x63941),f317(f317(f3(a899),x63942),x63943)))+~P1(f317(f317(f224(a899),x63943),x63942)) % 112.26/112.10 [6401]~P112(x64011)+~P1(f317(f317(f277(x64011),x64012),x64013))+P1(f317(f317(f277(x64011),f317(f70(x64011),x64012)),x64013)) % 112.26/112.10 [6402]~P114(x64021)+~P1(f317(f317(f277(x64021),x64022),x64023))+P1(f317(f317(f277(x64021),f317(f73(x64021),x64022)),x64023)) % 112.26/112.10 [6485]E(f317(f317(f74(a899),x64851),f632(x64851,x64852,x64853)),x64852)+P1(f317(f317(f225(a899),x64852),x64851))+P1(f317(x64853,f317(f317(f3(a899),x64852),x64851))) % 112.26/112.10 [6486]E(f317(f317(f74(a899),x64861),f654(x64861,x64862,x64863)),x64862)+P1(f317(f317(f225(a899),x64862),x64861))+P1(f317(x64863,f317(f317(f3(a899),x64862),x64861))) % 112.26/112.10 [6502]~P112(x65021)+E(f317(f317(f75(x65021),f317(f70(x65021),x65022)),x65023),f317(f70(x65021),f317(f317(f75(x65021),x65022),x65023)))+~P1(f317(f317(f224(x65021),f2(x65021)),x65023)) % 112.26/112.10 [6503]~P63(x65031)+E(f317(f317(f281(x65031),f317(f70(x65031),x65032)),x65033),f317(f70(x65031),f317(f317(f281(x65031),x65032),x65033)))+~P1(f317(f317(f225(x65031),f2(x65031)),x65033)) % 112.26/112.10 [6512]~P108(x65121)+~P1(f317(f29(x65121),x65123))+E(f317(f317(f59(x65121,x65121,f223(x65121)),x65122),x65123),f16(x65121,f317(f317(f299(x65121),x65122),x65123))) % 112.26/112.10 [6513]~P108(x65131)+~P1(f317(f29(x65131),x65133))+E(f317(f317(f59(x65131,x65131,f228(x65131)),x65132),x65133),f17(x65131,f317(f317(f299(x65131),x65132),x65133))) % 112.26/112.10 [6514]~P99(x65141)+~P1(f317(f29(x65141),x65143))+E(f317(f317(f59(x65141,x65141,f91(x65141)),x65142),x65143),f12(x65141,f317(f317(f299(x65141),x65142),x65143))) % 112.26/112.10 [6515]~P99(x65151)+~P1(f317(f29(x65151),x65153))+E(f317(f317(f59(x65151,x65151,f92(x65151)),x65152),x65153),f13(x65151,f317(f317(f299(x65151),x65152),x65153))) % 112.26/112.10 [6560]E(x65601,f103(x65602))+~E(f169(x65602,x65603),f103(f900(x65602)))+~P1(f317(f317(f319(f900(x65602)),x65601),f317(f162(f900(x65602)),x65603))) % 112.26/112.10 [6579]~P119(x65791)+~P1(f317(f317(f225(a899),f2(a899)),x65793))+P1(f317(f317(f277(x65791),x65792),f317(f317(f234(x65791),x65792),x65793))) % 112.26/112.10 [6607]~P1(f317(f127(x66071),x66073))+P1(f317(f317(f319(x66071),x66072),f317(f162(x66071),x66073)))+P1(f317(f127(x66071),f317(f317(f141(x66071),x66072),x66073))) % 112.26/112.10 [6618]~P97(x66181)+~P1(f317(f29(x66181),x66183))+E(f317(f58(x66181,f75(x66181)),f317(f317(f299(x66181),x66182),x66183)),f317(f317(f59(x66181,x66181,f75(x66181)),x66182),x66183)) % 112.26/112.10 [6640]~P108(x66401)+~P1(f317(f29(x66401),x66403))+E(f14(x66401,f223(x66401),f317(f317(f299(x66401),x66402),x66403)),f317(f317(f59(x66401,x66401,f223(x66401)),x66402),x66403)) % 112.26/112.10 [6641]~P108(x66411)+~P1(f317(f29(x66411),x66413))+E(f15(x66411,f228(x66411),f317(f317(f299(x66411),x66412),x66413)),f317(f317(f59(x66411,x66411,f228(x66411)),x66412),x66413)) % 112.26/112.10 [6643]P1(f317(x66431,f2(a899)))+~P1(f317(f317(f225(a899),x66432),x66433))+~P1(f317(x66431,f317(f317(f3(a899),x66432),x66433))) % 112.26/112.10 [6664]~P86(x66641)+P1(f317(f317(f224(x66641),x66642),x66643))+~P1(f317(f317(f224(x66641),f317(f70(x66641),x66642)),x66643)) % 112.26/112.10 [6665]~P112(x66651)+P1(f317(f317(f225(x66651),x66652),x66653))+~P1(f317(f317(f225(x66651),f317(f70(x66651),x66652)),x66653)) % 112.26/112.10 [6666]~P112(x66661)+P1(f317(f317(f277(x66661),x66662),x66663))+~P1(f317(f317(f277(x66661),f317(f70(x66661),x66662)),x66663)) % 112.26/112.10 [6667]~P114(x66671)+P1(f317(f317(f277(x66671),x66672),x66673))+~P1(f317(f317(f277(x66671),f317(f73(x66671),x66672)),x66673)) % 112.26/112.10 [6684]E(x66841,f103(x66842))+E(f317(f131(x66842),f317(f317(f128(x66842),x66843),x66841)),f317(f317(f154(x66842),x66841),x66843))+~P1(f317(f317(f225(a899),x66843),f317(f179(f900(x66842)),x66841))) % 112.26/112.10 [6739]~P1(f317(x67391,x67393))+P1(f317(x67391,f399(x67391,x67392)))+~P1(f317(f317(f319(a899),x67393),f317(f292(a899,f2(a899)),x67392))) % 112.26/112.10 [6759]P1(f317(x67591,x67592))+~P1(f317(f317(f225(a899),x67592),x67593))+P1(f317(f317(f319(a899),f375(x67591,x67593)),f317(f292(a899,f2(a899)),x67593))) % 112.26/112.10 [6774]~P126(x67741)+~P1(f317(f317(f224(x67741),f72(x67741)),x67742))+P1(f317(f317(f224(x67741),f72(x67741)),f317(f317(f234(x67741),x67742),x67743))) % 112.26/112.10 [6776]~P126(x67761)+~P1(f317(f317(f224(x67761),f2(x67761)),x67762))+P1(f317(f317(f224(x67761),f2(x67761)),f317(f317(f234(x67761),x67762),x67763))) % 112.26/112.10 [6778]~P126(x67781)+~P1(f317(f317(f225(x67781),f2(x67781)),x67782))+P1(f317(f317(f225(x67781),f2(x67781)),f317(f317(f234(x67781),x67782),x67783))) % 112.26/112.10 [6803]~P1(f317(x68031,x68033))+~P1(f317(f317(f225(a899),x68033),x68032))+P1(f317(f317(f319(a899),f374(x68031,x68032)),f317(f292(a899,f2(a899)),x68032))) % 112.26/112.10 [6811]P1(f317(f29(x68111),x68112))+~P1(f317(f29(x68111),x68113))+~P1(f317(f317(f224(f906(x68111,a895)),x68112),x68113)) % 112.26/112.10 [6818]~P1(f317(f317(f277(a899),x68181),x68182))+~P1(f317(f317(f277(a899),x68181),x68183))+P1(f317(f317(f277(a899),x68181),f317(f317(f3(a899),x68182),x68183))) % 112.26/112.10 [6819]P1(f317(x68191,x68192))+~P1(f317(x68191,f392(x68191,x68193)))+~P1(f317(f317(f319(a899),x68192),f317(f292(a899,f2(a899)),x68193))) % 112.26/112.10 [6832]E(x68321,f2(a899))+P1(f317(x68322,f344(x68321,x68323,x68322)))+~P1(f317(x68322,f317(f317(f31(a899),x68323),x68321))) % 112.26/112.10 [6840]~P127(x68402)+E(x68401,f2(x68402))+~E(f317(f317(f74(x68402),f317(f317(f75(x68402),x68403),x68403)),f317(f317(f75(x68402),x68401),x68401)),f2(x68402)) % 112.26/112.10 [6841]~P127(x68412)+E(x68411,f2(x68412))+~E(f317(f317(f74(x68412),f317(f317(f75(x68412),x68411),x68411)),f317(f317(f75(x68412),x68413),x68413)),f2(x68412)) % 112.26/112.10 [6887]E(x68871,f2(a899))+~P1(f317(x68872,f345(x68871,x68873,x68872)))+P1(f317(x68872,f317(f317(f31(a899),x68873),x68871))) % 112.26/112.10 [6892]~P108(x68921)+~P13(x68921,x68923)+P13(x68921,f317(f317(f138(x68921,x68921,f7(x68921)),x68922),x68923)) % 112.26/112.10 [6934]P1(f317(x69341,f344(x69342,x69343,x69341)))+P1(f317(x69341,f2(a899)))+~P1(f317(x69341,f317(f317(f31(a899),x69343),x69342))) % 112.26/112.10 [6940]~P94(x69401)+E(f317(f94(x69401),x69402),f317(f94(x69401),x69403))+~P27(x69401,f317(f94(x69401),f317(f317(f74(a1),x69402),f317(f73(a1),x69403)))) % 112.26/112.10 [7008]E(x70081,f2(a1))+E(x70082,f2(a1))+~P1(f317(f45(x70082,x70082),f317(f317(f242(a1,a1),x70083),x70081))) % 112.26/112.10 [7009]E(x70091,f72(a1))+E(x70092,f2(a1))+~P1(f317(f45(x70092,x70092),f317(f317(f242(a1,a1),x70091),x70093))) % 112.26/112.10 [7024]P1(f317(x70241,x70242))+P1(f317(f317(f225(a899),f392(x70241,x70243)),x70243))+~P1(f317(f317(f319(a899),x70242),f317(f292(a899,f2(a899)),x70243))) % 112.26/112.10 [7047]~P1(f317(x70471,f632(x70473,x70472,x70471)))+~P1(f317(x70471,f2(a899)))+P1(f317(x70471,f317(f317(f3(a899),x70472),x70473))) % 112.26/112.10 [7048]~P1(f317(x70481,f654(x70483,x70482,x70481)))+~P1(f317(x70481,f2(a899)))+P1(f317(x70481,f317(f317(f3(a899),x70482),x70483))) % 112.26/112.10 [7049]~P1(f317(x70491,f345(x70493,x70492,x70491)))+~P1(f317(x70491,f2(a899)))+P1(f317(x70491,f317(f317(f31(a899),x70492),x70493))) % 112.26/112.10 [7069]~P1(f317(x70691,x70693))+P1(f317(f317(f225(a899),f399(x70691,x70692)),x70692))+~P1(f317(f317(f319(a899),x70693),f317(f292(a899,f2(a899)),x70692))) % 112.26/112.10 [7070]E(f317(f317(f3(a899),f317(f317(f3(a899),x70701),x70702)),f317(f317(f3(a899),x70703),x70702)),f317(f317(f3(a899),x70701),x70703))+~P1(f317(f317(f224(a899),x70702),x70701))+~P1(f317(f317(f224(a899),x70702),x70703)) % 112.26/112.10 [7106]~P79(x71061)+~P1(f317(f317(f224(x71061),f317(f73(x71061),x71063)),x71062))+P1(f317(f317(f224(x71061),f317(f73(x71061),x71062)),x71063)) % 112.26/112.10 [7108]~P86(x71081)+~P1(f317(f317(f224(x71081),f317(f70(x71081),x71082)),x71083))+P1(f317(f317(f224(x71081),f317(f73(x71081),x71082)),x71083)) % 112.26/112.10 [7110]~P79(x71101)+~P1(f317(f317(f225(x71101),f317(f73(x71101),x71103)),x71102))+P1(f317(f317(f225(x71101),f317(f73(x71101),x71102)),x71103)) % 112.26/112.10 [7111]~P112(x71111)+~P1(f317(f317(f225(x71111),f317(f70(x71111),x71112)),x71113))+P1(f317(f317(f225(x71111),f317(f73(x71111),x71112)),x71113)) % 112.26/112.10 [7143]~P1(f317(x71433,f632(x71432,x71431,x71433)))+P1(f317(f317(f225(a899),x71431),x71432))+P1(f317(x71433,f317(f317(f3(a899),x71431),x71432))) % 112.26/112.10 [7144]~P1(f317(x71443,f654(x71442,x71441,x71443)))+P1(f317(f317(f225(a899),x71441),x71442))+P1(f317(x71443,f317(f317(f3(a899),x71441),x71442))) % 112.26/112.10 [7196]~E(f419(x71963,x71962,x71961),f420(x71963,x71962,x71961))+E(f317(f317(f92(f906(x71961,a895)),x71962),f32(f906(x71961,a895),x71963)),f178(f906(x71961,a895)))+P1(f317(f317(f319(f906(x71961,a895)),x71962),x71963)) % 112.26/112.10 [7204]~P1(f317(f29(x72041),x72043))+P1(f317(f29(x72041),f33(f906(x72041,a895),x72042)))+~P1(f317(f317(f319(f906(x72041,a895)),x72043),x72042)) % 112.26/112.10 [7264]~P108(x72641)+E(f317(f317(f91(f906(x72641,a895)),f317(f292(x72641,x72642),x72643)),f317(f317(f299(x72641),x72643),f178(f906(x72641,a895)))),f293(x72641,x72642,x72643))+~P1(f317(f317(f224(x72641),x72642),x72643)) % 112.26/112.10 [7267]E(x72671,f2(a899))+P1(f317(f317(f225(a899),f347(x72671,x72673,x72672)),x72671))+P1(f317(x72672,f317(f317(f31(a899),x72673),x72671))) % 112.26/112.10 [7296]P1(f317(f317(f225(a899),f317(f179(f900(x72961)),x72962)),f765(x72963,x72961)))+~P1(f317(f29(f900(x72961)),x72963))+~P1(f317(f317(f319(f900(x72961)),x72962),x72963)) % 112.26/112.10 [7302]E(x73021,x73022)+~P1(f317(f317(f224(f906(x73023,a895)),x73021),x73022))+P1(f317(f317(f225(f906(x73023,a895)),x73021),x73022)) % 112.26/112.10 [7313]E(x73131,x73132)+~E(f317(f179(f900(x73133)),x73131),f317(f179(f900(x73133)),x73132))+P1(f317(f317(f225(a899),f633(x73133,x73131,x73132)),f317(f179(f900(x73133)),x73132))) % 112.26/112.10 [7362]P8(x73621,x73622,x73623)+~E(f317(f254(x73621,x73621),x73623),x73622)+~E(f317(f317(f279(x73621,x73621,x73621),f317(f276(x73621,x73621),x73623)),x73623),x73623) % 112.26/112.10 [7442]~P1(f317(x74421,f2(a899)))+P1(f317(f317(f225(a899),f347(x74423,x74422,x74421)),x74423))+P1(f317(x74421,f317(f317(f31(a899),x74422),x74423))) % 112.26/112.10 [7452]~P108(x74521)+E(f317(f317(f91(f906(x74521,a895)),f296(x74521,x74522,x74523)),f317(f317(f299(x74521),x74523),f178(f906(x74521,a895)))),f295(x74521,x74522,x74523))+~P1(f317(f317(f225(x74521),x74522),x74523)) % 112.26/112.10 [7544]~P1(f317(f29(x75441),x75443))+P1(f317(f317(f224(a899),f317(f30(x75441),x75442)),f317(f30(x75441),x75443)))+~P1(f317(f317(f224(f906(x75441,a895)),x75442),x75443)) % 112.26/112.10 [7545]~P1(f317(f29(x75451),x75453))+P1(f317(f317(f225(a899),f317(f30(x75451),x75452)),f317(f30(x75451),x75453)))+~P1(f317(f317(f225(f906(x75451,a895)),x75452),x75453)) % 112.26/112.10 [7678]E(x76781,x76782)+~P1(f317(f317(f224(f906(x76783,a895)),x76782),x76781))+~P1(f317(f317(f224(f906(x76783,a895)),x76781),x76782)) % 112.26/112.10 [7681]~P108(x76811)+P13(x76811,x76812)+~P13(x76811,f317(f317(f138(x76811,x76811,f7(x76811)),x76813),x76812)) % 112.26/112.10 [7752]~P1(f317(f317(f225(a899),x77523),x77522))+~P1(f317(f317(f225(a899),x77523),x77521))+P1(f317(f317(f225(a899),f317(f317(f3(a899),x77521),x77522)),f317(f317(f3(a899),x77521),x77523))) % 112.26/112.10 [7753]~P1(f317(f317(f224(a899),x77532),x77531))+~P1(f317(f317(f225(a899),x77531),x77533))+P1(f317(f317(f225(a899),f317(f317(f3(a899),x77531),x77532)),f317(f317(f3(a899),x77533),x77532))) % 112.26/112.10 [7768]~P1(f317(f317(f225(a1),x77682),f2(a1)))+~P1(f317(f317(f224(a1),x77683),x77681))+P1(f317(f317(f224(a1),f317(f317(f31(a1),x77681),x77682)),f317(f317(f31(a1),x77683),x77682))) % 112.26/112.10 [7785]~P1(f317(f317(f225(a899),f2(a899)),x77853))+~P1(f317(f317(f224(a899),x77853),x77852))+P1(f317(f317(f224(a899),f317(f317(f31(a899),x77851),x77852)),f317(f317(f31(a899),x77851),x77853))) % 112.26/112.10 [7786]~P1(f317(f317(f225(a1),f2(a1)),x77862))+~P1(f317(f317(f224(a1),x77861),x77863))+P1(f317(f317(f224(a1),f317(f317(f31(a1),x77861),x77862)),f317(f317(f31(a1),x77863),x77862))) % 112.26/112.10 [7790]~P1(f317(f317(f225(a899),f2(a899)),x77902))+~P1(f317(f317(f225(a899),x77901),x77903))+P1(f317(f317(f225(a899),f317(f317(f75(a899),x77901),x77902)),f317(f317(f75(a899),x77903),x77902))) % 112.26/112.10 [7791]~P1(f317(f317(f225(a899),f2(a899)),x77911))+~P1(f317(f317(f225(a899),x77912),x77913))+P1(f317(f317(f225(a899),f317(f317(f75(a899),x77911),x77912)),f317(f317(f75(a899),x77911),x77913))) % 112.26/112.10 [7792]~P1(f317(f317(f225(a1),f2(a1)),x77921))+~P1(f317(f317(f225(a1),x77922),x77923))+P1(f317(f317(f225(a1),f317(f317(f75(a1),x77921),x77922)),f317(f317(f75(a1),x77921),x77923))) % 112.26/112.10 [7841]E(x78411,f2(a899))+E(f317(f317(f74(a899),f317(f317(f75(a899),x78411),f345(x78411,x78412,x78413))),f347(x78411,x78412,x78413)),x78412)+P1(f317(x78413,f317(f317(f31(a899),x78412),x78411))) % 112.26/112.10 [7901]E(f317(f317(f74(a899),f317(f317(f75(a899),x79011),f345(x79011,x79012,x79013))),f347(x79011,x79012,x79013)),x79012)+~P1(f317(x79013,f2(a899)))+P1(f317(x79013,f317(f317(f31(a899),x79012),x79011))) % 112.26/112.10 [7919]~P1(f317(f29(x79191),x79193))+P1(f317(f317(f319(x79191),f588(x79192,x79193,x79191)),x79193))+P1(f317(f317(f225(a899),f2(a899)),f317(f317(f11(x79191,a899),x79192),x79193))) % 112.26/112.10 [7920]~P1(f317(f29(x79201),x79203))+P1(f317(f317(f319(x79201),f849(x79202,x79203,x79201)),x79203))+P1(f317(f317(f225(a899),f2(a899)),f317(f317(f11(x79201,a899),x79202),x79203))) % 112.26/112.10 [8020]E(x80201,f2(a899))+P1(f317(f317(f277(a899),x80202),x80203))+~P1(f317(f317(f277(a899),f317(f317(f75(a899),x80201),x80202)),f317(f317(f75(a899),x80201),x80203))) % 112.26/112.10 [8210]E(x82101,f178(f906(x82102,a895)))+E(x82101,f317(f317(f299(x82102),x82103),f178(f906(x82102,a895))))+~P1(f317(f317(f224(f906(x82102,a895)),x82101),f317(f317(f299(x82102),x82103),f178(f906(x82102,a895))))) % 112.26/112.10 [8246]~P1(f317(f317(f225(a899),f72(a899)),x82463))+P1(f317(f317(f224(a899),x82461),x82462))+~P1(f317(f317(f277(a899),f317(f317(f234(a899),x82463),x82461)),f317(f317(f234(a899),x82463),x82462))) % 112.26/112.10 [8248]~P1(f317(f317(f225(a899),f2(a899)),x82483))+P1(f317(f317(f224(a899),x82481),x82482))+~P1(f317(f317(f224(a899),f317(f317(f75(a899),x82483),x82481)),f317(f317(f75(a899),x82483),x82482))) % 112.26/112.10 [8249]~P1(f317(f317(f225(a899),f2(a899)),x82493))+P1(f317(f317(f224(a899),x82491),x82492))+~P1(f317(f317(f224(a899),f317(f317(f75(a899),x82491),x82493)),f317(f317(f75(a899),x82492),x82493))) % 112.26/112.10 [8251]~P1(f317(f317(f225(a899),f2(a899)),x82513))+P1(f317(f317(f225(a899),x82511),x82512))+~P1(f317(f317(f225(a899),f317(f317(f234(a899),x82513),x82511)),f317(f317(f234(a899),x82513),x82512))) % 112.26/112.10 [8253]~P1(f317(f317(f225(a899),f2(a899)),x82533))+P1(f317(f317(f277(a899),x82531),x82532))+~P1(f317(f317(f277(a899),f317(f317(f75(a899),x82533),x82531)),f317(f317(f75(a899),x82533),x82532))) % 112.26/112.10 [8292]~E(f317(f317(f92(f906(x82921,a895)),f420(x82923,x82922,x82921)),f419(x82923,x82922,x82921)),f178(f906(x82921,a895)))+E(f317(f317(f92(f906(x82921,a895)),x82922),f32(f906(x82921,a895),x82923)),f178(f906(x82921,a895)))+P1(f317(f317(f319(f906(x82921,a895)),x82922),x82923)) % 112.26/112.10 [8306]E(x83061,f103(x83062))+~E(f317(f132(f900(x83062),f900(x83062),f124(x83062),f103(x83062)),x83063),f103(x83062))+~P1(f317(f317(f319(f900(x83062)),x83061),f317(f162(f900(x83062)),x83063))) % 112.26/112.10 [8362]E(x83621,f178(f906(f906(x83622,a895),a895)))+P1(f317(f317(f319(f906(x83622,a895)),f437(x83623,x83621,x83622)),x83621))+P1(f317(f317(f224(f906(x83622,a895)),f33(f906(x83622,a895),x83621)),x83623)) % 112.26/112.10 [8368]~P69(x83681)+~P75(x83681)+E(f317(f317(f8(a1,x83681),f317(f317(f10(a899,x83681,a1),x83682),a95)),f317(f300(a899,a1,f90(a1)),x83683)),f317(f317(f8(a899,x83681),x83682),x83683)) % 112.26/112.10 [8369]~P69(x83691)+~P75(x83691)+E(f317(f317(f11(a1,x83691),f317(f317(f10(a899,x83691,a1),x83692),a95)),f317(f300(a899,a1,f90(a1)),x83693)),f317(f317(f11(a899,x83691),x83692),x83693)) % 112.26/112.10 [8411]~P1(f317(f29(x84111),x84113))+~P1(f317(f317(f225(a899),f2(a899)),f317(x84112,f588(x84112,x84113,x84111))))+P1(f317(f317(f225(a899),f2(a899)),f317(f317(f11(x84111,a899),x84112),x84113))) % 112.26/112.10 [8412]~P1(f317(f29(x84121),x84123))+~P1(f317(f317(f225(a899),f2(a899)),f317(x84122,f849(x84122,x84123,x84121))))+P1(f317(f317(f225(a899),f2(a899)),f317(f317(f11(x84121,a899),x84122),x84123))) % 112.26/112.10 [8448]~P62(x84482)+E(x84481,f72(x84482))+E(f317(f317(f281(x84482),f317(f317(f3(x84482),f317(f317(f234(x84482),x84481),x84483)),f72(x84482))),f317(f317(f3(x84482),x84481),f72(x84482))),f317(f317(f8(a899,x84482),f317(f234(x84482),x84481)),f317(f292(a899,f2(a899)),x84483))) % 112.26/112.10 [8506]E(x85061,f2(a899))+~P1(f317(x85063,f317(f317(f31(a899),x85062),x85061)))+P1(f317(f317(f225(a899),x85062),f317(f317(f75(a899),x85061),f317(a102,f344(x85061,x85062,x85063))))) % 112.26/112.10 [8526]P1(f317(x85261,f2(a899)))+~P1(f317(x85261,f317(f317(f31(a899),x85262),x85263)))+P1(f317(f317(f225(a899),x85262),f317(f317(f75(a899),x85263),f317(a102,f344(x85263,x85262,x85261))))) % 112.26/112.10 [8564]E(x85641,f2(a899))+~P1(f317(x85643,f317(f317(f31(a899),x85642),x85641)))+P1(f317(f317(f224(a899),f317(f317(f75(a899),x85641),f344(x85641,x85642,x85643))),x85642)) % 112.26/112.10 [8595]P1(f317(x85951,f2(a899)))+~P1(f317(x85951,f317(f317(f31(a899),x85953),x85952)))+P1(f317(f317(f224(a899),f317(f317(f75(a899),x85952),f344(x85952,x85953,x85951))),x85953)) % 112.26/112.10 [8603]~P108(x86031)+E(f317(f317(f138(x86031,x86031,f7(x86031)),x86032),x86033),f139(x86031,x86031,f7(x86031),x86032,x86033))+P1(f317(f317(f319(x86031),x86032),f317(f162(x86031),x86033))) % 112.26/112.10 [8638]~E(f317(x86383,f572(x86382,x86383,x86381)),f317(x86383,f574(x86382,x86383,x86381)))+~P59(x86381,f317(x86383,f573(x86382,x86383,x86381)))+P59(x86381,f317(f317(f36(x86382,f906(x86381,f906(x86381,a895))),f232(f906(x86382,a895))),x86383)) % 112.26/112.10 [8647]E(x86471,f178(f906(f906(x86472,a895),a895)))+~P1(f317(f317(f224(f906(x86472,a895)),f437(x86473,x86471,x86472)),x86473))+P1(f317(f317(f224(f906(x86472,a895)),f33(f906(x86472,a895),x86471)),x86473)) % 112.26/112.10 [8707]~P64(x87071)+~P1(f317(f317(f225(x87071),x87072),x87073))+P1(f317(f317(f225(x87071),x87072),f317(f317(f281(x87071),f317(f317(f74(x87071),x87072),x87073)),f317(f317(f74(x87071),f72(x87071)),f72(x87071))))) % 112.26/112.10 [8765]~P1(f317(f317(x87651,f447(x87651,x87653,x87652)),f451(x87651,x87653,x87652)))+P1(f317(f317(x87651,x87652),x87653))+~P1(f317(f305(f905(a1,a1),a48),f317(f317(f242(a1,a1),x87652),x87653))) % 112.26/112.10 [8766]~P1(f317(f317(x87661,f454(x87661,x87663,x87662)),f455(x87661,x87663,x87662)))+P1(f317(f317(x87661,x87662),x87663))+~P1(f317(f305(f905(a1,a1),a54),f317(f317(f242(a1,a1),x87662),x87663))) % 112.26/112.10 [8767]~P1(f317(f317(x87671,f456(x87671,x87673,x87672)),f458(x87671,x87673,x87672)))+P1(f317(f317(x87671,x87672),x87673))+~P1(f317(f305(f905(a1,a1),a211),f317(f317(f242(a1,a1),x87672),x87673))) % 112.26/112.10 [8768]~P1(f317(f317(x87681,f459(x87681,x87683,x87682)),f460(x87681,x87683,x87682)))+P1(f317(f317(x87681,x87682),x87683))+~P1(f317(f305(f905(a899,a899),a209),f317(f317(f242(a899,a899),x87682),x87683))) % 112.26/112.10 [8769]~P1(f317(f317(x87691,f657(x87691,x87693,x87692)),f659(x87691,x87693,x87692)))+P1(f317(f317(x87691,x87692),x87693))+~P1(f317(f305(f905(a1,a1),a172),f317(f317(f242(a1,a1),x87692),x87693))) % 112.26/112.10 [8770]~P1(f317(f317(x87701,f753(x87701,x87703,x87702)),f754(x87701,x87703,x87702)))+P1(f317(f317(x87701,x87702),x87703))+~P1(f317(f305(f905(a1,a1),a123),f317(f317(f242(a1,a1),x87702),x87703))) % 112.26/112.10 [9043]P1(f317(f317(x90431,x90432),x90433))+P1(f317(f305(f905(a899,a899),a209),f317(f317(f242(a899,a899),f459(x90431,x90433,x90432)),f460(x90431,x90433,x90432))))+~P1(f317(f305(f905(a899,a899),a209),f317(f317(f242(a899,a899),x90432),x90433))) % 112.26/112.10 [9044]P1(f317(f317(x90441,x90442),x90443))+P1(f317(f305(f905(a1,a1),a48),f317(f317(f242(a1,a1),f447(x90441,x90443,x90442)),f451(x90441,x90443,x90442))))+~P1(f317(f305(f905(a1,a1),a48),f317(f317(f242(a1,a1),x90442),x90443))) % 112.26/112.10 [9045]P1(f317(f317(x90451,x90452),x90453))+P1(f317(f305(f905(a1,a1),a54),f317(f317(f242(a1,a1),f454(x90451,x90453,x90452)),f455(x90451,x90453,x90452))))+~P1(f317(f305(f905(a1,a1),a54),f317(f317(f242(a1,a1),x90452),x90453))) % 112.26/112.10 [9046]P1(f317(f317(x90461,x90462),x90463))+P1(f317(f305(f905(a1,a1),a211),f317(f317(f242(a1,a1),f456(x90461,x90463,x90462)),f458(x90461,x90463,x90462))))+~P1(f317(f305(f905(a1,a1),a211),f317(f317(f242(a1,a1),x90462),x90463))) % 112.26/112.10 [9047]P1(f317(f317(x90471,x90472),x90473))+P1(f317(f305(f905(a1,a1),a172),f317(f317(f242(a1,a1),f657(x90471,x90473,x90472)),f659(x90471,x90473,x90472))))+~P1(f317(f305(f905(a1,a1),a172),f317(f317(f242(a1,a1),x90472),x90473))) % 112.26/112.10 [9048]P1(f317(f317(x90481,x90482),x90483))+P1(f317(f305(f905(a1,a1),a123),f317(f317(f242(a1,a1),f753(x90481,x90483,x90482)),f754(x90481,x90483,x90482))))+~P1(f317(f305(f905(a1,a1),a123),f317(f317(f242(a1,a1),x90482),x90483))) % 112.26/112.10 [9383]~P1(f317(f29(x93831),x93833))+P1(f317(f317(f319(f905(f906(x93831,a895),f906(x93831,a895))),f317(f317(f242(f906(x93831,a895),f906(x93831,a895)),x93832),x93833)),f304(x93831)))+~P1(f317(f317(f225(f906(x93831,a895)),x93832),x93833)) % 112.26/112.10 [9459]~P59(x94591,f317(x94593,f573(x94592,x94593,x94591)))+P59(x94591,f317(f317(f36(x94592,f906(x94591,f906(x94591,a895))),f232(f906(x94592,a895))),x94593))+~E(f317(f317(f92(f906(x94591,a895)),f239(x94591,x94591,f317(x94593,f572(x94592,x94593,x94591)))),f240(x94591,x94591,f317(x94593,f574(x94592,x94593,x94591)))),f178(f906(x94591,a895))) % 112.26/112.10 [9670]P52(x96701,x96702,x96703)+P1(f317(f317(f319(f905(x96701,x96701)),f560(x96703,x96702,x96701)),x96703))+~P1(f317(f317(f319(f905(x96701,x96701)),f317(f317(f242(x96701,x96701),f559(x96703,x96702,x96701)),f559(x96703,x96702,x96701))),x96703)) % 112.26/112.10 [10263]P52(x102631,x102632,x102633)+~P1(f317(f317(f247(x102631,x102631,a895),f317(f317(f9(x102631,f906(x102631,a895),f906(x102631,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x102631,a895),f906(x102631,a895)),x102631),f10(a895,a895,x102631)),f317(f317(f10(a895,f906(a895,a895),x102631),a315),f317(f317(f9(x102631,f906(x102631,a895),a895),f319(x102631)),x102632)))),f317(f317(f9(x102631,f906(x102631,a895),a895),f319(x102631)),x102632))),f560(x102633,x102632,x102631)))+~P1(f317(f317(f319(f905(x102631,x102631)),f317(f317(f242(x102631,x102631),f559(x102633,x102632,x102631)),f559(x102633,x102632,x102631))),x102633)) % 112.26/112.10 [5731]~P3(x57312)+E(x57311,f2(x57312))+E(f317(f317(f31(x57312),f317(f317(f75(x57312),x57313),x57311)),x57311),x57313) % 112.26/112.10 [5732]~P3(x57322)+E(x57321,f2(x57322))+E(f317(f317(f31(x57322),f317(f317(f75(x57322),x57321),x57323)),x57321),x57323) % 112.26/112.10 [6395]~P3(x63951)+E(f317(f317(f75(x63951),f317(f317(f31(x63951),x63952),x63953)),x63953),x63952)+~P1(f317(f317(f277(x63951),x63953),x63952)) % 112.26/112.10 [6559]~P69(x65591)+~E(f317(x65592,f2(a899)),f2(x65591))+E(f317(f317(f8(a899,x65591),x65592),f317(f292(a899,f317(a102,f2(a899))),x65593)),f317(f317(f8(a899,x65591),x65592),f317(f292(a899,f2(a899)),x65593))) % 112.26/112.10 [6697]~P3(x66972)+E(x66971,f2(x66972))+E(f317(f317(f31(x66972),f317(f317(f74(x66972),x66973),x66971)),x66971),f317(f317(f74(x66972),f317(f317(f31(x66972),x66973),x66971)),f72(x66972))) % 112.26/112.10 [6698]~P3(x66982)+E(x66981,f2(x66982))+E(f317(f317(f31(x66982),f317(f317(f74(x66982),x66981),x66983)),x66981),f317(f317(f74(x66982),f317(f317(f31(x66982),x66983),x66981)),f72(x66982))) % 112.26/112.10 [6923]~P1(f317(x69233,f2(a1)))+P1(f317(f317(f224(a899),x69231),x69232))+P1(f317(x69233,f317(f90(a1),f317(f317(f3(a899),x69232),x69231)))) % 112.26/112.10 [7030]P1(f317(f317(f225(a899),x70302),x70301))+P1(f317(f317(f224(a899),x70301),x70302))+P1(f317(x70303,f317(f90(a1),f317(f317(f3(a899),x70302),x70301)))) % 112.26/112.10 [7104]E(f317(f317(f74(a899),f317(f94(a899),x71041)),f317(f317(f74(a899),f317(f94(a899),x71042)),x71043)),f317(f317(f74(a899),f317(f94(a899),x71041)),x71043))+P1(f317(a183,f317(f94(a1),x71041)))+~P1(f317(a183,f317(f94(a1),x71042))) % 112.26/112.10 [7183]~E(x71832,f317(f317(f31(a899),x71833),x71831))+~P1(f317(f317(f225(a899),f2(a899)),x71831))+P1(f317(f317(f224(a899),f317(f317(f75(a899),x71831),x71832)),x71833)) % 112.26/112.10 [7300]~P1(f317(f29(x73001),x73003))+~P1(f317(f29(x73001),x73002))+P1(f317(f29(x73001),f317(f317(f91(f906(x73001,a895)),x73002),x73003))) % 112.26/112.10 [7347]~P37(x73471,x73473)+~P37(x73471,x73472)+P37(x73471,f317(f317(f92(f906(f905(x73471,x73471),a895)),x73472),x73473)) % 112.26/112.10 [7348]~P51(x73481,x73483)+~P51(x73481,x73482)+P51(x73481,f317(f317(f91(f906(f905(x73481,x73481),a895)),x73482),x73483)) % 112.26/112.10 [7349]~P51(x73491,x73493)+~P51(x73491,x73492)+P51(x73491,f317(f317(f92(f906(f905(x73491,x73491),a895)),x73492),x73493)) % 112.26/112.10 [7592]~P108(x75921)+~P1(f317(f29(x75921),x75922))+E(f129(x75921,f317(f317(f3(f906(x75921,a895)),x75922),f317(f317(f299(x75921),x75923),f178(f906(x75921,a895))))),f160(x75921,x75923,f129(x75921,x75922))) % 112.26/112.10 [7657]P1(f317(x76571,f2(a1)))+~P1(f317(f317(f225(a899),x76572),x76573))+~P1(f317(x76571,f317(f90(a1),f317(f317(f3(a899),x76572),x76573)))) % 112.26/112.10 [7675]~P1(f317(f29(x76751),x76752))+E(f317(f30(x76751),f317(f317(f3(f906(x76751,a895)),x76752),f317(f317(f299(x76751),x76753),f178(f906(x76751,a895))))),f317(f30(x76751),x76752))+P1(f317(f317(f319(x76751),x76753),x76752)) % 112.26/112.10 [7808]~P126(x78081)+~P1(f317(f317(f225(x78081),f72(x78081)),x78082))+P1(f317(f317(f225(x78081),f72(x78081)),f317(f317(f75(x78081),x78082),f317(f317(f234(x78081),x78082),x78083)))) % 112.26/112.10 [7851]~P1(f317(f29(x78511),x78513))+E(f317(f317(f3(a899),f317(f30(x78511),x78512)),f317(f30(x78511),x78513)),f317(f30(x78511),f317(f317(f3(f906(x78511,a895)),x78512),x78513)))+~P1(f317(f317(f224(f906(x78511,a895)),x78513),x78512)) % 112.26/112.10 [7909]~P1(f317(f317(f224(a899),x79092),x79093))+~P1(f317(f317(f224(a899),x79091),f317(f317(f3(a899),x79093),x79092)))+P1(f317(f317(f224(a899),f317(f317(f74(a899),x79091),x79092)),x79093)) % 112.26/112.10 [7963]P1(f317(f29(x79631),x79632))+~P1(f317(f29(x79631),x79633))+~P1(f317(f29(x79631),f317(f317(f3(f906(x79631,a895)),x79632),x79633))) % 112.26/112.10 [7969]~P1(f317(f29(x79691),x79692))+E(f317(f30(x79691),f317(f317(f3(f906(x79691,a895)),x79692),f317(f317(f299(x79691),x79693),f178(f906(x79691,a895))))),f317(f317(f3(a899),f317(f30(x79691),x79692)),f72(a899)))+~P1(f317(f317(f319(x79691),x79693),x79692)) % 112.26/112.10 [8045]P59(x80451,x80452)+~P59(x80451,x80453)+~P1(f317(f317(f224(f906(x80451,f906(x80451,a895))),x80452),x80453)) % 112.26/112.10 [8085]~P1(f317(f317(f224(a899),x80853),x80852))+P1(f317(f317(f224(a899),x80851),f317(f317(f3(a899),x80852),x80853)))+~P1(f317(f317(f224(a899),f317(f317(f74(a899),x80851),x80853)),x80852)) % 112.26/112.10 [8103]P36(x81031,x81032)+~P36(x81031,x81033)+~P1(f317(f317(f224(f906(f905(x81031,x81031),a895)),x81032),x81033)) % 112.26/112.10 [8104]P57(x81041,x81042)+~P57(x81041,x81043)+~P1(f317(f317(f224(f906(f905(x81041,x81041),a895)),x81042),x81043)) % 112.26/112.10 [8105]P38(x81051,x81052)+~P38(x81051,x81053)+~P1(f317(f317(f224(f906(f905(x81051,x81051),a895)),x81052),x81053)) % 112.26/112.10 [8339]~P126(x83391)+~P1(f317(f317(f225(x83391),f72(x83391)),x83392))+P1(f317(f317(f225(x83391),f317(f317(f234(x83391),x83392),x83393)),f317(f317(f75(x83391),x83392),f317(f317(f234(x83391),x83392),x83393)))) % 112.26/112.10 [8430]~P1(f317(x84301,f2(a1)))+~P1(f317(x84301,f317(f317(f3(a1),f317(f90(a1),x84302)),f317(f90(a1),x84303))))+P1(f317(x84301,f317(f90(a1),f317(f317(f3(a899),x84302),x84303)))) % 112.26/112.10 [8445]~P1(f317(f317(f224(a899),x84453),x84452))+P1(f317(x84451,f317(f317(f3(a1),f317(f90(a1),x84452)),f317(f90(a1),x84453))))+~P1(f317(x84451,f317(f90(a1),f317(f317(f3(a899),x84452),x84453)))) % 112.26/112.10 [8465]P1(f317(f317(f225(a899),x84651),x84652))+~P1(f317(x84653,f317(f317(f3(a1),f317(f90(a1),x84651)),f317(f90(a1),x84652))))+P1(f317(x84653,f317(f90(a1),f317(f317(f3(a899),x84651),x84652)))) % 112.26/112.10 [8519]~P127(x85192)+E(x85191,f2(x85192))+P1(f317(f317(f225(x85192),f2(x85192)),f317(f317(f74(x85192),f317(f317(f75(x85192),x85193),x85193)),f317(f317(f75(x85192),x85191),x85191)))) % 112.26/112.10 [8520]~P127(x85202)+E(x85201,f2(x85202))+P1(f317(f317(f225(x85202),f2(x85202)),f317(f317(f74(x85202),f317(f317(f75(x85202),x85201),x85201)),f317(f317(f75(x85202),x85203),x85203)))) % 112.26/112.10 [8620]~P1(f317(f317(f225(a899),f2(a899)),x86201))+~P1(f317(f317(f225(a1),x86202),x86203))+P1(f317(f317(f225(a1),f317(f317(f75(a1),f317(f90(a1),x86201)),x86202)),f317(f317(f75(a1),f317(f90(a1),x86201)),x86203))) % 112.26/112.10 [8676]E(f317(f317(f92(f906(x86761,a895)),x86762),f32(f906(x86761,a895),x86763)),f178(f906(x86761,a895)))+P1(f317(f317(f319(f906(x86761,a895)),x86762),x86763))+P1(f317(f317(f319(f906(x86761,a895)),f420(x86763,x86762,x86761)),f317(f317(f299(f906(x86761,a895)),x86762),x86763))) % 112.26/112.10 [8677]E(f317(f317(f92(f906(x86771,a895)),x86772),f32(f906(x86771,a895),x86773)),f178(f906(x86771,a895)))+P1(f317(f317(f319(f906(x86771,a895)),x86772),x86773))+P1(f317(f317(f319(f906(x86771,a895)),f419(x86773,x86772,x86771)),f317(f317(f299(f906(x86771,a895)),x86772),x86773))) % 112.26/112.10 [8706]E(x87061,x87062)+~E(f317(f179(f900(x87063)),x87061),f317(f179(f900(x87063)),x87062))+P1(f317(f317(f319(f905(x87063,x87063)),f645(x87063,x87061,x87062)),f317(f162(f905(x87063,x87063)),f317(f317(f171(x87063,x87063),x87062),x87061)))) % 112.26/112.10 [8956]E(f297(x89561,x89562),f297(x89561,x89563))+~P1(f317(f317(f224(f906(f905(x89561,x89561),a895)),x89563),f297(x89561,x89562)))+~P1(f317(f317(f224(f906(f905(x89561,x89561),a895)),x89562),x89563)) % 112.26/112.10 [9023]~P52(x90231,f232(f906(x90231,a895)),x90233)+P1(f317(f317(f224(f906(f905(f900(x90231),f900(x90231)),a895)),f147(x90231,x90232)),f148(x90231,x90233)))+~P1(f317(f317(f224(f906(f905(x90231,x90231),a895)),x90232),x90233)) % 112.26/112.10 [9218]P36(x92181,x92182)+~P1(f317(f317(f319(x92181),x92183),f586(x92182,x92181)))+P1(f317(f317(f319(f905(x92181,x92181)),f317(f317(f242(x92181,x92181),f597(x92182,x92181,x92183)),x92183)),x92182)) % 112.26/112.10 [9253]~P1(f317(f29(x92531),x92532))+P1(f317(f29(f906(x92531,a895)),f317(f317(f56(x92531),x92532),x92533)))+~P1(f317(f317(f224(f906(f905(x92531,x92531),a895)),x92533),f317(f317(f244(x92531,x92531),x92532),f317(f18(f906(x92531,a895),x92531),x92532)))) % 112.26/112.10 [9289]P52(x92891,x92892,x92893)+P1(f317(f317(f319(x92891),f547(x92893,x92892,x92891)),x92892))+~P1(f317(f317(f224(f906(f905(x92891,x92891),a895)),x92893),f317(f317(f244(x92891,x92891),x92892),f317(f18(f906(x92891,a895),x92891),x92892)))) % 112.26/112.10 [9290]P52(x92901,x92902,x92903)+P1(f317(f317(f319(x92901),f553(x92902,x92903,x92901)),x92902))+~P1(f317(f317(f224(f906(f905(x92901,x92901),a895)),x92903),f317(f317(f244(x92901,x92901),x92902),f317(f18(f906(x92901,a895),x92901),x92902)))) % 112.26/112.10 [9325]~P64(x93251)+~P1(f317(f317(f225(x93251),x93252),x93253))+P1(f317(f317(f225(x93251),f317(f317(f281(x93251),f317(f317(f74(x93251),x93252),x93253)),f317(f317(f74(x93251),f72(x93251)),f72(x93251)))),x93253)) % 112.26/112.10 [9356]~P63(x93561)+P1(f317(f317(f224(x93561),x93562),x93563))+~P1(f317(f317(f224(x93561),f317(f317(f75(x93561),f836(x93563,x93562,x93561)),x93562)),x93563)) % 112.26/112.10 [9494]E(f317(f179(f900(f900(x94941))),f317(f126(f900(x94941),f317(f317(f10(a899,a895,f900(x94941)),f317(f225(a899),x94942)),f179(f900(x94941)))),f169(x94941,x94943))),f317(f179(f900(x94941)),f317(f317(f154(f900(x94941)),x94943),x94942)))+~P13(a899,f317(f158(a899),f317(f317(f144(f900(x94941),a899),f179(f900(x94941))),x94943)))+~P1(f317(f317(f225(a899),x94942),f317(f179(f900(f900(x94941))),x94943))) % 112.26/112.10 [9617]~P36(x96171,x96172)+P26(x96171,f317(f317(f242(f906(f905(x96171,x96171),a895),f906(f905(x96171,x96171),a895)),x96172),x96173))+~P1(f317(f317(f224(f906(f905(x96171,x96171),a895)),f317(f317(f279(x96171,x96171,x96171),x96172),x96173)),x96172)) % 112.26/112.10 [9622]E(f317(f317(f144(f900(x96221),x96221),f317(f317(f9(f900(x96221),a899,x96221),f154(x96221)),x96222)),f317(f126(f900(x96221),f317(f317(f10(a899,a895,f900(x96221)),f317(f225(a899),x96222)),f179(f900(x96221)))),f169(x96221,x96223))),f317(f317(f154(f900(x96221)),x96223),x96222))+~P13(a899,f317(f158(a899),f317(f317(f144(f900(x96221),a899),f179(f900(x96221))),x96223)))+~P1(f317(f317(f225(a899),x96222),f317(f179(f900(f900(x96221))),x96223))) % 112.26/112.10 [9758]P52(x97581,x97582,x97583)+~P1(f317(f317(f319(f905(x97581,x97581)),f317(f317(f242(x97581,x97581),f547(x97583,x97582,x97581)),f547(x97583,x97582,x97581))),x97583))+~P1(f317(f317(f224(f906(f905(x97581,x97581),a895)),x97583),f317(f317(f244(x97581,x97581),x97582),f317(f18(f906(x97581,a895),x97581),x97582)))) % 112.26/112.10 [9759]P52(x97591,x97592,x97593)+~P1(f317(f317(f319(f905(x97591,x97591)),f317(f317(f242(x97591,x97591),f553(x97592,x97593,x97591)),f553(x97592,x97593,x97591))),x97593))+~P1(f317(f317(f224(f906(f905(x97591,x97591),a895)),x97593),f317(f317(f244(x97591,x97591),x97592),f317(f18(f906(x97591,a895),x97591),x97592)))) % 112.26/112.10 [9929]~P141(x99291)+~P125(x99291)+E(f317(f317(f281(x99291),f317(f93(x99291),f317(f317(f67(f905(a1,a1),a1,x99292,f241(a1,a1)),f202(x99292)),x99293))),f317(f93(x99291),f317(f317(f67(f905(a1,a1),a1,x99292,f246(a1,a1)),f202(x99292)),x99293))),f212(x99292,x99291,x99293)) % 112.26/112.10 [10133]~E(x101333,f2(a899))+~E(f317(f179(f900(x101331)),f317(f317(f154(f900(x101331)),x101332),f694(x101333,x101331,x101332))),x101333)+E(f317(f317(f144(a899,f900(x101331)),f317(f317(f9(a899,f900(a899),f900(x101331)),f317(f317(f10(f906(a899,x101331),f906(f900(a899),f900(x101331)),a899),f144(a899,x101331)),f317(f9(a899,a899,x101331),f317(f317(f10(f900(x101331),f906(a899,x101331),a899),f154(x101331)),f317(f154(f900(x101331)),x101332))))),f129(a899,f317(f292(a899,f2(a899)),f317(f179(f900(f900(x101331))),x101332))))),f129(a899,f317(f292(a899,f2(a899)),x101333))),f169(x101331,x101332)) % 112.26/112.10 [10134]E(x101341,f103(f900(x101342)))+~E(f317(f179(f900(x101342)),f317(f317(f154(f900(x101342)),x101341),f694(x101343,x101342,x101341))),x101343)+E(f317(f317(f144(a899,f900(x101342)),f317(f317(f9(a899,f900(a899),f900(x101342)),f317(f317(f10(f906(a899,x101342),f906(f900(a899),f900(x101342)),a899),f144(a899,x101342)),f317(f9(a899,a899,x101342),f317(f317(f10(f900(x101342),f906(a899,x101342),a899),f154(x101342)),f317(f154(f900(x101342)),x101341))))),f129(a899,f317(f292(a899,f2(a899)),f317(f179(f900(f900(x101342))),x101341))))),f129(a899,f317(f292(a899,f2(a899)),x101343))),f169(x101342,x101341)) % 112.26/112.10 [10135]~E(x101353,f2(a899))+E(f317(f317(f144(a899,f900(x101351)),f317(f317(f9(a899,f900(a899),f900(x101351)),f317(f317(f10(f906(a899,x101351),f906(f900(a899),f900(x101351)),a899),f144(a899,x101351)),f317(f9(a899,a899,x101351),f317(f317(f10(f900(x101351),f906(a899,x101351),a899),f154(x101351)),f317(f154(f900(x101351)),x101352))))),f129(a899,f317(f292(a899,f2(a899)),f317(f179(f900(f900(x101351))),x101352))))),f129(a899,f317(f292(a899,f2(a899)),x101353))),f169(x101351,x101352))+P1(f317(f317(f225(a899),f694(x101353,x101351,x101352)),f317(f179(f900(f900(x101351))),x101352))) % 112.26/112.10 [10136]E(x101361,f103(f900(x101362)))+E(f317(f317(f144(a899,f900(x101362)),f317(f317(f9(a899,f900(a899),f900(x101362)),f317(f317(f10(f906(a899,x101362),f906(f900(a899),f900(x101362)),a899),f144(a899,x101362)),f317(f9(a899,a899,x101362),f317(f317(f10(f900(x101362),f906(a899,x101362),a899),f154(x101362)),f317(f154(f900(x101362)),x101361))))),f129(a899,f317(f292(a899,f2(a899)),f317(f179(f900(f900(x101362))),x101361))))),f129(a899,f317(f292(a899,f2(a899)),x101363))),f169(x101362,x101361))+P1(f317(f317(f225(a899),f694(x101363,x101362,x101361)),f317(f179(f900(f900(x101362))),x101361))) % 112.26/112.10 [7848]E(f317(f317(f74(a899),f317(f94(a899),x78481)),f317(f317(f74(a899),f317(f94(a899),x78482)),x78483)),f317(f317(f74(a899),f317(f94(a899),f317(f317(f74(a1),x78481),x78482))),x78483))+P1(f317(a183,f317(f94(a1),x78481)))+P1(f317(a183,f317(f94(a1),x78482))) % 112.26/112.10 [8612]~P1(f317(f29(x86121),x86122))+~P1(f317(f317(f319(x86121),x86123),x86122))+E(f317(a102,f317(f30(x86121),f317(f317(f3(f906(x86121,a895)),x86122),f317(f317(f299(x86121),x86123),f178(f906(x86121,a895)))))),f317(f30(x86121),x86122)) % 112.26/112.10 [8628]~P1(f317(f29(x86281),x86282))+~P1(f317(f317(f319(x86281),x86283),x86282))+E(f317(f317(f74(a899),f72(a899)),f317(f30(x86281),f317(f317(f3(f906(x86281,a895)),x86282),f317(f317(f299(x86281),x86283),f178(f906(x86281,a895)))))),f317(f30(x86281),x86282)) % 112.26/112.10 [8715]~P108(x87151)+~P1(f317(f29(x87151),x87153))+E(f317(f317(f138(x87151,x87151,f7(x87151)),x87152),f129(x87151,f317(f317(f3(f906(x87151,a895)),x87153),f317(f317(f299(x87151),x87152),f178(f906(x87151,a895)))))),f129(x87151,f317(f317(f299(x87151),x87152),x87153))) % 112.26/112.10 [8881]~P1(f317(f29(x88811),x88813))+~P1(f317(f29(x88811),x88812))+E(f317(f317(f74(a899),f317(f30(x88811),f317(f317(f91(f906(x88811,a895)),x88812),x88813))),f317(f30(x88811),f317(f317(f92(f906(x88811,a895)),x88812),x88813))),f317(f317(f74(a899),f317(f30(x88811),x88812)),f317(f30(x88811),x88813))) % 112.26/112.10 [10082]~P24(x100821,f906(f906(x100821,a895),a895),f317(f317(f9(x100821,f906(f905(x100821,x100821),a895),f906(f906(x100821,a895),a895)),f317(f317(f10(f906(x100821,a895),f906(f906(f905(x100821,x100821),a895),f906(f906(x100821,a895),a895)),x100821),f56(x100821)),f317(f317(f9(x100821,f906(x100821,a895),f906(x100821,a895)),f299(x100821)),f178(f906(x100821,a895))))),x100823),x100822)+~P1(f317(f29(x100821),x100822))+E(f317(f30(f906(x100821,a895)),f317(f317(f56(x100821),x100822),x100823)),f317(f30(x100821),x100822)) % 112.26/112.10 [8117]~P94(x81171)+P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x81173)))+E(f317(f317(f234(x81171),x81172),f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),x81173),x81173)),a87))),f72(x81171)) % 112.26/112.10 [9599]~P94(x95991)+~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x95993)))+E(f317(f317(f234(x95991),x95992),f317(f94(a899),f317(f317(f3(a1),f317(f317(f74(a1),x95993),x95993)),a87))),f317(f317(f80(x95991,x95991),f317(f317(f234(x95991),x95992),f317(f94(a899),x95993))),f317(f317(f20(x95991,x95991,x95991),f317(f317(f10(x95991,f906(x95991,x95991),x95991),f75(x95991)),f317(f75(x95991),x95992))),f7(x95991)))) % 112.26/112.10 [9991]~P1(f317(f127(x99911),x99913))+~P1(f317(f317(f319(x99911),x99912),f317(f162(x99911),x99913)))+E(f317(f317(f128(x99911),f317(f179(f900(x99911)),f167(x99911,f317(f317(f10(a895,a895,x99911),a312),f317(f317(f9(x99911,x99911,a895),a314),x99912)),f317(f158(x99911),x99913)))),f317(f158(x99911),x99913)),f317(f317(f141(x99911),x99912),f317(f158(x99911),f167(x99911,f317(f317(f10(a895,a895,x99911),a312),f317(f317(f9(x99911,x99911,a895),a314),x99912)),x99913)))) % 112.26/112.10 [10051]P1(f317(f317(f224(f906(f905(x100511,x100511),a895)),f297(x100511,x100512)),x100513))+~P1(f317(f317(f224(f906(f905(x100511,x100511),a895)),f297(x100511,f178(f906(f905(x100511,x100511),a895)))),x100513))+~P1(f317(f317(f224(f906(f905(x100511,x100511),a895)),f317(f317(f279(x100511,x100511,x100511),f317(f317(f92(f906(f905(x100511,x100511),a895)),f297(x100511,x100512)),x100513)),x100512)),x100513)) % 112.26/112.10 [9909]~P1(f317(f29(x99091),f317(f252(x99091),x99093)))+~P1(f317(f29(x99091),f317(f252(x99091),x99092)))+P1(f317(f29(x99091),f317(f252(x99091),f317(f317(f20(x99091,a895,a895),f317(f317(f10(a895,f906(a895,a895),x99091),a316),x99092)),x99093)))) % 112.26/112.10 [10198]P1(f317(f317(f224(f906(f905(x101981,x101981),a895)),f317(f317(f279(x101981,x101981,x101981),x101982),f297(x101981,x101982))),x101983))+~P1(f317(f317(f224(f906(f905(x101981,x101981),a895)),x101982),x101983))+~P1(f317(f317(f224(f906(f905(x101981,x101981),a895)),f317(f317(f279(x101981,x101981,x101981),f317(f317(f92(f906(f905(x101981,x101981),a895)),f317(f317(f279(x101981,x101981,x101981),x101982),f297(x101981,x101982))),x101983)),x101982)),x101983)) % 112.26/112.10 [10149]~P112(x101492)+E(x101491,f2(x101492))+~E(f317(f317(f74(x101492),f317(f317(f234(x101492),x101493),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x101492),x101491),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f2(x101492)) % 112.26/112.10 [10150]~P112(x101502)+E(x101501,f2(x101502))+~E(f317(f317(f74(x101502),f317(f317(f234(x101502),x101501),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x101502),x101503),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f2(x101502)) % 112.26/112.10 [10155]~P1(f317(f127(x101551),x101553))+~P1(f317(f317(f319(x101551),x101552),f317(f162(x101551),x101553)))+E(f317(f158(x101551),f317(f161(x101551),f317(f317(f128(x101551),f317(f179(f900(x101551)),f167(x101551,f317(f317(f10(a895,a895,x101551),a312),f317(f317(f9(x101551,x101551,a895),a314),x101552)),x101553))),x101553))),f167(x101551,f317(f317(f10(a895,a895,x101551),a312),f317(f317(f9(x101551,x101551,a895),a314),x101552)),f317(f158(x101551),x101553))) % 112.26/112.10 [10243]~P112(x102432)+E(x102431,f2(x102432))+P1(f317(f317(f225(x102432),f2(x102432)),f317(f317(f74(x102432),f317(f317(f234(x102432),x102433),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102432),x102431),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))))) % 112.26/112.10 [10244]~P112(x102442)+E(x102441,f2(x102442))+P1(f317(f317(f225(x102442),f2(x102442)),f317(f317(f74(x102442),f317(f317(f234(x102442),x102441),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102442),x102443),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))))) % 112.26/112.10 [10305]~P112(x103051)+P1(f317(f317(f224(x103051),f2(x103051)),x103052))+~P1(f317(f317(f224(x103051),f2(x103051)),f317(f317(f234(x103051),x103052),f317(a102,f317(f317(f75(a899),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),x103053))))) % 112.26/112.10 [5030]~E(x50302,f84(x50303,x50301))+P1(f317(x50301,x50302))+~P1(f317(x50301,x50304)) % 112.26/112.10 [5276]E(f63(x52763,x52762,x52764),x52762)+E(x52761,f756(x52762,x52763,x52764))+~P1(f317(x52764,x52761)) % 112.26/112.10 [6619]E(f63(x66191,x66192,x66193),f79(x66191,x66193))+~E(f757(x66192,x66191,x66193,x66194),x66194)+~P1(f317(x66193,x66194)) % 112.26/112.10 [6833]~P36(x68332,x68334)+~P36(x68331,x68333)+P36(f905(x68331,x68332),f310(x68331,x68332,x68333,x68334)) % 112.26/112.10 [6834]~P37(x68342,x68344)+~P37(x68341,x68343)+P37(f905(x68341,x68342),f310(x68341,x68342,x68343,x68344)) % 112.26/112.10 [5216]~P7(x52164,x52161)+~E(f317(x52161,x52162),f317(x52161,x52163))+P1(f317(f317(x52161,x52162),x52163)) % 112.26/112.10 [5375]~P7(x53754,x53751)+E(f317(x53751,x53752),f317(x53751,x53753))+~P1(f317(f317(x53751,x53752),x53753)) % 112.26/112.10 [5376]~P15(x53764,x53761)+E(f317(x53761,x53762),f317(x53761,x53763))+~P1(f317(f317(x53761,x53762),x53763)) % 112.26/112.10 [5470]~P18(x54703,x54704,x54701)+E(f317(x54701,x54702),f317(f58(x54703,x54704),x54702))+~P1(f317(f29(x54703),x54702)) % 112.26/112.10 [5471]~P9(x54713,x54714,x54711)+E(f317(x54711,x54712),f317(f58(x54713,x54714),x54712))+~P1(f317(f29(x54713),x54712)) % 112.26/112.10 [5598]~P7(x55984,x55981)+~P1(f317(f317(x55981,x55983),x55982))+P1(f317(f317(x55981,x55982),x55983)) % 112.26/112.10 [5599]~P50(x55994,x55991)+~P1(f317(f317(x55991,x55993),x55992))+P1(f317(f317(x55991,x55992),x55993)) % 112.26/112.10 [5600]~P15(x56004,x56001)+~P1(f317(f317(x56001,x56003),x56002))+P1(f317(f317(x56001,x56002),x56003)) % 112.26/112.10 [5601]~P15(x56013,x56011)+P1(f317(f317(x56011,x56012),x56012))+~P1(f317(f317(x56011,x56014),x56012)) % 112.26/112.10 [5602]~P15(x56023,x56021)+P1(f317(f317(x56021,x56022),x56022))+~P1(f317(f317(x56021,x56022),x56024)) % 112.26/112.10 [5672]E(x56721,x56722)+~E(f317(f241(x56723,x56724),x56721),f317(f241(x56723,x56724),x56722))+~E(f317(f246(x56723,x56724),x56721),f317(f246(x56723,x56724),x56722)) % 112.26/112.10 [5700]E(x57001,x57002)+~P1(f317(f44(x57003,x57004),x57002))+~P1(f317(f44(x57003,x57004),x57001)) % 112.26/112.10 [5900]~P69(x59002)+E(f221(x59001,x59002,x59003,x59004),f2(x59002))+P1(f317(f29(x59001),x59004)) % 112.26/112.10 [5948]~P7(x59483,x59482)+~P1(f317(x59481,x59484))+P1(f317(x59481,f802(x59481,x59482,x59483))) % 112.26/112.10 [6046]~P1(f317(f305(x60461,x60462),x60464))+P1(f317(f305(x60461,x60462),x60463))+~P1(f317(f317(x60462,x60463),x60464)) % 112.26/112.10 [6870]~P28(x68701,x68703,x68704)+P1(f317(x68701,x68702))+~P1(f317(f317(f319(a1),x68702),f293(a1,x68703,x68704))) % 112.26/112.10 [7066]~P7(x70661,x70663)+~P1(f317(x70662,x70664))+P1(f317(f317(f319(x70661),f802(x70662,x70663,x70661)),f260(x70661,x70663))) % 112.26/112.10 [7958]E(x79581,f2(a899))+~P1(f317(x79582,x79583))+P1(f317(x79582,f751(x79582,x79583,x79581,x79584))) % 112.26/112.10 [8040]~P108(x80402)+~P1(f317(f127(x80401),x80404))+P1(f317(f127(x80401),f140(x80401,x80402,x80403,x80404))) % 112.26/112.10 [8084]E(f63(x80841,x80842,x80843),f79(x80841,x80843))+~P1(f317(x80843,x80844))+P1(f317(x80843,f757(x80842,x80841,x80843,x80844))) % 112.26/112.10 [8266]~P1(f317(f29(x82662),x82664))+~P1(f317(f29(x82661),x82663))+P1(f317(f29(f904(x82661,x82662)),f303(x82661,x82662,x82663,x82664))) % 112.26/112.10 [8267]~P1(f317(f127(x82672),x82674))+~P1(f317(f127(x82671),x82673))+P1(f317(f127(f905(x82671,x82672)),f55(x82671,x82672,x82673,x82674))) % 112.26/112.10 [8270]P1(f317(f317(f319(f900(x82701)),f317(f317(f124(x82701),x82702),x82703)),f151(x82701,x82704)))+~P1(f317(f317(f319(f900(x82701)),x82703),f151(x82701,x82704)))+~P1(f317(f317(f319(f900(x82701)),x82702),f151(x82701,x82704))) % 112.26/112.10 [8550]E(x85501,f2(a899))+P1(f317(x85502,x85503))+~P1(f317(x85502,f752(x85502,x85503,x85501,x85504))) % 112.26/112.10 [8587]~P108(x85873)+~P1(f317(f127(x85871),f140(x85871,x85873,x85874,x85872)))+P1(f317(f127(x85871),x85872)) % 112.26/112.10 [8870]~P1(f317(f317(f319(f905(x88701,x88701)),f317(f317(f242(x88701,x88701),x88702),x88704)),f297(x88701,x88703)))+P1(f317(f317(f319(x88701),x88702),f306(x88701,x88703)))+~P1(f317(f317(f319(x88701),x88704),f306(x88701,x88703))) % 112.26/112.10 [5200]~P69(x52002)+E(f317(f317(f8(x52001,x52002),x52003),x52004),f2(x52002))+P1(f317(f29(x52001),x52004)) % 112.26/112.10 [5203]~P75(x52032)+E(f317(f317(f11(x52031,x52032),x52033),x52034),f72(x52032))+P1(f317(f29(x52031),x52034)) % 112.26/112.10 [5338]~P72(x53383)+E(x53381,x53382)+~E(f317(f317(f74(x53383),x53384),x53381),f317(f317(f74(x53383),x53384),x53382)) % 112.26/112.10 [5339]~P73(x53393)+E(x53391,x53392)+~E(f317(f317(f74(x53393),x53394),x53391),f317(f317(f74(x53393),x53394),x53392)) % 112.26/112.10 [5341]~P72(x53413)+E(x53411,x53412)+~E(f317(f317(f74(x53413),x53411),x53414),f317(f317(f74(x53413),x53412),x53414)) % 112.26/112.10 [5437]~P122(x54371)+~E(x54373,f317(f317(f75(x54371),x54372),x54374))+P1(f317(f317(f277(x54371),x54372),x54373)) % 112.26/112.10 [5465]~P5(x54653)+E(x54651,f178(f906(x54652,a895)))+E(f317(f317(f35(x54652,x54653),x54651),f317(f18(x54653,x54652),x54654)),x54654) % 112.26/112.10 [5466]~P5(x54663)+E(x54661,f178(f906(x54662,a895)))+E(f317(f317(f36(x54662,x54663),x54661),f317(f18(x54663,x54662),x54664)),x54664) % 112.26/112.10 [5686]~P109(x56863)+E(x56861,x56862)+~E(f293(x56863,x56864,x56861),f317(f317(f299(x56863),x56862),f178(f906(x56863,a895)))) % 112.26/112.10 [5687]~P109(x56873)+E(x56871,x56872)+~E(f293(x56873,x56871,x56872),f317(f317(f299(x56873),x56874),f178(f906(x56873,a895)))) % 112.26/112.10 [5747]~P34(x57473,x57471,x57474)+P34(x57473,x57471,f317(f317(f141(x57473),x57472),x57474))+P1(f317(x57471,x57472)) % 112.26/112.10 [5849]~P30(x58491,x58492,x58494)+~P1(f317(x58492,x58493))+P30(x58491,x58492,f317(f317(f141(x58491),x58493),x58494)) % 112.26/112.10 [6001]P1(f317(x60011,x60012))+~P1(f317(f238(x60013,x60011),x60014))+~P1(f317(f317(f319(x60013),x60012),x60014)) % 112.26/112.10 [6010]~P30(x60101,x60102,x60104)+~P30(x60101,x60102,x60103)+P30(x60101,x60102,f317(f317(f124(x60101),x60103),x60104)) % 112.26/112.10 [6025]P32(x60251,x60252,x60253)+~P32(x60251,x60252,f317(f317(f141(x60251),x60254),x60253))+P1(f317(x60252,x60254)) % 112.26/112.10 [6026]P34(x60261,x60262,x60263)+~P34(x60261,x60262,f317(f317(f141(x60261),x60264),x60263))+P1(f317(x60262,x60264)) % 112.26/112.10 [6101]P32(x61011,x61012,x61013)+P32(x61011,x61012,x61014)+~P32(x61011,x61012,f317(f317(f124(x61011),x61014),x61013)) % 112.26/112.10 [6122]~P69(x61221)+E(f317(f317(f8(a899,x61221),x61222),f317(f292(a899,x61223),f317(a102,x61224))),f2(x61221))+~P1(f317(f317(f225(a899),x61224),x61223)) % 112.26/112.10 [6127]~P4(x61271)+~E(f41(x61271,x61272,x61273),f41(x61271,x61274,x61273))+E(f41(x61271,f317(f73(x61271),x61272),x61273),f41(x61271,f317(f73(x61271),x61274),x61273)) % 112.26/112.10 [6195]P1(f317(x61951,x61952))+~E(f317(f126(x61953,x61951),x61954),x61954)+~P1(f317(f317(f319(x61953),x61952),f317(f162(x61953),x61954))) % 112.26/112.10 [6215]~E(f317(f317(f74(a899),x62153),x62152),f317(f317(f74(a899),x62151),x62154))+~P1(f317(f317(f225(a899),x62153),x62154))+P1(f317(f317(f225(a899),x62151),x62152)) % 112.26/112.10 [6221]P32(x62211,x62212,x62213)+~P1(f317(x62212,x62214))+~P1(f317(f317(f319(x62211),x62214),f317(f162(x62211),x62213))) % 112.26/112.10 [6224]~P3(x62241)+E(f41(x62241,f41(x62241,x62242,x62243),x62244),f41(x62241,x62242,x62244))+~P1(f317(f317(f277(x62241),x62244),x62243)) % 112.26/112.10 [6264]~P30(x62643,x62641,x62644)+P1(f317(x62641,x62642))+~P1(f317(f317(f319(x62643),x62642),f317(f162(x62643),x62644))) % 112.26/112.10 [6266]~E(f317(f126(x62661,x62662),x62663),f103(x62661))+~P1(f317(x62662,x62664))+~P1(f317(f317(f319(x62661),x62664),f317(f162(x62661),x62663))) % 112.26/112.10 [6267]~E(f167(x62673,x62671,x62674),x62674)+P1(f317(x62671,x62672))+~P1(f317(f317(f319(x62673),x62672),f317(f162(x62673),x62674))) % 112.26/112.10 [6294]~E(x62944,f178(f906(x62942,a895)))+~E(x62943,f178(f906(x62941,a895)))+E(f303(x62941,x62942,x62943,x62944),f178(f906(f904(x62941,x62942),a895))) % 112.26/112.10 [6446]P1(f317(x64461,x64462))+~P1(f317(f150(x64463,x64461),x64464))+~P1(f317(f317(f319(x64463),x64462),f317(f162(x64463),x64464))) % 112.26/112.10 [6588]~P29(x65881,x65883,x65884)+P1(f317(x65881,x65882))+~P1(f317(f317(f319(a899),x65882),f317(f292(a899,x65883),x65884))) % 112.26/112.10 [6727]~P69(x67271)+E(f317(f317(f8(a899,x67271),x67272),f293(a899,x67273,f317(a102,x67274))),f2(x67271))+~P1(f317(f317(f225(a899),f317(a102,x67274)),x67273)) % 112.26/112.10 [6873]~P108(x68731)+E(f317(f317(f3(f906(x68731,a895)),f317(f292(x68731,x68732),x68733)),f317(f292(x68731,x68732),x68734)),f317(f292(x68731,x68734),x68733))+~P1(f317(f317(f224(x68731),x68732),x68734)) % 112.26/112.10 [6944]~E(x69443,x69444)+E(x69441,f2(a899))+P1(f317(f317(f319(x69442),x69443),f317(f162(x69442),f159(x69442,x69441,x69444)))) % 112.26/112.10 [7229]~P1(f317(f317(f319(f900(x72291)),x72294),f151(x72291,x72293)))+P1(f317(f317(f319(x72291),x72292),x72293))+~P1(f317(f317(f319(x72291),x72292),f317(f162(x72291),x72294))) % 112.26/112.10 [7236]~P36(x72361,x72362)+P1(f317(f317(f319(x72361),f587(x72362,x72361,x72363)),x72363))+~P1(f317(f317(f319(x72361),x72364),x72363)) % 112.26/112.10 [7293]~P69(x72931)+E(f317(f317(f317(f60(x72931,x72932,f74(x72931)),x72933),f2(x72931)),x72934),f317(f317(f8(x72932,x72931),x72933),x72934))+~P1(f317(f29(x72932),x72934)) % 112.26/112.10 [7295]~P75(x72951)+E(f317(f317(f317(f60(x72951,x72952,f75(x72951)),x72953),f72(x72951)),x72954),f317(f317(f11(x72952,x72951),x72953),x72954))+~P1(f317(f29(x72952),x72954)) % 112.26/112.10 [7322]P24(x73221,x73222,x73223,x73224)+~E(f317(f30(x73222),f317(f300(x73221,x73222,x73223),x73224)),f317(f30(x73221),x73224))+~P1(f317(f29(x73221),x73224)) % 112.26/112.10 [7516]~P69(x75161)+E(f317(f317(f74(x75161),f317(x75162,x75163)),f317(f317(f8(a899,x75161),x75162),f295(a899,x75163,x75164))),f317(f317(f8(a899,x75161),x75162),f293(a899,x75163,x75164)))+~P1(f317(f317(f224(a899),x75163),x75164)) % 112.26/112.10 [7525]~P69(x75251)+~P24(x75252,x75251,x75253,x75254)+E(f317(f317(f8(x75251,x75251),f25(x75251)),f317(f300(x75252,x75251,x75253),x75254)),f317(f317(f8(x75252,x75251),x75253),x75254)) % 112.26/112.10 [7526]~P75(x75261)+~P24(x75262,x75261,x75263,x75264)+E(f317(f317(f11(x75261,x75261),f25(x75261)),f317(f300(x75262,x75261,x75263),x75264)),f317(f317(f11(x75262,x75261),x75263),x75264)) % 112.26/112.10 [7574]E(f317(f30(f904(x75741,x75742)),f303(x75741,x75742,x75743,x75744)),f317(f317(f74(a899),f317(f30(x75741),x75743)),f317(f30(x75742),x75744)))+~P1(f317(f29(x75742),x75744))+~P1(f317(f29(x75741),x75743)) % 112.26/112.10 [7658]E(x76581,x76582)+P1(f317(f317(f319(x76583),x76581),f317(f162(x76583),f160(x76583,x76582,x76584))))+~P1(f317(f317(f319(x76583),x76581),f317(f162(x76583),x76584))) % 112.26/112.10 [7888]~P69(x78881)+E(f317(f317(f74(x78881),f317(f317(f8(a899,x78881),x78882),f317(f292(a899,x78883),x78884))),f317(x78882,x78884)),f317(f317(f8(a899,x78881),x78882),f317(f292(a899,x78883),f317(a102,x78884))))+P1(f317(f317(f225(a899),x78884),x78883)) % 112.26/112.10 [7938]~P24(x79381,x79382,x79383,f232(f906(x79381,a895)))+~P1(f317(f29(x79382),x79384))+P1(f317(f29(x79381),f317(f301(x79381,x79382,x79383),x79384))) % 112.26/112.10 [8055]P1(f317(f317(f319(f900(x80551)),f317(f317(f141(x80551),x80552),x80553)),f151(x80551,x80554)))+~P1(f317(f317(f319(f900(x80551)),x80553),f151(x80551,x80554)))+~P1(f317(f317(f319(x80551),x80552),x80554)) % 112.26/112.10 [8141]~E(f317(f300(x81413,x81411,x81414),f232(f906(x81413,a895))),f232(f906(x81411,a895)))+P1(f317(f29(x81411),x81412))+~P1(f317(f29(x81413),f317(f301(x81413,x81411,x81414),x81412))) % 112.26/112.10 [8236]~P24(x82361,x82363,x82364,x82362)+P1(f317(f29(x82361),x82362))+~P1(f317(f29(x82363),f317(f300(x82361,x82363,x82364),x82362))) % 112.26/112.10 [8260]~E(x82602,x82603)+P1(f317(f317(f319(f905(x82601,x82601)),f317(f317(f242(x82601,x82601),x82602),x82603)),f253(x82601,x82604)))+~P1(f317(f317(f319(x82601),x82602),x82604)) % 112.26/112.10 [8293]~P69(x82931)+E(f317(f317(f74(x82931),f317(f317(f8(a899,x82931),x82932),f293(a899,x82933,x82934))),f317(x82932,f317(a102,x82934))),f317(f317(f8(a899,x82931),x82932),f293(a899,x82933,f317(a102,x82934))))+P1(f317(f317(f225(a899),f317(a102,x82934)),x82933)) % 112.26/112.10 [8353]P1(f317(x83531,x83532))+~P1(f317(x83531,f317(f317(f154(x83533),x83534),f642(x83531,x83534,x83533))))+~P1(f317(f317(f319(x83533),x83532),f317(f162(x83533),x83534))) % 112.26/112.10 [8494]~P1(f317(f317(f319(x84941),x84942),f306(x84941,x84944)))+P1(f317(f317(f319(f900(x84941)),f317(f317(f141(x84941),x84942),x84943)),f306(f900(x84941),f147(x84941,x84944))))+~P1(f317(f317(f319(f900(x84941)),x84943),f306(f900(x84941),f147(x84941,x84944)))) % 112.26/112.10 [8509]~P24(x85092,x85093,x85094,f520(x85094,x85093,x85092,x85091))+P24(x85092,x85093,x85094,f33(f906(x85092,a895),x85091))+E(x85091,f178(f906(f906(x85092,a895),a895))) % 112.26/112.10 [8779]E(x87791,x87792)+~P1(f317(f317(f319(f905(x87793,x87793)),f317(f317(f242(x87793,x87793),x87791),x87792)),f297(x87793,x87794)))+P1(f317(f317(f319(x87793),x87791),f317(f254(x87793,x87793),x87794))) % 112.26/112.10 [9057]E(x90571,f2(a899))+P1(f317(x90572,x90573))+P1(f317(f317(f319(x90574),f752(x90572,x90573,x90571,x90574)),f317(f162(x90574),f159(x90574,x90571,x90573)))) % 112.26/112.10 [9069]E(x90691,f2(a899))+~P1(f317(x90693,x90694))+P1(f317(f317(f319(x90692),f751(x90693,x90694,x90691,x90692)),f317(f162(x90692),f159(x90692,x90691,x90694)))) % 112.26/112.10 [9071]~P25(x90711,x90712,x90713,f232(f906(x90711,a895)),f232(f906(x90712,a895)))+~P1(f317(f29(x90712),x90714))+P1(f317(f29(x90711),f317(f301(x90711,x90712,x90713),x90714))) % 112.26/112.10 [9074]P24(x90742,x90743,x90744,f33(f906(x90742,a895),x90741))+E(x90741,f178(f906(f906(x90742,a895),a895)))+P1(f317(f317(f319(f906(x90742,a895)),f520(x90744,x90743,x90742,x90741)),x90741)) % 112.26/112.10 [9189]~P25(x91893,x91891,x91894,f232(f906(x91893,a895)),f232(f906(x91891,a895)))+P1(f317(f29(x91891),x91892))+~P1(f317(f29(x91893),f317(f301(x91893,x91891,x91894),x91892))) % 112.26/112.10 [9206]P1(f317(f29(x92061),x92062))+~P1(f317(f29(x92064),f317(f300(x92061,x92064,x92063),x92062)))+P1(f317(f317(f319(x92061),f561(x92063,x92064,x92062,x92061)),x92062)) % 112.26/112.10 [9301]~P5(x93012)+E(f317(f317(f59(x93011,x93012,f317(f317(f10(x93012,f906(x93012,x93012),x93011),f92(x93012)),x93013)),f232(x93012)),x93014),f317(f317(f35(x93011,x93012),x93014),x93013))+~P1(f317(f29(x93011),x93014)) % 112.26/112.10 [9302]~P5(x93022)+E(f317(f317(f59(x93021,x93022,f317(f317(f10(x93022,f906(x93022,x93022),x93021),f91(x93022)),x93023)),f178(x93022)),x93024),f317(f317(f36(x93021,x93022),x93024),x93023))+~P1(f317(f29(x93021),x93024)) % 112.26/112.10 [9332]~P1(f317(f317(f277(a899),x93323),x93324))+P1(f317(f317(f277(a899),x93321),x93322))+P1(f317(f317(f225(f906(a899,a895)),f280(a899,f277(a899),x93321,x93322)),f280(a899,f277(a899),x93323,x93324))) % 112.26/112.10 [9345]~P1(f317(f317(f277(a899),x93452),x93454))+~P1(f317(f317(f277(a899),x93453),x93451))+P1(f317(f317(f224(f906(a899,a895)),f280(a899,f277(a899),x93451,x93452)),f280(a899,f277(a899),x93453,x93454))) % 112.26/112.10 [9388]P1(f317(x93881,x93882))+~P1(f317(x93881,f317(f317(f154(x93883),x93884),f680(x93882,x93881,x93884,x93883))))+~P1(f317(f317(f319(x93883),x93882),f317(f162(x93883),x93884))) % 112.26/112.10 [9410]E(x94101,x94102)+~P1(f317(f317(f319(f905(x94103,x94103)),f317(f317(f242(x94103,x94103),x94101),x94102)),f297(x94103,x94104)))+P1(f317(f317(f319(f905(x94103,x94103)),f317(f317(f242(x94103,x94103),x94101),x94102)),f317(f317(f279(x94103,x94103,x94103),x94104),f297(x94103,x94104)))) % 112.26/112.10 [9460]~E(f317(f179(f900(x94601)),x94602),f317(f179(f900(x94601)),x94603))+~P1(f317(f317(f319(f905(f900(x94601),f900(x94601))),f317(f317(f242(f900(x94601),f900(x94601)),x94602),x94603)),f137(x94601,x94604)))+P1(f317(f317(f319(f905(f900(x94601),f900(x94601))),f317(f317(f242(f900(x94601),f900(x94601)),x94602),x94603)),f135(x94601,x94604))) % 112.26/112.10 [9583]P1(f317(f317(f277(a899),x95831),x95832))+~P1(f317(f317(f277(a899),x95833),x95831))+~P1(f317(f317(f224(f906(a899,a895)),f280(a899,f277(a899),x95833,x95831)),f280(a899,f277(a899),x95834,x95832))) % 112.26/112.10 [9584]P1(f317(f317(f277(a899),x95841),x95842))+~P1(f317(f317(f277(a899),x95843),x95841))+~P1(f317(f317(f225(f906(a899,a895)),f280(a899,f277(a899),x95843,x95841)),f280(a899,f277(a899),x95844,x95842))) % 112.26/112.10 [9585]P1(f317(f317(f277(a899),x95851),x95852))+~P1(f317(f317(f277(a899),x95852),x95853))+~P1(f317(f317(f224(f906(a899,a895)),f280(a899,f277(a899),x95852,x95853)),f280(a899,f277(a899),x95851,x95854))) % 112.26/112.10 [9586]P1(f317(f317(f277(a899),x95861),x95862))+~P1(f317(f317(f277(a899),x95862),x95863))+~P1(f317(f317(f225(f906(a899,a895)),f280(a899,f277(a899),x95862,x95863)),f280(a899,f277(a899),x95861,x95864))) % 112.26/112.10 [9706]P30(x97061,f317(f317(f20(x97061,a895,a895),f317(f317(f10(a895,f906(a895,a895),x97061),a316),f317(f317(f10(a895,a895,x97061),a312),x97062))),f317(a314,x97063)),x97064)+~P1(f317(x97062,x97063))+~P34(x97061,x97062,f317(f317(f141(x97061),x97063),x97064)) % 112.26/112.10 [9872]~P30(x98721,f317(f317(f20(x98721,a895,a895),f317(f317(f10(a895,f906(a895,a895),x98721),a316),f317(f317(f10(a895,a895,x98721),a312),x98722))),f317(a314,x98723)),x98724)+~P1(f317(x98722,x98723))+P34(x98721,x98722,f317(f317(f141(x98721),x98723),x98724)) % 112.26/112.10 [9876]~P34(x98761,x98762,x98764)+~P30(x98761,f317(f317(f20(x98761,a895,a895),f317(f317(f10(a895,f906(a895,a895),x98761),a316),f317(f317(f10(a895,a895,x98761),a312),x98762))),f317(a314,x98763)),x98764)+P34(x98761,x98762,f317(f317(f141(x98761),x98763),x98764)) % 112.26/112.10 [9910]~P68(x99101)+E(f317(f317(f8(a899,x99101),f317(f317(f20(a899,x99101,x99101),f317(f317(f10(x99101,f906(x99101,x99101),a899),f3(x99101)),x99102)),f317(f317(f10(a899,x99101,a899),x99102),f317(f317(f9(a899,a899,a899),f74(a899)),f72(a899))))),f293(a899,x99103,x99104)),f2(x99101))+P1(f317(f317(f224(a899),x99103),x99104)) % 112.26/112.10 [10148]~P36(x101482,x101484)+~P24(x101482,x101481,x101483,f232(f906(x101482,a895)))+P36(x101481,f317(f300(f905(x101482,x101482),f905(x101481,x101481),f248(x101482,x101481,x101482,x101481,x101483,x101483)),x101484)) % 112.26/112.10 [10340]~E(f317(f179(f900(x103401)),x103403),f317(f179(f900(x103401)),x103402))+P1(f317(f317(f319(f905(f900(x103401),f900(x103401))),f317(f317(f242(f900(x103401),f900(x103401)),x103402),x103403)),f148(x103401,x103404)))+~P1(f317(f317(f247(x103401,x103401,a895),f317(f317(f9(x103401,f906(f905(x103401,x103401),a895),f906(x103401,a895)),f317(f317(f10(f906(x103401,f906(f906(f905(x103401,x103401),a895),a895)),f906(f906(f905(x103401,x103401),a895),f906(x103401,a895)),x103401),f9(x103401,f906(f905(x103401,x103401),a895),a895)),f317(f317(f10(f906(x103401,f905(x103401,x103401)),f906(x103401,f906(f906(f905(x103401,x103401),a895),a895)),x103401),f317(f10(f905(x103401,x103401),f906(f906(f905(x103401,x103401),a895),a895),x103401),f319(f905(x103401,x103401)))),f242(x103401,x103401)))),x103404)),f646(x103404,x103403,x103402,x103401))) % 112.26/112.10 [6176]~P3(x61761)+~E(x61762,f2(x61761))+E(f317(f317(f31(x61761),f317(f317(f75(x61761),x61762),x61763)),f317(f317(f75(x61761),x61762),x61764)),f2(x61761)) % 112.26/112.10 [6218]E(x62181,f103(x62182))+E(x62183,f317(f317(f3(a899),f317(f179(f900(x62182)),x62181)),f72(a899)))+E(f134(x62182,f317(f317(f149(x62182,x62181),x62183),x62184)),f134(x62182,x62181)) % 112.26/112.10 [6255]E(x62551,x62552)+P1(f317(x62553,x62552))+~P1(f317(f317(f317(f299(x62554),x62551),x62553),x62552)) % 112.26/112.10 [6271]~P69(x62711)+~P1(f317(f127(x62712),x62714))+E(f317(f155(x62711),f317(f317(f144(x62712,x62711),x62713),x62714)),f317(f317(f8(x62712,x62711),x62713),f317(f162(x62712),x62714))) % 112.26/112.10 [6287]~P75(x62872)+~P1(f317(f29(x62871),x62874))+E(f317(f317(f11(x62871,x62872),f317(f18(x62872,x62871),x62873)),x62874),f317(f317(f234(x62872),x62873),f317(f30(x62871),x62874))) % 112.26/112.10 [6342]~P61(x63422)+E(x63421,f2(x63422))+E(f317(f317(f281(x63422),f317(f317(f75(x63422),x63423),x63421)),f317(f317(f75(x63422),x63424),x63421)),f317(f317(f281(x63422),x63423),x63424)) % 112.26/112.10 [6343]~P61(x63432)+E(x63431,f2(x63432))+E(f317(f317(f281(x63432),f317(f317(f75(x63432),x63431),x63433)),f317(f317(f75(x63432),x63431),x63434)),f317(f317(f281(x63432),x63433),x63434)) % 112.26/112.10 [6344]~P3(x63442)+E(x63441,f2(x63442))+E(f317(f317(f31(x63442),f317(f317(f75(x63442),x63443),x63441)),f317(f317(f75(x63442),x63444),x63441)),f317(f317(f31(x63442),x63443),x63444)) % 112.26/112.10 [6346]~P3(x63462)+E(x63461,f2(x63462))+E(f317(f317(f31(x63462),f317(f317(f75(x63462),x63461),x63463)),f317(f317(f75(x63462),x63461),x63464)),f317(f317(f31(x63462),x63463),x63464)) % 112.26/112.10 [6415]P1(f317(x64151,x64152))+~E(x64153,f317(f317(f74(a899),x64154),x64152))+~P1(f317(x64151,f317(f317(f3(a899),x64153),x64154))) % 112.26/112.10 [6501]~P1(f317(x65012,x65013))+~P1(f317(f150(x65011,x65012),x65014))+P1(f317(f150(x65011,x65012),f317(f317(f141(x65011),x65013),x65014))) % 112.26/112.10 [6542]E(x65421,f103(x65422))+~E(x65423,f317(f317(f3(a899),f317(f179(f900(x65422)),x65421)),f72(a899)))+E(f134(x65422,f317(f317(f149(x65422,x65421),x65423),x65424)),x65424) % 112.26/112.10 [6566]~P108(x65661)+~P1(f317(f317(f224(x65661),x65662),x65664))+P1(f317(f317(f224(x65661),x65662),f317(f317(f223(x65661),x65663),x65664))) % 112.26/112.10 [6568]~P108(x65681)+~P1(f317(f317(f224(x65681),x65682),x65683))+P1(f317(f317(f224(x65681),x65682),f317(f317(f223(x65681),x65683),x65684))) % 112.26/112.10 [6569]~P98(x65691)+~P1(f317(f317(f224(x65691),x65692),x65694))+P1(f317(f317(f224(x65691),x65692),f317(f317(f91(x65691),x65693),x65694))) % 112.26/112.10 [6570]~P98(x65701)+~P1(f317(f317(f224(x65701),x65702),x65703))+P1(f317(f317(f224(x65701),x65702),f317(f317(f91(x65701),x65703),x65704))) % 112.26/112.10 [6572]~P108(x65721)+~P1(f317(f317(f225(x65721),x65722),x65724))+P1(f317(f317(f225(x65721),x65722),f317(f317(f223(x65721),x65723),x65724))) % 112.26/112.10 [6574]~P108(x65741)+~P1(f317(f317(f225(x65741),x65742),x65743))+P1(f317(f317(f225(x65741),x65742),f317(f317(f223(x65741),x65743),x65744))) % 112.26/112.10 [6575]~P98(x65751)+~P1(f317(f317(f225(x65751),x65752),x65754))+P1(f317(f317(f225(x65751),x65752),f317(f317(f91(x65751),x65753),x65754))) % 112.26/112.10 [6576]~P98(x65761)+~P1(f317(f317(f225(x65761),x65762),x65763))+P1(f317(f317(f225(x65761),x65762),f317(f317(f91(x65761),x65763),x65764))) % 112.26/112.10 [6577]~P119(x65771)+~P1(f317(f317(f277(x65771),x65772),x65774))+P1(f317(f317(f277(x65771),x65772),f317(f317(f75(x65771),x65773),x65774))) % 112.26/112.10 [6578]~P119(x65781)+~P1(f317(f317(f277(x65781),x65782),x65783))+P1(f317(f317(f277(x65781),x65782),f317(f317(f75(x65781),x65783),x65784))) % 112.26/112.10 [6671]~E(f317(f317(f154(x66711),x66712),x66713),x66714)+E(f317(f317(f149(x66711,x66712),x66713),x66714),x66712)+~P1(f317(f317(f225(a899),x66713),f317(f179(f900(x66711)),x66712))) % 112.26/112.10 [6711]P1(f317(x67111,x67112))+~P1(f317(x67113,x67112))+~P1(f317(f317(f224(f906(x67114,a895)),x67113),x67111)) % 112.26/112.10 [6746]~E(f317(f317(f149(x67461,x67462),x67463),x67464),x67462)+E(f317(f317(f154(x67461),x67462),x67463),x67464)+~P1(f317(f317(f225(a899),x67463),f317(f179(f900(x67461)),x67462))) % 112.26/112.10 [6760]~P1(f317(f150(x67601,x67602),x67604))+~P1(f317(f150(x67601,x67602),x67603))+P1(f317(f150(x67601,x67602),f317(f317(f124(x67601),x67603),x67604))) % 112.26/112.10 [6869]E(x68691,f178(f906(x68692,a895)))+E(x68693,f178(f906(x68694,a895)))+~E(f317(f317(f244(x68694,x68692),x68693),f317(f18(f906(x68692,a895),x68694),x68691)),f178(f906(f905(x68694,x68692),a895))) % 112.26/112.10 [6889]E(x68891,x68892)+P1(f317(f317(f319(x68893),x68891),x68894))+~P1(f317(f317(f319(x68893),x68891),f317(f317(f299(x68893),x68892),x68894))) % 112.26/112.10 [6906]~P108(x69061)+P1(f317(f317(f224(x69061),x69062),x69063))+~P1(f317(f317(f224(x69061),x69062),f317(f317(f228(x69061),x69064),x69063))) % 112.26/112.10 [6908]~P108(x69081)+P1(f317(f317(f224(x69081),x69082),x69083))+~P1(f317(f317(f224(x69081),x69082),f317(f317(f228(x69081),x69083),x69084))) % 112.26/112.10 [6910]~P104(x69101)+P1(f317(f317(f224(x69101),x69102),x69103))+~P1(f317(f317(f224(x69101),x69102),f317(f317(f92(x69101),x69104),x69103))) % 112.26/112.10 [6912]~P104(x69121)+P1(f317(f317(f224(x69121),x69122),x69123))+~P1(f317(f317(f224(x69121),x69122),f317(f317(f92(x69121),x69123),x69124))) % 112.26/112.10 [6913]~P108(x69131)+P1(f317(f317(f225(x69131),x69132),x69133))+~P1(f317(f317(f225(x69131),x69132),f317(f317(f228(x69131),x69134),x69133))) % 112.26/112.10 [6914]~P108(x69141)+P1(f317(f317(f225(x69141),x69142),x69143))+~P1(f317(f317(f225(x69141),x69142),f317(f317(f228(x69141),x69143),x69144))) % 112.26/112.10 [6935]~E(f317(f317(f154(x69351),x69353),x69354),x69352)+P1(f317(f317(f319(x69351),x69352),f317(f162(x69351),x69353)))+~P1(f317(f317(f225(a899),x69354),f317(f179(f900(x69351)),x69353))) % 112.26/112.10 [6945]~P108(x69451)+~P13(x69451,f317(f317(f141(x69451),x69452),f317(f317(f141(x69451),x69453),x69454)))+P1(f317(f317(f224(x69451),x69452),x69453)) % 112.26/112.10 [7094]~P30(x70942,x70941,x70943)+P1(f317(x70941,f317(f317(f154(x70942),x70943),x70944)))+~P1(f317(f317(f225(a899),x70944),f317(f179(f900(x70942)),x70943))) % 112.26/112.10 [7112]E(x71121,f2(a1))+E(f317(f317(f31(a1),x71122),x71121),x71123)+~P1(f317(f45(x71122,x71121),f317(f317(f242(a1,a1),x71123),x71124))) % 112.26/112.10 [7134]E(f41(a1,x71342,x71341),x71343)+E(x71341,f2(a1))+~P1(f317(f45(x71342,x71341),f317(f317(f242(a1,a1),x71344),x71343))) % 112.26/112.10 [7253]P1(f317(f317(f319(x72531),x72532),x72533))+~P1(f317(f317(f319(x72531),x72532),x72534))+~P1(f317(f317(f225(f906(x72531,a895)),x72534),x72533)) % 112.26/112.10 [7254]P1(f317(f317(f319(x72541),x72542),x72543))+~P1(f317(f317(f319(x72541),x72542),x72544))+~P1(f317(f317(f224(f906(x72541,a895)),x72544),x72543)) % 112.26/112.10 [7265]~P121(x72651)+~E(x72653,f2(x72651))+P1(f317(f317(f277(x72651),f317(f317(f75(x72651),x72652),x72653)),f317(f317(f75(x72651),x72654),x72653))) % 112.26/112.10 [7266]~P121(x72661)+~E(x72662,f2(x72661))+P1(f317(f317(f277(x72661),f317(f317(f75(x72661),x72662),x72663)),f317(f317(f75(x72661),x72662),x72664))) % 112.26/112.10 [7366]P32(x73661,x73662,x73663)+~P1(f317(x73662,f317(f317(f154(x73661),x73663),x73664)))+~P1(f317(f317(f225(a899),x73664),f317(f179(f900(x73661)),x73663))) % 112.26/112.10 [7481]~P107(x74812)+~P1(f317(f317(f225(f906(x74811,x74812)),x74813),x74814))+P1(f317(f317(f224(f906(x74811,x74812)),x74813),x74814)) % 112.26/112.10 [7605]~P1(f317(f317(f319(x76051),x76052),x76054))+P1(f317(f317(f319(x76051),x76052),f32(f906(x76051,a895),x76053)))+~P1(f317(f317(f319(f906(x76051,a895)),x76054),x76053)) % 112.26/112.10 [7607]~P119(x76071)+~P1(f317(f317(f224(a899),x76073),x76074))+P1(f317(f317(f277(x76071),f317(f317(f234(x76071),x76072),x76073)),f317(f317(f234(x76071),x76072),x76074))) % 112.26/112.10 [7635]~P84(x76351)+~P1(f317(f317(f224(x76351),x76353),x76354))+P1(f317(f317(f224(x76351),f317(f317(f74(x76351),x76352),x76353)),f317(f317(f74(x76351),x76352),x76354))) % 112.26/112.10 [7636]~P85(x76361)+~P1(f317(f317(f224(x76361),x76363),x76364))+P1(f317(f317(f224(x76361),f317(f317(f74(x76361),x76362),x76363)),f317(f317(f74(x76361),x76362),x76364))) % 112.26/112.10 [7637]~P84(x76371)+~P1(f317(f317(f224(x76371),x76372),x76374))+P1(f317(f317(f224(x76371),f317(f317(f74(x76371),x76372),x76373)),f317(f317(f74(x76371),x76374),x76373))) % 112.26/112.10 [7638]~P85(x76381)+~P1(f317(f317(f224(x76381),x76382),x76384))+P1(f317(f317(f224(x76381),f317(f317(f74(x76381),x76382),x76383)),f317(f317(f74(x76381),x76384),x76383))) % 112.26/112.10 [7639]~P83(x76391)+~P1(f317(f317(f225(x76391),x76393),x76394))+P1(f317(f317(f225(x76391),f317(f317(f74(x76391),x76392),x76393)),f317(f317(f74(x76391),x76392),x76394))) % 112.26/112.10 [7640]~P84(x76401)+~P1(f317(f317(f225(x76401),x76403),x76404))+P1(f317(f317(f225(x76401),f317(f317(f74(x76401),x76402),x76403)),f317(f317(f74(x76401),x76402),x76404))) % 112.26/112.10 [7641]~P83(x76411)+~P1(f317(f317(f225(x76411),x76412),x76414))+P1(f317(f317(f225(x76411),f317(f317(f74(x76411),x76412),x76413)),f317(f317(f74(x76411),x76414),x76413))) % 112.26/112.10 [7642]~P84(x76421)+~P1(f317(f317(f225(x76421),x76422),x76424))+P1(f317(f317(f225(x76421),f317(f317(f74(x76421),x76422),x76423)),f317(f317(f74(x76421),x76424),x76423))) % 112.26/112.10 [7643]~P121(x76431)+~P1(f317(f317(f277(x76431),x76433),x76434))+P1(f317(f317(f277(x76431),f317(f317(f75(x76431),x76432),x76433)),f317(f317(f75(x76431),x76432),x76434))) % 112.26/112.10 [7644]~P121(x76441)+~P1(f317(f317(f277(x76441),x76442),x76444))+P1(f317(f317(f277(x76441),f317(f317(f75(x76441),x76442),x76443)),f317(f317(f75(x76441),x76444),x76443))) % 112.26/112.10 [7645]~P119(x76451)+~P1(f317(f317(f277(x76451),x76452),x76454))+P1(f317(f317(f277(x76451),f317(f317(f234(x76451),x76452),x76453)),f317(f317(f234(x76451),x76454),x76453))) % 112.26/112.10 [7652]~P110(x76521)+~P93(x76521)+E(f317(f317(f3(x76521),f317(f317(f75(x76521),x76522),f317(f94(x76521),x76523))),f317(f317(f75(x76521),x76524),f317(f94(x76521),x76523))),f317(f317(f75(x76521),f317(f317(f3(x76521),x76522),x76524)),f317(f94(x76521),x76523))) % 112.26/112.10 [7653]~P139(x76531)+~P93(x76531)+E(f317(f317(f74(x76531),f317(f317(f75(x76531),x76532),f317(f94(x76531),x76533))),f317(f317(f75(x76531),x76534),f317(f94(x76531),x76533))),f317(f317(f75(x76531),f317(f317(f74(x76531),x76532),x76534)),f317(f94(x76531),x76533))) % 112.26/112.10 [7689]~P69(x76891)+E(f317(f317(f74(x76891),f317(x76892,x76893)),f317(f317(f8(a899,x76891),x76892),f293(a899,f317(a102,x76893),x76894))),f317(f317(f8(a899,x76891),x76892),f293(a899,x76893,x76894)))+~P1(f317(f317(f224(a899),x76893),x76894)) % 112.26/112.10 [7701]~P24(x77012,x77011,x77013,f317(f162(x77012),x77014))+~P1(f317(f127(x77012),x77014))+P1(f317(f127(x77011),f317(f317(f144(x77012,x77011),x77013),x77014))) % 112.26/112.10 [7750]~P1(f317(f317(f224(a899),x77502),x77504))+~P1(f317(f317(f224(a899),x77501),x77503))+P1(f317(f317(f224(a899),f317(f317(f74(a899),x77501),x77502)),f317(f317(f74(a899),x77503),x77504))) % 112.26/112.10 [7751]~P1(f317(f317(f224(a899),x77512),x77514))+~P1(f317(f317(f224(a899),x77511),x77513))+P1(f317(f317(f224(a899),f317(f317(f75(a899),x77511),x77512)),f317(f317(f75(a899),x77513),x77514))) % 112.26/112.10 [7754]~P1(f317(f317(f225(a899),x77542),x77544))+~P1(f317(f317(f225(a899),x77541),x77543))+P1(f317(f317(f225(a899),f317(f317(f74(a899),x77541),x77542)),f317(f317(f74(a899),x77543),x77544))) % 112.26/112.10 [7755]~P1(f317(f317(f224(a1),x77552),x77554))+~P1(f317(f317(f225(a1),x77551),x77553))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x77551),x77552)),f317(f317(f74(a1),x77553),x77554))) % 112.26/112.10 [7803]P1(f317(f317(f319(x78031),x78032),x78033))+~P1(f317(f317(f319(x78031),x78032),f33(f906(x78031,a895),x78034)))+~P1(f317(f317(f319(f906(x78031,a895)),x78033),x78034)) % 112.26/112.10 [7820]~P1(f317(x78201,f640(x78201,x78203,x78202)))+P1(f317(x78201,f317(f317(f154(x78202),x78203),x78204)))+~P1(f317(f317(f225(a899),x78204),f317(f179(f900(x78202)),x78203))) % 112.26/112.10 [7825]P1(f317(x78251,x78252))+~P1(f317(f317(f319(x78254),x78252),f317(f162(x78254),x78253)))+P1(f317(f317(f225(a899),f642(x78251,x78253,x78254)),f317(f179(f900(x78254)),x78253))) % 112.26/112.10 [7872]~P107(x78721)+~P1(f317(f317(f225(f906(x78722,x78721)),x78724),x78723))+~P1(f317(f317(f224(f906(x78722,x78721)),x78723),x78724)) % 112.26/112.10 [7917]~P1(f317(x79174,x79172))+~P1(f317(f317(f319(x79171),x79172),x79173))+P1(f317(f317(f319(x79171),x79172),f317(f317(f92(f906(x79171,a895)),x79173),f317(f252(x79171),x79174)))) % 112.26/112.10 [8062]~P1(f317(f317(f319(x80621),x80623),x80624))+~P1(f317(f317(f225(f906(x80621,a895)),x80622),x80624))+P1(f317(f317(f225(f906(x80621,a895)),x80622),f317(f317(f299(x80621),x80623),x80624))) % 112.26/112.10 [8064]E(f317(f317(f92(f906(x80641,a895)),x80642),x80643),f178(f906(x80641,a895)))+~E(f317(f317(f92(f906(x80641,a895)),f32(f906(x80641,a895),x80644)),x80643),f178(f906(x80641,a895)))+~P1(f317(f317(f319(f906(x80641,a895)),x80642),x80644)) % 112.26/112.10 [8137]P1(f317(f317(f319(x81371),x81372),x81373))+~P1(f317(f317(f224(f906(x81371,a895)),x81373),f317(f317(f299(x81371),x81372),x81374)))+P1(f317(f317(f224(f906(x81371,a895)),x81373),x81374)) % 112.26/112.10 [8154]P1(f317(f317(f319(x81542),f640(x81541,x81543,x81542)),f317(f162(x81542),x81543)))+P1(f317(x81541,f317(f317(f154(x81542),x81543),x81544)))+~P1(f317(f317(f225(a899),x81544),f317(f179(f900(x81542)),x81543))) % 112.26/112.10 [8162]~P1(f317(f317(f224(f906(x81621,a895)),x81622),x81624))+P1(f317(f317(f224(f906(x81621,a895)),x81622),x81623))+~P1(f317(f317(f224(f906(x81621,a895)),x81624),x81623)) % 112.26/112.10 [8163]~P1(f317(f317(f225(f906(x81631,a895)),x81632),x81634))+~P1(f317(f317(f224(f906(x81631,a895)),x81634),x81633))+P1(f317(f317(f225(f906(x81631,a895)),x81632),x81633)) % 112.26/112.10 [8164]~P1(f317(f317(f224(f906(x81641,a895)),x81642),x81644))+~P1(f317(f317(f225(f906(x81641,a895)),x81644),x81643))+P1(f317(f317(f225(f906(x81641,a895)),x81642),x81643)) % 112.26/112.10 [8165]~P1(f317(f317(f225(f906(x81651,a895)),x81652),x81654))+P1(f317(f317(f225(f906(x81651,a895)),x81652),x81653))+~P1(f317(f317(f225(f906(x81651,a895)),x81654),x81653)) % 112.26/112.10 [8209]~P1(f317(f317(f319(x82091),x82094),x82093))+~P1(f317(f317(f225(f906(x82091,a895)),x82092),f317(f317(f299(x82091),x82094),x82093)))+P1(f317(f317(f225(f906(x82091,a895)),x82092),x82093)) % 112.26/112.10 [8220]~P84(x82201)+P1(f317(f317(f224(x82201),x82202),x82203))+~P1(f317(f317(f224(x82201),f317(f317(f74(x82201),x82204),x82202)),f317(f317(f74(x82201),x82204),x82203))) % 112.26/112.10 [8222]~P84(x82221)+P1(f317(f317(f224(x82221),x82222),x82223))+~P1(f317(f317(f224(x82221),f317(f317(f74(x82221),x82222),x82224)),f317(f317(f74(x82221),x82223),x82224))) % 112.26/112.10 [8224]~P84(x82241)+P1(f317(f317(f225(x82241),x82242),x82243))+~P1(f317(f317(f225(x82241),f317(f317(f74(x82241),x82244),x82242)),f317(f317(f74(x82241),x82244),x82243))) % 112.26/112.10 [8226]~P84(x82261)+P1(f317(f317(f225(x82261),x82262),x82263))+~P1(f317(f317(f225(x82261),f317(f317(f74(x82261),x82262),x82264)),f317(f317(f74(x82261),x82263),x82264))) % 112.26/112.10 [8277]P1(f317(x82771,x82772))+~E(f317(f317(f128(x82773),f317(f179(f900(x82773)),f167(x82773,x82771,x82774))),x82774),f103(x82773))+~P1(f317(f317(f319(x82773),x82772),f317(f162(x82773),x82774))) % 112.26/112.10 [8396]P1(f317(x83961,x83962))+~P1(f317(f317(f319(x83963),x83962),f317(f162(x83963),x83964)))+P1(f317(f317(f225(a899),f317(f179(f900(x83963)),f317(f126(x83963,x83961),x83964))),f317(f179(f900(x83963)),x83964))) % 112.26/112.10 [8886]~P1(f317(x88861,f734(x88861,x88863,x88862,x88864)))+P1(f317(x88861,f317(f317(f154(x88862),x88863),x88864)))+~P1(f317(f317(f225(a899),x88864),f317(f179(f900(x88862)),x88863))) % 112.37/112.10 [8910]~P24(x89104,x89103,x89101,f232(f906(x89104,a895)))+E(f317(x89101,f508(x89102,x89101,x89103,x89104)),x89102)+~P1(f317(f317(f319(x89103),x89102),f317(f300(x89104,x89103,x89101),f232(f906(x89104,a895))))) % 112.37/112.10 [8978]E(f167(x89781,x89782,x89783),f317(f317(f165(x89781),x89784),x89783))+P1(f317(f317(f225(a899),f705(x89782,x89783,x89781,x89784)),x89784))+P1(f317(f317(f225(a899),x89784),f317(f179(f900(x89781)),x89783))) % 112.37/112.10 [8981]E(f167(x89811,x89812,x89813),f317(f317(f165(x89811),x89814),x89813))+P1(f317(f317(f225(a899),f705(x89812,x89813,x89811,x89814)),x89814))+P1(f317(x89812,f317(f317(f154(x89811),x89813),x89814))) % 112.37/112.10 [9016]P1(f317(x90161,x90162))+~P1(f317(f317(f319(x90164),x90162),f317(f162(x90164),x90163)))+P1(f317(f317(f225(a899),f680(x90162,x90161,x90163,x90164)),f317(f179(f900(x90164)),x90163))) % 112.37/112.10 [9018]E(f167(x90181,x90182,x90183),f317(f317(f165(x90181),x90184),x90183))+P1(f317(f317(f225(a899),x90184),f317(f179(f900(x90181)),x90183)))+P1(f317(f317(f225(a899),f705(x90182,x90183,x90181,x90184)),f317(f179(f900(x90181)),x90183))) % 112.37/112.10 [9025]E(f167(x90251,x90252,x90253),f317(f317(f165(x90251),x90254),x90253))+P1(f317(x90252,f317(f317(f154(x90251),x90253),x90254)))+P1(f317(f317(f225(a899),f705(x90252,x90253,x90251,x90254)),f317(f179(f900(x90251)),x90253))) % 112.37/112.10 [9050]~P126(x90504)+P1(f317(f317(f319(x90501),f333(x90502,x90503,x90501,x90504)),x90503))+P1(f317(f317(f225(x90504),f2(x90504)),f317(f317(f11(x90501,x90504),x90502),x90503))) % 112.37/112.10 [9051]~P126(x90514)+P1(f317(f317(f319(x90511),f334(x90512,x90513,x90511,x90514)),x90513))+P1(f317(f317(f224(x90514),f2(x90514)),f317(f317(f11(x90511,x90514),x90512),x90513))) % 112.37/112.10 [9076]~P1(f317(f29(x90761),x90764))+P1(f317(f317(f319(x90761),f529(x90762,x90763,x90764,x90761)),x90764))+P1(f317(f29(f905(x90761,x90763)),f317(f317(f244(x90761,x90763),x90764),x90762))) % 112.37/112.10 [9108]P1(f317(f317(f319(x91082),f734(x91081,x91083,x91082,x91084)),f317(f162(x91082),x91083)))+P1(f317(x91081,f317(f317(f154(x91082),x91083),x91084)))+~P1(f317(f317(f225(a899),x91084),f317(f179(f900(x91082)),x91083))) % 112.37/112.10 [9237]P1(f317(f317(f224(a899),x92374),f317(f179(f900(x92372)),f167(x92372,x92373,x92371))))+P1(f317(f317(f225(a899),f706(x92371,x92372,x92373,x92374)),x92374))+~P1(f317(f317(f224(a899),x92374),f317(f179(f900(x92372)),x92371))) % 112.37/112.10 [9392]E(f167(x93921,x93922,x93923),f317(f317(f165(x93921),x93924),x93923))+~P1(f317(x93922,f317(f317(f154(x93921),x93923),f705(x93922,x93923,x93921,x93924))))+P1(f317(f317(f225(a899),x93924),f317(f179(f900(x93921)),x93923))) % 112.37/112.10 [9400]E(f167(x94001,x94002,x94003),f317(f317(f165(x94001),x94004),x94003))+~P1(f317(x94002,f317(f317(f154(x94001),x94003),f705(x94002,x94003,x94001,x94004))))+P1(f317(x94002,f317(f317(f154(x94001),x94003),x94004))) % 112.37/112.10 [9404]~P1(f317(f29(x94041),x94043))+~P1(f317(f29(x94042),f317(x94044,f529(x94044,x94042,x94043,x94041))))+P1(f317(f29(f905(x94041,x94042)),f317(f317(f244(x94041,x94042),x94043),x94044))) % 112.37/112.10 [9412]~P126(x94121)+~P1(f317(f317(f224(x94121),f2(x94121)),f317(x94123,f334(x94123,x94124,x94122,x94121))))+P1(f317(f317(f224(x94121),f2(x94121)),f317(f317(f11(x94122,x94121),x94123),x94124))) % 112.37/112.10 [9413]~P126(x94131)+~P1(f317(f317(f225(x94131),f2(x94131)),f317(x94133,f333(x94133,x94134,x94132,x94131))))+P1(f317(f317(f225(x94131),f2(x94131)),f317(f317(f11(x94132,x94131),x94133),x94134))) % 112.37/112.10 [9421]~E(f317(f179(f900(x94214)),x94212),f317(f179(f900(x94214)),x94213))+P1(f317(f317(f319(f905(f900(x94214),f900(x94214))),f317(f317(f242(f900(x94214),f900(x94214)),x94213),x94212)),f148(x94214,x94211)))+P1(f317(f317(f225(a899),f634(x94211,x94212,x94213,x94214)),f317(f179(f900(x94214)),x94213))) % 112.37/112.10 [9473]~P1(f317(x94733,f317(f317(f154(x94732),x94734),f706(x94734,x94732,x94733,x94731))))+P1(f317(f317(f224(a899),x94731),f317(f179(f900(x94732)),f167(x94732,x94733,x94734))))+~P1(f317(f317(f224(a899),x94731),f317(f179(f900(x94732)),x94734))) % 112.37/112.10 [9554]E(f317(f317(f165(x95541),f641(x95542,x95543,x95544,x95541)),x95543),f317(f317(f165(x95541),f641(x95542,x95543,x95544,x95541)),x95544))+~P1(f317(f317(f319(f905(f900(x95541),f900(x95541))),f317(f317(f242(f900(x95541),f900(x95541)),x95544),x95543)),f137(x95541,x95542)))+P1(f317(f317(f225(a899),f317(f179(f900(x95541)),x95544)),f317(f179(f900(x95541)),x95543))) % 112.37/112.10 [9619]~P1(f317(f317(f225(a899),f2(a899)),x96193))+~P1(f317(f317(f225(a899),x96194),x96191))+P1(f317(f317(f225(a899),f317(f317(f74(a899),f317(f317(f75(a899),x96191),f41(a899,x96192,x96193))),x96194)),f317(f317(f75(a899),x96191),x96193))) % 112.37/112.10 [9811]~P107(x98112)+~P1(f317(f317(f224(x98112),f317(x98113,f873(x98114,x98113,x98111,x98112))),f317(x98114,f873(x98114,x98113,x98111,x98112))))+P1(f317(f317(f224(f906(x98111,x98112)),x98113),x98114)) % 112.37/112.10 [9915]~P68(x99151)+E(f317(f317(f8(a899,x99151),f317(f317(f20(a899,x99151,x99151),f317(f317(f10(x99151,f906(x99151,x99151),a899),f3(x99151)),x99152)),f317(f317(f10(a899,x99151,a899),x99152),f317(f317(f9(a899,a899,a899),f74(a899)),f72(a899))))),f293(a899,x99153,x99154)),f317(f317(f3(x99151),f317(x99152,x99153)),f317(x99152,f317(f317(f74(a899),x99154),f72(a899)))))+~P1(f317(f317(f224(a899),x99153),x99154)) % 112.37/112.10 [9990]~P36(x99903,f317(f317(f279(x99903,x99903,x99903),x99902),f297(x99903,x99902)))+~P1(f317(f317(f319(f905(x99903,x99903)),f317(f317(f242(x99903,x99903),f317(x99901,f317(a102,f820(x99902,x99901,x99903)))),f317(x99901,f820(x99902,x99901,x99903)))),f297(x99903,x99902)))+E(f317(x99901,f317(f317(f74(a899),f819(x99902,x99901,x99903)),x99904)),f317(x99901,f819(x99902,x99901,x99903))) % 112.37/112.10 [6852]~P3(x68521)+E(f317(f317(f31(x68521),f317(f317(f75(x68521),x68522),x68523)),x68524),f317(f317(f75(x68521),x68522),f317(f317(f31(x68521),x68523),x68524)))+~P1(f317(f317(f277(x68521),x68524),x68523)) % 112.37/112.10 [6939]E(f317(f317(f124(x69391),x69392),x69393),x69394)+~E(x69393,f317(f317(f128(x69391),f317(f179(f900(x69391)),x69392)),x69394))+~E(f317(f317(f165(x69391),f317(f179(f900(x69391)),x69392)),x69394),x69392) % 112.37/112.10 [6995]~P62(x69952)+E(x69951,f2(x69952))+E(f317(f317(f281(x69952),f317(f317(f234(x69952),x69953),x69954)),f317(f317(f234(x69952),x69951),x69954)),f317(f317(f234(x69952),f317(f317(f281(x69952),x69953),x69951)),x69954)) % 112.37/112.10 [7142]~P3(x71421)+E(f317(f317(f31(x71421),f317(f317(f75(x71421),x71422),x71423)),x71424),f317(f317(f75(x71421),f317(f317(f31(x71421),x71422),x71424)),x71423))+~P1(f317(f317(f277(x71421),x71424),x71422)) % 112.37/112.10 [7151]~P108(x71511)+~P1(f317(f317(f224(x71511),x71513),x71514))+P1(f317(f317(f224(x71511),f317(f317(f228(x71511),x71512),x71513)),x71514)) % 112.37/112.11 [7153]~P108(x71531)+~P1(f317(f317(f224(x71531),x71532),x71534))+P1(f317(f317(f224(x71531),f317(f317(f228(x71531),x71532),x71533)),x71534)) % 112.37/112.11 [7154]~P104(x71541)+~P1(f317(f317(f224(x71541),x71543),x71544))+P1(f317(f317(f224(x71541),f317(f317(f92(x71541),x71542),x71543)),x71544)) % 112.37/112.11 [7155]~P104(x71551)+~P1(f317(f317(f224(x71551),x71552),x71554))+P1(f317(f317(f224(x71551),f317(f317(f92(x71551),x71552),x71553)),x71554)) % 112.37/112.11 [7157]~P108(x71571)+~P1(f317(f317(f225(x71571),x71573),x71574))+P1(f317(f317(f225(x71571),f317(f317(f228(x71571),x71572),x71573)),x71574)) % 112.37/112.11 [7159]~P108(x71591)+~P1(f317(f317(f225(x71591),x71592),x71594))+P1(f317(f317(f225(x71591),f317(f317(f228(x71591),x71592),x71593)),x71594)) % 112.37/112.11 [7160]~P104(x71601)+~P1(f317(f317(f225(x71601),x71603),x71604))+P1(f317(f317(f225(x71601),f317(f317(f92(x71601),x71602),x71603)),x71604)) % 112.37/112.11 [7161]~P104(x71611)+~P1(f317(f317(f225(x71611),x71612),x71614))+P1(f317(f317(f225(x71611),f317(f317(f92(x71611),x71612),x71613)),x71614)) % 112.37/112.11 [7184]~P1(f317(x71843,x71844))+~P1(f317(x71842,x71844))+P1(f317(f317(f317(f92(f906(x71841,a895)),x71842),x71843),x71844)) % 112.37/112.11 [7446]~P3(x74461)+E(f317(f317(f31(x74461),f317(f317(f234(x74461),x74462),x74463)),f317(f317(f234(x74461),x74464),x74463)),f317(f317(f234(x74461),f317(f317(f31(x74461),x74462),x74464)),x74463))+~P1(f317(f317(f277(x74461),x74464),x74462)) % 112.37/112.11 [7679]~P69(x76791)+E(f317(f317(f74(x76791),f317(x76792,x76793)),f317(f317(f8(a899,x76791),x76792),f317(f292(a899,f317(a102,x76793)),x76794))),f317(f317(f8(a899,x76791),x76792),f317(f292(a899,x76793),x76794)))+~P1(f317(f317(f225(a899),x76793),x76794)) % 112.37/112.11 [7697]E(x76971,x76972)+P1(f317(f317(f162(x76973),x76974),x76972))+~P1(f317(f317(f162(x76973),f317(f317(f141(x76973),x76971),x76974)),x76972)) % 112.37/112.11 [7709]~P108(x77091)+P1(f317(f317(f224(x77091),x77092),x77093))+~P1(f317(f317(f224(x77091),f317(f317(f223(x77091),x77094),x77092)),x77093)) % 112.37/112.11 [7711]~P108(x77111)+P1(f317(f317(f224(x77111),x77112),x77113))+~P1(f317(f317(f224(x77111),f317(f317(f223(x77111),x77112),x77114)),x77113)) % 112.37/112.11 [7713]~P98(x77131)+P1(f317(f317(f224(x77131),x77132),x77133))+~P1(f317(f317(f224(x77131),f317(f317(f91(x77131),x77134),x77132)),x77133)) % 112.37/112.11 [7715]~P98(x77151)+P1(f317(f317(f224(x77151),x77152),x77153))+~P1(f317(f317(f224(x77151),f317(f317(f91(x77151),x77152),x77154)),x77153)) % 112.37/112.11 [7716]~P108(x77161)+P1(f317(f317(f225(x77161),x77162),x77163))+~P1(f317(f317(f225(x77161),f317(f317(f223(x77161),x77164),x77162)),x77163)) % 112.37/112.11 [7717]~P108(x77171)+P1(f317(f317(f225(x77171),x77172),x77173))+~P1(f317(f317(f225(x77171),f317(f317(f223(x77171),x77172),x77174)),x77173)) % 112.37/112.11 [7718]~P119(x77181)+P1(f317(f317(f277(x77181),x77182),x77183))+~P1(f317(f317(f277(x77181),f317(f317(f75(x77181),x77184),x77182)),x77183)) % 112.37/112.11 [7719]~P119(x77191)+P1(f317(f317(f277(x77191),x77192),x77193))+~P1(f317(f317(f277(x77191),f317(f317(f75(x77191),x77192),x77194)),x77193)) % 112.37/112.11 [7795]~P1(f317(f317(f319(x77951),x77952),x77954))+P1(f317(f317(f319(x77951),x77952),x77953))+P1(f317(f317(f319(x77951),x77952),f317(f317(f3(f906(x77951,a895)),x77954),x77953))) % 112.37/112.11 [7879]P1(f317(x78791,x78792))+P1(f317(x78793,x78792))+~P1(f317(f317(f317(f91(f906(x78794,a895)),x78793),x78791),x78792)) % 112.37/112.11 [7891]~P1(f317(f317(f319(x78911),x78912),x78914))+~P1(f317(f317(f319(x78911),x78912),x78913))+P1(f317(f317(f319(x78911),x78912),f317(f317(f92(f906(x78911,a895)),x78913),x78914))) % 112.37/112.11 [7939]~P108(x79391)+~P1(f317(f29(x79391),x79394))+E(f317(f317(f59(x79391,x79391,f228(x79391)),x79392),f317(f317(f299(x79391),x79393),x79394)),f317(f317(f228(x79391),x79393),f317(f317(f59(x79391,x79391,f228(x79391)),x79392),x79394))) % 112.37/112.11 [7940]~P108(x79401)+~P1(f317(f29(x79401),x79404))+E(f317(f317(f59(x79401,x79401,f223(x79401)),x79402),f317(f317(f299(x79401),x79403),x79404)),f317(f317(f223(x79401),x79403),f317(f317(f59(x79401,x79401,f223(x79401)),x79402),x79404))) % 112.37/112.11 [7941]~P98(x79411)+~P1(f317(f29(x79411),x79414))+E(f317(f317(f59(x79411,x79411,f91(x79411)),x79412),f317(f317(f299(x79411),x79413),x79414)),f317(f317(f91(x79411),x79413),f317(f317(f59(x79411,x79411,f91(x79411)),x79412),x79414))) % 112.37/112.11 [7942]~P104(x79421)+~P1(f317(f29(x79421),x79424))+E(f317(f317(f59(x79421,x79421,f92(x79421)),x79422),f317(f317(f299(x79421),x79423),x79424)),f317(f317(f92(x79421),x79423),f317(f317(f59(x79421,x79421,f92(x79421)),x79422),x79424))) % 112.37/112.11 [7944]~P110(x79441)+~P93(x79441)+E(f317(f317(f3(x79441),f317(f317(f75(x79441),f317(f94(x79441),x79442)),x79443)),f317(f317(f75(x79441),f317(f94(x79441),x79442)),x79444)),f317(f317(f75(x79441),f317(f94(x79441),x79442)),f317(f317(f3(x79441),x79443),x79444))) % 112.37/112.11 [7945]~P139(x79451)+~P93(x79451)+E(f317(f317(f74(x79451),f317(f317(f75(x79451),f317(f94(x79451),x79452)),x79453)),f317(f317(f75(x79451),f317(f94(x79451),x79452)),x79454)),f317(f317(f75(x79451),f317(f94(x79451),x79452)),f317(f317(f74(x79451),x79453),x79454))) % 112.37/112.11 [8060]E(x80601,x80602)+P1(f317(f317(f319(x80603),x80601),f317(f162(x80603),x80604)))+~P1(f317(f317(f319(x80603),x80601),f317(f162(x80603),f317(f317(f141(x80603),x80602),x80604)))) % 112.37/112.11 [8231]P54(x82311,x82312,x82313)+~P54(x82311,x82312,x82314)+~P1(f317(f317(f224(f906(f905(x82311,x82312),a895)),x82313),x82314)) % 112.37/112.11 [8279]P1(f317(f317(f319(x82791),x82792),x82793))+P1(f317(f317(f319(x82791),x82792),x82794))+~P1(f317(f317(f319(x82791),x82792),f317(f317(f91(f906(x82791,a895)),x82794),x82793))) % 112.37/112.11 [8289]~P52(x82891,x82894,x82893)+~P1(f317(f317(f319(x82891),x82892),x82894))+P1(f317(f317(f319(f905(x82891,x82891)),f317(f317(f242(x82891,x82891),x82892),x82892)),x82893)) % 112.37/112.11 [8301]~P1(f317(f29(x83012),x83014))+~P1(f317(f29(x83011),x83013))+P1(f317(f29(f905(x83011,x83012)),f317(f317(f244(x83011,x83012),x83013),f317(f18(f906(x83012,a895),x83011),x83014)))) % 112.37/112.11 [8302]~P1(f317(f317(f319(x83021),x83022),x83024))+~P1(f317(f317(f224(f906(x83021,a895)),x83023),x83024))+P1(f317(f317(f224(f906(x83021,a895)),f317(f317(f299(x83021),x83022),x83023)),x83024)) % 112.37/112.11 [8309]~P75(x83092)+~P145(x83092)+E(f317(f317(f11(x83091,x83092),f317(f317(f10(a899,x83092,x83091),f90(x83092)),x83093)),x83094),f317(f90(x83092),f317(f317(f11(x83091,a899),x83093),x83094))) % 112.37/112.11 [8310]~P75(x83102)+~P141(x83102)+E(f317(f317(f11(x83101,x83102),f317(f317(f10(a1,x83102,x83101),f93(x83102)),x83103)),x83104),f317(f93(x83102),f317(f317(f11(x83101,a1),x83103),x83104))) % 112.37/112.11 [8334]E(f317(f317(f3(f906(x83341,a895)),x83342),f317(f317(f3(f906(x83341,a895)),x83343),x83344)),x83344)+~P1(f317(f317(f224(f906(x83341,a895)),x83342),x83343))+~P1(f317(f317(f224(f906(x83341,a895)),x83344),x83342)) % 112.37/112.11 [8431]~P1(f317(f29(x84311),x84314))+E(f317(f317(f3(a899),f317(f317(f8(x84311,a899),x84312),x84313)),f317(f317(f8(x84311,a899),x84312),x84314)),f317(f317(f8(x84311,a899),x84312),f317(f317(f3(f906(x84311,a895)),x84313),x84314)))+~P1(f317(f317(f224(f906(x84311,a895)),x84314),x84313)) % 112.37/112.11 [8584]~P8(x85841,x85844,x85843)+~P1(f317(f317(f319(x85841),x85842),x85844))+P1(f317(f317(f319(x85841),x85842),f317(f275(x85841,x85841,x85843),f317(f317(f299(x85841),x85842),f178(f906(x85841,a895)))))) % 112.37/112.11 [8645]~P1(f317(f317(f224(f906(x86451,a895)),x86452),x86453))+~P1(f317(f317(f224(f906(x86451,a895)),x86452),x86454))+P1(f317(f317(f224(f906(x86451,a895)),x86452),f317(f317(f92(f906(x86451,a895)),x86453),x86454))) % 112.37/112.11 [8747]E(x87471,f178(f906(x87472,a895)))+P1(f317(f29(x87473),x87474))+~P1(f317(f29(f905(x87473,x87472)),f317(f317(f244(x87473,x87472),x87474),f317(f18(f906(x87472,a895),x87473),x87471)))) % 112.37/112.11 [8748]E(x87481,f178(f906(x87482,a895)))+P1(f317(f29(x87483),x87484))+~P1(f317(f29(f905(x87482,x87483)),f317(f317(f244(x87482,x87483),x87481),f317(f18(f906(x87483,a895),x87482),x87484)))) % 112.37/112.11 [8821]P1(f317(f317(f319(x88211),x88212),f306(x88211,x88213)))+~P1(f317(f317(f319(x88211),x88214),f306(x88211,x88213)))+~P1(f317(f317(f319(f905(x88211,x88211)),f317(f317(f242(x88211,x88211),x88212),x88214)),x88213)) % 112.37/112.11 [8878]~P36(x88781,x88784)+P1(f317(f317(f319(f905(x88781,x88781)),f317(f317(f242(x88781,x88781),x88783),x88782)),f297(x88781,x88784)))+P36(x88781,f317(f317(f299(f905(x88781,x88781)),f317(f317(f242(x88781,x88781),x88782),x88783)),x88784)) % 112.37/112.11 [8879]~P57(x88791,x88794)+P1(f317(f317(f319(f905(x88791,x88791)),f317(f317(f242(x88791,x88791),x88793),x88792)),f297(x88791,x88794)))+P57(x88791,f317(f317(f299(f905(x88791,x88791)),f317(f317(f242(x88791,x88791),x88792),x88793)),x88794)) % 112.37/112.11 [8961]~E(x89612,x89613)+~P1(f317(f317(f319(x89611),x89612),f317(f162(x89611),x89614)))+P1(f317(f317(f319(f905(x89611,x89611)),f317(f317(f242(x89611,x89611),x89612),x89613)),f317(f162(f905(x89611,x89611)),f317(f317(f171(x89611,x89611),x89614),x89614)))) % 112.37/112.11 [9049]~E(x90493,x90494)+P1(f317(f317(f247(x90491,x90491,a895),a314),x90492))+~P1(f317(f317(f319(f905(x90491,x90491)),x90492),f317(f162(f905(x90491,x90491)),f317(f317(f171(x90491,x90491),x90493),x90494)))) % 112.37/112.11 [9093]P1(f317(f317(f319(f905(f900(x90931),f900(x90931))),f317(f317(f242(f900(x90931),f900(x90931)),x90932),x90933)),f137(x90931,x90934)))+~E(f317(f317(f165(x90931),f317(f179(f900(x90931)),x90932)),x90933),x90932)+~P1(f317(f317(f225(a899),f317(f179(f900(x90931)),x90932)),f317(f179(f900(x90931)),x90933))) % 112.37/112.11 [9096]~P51(x90961,x90964)+~P1(f317(f317(f319(f905(x90961,x90961)),f317(f317(f242(x90961,x90961),x90963),x90962)),x90964))+P1(f317(f317(f319(f905(x90961,x90961)),f317(f317(f242(x90961,x90961),x90962),x90963)),x90964)) % 112.37/112.11 [9187]~P1(f317(f29(x91871),x91874))+P1(f317(f317(f319(x91871),f471(x91872,x91873,x91874,x91871)),x91874))+P1(f317(f29(x91873),f317(f317(f36(x91871,f906(x91873,a895)),x91874),x91872))) % 112.37/112.11 [9188]~P1(f317(f29(x91881),x91884))+P1(f317(f317(f319(x91881),f571(x91882,x91883,x91884,x91881)),x91884))+P1(f317(f29(x91883),f317(f317(f36(x91881,f906(x91883,a895)),x91884),x91882))) % 112.37/112.11 [9273]P1(f317(f317(f319(f905(x92731,x92731)),x92732),f317(f317(f279(x92731,x92731,x92731),x92733),f297(x92731,x92733))))+~P1(f317(f317(f225(a899),f2(a899)),x92734))+~P1(f317(f317(f319(f905(x92731,x92731)),x92732),f317(f317(f173(f905(x92731,x92731),a895),x92734),x92733))) % 112.37/112.11 [9281]~P36(x92811,x92812)+~P1(f317(f317(f319(f905(x92811,x92811)),f317(f317(f242(x92811,x92811),x92814),x92813)),x92812))+~P1(f317(f317(f319(f905(x92811,x92811)),f317(f317(f242(x92811,x92811),x92813),x92814)),x92812)) % 112.37/112.11 [9411]~P1(f317(f29(x94111),x94114))+E(f317(f317(f8(x94111,a899),f317(f317(f10(f906(x94112,a895),a899,x94111),f30(x94112)),x94113)),x94114),f317(f30(f905(x94111,x94112)),f317(f317(f244(x94111,x94112),x94114),x94113)))+P1(f317(f317(f319(x94111),f530(x94113,x94112,x94114,x94111)),x94114)) % 112.37/112.11 [9415]~P1(f317(f127(x94151),x94152))+P1(f317(f127(x94151),f317(f317(f149(x94151,x94152),x94153),x94154)))+P1(f317(f317(f319(x94151),x94154),f317(f317(f3(f906(x94151,a895)),f317(f162(x94151),x94152)),f317(f317(f299(x94151),f317(f317(f154(x94151),x94152),x94153)),f178(f906(x94151,a895)))))) % 112.37/112.11 [9432]~P1(f317(f29(x94322),x94323))+~P1(f317(f29(x94321),f317(x94324,f471(x94324,x94321,x94323,x94322))))+P1(f317(f29(x94321),f317(f317(f36(x94322,f906(x94321,a895)),x94323),x94324))) % 112.37/112.11 [9433]~P1(f317(f29(x94332),x94333))+~P1(f317(f29(x94331),f317(x94334,f571(x94334,x94331,x94333,x94332))))+P1(f317(f29(x94331),f317(f317(f36(x94332,f906(x94331,a895)),x94333),x94334))) % 112.37/112.11 [9511]~P1(f317(f317(f319(f905(x95111,x95111)),x95112),f317(f317(f279(x95111,x95111,x95111),x95114),f297(x95111,x95114))))+P1(f317(f317(f319(f905(x95111,x95111)),x95112),f317(f317(f279(x95111,x95111,x95111),x95113),f297(x95111,x95113))))+~P1(f317(f317(f224(f906(f905(x95111,x95111),a895)),x95114),x95113)) % 112.37/112.11 [9521]E(f317(f317(f165(x95211),f641(x95214,x95213,x95212,x95211)),x95213),f317(f317(f165(x95211),f641(x95214,x95213,x95212,x95211)),x95212))+~P1(f317(f317(f319(f905(f900(x95211),f900(x95211))),f317(f317(f242(f900(x95211),f900(x95211)),x95212),x95213)),f137(x95211,x95214)))+E(f317(f317(f165(x95211),f317(f179(f900(x95211)),x95212)),x95213),x95212) % 112.37/112.11 [9537]~P1(f317(f29(x95371),x95374))+E(f317(f317(f8(x95371,a899),f317(f317(f10(f906(x95372,a895),a899,x95371),f30(x95372)),x95373)),x95374),f317(f30(f905(x95371,x95372)),f317(f317(f244(x95371,x95372),x95374),x95373)))+~P1(f317(f29(x95372),f317(x95373,f530(x95373,x95372,x95374,x95371)))) % 112.37/112.11 [9541]~E(f317(f179(f900(x95411)),x95413),f317(f179(f900(x95411)),x95412))+P1(f317(f317(f319(f905(f900(x95411),f900(x95411))),f317(f317(f242(f900(x95411),f900(x95411)),x95412),x95413)),f148(x95411,x95414)))+P1(f317(f317(f319(f905(x95411,x95411)),f646(x95414,x95413,x95412,x95411)),f317(f162(f905(x95411,x95411)),f317(f317(f171(x95411,x95411),x95412),x95413)))) % 112.37/112.11 [9630]~P1(f317(f317(f319(f905(f900(x96301),f900(x96301))),f317(f317(f242(f900(x96301),f900(x96301)),x96302),x96303)),f137(x96301,x96304)))+E(f317(f317(f165(x96301),f317(f179(f900(x96301)),x96302)),x96303),x96302)+P1(f317(f317(f225(a899),f641(x96304,x96303,x96302,x96301)),f317(f317(f228(a899),f317(f179(f900(x96301)),x96302)),f317(f179(f900(x96301)),x96303)))) % 112.37/112.11 [9654]~P1(f317(f317(f319(f905(f900(x96541),f900(x96541))),f317(f317(f242(f900(x96541),f900(x96541)),x96542),x96543)),f137(x96541,x96544)))+P1(f317(f317(f225(a899),f317(f179(f900(x96541)),x96542)),f317(f179(f900(x96541)),x96543)))+P1(f317(f317(f225(a899),f641(x96544,x96543,x96542,x96541)),f317(f317(f228(a899),f317(f179(f900(x96541)),x96542)),f317(f179(f900(x96541)),x96543)))) % 112.37/112.11 [10057]~P1(f317(f317(f319(f905(f900(x100571),f900(x100571))),f317(f317(f242(f900(x100571),f900(x100571)),x100572),x100573)),f137(x100571,x100574)))+E(f317(f317(f165(x100571),f317(f179(f900(x100571)),x100572)),x100573),x100572)+P1(f317(f317(f319(f905(x100571,x100571)),f317(f317(f242(x100571,x100571),f317(f317(f154(x100571),x100572),f641(x100574,x100573,x100572,x100571))),f317(f317(f154(x100571),x100573),f641(x100574,x100573,x100572,x100571)))),x100574)) % 112.37/112.11 [10058]~P1(f317(f317(f319(f905(f900(x100581),f900(x100581))),f317(f317(f242(f900(x100581),f900(x100581)),x100582),x100583)),f137(x100581,x100584)))+P1(f317(f317(f225(a899),f317(f179(f900(x100581)),x100582)),f317(f179(f900(x100581)),x100583)))+P1(f317(f317(f319(f905(x100581,x100581)),f317(f317(f242(x100581,x100581),f317(f317(f154(x100581),x100582),f641(x100584,x100583,x100582,x100581))),f317(f317(f154(x100581),x100583),f641(x100584,x100583,x100582,x100581)))),x100584)) % 112.37/112.11 [10126]~E(f317(f179(f900(x101261)),x101262),f317(f179(f900(x101261)),x101263))+P1(f317(f317(f319(f905(f900(x101261),f900(x101261))),f317(f317(f242(f900(x101261),f900(x101261)),x101262),x101263)),f148(x101261,x101264)))+~P1(f317(f317(f319(f905(x101261,x101261)),f317(f317(f242(x101261,x101261),f317(f317(f154(x101261),x101262),f634(x101264,x101263,x101262,x101261))),f317(f317(f154(x101261),x101263),f634(x101264,x101263,x101262,x101261)))),x101264)) % 112.37/112.11 [10274]~P69(x102741)+~P1(f317(f29(x102742),x102744))+E(f317(f155(x102741),f317(f317(f144(x102742,x102741),x102743),f84(f900(x102742),f317(f317(f20(f900(x102742),a895,a895),f317(f317(f10(a895,f906(a895,a895),f900(x102742)),a315),f317(f317(f9(f900(x102742),f906(x102742,a895),a895),f317(f317(f10(f906(x102742,a895),f906(f906(x102742,a895),a895),f900(x102742)),a314),f162(x102742))),x102744))),f127(x102742))))),f221(x102742,x102741,x102743,x102744)) % 112.37/112.11 [7527]~P61(x75272)+E(x75271,f2(x75272))+E(f317(f317(f281(x75272),f317(f317(f74(x75272),x75273),f317(f317(f75(x75272),x75274),x75271))),x75271),f317(f317(f74(x75272),x75274),f317(f317(f281(x75272),x75273),x75271))) % 112.37/112.11 [7528]~P3(x75282)+E(x75281,f2(x75282))+E(f317(f317(f31(x75282),f317(f317(f74(x75282),x75283),f317(f317(f75(x75282),x75284),x75281))),x75281),f317(f317(f74(x75282),x75284),f317(f317(f31(x75282),x75283),x75281))) % 112.37/112.11 [7529]~P3(x75292)+E(x75291,f2(x75292))+E(f317(f317(f31(x75292),f317(f317(f74(x75292),x75293),f317(f317(f75(x75292),x75291),x75294))),x75291),f317(f317(f74(x75292),x75294),f317(f317(f31(x75292),x75293),x75291))) % 112.37/112.11 [7758]~P62(x77582)+E(x77581,f2(x77582))+E(f317(f317(f281(x77582),f317(f317(f3(x77582),x77583),f317(f317(f75(x77582),x77581),x77584))),x77581),f317(f317(f3(x77582),f317(f317(f281(x77582),x77583),x77581)),x77584)) % 112.37/112.11 [7759]~P61(x77592)+E(x77591,f2(x77592))+E(f317(f317(f281(x77592),f317(f317(f74(x77592),x77593),f317(f317(f75(x77592),x77594),x77591))),x77591),f317(f317(f74(x77592),f317(f317(f281(x77592),x77593),x77591)),x77594)) % 112.37/112.11 [7760]~P62(x77602)+E(x77601,f2(x77602))+E(f317(f317(f281(x77602),f317(f317(f74(x77602),x77603),f317(f317(f75(x77602),x77601),x77604))),x77601),f317(f317(f74(x77602),f317(f317(f281(x77602),x77603),x77601)),x77604)) % 112.37/112.11 [8463]~P1(f317(f150(x84631,x84633),x84634))+~P1(f317(f150(x84631,x84632),x84634))+P1(f317(f150(x84631,f317(f317(f92(f906(x84631,a895)),x84632),x84633)),x84634)) % 112.37/112.11 [8836]~E(f317(f317(f279(x88361,x88361,x88361),x88362),x88364),f178(f906(f905(x88361,x88361),a895)))+~E(f317(f317(f279(x88361,x88361,x88361),x88362),x88363),f178(f906(f905(x88361,x88361),a895)))+E(f317(f317(f279(x88361,x88361,x88361),x88362),f317(f317(f91(f906(f905(x88361,x88361),a895)),x88363),x88364)),f178(f906(f905(x88361,x88361),a895))) % 112.37/112.11 [8962]~P1(f317(f317(f224(f906(x89621,a895)),x89623),x89624))+~P1(f317(f317(f224(f906(x89621,a895)),x89622),x89624))+P1(f317(f317(f224(f906(x89621,a895)),f317(f317(f91(f906(x89621,a895)),x89622),x89623)),x89624)) % 112.37/112.11 [9337]~P1(f317(f29(x93371),x93374))+~P1(f317(f29(x93371),x93373))+E(f317(f317(f3(a899),f317(f317(f74(a899),f317(f317(f8(x93371,a899),x93372),x93373)),f317(f317(f8(x93371,a899),x93372),x93374))),f317(f317(f8(x93371,a899),x93372),f317(f317(f92(f906(x93371,a895)),x93373),x93374))),f317(f317(f8(x93371,a899),x93372),f317(f317(f91(f906(x93371,a895)),x93373),x93374))) % 112.37/112.11 [9429]~P1(f317(f317(f319(x94291),x94293),x94292))+~P1(f317(f317(f224(f906(x94291,a895)),x94292),f317(f317(f299(x94291),x94293),x94294)))+P1(f317(f317(f224(f906(x94291,a895)),f317(f317(f3(f906(x94291,a895)),x94292),f317(f317(f299(x94291),x94293),f178(f906(x94291,a895))))),x94294)) % 112.37/112.11 [9605]~P1(f317(f317(f319(x96051),x96053),x96052))+P1(f317(f317(f224(f906(x96051,a895)),x96052),f317(f317(f299(x96051),x96053),x96054)))+~P1(f317(f317(f224(f906(x96051,a895)),f317(f317(f3(f906(x96051,a895)),x96052),f317(f317(f299(x96051),x96053),f178(f906(x96051,a895))))),x96054)) % 112.37/112.11 [9695]~P1(f317(f317(f224(a899),x96951),x96953))+~P1(f317(f317(f225(a899),x96952),x96954))+P1(f317(f317(f319(f905(f905(a899,a899),f905(a899,a899))),f317(f317(f242(f905(a899,a899),f905(a899,a899)),f317(f317(f242(a899,a899),x96951),x96952)),f317(f317(f242(a899,a899),x96953),x96954))),a26)) % 112.37/112.11 [9696]~P1(f317(f317(f224(a899),x96962),x96964))+~P1(f317(f317(f224(a899),x96961),x96963))+P1(f317(f317(f319(f905(f905(a899,a899),f905(a899,a899))),f317(f317(f242(f905(a899,a899),f905(a899,a899)),f317(f317(f242(a899,a899),x96961),x96962)),f317(f317(f242(a899,a899),x96963),x96964))),a65)) % 112.37/112.11 [9988]~P1(f317(f317(f319(f900(x99881)),x99884),f151(x99881,x99883)))+~P1(f317(f317(f319(f900(x99881)),x99884),f151(x99881,x99882)))+P1(f317(f150(x99881,f317(f317(f92(f906(x99881,a895)),f317(f317(f9(x99881,f906(x99881,a895),a895),f319(x99881)),x99882)),f317(f317(f9(x99881,f906(x99881,a895),a895),f319(x99881)),x99883))),x99884)) % 112.37/112.11 [10092]~P24(x100921,f906(f906(x100921,a895),a895),f317(f317(f9(x100921,f906(f905(x100921,x100921),a895),f906(f906(x100921,a895),a895)),f317(f317(f10(f906(x100921,a895),f906(f906(f905(x100921,x100921),a895),f906(f906(x100921,a895),a895)),x100921),f56(x100921)),f317(f317(f9(x100921,f906(x100921,a895),f906(x100921,a895)),f299(x100921)),f178(f906(x100921,a895))))),x100923),x100922)+~P1(f317(f317(f319(x100921),x100924),x100922))+E(f317(f317(f3(f906(f906(x100921,a895),a895)),f317(f317(f56(x100921),x100922),x100923)),f317(f317(f56(x100921),f317(f317(f299(x100921),x100924),f178(f906(x100921,a895)))),x100923)),f317(f317(f56(x100921),f317(f317(f3(f906(x100921,a895)),x100922),f317(f317(f299(x100921),x100924),f178(f906(x100921,a895))))),x100923)) % 112.37/112.11 [10228]~P52(x102281,x102282,x102284)+~P1(f317(f317(f319(f905(x102281,x102281)),x102283),x102284))+P1(f317(f317(f247(x102281,x102281,a895),f317(f317(f9(x102281,f906(x102281,a895),f906(x102281,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x102281,a895),f906(x102281,a895)),x102281),f10(a895,a895,x102281)),f317(f317(f10(a895,f906(a895,a895),x102281),a315),f317(f317(f9(x102281,f906(x102281,a895),a895),f319(x102281)),x102282)))),f317(f317(f9(x102281,f906(x102281,a895),a895),f319(x102281)),x102282))),x102283)) % 112.37/112.11 [10240]P1(f317(f29(x102401),x102402))+~P1(f317(f29(x102403),f317(f300(x102401,x102403,x102404),x102402)))+~P1(f317(f29(x102401),f317(f252(x102401),f317(f317(f20(x102401,a895,a895),f317(f317(f10(a895,f906(a895,a895),x102401),a315),f317(f317(f9(x102401,f906(x102401,a895),a895),f319(x102401)),x102402))),f317(f317(f9(x102401,x102403,a895),f317(f317(f10(x102403,f906(x102403,a895),x102401),a314),x102404)),f317(x102404,f561(x102404,x102403,x102402,x102401))))))) % 112.37/112.11 [8215]~P62(x82152)+E(x82151,f2(x82152))+E(f317(f317(f281(x82152),f317(f317(f3(x82152),f317(f317(f75(x82152),x82151),x82153)),x82154)),x82151),f317(f317(f3(x82152),x82153),f317(f317(f281(x82152),x82154),x82151))) % 112.37/112.11 [8216]~P62(x82162)+E(x82161,f2(x82162))+E(f317(f317(f281(x82162),f317(f317(f74(x82162),f317(f317(f75(x82162),x82161),x82163)),x82164)),x82161),f317(f317(f74(x82162),x82163),f317(f317(f281(x82162),x82164),x82161))) % 112.37/112.11 [9122]~E(f317(f317(f279(x91221,x91221,x91221),x91223),x91224),f178(f906(f905(x91221,x91221),a895)))+~E(f317(f317(f279(x91221,x91221,x91221),x91222),x91224),f178(f906(f905(x91221,x91221),a895)))+E(f317(f317(f279(x91221,x91221,x91221),f317(f317(f91(f906(f905(x91221,x91221),a895)),x91222),x91223)),x91224),f178(f906(f905(x91221,x91221),a895))) % 112.37/112.11 [9905]~P1(f317(f150(x99051,x99053),x99054))+~P1(f317(f150(x99051,x99052),x99054))+P1(f317(f150(x99051,f317(f317(f20(x99051,a895,a895),f317(f317(f10(a895,f906(a895,a895),x99051),a315),x99052)),x99053)),x99054)) % 112.37/112.11 [10166]P1(f317(x101661,f536(x101662,x101663,x101661,x101664)))+~P1(f317(f29(x101664),f317(f252(x101664),x101661)))+P1(f317(f29(x101663),f317(f252(x101663),f317(f317(f10(f906(x101664,a895),a895,x101663),f81(x101664)),f317(f317(f10(f906(x101664,a895),f906(x101664,a895),x101663),f317(f20(x101664,a895,a895),f317(f317(f10(a895,f906(a895,a895),x101664),a315),x101661))),x101662))))) % 112.37/112.11 [10184]~P1(f317(f29(x101842),f317(f252(x101842),x101843)))+~P1(f317(f29(x101841),f317(f252(x101841),f317(f317(f9(x101841,x101842,a895),x101844),f536(x101844,x101841,x101843,x101842)))))+P1(f317(f29(x101841),f317(f252(x101841),f317(f317(f10(f906(x101842,a895),a895,x101841),f81(x101842)),f317(f317(f10(f906(x101842,a895),f906(x101842,a895),x101841),f317(f20(x101842,a895,a895),f317(f317(f10(a895,f906(a895,a895),x101842),a315),x101843))),x101844))))) % 112.37/112.11 [10253]~P1(f317(f29(x102531),x102534))+P1(f317(f317(f319(x102531),f775(x102532,x102533,x102534,x102531)),x102534))+P1(f317(f29(x102533),f317(f252(x102533),f317(f317(f10(f906(x102531,a895),a895,x102533),f81(x102531)),f317(f317(f10(f906(x102531,a895),f906(x102531,a895),x102533),f317(f20(x102531,a895,a895),f317(f317(f10(a895,f906(a895,a895),x102531),a315),f317(f317(f9(x102531,f906(x102531,a895),a895),f319(x102531)),x102534)))),x102532))))) % 112.37/112.11 [10259]~P1(f317(f29(x102592),x102593))+~P1(f317(f29(x102591),f317(f252(x102591),f317(f317(f9(x102591,x102592,a895),x102594),f775(x102594,x102591,x102593,x102592)))))+P1(f317(f29(x102591),f317(f252(x102591),f317(f317(f10(f906(x102592,a895),a895,x102591),f81(x102592)),f317(f317(f10(f906(x102592,a895),f906(x102592,a895),x102591),f317(f20(x102592,a895,a895),f317(f317(f10(a895,f906(a895,a895),x102592),a315),f317(f317(f9(x102592,f906(x102592,a895),a895),f319(x102592)),x102593)))),x102594))))) % 112.37/112.11 [5108]~E(x51082,x51084)+E(f159(x51081,x51082,x51083),f159(x51081,x51084,x51085))+~E(x51082,f2(a899)) % 112.37/112.11 [5355]E(x53551,x53552)+~E(f159(x53554,x53553,x53551),f159(x53554,x53555,x53552))+E(x53553,f2(a899)) % 112.37/112.11 [6649]E(x66491,x66492)+~E(f317(x66493,x66491),f317(x66493,x66492))+~P24(x66494,x66495,x66493,f232(f906(x66494,a895))) % 112.37/112.11 [7559]E(x75591,x75592)+~P24(x75593,x75594,x75595,f232(f906(x75593,a895)))+~E(f317(f300(x75593,x75594,x75595),x75591),f317(f300(x75593,x75594,x75595),x75592)) % 112.37/112.11 [7813]P24(x78132,x78133,f498(x78134,x78133,x78132,x78131),x78131)+~E(f317(f300(x78133,x78132,x78135),x78134),x78131)+E(x78131,f178(f906(x78132,a895))) % 112.37/112.11 [8345]~P1(f317(f317(x83453,x83452),x83455))+~P1(f317(f317(x83453,x83454),x83452))+P1(f317(f317(f319(x83451),x83452),f280(x83451,x83453,x83454,x83455))) % 112.37/112.11 [8346]~P1(f317(f317(x83463,x83462),x83465))+~P1(f317(f317(x83463,x83464),x83462))+P1(f317(f317(f319(x83461),x83462),f289(x83461,x83463,x83464,x83465))) % 112.37/112.11 [8653]~P24(x86531,x86532,x86533,x86534)+P25(x86531,x86532,x86533,x86534,x86535)+~E(f317(f300(x86531,x86532,x86533),x86534),x86535) % 112.37/112.11 [8786]~P25(x87861,x87863,x87864,x87862,x87865)+~P1(f317(f29(x87863),x87865))+P1(f317(f29(x87861),x87862)) % 112.37/112.11 [8787]~P25(x87873,x87871,x87874,x87875,x87872)+~P1(f317(f29(x87873),x87875))+P1(f317(f29(x87871),x87872)) % 112.37/112.11 [8919]~P24(x89191,x89193,x89195,f232(f906(x89191,a895)))+~P24(x89193,x89192,x89194,f232(f906(x89193,a895)))+P24(x89191,x89192,f317(f67(x89193,x89192,x89191,x89194),x89195),f232(f906(x89191,a895))) % 112.37/112.11 [9488]P1(f317(f317(f319(f905(x94881,x94881)),f317(f317(f242(x94881,x94881),x94882),x94883)),f297(x94881,x94884)))+~P1(f317(f317(f319(f905(x94881,x94881)),f317(f317(f242(x94881,x94881),x94882),x94885)),f297(x94881,x94884)))+~P1(f317(f317(f319(f905(x94881,x94881)),f317(f317(f242(x94881,x94881),x94885),x94883)),f297(x94881,x94884))) % 112.37/112.11 [9528]~P108(x95282)+~P1(f317(f127(x95281),x95285))+P1(f317(f127(x95281),f139(x95281,x95282,x95283,x95284,x95285))) % 112.37/112.11 [5432]~E(x54322,f103(x54321))+E(f317(f317(f124(x54321),x54322),x54323),f317(f317(f141(x54321),x54324),x54325))+~E(x54323,f317(f317(f141(x54321),x54324),x54325)) % 112.37/112.11 [5433]~E(x54332,f103(x54331))+E(f317(f317(f124(x54331),x54332),x54333),f317(f317(f141(x54331),x54334),x54335))+~E(f317(f317(f141(x54331),x54334),x54335),x54333) % 112.37/112.11 [6605]~E(f317(f179(f900(x66051)),x66055),f317(f179(f900(x66052)),x66054))+E(f317(f317(f144(f905(x66051,x66052),x66052),f246(x66051,x66052)),x66053),x66054)+~E(f317(f317(f171(x66051,x66052),x66055),x66054),x66053) % 112.37/112.11 [6606]~E(f317(f179(f900(x66061)),x66064),f317(f179(f900(x66062)),x66065))+E(f317(f317(f144(f905(x66061,x66062),x66061),f241(x66061,x66062)),x66063),x66064)+~E(f317(f317(f171(x66061,x66062),x66064),x66065),x66063) % 112.37/112.11 [7095]~P108(x70951)+~P13(x70951,f317(f317(f144(x70952,x70951),x70953),x70955))+P13(x70951,f317(f317(f144(x70952,x70951),x70953),f317(f126(x70952,x70954),x70955))) % 112.37/112.11 [7237]~P108(x72371)+P13(x72371,f317(f317(f144(x72372,x72371),x72373),f160(x72372,x72374,x72375)))+~P13(x72371,f317(f317(f144(x72372,x72371),x72373),x72375)) % 112.37/112.11 [7260]~P54(x72603,x72602,x72605)+~P54(x72601,x72603,x72604)+P54(x72601,x72602,f317(f317(f279(x72601,x72603,x72602),x72604),x72605)) % 112.37/112.11 [7355]E(x73551,x73552)+~P24(x73553,x73554,x73555,f232(f906(x73553,a895)))+~E(f317(f317(f144(x73553,x73554),x73555),x73551),f317(f317(f144(x73553,x73554),x73555),x73552)) % 112.37/112.11 [7514]~P1(f317(f317(f224(a899),x75141),f317(x75143,x75145)))+P1(f317(f317(f224(a899),x75141),f145(x75142,x75143,x75144)))+~P1(f317(f317(f319(x75142),x75145),f317(f162(x75142),x75144))) % 112.37/112.11 [7515]~P1(f317(f317(f225(a899),x75151),f317(x75153,x75155)))+P1(f317(f317(f225(a899),x75151),f145(x75152,x75153,x75154)))+~P1(f317(f317(f319(x75152),x75155),f317(f162(x75152),x75154))) % 112.37/112.11 [7910]P1(f317(x79101,x79102))+~P1(f317(x79101,x79103))+~P1(f317(f317(f319(x79104),x79102),f317(f162(x79104),f159(x79104,x79105,x79103)))) % 112.37/112.11 [7911]P1(f317(x79111,x79112))+~P1(f317(x79111,x79113))+~P1(f317(f317(f319(x79114),x79113),f317(f162(x79114),f159(x79114,x79115,x79112)))) % 112.37/112.11 [7916]~P109(x79161)+P1(f317(f317(f224(f906(x79161,a895)),f293(x79161,x79162,x79163)),f293(x79161,x79164,x79165)))+P1(f317(f317(f224(x79161),x79162),x79163)) % 112.37/112.11 [7937]~P5(x79371)+P1(f317(f317(f224(x79371),f317(f317(f35(x79372,x79371),x79373),x79374)),f317(x79374,x79375)))+~P1(f317(f317(f319(x79372),x79375),x79373)) % 112.37/112.11 [8006]~P24(x80061,x80062,x80064,x80063)+E(f317(f71(x80061,x80062,x80063,x80064),f317(x80064,x80065)),x80065)+~P1(f317(f317(f319(x80061),x80065),x80063)) % 112.37/112.11 [8007]~P24(x80071,x80072,x80074,x80073)+E(f317(f85(x80071,x80072,x80073,x80074),f317(x80074,x80075)),x80075)+~P1(f317(f317(f319(x80071),x80075),x80073)) % 112.37/112.11 [8204]~P1(f317(x82041,x82045))+P1(f317(x82041,f393(x82041,x82042,x82043,x82044)))+~P1(f317(f317(f319(x82044),x82045),x82043)) % 112.37/112.11 [8205]~P1(f317(x82051,x82055))+P1(f317(x82051,f393(x82051,x82052,x82053,x82054)))+~P1(f317(f317(f319(x82054),x82055),x82052)) % 112.37/112.11 [8299]P1(f317(f29(x82991),x82992))+~P1(f317(f29(x82993),x82994))+~P1(f317(f317(f224(f906(x82991,a895)),x82992),f317(f300(x82993,x82991,x82995),x82994))) % 112.37/112.11 [8467]E(x84671,x84672)+~P24(x84673,x84674,x84675,f317(f317(f91(f906(x84673,a895)),f317(f162(x84673),x84671)),f317(f162(x84673),x84672)))+~E(f317(f317(f144(x84673,x84674),x84675),x84671),f317(f317(f144(x84673,x84674),x84675),x84672)) % 112.37/112.11 [8521]~P109(x85211)+~P1(f317(f317(f225(f906(x85211,a895)),f293(x85211,x85214,x85215)),f293(x85211,x85212,x85213)))+P1(f317(f317(f224(x85211),x85212),x85213)) % 112.37/112.11 [8583]~P24(x85831,x85834,x85835,f232(f906(x85831,a895)))+~P1(f317(f317(f319(x85834),f317(x85835,x85832)),f317(f300(x85831,x85834,x85835),x85833)))+P1(f317(f317(f319(x85831),x85832),x85833)) % 112.37/112.11 [8659]P1(f317(x86591,x86592))+~P1(f317(x86591,f391(x86591,x86593,x86594,x86595)))+~P1(f317(f317(f319(x86595),x86592),x86594)) % 112.37/112.11 [8660]P1(f317(x86601,x86602))+~P1(f317(x86601,f391(x86601,x86603,x86604,x86605)))+~P1(f317(f317(f319(x86605),x86602),x86603)) % 112.37/112.11 [8959]~P24(x89592,x89593,x89591,x89594)+E(f317(x89591,f317(f71(x89592,x89593,x89594,x89591),x89595)),x89595)+~P1(f317(f317(f319(x89593),x89595),f317(f300(x89592,x89593,x89591),x89594))) % 112.37/112.11 [9062]E(x90621,f103(x90622))+E(f317(f317(f141(x90622),x90623),f660(x90624,x90623,x90625,x90621,x90622)),x90621)+~E(f317(f317(f124(x90622),x90621),x90625),f317(f317(f141(x90622),x90623),x90624)) % 112.37/112.11 [9063]E(x90631,f103(x90632))+E(f317(f317(f141(x90632),x90633),f661(x90634,x90631,x90635,x90633,x90632)),x90631)+~E(f317(f317(f124(x90632),x90631),x90634),f317(f317(f141(x90632),x90633),x90635)) % 112.37/112.11 [9081]E(f317(f317(f141(x90812),x90813),f660(x90814,x90813,x90811,x90815,x90812)),x90815)+~E(f317(f317(f124(x90812),x90815),x90811),f317(f317(f141(x90812),x90813),x90814))+E(x90811,f317(f317(f141(x90812),x90813),x90814)) % 112.37/112.11 [9082]E(f317(f317(f141(x90821),x90822),f661(x90824,x90825,x90823,x90822,x90821)),x90825)+~E(f317(f317(f124(x90821),x90825),x90824),f317(f317(f141(x90821),x90822),x90823))+E(f317(f317(f141(x90821),x90822),x90823),x90824) % 112.37/112.11 [9158]~E(f317(f300(x91583,x91582,x91584),f232(f906(x91583,a895))),f232(f906(x91582,a895)))+~E(f317(f300(x91581,x91583,x91585),f232(f906(x91581,a895))),f232(f906(x91583,a895)))+E(f317(f300(x91581,x91582,f317(f67(x91583,x91582,x91581,x91584),x91585)),f232(f906(x91581,a895))),f232(f906(x91582,a895))) % 112.37/112.11 [9394]E(f317(f300(x93941,x93942,x93943),f457(x93944,x93943,x93941,x93945,x93942)),x93945)+~P1(f317(f29(x93942),x93945))+~P1(f317(f317(f224(f906(x93942,a895)),x93945),f317(f300(x93941,x93942,x93943),x93944))) % 112.37/112.11 [9534]E(x95341,f103(x95342))+~E(f317(f317(f124(x95342),x95341),x95343),f317(f317(f141(x95342),x95345),x95344))+E(f317(f317(f124(x95342),f661(x95343,x95341,x95344,x95345,x95342)),x95343),x95344) % 112.37/112.11 [9535]E(x95351,f103(x95352))+~E(f317(f317(f124(x95352),x95351),x95355),f317(f317(f141(x95352),x95354),x95353))+E(f317(f317(f124(x95352),f660(x95353,x95354,x95355,x95351,x95352)),x95355),x95353) % 112.37/112.11 [9542]E(f317(f317(f124(x95422),f660(x95424,x95423,x95421,x95425,x95422)),x95421),x95424)+~E(f317(f317(f124(x95422),x95425),x95421),f317(f317(f141(x95422),x95423),x95424))+E(x95421,f317(f317(f141(x95422),x95423),x95424)) % 112.37/112.11 [9543]~E(f317(f317(f124(x95431),x95435),x95434),f317(f317(f141(x95431),x95432),x95433))+E(f317(f317(f124(x95431),f661(x95434,x95435,x95433,x95432,x95431)),x95434),x95433)+E(f317(f317(f141(x95431),x95432),x95433),x95434) % 112.37/112.11 [9544]E(f317(f317(f124(x95441),x95445),f663(x95443,x95442,x95444,x95445,x95441)),x95442)+E(f317(f317(f124(x95441),x95442),f662(x95443,x95442,x95444,x95445,x95441)),x95445)+~E(f317(f317(f124(x95441),x95445),x95444),f317(f317(f124(x95441),x95442),x95443)) % 112.37/112.11 [9581]~P108(x95811)+P13(x95811,f317(f317(f144(x95812,x95811),x95813),f139(x95812,x95811,x95813,x95814,x95815)))+~P13(x95811,f317(f317(f144(x95812,x95811),x95813),x95815)) % 112.37/112.11 [9600]~P58(x96005,x96001,x96004,x96003)+P1(f317(f317(x96001,x96002),f518(x96003,x96004,x96001,x96005,x96002)))+~P1(f317(f317(f319(x96005),x96002),x96004)) % 112.37/112.11 [9601]~P58(x96015,x96011,x96014,x96013)+P1(f317(f317(x96011,x96012),f781(x96013,x96014,x96011,x96015,x96012)))+~P1(f317(f317(f319(x96015),x96012),x96014)) % 112.37/112.11 [9655]~P1(f317(f29(x96555),x96554))+P1(f317(f29(x96551),f457(x96552,x96553,x96551,x96554,x96555)))+~P1(f317(f317(f224(f906(x96555,a895)),x96554),f317(f300(x96551,x96555,x96553),x96552))) % 112.37/112.11 [9707]~P1(f317(f317(f319(f905(x97071,x97071)),f317(f317(f242(x97071,x97071),x97075),x97073)),f297(x97071,x97074)))+P1(f317(f317(f319(f905(x97071,x97071)),f317(f317(f242(x97071,x97071),x97072),x97073)),f317(f317(f279(x97071,x97071,x97071),x97074),f297(x97071,x97074))))+~P1(f317(f317(f319(f905(x97071,x97071)),f317(f317(f242(x97071,x97071),x97072),x97075)),f317(f317(f279(x97071,x97071,x97071),x97074),f297(x97071,x97074)))) % 112.37/112.11 [9708]~P1(f317(f317(f319(f905(x97081,x97081)),f317(f317(f242(x97081,x97081),x97082),x97085)),f297(x97081,x97084)))+P1(f317(f317(f319(f905(x97081,x97081)),f317(f317(f242(x97081,x97081),x97082),x97083)),f317(f317(f279(x97081,x97081,x97081),x97084),f297(x97081,x97084))))+~P1(f317(f317(f319(f905(x97081,x97081)),f317(f317(f242(x97081,x97081),x97085),x97083)),f317(f317(f279(x97081,x97081,x97081),x97084),f297(x97081,x97084)))) % 112.37/112.11 [9710]P1(f317(f317(f319(f905(f900(x97101),f900(x97101))),f317(f317(f242(f900(x97101),f900(x97101)),x97102),x97103)),f148(x97101,f297(x97101,x97104))))+~P1(f317(f317(f319(f905(f900(x97101),f900(x97101))),f317(f317(f242(f900(x97101),f900(x97101)),x97102),x97105)),f148(x97101,f297(x97101,x97104))))+~P1(f317(f317(f319(f905(f900(x97101),f900(x97101))),f317(f317(f242(f900(x97101),f900(x97101)),x97105),x97103)),f148(x97101,f297(x97101,x97104)))) % 112.37/112.11 [9714]E(f317(f317(f124(x97141),x97142),f662(x97143,x97142,x97144,x97145,x97141)),x97145)+E(f317(f317(f124(x97141),f663(x97143,x97142,x97144,x97145,x97141)),x97143),x97144)+~E(f317(f317(f124(x97141),x97142),x97143),f317(f317(f124(x97141),x97145),x97144)) % 112.37/112.11 [9715]E(f317(f317(f124(x97151),x97152),f663(x97153,x97154,x97155,x97152,x97151)),x97154)+E(f317(f317(f124(x97151),f662(x97153,x97154,x97155,x97152,x97151)),x97155),x97153)+~E(f317(f317(f124(x97151),x97152),x97155),f317(f317(f124(x97151),x97154),x97153)) % 112.37/112.11 [9769]P1(f317(f317(f319(f905(x97691,x97691)),f317(f317(f242(x97691,x97691),x97692),x97693)),f317(f317(f279(x97691,x97691,x97691),x97694),f297(x97691,x97694))))+~P1(f317(f317(f319(f905(x97691,x97691)),f317(f317(f242(x97691,x97691),x97692),x97695)),f317(f317(f279(x97691,x97691,x97691),x97694),f297(x97691,x97694))))+~P1(f317(f317(f319(f905(x97691,x97691)),f317(f317(f242(x97691,x97691),x97695),x97693)),f317(f317(f279(x97691,x97691,x97691),x97694),f297(x97691,x97694)))) % 112.37/112.11 [9796]P33(x97961,x97962,x97963,x97964,x97965)+~E(f317(f179(f900(x97961)),x97964),f317(f179(f900(x97962)),x97965))+~P1(f317(f317(f247(x97961,x97962,a895),x97963),f681(x97965,x97964,x97963,x97962,x97961))) % 112.37/112.11 [9797]P33(x97971,x97972,x97973,x97974,x97975)+~E(f317(f179(f900(x97971)),x97974),f317(f179(f900(x97972)),x97975))+~P1(f317(f317(f247(x97971,x97972,a895),x97973),f682(x97973,x97975,x97974,x97972,x97971))) % 112.37/112.11 [9802]E(f317(f317(f124(x98021),f662(x98022,x98023,x98024,x98025,x98021)),x98024),x98022)+~E(f317(f317(f124(x98021),x98023),x98022),f317(f317(f124(x98021),x98025),x98024))+E(f317(f317(f124(x98021),f663(x98022,x98023,x98024,x98025,x98021)),x98022),x98024) % 112.37/112.11 [9817]~P108(x98172)+E(f317(f317(f138(x98171,x98172,x98173),x98174),x98175),f317(f317(f141(x98171),x98174),x98175))+P1(f317(f317(f319(x98171),f725(x98174,x98173,x98175,x98171,x98172)),f317(f162(x98171),x98175))) % 112.37/112.11 [9821]~P58(x98211,x98214,x98213,x98212)+~P1(f317(f317(f319(x98211),x98215),x98213))+P1(f317(f317(f319(x98211),f518(x98212,x98213,x98214,x98211,x98215)),x98212)) % 112.37/112.11 [9822]~P58(x98221,x98224,x98223,x98222)+~P1(f317(f317(f319(x98221),x98225),x98223))+P1(f317(f317(f319(x98221),f781(x98222,x98223,x98224,x98221,x98225)),x98222)) % 112.37/112.11 [9877]~P1(f317(f29(x98775),x98774))+~P1(f317(f317(f224(f906(x98775,a895)),x98774),f317(f300(x98771,x98775,x98773),x98772)))+P1(f317(f317(f224(f906(x98771,a895)),f457(x98772,x98773,x98771,x98774,x98775)),x98772)) % 112.37/112.11 [9938]~P1(f317(f317(f319(f905(f906(x99381,a895),f906(x99381,a895))),f317(f317(f242(f906(x99381,a895),f906(x99381,a895)),x99384),x99383)),f309(x99381,x99382)))+~P1(f317(f317(f319(x99381),x99385),x99384))+P1(f317(f317(f319(x99381),f593(x99382,x99383,x99384,x99381,x99385)),x99383)) % 112.37/112.11 [9948]~P108(x99482)+E(f317(f317(f138(x99481,x99482,x99483),x99484),x99485),f317(f317(f141(x99481),x99484),x99485))+~P1(f317(f317(f224(x99482),f317(x99483,x99484)),f317(x99483,f725(x99484,x99483,x99485,x99481,x99482)))) % 112.37/112.11 [9997]~P24(x99973,x99974,x99975,f232(f906(x99973,a895)))+P1(f317(x99971,x99972))+~P1(f317(x99971,f317(f85(x99973,x99974,f232(f906(x99973,a895)),x99975),f794(x99972,x99971,x99975,x99974,x99973)))) % 112.37/112.11 [10143]P33(x101431,x101432,x101433,x101434,x101435)+~E(f317(f179(f900(x101431)),x101434),f317(f179(f900(x101432)),x101435))+~P1(f317(f317(x101433,f317(f317(f154(x101431),x101434),f683(x101435,x101434,x101433,x101432,x101431))),f317(f317(f154(x101432),x101435),f683(x101435,x101434,x101433,x101432,x101431)))) % 112.37/112.11 [10144]P33(x101441,x101442,x101443,x101444,x101445)+~E(f317(f179(f900(x101441)),x101444),f317(f179(f900(x101442)),x101445))+~P1(f317(f317(x101443,f317(f317(f154(x101441),x101444),f718(x101443,x101445,x101442,x101444,x101441))),f317(f317(f154(x101442),x101445),f718(x101443,x101445,x101442,x101444,x101441)))) % 112.37/112.11 [6680]~P17(x66802,x66805,x66801)+~P1(f317(f29(x66802),x66804))+E(f317(x66801,f317(f317(f299(x66802),x66803),x66804)),f317(f317(f59(x66802,x66802,x66805),x66803),x66804)) % 112.37/112.11 [6681]~E(x66813,x66814)+~E(x66812,x66815)+E(f317(f317(f299(x66811),x66812),f317(f317(f299(x66811),x66813),f178(f906(x66811,a895)))),f317(f317(f299(x66811),x66814),f317(f317(f299(x66811),x66815),f178(f906(x66811,a895))))) % 112.37/112.11 [6692]P1(f317(x66922,x66925))+E(f167(x66921,x66922,f317(f317(f124(x66921),x66923),x66924)),f167(x66921,x66922,x66923))+~P1(f317(f317(f319(x66921),x66925),f317(f162(x66921),x66923))) % 112.37/112.11 [6730]E(f317(x67301,x67302),f178(f906(x67303,a895)))+~E(f317(f317(f36(x67304,f906(x67303,a895)),x67305),x67301),f178(f906(x67303,a895)))+~P1(f317(f317(f319(x67304),x67302),x67305)) % 112.37/112.11 [6731]E(f317(x67311,x67312),f232(f906(x67313,a895)))+~E(f317(f317(f35(x67314,f906(x67313,a895)),x67315),x67311),f232(f906(x67313,a895)))+~P1(f317(f317(f319(x67314),x67312),x67315)) % 112.37/112.11 [7247]~E(x72472,x72474)+~P143(x72471)+E(f317(f317(f74(x72471),f317(f317(f75(x72471),x72472),x72473)),f317(f317(f75(x72471),x72474),x72475)),f317(f317(f74(x72471),f317(f317(f75(x72471),x72472),x72475)),f317(f317(f75(x72471),x72474),x72473))) % 112.37/112.11 [7309]~P5(x73091)+~P1(f317(f317(f319(x73094),x73093),x73095))+P1(f317(f317(f224(x73091),f317(x73092,x73093)),f317(f317(f36(x73094,x73091),x73095),x73092))) % 112.37/112.11 [7360]~P107(x73601)+P1(f317(f317(f224(x73601),f317(x73602,x73603)),f317(x73604,x73603)))+~P1(f317(f317(f224(f906(x73605,x73601)),x73602),x73604)) % 112.37/112.11 [7483]E(x74831,x74832)+E(x74833,x74831)+~E(f317(f317(f299(x74834),x74831),f317(f317(f299(x74834),x74835),f178(f906(x74834,a895)))),f317(f317(f299(x74834),x74832),f317(f317(f299(x74834),x74833),f178(f906(x74834,a895))))) % 112.37/112.11 [7484]E(x74841,x74842)+E(x74843,x74841)+~E(f317(f317(f299(x74844),x74843),f317(f317(f299(x74844),x74842),f178(f906(x74844,a895)))),f317(f317(f299(x74844),x74845),f317(f317(f299(x74844),x74841),f178(f906(x74844,a895))))) % 112.37/112.11 [7485]E(x74851,x74852)+E(x74851,x74853)+~E(f317(f317(f299(x74854),x74853),f317(f317(f299(x74854),x74852),f178(f906(x74854,a895)))),f317(f317(f299(x74854),x74855),f317(f317(f299(x74854),x74851),f178(f906(x74854,a895))))) % 112.37/112.11 [7486]E(x74861,x74862)+E(x74861,x74863)+~E(f317(f317(f299(x74864),x74861),f317(f317(f299(x74864),x74865),f178(f906(x74864,a895)))),f317(f317(f299(x74864),x74862),f317(f317(f299(x74864),x74863),f178(f906(x74864,a895))))) % 112.37/112.11 [8016]P24(x80161,x80162,x80163,x80164)+~P24(x80161,x80162,x80163,x80165)+~P1(f317(f317(f224(f906(x80161,a895)),x80164),x80165)) % 112.37/112.11 [8046]~E(f317(x80463,x80465),x80464)+~P24(x80461,x80462,x80463,f232(f906(x80461,a895)))+E(f317(f85(x80461,x80462,f232(f906(x80461,a895)),x80463),x80464),x80465) % 112.37/112.11 [8192]E(x81921,x81922)+~E(f317(f300(x81923,x81924,x81925),x81921),f317(f300(x81923,x81924,x81925),x81922))+~P24(x81923,x81924,x81925,f317(f317(f91(f906(x81923,a895)),x81921),x81922)) % 112.37/112.11 [8269]P1(f317(x82692,x82694))+E(f317(f317(f128(x82691),f317(f179(f900(x82691)),f167(x82691,x82692,x82693))),x82693),f317(f317(f141(x82691),x82694),x82695))+~E(f317(f317(f124(x82691),f167(x82691,x82692,x82693)),f317(f317(f141(x82691),x82694),x82695)),x82693) % 112.37/112.11 [8297]~P24(x82971,x82972,x82973,x82975)+~P24(x82971,x82972,x82973,x82974)+P24(x82971,x82972,x82973,f317(f317(f92(f906(x82971,a895)),x82974),x82975)) % 112.37/112.11 [8405]~P69(x84051)+E(f317(f317(f74(x84051),f317(x84052,x84053)),f317(f155(x84051),f317(f317(f144(x84054,x84051),x84052),f160(x84054,x84053,x84055)))),f317(f155(x84051),f317(f317(f144(x84054,x84051),x84052),x84055)))+~P1(f317(f317(f319(x84054),x84053),f317(f162(x84054),x84055))) % 112.37/112.11 [8493]~P108(x84931)+~P13(x84931,f317(f317(f144(x84932,x84931),x84933),x84935))+P13(x84931,f317(f317(f144(x84932,x84931),x84933),f317(f317(f138(x84932,x84931,x84933),x84934),x84935))) % 112.37/112.11 [8579]~P5(x85791)+P1(f317(f317(f224(x85791),f317(f317(f35(x85792,x85791),x85793),x85794)),f317(f317(f35(x85792,x85791),x85795),x85794)))+~P1(f317(f317(f224(f906(x85792,a895)),x85795),x85793)) % 112.37/112.11 [8580]~P5(x85801)+P1(f317(f317(f224(x85801),f317(f317(f36(x85802,x85801),x85803),x85804)),f317(f317(f36(x85802,x85801),x85805),x85804)))+~P1(f317(f317(f224(f906(x85802,a895)),x85803),x85805)) % 112.37/112.11 [8613]~P108(x86133)+P1(f317(f127(x86131),x86132))+~P1(f317(f127(x86131),f317(f317(f138(x86131,x86133,x86134),x86135),x86132))) % 112.37/112.11 [8758]~P108(x87581)+~P1(f317(f317(f319(x87582),x87583),f317(f162(x87582),x87584)))+~P1(f317(f127(x87582),f317(f317(f138(x87582,x87581,x87585),x87583),x87584))) % 112.37/112.11 [8848]~P108(x88481)+P13(x88481,f317(f317(f144(x88482,x88481),x88483),x88484))+~P13(x88481,f317(f317(f144(x88482,x88481),x88483),f317(f317(f138(x88482,x88481,x88483),x88485),x88484))) % 112.37/112.11 [8894]~P24(x88942,x88941,x88944,x88943)+E(f317(f300(x88941,x88942,f85(x88942,x88941,x88943,x88944)),f317(f300(x88942,x88941,x88944),x88945)),x88945)+~P1(f317(f317(f224(f906(x88942,a895)),x88945),x88943)) % 112.37/112.11 [8947]~P108(x89472)+E(f317(f317(f138(x89471,x89472,x89473),x89474),x89475),f139(x89471,x89472,x89473,x89474,x89475))+P1(f317(f317(f319(x89472),f317(x89473,x89474)),f317(f300(x89471,x89472,x89473),f317(f162(x89471),x89475)))) % 112.37/112.11 [9028]~P108(x90282)+E(f139(x90281,x90282,x90283,x90284,x90285),x90285)+~P1(f317(f317(f319(x90282),f317(x90283,x90284)),f317(f300(x90281,x90282,x90283),f317(f162(x90281),x90285)))) % 112.37/112.11 [9042]~P24(x90422,x90421,x90423,x90425)+P1(f317(f317(f225(f906(x90421,a895)),f317(f300(x90422,x90421,x90423),x90424)),f317(f300(x90422,x90421,x90423),x90425)))+~P1(f317(f317(f225(f906(x90422,a895)),x90424),x90425)) % 112.37/112.11 [9199]~P24(x91991,x91992,x91993,f232(f906(x91991,a895)))+~P1(f317(f317(f224(f906(x91992,a895)),x91994),f317(f300(x91991,x91992,x91993),x91995)))+P1(f317(f317(f224(f906(x91991,a895)),f317(f301(x91991,x91992,x91993),x91994)),x91995)) % 112.37/112.11 [9222]~E(f317(f300(x92223,x92221,x92224),f232(f906(x92223,a895))),f232(f906(x92221,a895)))+P1(f317(f317(f224(f906(x92221,a895)),x92222),f317(f300(x92223,x92221,x92224),x92225)))+~P1(f317(f317(f224(f906(x92223,a895)),f317(f301(x92223,x92221,x92224),x92222)),x92225)) % 112.37/112.11 [9329]~P24(x93291,x93294,x93295,f232(f906(x93291,a895)))+~P1(f317(f317(f224(f906(x93294,a895)),f317(f300(x93291,x93294,x93295),x93292)),f317(f300(x93291,x93294,x93295),x93293)))+P1(f317(f317(f224(f906(x93291,a895)),x93292),x93293)) % 112.37/112.11 [9456]~P81(x94561)+~E(f317(x94563,f702(x94563,x94564,x94565,x94562,x94561)),f2(x94561))+E(f317(f155(x94561),f317(f317(f144(x94562,x94561),x94563),f317(f126(x94562,x94564),x94565))),f317(f155(x94561),f317(f317(f144(x94562,x94561),x94563),x94565))) % 112.37/112.11 [9483]~P25(x94831,x94832,x94833,f232(f906(x94831,a895)),f232(f906(x94832,a895)))+~P1(f317(f317(f224(f906(x94832,a895)),x94834),f317(f300(x94831,x94832,x94833),x94835)))+P1(f317(f317(f224(f906(x94831,a895)),f317(f301(x94831,x94832,x94833),x94834)),x94835)) % 112.37/112.11 [9512]~P25(x95123,x95121,x95124,f232(f906(x95123,a895)),f232(f906(x95121,a895)))+P1(f317(f317(f224(f906(x95121,a895)),x95122),f317(f300(x95123,x95121,x95124),x95125)))+~P1(f317(f317(f224(f906(x95123,a895)),f317(f301(x95123,x95121,x95124),x95122)),x95125)) % 112.37/112.11 [9647]~P16(x96471,x96472,x96473)+~P1(f317(f29(x96471),x96475))+P1(f317(f61(x96471,x96472,x96473,x96474,x96475),f317(f317(f59(x96471,x96472,x96473),x96474),x96475))) % 112.37/112.11 [9727]~P25(x97272,x97271,x97274,f232(f906(x97272,a895)),f232(f906(x97271,a895)))+~P25(x97271,x97273,x97275,f232(f906(x97271,a895)),f232(f906(x97273,a895)))+E(f317(f67(x97271,x97272,x97273,f85(x97272,x97271,f232(f906(x97272,a895)),x97274)),f85(x97271,x97273,f232(f906(x97271,a895)),x97275)),f85(x97272,x97273,f232(f906(x97272,a895)),f317(f67(x97271,x97273,x97272,x97275),x97274))) % 112.37/112.11 [9728]P1(f317(x97281,f625(x97282,x97281,x97283,x97284,x97285)))+~P1(f317(f317(f224(f906(x97285,a895)),x97284),x97283))+P1(f317(f317(f224(f906(x97285,a895)),f317(f317(f92(f906(x97285,a895)),x97284),f317(f252(x97285),x97281))),f317(f317(f92(f906(x97285,a895)),x97283),f317(f252(x97285),x97282)))) % 112.37/112.11 [9742]~P81(x97421)+~P1(f317(x97424,f702(x97423,x97424,x97425,x97422,x97421)))+E(f317(f155(x97421),f317(f317(f144(x97422,x97421),x97423),f317(f126(x97422,x97424),x97425))),f317(f155(x97421),f317(f317(f144(x97422,x97421),x97423),x97425))) % 112.37/112.11 [9819]~P5(x98195)+P1(f317(f317(f319(x98191),f474(x98192,x98193,x98191,x98194,x98195)),x98193))+P1(f317(f317(f224(x98195),x98194),f317(f317(f35(x98191,x98195),x98193),x98192))) % 112.37/112.11 [9823]~P81(x98231)+E(f317(f155(x98231),f317(f317(f144(x98232,x98231),x98233),f317(f126(x98232,x98234),x98235))),f317(f155(x98231),f317(f317(f144(x98232,x98231),x98233),x98235)))+P1(f317(f317(f319(x98232),f702(x98233,x98234,x98235,x98232,x98231)),f317(f162(x98232),x98235))) % 112.37/112.11 [9833]~P1(f317(x98335,f625(x98335,x98333,x98334,x98332,x98331)))+~P1(f317(f317(f224(f906(x98331,a895)),x98332),x98334))+P1(f317(f317(f224(f906(x98331,a895)),f317(f317(f92(f906(x98331,a895)),x98332),f317(f252(x98331),x98333))),f317(f317(f92(f906(x98331,a895)),x98334),f317(f252(x98331),x98335)))) % 112.37/112.11 [9849]~P24(x98495,x98493,x98494,f232(f906(x98495,a895)))+P1(f317(x98491,x98492))+P1(f317(f317(f319(x98493),f794(x98492,x98491,x98494,x98493,x98495)),f317(f300(x98495,x98493,x98494),f232(f906(x98495,a895))))) % 112.37/112.11 [9873]P33(x98731,x98732,x98733,x98734,x98735)+~E(f317(f179(f900(x98732)),x98735),f317(f179(f900(x98731)),x98734))+P1(f317(f317(f225(a899),f683(x98735,x98734,x98733,x98732,x98731)),f317(f179(f900(x98731)),x98734))) % 112.37/112.11 [9874]P33(x98741,x98742,x98743,x98744,x98745)+~E(f317(f179(f900(x98742)),x98745),f317(f179(f900(x98741)),x98744))+P1(f317(f317(f225(a899),f718(x98743,x98745,x98742,x98744,x98741)),f317(f179(f900(x98741)),x98744))) % 112.37/112.11 [9906]P1(f317(f317(f319(x99061),f625(x99062,x99063,x99064,x99065,x99061)),x99065))+~P1(f317(f317(f224(f906(x99061,a895)),x99065),x99064))+P1(f317(f317(f224(f906(x99061,a895)),f317(f317(f92(f906(x99061,a895)),x99065),f317(f252(x99061),x99063))),f317(f317(f92(f906(x99061,a895)),x99064),f317(f252(x99061),x99062)))) % 112.37/112.11 [9949]~P5(x99491)+~P1(f317(f317(f224(x99491),x99492),f317(x99495,f474(x99495,x99494,x99493,x99492,x99491))))+P1(f317(f317(f224(x99491),x99492),f317(f317(f35(x99493,x99491),x99494),x99495))) % 112.37/112.11 [9986]~P75(x99861)+~P1(f317(f29(x99862),x99865))+E(f317(f317(f317(f60(x99861,x99862,f75(x99861)),f317(f317(f20(x99862,x99861,x99861),f317(f317(f10(x99861,f906(x99861,x99861),x99862),f75(x99861)),x99863)),x99864)),f72(x99861)),x99865),f317(f317(f75(x99861),f317(f317(f317(f60(x99861,x99862,f75(x99861)),x99863),f72(x99861)),x99865)),f317(f317(f317(f60(x99861,x99862,f75(x99861)),x99864),f72(x99861)),x99865))) % 112.37/112.11 [10041]~P1(f317(f317(f319(f905(f906(x100411,a895),f906(x100411,a895))),f317(f317(f242(f906(x100411,a895),f906(x100411,a895)),x100415),x100414)),f309(x100411,x100413)))+~P1(f317(f317(f319(x100411),x100412),x100415))+P1(f317(f317(f319(f905(x100411,x100411)),f317(f317(f242(x100411,x100411),x100412),f593(x100413,x100414,x100415,x100411,x100412))),x100413)) % 112.37/112.11 [10181]~P1(f317(f317(f319(f905(f900(x101811),f900(x101811))),f317(f317(f242(f900(x101811),f900(x101811)),f317(f317(f124(x101811),x101815),x101812)),f317(f317(f124(x101811),x101815),x101813))),f137(x101811,x101814)))+P1(f317(f317(f319(f905(f900(x101811),f900(x101811))),f317(f317(f242(f900(x101811),f900(x101811)),x101812),x101813)),f137(x101811,x101814)))+P1(f317(f317(f319(f905(x101811,x101811)),f317(f317(f242(x101811,x101811),f671(x101814,x101813,x101812,x101815,x101811)),f671(x101814,x101813,x101812,x101815,x101811))),x101814)) % 112.37/112.11 [7363]~E(x73633,x73635)+E(f317(f317(f154(x73631),f317(f317(f149(x73631,x73632),x73633),x73634)),x73635),x73634)+~P1(f317(f317(f225(a899),x73633),f317(f179(f900(x73631)),x73632))) % 112.37/112.11 [7479]~E(f317(f317(f124(x74791),x74792),x74794),f317(f317(f124(x74791),x74793),x74795))+E(f317(f317(f165(x74791),f317(f179(f900(x74791)),x74792)),x74793),x74792)+P1(f317(f317(f224(a899),f317(f179(f900(x74791)),x74793)),f317(f179(f900(x74791)),x74792))) % 112.37/112.11 [7977]~E(f317(f317(f124(x79771),x79772),x79774),f317(f317(f124(x79771),x79773),x79775))+E(f317(f317(f165(x79771),f317(f179(f900(x79771)),x79772)),x79773),x79772)+~P1(f317(f317(f224(a899),f317(f179(f900(x79771)),x79772)),f317(f179(f900(x79771)),x79773))) % 112.37/112.11 [8001]~P1(f317(f29(x80011),f317(x80014,x80015)))+~P1(f317(f317(f319(x80012),x80015),x80013))+P1(f317(f29(x80011),f317(f317(f35(x80012,f906(x80011,a895)),x80013),x80014))) % 112.37/112.11 [8176]~P52(x81761,x81763,x81765)+~P52(x81761,x81762,x81764)+P52(x81761,f317(f317(f91(f906(x81761,a895)),x81762),x81763),f317(f317(f91(f906(f905(x81761,x81761),a895)),x81764),x81765)) % 112.37/112.11 [8177]~P52(x81771,x81773,x81775)+~P52(x81771,x81772,x81774)+P52(x81771,f317(f317(f92(f906(x81771,a895)),x81772),x81773),f317(f317(f92(f906(f905(x81771,x81771),a895)),x81774),x81775)) % 112.37/112.11 [8534]E(f317(f317(f242(x85341,x85342),f317(f317(f154(x85341),x85343),x85344)),f317(f317(f154(x85342),x85345),x85344)),f317(f317(f154(f905(x85341,x85342)),f317(f317(f171(x85341,x85342),x85343),x85345)),x85344))+~P1(f317(f317(f225(a899),x85344),f317(f179(f900(x85341)),x85343)))+~P1(f317(f317(f225(a899),x85344),f317(f179(f900(x85342)),x85345))) % 112.37/112.11 [8687]~P52(x86871,x86873,x86874)+P1(f317(f317(f319(x86871),x86872),x86873))+~P1(f317(f317(f319(f905(x86871,x86871)),f317(f317(f242(x86871,x86871),x86875),x86872)),x86874)) % 112.37/112.11 [8688]~P52(x86881,x86883,x86884)+P1(f317(f317(f319(x86881),x86882),x86883))+~P1(f317(f317(f319(f905(x86881,x86881)),f317(f317(f242(x86881,x86881),x86882),x86885)),x86884)) % 112.37/112.11 [8689]~P8(x86891,x86893,x86894)+P1(f317(f317(f319(x86891),x86892),x86893))+~P1(f317(f317(f319(f905(x86891,x86891)),f317(f317(f242(x86891,x86891),x86895),x86892)),x86894)) % 112.37/112.11 [8690]~P8(x86901,x86903,x86904)+P1(f317(f317(f319(x86901),x86902),x86903))+~P1(f317(f317(f319(f905(x86901,x86901)),f317(f317(f242(x86901,x86901),x86902),x86905)),x86904)) % 112.37/112.11 [8971]~P8(x89711,x89715,x89712)+E(f317(f275(x89711,x89711,x89712),f317(f317(f299(x89711),x89713),f178(f906(x89711,a895)))),f317(f275(x89711,x89711,x89712),f317(f317(f299(x89711),x89714),f178(f906(x89711,a895)))))+~P1(f317(f317(f319(f905(x89711,x89711)),f317(f317(f242(x89711,x89711),x89713),x89714)),x89712)) % 112.37/112.11 [9155]P1(f317(x91551,x91552))+~P1(f317(f317(f319(x91553),x91552),x91555))+P1(f317(f317(f319(x91553),f391(x91551,x91554,x91555,x91553)),f317(f317(f91(f906(x91553,a895)),x91555),x91554))) % 112.37/112.11 [9156]P1(f317(x91561,x91562))+~P1(f317(f317(f319(x91563),x91562),x91564))+P1(f317(f317(f319(x91563),f391(x91561,x91564,x91565,x91563)),f317(f317(f91(f906(x91563,a895)),x91565),x91564))) % 112.37/112.11 [9164]~P1(f317(x91642,x91645))+~P1(f317(f317(f319(x91641),x91645),x91644))+P1(f317(f317(f319(x91641),f393(x91642,x91643,x91644,x91641)),f317(f317(f91(f906(x91641,a895)),x91644),x91643))) % 112.37/112.11 [9165]~P1(f317(x91652,x91655))+~P1(f317(f317(f319(x91651),x91655),x91653))+P1(f317(f317(f319(x91651),f393(x91652,x91653,x91654,x91651)),f317(f317(f91(f906(x91651,a895)),x91654),x91653))) % 112.37/112.11 [9180]~P1(f317(f317(f224(f906(x91801,a895)),x91805),x91803))+~P1(f317(f317(f224(f906(x91801,a895)),x91802),x91804))+P1(f317(f317(f224(f906(x91801,a895)),f317(f317(f3(f906(x91801,a895)),x91802),x91803)),f317(f317(f3(f906(x91801,a895)),x91804),x91805))) % 112.37/112.11 [9181]~P1(f317(f317(f224(f906(x91811,a895)),x91813),x91815))+~P1(f317(f317(f224(f906(x91811,a895)),x91812),x91814))+P1(f317(f317(f224(f906(x91811,a895)),f317(f317(f91(f906(x91811,a895)),x91812),x91813)),f317(f317(f91(f906(x91811,a895)),x91814),x91815))) % 112.37/112.11 [9182]~P1(f317(f317(f224(f906(x91821,a895)),x91823),x91825))+~P1(f317(f317(f224(f906(x91821,a895)),x91822),x91824))+P1(f317(f317(f224(f906(x91821,a895)),f317(f317(f92(f906(x91821,a895)),x91822),x91823)),f317(f317(f92(f906(x91821,a895)),x91824),x91825))) % 112.37/112.11 [9276]P1(f317(f317(f319(f905(x92761,x92761)),f317(f317(f242(x92761,x92761),x92762),x92763)),f311(x92761,x92764,x92765)))+~P1(f317(f317(f224(a899),f317(x92764,x92762)),f317(x92764,x92763)))+~P1(f317(f317(f319(f905(x92761,x92761)),f317(f317(f242(x92761,x92761),x92762),x92763)),x92765)) % 112.37/112.11 [9466]P1(f317(f317(f319(f905(x94661,x94661)),f317(f317(f242(x94661,x94661),x94662),x94663)),f297(x94661,x94664)))+~P1(f317(f317(f319(f905(x94661,x94661)),f317(f317(f242(x94661,x94661),x94662),x94665)),f297(x94661,x94664)))+~P1(f317(f317(f319(f905(x94661,x94661)),f317(f317(f242(x94661,x94661),x94665),x94663)),x94664)) % 112.37/112.11 [9467]P1(f317(f317(f319(f905(x94671,x94671)),f317(f317(f242(x94671,x94671),x94672),x94673)),f297(x94671,x94674)))+~P1(f317(f317(f319(f905(x94671,x94671)),f317(f317(f242(x94671,x94671),x94675),x94673)),f297(x94671,x94674)))+~P1(f317(f317(f319(f905(x94671,x94671)),f317(f317(f242(x94671,x94671),x94672),x94675)),x94674)) % 112.37/112.11 [9568]E(x95681,x95682)+E(f317(a102,f607(x95683,x95684,x95681,x95682,x95685)),x95684)+~P1(f317(f317(f319(f905(x95685,x95685)),f317(f317(f242(x95685,x95685),x95682),x95681)),f317(f317(f173(f905(x95685,x95685),a895),x95684),x95683))) % 112.37/112.11 [9569]E(x95691,x95692)+E(f317(a102,f611(x95693,x95694,x95691,x95692,x95695)),x95694)+~P1(f317(f317(f319(f905(x95695,x95695)),f317(f317(f242(x95695,x95695),x95692),x95691)),f317(f317(f173(f905(x95695,x95695),a895),x95694),x95693))) % 112.37/112.11 [9570]E(x95701,f2(a899))+E(f317(a102,f607(x95702,x95701,x95703,x95704,x95705)),x95701)+~P1(f317(f317(f319(f905(x95705,x95705)),f317(f317(f242(x95705,x95705),x95704),x95703)),f317(f317(f173(f905(x95705,x95705),a895),x95701),x95702))) % 112.37/112.11 [9571]E(x95711,f2(a899))+E(f317(a102,f611(x95712,x95711,x95713,x95714,x95715)),x95711)+~P1(f317(f317(f319(f905(x95715,x95715)),f317(f317(f242(x95715,x95715),x95714),x95713)),f317(f317(f173(f905(x95715,x95715),a895),x95711),x95712))) % 112.37/112.11 [9596]P1(f317(f317(f319(f905(x95961,x95961)),f317(f317(f242(x95961,x95961),x95962),x95963)),f317(f317(f279(x95961,x95961,x95961),x95964),f297(x95961,x95964))))+~P1(f317(f317(f319(f905(x95961,x95961)),f317(f317(f242(x95961,x95961),x95962),x95965)),x95964))+~P1(f317(f317(f319(f905(x95961,x95961)),f317(f317(f242(x95961,x95961),x95965),x95963)),x95964)) % 112.37/112.11 [9606]~P1(f317(f317(f319(f905(x96061,x96061)),f317(f317(f242(x96061,x96061),x96062),x96065)),f297(x96061,x96064)))+P1(f317(f317(f319(f905(x96061,x96061)),f317(f317(f242(x96061,x96061),x96062),x96063)),f317(f317(f279(x96061,x96061,x96061),x96064),f297(x96061,x96064))))+~P1(f317(f317(f319(f905(x96061,x96061)),f317(f317(f242(x96061,x96061),x96065),x96063)),x96064)) % 112.37/112.11 [9641]~P8(x96411,x96415,x96412)+~P1(f317(f317(f319(f905(x96411,x96411)),f317(f317(f242(x96411,x96411),x96413),x96414)),x96412))+P1(f317(f317(f224(f906(x96411,a895)),f317(f275(x96411,x96411,x96412),f317(f317(f299(x96411),x96413),f178(f906(x96411,a895))))),f317(f275(x96411,x96411,x96412),f317(f317(f299(x96411),x96414),f178(f906(x96411,a895)))))) % 112.37/112.11 [9700]P1(f317(f317(f319(f905(x97001,x97001)),f317(f317(f242(x97001,x97001),x97002),x97003)),f317(f317(f279(x97001,x97001,x97001),x97004),f297(x97001,x97004))))+~P1(f317(f317(f319(f905(x97001,x97001)),f317(f317(f242(x97001,x97001),x97002),x97005)),f317(f317(f279(x97001,x97001,x97001),x97004),f297(x97001,x97004))))+~P1(f317(f317(f319(f905(x97001,x97001)),f317(f317(f242(x97001,x97001),x97005),x97003)),x97004)) % 112.37/112.11 [9701]P1(f317(f317(f319(f905(x97011,x97011)),f317(f317(f242(x97011,x97011),x97012),x97013)),f317(f317(f279(x97011,x97011,x97011),x97014),f297(x97011,x97014))))+~P1(f317(f317(f319(f905(x97011,x97011)),f317(f317(f242(x97011,x97011),x97015),x97013)),f317(f317(f279(x97011,x97011,x97011),x97014),f297(x97011,x97014))))+~P1(f317(f317(f319(f905(x97011,x97011)),f317(f317(f242(x97011,x97011),x97012),x97015)),x97014)) % 112.37/112.11 [9751]~P1(f317(f61(x97511,x97511,x97514,x97512,x97513),x97515))+P1(f317(f317(f319(x97511),x97512),x97513))+P1(f317(f57(x97511,x97514,f317(f317(f299(x97511),x97512),x97513)),x97515)) % 112.37/112.11 [9789]~E(f317(f300(x97893,x97892,x97895),x97894),x97891)+E(x97891,f178(f906(x97892,a895)))+P1(f317(f317(f224(f906(x97893,a895)),f317(f300(x97892,x97893,f498(x97894,x97893,x97892,x97891)),x97891)),x97894)) % 112.37/112.11 [9836]~P5(x98365)+P1(f317(f317(f319(x98361),f476(x98362,x98363,x98364,x98361,x98365)),x98364))+P1(f317(f317(f224(x98365),f317(f317(f36(x98361,x98365),x98364),x98363)),x98362)) % 112.37/112.11 [9893]P33(x98931,x98932,x98933,x98934,x98935)+~E(f317(f179(f900(x98931)),x98934),f317(f179(f900(x98932)),x98935))+P1(f317(f317(f319(f905(x98931,x98932)),f681(x98935,x98934,x98933,x98932,x98931)),f317(f162(f905(x98931,x98932)),f317(f317(f171(x98931,x98932),x98934),x98935)))) % 112.37/112.11 [9894]P33(x98941,x98942,x98943,x98944,x98945)+~E(f317(f179(f900(x98941)),x98944),f317(f179(f900(x98942)),x98945))+P1(f317(f317(f319(f905(x98941,x98942)),f682(x98943,x98945,x98944,x98942,x98941)),f317(f162(f905(x98941,x98942)),f317(f317(f171(x98941,x98942),x98944),x98945)))) % 112.37/112.11 [10020]E(x100201,x100202)+P1(f317(f317(f319(f905(x100203,x100203)),f317(f317(f242(x100203,x100203),x100201),f609(x100204,x100205,x100202,x100201,x100203))),x100204))+~P1(f317(f317(f319(f905(x100203,x100203)),f317(f317(f242(x100203,x100203),x100201),x100202)),f317(f317(f173(f905(x100203,x100203),a895),x100205),x100204))) % 112.37/112.11 [10021]E(x100211,f2(a899))+P1(f317(f317(f319(f905(x100212,x100212)),f317(f317(f242(x100212,x100212),x100213),f609(x100214,x100211,x100215,x100213,x100212))),x100214))+~P1(f317(f317(f319(f905(x100212,x100212)),f317(f317(f242(x100212,x100212),x100213),x100215)),f317(f317(f173(f905(x100212,x100212),a895),x100211),x100214))) % 112.37/112.11 [10060]~P5(x100601)+~P1(f317(f317(f224(x100601),f317(x100604,f476(x100605,x100604,x100603,x100602,x100601))),x100605))+P1(f317(f317(f224(x100601),f317(f317(f36(x100602,x100601),x100603),x100604)),x100605)) % 112.37/112.11 [10113]E(x101131,x101132)+P1(f317(f317(f319(f905(x101133,x101133)),f317(f317(f242(x101133,x101133),f608(x101134,x101135,x101131,x101132,x101133)),x101131)),x101134))+~P1(f317(f317(f319(f905(x101133,x101133)),f317(f317(f242(x101133,x101133),x101132),x101131)),f317(f317(f173(f905(x101133,x101133),a895),x101135),x101134))) % 112.37/112.11 [10114]E(x101141,f2(a899))+P1(f317(f317(f319(f905(x101142,x101142)),f317(f317(f242(x101142,x101142),f608(x101143,x101141,x101144,x101145,x101142)),x101144)),x101143))+~P1(f317(f317(f319(f905(x101142,x101142)),f317(f317(f242(x101142,x101142),x101145),x101144)),f317(f317(f173(f905(x101142,x101142),a895),x101141),x101143))) % 112.37/112.11 [10118]E(x101181,x101182)+P1(f317(f317(f319(f905(x101183,x101183)),f317(f317(f242(x101183,x101183),x101181),f608(x101184,x101185,x101182,x101181,x101183))),f317(f317(f173(f905(x101183,x101183),a895),f607(x101184,x101185,x101182,x101181,x101183)),x101184)))+~P1(f317(f317(f319(f905(x101183,x101183)),f317(f317(f242(x101183,x101183),x101181),x101182)),f317(f317(f173(f905(x101183,x101183),a895),x101185),x101184))) % 112.37/112.11 [10119]E(x101191,f2(a899))+P1(f317(f317(f319(f905(x101192,x101192)),f317(f317(f242(x101192,x101192),x101193),f608(x101194,x101191,x101195,x101193,x101192))),f317(f317(f173(f905(x101192,x101192),a895),f607(x101194,x101191,x101195,x101193,x101192)),x101194)))+~P1(f317(f317(f319(f905(x101192,x101192)),f317(f317(f242(x101192,x101192),x101193),x101195)),f317(f317(f173(f905(x101192,x101192),a895),x101191),x101194))) % 112.37/112.11 [10172]E(x101721,x101722)+P1(f317(f317(f319(f905(x101723,x101723)),f317(f317(f242(x101723,x101723),f609(x101724,x101725,x101721,x101722,x101723)),x101721)),f317(f317(f173(f905(x101723,x101723),a895),f611(x101724,x101725,x101721,x101722,x101723)),x101724)))+~P1(f317(f317(f319(f905(x101723,x101723)),f317(f317(f242(x101723,x101723),x101722),x101721)),f317(f317(f173(f905(x101723,x101723),a895),x101725),x101724))) % 112.37/112.11 [10173]E(x101731,f2(a899))+P1(f317(f317(f319(f905(x101732,x101732)),f317(f317(f242(x101732,x101732),f609(x101733,x101731,x101734,x101735,x101732)),x101734)),f317(f317(f173(f905(x101732,x101732),a895),f611(x101733,x101731,x101734,x101735,x101732)),x101733)))+~P1(f317(f317(f319(f905(x101732,x101732)),f317(f317(f242(x101732,x101732),x101735),x101734)),f317(f317(f173(f905(x101732,x101732),a895),x101731),x101733))) % 112.37/112.11 [10206]~P69(x102062)+~P1(f317(f29(x102061),x102065))+E(f317(f317(f8(x102061,x102062),f317(f317(f9(x102061,x102062,x102062),f317(f317(f20(x102061,x102062,f906(x102062,x102062)),f317(f317(f10(a895,f906(x102062,f906(x102062,x102062)),x102061),f86(x102062)),f317(f317(f9(x102061,f906(x102061,a895),a895),f319(x102061)),x102063))),x102064)),f2(x102062))),x102065),f317(f317(f8(x102061,x102062),x102064),f317(f317(f92(f906(x102061,a895)),x102065),x102063))) % 112.37/112.11 [8755]~P69(x87551)+~P1(f317(f29(x87554),x87555))+E(f317(f317(f74(x87551),f317(x87552,x87553)),f317(f317(f8(x87554,x87551),x87552),f317(f317(f3(f906(x87554,a895)),x87555),f317(f317(f299(x87554),x87553),f178(f906(x87554,a895)))))),f317(f317(f8(x87554,x87551),x87552),f317(f317(f299(x87554),x87553),x87555))) % 112.37/112.11 [8756]~P75(x87561)+~P1(f317(f29(x87564),x87565))+E(f317(f317(f75(x87561),f317(x87562,x87563)),f317(f317(f11(x87564,x87561),x87562),f317(f317(f3(f906(x87564,a895)),x87565),f317(f317(f299(x87564),x87563),f178(f906(x87564,a895)))))),f317(f317(f11(x87564,x87561),x87562),f317(f317(f299(x87564),x87563),x87565))) % 112.37/112.11 [9088]~P108(x90882)+~P13(x90882,f317(f158(x90882),f317(f317(f144(x90881,x90882),x90884),x90885)))+E(f317(f126(x90881,f317(f317(f10(x90882,a895,x90881),f317(f225(x90882),x90883)),x90884)),x90885),f167(x90881,f317(f317(f10(x90882,a895,x90881),f317(f225(x90882),x90883)),x90884),x90885)) % 112.37/112.11 [9112]~P69(x91121)+E(f317(f317(f74(x91121),f317(f317(f8(a899,x91121),x91122),f293(a899,x91123,x91124))),f317(f317(f8(a899,x91121),x91122),f293(a899,f317(f317(f74(a899),x91124),f72(a899)),f317(f317(f74(a899),x91124),x91125)))),f317(f317(f8(a899,x91121),x91122),f293(a899,x91123,f317(f317(f74(a899),x91124),x91125))))+~P1(f317(f317(f224(a899),x91123),f317(f317(f74(a899),x91124),f72(a899)))) % 112.37/112.11 [9113]~P1(f317(f317(f319(x91131),x91134),x91135))+~P1(f317(f317(f224(f906(x91131,a895)),f317(f162(x91131),x91132)),x91135))+P1(f317(f317(f224(f906(x91131,a895)),f317(f162(x91131),f317(f317(f149(x91131,x91132),x91133),x91134))),x91135)) % 112.37/112.11 [9338]~P5(x93382)+~P1(f317(f29(x93381),x93385))+E(f317(f317(f59(x93381,x93382,f317(f317(f10(x93382,f906(x93382,x93382),x93381),f91(x93382)),x93383)),x93384),x93385),f317(f317(f91(x93382),x93384),f317(f317(f36(x93381,x93382),x93385),x93383))) % 112.37/112.11 [9339]~P5(x93392)+~P1(f317(f29(x93391),x93395))+E(f317(f317(f59(x93391,x93392,f317(f317(f10(x93392,f906(x93392,x93392),x93391),f92(x93392)),x93393)),x93394),x93395),f317(f317(f92(x93392),x93394),f317(f317(f35(x93391,x93392),x93395),x93393))) % 112.37/112.11 [9390]E(f317(x93901,x93902),f317(x93901,x93903))+P1(f317(f317(f225(a899),f317(x93901,x93902)),f317(x93901,x93903)))+~P1(f317(f317(f319(f905(x93904,x93904)),f317(f317(f242(x93904,x93904),x93902),x93903)),f143(x93904,f317(f317(f141(f906(x93904,a899)),x93901),x93905)))) % 112.37/112.11 [9424]~E(f317(x94244,x94242),f317(x94244,x94243))+~P1(f317(f317(f319(f905(x94241,x94241)),f317(f317(f242(x94241,x94241),x94242),x94243)),f143(x94241,x94245)))+P1(f317(f317(f319(f905(x94241,x94241)),f317(f317(f242(x94241,x94241),x94242),x94243)),f143(x94241,f317(f317(f141(f906(x94241,a899)),x94244),x94245)))) % 112.37/112.11 [9444]~P24(x94441,x94442,x94443,x94445)+P24(x94441,x94442,x94443,f317(f317(f299(x94441),x94444),x94445))+P1(f317(f317(f319(x94442),f317(x94443,x94444)),f317(f300(x94441,x94442,x94443),f317(f317(f3(f906(x94441,a895)),x94445),f317(f317(f299(x94441),x94444),f178(f906(x94441,a895))))))) % 112.37/112.11 [9447]P1(f317(x94472,x94475))+~P1(f317(f317(f319(x94471),x94475),f317(f162(x94471),x94473)))+E(f317(f317(f128(x94471),f317(f179(f900(x94471)),f167(x94471,x94472,f317(f317(f124(x94471),x94473),x94474)))),f317(f317(f124(x94471),x94473),x94474)),f317(f317(f124(x94471),f317(f317(f128(x94471),f317(f179(f900(x94471)),f167(x94471,x94472,x94473))),x94473)),x94474)) % 112.37/112.11 [9452]~P1(f317(f317(f319(f905(x94521,x94521)),f317(f317(f242(x94521,x94521),x94522),x94523)),f143(x94521,x94525)))+~P1(f317(f317(f224(a899),f317(x94524,x94522)),f317(x94524,x94523)))+P1(f317(f317(f319(f905(x94521,x94521)),f317(f317(f242(x94521,x94521),x94522),x94523)),f143(x94521,f317(f317(f141(f906(x94521,a899)),x94524),x94525)))) % 112.37/112.11 [9519]P1(f317(f317(f319(f905(x95194,x95194)),f317(f317(f242(x95194,x95194),x95192),x95193)),f143(x95194,x95195)))+P1(f317(f317(f225(a899),f317(x95191,x95192)),f317(x95191,x95193)))+~P1(f317(f317(f319(f905(x95194,x95194)),f317(f317(f242(x95194,x95194),x95192),x95193)),f143(x95194,f317(f317(f141(f906(x95194,a899)),x95191),x95195)))) % 112.37/112.11 [9672]~P1(f317(f317(f319(f905(f900(x96721),f900(x96721))),f317(f317(f242(f900(x96721),f900(x96721)),x96722),x96724)),f148(x96721,x96725)))+~P1(f317(f317(f225(a899),x96723),f317(f179(f900(x96721)),x96722)))+P1(f317(f317(f319(f905(x96721,x96721)),f317(f317(f242(x96721,x96721),f317(f317(f154(x96721),x96722),x96723)),f317(f317(f154(x96721),x96724),x96723))),x96725)) % 112.37/112.11 [9916]E(x99161,f2(a1))+~P1(f317(f45(x99163,x99161),f317(f317(f242(a1,a1),x99164),x99165)))+P1(f317(f45(f317(f317(f75(a1),x99162),x99163),x99161),f317(f317(f242(a1,a1),f317(f317(f74(a1),f317(f317(f75(a1),x99162),x99164)),f317(f317(f31(a1),f317(f317(f75(a1),x99162),x99165)),x99161))),f41(a1,f317(f317(f75(a1),x99162),x99165),x99161)))) % 112.37/112.11 [9917]~P1(f317(f317(f225(a899),f2(a899)),x99173))+~P1(f317(f44(x99172,x99173),f317(f317(f242(a899,a899),x99174),x99175)))+P1(f317(f44(f317(f317(f75(a899),x99171),x99172),x99173),f317(f317(f242(a899,a899),f317(f317(f74(a899),f317(f317(f75(a899),x99171),x99174)),f317(f317(f31(a899),f317(f317(f75(a899),x99171),x99175)),x99173))),f41(a899,f317(f317(f75(a899),x99171),x99175),x99173)))) % 112.37/112.11 [10229]~P69(x102292)+~P1(f317(f29(x102291),x102294))+E(f317(f317(f8(x102291,x102292),x102293),f317(f252(x102291),f317(f317(f20(x102291,a895,a895),f317(f317(f10(a895,f906(a895,a895),x102291),a315),f317(f317(f9(x102291,f906(x102291,a895),a895),f319(x102291)),x102294))),f317(f317(f9(x102291,f906(x102291,a895),a895),f319(x102291)),x102295)))),f317(f317(f8(x102291,x102292),f317(f317(f9(x102291,x102292,x102292),f317(f317(f20(x102291,x102292,f906(x102292,x102292)),f317(f317(f10(a895,f906(x102292,f906(x102292,x102292)),x102291),f86(x102292)),f317(f317(f9(x102291,f906(x102291,a895),a895),f319(x102291)),x102295))),x102293)),f2(x102292))),x102294)) % 112.37/112.11 [8384]~E(f317(f317(f124(x83841),x83842),x83845),f317(f317(f124(x83841),x83843),x83844))+E(f317(f317(f124(x83841),f317(f317(f128(x83841),f317(f179(f900(x83841)),x83842)),x83843)),x83844),x83845)+P1(f317(f317(f224(a899),f317(f179(f900(x83841)),x83843)),f317(f179(f900(x83841)),x83842))) % 112.37/112.11 [8582]~E(f317(f317(f124(x85822),x85823),x85821),f317(f317(f124(x85822),x85824),x85825))+E(x85821,f317(f317(f124(x85822),f317(f317(f128(x85822),f317(f179(f900(x85822)),x85823)),x85824)),x85825))+~P1(f317(f317(f224(a899),f317(f179(f900(x85822)),x85823)),f317(f179(f900(x85822)),x85824))) % 112.37/112.11 [8670]~E(f317(f317(f74(a899),f317(f317(f75(a899),x86703),x86704)),x86701),f317(f317(f74(a899),f317(f317(f75(a899),x86702),x86704)),x86705))+~P1(f317(f317(f224(a899),x86703),x86702))+E(x86701,f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x86702),x86703)),x86704)),x86705)) % 112.37/112.11 [8671]~E(f317(f317(f74(a899),f317(f317(f75(a899),x86711),x86713)),x86714),f317(f317(f74(a899),f317(f317(f75(a899),x86712),x86713)),x86715))+~P1(f317(f317(f224(a899),x86712),x86711))+E(f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x86711),x86712)),x86713)),x86714),x86715) % 112.37/112.11 [8839]E(f317(f317(f74(a899),f317(f317(f75(a899),x88391),x88392)),x88393),f317(f317(f74(a899),f317(f317(f75(a899),x88394),x88392)),x88395))+~P1(f317(f317(f224(a899),x88394),x88391))+~E(x88395,f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x88391),x88394)),x88392)),x88393)) % 112.37/112.11 [8840]E(f317(f317(f74(a899),f317(f317(f75(a899),x88401),x88402)),x88403),f317(f317(f74(a899),f317(f317(f75(a899),x88404),x88402)),x88405))+~P1(f317(f317(f224(a899),x88404),x88401))+~E(f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x88401),x88404)),x88402)),x88403),x88405) % 112.37/112.11 [9726]~P61(x97262)+~P1(f317(f29(x97261),x97265))+E(f317(f317(f11(x97261,x97262),f317(f317(f20(x97261,x97262,x97262),f317(f317(f10(x97262,f906(x97262,x97262),x97261),f281(x97262)),x97263)),x97264)),x97265),f317(f317(f281(x97262),f317(f317(f11(x97261,x97262),x97263),x97265)),f317(f317(f11(x97261,x97262),x97264),x97265))) % 112.37/112.11 [9856]~E(f613(x98565,x98564,x98563,x98562,x98561),f614(x98565,x98564,x98563,x98562,x98561))+P1(f317(f317(f319(f905(x98561,x98561)),f317(f317(f242(x98561,x98561),x98562),x98563)),f297(x98561,x98564)))+~P1(f317(f317(f319(f905(x98561,x98561)),f317(f317(f242(x98561,x98561),x98562),x98563)),f297(x98561,f317(f317(f91(f906(f905(x98561,x98561),a895)),x98564),x98565)))) % 112.37/112.11 [9857]~E(f615(x98575,x98574,x98573,x98572,x98571),f616(x98575,x98574,x98573,x98572,x98571))+P1(f317(f317(f319(f905(x98571,x98571)),f317(f317(f242(x98571,x98571),x98572),x98573)),f297(x98571,x98574)))+~P1(f317(f317(f319(f905(x98571,x98571)),f317(f317(f242(x98571,x98571),x98572),x98573)),f297(x98571,f317(f317(f91(f906(f905(x98571,x98571),a895)),x98574),x98575)))) % 112.37/112.11 [10050]P1(f317(f317(f319(f905(x100501,x100501)),f317(f317(f242(x100501,x100501),x100502),f616(x100505,x100504,x100503,x100502,x100501))),f297(x100501,x100504)))+P1(f317(f317(f319(f905(x100501,x100501)),f317(f317(f242(x100501,x100501),x100502),x100503)),f297(x100501,x100504)))+~P1(f317(f317(f319(f905(x100501,x100501)),f317(f317(f242(x100501,x100501),x100502),x100503)),f297(x100501,f317(f317(f91(f906(f905(x100501,x100501),a895)),x100504),x100505)))) % 112.37/112.11 [10140]P1(f317(f317(f319(f905(x101401,x101401)),f317(f317(f242(x101401,x101401),f614(x101405,x101404,x101403,x101402,x101401)),x101403)),f297(x101401,x101404)))+P1(f317(f317(f319(f905(x101401,x101401)),f317(f317(f242(x101401,x101401),x101402),x101403)),f297(x101401,x101404)))+~P1(f317(f317(f319(f905(x101401,x101401)),f317(f317(f242(x101401,x101401),x101402),x101403)),f297(x101401,f317(f317(f91(f906(f905(x101401,x101401),a895)),x101404),x101405)))) % 112.37/112.11 [10179]P1(f317(f317(f319(f905(x101791,x101791)),f317(f317(f242(x101791,x101791),x101792),x101793)),f297(x101791,x101794)))+P1(f317(f317(f319(f905(x101791,x101791)),f317(f317(f242(x101791,x101791),f613(x101795,x101794,x101793,x101792,x101791)),f614(x101795,x101794,x101793,x101792,x101791))),x101795))+~P1(f317(f317(f319(f905(x101791,x101791)),f317(f317(f242(x101791,x101791),x101792),x101793)),f297(x101791,f317(f317(f91(f906(f905(x101791,x101791),a895)),x101794),x101795)))) % 112.37/112.11 [10180]P1(f317(f317(f319(f905(x101801,x101801)),f317(f317(f242(x101801,x101801),x101802),x101803)),f297(x101801,x101804)))+P1(f317(f317(f319(f905(x101801,x101801)),f317(f317(f242(x101801,x101801),f616(x101805,x101804,x101803,x101802,x101801)),f615(x101805,x101804,x101803,x101802,x101801))),x101805))+~P1(f317(f317(f319(f905(x101801,x101801)),f317(f317(f242(x101801,x101801),x101802),x101803)),f297(x101801,f317(f317(f91(f906(f905(x101801,x101801),a895)),x101804),x101805)))) % 112.37/112.11 [10327]~P1(f317(f317(f319(f905(f900(x103271),f900(x103271))),f317(f317(f242(f900(x103271),f900(x103271)),x103274),x103275)),f148(x103271,x103272)))+~P1(f317(f317(f319(f905(x103271,x103271)),x103273),f317(f162(f905(x103271,x103271)),f317(f317(f171(x103271,x103271),x103274),x103275))))+P1(f317(f317(f247(x103271,x103271,a895),f317(f317(f9(x103271,f906(f905(x103271,x103271),a895),f906(x103271,a895)),f317(f317(f10(f906(x103271,f906(f906(f905(x103271,x103271),a895),a895)),f906(f906(f905(x103271,x103271),a895),f906(x103271,a895)),x103271),f9(x103271,f906(f905(x103271,x103271),a895),a895)),f317(f317(f10(f906(x103271,f905(x103271,x103271)),f906(x103271,f906(f906(f905(x103271,x103271),a895),a895)),x103271),f317(f10(f905(x103271,x103271),f906(f906(f905(x103271,x103271),a895),a895),x103271),f319(f905(x103271,x103271)))),f242(x103271,x103271)))),x103272)),x103273)) % 112.37/112.11 [9755]~P1(f317(f317(f224(a899),x97553),x97552))+~P1(f317(f317(f224(a899),f317(f317(f74(a899),f317(f317(f75(a899),x97553),x97554)),x97551)),f317(f317(f74(a899),f317(f317(f75(a899),x97552),x97554)),x97555)))+P1(f317(f317(f224(a899),x97551),f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x97552),x97553)),x97554)),x97555))) % 112.37/112.11 [9756]~P1(f317(f317(f224(a899),x97563),x97562))+~P1(f317(f317(f225(a899),f317(f317(f74(a899),f317(f317(f75(a899),x97563),x97564)),x97561)),f317(f317(f74(a899),f317(f317(f75(a899),x97562),x97564)),x97565)))+P1(f317(f317(f225(a899),x97561),f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x97562),x97563)),x97564)),x97565))) % 112.37/112.11 [9773]~P1(f317(f317(f224(a899),x97731),x97734))+P1(f317(f317(f224(a899),f317(f317(f74(a899),f317(f317(f75(a899),x97731),x97732)),x97733)),f317(f317(f74(a899),f317(f317(f75(a899),x97734),x97732)),x97735)))+~P1(f317(f317(f224(a899),x97733),f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x97734),x97731)),x97732)),x97735))) % 112.37/112.11 [9774]~P1(f317(f317(f224(a899),x97741),x97744))+P1(f317(f317(f225(a899),f317(f317(f74(a899),f317(f317(f75(a899),x97741),x97742)),x97743)),f317(f317(f74(a899),f317(f317(f75(a899),x97744),x97742)),x97745)))+~P1(f317(f317(f225(a899),x97743),f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x97744),x97741)),x97742)),x97745))) % 112.37/112.11 [9891]~P1(f317(f317(f224(a899),x98912),x98911))+~P1(f317(f317(f224(a899),f317(f317(f74(a899),f317(f317(f75(a899),x98911),x98913)),x98914)),f317(f317(f74(a899),f317(f317(f75(a899),x98912),x98913)),x98915)))+P1(f317(f317(f224(a899),f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x98911),x98912)),x98913)),x98914)),x98915)) % 112.37/112.11 [9892]~P1(f317(f317(f224(a899),x98922),x98921))+~P1(f317(f317(f225(a899),f317(f317(f74(a899),f317(f317(f75(a899),x98921),x98923)),x98924)),f317(f317(f74(a899),f317(f317(f75(a899),x98922),x98923)),x98925)))+P1(f317(f317(f225(a899),f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x98921),x98922)),x98923)),x98924)),x98925)) % 112.37/112.11 [9935]~P1(f317(f317(f224(a899),x99354),x99351))+P1(f317(f317(f224(a899),f317(f317(f74(a899),f317(f317(f75(a899),x99351),x99352)),x99353)),f317(f317(f74(a899),f317(f317(f75(a899),x99354),x99352)),x99355)))+~P1(f317(f317(f224(a899),f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x99351),x99354)),x99352)),x99353)),x99355)) % 112.37/112.11 [9936]~P1(f317(f317(f224(a899),x99364),x99361))+P1(f317(f317(f225(a899),f317(f317(f74(a899),f317(f317(f75(a899),x99361),x99362)),x99363)),f317(f317(f74(a899),f317(f317(f75(a899),x99364),x99362)),x99365)))+~P1(f317(f317(f225(a899),f317(f317(f74(a899),f317(f317(f75(a899),f317(f317(f3(a899),x99361),x99364)),x99362)),x99363)),x99365)) % 112.37/112.11 [10167]~P11(x101671,x101672,x101675,x101673)+~P1(f317(f317(f319(f905(x101671,x101671)),x101674),x101675))+P1(f317(f317(f247(x101671,x101671,a895),f317(f317(f9(x101671,f906(x101671,x101672),f906(x101671,a895)),f317(f317(f10(f906(x101672,a895),f906(f906(x101671,x101672),f906(x101671,a895)),x101671),f10(x101672,a895,x101671)),f317(f317(f10(x101672,f906(x101672,a895),x101671),a314),x101673))),x101673)),x101674)) % 112.37/112.11 [8546]~P19(x85466,x85461,x85462,x85464)+E(f317(f67(x85461,x85461,x85461,f317(x85462,x85463)),f317(x85464,x85465)),f317(f67(x85461,x85461,x85461,f317(x85464,x85465)),f317(x85462,x85463)))+~P1(f317(f29(x85466),x85465)) % 112.37/112.11 [8983]~P24(x89831,x89833,x89835,x89836)+~P24(x89833,x89832,x89834,f317(f300(x89831,x89833,x89835),x89836))+P24(x89831,x89832,f317(f67(x89833,x89832,x89831,x89834),x89835),x89836) % 112.37/112.11 [9551]~P1(f317(f317(x95514,x95512),x95516))+~P1(f317(f317(x95513,x95515),x95512))+P1(f317(f317(f319(x95511),x95512),f287(x95511,x95513,x95514,x95515,x95516))) % 112.37/112.11 [9552]~P1(f317(f317(x95523,x95522),x95526))+~P1(f317(f317(x95524,x95525),x95522))+P1(f317(f317(f319(x95521),x95522),f290(x95521,x95523,x95524,x95525,x95526))) % 112.37/112.11 [9673]E(x96731,x96732)+E(x96733,x96734)+~P1(f317(f317(f319(f905(f900(x96735),f900(x96735))),f317(f317(f242(f900(x96735),f900(x96735)),f317(f317(f141(x96735),x96733),x96731)),f317(f317(f141(x96735),x96734),x96732))),f147(x96735,x96736))) % 112.37/112.11 [9682]~E(x96822,x96824)+P1(f317(f317(f319(f905(f900(x96821),f900(x96821))),f317(f317(f242(f900(x96821),f900(x96821)),f317(f317(f141(x96821),x96822),x96823)),f317(f317(f141(x96821),x96824),x96825))),f135(x96821,x96826)))+~P1(f317(f317(f319(f905(f900(x96821),f900(x96821))),f317(f317(f242(f900(x96821),f900(x96821)),x96823),x96825)),f135(x96821,x96826))) % 112.37/112.11 [9683]~E(x96832,x96834)+P1(f317(f317(f319(f905(f900(x96831),f900(x96831))),f317(f317(f242(f900(x96831),f900(x96831)),f317(f317(f141(x96831),x96832),x96833)),f317(f317(f141(x96831),x96834),x96835))),f137(x96831,x96836)))+~P1(f317(f317(f319(f905(f900(x96831),f900(x96831))),f317(f317(f242(f900(x96831),f900(x96831)),x96833),x96835)),f137(x96831,x96836))) % 112.37/112.11 [9684]~E(x96842,x96844)+P1(f317(f317(f319(f905(f900(x96841),f900(x96841))),f317(f317(f242(f900(x96841),f900(x96841)),f317(f317(f141(x96841),x96842),x96843)),f317(f317(f141(x96841),x96844),x96845))),f147(x96841,x96846)))+~P1(f317(f317(f319(f905(f900(x96841),f900(x96841))),f317(f317(f242(f900(x96841),f900(x96841)),x96843),x96845)),f147(x96841,x96846))) % 112.37/112.11 [9685]~E(x96852,x96854)+P1(f317(f317(f319(f905(f900(x96851),f900(x96851))),f317(f317(f242(f900(x96851),f900(x96851)),f317(f317(f124(x96851),x96852),x96853)),f317(f317(f124(x96851),x96854),x96855))),f147(x96851,x96856)))+~P1(f317(f317(f319(f905(f900(x96851),f900(x96851))),f317(f317(f242(f900(x96851),f900(x96851)),x96853),x96855)),f147(x96851,x96856))) % 112.37/112.11 [9686]~E(x96863,x96865)+P1(f317(f317(f319(f905(f900(x96861),f900(x96861))),f317(f317(f242(f900(x96861),f900(x96861)),f317(f317(f124(x96861),x96862),x96863)),f317(f317(f124(x96861),x96864),x96865))),f147(x96861,x96866)))+~P1(f317(f317(f319(f905(f900(x96861),f900(x96861))),f317(f317(f242(f900(x96861),f900(x96861)),x96862),x96864)),f147(x96861,x96866))) % 112.37/112.11 [9743]E(x97431,x97432)+P1(f317(f317(f319(f905(f900(x97433),f900(x97433))),f317(f317(f242(f900(x97433),f900(x97433)),x97431),x97432)),f147(x97433,x97434)))+~P1(f317(f317(f319(f905(f900(x97433),f900(x97433))),f317(f317(f242(f900(x97433),f900(x97433)),f317(f317(f141(x97433),x97435),x97431)),f317(f317(f141(x97433),x97436),x97432))),f147(x97433,x97434))) % 112.37/112.11 [9895]~E(x98953,x98955)+P1(f317(f317(f319(f905(f900(x98951),f900(x98951))),f317(f317(f242(f900(x98951),f900(x98951)),f317(f317(f124(x98951),x98952),f317(f317(f141(x98951),x98953),f103(x98951)))),f317(f317(f124(x98951),x98954),f317(f317(f141(x98951),x98955),f103(x98951))))),f147(x98951,x98956)))+~P1(f317(f317(f319(f905(f900(x98951),f900(x98951))),f317(f317(f242(f900(x98951),f900(x98951)),x98952),x98954)),f147(x98951,x98956))) % 112.37/112.11 [9939]E(x99391,x99392)+E(x99393,x99394)+~P1(f317(f317(f319(f905(f900(x99395),f900(x99395))),f317(f317(f242(f900(x99395),f900(x99395)),f317(f317(f124(x99395),x99393),f317(f317(f141(x99395),x99391),f103(x99395)))),f317(f317(f124(x99395),x99394),f317(f317(f141(x99395),x99392),f103(x99395))))),f147(x99395,x99396))) % 112.37/112.11 [9965]E(x99651,x99652)+~P1(f317(f317(f319(f905(f900(x99653),f900(x99653))),f317(f317(f242(f900(x99653),f900(x99653)),f317(f317(f124(x99653),x99651),f317(f317(f141(x99653),x99655),f103(x99653)))),f317(f317(f124(x99653),x99652),f317(f317(f141(x99653),x99656),f103(x99653))))),f147(x99653,x99654)))+P1(f317(f317(f319(f905(f900(x99653),f900(x99653))),f317(f317(f242(f900(x99653),f900(x99653)),x99651),x99652)),f147(x99653,x99654))) % 112.37/112.11 [10003]~P1(f317(f317(f319(f905(f906(x100031,a895),f906(x100031,a895))),f317(f317(f242(f906(x100031,a895),f906(x100031,a895)),x100032),x100034)),f309(x100031,x100036)))+~P1(f317(f317(f319(f905(f906(x100031,a895),f906(x100031,a895))),f317(f317(f242(f906(x100031,a895),f906(x100031,a895)),x100033),x100035)),f309(x100031,x100036)))+P1(f317(f317(f319(f905(f906(x100031,a895),f906(x100031,a895))),f317(f317(f242(f906(x100031,a895),f906(x100031,a895)),f317(f317(f91(f906(x100031,a895)),x100032),x100033)),f317(f317(f91(f906(x100031,a895)),x100034),x100035))),f309(x100031,x100036))) % 112.37/112.11 [5739]~E(f317(f317(f124(x57391),x57396),x57393),x57395)+E(f317(f317(f124(x57391),x57392),x57393),f317(f317(f141(x57391),x57394),x57395))+~E(x57392,f317(f317(f141(x57391),x57394),x57396)) % 112.37/112.11 [5740]~E(f317(f317(f124(x57401),x57406),x57403),x57405)+E(f317(f317(f124(x57401),x57402),x57403),f317(f317(f124(x57401),x57404),x57405))+~E(x57402,f317(f317(f124(x57401),x57404),x57406)) % 112.37/112.11 [5742]E(f317(f317(f124(x57421),x57422),x57423),f317(f317(f141(x57421),x57424),x57425))+~E(f317(f317(f141(x57421),x57424),x57426),x57422)+~E(x57425,f317(f317(f124(x57421),x57426),x57423)) % 112.37/112.11 [5744]~E(f317(f317(f124(x57441),x57442),x57446),x57444)+E(f317(f317(f124(x57441),x57442),x57443),f317(f317(f124(x57441),x57444),x57445))+~E(x57443,f317(f317(f124(x57441),x57446),x57445)) % 112.37/112.11 [6921]E(f317(x69211,x69212),f317(x69213,x69212))+~E(f317(f317(f144(x69214,x69215),x69211),x69216),f317(f317(f144(x69214,x69215),x69213),x69216))+~P1(f317(f317(f319(x69214),x69212),f317(f162(x69214),x69216))) % 112.37/112.11 [7310]~P19(x73104,x73105,x73106,x73101)+E(f317(f317(x73101,x73102),x73103),f317(f317(f59(x73104,x73105,x73106),x73103),x73102))+~P1(f317(f29(x73104),x73102)) % 112.37/112.11 [7381]~E(x73812,f317(x73814,x73816))+~P1(f317(f317(f319(x73813),x73816),x73815))+P1(f317(f317(f319(x73811),x73812),f317(f300(x73813,x73811,x73814),x73815))) % 112.37/112.11 [7382]~E(f317(x73824,x73822),x73826)+~P1(f317(f317(f319(x73823),x73826),x73825))+P1(f317(f317(f319(x73821),x73822),f317(f301(x73821,x73823,x73824),x73825))) % 112.37/112.11 [7834]~P31(x78341,x78342,x78344,x78346)+P31(x78341,x78342,f317(f317(f141(x78341),x78343),x78344),f317(f317(f141(x78341),x78345),x78346))+~P1(f317(f317(x78342,x78343),x78345)) % 112.37/112.11 [8849]~P56(x88494,x88495,x88491,x88492,x88496)+E(f317(x88491,f317(x88492,x88493)),x88493)+~P1(f317(f317(f319(x88495),x88493),x88496)) % 112.37/112.11 [9348]~P25(x93482,x93481,x93485,x93484,x93483)+E(f317(f85(x93481,x93482,x93483,f85(x93482,x93481,x93484,x93485)),x93486),f317(x93485,x93486))+~P1(f317(f317(f319(x93482),x93486),x93484)) % 112.37/112.11 [9359]~P24(x93591,x93592,x93593,x93596)+P24(x93591,x93592,f69(x93591,x93592,x93593,x93594,x93595),x93596)+P1(f317(f317(f319(x93592),x93595),f317(f300(x93591,x93592,x93593),x93596))) % 112.37/112.11 [9675]E(x96751,x96752)+E(f317(f179(f900(x96753)),x96754),f317(f179(f900(x96753)),x96755))+~P1(f317(f317(f319(f905(f900(x96753),f900(x96753))),f317(f317(f242(f900(x96753),f900(x96753)),f317(f317(f141(x96753),x96751),x96754)),f317(f317(f141(x96753),x96752),x96755))),f135(x96753,x96756))) % 112.37/112.11 [9738]~P16(x97381,x97382,x97383)+E(f317(f317(f59(x97381,x97382,x97383),x97384),x97385),x97386)+~P1(f317(f61(x97381,x97382,x97383,x97384,x97385),x97386)) % 112.37/112.11 [9746]E(f317(f179(f900(x97461)),x97462),f317(f179(f900(x97461)),x97463))+P1(f317(f317(f319(f905(f900(x97461),f900(x97461))),f317(f317(f242(f900(x97461),f900(x97461)),x97462),x97463)),f135(x97461,x97464)))+~P1(f317(f317(f319(f905(f900(x97461),f900(x97461))),f317(f317(f242(f900(x97461),f900(x97461)),f317(f317(f141(x97461),x97465),x97462)),f317(f317(f141(x97461),x97466),x97463))),f135(x97461,x97464))) % 112.37/112.11 [9767]~P1(f317(f317(f319(f905(x97671,x97671)),f317(f317(f242(x97671,x97671),x97672),x97674)),f297(x97671,x97676)))+P1(f317(f317(f319(f905(f900(x97671),f900(x97671))),f317(f317(f242(f900(x97671),f900(x97671)),f317(f317(f141(x97671),x97672),x97673)),f317(f317(f141(x97671),x97674),x97675))),f297(f900(x97671),f147(x97671,x97676))))+~P1(f317(f317(f319(f905(f900(x97671),f900(x97671))),f317(f317(f242(f900(x97671),f900(x97671)),x97673),x97675)),f297(f900(x97671),f147(x97671,x97676)))) % 112.37/112.11 [9945]~P1(f317(x99452,x99456))+~E(f317(f126(x99451,x99452),x99453),f317(f317(f141(x99451),x99454),x99455))+~P1(f317(f317(f319(x99451),x99456),f317(f162(x99451),f726(x99455,x99454,x99453,x99452,x99451)))) % 112.37/112.11 [9946]~P1(f317(x99464,x99466))+~E(f317(f317(f141(x99461),x99462),x99463),f317(f126(x99461,x99464),x99465))+~P1(f317(f317(f319(x99461),x99466),f317(f162(x99461),f728(x99465,x99464,x99463,x99462,x99461)))) % 112.37/112.11 [10264]~P69(x102642)+E(f317(f317(f8(x102641,x102642),f317(f317(f10(f906(x102643,a895),x102642,x102641),f317(f8(x102643,x102642),x102644)),f317(f317(f10(f906(x102643,a895),f906(x102643,a895),x102641),f252(x102643)),f317(f317(f10(f906(x102643,a895),f906(x102643,a895),x102641),f317(f20(x102643,a895,a895),f317(f317(f10(a895,f906(a895,a895),x102643),a315),f317(f317(f9(x102643,f906(x102643,a895),a895),f319(x102643)),x102645)))),f317(f9(x102643,x102641,a895),f317(f317(f10(x102641,f906(x102641,a895),x102643),a314),x102646)))))),f317(f300(x102643,x102641,x102646),x102645)),f317(f317(f8(x102643,x102642),x102644),x102645))+~P1(f317(f29(x102643),x102645)) % 112.37/112.11 [6979]~P108(x69793)+P1(f317(x69792,x69795))+E(f317(f126(x69791,x69792),f317(f317(f138(x69791,x69793,x69794),x69795),x69796)),f317(f126(x69791,x69792),x69796)) % 112.37/112.11 [6981]P1(f317(x69811,x69812))+~E(f156(x69813,x69811,x69814),f317(f317(f242(f900(x69813),f900(x69813)),x69815),x69816))+~P1(f317(f317(f319(x69813),x69812),f317(f162(x69813),x69815))) % 112.37/112.11 [7028]~P1(f317(x70282,x70286))+~E(f156(x70281,x70282,x70283),f317(f317(f242(f900(x70281),f900(x70281)),x70284),x70285))+~P1(f317(f317(f319(x70281),x70286),f317(f162(x70281),x70285))) % 112.37/112.11 [7696]~P14(x76961,x76962,x76963)+~P1(f317(f29(x76961),x76966))+E(f317(f317(f59(x76961,x76962,x76963),x76964),f317(f317(f299(x76961),x76965),x76966)),f317(f317(f59(x76961,x76962,x76963),f317(f317(x76963,x76965),x76964)),x76966)) % 112.37/112.11 [7749]~P108(x77492)+~P1(f317(f317(f224(x77492),f317(x77493,x77494)),f317(x77493,x77495)))+E(f317(f317(f138(x77491,x77492,x77493),x77494),f317(f317(f141(x77491),x77495),x77496)),f317(f317(f141(x77491),x77494),f317(f317(f141(x77491),x77495),x77496))) % 112.37/112.11 [7862]E(x78621,x78622)+~E(f317(f317(f244(x78623,x78624),x78621),f317(f18(f906(x78624,a895),x78623),x78625)),f317(f317(f244(x78623,x78624),x78622),f317(f18(f906(x78624,a895),x78623),x78625)))+~P1(f317(f317(f319(x78624),x78626),x78625)) % 112.37/112.11 [7929]~P14(x79291,x79292,x79293)+~P1(f317(f29(x79291),x79296))+E(f317(f317(f59(x79291,x79292,x79293),x79294),f317(f317(f299(x79291),x79295),x79296)),f317(f317(x79293,x79295),f317(f317(f59(x79291,x79292,x79293),x79294),x79296))) % 112.37/112.11 [8047]~P16(x80471,x80472,x80473)+~P1(f317(f29(x80471),x80476))+E(f317(f317(f59(x80471,x80472,x80473),f317(f317(x80473,x80474),x80475)),x80476),f317(f317(x80473,x80474),f317(f317(f59(x80471,x80472,x80473),x80475),x80476))) % 112.37/112.11 [8115]~P20(x81152,x81155,x81156,x81151)+~P1(f317(f29(x81152),x81154))+E(f317(x81151,f317(f317(f299(x81152),x81153),x81154)),f317(f67(x81155,x81155,x81155,f317(x81151,x81154)),f317(x81156,x81153))) % 112.37/112.11 [8147]~P108(x81472)+P1(f317(f317(f224(x81472),f317(x81473,x81474)),f317(x81473,x81475)))+E(f317(f317(f138(x81471,x81472,x81473),x81474),f317(f317(f141(x81471),x81475),x81476)),f317(f317(f141(x81471),x81475),f317(f317(f138(x81471,x81472,x81473),x81474),x81476))) % 112.37/112.11 [8290]~E(f317(f179(f900(x82901)),x82905),f317(f179(f900(x82902)),x82906))+~E(f317(f179(f900(x82901)),x82903),f317(f179(f900(x82902)),x82904))+E(f317(f317(f124(f905(x82901,x82902)),f317(f317(f171(x82901,x82902),x82903),x82904)),f317(f317(f171(x82901,x82902),x82905),x82906)),f317(f317(f171(x82901,x82902),f317(f317(f124(x82901),x82903),x82905)),f317(f317(f124(x82902),x82904),x82906))) % 112.37/112.11 [8402]~E(x84022,f317(f300(x84023,x84021,x84024),x84026))+P1(f317(f317(f224(f906(x84021,a895)),x84022),f317(f300(x84023,x84021,x84024),x84025)))+~P1(f317(f317(f224(f906(x84023,a895)),x84026),x84025)) % 112.37/112.11 [8504]~P108(x85045)+E(f317(x85041,x85042),f317(x85041,x85043))+E(f317(f317(f138(x85044,x85045,x85041),x85042),f317(f317(f138(x85044,x85045,x85041),x85043),x85046)),f317(f317(f138(x85044,x85045,x85041),x85043),f317(f317(f138(x85044,x85045,x85041),x85042),x85046))) % 112.37/112.11 [8679]~P1(f317(f317(f319(x86792),x86794),f317(x86796,x86793)))+~P1(f317(f317(f319(x86791),x86793),x86795))+P1(f317(f317(f319(f905(x86791,x86792)),f317(f317(f242(x86791,x86792),x86793),x86794)),f317(f317(f244(x86791,x86792),x86795),x86796))) % 112.37/112.11 [9153]~P69(x91532)+~P24(x91534,x91531,x91535,x91536)+E(f317(f317(f8(x91531,x91532),x91533),f317(f300(x91534,x91531,x91535),x91536)),f317(f317(f8(x91534,x91532),f317(f67(x91531,x91532,x91534,x91533),x91535)),x91536)) % 112.37/112.11 [9154]~P75(x91542)+~P24(x91544,x91541,x91545,x91546)+E(f317(f317(f11(x91541,x91542),x91543),f317(f300(x91544,x91541,x91545),x91546)),f317(f317(f11(x91544,x91542),f317(f67(x91541,x91542,x91544,x91543),x91545)),x91546)) % 112.37/112.11 [9201]~P33(x92012,x92015,x92011,x92013,x92016)+P1(f317(f317(x92011,f317(f317(f154(x92012),x92013),x92014)),f317(f317(f154(x92015),x92016),x92014)))+~P1(f317(f317(f225(a899),x92014),f317(f179(f900(x92015)),x92016))) % 112.37/112.11 [9202]~P33(x92022,x92025,x92021,x92023,x92026)+P1(f317(f317(x92021,f317(f317(f154(x92022),x92023),x92024)),f317(f317(f154(x92025),x92026),x92024)))+~P1(f317(f317(f225(a899),x92024),f317(f179(f900(x92022)),x92023))) % 112.37/112.11 [9213]~E(f317(f300(x92131,x92132,x92133),x92134),x92136)+E(f317(f300(x92131,x92132,x92133),f317(f300(x92132,x92131,f85(x92131,x92132,x92134,x92133)),x92135)),x92135)+~P1(f317(f317(f224(f906(x92132,a895)),x92135),x92136)) % 112.37/112.11 [9419]~P19(x94193,x94191,x94196,x94192)+~P1(f317(f29(x94193),x94194))+E(f317(f67(x94191,x94191,x94191,f317(x94192,f317(f317(f3(f906(x94193,a895)),x94194),f317(f317(f299(x94193),x94195),f178(f906(x94193,a895)))))),f317(x94196,x94195)),f317(x94192,f317(f317(f299(x94193),x94195),x94194))) % 112.37/112.11 [10032]~E(f317(f300(x100322,x100324,x100326),f232(f906(x100322,a895))),f232(f906(x100324,a895)))+~E(f317(f300(x100321,x100323,x100325),f232(f906(x100321,a895))),f232(f906(x100323,a895)))+E(f317(f300(f905(x100321,x100322),f905(x100323,x100324),f248(x100321,x100323,x100322,x100324,x100325,x100326)),f232(f906(f905(x100321,x100322),a895))),f232(f906(f905(x100323,x100324),a895))) % 112.37/112.11 [10090]~P24(x100903,x100904,x100905,f317(x100906,f523(x100906,x100905,x100904,x100903,x100902,x100901)))+P24(x100903,x100904,x100905,f317(f317(f35(x100902,f906(x100903,a895)),x100901),x100906))+E(x100901,f178(f906(x100902,a895))) % 112.37/112.11 [10147]P24(x101476,x101475,x101474,f317(f317(f35(x101472,f906(x101476,a895)),x101471),x101473))+E(x101471,f178(f906(x101472,a895)))+P1(f317(f317(f319(x101472),f523(x101473,x101474,x101475,x101476,x101472,x101471)),x101471)) % 112.37/112.11 [10152]P1(f317(f317(f319(x101521),f590(x101522,x101523,x101524,x101525,x101526,x101521)),x101526))+P1(f317(f317(f224(f906(f905(x101521,x101524),a895)),f317(f317(f244(x101521,x101524),x101526),x101523)),f317(f317(f244(x101521,x101524),x101525),x101522)))+~P1(f317(f317(f224(f906(x101521,a895)),x101526),x101525)) % 112.37/112.11 [10282]~P1(f317(f317(f224(f906(x102822,a895)),f317(x102824,f590(x102826,x102824,x102822,x102825,x102823,x102821))),f317(x102826,f590(x102826,x102824,x102822,x102825,x102823,x102821))))+~P1(f317(f317(f224(f906(x102821,a895)),x102823),x102825))+P1(f317(f317(f224(f906(f905(x102821,x102822),a895)),f317(f317(f244(x102821,x102822),x102823),x102824)),f317(f317(f244(x102821,x102822),x102825),x102826))) % 112.37/112.11 [7885]~P1(f317(x78851,x78855))+~P1(f317(x78856,x78854))+P1(f317(x78851,f317(f246(x78852,x78853),f317(f317(f242(x78852,x78853),x78854),x78855)))) % 112.37/112.11 [7886]~P1(f317(x78861,x78864))+~P1(f317(x78866,x78865))+P1(f317(x78861,f317(f241(x78862,x78863),f317(f317(f242(x78862,x78863),x78864),x78865)))) % 112.37/112.11 [7934]~P1(f317(f317(x79344,x79346),x79345))+~P1(f317(f317(f319(x79341),x79346),x79343))+P1(f317(f317(f317(f36(x79341,f906(x79342,a895)),x79343),x79344),x79345)) % 112.37/112.11 [8240]~P1(f317(f317(f319(x82401),x82402),f317(x82405,x82406)))+~P1(f317(f317(f319(x82403),x82406),x82404))+P1(f317(f317(f319(x82401),x82402),f317(f317(f36(x82403,f906(x82401,a895)),x82404),x82405))) % 112.37/112.11 [8284]P1(f317(f317(x82841,x82842),x82843))+~P1(f317(f317(x82844,x82842),x82843))+~P1(f317(f317(f224(f906(x82845,f906(x82846,a895))),x82844),x82841)) % 112.37/112.11 [8425]P1(f317(f317(x84251,x84252),x84253))+~P1(f317(f317(f319(x84254),x84252),x84255))+~P1(f317(f317(f317(f35(x84254,f906(x84256,a895)),x84255),x84251),x84253)) % 112.37/112.11 [8561]P1(f317(f317(f319(x85611),x85612),f317(x85613,x85614)))+~P1(f317(f317(f319(x85615),x85614),x85616))+~P1(f317(f317(f319(x85611),x85612),f317(f317(f35(x85615,f906(x85611,a895)),x85616),x85613))) % 112.37/112.11 [8828]~P11(x88284,x88285,x88286,x88281)+E(f317(x88281,x88282),f317(x88281,x88283))+~P1(f317(f317(f319(f905(x88284,x88284)),f317(f317(f242(x88284,x88284),x88282),x88283)),x88286)) % 112.37/112.11 [8863]P1(f317(f317(f224(f906(x88631,a895)),x88632),f317(x88633,x88634)))+~P1(f317(f317(f319(x88635),x88634),x88636))+~P1(f317(f317(f224(f906(x88631,a895)),x88632),f317(f317(f35(x88635,f906(x88631,a895)),x88636),x88633))) % 112.37/112.11 [8896]~P54(x88963,x88964,f317(f276(x88964,x88963),x88965))+E(x88961,f178(f906(x88962,a895)))+E(f317(f317(f35(x88962,f906(x88963,a895)),x88961),f317(f317(f10(f906(x88964,a895),f906(x88963,a895),x88962),f275(x88964,x88963,x88965)),x88966)),f317(f275(x88964,x88963,x88965),f317(f317(f35(x88962,f906(x88964,a895)),x88961),x88966))) % 112.37/112.11 [8974]P1(f317(f317(f319(x89741),x89742),f317(f275(x89743,x89741,x89744),x89745)))+~P1(f317(f317(f319(x89743),x89746),x89745))+~P1(f317(f317(f319(f905(x89743,x89741)),f317(f317(f242(x89743,x89741),x89746),x89742)),x89744)) % 112.37/112.11 [9278]P1(f317(f317(f224(f906(x92781,a895)),f317(f275(x92782,x92781,x92783),x92784)),f317(f275(x92782,x92781,x92785),x92786)))+~P1(f317(f317(f224(f906(x92782,a895)),x92784),x92786))+~P1(f317(f317(f224(f906(f905(x92782,x92781),a895)),x92783),x92785)) % 112.37/112.11 [9468]~P1(f317(f317(f319(x94682),x94686),x94684))+~P1(f317(f317(f224(f906(x94681,a895)),x94683),x94685))+P1(f317(f317(f224(f906(f905(x94681,x94682),a895)),f317(f317(f244(x94681,x94682),x94683),f317(f18(f906(x94682,a895),x94681),x94684))),f317(f317(f244(x94681,x94682),x94685),f317(f18(f906(x94682,a895),x94681),x94684)))) % 112.37/112.11 [9480]~P33(x94801,x94802,x94803,x94805,x94806)+P1(f317(f317(f247(x94801,x94802,a895),x94803),x94804))+~P1(f317(f317(f319(f905(x94801,x94802)),x94804),f317(f162(f905(x94801,x94802)),f317(f317(f171(x94801,x94802),x94805),x94806)))) % 112.37/112.11 [9628]~E(x96283,x96285)+P1(f317(f317(f319(f905(f900(x96281),f900(x96281))),f317(f317(f242(f900(x96281),f900(x96281)),f317(f317(f141(x96281),x96282),x96283)),f317(f317(f141(x96281),x96284),x96285))),f147(x96281,x96286)))+~P1(f317(f317(f319(f905(x96281,x96281)),f317(f317(f242(x96281,x96281),x96282),x96284)),x96286)) % 112.37/112.11 [9634]~E(f317(f179(f900(x96341)),x96343),f317(f179(f900(x96341)),x96345))+P1(f317(f317(f319(f905(f900(x96341),f900(x96341))),f317(f317(f242(f900(x96341),f900(x96341)),f317(f317(f141(x96341),x96342),x96343)),f317(f317(f141(x96341),x96344),x96345))),f135(x96341,x96346)))+~P1(f317(f317(f319(f905(x96341,x96341)),f317(f317(f242(x96341,x96341),x96342),x96344)),x96346)) % 112.37/112.11 [9667]P1(f317(f317(f319(f905(x96671,x96671)),f317(f317(f242(x96671,x96671),x96672),x96673)),f317(f317(f173(f905(x96671,x96671),a895),f317(a102,x96674)),x96675)))+~P1(f317(f317(f319(f905(x96671,x96671)),f317(f317(f242(x96671,x96671),x96676),x96673)),x96675))+~P1(f317(f317(f319(f905(x96671,x96671)),f317(f317(f242(x96671,x96671),x96672),x96676)),f317(f317(f173(f905(x96671,x96671),a895),x96674),x96675))) % 112.37/112.11 [9668]P1(f317(f317(f319(f905(x96681,x96681)),f317(f317(f242(x96681,x96681),x96682),x96683)),f317(f317(f173(f905(x96681,x96681),a895),f317(a102,x96684)),x96685)))+~P1(f317(f317(f319(f905(x96681,x96681)),f317(f317(f242(x96681,x96681),x96682),x96686)),x96685))+~P1(f317(f317(f319(f905(x96681,x96681)),f317(f317(f242(x96681,x96681),x96686),x96683)),f317(f317(f173(f905(x96681,x96681),a895),x96684),x96685))) % 112.37/112.11 [9671]~P1(f317(f317(f319(x96714),x96715),x96716))+P1(f317(f317(f224(f906(x96711,a895)),x96712),x96713))+~P1(f317(f317(f224(f906(f905(x96711,x96714),a895)),f317(f317(f244(x96711,x96714),x96712),f317(f18(f906(x96714,a895),x96711),x96716))),f317(f317(f244(x96711,x96714),x96713),f317(f18(f906(x96714,a895),x96711),x96716)))) % 112.37/112.11 [9716]E(x97161,x97162)+~P1(f317(f317(f319(f905(f900(x97163),f900(x97163))),f317(f317(f242(f900(x97163),f900(x97163)),f317(f317(f141(x97163),x97161),x97165)),f317(f317(f141(x97163),x97162),x97166))),f135(x97163,x97164)))+P1(f317(f317(f319(f905(x97163,x97163)),f317(f317(f242(x97163,x97163),x97161),x97162)),x97164)) % 112.37/112.11 [9717]E(x97171,x97172)+~P1(f317(f317(f319(f905(f900(x97173),f900(x97173))),f317(f317(f242(f900(x97173),f900(x97173)),f317(f317(f141(x97173),x97171),x97175)),f317(f317(f141(x97173),x97172),x97176))),f137(x97173,x97174)))+P1(f317(f317(f319(f905(x97173,x97173)),f317(f317(f242(x97173,x97173),x97171),x97172)),x97174)) % 112.37/112.11 [9718]E(x97181,x97182)+~P1(f317(f317(f319(f905(f900(x97183),f900(x97183))),f317(f317(f242(f900(x97183),f900(x97183)),f317(f317(f141(x97183),x97181),x97185)),f317(f317(f141(x97183),x97182),x97186))),f147(x97183,x97184)))+P1(f317(f317(f319(f905(x97183,x97183)),f317(f317(f242(x97183,x97183),x97181),x97182)),x97184)) % 112.37/112.11 [9754]P1(f317(f317(f319(f905(f900(x97541),f900(x97541))),f317(f317(f242(f900(x97541),f900(x97541)),f317(f317(f141(x97541),x97542),x97543)),f317(f317(f141(x97541),x97544),x97545))),f148(x97541,x97546)))+~P1(f317(f317(f319(f905(f900(x97541),f900(x97541))),f317(f317(f242(f900(x97541),f900(x97541)),x97543),x97545)),f148(x97541,x97546)))+~P1(f317(f317(f319(f905(x97541,x97541)),f317(f317(f242(x97541,x97541),x97542),x97544)),x97546)) % 112.37/112.11 [9771]P1(f317(x97711,x97712))+~P1(f317(x97711,f485(x97711,x97713,x97714,x97715,x97716)))+~P1(f317(f317(f319(x97716),x97712),f317(f317(f36(x97715,f906(x97716,a895)),x97714),x97713))) % 112.37/112.11 [9776]~P1(f317(f317(f319(f905(f900(x97761),f900(x97761))),f317(f317(f242(f900(x97761),f900(x97761)),f317(f317(f141(x97761),x97762),x97765)),f317(f317(f141(x97761),x97763),x97766))),f135(x97761,x97764)))+P1(f317(f317(f319(f905(f900(x97761),f900(x97761))),f317(f317(f242(f900(x97761),f900(x97761)),x97765),x97766)),f135(x97761,x97764)))+P1(f317(f317(f319(f905(x97761,x97761)),f317(f317(f242(x97761,x97761),x97762),x97763)),x97764)) % 112.37/112.11 [9777]~P1(f317(f317(f319(f905(f900(x97771),f900(x97771))),f317(f317(f242(f900(x97771),f900(x97771)),f317(f317(f141(x97771),x97772),x97775)),f317(f317(f141(x97771),x97773),x97776))),f137(x97771,x97774)))+P1(f317(f317(f319(f905(f900(x97771),f900(x97771))),f317(f317(f242(f900(x97771),f900(x97771)),x97775),x97776)),f137(x97771,x97774)))+P1(f317(f317(f319(f905(x97771,x97771)),f317(f317(f242(x97771,x97771),x97772),x97773)),x97774)) % 112.37/112.11 [9778]~P1(f317(f317(f319(f905(f900(x97781),f900(x97781))),f317(f317(f242(f900(x97781),f900(x97781)),f317(f317(f141(x97781),x97782),x97785)),f317(f317(f141(x97781),x97783),x97786))),f147(x97781,x97784)))+P1(f317(f317(f319(f905(f900(x97781),f900(x97781))),f317(f317(f242(f900(x97781),f900(x97781)),x97785),x97786)),f147(x97781,x97784)))+P1(f317(f317(f319(f905(x97781,x97781)),f317(f317(f242(x97781,x97781),x97782),x97783)),x97784)) % 112.37/112.11 [9867]P1(f317(x98671,x98672))+P1(f317(f317(f319(x98673),f486(x98671,x98674,x98675,x98673,x98676)),x98675))+~P1(f317(f317(f319(x98676),x98672),f317(f317(f36(x98673,f906(x98676,a895)),x98675),x98674))) % 112.37/112.11 [9879]~E(x98792,x98794)+P1(f317(f317(f319(f905(f900(x98791),f900(x98791))),f317(f317(f242(f900(x98791),f900(x98791)),f317(f317(f124(x98791),x98792),f317(f317(f141(x98791),x98793),f103(x98791)))),f317(f317(f124(x98791),x98794),f317(f317(f141(x98791),x98795),f103(x98791))))),f147(x98791,x98796)))+~P1(f317(f317(f319(f905(x98791,x98791)),f317(f317(f242(x98791,x98791),x98793),x98795)),x98796)) % 112.37/112.11 [9953]E(x99531,x99532)+~P1(f317(f317(f319(f905(f900(x99533),f900(x99533))),f317(f317(f242(f900(x99533),f900(x99533)),f317(f317(f124(x99533),x99535),f317(f317(f141(x99533),x99531),f103(x99533)))),f317(f317(f124(x99533),x99536),f317(f317(f141(x99533),x99532),f103(x99533))))),f147(x99533,x99534)))+P1(f317(f317(f319(f905(x99533,x99533)),f317(f317(f242(x99533,x99533),x99531),x99532)),x99534)) % 112.37/112.11 [9984]~P1(f317(f317(f319(f905(f900(x99841),f900(x99841))),f317(f317(f242(f900(x99841),f900(x99841)),f317(f317(f124(x99841),x99845),f317(f317(f141(x99841),x99842),f103(x99841)))),f317(f317(f124(x99841),x99846),f317(f317(f141(x99841),x99843),f103(x99841))))),f147(x99841,x99844)))+P1(f317(f317(f319(f905(f900(x99841),f900(x99841))),f317(f317(f242(f900(x99841),f900(x99841)),x99845),x99846)),f147(x99841,x99844)))+P1(f317(f317(f319(f905(x99841,x99841)),f317(f317(f242(x99841,x99841),x99842),x99843)),x99844)) % 112.37/112.11 [10004]P1(f317(x100041,x100042))+P1(f317(f317(f319(x100043),f485(x100041,x100044,x100045,x100046,x100043)),f317(x100044,f486(x100041,x100044,x100045,x100046,x100043))))+~P1(f317(f317(f319(x100043),x100042),f317(f317(f36(x100046,f906(x100043,a895)),x100045),x100044))) % 112.37/112.11 [10156]P1(f317(f317(f319(x101561),f821(x101562,x101563,x101564,x101565,x101566,x101561)),x101565))+~P1(f317(f317(f224(f906(x101561,a895)),x101566),x101565))+P1(f317(f317(f224(f906(x101564,a895)),f317(f317(f35(x101561,f906(x101564,a895)),x101565),x101563)),f317(f317(f35(x101561,f906(x101564,a895)),x101565),x101562))) % 112.37/112.11 [10283]~P1(f317(f317(f224(f906(x102831,a895)),f317(x102834,f821(x102835,x102834,x102831,x102833,x102836,x102832))),f317(x102835,f821(x102835,x102834,x102831,x102833,x102836,x102832))))+~P1(f317(f317(f224(f906(x102832,a895)),x102836),x102833))+P1(f317(f317(f224(f906(x102831,a895)),f317(f317(f35(x102832,f906(x102831,a895)),x102833),x102834)),f317(f317(f35(x102832,f906(x102831,a895)),x102833),x102835))) % 112.37/112.11 [8994]~P16(x89943,x89944,x89941)+~P1(f317(f29(x89943),x89946))+E(f317(f317(x89941,x89942),f317(f317(f59(x89943,x89944,x89941),x89945),f317(f317(f3(f906(x89943,a895)),x89946),f317(f317(f299(x89943),x89942),f178(f906(x89943,a895)))))),f317(f317(f59(x89943,x89944,x89941),x89945),f317(f317(f299(x89943),x89942),x89946))) % 112.37/112.11 [9287]~P1(f317(f317(f319(x92875),x92873),x92876))+P1(f317(f317(f224(f906(x92871,a895)),f317(x92872,x92873)),x92874))+~P1(f317(f317(f224(f906(x92871,a895)),f317(f317(f36(x92875,f906(x92871,a895)),x92876),x92872)),x92874)) % 112.37/112.11 [9928]~P8(x99281,x99285,x99284)+P1(f317(f317(f319(f905(x99281,x99281)),f317(f317(f242(x99281,x99281),x99282),x99283)),x99284))+~P1(f317(f317(f319(x99281),x99286),f317(f317(f92(f906(x99281,a895)),f317(f275(x99281,x99281,x99284),f317(f317(f299(x99281),x99282),f178(f906(x99281,a895))))),f317(f275(x99281,x99281,x99284),f317(f317(f299(x99281),x99283),f178(f906(x99281,a895))))))) % 112.37/112.11 [8716]~P110(x87162)+~E(f317(f317(f74(x87162),f317(f317(f75(x87162),x87164),x87165)),x87161),f317(f317(f74(x87162),f317(f317(f75(x87162),x87163),x87165)),x87166))+E(x87161,f317(f317(f74(x87162),f317(f317(f75(x87162),f317(f317(f3(x87162),x87163),x87164)),x87165)),x87166)) % 112.37/112.11 [8717]~P110(x87171)+~E(f317(f317(f74(x87171),f317(f317(f75(x87171),x87172),x87174)),x87175),f317(f317(f74(x87171),f317(f317(f75(x87171),x87173),x87174)),x87176))+E(f317(f317(f74(x87171),f317(f317(f75(x87171),f317(f317(f3(x87171),x87172),x87173)),x87174)),x87175),x87176) % 112.37/112.11 [8899]~P110(x88991)+E(f317(f317(f74(x88991),f317(f317(f75(x88991),x88992),x88993)),x88994),f317(f317(f74(x88991),f317(f317(f75(x88991),x88995),x88993)),x88996))+~E(x88996,f317(f317(f74(x88991),f317(f317(f75(x88991),f317(f317(f3(x88991),x88992),x88995)),x88993)),x88994)) % 112.37/112.11 [8900]~P110(x89001)+E(f317(f317(f74(x89001),f317(f317(f75(x89001),x89002),x89003)),x89004),f317(f317(f74(x89001),f317(f317(f75(x89001),x89005),x89003)),x89006))+~E(f317(f317(f74(x89001),f317(f317(f75(x89001),f317(f317(f3(x89001),x89002),x89005)),x89003)),x89004),x89006) % 112.37/112.11 [9224]~P1(f317(f317(x92244,x92245),x92246))+~P1(f317(f317(x92243,x92245),x92246))+P1(f317(f317(f317(f317(f92(f906(x92241,f906(x92242,a895))),x92243),x92244),x92245),x92246)) % 112.37/112.11 [9489]P1(f317(f317(x94891,x94892),x94893))+P1(f317(f317(x94894,x94892),x94893))+~P1(f317(f317(f317(f317(f91(f906(x94895,f906(x94896,a895))),x94894),x94891),x94892),x94893)) % 112.37/112.11 [9791]~P111(x97911)+~P1(f317(f317(f224(x97911),f317(f317(f74(x97911),f317(f317(f75(x97911),x97914),x97915)),x97912)),f317(f317(f74(x97911),f317(f317(f75(x97911),x97913),x97915)),x97916)))+P1(f317(f317(f224(x97911),x97912),f317(f317(f74(x97911),f317(f317(f75(x97911),f317(f317(f3(x97911),x97913),x97914)),x97915)),x97916))) % 112.37/112.11 [9792]~P111(x97921)+~P1(f317(f317(f225(x97921),f317(f317(f74(x97921),f317(f317(f75(x97921),x97924),x97925)),x97922)),f317(f317(f74(x97921),f317(f317(f75(x97921),x97923),x97925)),x97926)))+P1(f317(f317(f225(x97921),x97922),f317(f317(f74(x97921),f317(f317(f75(x97921),f317(f317(f3(x97921),x97923),x97924)),x97925)),x97926))) % 112.37/112.11 [9815]~P111(x98151)+P1(f317(f317(f224(x98151),f317(f317(f74(x98151),f317(f317(f75(x98151),x98152),x98153)),x98154)),f317(f317(f74(x98151),f317(f317(f75(x98151),x98155),x98153)),x98156)))+~P1(f317(f317(f224(x98151),x98154),f317(f317(f74(x98151),f317(f317(f75(x98151),f317(f317(f3(x98151),x98155),x98152)),x98153)),x98156))) % 112.37/112.11 [9816]~P111(x98161)+P1(f317(f317(f225(x98161),f317(f317(f74(x98161),f317(f317(f75(x98161),x98162),x98163)),x98164)),f317(f317(f74(x98161),f317(f317(f75(x98161),x98165),x98163)),x98166)))+~P1(f317(f317(f225(x98161),x98164),f317(f317(f74(x98161),f317(f317(f75(x98161),f317(f317(f3(x98161),x98165),x98162)),x98163)),x98166))) % 112.37/112.11 [9920]~P111(x99201)+~P1(f317(f317(f224(x99201),f317(f317(f74(x99201),f317(f317(f75(x99201),x99202),x99204)),x99205)),f317(f317(f74(x99201),f317(f317(f75(x99201),x99203),x99204)),x99206)))+P1(f317(f317(f224(x99201),f317(f317(f74(x99201),f317(f317(f75(x99201),f317(f317(f3(x99201),x99202),x99203)),x99204)),x99205)),x99206)) % 112.37/112.11 [9921]~P111(x99211)+~P1(f317(f317(f225(x99211),f317(f317(f74(x99211),f317(f317(f75(x99211),x99212),x99214)),x99215)),f317(f317(f74(x99211),f317(f317(f75(x99211),x99213),x99214)),x99216)))+P1(f317(f317(f225(x99211),f317(f317(f74(x99211),f317(f317(f75(x99211),f317(f317(f3(x99211),x99212),x99213)),x99214)),x99215)),x99216)) % 112.37/112.11 [9967]~P111(x99671)+P1(f317(f317(f224(x99671),f317(f317(f74(x99671),f317(f317(f75(x99671),x99672),x99673)),x99674)),f317(f317(f74(x99671),f317(f317(f75(x99671),x99675),x99673)),x99676)))+~P1(f317(f317(f224(x99671),f317(f317(f74(x99671),f317(f317(f75(x99671),f317(f317(f3(x99671),x99672),x99675)),x99673)),x99674)),x99676)) % 112.37/112.11 [9968]~P111(x99681)+P1(f317(f317(f225(x99681),f317(f317(f74(x99681),f317(f317(f75(x99681),x99682),x99683)),x99684)),f317(f317(f74(x99681),f317(f317(f75(x99681),x99685),x99683)),x99686)))+~P1(f317(f317(f225(x99681),f317(f317(f74(x99681),f317(f317(f75(x99681),f317(f317(f3(x99681),x99682),x99685)),x99683)),x99684)),x99686)) % 112.37/112.11 [10141]~P69(x101412)+~P1(f317(f29(x101411),x101416))+E(f317(f317(f8(x101411,x101412),f317(f317(f20(x101411,x101412,x101412),f317(f317(f20(x101411,x101412,f906(x101412,x101412)),f317(f317(f10(a895,f906(x101412,f906(x101412,x101412)),x101411),f86(x101412)),x101413)),x101414)),x101415)),x101416),f317(f317(f74(x101412),f317(f317(f8(x101411,x101412),x101414),f317(f317(f92(f906(x101411,a895)),x101416),f317(f252(x101411),x101413)))),f317(f317(f8(x101411,x101412),x101415),f317(f317(f92(f906(x101411,a895)),x101416),f317(f73(f906(x101411,a895)),f317(f252(x101411),x101413)))))) % 112.37/112.11 [10202]P1(f317(f317(f319(x102022),x102024),x102026))+P1(f317(f317(f319(x102022),x102025),x102026))+E(f317(f301(x102021,x102022,f317(f317(f9(x102021,x102022,x102022),f317(f317(f9(x102021,x102022,f906(x102022,x102022)),f317(f317(f10(a895,f906(x102022,f906(x102022,x102022)),x102021),f86(x102022)),f317(f317(f9(x102021,f906(x102021,a895),a895),f319(x102021)),x102023))),x102024)),x102025)),x102026),f178(f906(x102021,a895))) % 112.37/112.11 [10203]P1(f317(f317(f319(x102032),x102035),x102036))+~P1(f317(f317(f319(x102032),x102034),x102036))+E(f317(f301(x102031,x102032,f317(f317(f9(x102031,x102032,x102032),f317(f317(f9(x102031,x102032,f906(x102032,x102032)),f317(f317(f10(a895,f906(x102032,f906(x102032,x102032)),x102031),f86(x102032)),f317(f317(f9(x102031,f906(x102031,a895),a895),f319(x102031)),x102033))),x102034)),x102035)),x102036),x102033) % 112.37/112.11 [10204]P1(f317(f317(f319(x102042),x102044),x102046))+~P1(f317(f317(f319(x102042),x102045),x102046))+E(f317(f301(x102041,x102042,f317(f317(f9(x102041,x102042,x102042),f317(f317(f9(x102041,x102042,f906(x102042,x102042)),f317(f317(f10(a895,f906(x102042,f906(x102042,x102042)),x102041),f86(x102042)),f317(f317(f9(x102041,f906(x102041,a895),a895),f319(x102041)),x102043))),x102044)),x102045)),x102046),f317(f73(f906(x102041,a895)),x102043)) % 112.37/112.11 [10205]~P1(f317(f317(f319(x102052),x102054),x102056))+~P1(f317(f317(f319(x102052),x102055),x102056))+E(f317(f301(x102051,x102052,f317(f317(f9(x102051,x102052,x102052),f317(f317(f9(x102051,x102052,f906(x102052,x102052)),f317(f317(f10(a895,f906(x102052,f906(x102052,x102052)),x102051),f86(x102052)),f317(f317(f9(x102051,f906(x102051,a895),a895),f319(x102051)),x102053))),x102054)),x102055)),x102056),f232(f906(x102051,a895))) % 112.37/112.11 [8749]E(x87491,x87492)+~P56(x87494,x87495,x87493,x87496,x87497)+~E(f317(x87493,x87491),f317(x87493,x87492)) % 112.37/112.11 [8778]~P10(x87786,x87785,x87787,x87784,x87781)+E(f317(f317(x87781,x87782),x87783),x87784)+P1(f317(f29(x87785),x87783)) % 112.37/112.11 [9658]P41(x96581,x96582,x96583,x96584,x96585,f317(f317(x96583,x96586),x96587))+~E(f317(f317(x96583,x96586),x96587),x96584)+~E(x96585,f178(f906(x96581,a895))) % 112.37/112.11 [9837]~P1(f317(x98376,x98373))+~P1(f317(f317(f319(f905(x98372,x98372)),f317(f317(f242(x98372,x98372),x98374),x98375)),f317(x98377,x98373)))+P1(f317(f317(f319(f905(f905(x98371,x98372),f905(x98371,x98372))),f317(f317(f242(f905(x98371,x98372),f905(x98371,x98372)),f317(f317(f242(x98371,x98372),x98373),x98374)),f317(f317(f242(x98371,x98372),x98373),x98375))),f270(x98371,x98372,x98376,x98377))) % 112.37/112.11 [10267]~P41(x102672,x102677,x102673,x102676,x102671,f317(f317(x102673,x102675),x102674))+E(f317(f317(x102673,f427(x102674,x102675,x102671,x102676,x102673,x102677,x102672)),f433(x102674,x102675,x102671,x102676,x102673,x102677,x102672)),f317(f317(x102673,x102675),x102674))+E(x102671,f178(f906(x102672,a895))) % 112.37/112.11 [10268]~P41(x102687,x102686,x102681,x102684,x102685,f317(f317(x102681,x102682),x102683))+E(f317(f317(x102681,f427(x102683,x102682,x102685,x102684,x102681,x102686,x102687)),f433(x102683,x102682,x102685,x102684,x102681,x102686,x102687)),f317(f317(x102681,x102682),x102683))+E(f317(f317(x102681,x102682),x102683),x102684) % 112.37/112.11 [9321]~P33(x93211,x93212,x93213,x93215,x93217)+P33(x93211,x93212,x93213,f317(f317(f141(x93211),x93214),x93215),f317(f317(f141(x93212),x93216),x93217))+~P1(f317(f317(x93213,x93214),x93216)) % 112.37/112.11 [9340]P33(x93401,x93402,x93403,x93404,x93405)+~P33(x93401,x93402,x93403,f317(f317(f124(x93401),x93406),x93404),f317(f317(f124(x93402),x93407),x93405))+~E(f317(f179(f900(x93401)),x93406),f317(f179(f900(x93402)),x93407)) % 112.37/112.11 [9341]P33(x93411,x93412,x93413,x93414,x93415)+~P33(x93411,x93412,x93413,f317(f317(f124(x93411),x93414),x93416),f317(f317(f124(x93412),x93415),x93417))+~E(f317(f179(f900(x93411)),x93414),f317(f179(f900(x93412)),x93415)) % 112.37/112.11 [9556]~P33(x95561,x95562,x95563,x95565,x95567)+~P33(x95561,x95562,x95563,x95564,x95566)+P33(x95561,x95562,x95563,f317(f317(f124(x95561),x95564),x95565),f317(f317(f124(x95562),x95566),x95567)) % 112.37/112.11 [9913]~P1(f317(f61(x99131,x99134,x99135,x99136,x99133),x99137))+P1(f317(f61(x99131,x99134,x99135,x99136,f317(f317(f299(x99131),x99132),x99133)),f317(f317(x99135,x99132),x99137)))+P1(f317(f317(f319(x99131),x99132),x99133)) % 112.37/112.11 [10299]~P41(x102992,x102997,x102996,x102995,x102991,f317(f317(x102996,x102994),x102993))+E(x102991,f178(f906(x102992,a895)))+P1(f317(f317(f319(x102992),f427(x102993,x102994,x102991,x102995,x102996,x102997,x102992)),x102991)) % 112.37/112.11 [10300]~P41(x103005,x103007,x103001,x103004,x103006,f317(f317(x103001,x103002),x103003))+E(f317(f317(x103001,x103002),x103003),x103004)+P1(f317(f317(f319(x103005),f427(x103003,x103002,x103006,x103004,x103001,x103007,x103005)),x103006)) % 112.37/112.11 [10387]E(f317(f317(f242(x103871,x103872),x103873),x103874),f317(f317(f242(x103871,x103872),x103875),x103876))+P1(f317(f317(f319(f905(f905(x103871,x103872),f905(x103871,x103872))),f317(f317(f242(f905(x103871,x103872),f905(x103871,x103872)),f317(f317(f242(x103871,x103872),f823(x103877,x103874,x103873,x103876,x103875,x103872,x103871)),f824(x103877,x103874,x103873,x103876,x103875,x103872,x103871))),f317(f317(f242(x103871,x103872),x103873),x103874))),f297(f905(x103871,x103872),x103877)))+~P1(f317(f317(f319(f905(f905(x103871,x103872),f905(x103871,x103872))),f317(f317(f242(f905(x103871,x103872),f905(x103871,x103872)),f317(f317(f242(x103871,x103872),x103875),x103876)),f317(f317(f242(x103871,x103872),x103873),x103874))),f297(f905(x103871,x103872),x103877))) % 112.37/112.11 [9019]~P21(x90194,x90195,x90196,x90197,x90191)+~P1(f317(f29(x90195),x90193))+E(f317(f317(x90191,x90192),x90193),f317(f317(f317(f60(x90194,x90195,x90196),x90192),x90197),x90193)) % 112.37/112.11 [9020]~P10(x90204,x90205,x90206,x90207,x90201)+~P1(f317(f29(x90205),x90203))+E(f317(f317(x90201,x90202),x90203),f317(f317(f317(f60(x90204,x90205,x90206),x90202),x90207),x90203)) % 112.37/112.11 [9810]~P23(x98103,x98104,x98105,x98107,x98106,x98101)+~P1(f317(f29(x98104),x98102))+E(f317(x98101,x98102),f317(f317(f317(f60(x98103,x98104,x98105),x98106),x98107),x98102)) % 112.37/112.11 [9962]P41(x99621,x99622,x99623,x99624,x99625,f317(f317(x99623,x99626),x99627))+~P41(x99621,x99622,x99623,x99624,f317(f317(f3(f906(x99621,a895)),x99625),f317(f317(f299(x99621),x99626),f178(f906(x99621,a895)))),x99627)+~P1(f317(f317(f319(x99621),x99626),x99625)) % 112.37/112.11 [10323]P1(f317(f317(x103237,f771(x103234,x103235,x103231,x103236,x103233,x103232,x103237)),f772(x103234,x103235,x103231,x103236,x103233,x103232,x103237)))+~P1(f317(f317(x103237,f317(f246(x103232,x103233),x103236)),f317(f241(x103232,x103233),x103236)))+P1(f317(x103231,f317(f317(f247(x103232,x103233,x103234),x103235),x103236))) % 112.37/112.11 [10333]~P41(x103332,x103333,x103334,x103335,x103331,f317(f317(x103334,x103337),x103336))+P41(x103332,x103333,x103334,x103335,f317(f317(f3(f906(x103332,a895)),x103331),f317(f317(f299(x103332),f427(x103336,x103337,x103331,x103335,x103334,x103333,x103332)),f178(f906(x103332,a895)))),f433(x103336,x103337,x103331,x103335,x103334,x103333,x103332))+E(x103331,f178(f906(x103332,a895))) % 112.37/112.11 [10334]~P41(x103345,x103346,x103341,x103344,x103347,f317(f317(x103341,x103342),x103343))+P41(x103345,x103346,x103341,x103344,f317(f317(f3(f906(x103345,a895)),x103347),f317(f317(f299(x103345),f427(x103343,x103342,x103347,x103344,x103341,x103346,x103345)),f178(f906(x103345,a895)))),f433(x103343,x103342,x103347,x103344,x103341,x103346,x103345))+E(f317(f317(x103341,x103342),x103343),x103344) % 112.37/112.11 [10354]~P1(f317(x103541,f317(f317(x103545,f772(x103544,x103545,x103541,x103546,x103543,x103542,x103547)),f771(x103544,x103545,x103541,x103546,x103543,x103542,x103547))))+~P1(f317(f317(x103547,f317(f246(x103542,x103543),x103546)),f317(f241(x103542,x103543),x103546)))+P1(f317(x103541,f317(f317(f247(x103542,x103543,x103544),x103545),x103546))) % 112.37/112.11 [9642]P1(f317(f317(f224(f906(f905(x96421,x96422),a895)),f317(f317(f279(x96421,x96423,x96422),x96424),x96425)),f317(f317(f279(x96421,x96423,x96422),x96426),x96427)))+~P1(f317(f317(f224(f906(f905(x96423,x96422),a895)),x96425),x96427))+~P1(f317(f317(f224(f906(f905(x96421,x96423),a895)),x96424),x96426)) % 112.37/112.11 [10381]E(f317(f317(f242(x103811,x103812),x103813),x103814),f317(f317(f242(x103811,x103812),x103815),x103816))+~P1(f317(f317(f319(f905(f905(x103811,x103812),f905(x103811,x103812))),f317(f317(f242(f905(x103811,x103812),f905(x103811,x103812)),f317(f317(f242(x103811,x103812),x103813),x103814)),f317(f317(f242(x103811,x103812),x103815),x103816))),f297(f905(x103811,x103812),x103817)))+P1(f317(f317(f319(f905(f905(x103811,x103812),f905(x103811,x103812))),f317(f317(f242(f905(x103811,x103812),f905(x103811,x103812)),f317(f317(f242(x103811,x103812),x103813),x103814)),f317(f317(f242(x103811,x103812),f823(x103817,x103816,x103815,x103814,x103813,x103812,x103811)),f824(x103817,x103816,x103815,x103814,x103813,x103812,x103811)))),x103817)) % 112.37/112.11 [9973]~P1(f317(f317(f319(x99731),x99736),x99735))+P1(f317(f61(x99731,x99732,x99733,x99734,x99735),f317(f317(x99733,x99736),x99737)))+~P1(f317(f61(x99731,x99732,x99733,x99734,f317(f317(f3(f906(x99731,a895)),x99735),f317(f317(f299(x99731),x99736),f178(f906(x99731,a895))))),x99737)) % 112.37/112.11 [10394]~P146(x103941)+~P24(f905(x103942,x103943),x103941,f317(f247(x103942,x103943,x103941),f317(f317(f9(x103942,f906(x103943,x103941),f906(x103943,x103941)),f317(f317(f10(f906(x103941,x103941),f906(f906(x103943,x103941),f906(x103943,x103941)),x103942),f10(x103941,x103941,x103943)),f317(f317(f10(x103941,f906(x103941,x103941),x103942),f75(x103941)),x103944))),x103945)),f317(f317(f244(x103942,x103943),x103946),f317(f18(f906(x103943,a895),x103942),x103947)))+E(f317(f317(f8(x103941,x103941),f25(x103941)),f317(f252(x103941),f317(f317(f10(f906(x103942,a895),a895,x103941),f81(x103942)),f317(f317(f10(f906(x103942,f906(x103943,a895)),f906(x103942,a895),x103941),f317(f10(f906(x103943,a895),a895,x103942),f81(x103943))),f317(f317(f9(x103941,f906(x103942,f906(x103943,a895)),f906(x103942,f906(x103943,a895))),f317(f317(f10(f906(x103942,f906(f906(x103943,a895),f906(x103943,a895))),f906(f906(x103942,f906(x103943,a895)),f906(x103942,f906(x103943,a895))),x103941),f20(x103942,f906(x103943,a895),f906(x103943,a895))),f317(f317(f10(f906(x103942,f906(x103943,f906(a895,a895))),f906(x103942,f906(f906(x103943,a895),f906(x103943,a895))),x103941),f317(f10(f906(x103943,f906(a895,a895)),f906(f906(x103943,a895),f906(x103943,a895)),x103942),f20(x103943,a895,a895))),f317(f317(f10(f906(x103942,f906(x103943,a895)),f906(x103942,f906(x103943,f906(a895,a895))),x103941),f317(f10(f906(x103943,a895),f906(x103943,f906(a895,a895)),x103942),f317(f10(a895,f906(a895,a895),x103943),a315))),f317(f317(f9(x103941,f906(x103942,f906(x103943,x103941)),f906(x103942,f906(x103943,a895))),f317(f317(f10(f906(f906(x103943,x103941),f906(x103943,a895)),f906(f906(x103942,f906(x103943,x103941)),f906(x103942,f906(x103943,a895))),x103941),f10(f906(x103943,x103941),f906(x103943,a895),x103942)),f317(f317(f10(f906(x103941,a895),f906(f906(x103943,x103941),f906(x103943,a895)),x103941),f10(x103941,a895,x103943)),a314))),f317(f317(f9(x103942,f906(x103943,x103941),f906(x103943,x103941)),f317(f317(f10(f906(x103941,x103941),f906(f906(x103943,x103941),f906(x103943,x103941)),x103942),f10(x103941,x103941,x103943)),f317(f317(f10(x103941,f906(x103941,x103941),x103942),f75(x103941)),x103944))),x103945)))))),f317(f317(f9(x103942,f906(x103943,a895),f906(x103943,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x103943,a895),f906(x103943,a895)),x103942),f10(a895,a895,x103943)),f317(f317(f10(a895,f906(a895,a895),x103942),a315),f317(f317(f9(x103942,f906(x103942,a895),a895),f319(x103942)),x103946)))),f317(f317(f9(x103943,f906(x103943,a895),a895),f319(x103943)),x103947))))))),f317(f317(f75(x103941),f317(f317(f8(x103942,x103941),x103944),x103946)),f317(f317(f8(x103943,x103941),x103945),x103947))) % 112.37/112.11 [9646]~P25(x96461,x96463,x96465,x96466,x96468)+~P25(x96463,x96462,x96464,x96468,x96467)+P25(x96461,x96462,f317(f67(x96463,x96462,x96461,x96464),x96465),x96466,x96467) % 112.37/112.11 [9676]P25(x96761,x96762,x96763,x96764,x96765)+~P25(x96766,x96761,x96767,x96768,x96764)+~P25(x96766,x96762,f317(f67(x96761,x96762,x96766,x96763),x96767),x96768,x96765) % 112.37/112.11 [9808]~P1(f317(f317(x98084,x98086),x98088))+~P1(f317(f317(x98085,x98088),x98087))+P1(f317(f317(f243(x98081,x98082,x98083,x98084,x98085),x98086),x98087)) % 112.37/112.11 [9396]~P19(x93968,x93961,x93963,x93965)+~P1(f317(f29(x93968),x93966))+E(f317(f67(x93961,x93961,x93962,f317(x93963,x93964)),f317(f67(x93961,x93961,x93962,f317(x93965,x93966)),x93967)),f317(f67(x93961,x93961,x93962,f317(x93965,x93966)),f317(f67(x93961,x93961,x93962,f317(x93963,x93964)),x93967))) % 112.37/112.11 [9798]~P22(x97987,x97982,x97985,x97988,x97986,x97981)+~P1(f317(f29(x97982),x97984))+E(f317(x97981,f317(f317(f299(x97982),x97983),x97984)),f317(f317(x97985,f317(x97986,x97983)),f317(x97981,x97984))) % 112.37/112.11 [9918]~P24(x99182,x99184,x99186,x99188)+~P24(x99181,x99183,x99185,x99187)+P24(f905(x99181,x99182),f905(x99183,x99184),f248(x99181,x99183,x99182,x99184,x99185,x99186),f317(f317(f244(x99181,x99182),x99187),f317(f18(f906(x99182,a895),x99181),x99188))) % 112.37/112.11 [9582]P1(f317(f317(f319(f905(x95821,x95822)),f317(f317(f242(x95821,x95822),x95823),x95824)),f317(f317(f279(x95821,x95825,x95822),x95826),x95827)))+~P1(f317(f317(f319(f905(x95821,x95825)),f317(f317(f242(x95821,x95825),x95823),x95828)),x95826))+~P1(f317(f317(f319(f905(x95825,x95822)),f317(f317(f242(x95825,x95822),x95828),x95824)),x95827)) % 112.37/112.11 [9779]~P1(f317(f317(f224(f906(f905(x97793,x97792),a895)),x97795),f317(f317(f244(x97793,x97792),x97798),f317(f18(f906(x97792,a895),x97793),x97797))))+~P1(f317(f317(f224(f906(f905(x97791,x97793),a895)),x97794),f317(f317(f244(x97791,x97793),x97796),f317(f18(f906(x97793,a895),x97791),x97798))))+P1(f317(f317(f224(f906(f905(x97791,x97792),a895)),f317(f317(f279(x97791,x97793,x97792),x97794),x97795)),f317(f317(f244(x97791,x97792),x97796),f317(f18(f906(x97792,a895),x97791),x97797)))) % 112.37/112.11 [9832]~E(x98323,x98325)+P1(f317(f317(f319(f905(f905(x98321,x98322),f905(x98321,x98322))),f317(f317(f242(f905(x98321,x98322),f905(x98321,x98322)),f317(f317(f242(x98321,x98322),x98323),x98324)),f317(f317(f242(x98321,x98322),x98325),x98326))),f310(x98321,x98322,x98327,x98328)))+~P1(f317(f317(f319(f905(x98322,x98322)),f317(f317(f242(x98322,x98322),x98324),x98326)),x98328)) % 112.37/112.11 [9937]E(x99371,x99372)+~P1(f317(f317(f319(f905(f905(x99373,x99375),f905(x99373,x99375))),f317(f317(f242(f905(x99373,x99375),f905(x99373,x99375)),f317(f317(f242(x99373,x99375),x99371),x99376)),f317(f317(f242(x99373,x99375),x99372),x99377))),f310(x99373,x99375,x99374,x99378)))+P1(f317(f317(f319(f905(x99373,x99373)),f317(f317(f242(x99373,x99373),x99371),x99372)),x99374)) % 112.37/112.11 [9952]~P1(f317(f317(f319(f905(f905(x99521,x99525),f905(x99521,x99525))),f317(f317(f242(f905(x99521,x99525),f905(x99521,x99525)),f317(f317(f242(x99521,x99525),x99522),x99526)),f317(f317(f242(x99521,x99525),x99523),x99527))),f310(x99521,x99525,x99524,x99528)))+P1(f317(f317(f319(f905(x99521,x99521)),f317(f317(f242(x99521,x99521),x99522),x99523)),x99524))+P1(f317(f317(f319(f905(x99525,x99525)),f317(f317(f242(x99525,x99525),x99526),x99527)),x99528)) % 112.37/112.11 [9868]~P23(x98687,x98685,x98681,x98688,x98682,x98684)+~P1(f317(f29(x98685),x98686))+E(f317(f317(x98681,f317(x98682,x98683)),f317(x98684,f317(f317(f3(f906(x98685,a895)),x98686),f317(f317(f299(x98685),x98683),f178(f906(x98685,a895)))))),f317(x98684,f317(f317(f299(x98685),x98683),x98686))) % 112.37/112.11 [9347]~P1(f317(f317(f317(x93475,x93478),x93476),x93477))+~P1(f317(f317(f319(x93471),x93478),x93474))+P1(f317(f317(f317(f317(f36(x93471,f906(x93472,f906(x93473,a895))),x93474),x93475),x93476),x93477)) % 112.37/112.11 [9567]P1(f317(f317(f317(x95671,x95672),x95673),x95674))+~P1(f317(f317(f319(x95675),x95672),x95676))+~P1(f317(f317(f317(f317(f35(x95675,f906(x95677,f906(x95678,a895))),x95676),x95671),x95673),x95674)) % 112.37/112.11 [9772]~P21(x97723,x97722,x97724,x97728,x97721)+~P1(f317(f29(x97722),x97727))+E(f317(f317(x97721,f317(f317(f20(x97722,x97723,x97723),f317(f317(f10(x97723,f906(x97723,x97723),x97722),x97724),x97725)),x97726)),x97727),f317(f317(x97724,f317(f317(x97721,x97725),x97727)),f317(f317(x97721,x97726),x97727))) % 112.37/112.11 [10038]~E(f317(f300(x100382,x100384,x100386),x100388),x1003810)+~E(f317(f300(x100381,x100383,x100385),x100387),x100389)+E(f317(f300(f905(x100381,x100382),f905(x100383,x100384),f248(x100381,x100383,x100382,x100384,x100385,x100386)),f317(f317(f244(x100381,x100382),x100387),f317(f18(f906(x100382,a895),x100381),x100388))),f317(f317(f244(x100383,x100384),x100389),f317(f18(f906(x100384,a895),x100383),x1003810))) % 112.37/112.11 [4948]~P42(x49481,x49482)+~P49(x49481,x49482)+~P50(x49481,x49482)+P7(x49481,x49482) % 112.37/112.11 [4904]~P108(x49042)+~P13(x49042,x49041)+P13(x49042,f104(x49042,x49041))+E(x49041,f103(x49042)) % 112.37/112.11 [4905]~P108(x49052)+~P13(x49052,x49051)+P13(x49052,f690(x49051,x49052))+E(x49051,f103(x49052)) % 112.37/112.11 [5152]~P5(x51522)+E(f12(x51522,x51521),f32(x51522,x51521))+E(x51521,f178(f906(x51522,a895)))+~P1(f317(f29(x51522),x51521)) % 112.37/112.11 [5153]~P5(x51532)+E(f13(x51532,x51531),f33(x51532,x51531))+E(x51531,f178(f906(x51532,a895)))+~P1(f317(f29(x51532),x51531)) % 112.37/112.11 [5310]~P108(x53102)+~P13(x53102,x53101)+E(x53101,f103(x53102))+E(f317(f317(f141(x53102),f709(x53101,x53102)),f690(x53101,x53102)),x53101) % 112.37/112.11 [6133]~P99(x61332)+E(x61331,f178(f906(x61332,a895)))+P1(f317(f317(f224(x61332),f13(x61332,x61331)),f12(x61332,x61331)))+~P1(f317(f29(x61332),x61331)) % 112.37/112.11 [6144]~P39(x61442)+~P39(x61441)+E(x61441,x61442)+~E(f317(f300(a1,a899,a95),x61441),f317(f300(a1,a899,a95),x61442)) % 112.37/112.11 [9203]~P112(x92031)+~P1(f317(f317(f319(x92031),x92032),f100(x92031)))+P1(f317(f317(f225(x92031),f317(f317(f74(x92031),f317(f317(f74(x92031),f72(x92031)),x92032)),x92032)),f2(x92031)))+~P1(f317(f317(f225(x92031),x92032),f2(x92031))) % 112.37/112.11 [9449]~P112(x94491)+~P1(f317(f317(f319(x94491),x94492),f100(x94491)))+~P1(f317(f317(f225(x94491),f317(f317(f74(x94491),f317(f317(f74(x94491),f72(x94491)),x94492)),x94492)),f2(x94491)))+P1(f317(f317(f225(x94491),x94492),f2(x94491))) % 112.37/112.11 [4963]~P115(x49632)+~P146(x49632)+E(x49631,f2(a899))+E(f317(f317(f234(x49632),f2(x49632)),x49631),f2(x49632)) % 112.37/112.11 [4966]~P115(x49661)+~P146(x49661)+~E(x49662,f2(a899))+E(f317(f317(f234(x49661),f2(x49661)),x49662),f72(x49661)) % 112.37/112.11 [5138]~P142(x51382)+E(x51381,f72(x51382))+E(x51381,f317(f73(x51382),f72(x51382)))+~E(f317(f317(f75(x51382),x51381),x51381),f72(x51382)) % 112.37/112.11 [5387]~P90(x53872)+E(x53871,f2(x53872))+E(f76(x53872,x53871),f317(f73(x53872),f72(x53872)))+P1(f317(f317(f225(x53872),f2(x53872)),x53871)) % 112.37/112.11 [5629]~P90(x56292)+E(f76(x56292,x56291),f72(x56292))+E(x56291,f2(x56292))+~P1(f317(f317(f225(x56292),f2(x56292)),x56291)) % 112.37/112.11 [5638]E(x56381,x56382)+~E(f317(f94(a899),x56381),f317(f94(a899),x56382))+P1(f317(a183,f317(f94(a1),x56382)))+P1(f317(a183,f317(f94(a1),x56381))) % 112.37/112.11 [5689]~P92(x56891)+~E(x56892,f2(x56891))+E(f317(f317(f74(x56891),x56892),x56892),f2(x56891))+~P1(f317(f317(f319(x56891),x56892),f100(x56891))) % 112.37/112.11 [5728]E(x57281,f2(a1))+~E(f317(f317(f31(a1),x57282),x57281),f2(a1))+P1(f317(f317(f225(a1),x57281),x57282))+P1(f317(f317(f225(a1),x57282),x57281)) % 112.37/112.11 [5758]E(x57581,f2(a1))+~E(f317(f317(f31(a1),x57582),x57581),f2(a1))+P1(f317(f317(f224(a1),x57582),f2(a1)))+P1(f317(f317(f225(a1),x57582),x57581)) % 112.37/112.11 [5792]E(x57921,f2(a1))+~E(f317(f317(f31(a1),x57922),x57921),f2(a1))+P1(f317(f317(f224(a1),f2(a1)),x57922))+P1(f317(f317(f225(a1),x57921),x57922)) % 112.37/112.11 [5827]~P92(x58272)+E(x58271,f2(x58272))+~E(f317(f317(f74(x58272),x58271),x58271),f2(x58272))+~P1(f317(f317(f319(x58272),x58271),f100(x58272))) % 112.37/112.11 [5898]E(f317(f94(a899),x58981),f317(f94(a899),x58982))+~E(f317(f94(a1),x58982),f2(a1))+P1(f317(a183,f317(f94(a1),x58982)))+~P1(f317(a183,f317(f94(a1),x58981))) % 112.37/112.11 [5927]~E(f317(f94(a899),x59272),f317(f94(a899),x59271))+E(f317(f94(a1),x59271),f2(a1))+P1(f317(a183,f317(f94(a1),x59271)))+~P1(f317(a183,f317(f94(a1),x59272))) % 112.37/112.11 [5937]~P108(x59372)+E(x59371,f178(f906(x59372,a895)))+~P1(f317(f29(x59372),x59371))+P1(f317(f317(f319(x59372),f16(x59372,x59371)),x59371)) % 112.37/112.11 [5938]~P108(x59382)+E(x59381,f178(f906(x59382,a895)))+~P1(f317(f29(x59382),x59381))+P1(f317(f317(f319(x59382),f17(x59382,x59381)),x59381)) % 112.37/112.11 [6110]~P112(x61101)+~P94(x61101)+P1(f317(f317(f224(x61101),f2(x61101)),f317(f94(x61101),x61102)))+~P1(f317(f317(f224(a1),a77),x61102)) % 112.37/112.11 [6111]~P112(x61111)+~P94(x61111)+P1(f317(f317(f225(x61111),f2(x61111)),f317(f94(x61111),x61112)))+~P1(f317(f317(f225(a1),a77),x61112)) % 112.37/112.11 [6132]~P112(x61321)+~P94(x61321)+E(f317(f70(x61321),f317(f94(x61321),x61322)),f317(f94(x61321),x61322))+P1(f317(f317(f225(x61321),f317(f94(x61321),x61322)),f2(x61321))) % 112.37/112.11 [6168]E(x61681,x61682)+~E(f317(a95,x61681),f317(a95,x61682))+~P1(f317(f317(f224(a1),f2(a1)),x61682))+~P1(f317(f317(f224(a1),f2(a1)),x61681)) % 112.37/112.11 [6369]~P94(x63692)+~P112(x63692)+~P1(f317(f317(f224(x63692),f2(x63692)),f317(f94(x63692),x63691)))+P1(f317(f317(f224(a1),a77),x63691)) % 112.37/112.11 [6370]~P94(x63702)+~P112(x63702)+~P1(f317(f317(f225(x63702),f2(x63702)),f317(f94(x63702),x63701)))+P1(f317(f317(f225(a1),a77),x63701)) % 112.37/112.11 [6375]~P112(x63751)+~P94(x63751)+P1(f317(f317(f224(x63751),f317(f94(x63751),x63752)),f2(x63751)))+~P1(f317(f317(f224(a1),x63752),a77)) % 112.37/112.11 [6376]~P112(x63761)+~P94(x63761)+P1(f317(f317(f225(x63761),f317(f94(x63761),x63762)),f2(x63761)))+~P1(f317(f317(f225(a1),x63762),a77)) % 112.37/112.11 [6702]~P94(x67022)+~P112(x67022)+~P1(f317(f317(f224(x67022),f317(f94(x67022),x67021)),f2(x67022)))+P1(f317(f317(f224(a1),x67021),a77)) % 112.37/112.11 [6703]~P94(x67032)+~P112(x67032)+~P1(f317(f317(f225(x67032),f317(f94(x67032),x67031)),f2(x67032)))+P1(f317(f317(f225(a1),x67031),a77)) % 112.37/112.11 [6796]~P112(x67961)+~P94(x67961)+E(f317(f70(x67961),f317(f94(x67961),x67962)),f317(f73(x67961),f317(f94(x67961),x67962)))+~P1(f317(f317(f225(x67961),f317(f94(x67961),x67962)),f2(x67961))) % 112.37/112.11 [6815]E(f317(f94(a899),x68151),f317(f94(a899),x68152))+~E(f317(f94(a1),x68152),f2(a1))+~P1(f317(f317(f224(a1),f317(f94(a1),x68151)),f2(a1)))+~P1(f317(a183,f317(f94(a1),x68151))) % 112.37/112.11 [7703]~P108(x77032)+E(x77031,f178(f906(x77032,a895)))+~P1(f317(f29(x77032),x77031))+P1(f317(f317(f224(x77032),f15(x77032,f228(x77032),x77031)),f14(x77032,f223(x77032),x77031))) % 112.37/112.11 [8023]~P39(x80232)+~P6(x80231)+P1(f317(f317(f319(a1),x80231),x80232))+~P1(f317(f317(f319(a899),f317(a95,x80231)),f317(f300(a1,a899,a95),x80232))) % 112.37/112.11 [5933]~P141(x59332)+E(x59331,f2(a1))+E(f317(f73(x59332),f317(f93(x59332),f317(f73(a1),x59331))),f317(f93(x59332),x59331))+~P1(f317(f317(f225(a1),x59331),f2(a1))) % 112.37/112.11 [6012]~P92(x60121)+~P94(x60121)+~P27(x60121,f317(f94(x60121),x60122))+P27(x60121,f317(f94(x60121),f317(f317(f74(a1),x60122),x60122))) % 112.37/112.11 [6358]~P77(x63582)+E(x63581,f178(f906(x63582,a895)))+E(f17(x63582,f317(f300(x63582,x63582,f73(x63582)),x63581)),f317(f73(x63582),f16(x63582,x63581)))+~P1(f317(f29(x63582),x63581)) % 112.37/112.11 [6359]~P77(x63592)+E(x63591,f178(f906(x63592,a895)))+E(f16(x63592,f317(f300(x63592,x63592,f73(x63592)),x63591)),f317(f73(x63592),f17(x63592,x63591)))+~P1(f317(f29(x63592),x63591)) % 112.37/112.11 [6393]~P92(x63931)+~P94(x63931)+P27(x63931,f317(f94(x63931),x63932))+~P27(x63931,f317(f94(x63931),f317(f317(f74(a1),x63932),x63932))) % 112.37/112.11 [6487]E(x64871,f2(a1))+E(f317(a47,f46(f317(f73(a1),x64871),f317(f73(a1),x64872))),f42(x64871,x64872))+P1(f317(f317(f224(a1),f2(a1)),x64872))+~P1(f317(f317(f224(a1),f2(a1)),x64871)) % 112.37/112.11 [8806]~P39(x88062)+~P39(x88061)+P1(f317(f317(f225(f906(a899,a895)),f317(f300(a1,a899,a95),x88061)),f317(f300(a1,a899,a95),x88062)))+~P1(f317(f317(f225(f906(a1,a895)),x88061),x88062)) % 112.37/112.11 [9037]~E(f711(x90372,x90371),f712(x90372,x90371))+~P1(f317(f127(x90371),f713(x90372,x90371)))+~P1(f317(f127(f900(x90371)),x90372))+P1(f317(f127(x90371),f317(f132(f900(x90371),f900(x90371),f124(x90371),f103(x90371)),x90372))) % 112.37/112.11 [9123]~P39(x91232)+~P39(x91231)+~P1(f317(f317(f224(f906(a899,a895)),f317(f300(a1,a899,a95),x91231)),f317(f300(a1,a899,a95),x91232)))+P1(f317(f317(f224(f906(a1,a895)),x91231),x91232)) % 112.37/112.11 [9124]~P39(x91242)+~P39(x91241)+~P1(f317(f317(f225(f906(a899,a895)),f317(f300(a1,a899,a95),x91241)),f317(f300(a1,a899,a95),x91242)))+P1(f317(f317(f225(f906(a1,a895)),x91241),x91242)) % 112.37/112.11 [9130]~E(f711(x91302,x91301),f712(x91302,x91301))+~P1(f317(f127(f900(x91301)),x91302))+P1(f317(f127(x91301),f317(f132(f900(x91301),f900(x91301),f124(x91301),f103(x91301)),x91302)))+P1(f317(f317(f319(f900(x91301)),f713(x91302,x91301)),f317(f162(f900(x91301)),x91302))) % 112.37/112.11 [9171]~P1(f317(f127(x91711),f713(x91712,x91711)))+~P1(f317(f127(f900(x91711)),x91712))+P1(f317(f127(x91711),f317(f132(f900(x91711),f900(x91711),f124(x91711),f103(x91711)),x91712)))+P1(f317(f317(f319(f900(x91711)),f712(x91712,x91711)),f317(f162(f900(x91711)),x91712))) % 112.37/112.11 [9172]~P1(f317(f127(x91721),f713(x91722,x91721)))+~P1(f317(f127(f900(x91721)),x91722))+P1(f317(f127(x91721),f317(f132(f900(x91721),f900(x91721),f124(x91721),f103(x91721)),x91722)))+P1(f317(f317(f319(f900(x91721)),f711(x91722,x91721)),f317(f162(f900(x91721)),x91722))) % 112.37/112.11 [9249]~P1(f317(f127(f900(x92491)),x92492))+P1(f317(f127(x92491),f317(f132(f900(x92491),f900(x92491),f124(x92491),f103(x92491)),x92492)))+P1(f317(f317(f319(f900(x92491)),f712(x92492,x92491)),f317(f162(f900(x92491)),x92492)))+P1(f317(f317(f319(f900(x92491)),f713(x92492,x92491)),f317(f162(f900(x92491)),x92492))) % 112.37/112.11 [9250]~P1(f317(f127(f900(x92501)),x92502))+P1(f317(f127(x92501),f317(f132(f900(x92501),f900(x92501),f124(x92501),f103(x92501)),x92502)))+P1(f317(f317(f319(f900(x92501)),f711(x92502,x92501)),f317(f162(f900(x92501)),x92502)))+P1(f317(f317(f319(f900(x92501)),f713(x92502,x92501)),f317(f162(f900(x92501)),x92502))) % 112.37/112.11 [9264]~E(f317(f317(f92(f906(x92641,a895)),f317(f162(x92641),f712(x92642,x92641))),f317(f162(x92641),f711(x92642,x92641))),f178(f906(x92641,a895)))+~P1(f317(f127(x92641),f713(x92642,x92641)))+~P1(f317(f127(f900(x92641)),x92642))+P1(f317(f127(x92641),f317(f132(f900(x92641),f900(x92641),f124(x92641),f103(x92641)),x92642))) % 112.37/112.11 [9327]~E(f317(f317(f92(f906(x93271,a895)),f317(f162(x93271),f712(x93272,x93271))),f317(f162(x93271),f711(x93272,x93271))),f178(f906(x93271,a895)))+~P1(f317(f127(f900(x93271)),x93272))+P1(f317(f127(x93271),f317(f132(f900(x93271),f900(x93271),f124(x93271),f103(x93271)),x93272)))+P1(f317(f317(f319(f900(x93271)),f713(x93272,x93271)),f317(f162(f900(x93271)),x93272))) % 112.37/112.11 [9615]E(x96151,f2(a1))+E(x96152,f2(a1))+E(f317(f317(f80(a1,f905(a1,a1)),f317(f317(a207,x96152),x96151)),f317(f317(f20(a1,a1,f905(a1,a1)),f317(f317(f10(a1,f906(a1,f905(a1,a1)),a1),f242(a1,a1)),f317(f31(a1),x96152))),f317(f31(a1),x96151))),f205(x96152,x96151))+P1(f317(f317(f225(a1),x96151),f2(a1))) % 112.37/112.11 [8349]~P94(x83492)+~P112(x83492)+~P1(f317(f317(f224(x83492),f317(f94(x83492),x83491)),f72(x83492)))+P1(f317(f317(f224(a1),x83491),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))) % 112.37/112.11 [8350]~P94(x83502)+~P112(x83502)+~P1(f317(f317(f225(x83502),f317(f94(x83502),x83501)),f72(x83502)))+P1(f317(f317(f225(a1),x83501),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))) % 112.37/112.11 [8622]~P112(x86221)+~P94(x86221)+P1(f317(f317(f224(x86221),f317(f94(x86221),x86222)),f72(x86221)))+~P1(f317(f317(f224(a1),x86222),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))) % 112.37/112.11 [8623]~P112(x86231)+~P94(x86231)+P1(f317(f317(f225(x86231),f317(f94(x86231),x86232)),f72(x86231)))+~P1(f317(f317(f225(a1),x86232),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))) % 112.37/112.11 [8834]~P94(x88342)+~P112(x88342)+~P1(f317(f317(f224(x88342),f72(x88342)),f317(f94(x88342),x88341)))+P1(f317(f317(f224(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),x88341)) % 112.37/112.11 [8835]~P94(x88352)+~P112(x88352)+~P1(f317(f317(f225(x88352),f72(x88352)),f317(f94(x88352),x88351)))+P1(f317(f317(f225(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),x88351)) % 112.37/112.11 [9209]~P112(x92091)+~P94(x92091)+P1(f317(f317(f224(x92091),f72(x92091)),f317(f94(x92091),x92092)))+~P1(f317(f317(f224(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),x92092)) % 112.37/112.11 [9210]~P112(x92101)+~P94(x92101)+P1(f317(f317(f225(x92101),f72(x92101)),f317(f94(x92101),x92102)))+~P1(f317(f317(f225(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),x92102)) % 112.37/112.11 [9745]~P142(x97452)+E(x97451,f72(x97452))+E(x97451,f317(f73(x97452),f72(x97452)))+~E(f317(f317(f234(x97452),x97451),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f72(x97452)) % 112.37/112.11 [10014]~P63(x100141)+~P94(x100141)+~P1(f317(f317(f225(x100141),f2(x100141)),x100142))+P1(f317(f317(f225(x100141),f2(x100141)),f317(f317(f281(x100141),x100142),f317(f94(x100141),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))) % 112.37/112.11 [10067]~P63(x100671)+~P94(x100671)+P1(f317(f317(f225(x100671),f2(x100671)),x100672))+~P1(f317(f317(f225(x100671),f2(x100671)),f317(f317(f281(x100671),x100672),f317(f94(x100671),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))) % 112.37/112.11 [10361]~P141(x103612)+E(x103611,f2(a1))+P1(f317(f317(f225(a1),x103611),f2(a1)))+E(f317(f317(f247(a1,a1,x103612),f317(f317(f9(a1,f906(a1,f906(x103612,x103612)),f906(a1,x103612)),f317(f317(f10(f906(f906(x103612,x103612),x103612),f906(f906(a1,f906(x103612,x103612)),f906(a1,x103612)),a1),f10(f906(x103612,x103612),x103612,a1)),f317(f317(f10(x103612,f906(f906(x103612,x103612),x103612),a1),f80(x103612,x103612)),f93(x103612)))),f317(f317(f9(a1,f906(x103612,x103612),f906(x103612,x103612)),f317(f317(f10(f906(x103612,f906(x103612,x103612)),f906(f906(x103612,x103612),f906(x103612,x103612)),a1),f20(x103612,x103612,x103612)),f317(f317(f9(a1,f906(x103612,x103612),f906(x103612,f906(x103612,x103612))),f317(f317(f10(f906(x103612,f906(x103612,x103612)),f906(f906(x103612,x103612),f906(x103612,f906(x103612,x103612))),a1),f10(x103612,f906(x103612,x103612),x103612)),f317(f317(f10(a895,f906(x103612,f906(x103612,x103612)),a1),f86(x103612)),f317(f317(f9(a1,a1,a895),a314),f2(a1))))),f317(f317(f20(x103612,x103612,x103612),f74(x103612)),f7(x103612))))),f317(f317(f9(x103612,x103612,x103612),f317(f317(f10(x103612,f906(x103612,x103612),x103612),f74(x103612)),f317(f317(f20(x103612,x103612,x103612),f74(x103612)),f7(x103612)))),f72(x103612))))),f42(x103611,f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f93(x103612),x103611)) % 112.37/112.11 [5396]~P37(x53961,x53963)+~P51(x53961,x53963)+~P52(x53961,x53962,x53963)+P8(x53961,x53962,x53963) % 112.37/112.11 [4932]~P92(x49323)+~P94(x49323)+E(x49321,x49322)+~E(f317(f94(x49323),x49321),f317(f94(x49323),x49322)) % 112.37/112.11 [5406]~P49(x54061,x54062)+~P50(x54061,x54062)+P15(x54061,x54062)+~P1(f317(f317(x54062,x54063),x54063)) % 112.37/112.11 [5913]P15(x59132,x59131)+E(f317(x59131,f787(x59131)),f317(x59131,f789(x59131)))+P1(f317(f317(x59131,f787(x59131)),f789(x59131)))+~P1(f317(f317(x59131,x59133),x59133)) % 112.37/112.11 [6120]~P1(f317(x61201,x61202))+~P1(f317(x61201,x61203))+~P1(f317(f317(f224(a899),x61203),f790(x61202,x61201)))+P1(f317(x61201,f2(a899))) % 112.37/112.11 [6187]P15(x61871,x61872)+P1(f317(f317(x61872,f787(x61872)),f787(x61872)))+P1(f317(f317(x61872,f787(x61872)),f789(x61872)))+~P1(f317(f317(x61872,x61873),x61873)) % 112.37/112.11 [6188]P15(x61881,x61882)+P1(f317(f317(x61882,f787(x61882)),f789(x61882)))+P1(f317(f317(x61882,f789(x61882)),f789(x61882)))+~P1(f317(f317(x61882,x61883),x61883)) % 112.37/112.11 [6552]P148(x65522,x65523,x65521)+E(x65521,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f838(x65521,x65523,x65522)))+P1(f317(f317(f225(a1),x65521),f2(a1))) % 112.37/112.11 [6553]P147(x65532,x65533,x65531)+E(x65531,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f846(x65531,x65533,x65532)))+P1(f317(f317(f225(a1),x65531),f2(a1))) % 112.37/112.11 [6682]P147(x66821,x66822,x66823)+~P1(f317(x66821,x66822))+P1(f317(f317(f224(a1),f2(a1)),f846(x66823,x66822,x66821)))+P1(f317(f317(f225(a1),x66823),f2(a1))) % 112.37/112.11 [6708]P148(x67081,x67082,x67083)+P1(f317(f317(f224(a1),f2(a1)),f838(x67083,x67082,x67081)))+~P1(f317(x67081,f2(a1)))+P1(f317(f317(f225(a1),x67083),f2(a1))) % 112.37/112.11 [6740]P148(x67402,x67403,x67401)+E(x67401,f2(a1))+~P1(f317(x67402,f839(x67401,x67403,x67402)))+P1(f317(f317(f225(a1),x67401),f2(a1))) % 112.37/112.11 [6741]P147(x67412,x67413,x67411)+E(x67411,f2(a1))+~P1(f317(x67412,f846(x67411,x67413,x67412)))+P1(f317(f317(f225(a1),x67411),f2(a1))) % 112.37/112.11 [6843]~P108(x68431)+~P5(x68431)+~P1(f317(f317(f225(x68431),x68432),f32(x68431,x68433)))+P1(f317(f317(f225(x68431),x68432),f407(x68433,x68432,x68431))) % 112.37/112.11 [6853]P147(x68531,x68532,x68533)+~P1(f317(x68531,x68532))+~P1(f317(x68531,f846(x68533,x68532,x68531)))+P1(f317(f317(f225(a1),x68533),f2(a1))) % 112.37/112.11 [6885]P148(x68851,x68852,x68853)+~P1(f317(x68851,f839(x68853,x68852,x68851)))+~P1(f317(x68851,f2(a1)))+P1(f317(f317(f225(a1),x68853),f2(a1))) % 112.37/112.11 [7138]P148(x71382,x71383,x71381)+E(x71381,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f838(x71381,x71383,x71382)))+P1(f317(f317(f225(a1),x71381),f837(x71381,x71383,x71382))) % 112.37/112.11 [7139]P147(x71392,x71393,x71391)+E(x71391,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f846(x71391,x71393,x71392)))+P1(f317(f317(f225(a1),x71391),f845(x71391,x71393,x71392))) % 112.37/112.11 [7259]P147(x72591,x72592,x72593)+~P1(f317(x72591,x72592))+P1(f317(f317(f224(a1),f2(a1)),f846(x72593,x72592,x72591)))+P1(f317(f317(f225(a1),x72593),f845(x72593,x72592,x72591))) % 112.37/112.11 [7280]P148(x72801,x72802,x72803)+P1(f317(f317(f224(a1),f2(a1)),f838(x72803,x72802,x72801)))+P1(f317(f317(f225(a1),x72803),f837(x72803,x72802,x72801)))+~P1(f317(x72801,f2(a1))) % 112.37/112.11 [7311]P148(x73112,x73113,x73111)+E(x73111,f2(a1))+~P1(f317(x73112,f839(x73111,x73113,x73112)))+P1(f317(f317(f225(a1),x73111),f837(x73111,x73113,x73112))) % 112.37/112.11 [7312]P147(x73122,x73123,x73121)+E(x73121,f2(a1))+~P1(f317(x73122,f846(x73121,x73123,x73122)))+P1(f317(f317(f225(a1),x73121),f845(x73121,x73123,x73122))) % 112.37/112.11 [7356]P148(x73562,x73563,x73561)+E(x73561,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f838(x73561,x73563,x73562)))+~P1(f317(x73562,f843(x73561,x73563,x73562))) % 112.37/112.11 [7357]P147(x73572,x73573,x73571)+E(x73571,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f846(x73571,x73573,x73572)))+~P1(f317(x73572,f845(x73571,x73573,x73572))) % 112.37/112.11 [7454]P147(x74541,x74542,x74543)+~P1(f317(x74541,x74542))+~P1(f317(x74541,f846(x74543,x74542,x74541)))+P1(f317(f317(f225(a1),x74543),f845(x74543,x74542,x74541))) % 112.37/112.11 [7469]P148(x74691,x74692,x74693)+~P1(f317(x74691,f839(x74693,x74692,x74691)))+P1(f317(f317(f225(a1),x74693),f837(x74693,x74692,x74691)))+~P1(f317(x74691,f2(a1))) % 112.37/112.11 [7472]P147(x74721,x74722,x74723)+~P1(f317(x74721,x74722))+P1(f317(f317(f224(a1),f2(a1)),f846(x74723,x74722,x74721)))+~P1(f317(x74721,f845(x74723,x74722,x74721))) % 112.37/112.11 [7489]P148(x74891,x74892,x74893)+P1(f317(f317(f224(a1),f2(a1)),f838(x74893,x74892,x74891)))+~P1(f317(x74891,f843(x74893,x74892,x74891)))+~P1(f317(x74891,f2(a1))) % 112.37/112.11 [7512]P148(x75122,x75123,x75121)+E(x75121,f2(a1))+~P1(f317(x75122,f839(x75121,x75123,x75122)))+~P1(f317(x75122,f843(x75121,x75123,x75122))) % 112.37/112.11 [7513]P147(x75132,x75133,x75131)+E(x75131,f2(a1))+~P1(f317(x75132,f846(x75131,x75133,x75132)))+~P1(f317(x75132,f845(x75131,x75133,x75132))) % 112.37/112.11 [7597]P147(x75971,x75972,x75973)+~P1(f317(x75971,x75972))+~P1(f317(x75971,f846(x75973,x75972,x75971)))+~P1(f317(x75971,f845(x75973,x75972,x75971))) % 112.37/112.11 [7615]P148(x76151,x76152,x76153)+~P1(f317(x76151,f839(x76153,x76152,x76151)))+~P1(f317(x76151,f843(x76153,x76152,x76151)))+~P1(f317(x76151,f2(a1))) % 112.37/112.11 [7662]P148(x76622,x76623,x76621)+E(x76621,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f838(x76621,x76623,x76622)))+P1(f317(f317(f224(a1),f837(x76621,x76623,x76622)),f2(a1))) % 112.37/112.11 [7663]P147(x76632,x76633,x76631)+E(x76631,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f846(x76631,x76633,x76632)))+P1(f317(f317(f224(a1),f845(x76631,x76633,x76632)),f2(a1))) % 112.37/112.11 [7664]~P88(x76641)+~P1(f317(f317(f224(x76641),x76643),f2(x76641)))+~P1(f317(f317(f224(x76641),x76642),f2(x76641)))+P1(f317(f317(f224(x76641),f317(f317(f74(x76641),x76642),x76643)),f2(x76641))) % 112.37/112.11 [7665]~P141(x76651)+~P1(f317(f317(f319(x76651),x76653),f100(x76651)))+~P1(f317(f317(f319(x76651),x76652),f100(x76651)))+P1(f317(f317(f319(x76651),f317(f317(f3(x76651),x76652),x76653)),f100(x76651))) % 112.37/112.11 [7666]~P141(x76661)+~P1(f317(f317(f319(x76661),x76663),f100(x76661)))+~P1(f317(f317(f319(x76661),x76662),f100(x76661)))+P1(f317(f317(f319(x76661),f317(f317(f74(x76661),x76662),x76663)),f100(x76661))) % 112.37/112.11 [7667]~P145(x76671)+~P1(f317(f317(f319(x76671),x76673),f176(x76671)))+~P1(f317(f317(f319(x76671),x76672),f176(x76671)))+P1(f317(f317(f319(x76671),f317(f317(f74(x76671),x76672),x76673)),f176(x76671))) % 112.37/112.11 [7668]~P141(x76681)+~P1(f317(f317(f319(x76681),x76683),f100(x76681)))+~P1(f317(f317(f319(x76681),x76682),f100(x76681)))+P1(f317(f317(f319(x76681),f317(f317(f75(x76681),x76682),x76683)),f100(x76681))) % 112.37/112.11 [7669]~P145(x76691)+~P1(f317(f317(f319(x76691),x76693),f176(x76691)))+~P1(f317(f317(f319(x76691),x76692),f176(x76691)))+P1(f317(f317(f319(x76691),f317(f317(f75(x76691),x76692),x76693)),f176(x76691))) % 112.37/112.11 [7670]~P88(x76701)+~P1(f317(f317(f224(x76701),x76703),f2(x76701)))+~P1(f317(f317(f225(x76701),x76702),f2(x76701)))+P1(f317(f317(f225(x76701),f317(f317(f74(x76701),x76702),x76703)),f2(x76701))) % 112.37/112.11 [7671]~P88(x76711)+~P1(f317(f317(f224(x76711),x76712),f2(x76711)))+~P1(f317(f317(f225(x76711),x76713),f2(x76711)))+P1(f317(f317(f225(x76711),f317(f317(f74(x76711),x76712),x76713)),f2(x76711))) % 112.37/112.11 [7672]~P88(x76721)+~P1(f317(f317(f225(x76721),x76723),f2(x76721)))+~P1(f317(f317(f225(x76721),x76722),f2(x76721)))+P1(f317(f317(f225(x76721),f317(f317(f74(x76721),x76722),x76723)),f2(x76721))) % 112.37/112.11 [7699]P148(x76993,x76992,x76991)+E(x76991,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x76991),f839(x76991,x76992,x76993))),f838(x76991,x76992,x76993)),x76992)+P1(f317(f317(f225(a1),x76991),f2(a1))) % 112.37/112.11 [7700]P147(x77003,x77002,x77001)+E(x77001,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x77001),f847(x77001,x77002,x77003))),f846(x77001,x77002,x77003)),x77002)+P1(f317(f317(f225(a1),x77001),f2(a1))) % 112.37/112.11 [7783]P147(x77831,x77832,x77833)+~P1(f317(x77831,x77832))+P1(f317(f317(f224(a1),f2(a1)),f846(x77833,x77832,x77831)))+P1(f317(f317(f224(a1),f845(x77833,x77832,x77831)),f2(a1))) % 112.37/112.11 [7814]P148(x78141,x78142,x78143)+P1(f317(f317(f224(a1),f2(a1)),f838(x78143,x78142,x78141)))+~P1(f317(x78141,f2(a1)))+P1(f317(f317(f224(a1),f837(x78143,x78142,x78141)),f2(a1))) % 112.37/112.11 [7823]P147(x78233,x78232,x78231)+~P1(f317(x78233,x78232))+E(f317(f317(f74(a1),f317(f317(f75(a1),x78231),f847(x78231,x78232,x78233))),f846(x78231,x78232,x78233)),x78232)+P1(f317(f317(f225(a1),x78231),f2(a1))) % 112.37/112.11 [7829]P148(x78292,x78293,x78291)+E(x78291,f2(a1))+~P1(f317(x78292,f839(x78291,x78293,x78292)))+P1(f317(f317(f224(a1),f837(x78291,x78293,x78292)),f2(a1))) % 112.37/112.11 [7830]P147(x78302,x78303,x78301)+E(x78301,f2(a1))+~P1(f317(x78302,f846(x78301,x78303,x78302)))+P1(f317(f317(f224(a1),f845(x78301,x78303,x78302)),f2(a1))) % 112.37/112.11 [7835]P148(x78353,x78352,x78351)+E(f317(f317(f74(a1),f317(f317(f75(a1),x78351),f839(x78351,x78352,x78353))),f838(x78351,x78352,x78353)),x78352)+~P1(f317(x78353,f2(a1)))+P1(f317(f317(f225(a1),x78351),f2(a1))) % 112.37/112.11 [7892]P147(x78921,x78922,x78923)+~P1(f317(x78921,x78922))+~P1(f317(x78921,f846(x78923,x78922,x78921)))+P1(f317(f317(f224(a1),f845(x78923,x78922,x78921)),f2(a1))) % 112.37/112.11 [7896]P148(x78961,x78962,x78963)+~P1(f317(x78961,f839(x78963,x78962,x78961)))+~P1(f317(x78961,f2(a1)))+P1(f317(f317(f224(a1),f837(x78963,x78962,x78961)),f2(a1))) % 112.37/112.11 [7964]~P127(x79641)+~P1(f317(f317(f224(x79641),f317(f317(f75(x79641),x79643),x79642)),f2(x79641)))+P1(f317(f317(f224(x79641),x79642),f2(x79641)))+P1(f317(f317(f224(x79641),x79643),f2(x79641))) % 112.37/112.11 [7965]~P63(x79651)+~P1(f317(f317(f224(x79651),f317(f317(f281(x79651),x79653),x79652)),f2(x79651)))+P1(f317(f317(f224(x79651),x79652),f2(x79651)))+P1(f317(f317(f224(x79651),x79653),f2(x79651))) % 112.37/112.11 [7966]~P63(x79661)+~P1(f317(f317(f225(x79661),f317(f317(f281(x79661),x79663),x79662)),f2(x79661)))+P1(f317(f317(f225(x79661),x79662),f2(x79661)))+P1(f317(f317(f225(x79661),x79663),f2(x79661))) % 112.37/112.11 [8079]P148(x80793,x80792,x80791)+E(x80791,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x80791),f839(x80791,x80792,x80793))),f838(x80791,x80792,x80793)),x80792)+P1(f317(f317(f225(a1),x80791),f837(x80791,x80792,x80793))) % 112.37/112.11 [8080]P147(x80803,x80802,x80801)+E(x80801,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x80801),f847(x80801,x80802,x80803))),f846(x80801,x80802,x80803)),x80802)+P1(f317(f317(f225(a1),x80801),f845(x80801,x80802,x80803))) % 112.37/112.11 [8092]P148(x80923,x80922,x80921)+E(x80921,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x80921),f843(x80921,x80922,x80923))),f837(x80921,x80922,x80923)),x80922)+P1(f317(f317(f224(a1),f2(a1)),f838(x80921,x80922,x80923))) % 112.37/112.11 [8093]P147(x80933,x80932,x80931)+E(x80931,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x80931),f848(x80931,x80932,x80933))),f845(x80931,x80932,x80933)),x80932)+P1(f317(f317(f224(a1),f2(a1)),f846(x80931,x80932,x80933))) % 112.37/112.11 [8135]P147(x81353,x81352,x81351)+~P1(f317(x81353,x81352))+E(f317(f317(f74(a1),f317(f317(f75(a1),x81351),f847(x81351,x81352,x81353))),f846(x81351,x81352,x81353)),x81352)+P1(f317(f317(f225(a1),x81351),f845(x81351,x81352,x81353))) % 112.37/112.11 [8144]P148(x81443,x81442,x81441)+E(f317(f317(f74(a1),f317(f317(f75(a1),x81441),f839(x81441,x81442,x81443))),f838(x81441,x81442,x81443)),x81442)+P1(f317(f317(f225(a1),x81441),f837(x81441,x81442,x81443)))+~P1(f317(x81443,f2(a1))) % 112.37/112.11 [8150]P147(x81503,x81502,x81501)+~P1(f317(x81503,x81502))+E(f317(f317(f74(a1),f317(f317(f75(a1),x81501),f848(x81501,x81502,x81503))),f845(x81501,x81502,x81503)),x81502)+P1(f317(f317(f224(a1),f2(a1)),f846(x81501,x81502,x81503))) % 112.37/112.11 [8156]P148(x81563,x81562,x81561)+E(f317(f317(f74(a1),f317(f317(f75(a1),x81561),f843(x81561,x81562,x81563))),f837(x81561,x81562,x81563)),x81562)+P1(f317(f317(f224(a1),f2(a1)),f838(x81561,x81562,x81563)))+~P1(f317(x81563,f2(a1))) % 112.37/112.11 [8167]P148(x81673,x81672,x81671)+E(x81671,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x81671),f839(x81671,x81672,x81673))),f838(x81671,x81672,x81673)),x81672)+~P1(f317(x81673,f843(x81671,x81672,x81673))) % 112.37/112.11 [8168]P147(x81683,x81682,x81681)+E(x81681,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x81681),f847(x81681,x81682,x81683))),f846(x81681,x81682,x81683)),x81682)+~P1(f317(x81683,f845(x81681,x81682,x81683))) % 112.37/112.11 [8169]P148(x81693,x81692,x81691)+E(x81691,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x81691),f843(x81691,x81692,x81693))),f837(x81691,x81692,x81693)),x81692)+~P1(f317(x81693,f839(x81691,x81692,x81693))) % 112.37/112.11 [8170]P147(x81703,x81702,x81701)+E(x81701,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x81701),f848(x81701,x81702,x81703))),f845(x81701,x81702,x81703)),x81702)+~P1(f317(x81703,f846(x81701,x81702,x81703))) % 112.37/112.11 [8229]P147(x82293,x82292,x82291)+~P1(f317(x82293,x82292))+E(f317(f317(f74(a1),f317(f317(f75(a1),x82291),f847(x82291,x82292,x82293))),f846(x82291,x82292,x82293)),x82292)+~P1(f317(x82293,f845(x82291,x82292,x82293))) % 112.37/112.11 [8230]P147(x82303,x82302,x82301)+~P1(f317(x82303,x82302))+E(f317(f317(f74(a1),f317(f317(f75(a1),x82301),f848(x82301,x82302,x82303))),f845(x82301,x82302,x82303)),x82302)+~P1(f317(x82303,f846(x82301,x82302,x82303))) % 112.37/112.11 [8243]P148(x82433,x82432,x82431)+E(f317(f317(f74(a1),f317(f317(f75(a1),x82431),f839(x82431,x82432,x82433))),f838(x82431,x82432,x82433)),x82432)+~P1(f317(x82433,f843(x82431,x82432,x82433)))+~P1(f317(x82433,f2(a1))) % 112.37/112.11 [8244]P148(x82443,x82442,x82441)+E(f317(f317(f74(a1),f317(f317(f75(a1),x82441),f843(x82441,x82442,x82443))),f837(x82441,x82442,x82443)),x82442)+~P1(f317(x82443,f839(x82441,x82442,x82443)))+~P1(f317(x82443,f2(a1))) % 112.37/112.11 [8342]P148(x83423,x83422,x83421)+E(x83421,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x83421),f839(x83421,x83422,x83423))),f838(x83421,x83422,x83423)),x83422)+P1(f317(f317(f224(a1),f837(x83421,x83422,x83423)),f2(a1))) % 112.37/112.11 [8343]P147(x83433,x83432,x83431)+E(x83431,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x83431),f847(x83431,x83432,x83433))),f846(x83431,x83432,x83433)),x83432)+P1(f317(f317(f224(a1),f845(x83431,x83432,x83433)),f2(a1))) % 112.37/112.11 [8383]P147(x83833,x83832,x83831)+~P1(f317(x83833,x83832))+E(f317(f317(f74(a1),f317(f317(f75(a1),x83831),f847(x83831,x83832,x83833))),f846(x83831,x83832,x83833)),x83832)+P1(f317(f317(f224(a1),f845(x83831,x83832,x83833)),f2(a1))) % 112.37/112.11 [8388]P148(x83883,x83882,x83881)+E(f317(f317(f74(a1),f317(f317(f75(a1),x83881),f839(x83881,x83882,x83883))),f838(x83881,x83882,x83883)),x83882)+~P1(f317(x83883,f2(a1)))+P1(f317(f317(f224(a1),f837(x83881,x83882,x83883)),f2(a1))) % 112.37/112.11 [8524]P148(x85243,x85242,x85241)+E(x85241,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x85241),f843(x85241,x85242,x85243))),f837(x85241,x85242,x85243)),x85242)+E(f317(f317(f74(a1),f317(f317(f75(a1),x85241),f839(x85241,x85242,x85243))),f838(x85241,x85242,x85243)),x85242) % 112.37/112.11 [8525]P147(x85253,x85252,x85251)+E(x85251,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x85251),f848(x85251,x85252,x85253))),f845(x85251,x85252,x85253)),x85252)+E(f317(f317(f74(a1),f317(f317(f75(a1),x85251),f847(x85251,x85252,x85253))),f846(x85251,x85252,x85253)),x85252) % 112.37/112.11 [8545]P147(x85453,x85452,x85451)+~P1(f317(x85453,x85452))+E(f317(f317(f74(a1),f317(f317(f75(a1),x85451),f848(x85451,x85452,x85453))),f845(x85451,x85452,x85453)),x85452)+E(f317(f317(f74(a1),f317(f317(f75(a1),x85451),f847(x85451,x85452,x85453))),f846(x85451,x85452,x85453)),x85452) % 112.37/112.11 [8556]P148(x85563,x85562,x85561)+E(f317(f317(f74(a1),f317(f317(f75(a1),x85561),f843(x85561,x85562,x85563))),f837(x85561,x85562,x85563)),x85562)+E(f317(f317(f74(a1),f317(f317(f75(a1),x85561),f839(x85561,x85562,x85563))),f838(x85561,x85562,x85563)),x85562)+~P1(f317(x85563,f2(a1))) % 112.37/112.11 [9217]~P127(x92171)+~E(x92173,f2(x92171))+~E(x92172,f2(x92171))+P1(f317(f317(f224(x92171),f317(f317(f74(x92171),f317(f317(f75(x92171),x92172),x92172)),f317(f317(f75(x92171),x92173),x92173))),f2(x92171))) % 112.37/112.11 [10302]~P112(x103021)+~E(x103023,f2(x103021))+~E(x103022,f2(x103021))+P1(f317(f317(f224(x103021),f317(f317(f74(x103021),f317(f317(f234(x103021),x103022),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x103021),x103023),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f2(x103021))) % 112.37/112.11 [4880]~E(x48803,x48801)+~P123(x48802)+E(x48801,f2(x48802))+E(f317(f317(f281(x48802),x48803),x48801),f72(x48802)) % 112.37/112.11 [4933]~P100(x49331)+~E(x49333,f178(x49331))+~E(x49332,f178(x49331))+E(f317(f317(f91(x49331),x49332),x49333),f178(x49331)) % 112.37/112.11 [4934]~P102(x49341)+~E(x49343,f232(x49341))+~E(x49342,f232(x49341))+E(f317(f317(f92(x49341),x49342),x49343),f232(x49341)) % 112.37/112.11 [5031]~P123(x50313)+E(x50311,x50312)+E(x50312,f2(x50313))+~E(f317(f317(f281(x50313),x50311),x50312),f72(x50313)) % 112.37/112.11 [5049]~P132(x50492)+E(x50491,f2(x50492))+E(x50493,f2(x50492))+~E(f317(f317(f75(x50492),x50493),x50491),f2(x50492)) % 112.37/112.11 [5050]~P140(x50502)+E(x50501,f2(x50502))+E(x50503,f2(x50502))+~E(f317(f317(f75(x50502),x50503),x50501),f2(x50502)) % 112.37/112.11 [5425]~P121(x54253)+E(x54251,x54252)+E(x54251,f317(f73(x54253),x54252))+~E(f317(f317(f75(x54253),x54251),x54251),f317(f317(f75(x54253),x54252),x54252)) % 112.37/112.11 [5464]~P96(x54641)+E(f317(f73(x54641),x54642),x54643)+~E(f317(f317(f91(x54641),x54642),x54643),f232(x54641))+~E(f317(f317(f92(x54641),x54642),x54643),f178(x54641)) % 112.37/112.11 [5545]~P112(x55453)+E(x55451,x55452)+P1(f317(f317(f225(x55453),x55452),x55451))+P1(f317(f317(f225(x55453),x55451),x55452)) % 112.37/112.11 [5546]~P108(x55463)+E(x55461,x55462)+P1(f317(f317(f225(x55463),x55462),x55461))+P1(f317(f317(f225(x55463),x55461),x55462)) % 112.37/112.11 [5547]~E(x55472,x55473)+~P108(x55471)+P1(f317(f317(f225(x55471),x55472),x55473))+P1(f317(f317(f224(x55471),x55472),x55473)) % 112.37/112.11 [5808]~P109(x58083)+E(x58081,x58082)+~P1(f317(f317(f224(x58083),x58082),x58081))+P1(f317(f317(f225(x58083),x58082),x58081)) % 112.37/112.11 [5810]~P108(x58103)+E(x58101,x58102)+~P1(f317(f317(f224(x58103),x58101),x58102))+P1(f317(f317(f225(x58103),x58101),x58102)) % 112.37/112.11 [5816]~P109(x58163)+E(x58161,x58162)+~P1(f317(f317(f224(x58163),x58161),x58162))+P1(f317(f317(f225(x58163),x58161),x58162)) % 112.37/112.11 [5930]P147(x59301,x59302,x59303)+~P1(f317(x59301,x59302))+P1(f317(f317(f225(a1),x59303),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x59303)) % 112.37/112.11 [5984]P148(x59841,x59842,x59843)+~P1(f317(x59841,f2(a1)))+P1(f317(f317(f225(a1),x59843),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x59843)) % 112.37/112.11 [5989]~P99(x59891)+E(f317(f317(f91(x59891),x59892),f13(x59891,x59893)),x59892)+~P1(f317(f29(x59891),x59893))+~P1(f317(f317(f319(x59891),x59892),x59893)) % 112.37/112.11 [5990]~P99(x59901)+E(f317(f317(f92(x59901),x59902),f12(x59901,x59903)),x59902)+~P1(f317(f29(x59901),x59903))+~P1(f317(f317(f319(x59901),x59902),x59903)) % 112.37/112.11 [6029]~P108(x60291)+E(f317(f317(f228(x60291),x60292),f17(x60291,x60293)),f17(x60291,x60293))+~P1(f317(f29(x60291),x60293))+~P1(f317(f317(f319(x60291),x60292),x60293)) % 112.37/112.11 [6030]~P108(x60301)+E(f317(f317(f223(x60301),x60302),f16(x60301,x60303)),f16(x60301,x60303))+~P1(f317(f29(x60301),x60303))+~P1(f317(f317(f319(x60301),x60302),x60303)) % 112.37/112.11 [6031]~P99(x60311)+E(f317(f317(f91(x60311),x60312),f12(x60311,x60313)),f12(x60311,x60313))+~P1(f317(f29(x60311),x60313))+~P1(f317(f317(f319(x60311),x60312),x60313)) % 112.37/112.11 [6032]~P99(x60321)+E(f317(f317(f92(x60321),x60322),f13(x60321,x60323)),f13(x60321,x60323))+~P1(f317(f29(x60321),x60323))+~P1(f317(f317(f319(x60321),x60322),x60323)) % 112.37/112.11 [6071]E(x60711,x60712)+~P109(x60713)+~P1(f317(f317(f224(x60713),x60712),x60711))+~P1(f317(f317(f224(x60713),x60711),x60712)) % 112.37/112.11 [6216]~P65(x62161)+P1(f317(f317(f225(x62161),x62163),x62162))+~P1(f317(f317(f224(x62161),x62163),x62162))+P1(f317(f317(f224(x62161),x62162),x62163)) % 112.37/112.11 [6244]~P108(x62441)+~P1(f317(f29(x62441),x62443))+P1(f317(f317(f224(x62441),x62442),f16(x62441,x62443)))+~P1(f317(f317(f319(x62441),x62442),x62443)) % 112.37/112.11 [6292]~P108(x62921)+E(f317(f317(f228(x62921),x62922),f14(x62921,f223(x62921),x62923)),x62922)+~P1(f317(f29(x62921),x62923))+~P1(f317(f317(f319(x62921),x62922),x62923)) % 112.37/112.11 [6293]~P108(x62931)+E(f317(f317(f223(x62931),x62932),f15(x62931,f228(x62931),x62933)),x62932)+~P1(f317(f29(x62931),x62933))+~P1(f317(f317(f319(x62931),x62932),x62933)) % 112.37/112.11 [6439]E(x64391,x64392)+~E(f317(f317(f3(a899),x64391),x64393),f317(f317(f3(a899),x64392),x64393))+~P1(f317(f317(f224(a899),x64393),x64391))+~P1(f317(f317(f224(a899),x64393),x64392)) % 112.37/112.11 [6466]~P108(x64661)+~P1(f317(f29(x64661),x64662))+~P1(f317(f317(f319(x64661),x64663),x64662))+P1(f317(f317(f224(x64661),f17(x64661,x64662)),x64663)) % 112.37/112.11 [6531]P148(x65312,x65313,x65311)+E(x65311,f2(a1))+P1(f317(f317(f225(a1),x65311),f837(x65311,x65313,x65312)))+P1(f317(f317(f225(a1),f2(a1)),x65311)) % 112.37/112.11 [6532]P147(x65322,x65323,x65321)+E(x65321,f2(a1))+P1(f317(f317(f225(a1),x65321),f845(x65321,x65323,x65322)))+P1(f317(f317(f225(a1),f2(a1)),x65321)) % 112.37/112.11 [6533]~P108(x65331)+E(f317(f317(f228(x65331),x65332),f15(x65331,f228(x65331),x65333)),f15(x65331,f228(x65331),x65333))+~P1(f317(f29(x65331),x65333))+~P1(f317(f317(f319(x65331),x65332),x65333)) % 112.37/112.11 [6534]~P108(x65341)+E(f317(f317(f223(x65341),x65342),f14(x65341,f223(x65341),x65343)),f14(x65341,f223(x65341),x65343))+~P1(f317(f29(x65341),x65343))+~P1(f317(f317(f319(x65341),x65342),x65343)) % 112.37/112.11 [6539]~P1(f317(x65391,x65392))+P1(f317(x65391,f376(x65392,x65391,x65393)))+P1(f317(x65391,f2(a899)))+~P1(f317(f317(f225(a899),x65392),x65393)) % 112.37/112.11 [6600]~P1(f317(x66001,x66002))+~P1(f317(f29(x66003),x66002))+P1(f317(x66001,f406(x66001,x66002,x66003)))+P1(f317(x66001,f178(f906(x66003,a895)))) % 112.37/112.11 [6613]~P112(x66131)+~P94(x66131)+P1(f317(f317(f224(x66131),f317(f94(x66131),x66132)),f317(f94(x66131),x66133)))+~P1(f317(f317(f224(a1),x66132),x66133)) % 112.37/112.11 [6614]~P112(x66141)+~P94(x66141)+P1(f317(f317(f225(x66141),f317(f94(x66141),x66142)),f317(f94(x66141),x66143)))+~P1(f317(f317(f225(a1),x66142),x66143)) % 112.37/112.11 [6617]~P1(f317(x66171,x66173))+~P1(f317(f29(x66172),x66173))+P1(f317(f29(x66172),f406(x66171,x66173,x66172)))+P1(f317(x66171,f178(f906(x66172,a895)))) % 112.37/112.11 [6651]P147(x66511,x66512,x66513)+~P1(f317(x66511,x66512))+P1(f317(f317(f225(a1),x66513),f845(x66513,x66512,x66511)))+P1(f317(f317(f225(a1),f2(a1)),x66513)) % 112.37/112.11 [6689]P148(x66891,x66892,x66893)+P1(f317(f317(f225(a1),x66893),f837(x66893,x66892,x66891)))+~P1(f317(x66891,f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x66893)) % 112.37/112.11 [6719]~P107(x67191)+~P93(x67191)+E(f317(f317(f228(x67191),f317(f94(x67191),x67192)),f317(f94(x67191),x67193)),f317(f94(x67191),x67193))+P1(f317(f317(f224(x67191),f317(f94(x67191),x67192)),f317(f94(x67191),x67193))) % 112.37/112.11 [6720]~P107(x67201)+~P93(x67201)+E(f317(f317(f223(x67201),f317(f94(x67201),x67202)),f317(f94(x67201),x67203)),f317(f94(x67201),x67202))+P1(f317(f317(f224(x67201),f317(f94(x67201),x67202)),f317(f94(x67201),x67203))) % 112.37/112.11 [6780]P148(x67802,x67803,x67801)+E(x67801,f2(a1))+~P1(f317(x67802,f843(x67801,x67803,x67802)))+P1(f317(f317(f225(a1),f2(a1)),x67801)) % 112.37/112.11 [6781]P147(x67812,x67813,x67811)+E(x67811,f2(a1))+~P1(f317(x67812,f845(x67811,x67813,x67812)))+P1(f317(f317(f225(a1),f2(a1)),x67811)) % 112.37/112.11 [6785]P1(f317(x67851,x67852))+~P1(f317(f29(x67853),x67852))+P1(f317(x67851,f390(x67851,x67852,x67853)))+~P1(f317(x67851,f178(f906(x67853,a895)))) % 112.37/112.11 [6806]P1(f317(x68061,x68062))+P1(f317(f29(x68063),f390(x68061,x68062,x68063)))+~P1(f317(f29(x68063),x68062))+~P1(f317(x68061,f178(f906(x68063,a895)))) % 112.37/112.11 [6874]P147(x68741,x68742,x68743)+~P1(f317(x68741,x68742))+~P1(f317(x68741,f845(x68743,x68742,x68741)))+P1(f317(f317(f225(a1),f2(a1)),x68743)) % 112.37/112.11 [6904]P148(x69041,x69042,x69043)+~P1(f317(x69041,f843(x69043,x69042,x69041)))+~P1(f317(x69041,f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x69043)) % 112.37/112.11 [7014]~P94(x70143)+~P112(x70143)+~P1(f317(f317(f224(x70143),f317(f94(x70143),x70141)),f317(f94(x70143),x70142)))+P1(f317(f317(f224(a1),x70141),x70142)) % 112.37/112.11 [7015]~P94(x70153)+~P112(x70153)+~P1(f317(f317(f225(x70153),f317(f94(x70153),x70151)),f317(f94(x70153),x70152)))+P1(f317(f317(f225(a1),x70151),x70152)) % 112.37/112.11 [7043]~P108(x70431)+~P13(x70431,x70433)+P13(x70431,f317(f317(f141(x70431),x70432),x70433))+~P1(f317(f317(f224(x70431),x70432),f693(x70433,x70432,x70431))) % 112.37/112.11 [7044]~P108(x70441)+~P13(x70441,x70443)+P13(x70441,f317(f317(f141(x70441),x70442),x70443))+~P1(f317(f317(f224(x70441),x70442),f695(x70443,x70442,x70441))) % 112.37/112.11 [7045]~P108(x70451)+~P13(x70451,x70453)+P13(x70451,f317(f317(f141(x70451),x70452),x70453))+~P1(f317(f317(f224(x70451),x70452),f733(x70452,x70453,x70451))) % 112.37/112.11 [7132]P148(x71322,x71323,x71321)+E(x71321,f2(a1))+P1(f317(f317(f225(a1),x71321),f2(a1)))+P1(f317(f317(f225(a1),f838(x71321,x71323,x71322)),x71321)) % 112.37/112.11 [7133]P147(x71332,x71333,x71331)+E(x71331,f2(a1))+P1(f317(f317(f225(a1),x71331),f2(a1)))+P1(f317(f317(f225(a1),f846(x71331,x71333,x71332)),x71331)) % 112.37/112.11 [7169]P148(x71692,x71693,x71691)+E(x71691,f2(a1))+P1(f317(f317(f224(a1),f837(x71691,x71693,x71692)),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x71691)) % 112.37/112.11 [7170]P147(x71702,x71703,x71701)+E(x71701,f2(a1))+P1(f317(f317(f224(a1),f845(x71701,x71703,x71702)),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x71701)) % 112.37/112.11 [7195]~P108(x71951)+~P13(x71951,x71953)+E(f317(f317(f138(x71951,x71951,f7(x71951)),x71952),f160(x71951,x71952,x71953)),x71953)+~P1(f317(f317(f319(x71951),x71952),f317(f162(x71951),x71953))) % 112.37/112.11 [7242]P147(x72421,x72422,x72423)+~P1(f317(x72421,x72422))+P1(f317(f317(f225(a1),x72423),f2(a1)))+P1(f317(f317(f225(a1),f846(x72423,x72422,x72421)),x72423)) % 112.37/112.11 [7248]~P107(x72481)+~P93(x72481)+E(f317(f317(f228(x72481),f317(f94(x72481),x72482)),f317(f94(x72481),x72483)),f317(f94(x72481),x72482))+~P1(f317(f317(f224(x72481),f317(f94(x72481),x72482)),f317(f94(x72481),x72483))) % 112.37/112.11 [7249]~P107(x72491)+~P93(x72491)+E(f317(f317(f223(x72491),f317(f94(x72491),x72492)),f317(f94(x72491),x72493)),f317(f94(x72491),x72493))+~P1(f317(f317(f224(x72491),f317(f94(x72491),x72492)),f317(f94(x72491),x72493))) % 112.37/112.11 [7263]P148(x72631,x72632,x72633)+~P1(f317(x72631,f2(a1)))+P1(f317(f317(f225(a1),x72633),f2(a1)))+P1(f317(f317(f225(a1),f838(x72633,x72632,x72631)),x72633)) % 112.37/112.11 [7273]P147(x72731,x72732,x72733)+~P1(f317(x72731,x72732))+P1(f317(f317(f224(a1),f845(x72733,x72732,x72731)),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x72733)) % 112.37/112.11 [7297]P148(x72971,x72972,x72973)+~P1(f317(x72971,f2(a1)))+P1(f317(f317(f224(a1),f837(x72973,x72972,x72971)),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x72973)) % 112.37/112.11 [7323]~P1(f317(x73231,x73232))+P1(f317(x73231,f2(a899)))+~P1(f317(f317(f225(a899),x73232),x73233))+P1(f317(f317(f225(a899),f376(x73232,x73231,x73233)),x73233)) % 112.37/112.11 [7340]~P108(x73401)+~P13(x73401,x73403)+P13(x73401,f317(f317(f141(x73401),x73402),x73403))+P1(f317(f317(f319(x73401),f693(x73403,x73402,x73401)),f317(f162(x73401),x73403))) % 112.37/112.11 [7341]~P108(x73411)+~P13(x73411,x73413)+P13(x73411,f317(f317(f141(x73411),x73412),x73413))+P1(f317(f317(f319(x73411),f695(x73413,x73412,x73411)),f317(f162(x73411),x73413))) % 112.37/112.11 [7342]~P108(x73421)+~P13(x73421,x73423)+P13(x73421,f317(f317(f141(x73421),x73422),x73423))+P1(f317(f317(f319(x73421),f733(x73422,x73423,x73421)),f317(f162(x73421),x73423))) % 112.37/112.11 [7458]~P108(x74581)+~P5(x74581)+~P1(f317(f317(f225(x74581),x74583),f32(x74581,x74582)))+P1(f317(f317(f319(x74581),f407(x74582,x74583,x74581)),x74582)) % 112.37/112.11 [7613]~P108(x76131)+~P5(x76131)+~P1(f317(f317(f225(x76131),f33(x76131,x76133)),x76132))+P1(f317(f317(f319(x76131),f431(x76132,x76133,x76131)),x76133)) % 112.37/112.11 [7614]~P108(x76141)+~P5(x76141)+~P1(f317(f317(f225(x76141),f33(x76141,x76143)),x76142))+P1(f317(f317(f225(x76141),f431(x76142,x76143,x76141)),x76142)) % 112.37/112.11 [7627]P148(x76272,x76273,x76271)+E(x76271,f2(a1))+P1(f317(f317(f225(a1),x76271),f837(x76271,x76273,x76272)))+P1(f317(f317(f225(a1),f838(x76271,x76273,x76272)),x76271)) % 112.37/112.11 [7628]P147(x76282,x76283,x76281)+E(x76281,f2(a1))+P1(f317(f317(f225(a1),x76281),f845(x76281,x76283,x76282)))+P1(f317(f317(f225(a1),f846(x76281,x76283,x76282)),x76281)) % 112.37/112.11 [7722]P148(x77223,x77222,x77221)+E(x77221,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x77221),f843(x77221,x77222,x77223))),f837(x77221,x77222,x77223)),x77222)+P1(f317(f317(f225(a1),f2(a1)),x77221)) % 112.37/112.11 [7723]P147(x77233,x77232,x77231)+E(x77231,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x77231),f848(x77231,x77232,x77233))),f845(x77231,x77232,x77233)),x77232)+P1(f317(f317(f225(a1),f2(a1)),x77231)) % 112.37/112.11 [7726]~P135(x77261)+~P1(f317(f317(f224(x77261),x77263),f2(x77261)))+P1(f317(f317(f224(x77261),f317(f317(f75(x77261),x77262),x77263)),f2(x77261)))+~P1(f317(f317(f224(x77261),f2(x77261)),x77262)) % 112.37/112.11 [7728]~P135(x77281)+~P1(f317(f317(f224(x77281),x77282),f2(x77281)))+P1(f317(f317(f224(x77281),f317(f317(f75(x77281),x77282),x77283)),f2(x77281)))+~P1(f317(f317(f224(x77281),f2(x77281)),x77283)) % 112.37/112.11 [7729]~P127(x77291)+~P1(f317(f317(f224(x77291),x77293),f2(x77291)))+P1(f317(f317(f224(x77291),f317(f317(f75(x77291),x77292),x77293)),f2(x77291)))+~P1(f317(f317(f224(x77291),f2(x77291)),x77292)) % 112.37/112.11 [7730]~P127(x77301)+~P1(f317(f317(f224(x77301),x77302),f2(x77301)))+P1(f317(f317(f224(x77301),f317(f317(f75(x77301),x77302),x77303)),f2(x77301)))+~P1(f317(f317(f224(x77301),f2(x77301)),x77303)) % 112.37/112.11 [7731]~P63(x77311)+~P1(f317(f317(f224(x77311),x77313),f2(x77311)))+P1(f317(f317(f224(x77311),f317(f317(f281(x77311),x77312),x77313)),f2(x77311)))+~P1(f317(f317(f224(x77311),f2(x77311)),x77312)) % 112.37/112.11 [7732]~P63(x77321)+~P1(f317(f317(f224(x77321),x77322),f2(x77321)))+P1(f317(f317(f224(x77321),f317(f317(f281(x77321),x77322),x77323)),f2(x77321)))+~P1(f317(f317(f224(x77321),f2(x77321)),x77323)) % 112.37/112.11 [7733]~P64(x77331)+~P1(f317(f317(f224(x77331),x77332),f2(x77331)))+P1(f317(f317(f224(x77331),f317(f317(f281(x77331),x77332),x77333)),f2(x77331)))+~P1(f317(f317(f225(x77331),f2(x77331)),x77333)) % 112.37/112.11 [7734]~P64(x77341)+~P1(f317(f317(f225(x77341),x77343),f2(x77341)))+P1(f317(f317(f224(x77341),f317(f317(f281(x77341),x77342),x77343)),f2(x77341)))+~P1(f317(f317(f224(x77341),f2(x77341)),x77342)) % 112.37/112.11 [7736]~P134(x77361)+~P1(f317(f317(f225(x77361),x77363),f2(x77361)))+P1(f317(f317(f225(x77361),f317(f317(f75(x77361),x77362),x77363)),f2(x77361)))+~P1(f317(f317(f225(x77361),f2(x77361)),x77362)) % 112.37/112.11 [7737]~P134(x77371)+~P1(f317(f317(f225(x77371),x77372),f2(x77371)))+P1(f317(f317(f225(x77371),f317(f317(f75(x77371),x77372),x77373)),f2(x77371)))+~P1(f317(f317(f225(x77371),f2(x77371)),x77373)) % 112.37/112.11 [7738]~P63(x77381)+~P1(f317(f317(f225(x77381),x77383),f2(x77381)))+P1(f317(f317(f225(x77381),f317(f317(f281(x77381),x77382),x77383)),f2(x77381)))+~P1(f317(f317(f225(x77381),f2(x77381)),x77382)) % 112.37/112.11 [7739]~P63(x77391)+~P1(f317(f317(f225(x77391),x77392),f2(x77391)))+P1(f317(f317(f225(x77391),f317(f317(f281(x77391),x77392),x77393)),f2(x77391)))+~P1(f317(f317(f225(x77391),f2(x77391)),x77393)) % 112.37/112.11 [7740]~P64(x77401)+~P1(f317(f317(f225(x77401),x77403),f2(x77401)))+P1(f317(f317(f225(x77401),f317(f317(f281(x77401),x77402),x77403)),f2(x77401)))+~P1(f317(f317(f225(x77401),f2(x77401)),x77402)) % 112.37/112.11 [7741]~P64(x77411)+~P1(f317(f317(f225(x77411),x77412),f2(x77411)))+P1(f317(f317(f225(x77411),f317(f317(f281(x77411),x77412),x77413)),f2(x77411)))+~P1(f317(f317(f225(x77411),f2(x77411)),x77413)) % 112.37/112.11 [7756]P147(x77561,x77562,x77563)+~P1(f317(x77561,x77562))+P1(f317(f317(f225(a1),x77563),f845(x77563,x77562,x77561)))+P1(f317(f317(f225(a1),f846(x77563,x77562,x77561)),x77563)) % 112.37/112.11 [7769]P148(x77691,x77692,x77693)+P1(f317(f317(f225(a1),x77693),f837(x77693,x77692,x77691)))+~P1(f317(x77691,f2(a1)))+P1(f317(f317(f225(a1),f838(x77693,x77692,x77691)),x77693)) % 112.37/112.11 [7821]P148(x78212,x78213,x78211)+E(x78211,f2(a1))+~P1(f317(x78212,f843(x78211,x78213,x78212)))+P1(f317(f317(f225(a1),f838(x78211,x78213,x78212)),x78211)) % 112.37/112.11 [7822]P147(x78222,x78223,x78221)+E(x78221,f2(a1))+~P1(f317(x78222,f845(x78221,x78223,x78222)))+P1(f317(f317(f225(a1),f846(x78221,x78223,x78222)),x78221)) % 112.37/112.11 [7832]P147(x78323,x78322,x78321)+~P1(f317(x78323,x78322))+E(f317(f317(f74(a1),f317(f317(f75(a1),x78321),f848(x78321,x78322,x78323))),f845(x78321,x78322,x78323)),x78322)+P1(f317(f317(f225(a1),f2(a1)),x78321)) % 112.37/112.11 [7847]P148(x78473,x78472,x78471)+E(f317(f317(f74(a1),f317(f317(f75(a1),x78471),f843(x78471,x78472,x78473))),f837(x78471,x78472,x78473)),x78472)+~P1(f317(x78473,f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x78471)) % 112.37/112.11 [7875]~P1(f317(x78751,x78753))+~P1(f317(f29(x78752),x78753))+P1(f317(f317(f319(x78752),f400(x78751,x78753,x78752)),f406(x78751,x78753,x78752)))+P1(f317(x78751,f178(f906(x78752,a895)))) % 112.37/112.11 [7887]P147(x78871,x78872,x78873)+~P1(f317(x78871,x78872))+~P1(f317(x78871,f845(x78873,x78872,x78871)))+P1(f317(f317(f225(a1),f846(x78873,x78872,x78871)),x78873)) % 112.37/112.11 [7893]P148(x78931,x78932,x78933)+~P1(f317(x78931,f843(x78933,x78932,x78931)))+~P1(f317(x78931,f2(a1)))+P1(f317(f317(f225(a1),f838(x78933,x78932,x78931)),x78933)) % 112.37/112.11 [7995]~P127(x79951)+~P1(f317(f317(f224(x79951),f317(f317(f75(x79951),x79953),x79952)),f2(x79951)))+P1(f317(f317(f224(x79951),x79952),f2(x79951)))+P1(f317(f317(f224(x79951),f2(x79951)),x79952)) % 112.37/112.11 [7996]~P127(x79961)+~P1(f317(f317(f224(x79961),f317(f317(f75(x79961),x79962),x79963)),f2(x79961)))+P1(f317(f317(f224(x79961),x79962),f2(x79961)))+P1(f317(f317(f224(x79961),f2(x79961)),x79962)) % 112.37/112.11 [7997]~P63(x79971)+~P1(f317(f317(f224(x79971),f317(f317(f281(x79971),x79973),x79972)),f2(x79971)))+P1(f317(f317(f224(x79971),x79972),f2(x79971)))+P1(f317(f317(f224(x79971),f2(x79971)),x79972)) % 112.37/112.11 [7998]~P63(x79981)+~P1(f317(f317(f224(x79981),f317(f317(f281(x79981),x79982),x79983)),f2(x79981)))+P1(f317(f317(f224(x79981),x79982),f2(x79981)))+P1(f317(f317(f224(x79981),f2(x79981)),x79982)) % 112.37/112.11 [7999]~P63(x79991)+~P1(f317(f317(f225(x79991),f317(f317(f281(x79991),x79993),x79992)),f2(x79991)))+P1(f317(f317(f225(x79991),x79992),f2(x79991)))+P1(f317(f317(f225(x79991),f2(x79991)),x79992)) % 112.37/112.11 [8000]~P63(x80001)+~P1(f317(f317(f225(x80001),f317(f317(f281(x80001),x80002),x80003)),f2(x80001)))+P1(f317(f317(f225(x80001),x80002),f2(x80001)))+P1(f317(f317(f225(x80001),f2(x80001)),x80002)) % 112.37/112.11 [8024]~P127(x80241)+~P1(f317(f317(f224(x80241),f317(f317(f75(x80241),x80242),x80243)),f2(x80241)))+P1(f317(f317(f224(x80241),f2(x80241)),x80242))+P1(f317(f317(f224(x80241),f2(x80241)),x80243)) % 112.37/112.11 [8025]~P63(x80251)+~P1(f317(f317(f224(x80251),f317(f317(f281(x80251),x80252),x80253)),f2(x80251)))+P1(f317(f317(f224(x80251),f2(x80251)),x80252))+P1(f317(f317(f224(x80251),f2(x80251)),x80253)) % 112.37/112.11 [8026]~P63(x80261)+~P1(f317(f317(f225(x80261),f317(f317(f281(x80261),x80262),x80263)),f2(x80261)))+P1(f317(f317(f225(x80261),f2(x80261)),x80262))+P1(f317(f317(f225(x80261),f2(x80261)),x80263)) % 112.37/112.11 [8048]P148(x80482,x80483,x80481)+E(x80481,f2(a1))+P1(f317(f317(f224(a1),f837(x80481,x80483,x80482)),f2(a1)))+P1(f317(f317(f225(a1),f838(x80481,x80483,x80482)),x80481)) % 112.37/112.11 [8049]P147(x80492,x80493,x80491)+E(x80491,f2(a1))+P1(f317(f317(f224(a1),f845(x80491,x80493,x80492)),f2(a1)))+P1(f317(f317(f225(a1),f846(x80491,x80493,x80492)),x80491)) % 112.37/112.11 [8056]~P126(x80561)+~P1(f317(f317(f225(x80561),x80562),f72(x80561)))+P1(f317(f317(f225(x80561),f317(f317(f234(x80561),x80562),f317(a102,x80563))),f72(x80561)))+~P1(f317(f317(f225(x80561),f2(x80561)),x80562)) % 112.37/112.11 [8109]~P108(x81091)+~E(x81093,f103(x81091))+~P13(x81091,f317(f158(x81091),x81093))+E(f317(f132(x81091,x81091,f317(f9(x81091,x81091,x81091),f223(x81091)),x81092),f317(f158(x81091),x81093)),x81092) % 112.37/112.11 [8112]P147(x81121,x81122,x81123)+~P1(f317(x81121,x81122))+P1(f317(f317(f224(a1),f845(x81123,x81122,x81121)),f2(a1)))+P1(f317(f317(f225(a1),f846(x81123,x81122,x81121)),x81123)) % 112.37/112.11 [8119]P148(x81191,x81192,x81193)+~P1(f317(x81191,f2(a1)))+P1(f317(f317(f224(a1),f837(x81193,x81192,x81191)),f2(a1)))+P1(f317(f317(f225(a1),f838(x81193,x81192,x81191)),x81193)) % 112.37/112.11 [8337]P148(x83373,x83372,x83371)+E(x83371,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x83371),f843(x83371,x83372,x83373))),f837(x83371,x83372,x83373)),x83372)+P1(f317(f317(f225(a1),f838(x83371,x83372,x83373)),x83371)) % 112.37/112.11 [8338]P147(x83383,x83382,x83381)+E(x83381,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x83381),f848(x83381,x83382,x83383))),f845(x83381,x83382,x83383)),x83382)+P1(f317(f317(f225(a1),f846(x83381,x83382,x83383)),x83381)) % 112.37/112.11 [8374]P147(x83743,x83742,x83741)+~P1(f317(x83743,x83742))+E(f317(f317(f74(a1),f317(f317(f75(a1),x83741),f848(x83741,x83742,x83743))),f845(x83741,x83742,x83743)),x83742)+P1(f317(f317(f225(a1),f846(x83741,x83742,x83743)),x83741)) % 112.37/112.11 [8375]~P69(x83751)+~P75(x83751)+~P39(x83753)+E(f317(f317(f8(a899,x83751),f317(f317(f10(a1,x83751,a899),x83752),f90(a1))),f317(f300(a1,a899,a95),x83753)),f317(f317(f8(a1,x83751),x83752),x83753)) % 112.37/112.11 [8376]~P69(x83761)+~P75(x83761)+~P39(x83763)+E(f317(f317(f11(a899,x83761),f317(f317(f10(a1,x83761,a899),x83762),f90(a1))),f317(f300(a1,a899,a95),x83763)),f317(f317(f11(a1,x83761),x83762),x83763)) % 112.37/112.11 [8385]P148(x83853,x83852,x83851)+E(f317(f317(f74(a1),f317(f317(f75(a1),x83851),f843(x83851,x83852,x83853))),f837(x83851,x83852,x83853)),x83852)+~P1(f317(x83853,f2(a1)))+P1(f317(f317(f225(a1),f838(x83851,x83852,x83853)),x83851)) % 112.37/112.11 [8407]~E(x84072,f2(a899))+~E(f317(f241(a899,a899),x84073),f2(a899))+~E(x84071,f317(f317(f74(a899),f317(f317(f75(a899),f317(f241(a899,a899),x84073)),x84072)),f317(f246(a899,a899),x84073)))+P1(f317(f44(x84071,x84072),x84073)) % 112.37/112.11 [8464]P1(f317(x84641,x84642))+~P1(f317(f317(f319(x84643),f379(x84641,x84642,x84643)),f390(x84641,x84642,x84643)))+~P1(f317(f29(x84643),x84642))+~P1(f317(x84641,f178(f906(x84643,a895)))) % 112.37/112.11 [9089]P1(f317(x90891,x90892))+~P1(f317(f29(x90893),x90892))+~P1(f317(x90891,f317(f317(f299(x90893),f379(x90891,x90892,x90893)),f390(x90891,x90892,x90893))))+~P1(f317(x90891,f178(f906(x90893,a895)))) % 112.37/112.11 [9320]P1(f317(f317(f224(a1),x93201),f2(a1)))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),f317(f317(f75(a1),x93203),x93201)),x93202)),f2(a1)))+~P1(f317(f317(f224(a1),f2(a1)),x93202))+~P1(f317(f317(f225(a1),f2(a1)),x93203)) % 112.37/112.11 [5878]~P108(x58782)+E(x58781,f178(f906(x58782,a895)))+~P1(f317(f29(x58782),x58781))+E(f16(x58782,f317(f317(f299(x58782),x58783),x58781)),f317(f317(f223(x58782),x58783),f16(x58782,x58781))) % 112.37/112.11 [5879]~P108(x58792)+E(x58791,f178(f906(x58792,a895)))+~P1(f317(f29(x58792),x58791))+E(f17(x58792,f317(f317(f299(x58792),x58793),x58791)),f317(f317(f228(x58792),x58793),f17(x58792,x58791))) % 112.37/112.11 [5880]~P99(x58802)+E(x58801,f178(f906(x58802,a895)))+~P1(f317(f29(x58802),x58801))+E(f12(x58802,f317(f317(f299(x58802),x58803),x58801)),f317(f317(f91(x58802),x58803),f12(x58802,x58801))) % 112.37/112.11 [5881]~P99(x58812)+E(x58811,f178(f906(x58812,a895)))+~P1(f317(f29(x58812),x58811))+E(f13(x58812,f317(f317(f299(x58812),x58813),x58811)),f317(f317(f92(x58812),x58813),f13(x58812,x58811))) % 112.37/112.11 [6212]~P127(x62121)+~E(x62123,f2(x62121))+~E(x62122,f2(x62121))+E(f317(f317(f74(x62121),f317(f317(f75(x62121),x62122),x62122)),f317(f317(f75(x62121),x62123),x62123)),f2(x62121)) % 112.37/112.11 [6285]~P97(x62852)+E(x62851,f178(f906(x62852,a895)))+~P1(f317(f29(x62852),x62851))+E(f317(f58(x62852,f75(x62852)),f317(f317(f299(x62852),x62853),x62851)),f317(f317(f75(x62852),x62853),f317(f58(x62852,f75(x62852)),x62851))) % 112.37/112.11 [6416]~P108(x64162)+E(x64161,f178(f906(x64162,a895)))+~P1(f317(f29(x64162),x64161))+E(f14(x64162,f223(x64162),f317(f317(f299(x64162),x64163),x64161)),f317(f317(f223(x64162),x64163),f14(x64162,f223(x64162),x64161))) % 112.37/112.11 [6417]~P108(x64172)+E(x64171,f178(f906(x64172,a895)))+~P1(f317(f29(x64172),x64171))+E(f15(x64172,f228(x64172),f317(f317(f299(x64172),x64173),x64171)),f317(f317(f228(x64172),x64173),f15(x64172,f228(x64172),x64171))) % 112.37/112.11 [6938]~P70(x69381)+~P1(f317(f29(x69381),x69383))+E(f317(f58(x69381,f75(x69381)),f317(f317(f299(x69381),x69382),x69383)),f317(f317(f59(x69381,x69381,f75(x69381)),x69382),x69383))+P1(f317(f317(f319(x69381),x69382),x69383)) % 112.37/112.11 [7021]~E(f317(f317(f74(a1),x70212),f317(f317(f75(a1),x70213),x70211)),x70213)+~P1(f317(f317(f225(a1),f2(a1)),x70213))+P1(f317(f317(f224(a1),f72(a1)),x70211))+~P1(f317(f317(f225(a1),x70212),x70213)) % 112.37/112.11 [7050]~E(f317(f317(f74(a1),x70502),f317(f317(f75(a1),x70503),x70501)),x70503)+P1(f317(f317(f224(a1),x70501),f72(a1)))+~P1(f317(f317(f224(a1),f2(a1)),x70502))+~P1(f317(f317(f225(a1),f2(a1)),x70503)) % 112.37/112.11 [7068]E(x70681,f2(a899))+~P1(f317(f44(x70683,x70681),x70682))+~P1(f317(f317(f225(a899),f2(a899)),x70681))+P1(f317(f317(f225(a899),f317(f246(a899,a899),x70682)),x70681)) % 112.37/112.11 [7099]~P138(x70991)+~P1(f317(f317(f224(x70991),x70992),f2(x70991)))+~P1(f317(f317(f224(x70991),x70993),f2(x70991)))+E(f317(f317(f75(x70991),f317(f70(x70991),x70992)),f317(f70(x70991),x70993)),f317(f70(x70991),f317(f317(f75(x70991),x70992),x70993))) % 112.37/112.11 [7146]~P138(x71461)+~P1(f317(f317(f224(x71461),x71462),f2(x71461)))+E(f317(f317(f75(x71461),f317(f70(x71461),x71462)),f317(f70(x71461),x71463)),f317(f70(x71461),f317(f317(f75(x71461),x71462),x71463)))+~P1(f317(f317(f224(x71461),f2(x71461)),x71463)) % 112.37/112.11 [7147]~P138(x71471)+~P1(f317(f317(f224(x71471),x71473),f2(x71471)))+E(f317(f317(f75(x71471),f317(f70(x71471),x71472)),f317(f70(x71471),x71473)),f317(f70(x71471),f317(f317(f75(x71471),x71472),x71473)))+~P1(f317(f317(f224(x71471),f2(x71471)),x71472)) % 112.37/112.11 [7203]~P138(x72031)+E(f317(f317(f75(x72031),f317(f70(x72031),x72032)),f317(f70(x72031),x72033)),f317(f70(x72031),f317(f317(f75(x72031),x72032),x72033)))+~P1(f317(f317(f224(x72031),f2(x72031)),x72032))+~P1(f317(f317(f224(x72031),f2(x72031)),x72033)) % 112.37/112.11 [7220]~P111(x72201)+~P1(f317(f317(f224(x72201),x72203),f2(x72201)))+~P1(f317(f317(f224(x72201),x72202),f2(x72201)))+P1(f317(f317(f224(x72201),f2(x72201)),f317(f317(f75(x72201),x72202),x72203))) % 112.37/112.11 [7221]~P127(x72211)+~P1(f317(f317(f224(x72211),x72213),f2(x72211)))+~P1(f317(f317(f224(x72211),x72212),f2(x72211)))+P1(f317(f317(f224(x72211),f2(x72211)),f317(f317(f75(x72211),x72212),x72213))) % 112.37/112.11 [7222]~P63(x72221)+~P1(f317(f317(f224(x72221),x72223),f2(x72221)))+~P1(f317(f317(f224(x72221),x72222),f2(x72221)))+P1(f317(f317(f224(x72221),f2(x72221)),f317(f317(f281(x72221),x72222),x72223))) % 112.37/112.11 [7223]~P64(x72231)+~P1(f317(f317(f225(x72231),x72233),f2(x72231)))+~P1(f317(f317(f224(x72231),x72232),f2(x72231)))+P1(f317(f317(f224(x72231),f2(x72231)),f317(f317(f281(x72231),x72232),x72233))) % 112.37/112.11 [7224]~P127(x72241)+~P1(f317(f317(f225(x72241),x72243),f2(x72241)))+~P1(f317(f317(f225(x72241),x72242),f2(x72241)))+P1(f317(f317(f225(x72241),f2(x72241)),f317(f317(f75(x72241),x72242),x72243))) % 112.37/112.11 [7225]~P63(x72251)+~P1(f317(f317(f225(x72251),x72253),f2(x72251)))+~P1(f317(f317(f225(x72251),x72252),f2(x72251)))+P1(f317(f317(f225(x72251),f2(x72251)),f317(f317(f281(x72251),x72252),x72253))) % 112.37/112.11 [7226]~P64(x72261)+~P1(f317(f317(f225(x72261),x72263),f2(x72261)))+~P1(f317(f317(f225(x72261),x72262),f2(x72261)))+P1(f317(f317(f225(x72261),f2(x72261)),f317(f317(f281(x72261),x72262),x72263))) % 112.37/112.11 [7227]~P126(x72271)+~P1(f317(f317(f225(a899),f2(a899)),x72273))+~P1(f317(f317(f225(x72271),f72(x72271)),x72272))+P1(f317(f317(f225(x72271),f72(x72271)),f317(f317(f234(x72271),x72272),x72273))) % 112.37/112.11 [7325]~P111(x73251)+~P1(f317(f317(f224(x73251),f2(x73251)),x73253))+~P1(f317(f317(f224(x73251),f2(x73251)),x73252))+P1(f317(f317(f224(x73251),f2(x73251)),f317(f317(f75(x73251),x73252),x73253))) % 112.37/112.11 [7326]~P135(x73261)+~P1(f317(f317(f224(x73261),f2(x73261)),x73263))+~P1(f317(f317(f224(x73261),f2(x73261)),x73262))+P1(f317(f317(f224(x73261),f2(x73261)),f317(f317(f75(x73261),x73262),x73263))) % 112.37/112.11 [7327]~P127(x73271)+~P1(f317(f317(f224(x73271),f2(x73271)),x73273))+~P1(f317(f317(f224(x73271),f2(x73271)),x73272))+P1(f317(f317(f224(x73271),f2(x73271)),f317(f317(f75(x73271),x73272),x73273))) % 112.37/112.11 [7328]~P63(x73281)+~P1(f317(f317(f224(x73281),f2(x73281)),x73283))+~P1(f317(f317(f224(x73281),f2(x73281)),x73282))+P1(f317(f317(f224(x73281),f2(x73281)),f317(f317(f281(x73281),x73282),x73283))) % 112.37/112.11 [7329]~P64(x73291)+~P1(f317(f317(f225(x73291),f2(x73291)),x73293))+~P1(f317(f317(f224(x73291),f2(x73291)),x73292))+P1(f317(f317(f224(x73291),f2(x73291)),f317(f317(f281(x73291),x73292),x73293))) % 112.37/112.11 [7330]~P126(x73301)+~P1(f317(f317(f225(x73301),f72(x73301)),x73303))+~P1(f317(f317(f225(x73301),f72(x73301)),x73302))+P1(f317(f317(f225(x73301),f72(x73301)),f317(f317(f75(x73301),x73302),x73303))) % 112.37/112.11 [7333]~P88(x73331)+~P1(f317(f317(f225(x73331),f2(x73331)),x73333))+~P1(f317(f317(f225(x73331),f2(x73331)),x73332))+P1(f317(f317(f225(x73331),f2(x73331)),f317(f317(f74(x73331),x73332),x73333))) % 112.37/112.11 [7334]~P134(x73341)+~P1(f317(f317(f225(x73341),f2(x73341)),x73343))+~P1(f317(f317(f225(x73341),f2(x73341)),x73342))+P1(f317(f317(f225(x73341),f2(x73341)),f317(f317(f75(x73341),x73342),x73343))) % 112.37/112.11 [7335]~P63(x73351)+~P1(f317(f317(f225(x73351),f2(x73351)),x73353))+~P1(f317(f317(f225(x73351),f2(x73351)),x73352))+P1(f317(f317(f225(x73351),f2(x73351)),f317(f317(f281(x73351),x73352),x73353))) % 112.37/112.11 [7336]~P64(x73361)+~P1(f317(f317(f225(x73361),f2(x73361)),x73363))+~P1(f317(f317(f225(x73361),f2(x73361)),x73362))+P1(f317(f317(f225(x73361),f2(x73361)),f317(f317(f281(x73361),x73362),x73363))) % 112.37/112.11 [7415]~P108(x74151)+~P1(f317(f29(x74151),x74153))+E(f16(x74151,f317(f317(f299(x74151),x74152),x74153)),x74152)+~E(f317(f317(f3(f906(x74151,a895)),x74153),f317(f317(f299(x74151),x74152),f178(f906(x74151,a895)))),f178(f906(x74151,a895))) % 112.37/112.11 [7416]~P108(x74161)+~P1(f317(f29(x74161),x74163))+E(f17(x74161,f317(f317(f299(x74161),x74162),x74163)),x74162)+~E(f317(f317(f3(f906(x74161,a895)),x74163),f317(f317(f299(x74161),x74162),f178(f906(x74161,a895)))),f178(f906(x74161,a895))) % 112.37/112.11 [7417]~P99(x74171)+~P1(f317(f29(x74171),x74173))+E(f12(x74171,f317(f317(f299(x74171),x74172),x74173)),x74172)+~E(f317(f317(f3(f906(x74171,a895)),x74173),f317(f317(f299(x74171),x74172),f178(f906(x74171,a895)))),f178(f906(x74171,a895))) % 112.37/112.11 [7418]~P99(x74181)+~P1(f317(f29(x74181),x74183))+E(f13(x74181,f317(f317(f299(x74181),x74182),x74183)),x74182)+~E(f317(f317(f3(f906(x74181,a895)),x74183),f317(f317(f299(x74181),x74182),f178(f906(x74181,a895)))),f178(f906(x74181,a895))) % 112.37/112.11 [7420]~P127(x74201)+P1(f317(f317(f224(x74201),x74202),f2(x74201)))+P1(f317(f317(f224(x74201),f2(x74201)),x74203))+~P1(f317(f317(f224(x74201),f2(x74201)),f317(f317(f75(x74201),x74203),x74202))) % 112.37/112.11 [7421]~P127(x74211)+P1(f317(f317(f224(x74211),x74212),f2(x74211)))+P1(f317(f317(f224(x74211),f2(x74211)),x74213))+~P1(f317(f317(f224(x74211),f2(x74211)),f317(f317(f75(x74211),x74212),x74213))) % 112.37/112.11 [7422]~P63(x74221)+P1(f317(f317(f224(x74221),x74222),f2(x74221)))+P1(f317(f317(f224(x74221),f2(x74221)),x74223))+~P1(f317(f317(f224(x74221),f2(x74221)),f317(f317(f281(x74221),x74223),x74222))) % 112.37/112.11 [7423]~P63(x74231)+P1(f317(f317(f224(x74231),x74232),f2(x74231)))+P1(f317(f317(f224(x74231),f2(x74231)),x74233))+~P1(f317(f317(f224(x74231),f2(x74231)),f317(f317(f281(x74231),x74232),x74233))) % 112.37/112.11 [7424]~P127(x74241)+P1(f317(f317(f224(x74241),x74242),f2(x74241)))+P1(f317(f317(f224(x74241),f2(x74241)),x74242))+~P1(f317(f317(f224(x74241),f2(x74241)),f317(f317(f75(x74241),x74243),x74242))) % 112.37/112.11 [7425]~P127(x74251)+P1(f317(f317(f224(x74251),x74252),f2(x74251)))+P1(f317(f317(f224(x74251),f2(x74251)),x74252))+~P1(f317(f317(f224(x74251),f2(x74251)),f317(f317(f75(x74251),x74252),x74253))) % 112.37/112.11 [7426]~P63(x74261)+P1(f317(f317(f224(x74261),x74262),f2(x74261)))+P1(f317(f317(f224(x74261),f2(x74261)),x74262))+~P1(f317(f317(f224(x74261),f2(x74261)),f317(f317(f281(x74261),x74263),x74262))) % 112.37/112.11 [7427]~P63(x74271)+P1(f317(f317(f224(x74271),x74272),f2(x74271)))+P1(f317(f317(f224(x74271),f2(x74271)),x74272))+~P1(f317(f317(f224(x74271),f2(x74271)),f317(f317(f281(x74271),x74272),x74273))) % 112.37/112.11 [7428]~P63(x74281)+P1(f317(f317(f225(x74281),x74282),f2(x74281)))+P1(f317(f317(f225(x74281),f2(x74281)),x74283))+~P1(f317(f317(f225(x74281),f2(x74281)),f317(f317(f281(x74281),x74283),x74282))) % 112.37/112.11 [7429]~P63(x74291)+P1(f317(f317(f225(x74291),x74292),f2(x74291)))+P1(f317(f317(f225(x74291),f2(x74291)),x74293))+~P1(f317(f317(f225(x74291),f2(x74291)),f317(f317(f281(x74291),x74292),x74293))) % 112.37/112.11 [7430]~P63(x74301)+P1(f317(f317(f225(x74301),x74302),f2(x74301)))+P1(f317(f317(f225(x74301),f2(x74301)),x74302))+~P1(f317(f317(f225(x74301),f2(x74301)),f317(f317(f281(x74301),x74303),x74302))) % 112.37/112.11 [7431]~P63(x74311)+P1(f317(f317(f225(x74311),x74312),f2(x74311)))+P1(f317(f317(f225(x74311),f2(x74311)),x74312))+~P1(f317(f317(f225(x74311),f2(x74311)),f317(f317(f281(x74311),x74312),x74313))) % 112.37/112.11 [7504]~P1(f317(f317(f277(a899),x75041),x75043))+P1(f317(f317(f277(a899),x75041),x75042))+~P1(f317(f317(f224(a899),x75042),x75043))+~P1(f317(f317(f277(a899),x75041),f317(f317(f3(a899),x75043),x75042))) % 112.37/112.11 [7505]~P1(f317(f317(f277(a899),x75051),x75053))+P1(f317(f317(f277(a899),x75051),x75052))+~P1(f317(f317(f224(a899),x75053),x75052))+~P1(f317(f317(f277(a899),x75051),f317(f317(f3(a899),x75052),x75053))) % 112.37/112.11 [7520]~E(f317(f317(f92(f906(x75201,a895)),f317(f162(x75201),x75202)),f317(f162(x75201),x75203)),f178(f906(x75201,a895)))+~P1(f317(f127(x75201),x75203))+~P1(f317(f127(x75201),x75202))+P1(f317(f127(x75201),f317(f317(f124(x75201),x75202),x75203))) % 112.37/112.11 [7521]~P108(x75211)+~P1(f317(f29(x75211),x75213))+E(f14(x75211,f223(x75211),f317(f317(f299(x75211),x75212),x75213)),x75212)+~E(f317(f317(f3(f906(x75211,a895)),x75213),f317(f317(f299(x75211),x75212),f178(f906(x75211,a895)))),f178(f906(x75211,a895))) % 112.37/112.11 [7522]~P108(x75221)+~P1(f317(f29(x75221),x75223))+E(f15(x75221,f228(x75221),f317(f317(f299(x75221),x75222),x75223)),x75222)+~E(f317(f317(f3(f906(x75221,a895)),x75223),f317(f317(f299(x75221),x75222),f178(f906(x75221,a895)))),f178(f906(x75221,a895))) % 112.37/112.11 [7535]~P86(x75351)+~P1(f317(f317(f224(x75351),x75352),x75353))+~P1(f317(f317(f224(x75351),f317(f73(x75351),x75352)),x75353))+P1(f317(f317(f224(x75351),f317(f70(x75351),x75352)),x75353)) % 112.37/112.11 [7536]~P112(x75361)+~P1(f317(f317(f225(x75361),x75362),x75363))+~P1(f317(f317(f225(x75361),f317(f73(x75361),x75362)),x75363))+P1(f317(f317(f225(x75361),f317(f70(x75361),x75362)),x75363)) % 112.37/112.11 [7602]~P134(x76021)+P1(f317(f317(f225(x76021),f2(x76021)),x76022))+~P1(f317(f317(f225(x76021),f2(x76021)),x76023))+~P1(f317(f317(f225(x76021),f2(x76021)),f317(f317(f75(x76021),x76023),x76022))) % 112.37/112.11 [7603]~P134(x76031)+P1(f317(f317(f225(x76031),f2(x76031)),x76032))+~P1(f317(f317(f225(x76031),f2(x76031)),x76033))+~P1(f317(f317(f225(x76031),f2(x76031)),f317(f317(f75(x76031),x76032),x76033))) % 112.37/112.11 [7907]E(x79071,x79072)+~P1(f317(f29(x79073),x79071))+~P1(f317(f317(f224(a899),f317(f30(x79073),x79071)),f317(f30(x79073),x79072)))+~P1(f317(f317(f224(f906(x79073,a895)),x79072),x79071)) % 112.37/112.11 [8053]~P1(f317(f317(f225(a1),x80531),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x80532))+~P1(f317(f317(f224(a1),x80532),x80533))+P1(f317(f317(f224(a1),f317(f317(f31(a1),x80531),x80532)),f317(f317(f31(a1),x80531),x80533))) % 112.37/112.11 [8063]~P1(f317(f317(f224(a1),f2(a1)),x80631))+~P1(f317(f317(f225(a1),f2(a1)),x80633))+~P1(f317(f317(f224(a1),x80633),x80632))+P1(f317(f317(f224(a1),f317(f317(f31(a1),x80631),x80632)),f317(f317(f31(a1),x80631),x80633))) % 112.37/112.11 [8197]E(f317(x81971,f327(x81972,x81971,x81973)),x81972)+~P1(f317(f317(f224(a1),x81972),f317(x81971,x81973)))+P1(f317(f317(f225(a899),f892(x81972,x81971,x81973)),x81973))+~P1(f317(f317(f224(a1),f317(x81971,f2(a899))),x81972)) % 112.37/112.11 [8198]E(f317(x81981,f328(x81982,x81981,x81983)),x81982)+~P1(f317(f317(f224(a1),x81982),f317(x81981,x81983)))+P1(f317(f317(f225(a899),f329(x81982,x81981,x81983)),x81983))+~P1(f317(f317(f224(a1),f317(x81981,f2(a899))),x81982)) % 112.37/112.11 [8300]~P1(f317(f29(x83001),x83003))+~P1(f317(f317(f225(a899),f317(f30(x83001),x83002)),f317(f30(x83001),x83003)))+~P1(f317(f317(f224(f906(x83001,a895)),x83002),x83003))+P1(f317(f317(f225(f906(x83001,a895)),x83002),x83003)) % 112.37/112.11 [8327]E(f317(f317(f74(a1),f354(x83273,x83271,x83272)),f355(x83273,x83271,x83272)),x83271)+E(f317(f317(f3(a1),x83271),x83272),x83271)+~P1(f317(f317(f225(a1),f2(a1)),x83272))+~P1(f317(f317(f319(a1),f317(f317(f3(a1),x83271),f72(a1))),x83273)) % 112.37/112.11 [8328]E(f317(f317(f3(a1),f361(x83283,x83281,x83282)),f362(x83283,x83281,x83282)),x83281)+E(f317(f317(f74(a1),x83281),x83282),x83281)+~P1(f317(f317(f225(a1),f2(a1)),x83282))+~P1(f317(f317(f319(a1),f317(f317(f74(a1),x83281),f72(a1))),x83283)) % 112.37/112.11 [8380]~P1(f317(f317(f224(a899),x83803),x83801))+P1(f317(f317(f224(a899),x83801),x83802))+~P1(f317(f317(f224(a899),x83803),x83802))+~P1(f317(f317(f224(a899),f317(f317(f3(a899),x83801),x83803)),f317(f317(f3(a899),x83802),x83803))) % 112.37/112.11 [8381]~P1(f317(f317(f224(a899),x83813),x83811))+P1(f317(f317(f225(a899),x83811),x83812))+~P1(f317(f317(f224(a899),x83813),x83812))+~P1(f317(f317(f225(a899),f317(f317(f3(a899),x83811),x83813)),f317(f317(f3(a899),x83812),x83813))) % 112.37/112.11 [8400]~P108(x84002)+E(x84001,f103(x84002))+~P13(x84002,f317(f158(x84002),x84001))+E(f317(f132(x84002,x84002,f317(f9(x84002,x84002,x84002),f223(x84002)),x84003),f317(f158(x84002),x84001)),f317(f317(f223(x84002),f317(f317(f154(x84002),x84001),f2(a899))),x84003)) % 112.37/112.11 [8469]E(f317(f317(f3(a1),x84691),x84692),x84691)+~P1(f317(f317(f225(a1),f2(a1)),x84692))+P1(f317(f317(f319(a1),f354(x84693,x84691,x84692)),x84693))+~P1(f317(f317(f319(a1),f317(f317(f3(a1),x84691),f72(a1))),x84693)) % 112.37/112.11 [8470]E(f317(f317(f74(a1),x84701),x84702),x84701)+~P1(f317(f317(f225(a1),f2(a1)),x84702))+P1(f317(f317(f319(a1),f361(x84703,x84701,x84702)),x84703))+~P1(f317(f317(f319(a1),f317(f317(f74(a1),x84701),f72(a1))),x84703)) % 112.37/112.11 [8543]~P1(f317(f317(f224(a1),x85431),f317(x85432,x85433)))+P1(f317(f317(f225(a899),f892(x85431,x85432,x85433)),x85433))+P1(f317(f317(f224(a899),f327(x85431,x85432,x85433)),x85433))+~P1(f317(f317(f224(a1),f317(x85432,f2(a899))),x85431)) % 112.37/112.11 [8544]~P1(f317(f317(f224(a1),x85441),f317(x85442,x85443)))+P1(f317(f317(f225(a899),f329(x85441,x85442,x85443)),x85443))+P1(f317(f317(f224(a899),f328(x85441,x85442,x85443)),x85443))+~P1(f317(f317(f224(a1),f317(x85442,f2(a899))),x85441)) % 112.37/112.11 [8616]E(f317(f317(f3(a1),x86161),x86162),x86161)+~P1(f317(f317(f225(a1),f2(a1)),x86162))+P1(f317(f317(f319(a1),f355(x86163,x86161,x86162)),f293(a1,f72(a1),x86162)))+~P1(f317(f317(f319(a1),f317(f317(f3(a1),x86161),f72(a1))),x86163)) % 112.37/112.11 [8617]E(f317(f317(f74(a1),x86171),x86172),x86171)+~P1(f317(f317(f225(a1),f2(a1)),x86172))+P1(f317(f317(f319(a1),f362(x86173,x86171,x86172)),f293(a1,f72(a1),x86172)))+~P1(f317(f317(f319(a1),f317(f317(f74(a1),x86171),f72(a1))),x86173)) % 112.37/112.11 [8750]~P126(x87501)+~P1(f317(f317(f225(x87501),x87502),f72(x87501)))+~P1(f317(f317(f225(x87501),f2(x87501)),x87502))+P1(f317(f317(f225(x87501),f317(f317(f75(x87501),x87502),f317(f317(f234(x87501),x87502),x87503))),f317(f317(f234(x87501),x87502),x87503))) % 112.37/112.11 [8843]~P1(f317(x88431,x88432))+P1(f317(x88431,f2(a899)))+~P1(f317(f317(f225(a899),x88432),x88433))+~P1(f317(x88431,f41(a899,f317(a102,f376(x88432,x88431,x88433)),x88433))) % 112.37/112.11 [8995]E(f460(x89951,x89952,x89953),f2(a899))+P1(f317(f317(x89951,x89953),x89952))+P1(f317(f317(x89951,f460(x89951,x89952,x89953)),f41(a899,f459(x89951,x89952,x89953),f460(x89951,x89952,x89953))))+~P1(f317(f305(f905(a899,a899),a209),f317(f317(f242(a899,a899),x89953),x89952))) % 112.37/112.11 [9031]~P24(x90311,x90311,x90312,x90313)+E(f317(f300(x90311,x90311,x90312),x90313),x90313)+~P1(f317(f29(x90311),x90313))+~P1(f317(f317(f224(f906(x90311,a895)),f317(f300(x90311,x90311,x90312),x90313)),x90313)) % 112.37/112.11 [9246]P1(f317(f317(x92461,x92462),x92463))+P1(f317(f317(f225(a1),f753(x92461,x92463,x92462)),f754(x92461,x92463,x92462)))+P1(f317(f317(x92461,f753(x92461,x92463,x92462)),f317(f317(f74(a1),f754(x92461,x92463,x92462)),f72(a1))))+~P1(f317(f305(f905(a1,a1),a123),f317(f317(f242(a1,a1),x92462),x92463))) % 112.37/112.11 [9263]P1(f317(f317(x92631,x92632),x92633))+~P1(f317(f317(f225(a1),f458(x92631,x92633,x92632)),f2(a1)))+P1(f317(f317(x92631,f317(f73(a1),f456(x92631,x92633,x92632))),f317(f73(a1),f458(x92631,x92633,x92632))))+~P1(f317(f305(f905(a1,a1),a211),f317(f317(f242(a1,a1),x92632),x92633))) % 112.37/112.11 [9455]P1(f317(f317(x94551,x94552),x94553))+P1(f317(f317(x94551,f317(f317(f74(a1),f657(x94551,x94553,x94552)),f72(a1))),f659(x94551,x94553,x94552)))+~P1(f317(f317(f224(a1),f657(x94551,x94553,x94552)),f659(x94551,x94553,x94552)))+~P1(f317(f305(f905(a1,a1),a172),f317(f317(f242(a1,a1),x94552),x94553))) % 112.37/112.11 [9900]~P60(x99002)+~P60(x99001)+~P1(f317(f52(f905(x99001,x99002)),x99003))+P1(f317(f52(x99001),f317(f317(f10(f906(x99002,a895),a895,x99001),f52(x99002)),f317(f317(f10(f906(x99002,f905(x99001,x99002)),f906(x99002,a895),x99001),f317(f10(f905(x99001,x99002),a895,x99002),x99003)),f242(x99001,x99002))))) % 112.37/112.11 [9901]~P60(x99012)+~P60(x99011)+~P1(f317(f53(f905(x99011,x99012)),x99013))+P1(f317(f53(x99011),f317(f317(f10(f906(x99012,a895),a895,x99011),f53(x99012)),f317(f317(f10(f906(x99012,f905(x99011,x99012)),f906(x99012,a895),x99011),f317(f10(f905(x99011,x99012),a895,x99012),x99013)),f242(x99011,x99012))))) % 112.37/112.11 [9995]~P60(x99952)+~P60(x99951)+P1(f317(f52(f905(x99951,x99952)),x99953))+~P1(f317(f52(x99951),f317(f317(f10(f906(x99952,a895),a895,x99951),f52(x99952)),f317(f317(f10(f906(x99952,f905(x99951,x99952)),f906(x99952,a895),x99951),f317(f10(f905(x99951,x99952),a895,x99952),x99953)),f242(x99951,x99952))))) % 112.37/112.11 [9996]~P60(x99962)+~P60(x99961)+P1(f317(f53(f905(x99961,x99962)),x99963))+~P1(f317(f53(x99961),f317(f317(f10(f906(x99962,a895),a895,x99961),f53(x99962)),f317(f317(f10(f906(x99962,f905(x99961,x99962)),f906(x99962,a895),x99961),f317(f10(f905(x99961,x99962),a895,x99962),x99963)),f242(x99961,x99962))))) % 112.37/112.11 [10170]E(f317(x101701,f327(x101702,x101701,x101703)),x101702)+~P1(f317(f317(f224(a1),x101702),f317(x101701,x101703)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f3(a1),f317(x101701,f317(f317(f74(a899),f892(x101702,x101701,x101703)),f72(a899)))),f317(x101701,f892(x101702,x101701,x101703))))),f72(a1)))+~P1(f317(f317(f224(a1),f317(x101701,f2(a899))),x101702)) % 112.37/112.11 [10171]E(f317(x101711,f328(x101712,x101711,x101713)),x101712)+~P1(f317(f317(f224(a1),x101712),f317(x101711,x101713)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f3(a1),f317(x101711,f317(f317(f74(a899),f329(x101712,x101711,x101713)),f72(a899)))),f317(x101711,f329(x101712,x101711,x101713))))),f72(a1)))+~P1(f317(f317(f224(a1),f317(x101711,f2(a899))),x101712)) % 112.37/112.11 [10174]~P1(f317(f317(f224(a1),x101741),f317(x101742,x101743)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f3(a1),f317(x101742,f317(f317(f74(a899),f892(x101741,x101742,x101743)),f72(a899)))),f317(x101742,f892(x101741,x101742,x101743))))),f72(a1)))+P1(f317(f317(f224(a899),f327(x101741,x101742,x101743)),x101743))+~P1(f317(f317(f224(a1),f317(x101742,f2(a899))),x101741)) % 112.37/112.11 [10175]~P1(f317(f317(f224(a1),x101751),f317(x101752,x101753)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f3(a1),f317(x101752,f317(f317(f74(a899),f329(x101751,x101752,x101753)),f72(a899)))),f317(x101752,f329(x101751,x101752,x101753))))),f72(a1)))+P1(f317(f317(f224(a899),f328(x101751,x101752,x101753)),x101753))+~P1(f317(f317(f224(a1),f317(x101752,f2(a899))),x101751)) % 112.37/112.11 [10232]E(x102321,x102322)+~E(f317(f132(f900(x102323),f900(x102323),f124(x102323),f103(x102323)),x102321),f317(f132(f900(x102323),f900(x102323),f124(x102323),f103(x102323)),x102322))+~E(f317(f179(f900(f900(x102323))),x102321),f317(f179(f900(f900(x102323))),x102322))+~P1(f317(f317(f247(f900(x102323),f900(x102323),a895),f317(f317(f9(f900(x102323),f906(f900(x102323),a899),f906(f900(x102323),a895)),f317(f317(f10(f906(a899,a895),f906(f906(f900(x102323),a899),f906(f900(x102323),a895)),f900(x102323)),f10(a899,a895,f900(x102323))),f317(f317(f10(a899,f906(a899,a895),f900(x102323)),a314),f179(f900(x102323))))),f179(f900(x102323)))),f685(x102322,x102321,x102323))) % 112.37/112.11 [10233]E(x102331,x102332)+~E(f317(f132(f900(x102333),f900(x102333),f124(x102333),f103(x102333)),x102331),f317(f132(f900(x102333),f900(x102333),f124(x102333),f103(x102333)),x102332))+~E(f317(f179(f900(f900(x102333))),x102331),f317(f179(f900(f900(x102333))),x102332))+~P1(f317(f317(f247(f900(x102333),f900(x102333),a895),f317(f317(f9(f900(x102333),f906(f900(x102333),a899),f906(f900(x102333),a895)),f317(f317(f10(f906(a899,a895),f906(f906(f900(x102333),a899),f906(f900(x102333),a895)),f900(x102333)),f10(a899,a895,f900(x102333))),f317(f317(f10(a899,f906(a899,a895),f900(x102333)),a314),f179(f900(x102333))))),f179(f900(x102333)))),f686(x102331,x102332,x102333))) % 112.37/112.11 [6926]~E(f72(a899),f2(a899))+~P1(f317(f29(x69261),x69263))+~P1(f317(f29(x69261),x69262))+E(f317(f317(f74(a899),f317(f30(x69261),x69262)),f317(f30(x69261),x69263)),f317(f30(x69261),f317(f317(f91(f906(x69261,a895)),x69262),x69263))) % 112.37/112.11 [7343]~P108(x73431)+~P1(f317(f29(x73431),x73432))+~P1(f317(f317(f319(x73431),x73433),x73432))+P1(f317(f317(f224(x73431),f317(f58(x73431,f228(x73431)),x73432)),x73433)) % 112.37/112.11 [7344]~P104(x73441)+~P1(f317(f29(x73441),x73442))+~P1(f317(f317(f319(x73441),x73443),x73442))+P1(f317(f317(f224(x73441),f317(f58(x73441,f92(x73441)),x73442)),x73443)) % 112.37/112.11 [7596]~P1(f317(f29(x75961),x75963))+~P1(f317(f29(x75961),x75962))+~E(f317(f317(f92(f906(x75961,a895)),x75962),x75963),f178(f906(x75961,a895)))+E(f317(f317(f74(a899),f317(f30(x75961),x75962)),f317(f30(x75961),x75963)),f317(f30(x75961),f317(f317(f91(f906(x75961,a895)),x75962),x75963))) % 112.37/112.11 [8386]~P36(x83861,x83863)+~P36(x83861,x83862)+~E(f317(f317(f92(f906(x83861,a895)),f317(f254(x83861,x83861),x83862)),f317(f274(x83861,x83861),x83863)),f178(f906(x83861,a895)))+P36(x83861,f317(f317(f91(f906(f905(x83861,x83861),a895)),x83862),x83863)) % 112.37/112.11 [8481]E(x84811,f317(f317(f31(a899),x84812),x84813))+~P1(f317(f317(f225(a899),f2(a899)),x84813))+~P1(f317(f317(f225(a899),x84812),f317(f317(f75(a899),x84813),f317(a102,x84811))))+~P1(f317(f317(f224(a899),f317(f317(f75(a899),x84813),x84811)),x84812)) % 112.37/112.11 [8614]~P1(f317(f29(x86141),x86142))+~P1(f317(f29(x86141),x86143))+E(f317(f317(f74(a899),f317(f30(x86141),x86142)),f317(f30(x86141),x86143)),f317(f30(x86141),f317(f317(f91(f906(x86141,a895)),x86142),x86143)))+P1(f317(f317(f319(x86141),f411(x86143,x86142,x86141)),f317(f317(f92(f906(x86141,a895)),x86142),x86143))) % 112.37/112.11 [9007]~P127(x90072)+~E(x90071,f2(x90072))+~E(x90073,f2(x90072))+~P1(f317(f317(f225(x90072),f2(x90072)),f317(f317(f74(x90072),f317(f317(f75(x90072),x90073),x90073)),f317(f317(f75(x90072),x90071),x90071)))) % 112.37/112.11 [9536]~P36(x95361,x95363)+~P36(x95361,x95362)+P36(x95361,f317(f317(f91(f906(f905(x95361,x95361),a895)),x95362),x95363))+~P1(f317(f317(f224(f906(f905(x95361,x95361),a895)),f317(f317(f279(x95361,x95361,x95361),x95362),x95363)),x95362)) % 112.37/112.11 [9674]~P1(f317(x96741,x96743))+~P1(f317(f29(x96742),x96743))+P1(f317(x96741,f178(f906(x96742,a895))))+~P1(f317(x96741,f317(f317(f3(f906(x96742,a895)),f406(x96741,x96743,x96742)),f317(f317(f299(x96742),f400(x96741,x96743,x96742)),f178(f906(x96742,a895)))))) % 112.37/112.11 [8790]~P1(f317(f317(f225(a1),f2(a1)),x87903))+P1(f317(f317(f224(a1),f2(a1)),x87901))+~P1(f317(f317(f225(a1),x87902),x87903))+~P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),f317(f317(f75(a1),x87903),x87901)),x87902))) % 112.37/112.11 [8814]~P108(x88141)+~P1(f317(f29(x88141),x88142))+E(f317(f317(f3(f906(x88141,a895)),x88142),f317(f317(f299(x88141),x88143),f178(f906(x88141,a895)))),f178(f906(x88141,a895)))+E(f317(f317(f223(x88141),x88143),f16(x88141,f317(f317(f3(f906(x88141,a895)),x88142),f317(f317(f299(x88141),x88143),f178(f906(x88141,a895)))))),f16(x88141,f317(f317(f299(x88141),x88143),x88142))) % 112.37/112.11 [8815]~P108(x88151)+~P1(f317(f29(x88151),x88152))+E(f317(f317(f3(f906(x88151,a895)),x88152),f317(f317(f299(x88151),x88153),f178(f906(x88151,a895)))),f178(f906(x88151,a895)))+E(f317(f317(f228(x88151),x88153),f17(x88151,f317(f317(f3(f906(x88151,a895)),x88152),f317(f317(f299(x88151),x88153),f178(f906(x88151,a895)))))),f17(x88151,f317(f317(f299(x88151),x88153),x88152))) % 112.37/112.11 [8816]~P99(x88161)+~P1(f317(f29(x88161),x88162))+E(f317(f317(f3(f906(x88161,a895)),x88162),f317(f317(f299(x88161),x88163),f178(f906(x88161,a895)))),f178(f906(x88161,a895)))+E(f317(f317(f91(x88161),x88163),f12(x88161,f317(f317(f3(f906(x88161,a895)),x88162),f317(f317(f299(x88161),x88163),f178(f906(x88161,a895)))))),f12(x88161,f317(f317(f299(x88161),x88163),x88162))) % 112.37/112.11 [8817]~P99(x88171)+~P1(f317(f29(x88171),x88172))+E(f317(f317(f3(f906(x88171,a895)),x88172),f317(f317(f299(x88171),x88173),f178(f906(x88171,a895)))),f178(f906(x88171,a895)))+E(f317(f317(f92(x88171),x88173),f13(x88171,f317(f317(f3(f906(x88171,a895)),x88172),f317(f317(f299(x88171),x88173),f178(f906(x88171,a895)))))),f13(x88171,f317(f317(f299(x88171),x88173),x88172))) % 112.37/112.11 [8889]~P108(x88891)+~P1(f317(f29(x88891),x88892))+E(f317(f317(f3(f906(x88891,a895)),x88892),f317(f317(f299(x88891),x88893),f178(f906(x88891,a895)))),f178(f906(x88891,a895)))+E(f317(f317(f223(x88891),x88893),f14(x88891,f223(x88891),f317(f317(f3(f906(x88891,a895)),x88892),f317(f317(f299(x88891),x88893),f178(f906(x88891,a895)))))),f14(x88891,f223(x88891),f317(f317(f299(x88891),x88893),x88892))) % 112.37/112.11 [8890]~P108(x88901)+~P1(f317(f29(x88901),x88902))+E(f317(f317(f3(f906(x88901,a895)),x88902),f317(f317(f299(x88901),x88903),f178(f906(x88901,a895)))),f178(f906(x88901,a895)))+E(f317(f317(f228(x88901),x88903),f15(x88901,f228(x88901),f317(f317(f3(f906(x88901,a895)),x88902),f317(f317(f299(x88901),x88903),f178(f906(x88901,a895)))))),f15(x88901,f228(x88901),f317(f317(f299(x88901),x88903),x88902))) % 112.37/112.11 [9474]E(x94741,x94742)+~E(f317(f132(f900(x94743),f900(x94743),f124(x94743),f103(x94743)),x94741),f317(f132(f900(x94743),f900(x94743),f124(x94743),f103(x94743)),x94742))+~E(f317(f179(f900(f900(x94743))),x94741),f317(f179(f900(f900(x94743))),x94742))+P1(f317(f317(f319(f905(f900(x94743),f900(x94743))),f685(x94742,x94741,x94743)),f317(f162(f905(f900(x94743),f900(x94743))),f317(f317(f171(f900(x94743),f900(x94743)),x94741),x94742)))) % 112.37/112.11 [9475]E(x94751,x94752)+~E(f317(f132(f900(x94753),f900(x94753),f124(x94753),f103(x94753)),x94751),f317(f132(f900(x94753),f900(x94753),f124(x94753),f103(x94753)),x94752))+~E(f317(f179(f900(f900(x94753))),x94751),f317(f179(f900(f900(x94753))),x94752))+P1(f317(f317(f319(f905(f900(x94753),f900(x94753))),f686(x94751,x94752,x94753)),f317(f162(f905(f900(x94753),f900(x94753))),f317(f317(f171(f900(x94753),f900(x94753)),x94752),x94751)))) % 112.37/112.11 [10341]~P78(x103412)+E(x103411,f178(f906(x103412,a895)))+~P1(f317(f29(x103412),x103411))+E(f16(x103412,f317(f252(x103412),f317(f317(f10(f906(x103412,a895),a895,x103412),f81(x103412)),f317(f317(f9(x103412,f906(x103412,a895),f906(x103412,a895)),f317(f317(f10(f906(x103412,f906(a895,a895)),f906(f906(x103412,a895),f906(x103412,a895)),x103412),f20(x103412,a895,a895)),f317(f317(f10(f906(x103412,a895),f906(x103412,f906(a895,a895)),x103412),f317(f10(a895,f906(a895,a895),x103412),a315)),f317(f317(f9(x103412,f906(x103412,x103412),f906(x103412,a895)),f317(f317(f10(f906(x103412,a895),f906(f906(x103412,x103412),f906(x103412,a895)),x103412),f10(x103412,a895,x103412)),a314)),f317(f74(x103412),x103413))))),f317(f317(f9(x103412,f906(x103412,a895),a895),f319(x103412)),x103411))))),f317(f317(f74(x103412),x103413),f16(x103412,x103411))) % 112.37/112.11 [10342]~P78(x103422)+E(x103421,f178(f906(x103422,a895)))+~P1(f317(f29(x103422),x103421))+E(f17(x103422,f317(f252(x103422),f317(f317(f10(f906(x103422,a895),a895,x103422),f81(x103422)),f317(f317(f9(x103422,f906(x103422,a895),f906(x103422,a895)),f317(f317(f10(f906(x103422,f906(a895,a895)),f906(f906(x103422,a895),f906(x103422,a895)),x103422),f20(x103422,a895,a895)),f317(f317(f10(f906(x103422,a895),f906(x103422,f906(a895,a895)),x103422),f317(f10(a895,f906(a895,a895),x103422),a315)),f317(f317(f9(x103422,f906(x103422,x103422),f906(x103422,a895)),f317(f317(f10(f906(x103422,a895),f906(f906(x103422,x103422),f906(x103422,a895)),x103422),f10(x103422,a895,x103422)),a314)),f317(f74(x103422),x103423))))),f317(f317(f9(x103422,f906(x103422,a895),a895),f319(x103422)),x103421))))),f317(f317(f74(x103422),x103423),f17(x103422,x103421))) % 112.37/112.11 [10343]~P103(x103432)+E(x103431,f178(f906(x103432,a895)))+~P1(f317(f29(x103432),x103431))+E(f13(x103432,f317(f252(x103432),f317(f317(f10(f906(x103432,a895),a895,x103432),f81(x103432)),f317(f317(f9(x103432,f906(x103432,a895),f906(x103432,a895)),f317(f317(f10(f906(x103432,f906(a895,a895)),f906(f906(x103432,a895),f906(x103432,a895)),x103432),f20(x103432,a895,a895)),f317(f317(f10(f906(x103432,a895),f906(x103432,f906(a895,a895)),x103432),f317(f10(a895,f906(a895,a895),x103432),a315)),f317(f317(f9(x103432,f906(x103432,x103432),f906(x103432,a895)),f317(f317(f10(f906(x103432,a895),f906(f906(x103432,x103432),f906(x103432,a895)),x103432),f10(x103432,a895,x103432)),a314)),f317(f91(x103432),x103433))))),f317(f317(f9(x103432,f906(x103432,a895),a895),f319(x103432)),x103431))))),f317(f317(f91(x103432),x103433),f13(x103432,x103431))) % 112.37/112.11 [10344]~P103(x103442)+E(x103441,f178(f906(x103442,a895)))+~P1(f317(f29(x103442),x103441))+E(f12(x103442,f317(f252(x103442),f317(f317(f10(f906(x103442,a895),a895,x103442),f81(x103442)),f317(f317(f9(x103442,f906(x103442,a895),f906(x103442,a895)),f317(f317(f10(f906(x103442,f906(a895,a895)),f906(f906(x103442,a895),f906(x103442,a895)),x103442),f20(x103442,a895,a895)),f317(f317(f10(f906(x103442,a895),f906(x103442,f906(a895,a895)),x103442),f317(f10(a895,f906(a895,a895),x103442),a315)),f317(f317(f9(x103442,f906(x103442,x103442),f906(x103442,a895)),f317(f317(f10(f906(x103442,a895),f906(f906(x103442,x103442),f906(x103442,a895)),x103442),f10(x103442,a895,x103442)),a314)),f317(f92(x103442),x103443))))),f317(f317(f9(x103442,f906(x103442,a895),a895),f319(x103442)),x103441))))),f317(f317(f92(x103442),x103443),f12(x103442,x103441))) % 112.37/112.11 [10345]~P108(x103452)+E(x103451,f178(f906(x103452,a895)))+~P1(f317(f29(x103452),x103451))+E(f14(x103452,f223(x103452),f317(f252(x103452),f317(f317(f10(f906(x103452,a895),a895,x103452),f81(x103452)),f317(f317(f9(x103452,f906(x103452,a895),f906(x103452,a895)),f317(f317(f10(f906(x103452,f906(a895,a895)),f906(f906(x103452,a895),f906(x103452,a895)),x103452),f20(x103452,a895,a895)),f317(f317(f10(f906(x103452,a895),f906(x103452,f906(a895,a895)),x103452),f317(f10(a895,f906(a895,a895),x103452),a315)),f317(f317(f9(x103452,f906(x103452,x103452),f906(x103452,a895)),f317(f317(f10(f906(x103452,a895),f906(f906(x103452,x103452),f906(x103452,a895)),x103452),f10(x103452,a895,x103452)),a314)),f317(f228(x103452),x103453))))),f317(f317(f9(x103452,f906(x103452,a895),a895),f319(x103452)),x103451))))),f317(f317(f228(x103452),x103453),f14(x103452,f223(x103452),x103451))) % 112.37/112.11 [10346]~P108(x103462)+E(x103461,f178(f906(x103462,a895)))+~P1(f317(f29(x103462),x103461))+E(f15(x103462,f228(x103462),f317(f252(x103462),f317(f317(f10(f906(x103462,a895),a895,x103462),f81(x103462)),f317(f317(f9(x103462,f906(x103462,a895),f906(x103462,a895)),f317(f317(f10(f906(x103462,f906(a895,a895)),f906(f906(x103462,a895),f906(x103462,a895)),x103462),f20(x103462,a895,a895)),f317(f317(f10(f906(x103462,a895),f906(x103462,f906(a895,a895)),x103462),f317(f10(a895,f906(a895,a895),x103462),a315)),f317(f317(f9(x103462,f906(x103462,x103462),f906(x103462,a895)),f317(f317(f10(f906(x103462,a895),f906(f906(x103462,x103462),f906(x103462,a895)),x103462),f10(x103462,a895,x103462)),a314)),f317(f223(x103462),x103463))))),f317(f317(f9(x103462,f906(x103462,a895),a895),f319(x103462)),x103461))))),f317(f317(f223(x103462),x103463),f15(x103462,f228(x103462),x103461))) % 112.37/112.11 [10059]~P112(x100591)+~E(x100593,f2(x100591))+~E(x100592,f2(x100591))+E(f317(f317(f74(x100591),f317(f317(f234(x100591),x100592),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x100591),x100593),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f2(x100591)) % 112.37/112.11 [10213]~P126(x102131)+~P1(f317(f317(f224(x102131),f2(x102131)),x102133))+P1(f317(f317(f224(x102131),x102132),x102133))+~P1(f317(f317(f224(x102131),f317(f317(f234(x102131),x102132),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102131),x102133),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))))) % 112.37/112.11 [10270]~P112(x102702)+~E(x102701,f2(x102702))+~E(x102703,f2(x102702))+~P1(f317(f317(f225(x102702),f2(x102702)),f317(f317(f74(x102702),f317(f317(f234(x102702),x102703),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102702),x102701),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))))) % 112.37/112.11 [6804]~P7(x68043,x68042)+~P1(f317(x68041,x68044))+~P1(f317(f317(f319(x68043),x68044),f260(x68043,x68042)))+P1(f317(x68041,f803(x68041,x68042,x68043))) % 112.37/112.11 [8725]P25(x87251,x87252,f807(x87253,x87252,x87254,x87251),x87254,x87253)+~E(f317(f30(x87251),x87254),f317(f30(x87252),x87253))+~P1(f317(f29(x87252),x87253))+~P1(f317(f29(x87251),x87254)) % 112.37/112.11 [9437]E(x94371,x94372)+~E(f629(x94371,x94372,x94374,x94373),f631(x94371,x94372,x94374,x94373))+P1(f317(f317(f319(f905(f900(x94373),f900(x94373))),f317(f317(f242(f900(x94373),f900(x94373)),x94372),x94371)),f137(x94373,x94374)))+P1(f317(f317(f319(f905(f900(x94373),f900(x94373))),f317(f317(f242(f900(x94373),f900(x94373)),x94371),x94372)),f137(x94373,x94374))) % 112.37/112.11 [4918]~P61(x49182)+~E(x49184,f2(x49182))+~E(x49181,f2(x49182))+E(x49181,f317(f317(f281(x49182),x49183),x49184)) % 112.37/112.11 [4919]~P61(x49191)+~E(x49193,f2(x49191))+~E(x49194,f2(x49191))+E(f317(f317(f281(x49191),x49192),x49193),x49194) % 112.37/112.11 [5039]~P61(x50392)+E(x50391,f2(x50392))+~E(x50393,f2(x50392))+~E(x50391,f317(f317(f281(x50392),x50394),x50393)) % 112.37/112.11 [5040]~P61(x50402)+E(x50401,f2(x50402))+~E(x50403,f2(x50402))+~E(f317(f317(f281(x50402),x50404),x50403),x50401) % 112.37/112.11 [5223]~P123(x52232)+E(x52231,f2(x52232))+~E(f317(f317(f281(x52232),x52233),x52231),x52234)+E(x52233,f317(f317(f75(x52232),x52234),x52231)) % 112.37/112.11 [5225]~P123(x52252)+E(x52251,f2(x52252))+~E(f317(f317(f75(x52252),x52253),x52251),x52254)+E(x52253,f317(f317(f281(x52252),x52254),x52251)) % 112.37/112.11 [5226]~P61(x52262)+E(x52261,f2(x52262))+~E(f317(f317(f281(x52262),x52263),x52261),x52264)+E(x52263,f317(f317(f75(x52262),x52264),x52261)) % 112.37/112.11 [5227]~P61(x52272)+E(x52271,f2(x52272))+~E(f317(f317(f75(x52272),x52273),x52271),x52274)+E(x52273,f317(f317(f281(x52272),x52274),x52271)) % 112.37/112.11 [5228]~P123(x52282)+E(x52281,f2(x52282))+~E(x52283,f317(f317(f281(x52282),x52284),x52281))+E(f317(f317(f75(x52282),x52283),x52281),x52284) % 112.37/112.11 [5230]~P123(x52302)+E(x52301,f2(x52302))+~E(x52303,f317(f317(f75(x52302),x52304),x52301))+E(f317(f317(f281(x52302),x52303),x52301),x52304) % 112.37/112.11 [5231]~P61(x52312)+E(x52311,f2(x52312))+~E(x52313,f317(f317(f281(x52312),x52314),x52311))+E(f317(f317(f75(x52312),x52313),x52311),x52314) % 112.37/112.11 [5232]~P61(x52322)+E(x52321,f2(x52322))+~E(x52323,f317(f317(f75(x52322),x52324),x52321))+E(f317(f317(f281(x52322),x52323),x52321),x52324) % 112.37/112.11 [5256]~P61(x52562)+~E(x52561,f2(x52562))+~E(f317(f317(f75(x52562),x52561),x52564),x52563)+E(x52561,f317(f317(f281(x52562),x52563),x52564)) % 112.37/112.11 [5257]~P61(x52571)+~E(x52574,f2(x52571))+~E(x52572,f317(f317(f75(x52571),x52574),x52573))+E(f317(f317(f281(x52571),x52572),x52573),x52574) % 112.37/112.11 [5331]~E(x53313,x53314)+~E(x53312,x53313)+~P109(x53311)+E(f293(x53311,x53312,x53313),f317(f317(f299(x53311),x53314),f178(f906(x53311,a895)))) % 112.37/112.11 [5535]~E(f104(x55352,x55351),x55353)+~E(f134(x55352,x55351),x55354)+E(x55351,f103(x55352))+E(f317(f317(f124(x55352),x55353),f317(f317(f141(x55352),x55354),f103(x55352))),x55351) % 112.37/112.11 [6178]~P126(x61783)+E(x61781,x61782)+~E(f317(f317(f234(x61783),x61784),x61781),f317(f317(f234(x61783),x61784),x61782))+~P1(f317(f317(f225(x61783),f72(x61783)),x61784)) % 112.37/112.11 [6179]E(x61791,x61792)+~E(f317(f317(f299(x61793),x61794),x61791),f317(f317(f299(x61793),x61794),x61792))+P1(f317(f317(f319(x61793),x61794),x61792))+P1(f317(f317(f319(x61793),x61794),x61791)) % 112.37/112.11 [6222]E(f317(x62221,x62222),f72(a899))+~E(f317(f317(f11(x62223,a899),x62221),x62224),f72(a899))+~P1(f317(f29(x62223),x62224))+~P1(f317(f317(f319(x62223),x62222),x62224)) % 112.37/112.11 [6223]E(f317(x62231,x62232),f2(a899))+~E(f317(f317(f8(x62233,a899),x62231),x62234),f2(a899))+~P1(f317(f29(x62233),x62234))+~P1(f317(f317(f319(x62233),x62232),x62234)) % 112.37/112.11 [6450]~P109(x64501)+~P1(f317(f317(f224(x64501),x64504),x64503))+P1(f317(f317(f224(x64501),x64502),x64503))+~P1(f317(f317(f224(x64501),x64502),x64504)) % 112.37/112.11 [6451]~P65(x64511)+~P1(f317(f317(f224(x64511),x64512),x64514))+P1(f317(f317(f224(x64511),x64512),x64513))+~P1(f317(f317(f224(x64511),x64514),x64513)) % 112.37/112.11 [6452]~P109(x64521)+~P1(f317(f317(f225(x64521),x64524),x64523))+P1(f317(f317(f225(x64521),x64522),x64523))+~P1(f317(f317(f224(x64521),x64522),x64524)) % 112.37/112.11 [6453]~P109(x64531)+~P1(f317(f317(f225(x64531),x64532),x64534))+P1(f317(f317(f225(x64531),x64532),x64533))+~P1(f317(f317(f224(x64531),x64534),x64533)) % 112.37/112.11 [6454]~P109(x64541)+~P1(f317(f317(f225(x64541),x64544),x64543))+P1(f317(f317(f225(x64541),x64542),x64543))+~P1(f317(f317(f225(x64541),x64542),x64544)) % 112.37/112.11 [6455]~P65(x64551)+~P1(f317(f317(f225(x64551),x64552),x64554))+P1(f317(f317(f225(x64551),x64552),x64553))+~P1(f317(f317(f224(x64551),x64554),x64553)) % 112.37/112.11 [6456]~P65(x64561)+~P1(f317(f317(f225(x64561),x64564),x64563))+P1(f317(f317(f225(x64561),x64562),x64563))+~P1(f317(f317(f224(x64561),x64562),x64564)) % 112.37/112.11 [6457]~P65(x64571)+~P1(f317(f317(f225(x64571),x64572),x64574))+P1(f317(f317(f225(x64571),x64572),x64573))+~P1(f317(f317(f225(x64571),x64574),x64573)) % 112.37/112.11 [6458]~P119(x64581)+~P1(f317(f317(f277(x64581),x64582),x64584))+P1(f317(f317(f277(x64581),x64582),x64583))+~P1(f317(f317(f277(x64581),x64584),x64583)) % 112.37/112.11 [6540]~P34(x65404,x65403,x65402)+E(x65401,f739(x65402,x65403,x65404))+~P1(f317(x65403,x65401))+~P1(f317(f317(f319(x65404),x65401),f317(f162(x65404),x65402))) % 112.37/112.11 [6541]~P34(x65414,x65413,x65412)+E(x65411,f749(x65412,x65413,x65414))+~P1(f317(x65413,x65411))+~P1(f317(f317(f319(x65414),x65411),f317(f162(x65414),x65412))) % 112.37/112.11 [6695]~P5(x66951)+~P1(f317(f317(f224(x66951),x66952),f33(x66951,x66954)))+P1(f317(f317(f224(x66951),x66952),x66953))+~P1(f317(f317(f319(x66951),x66953),x66954)) % 112.37/112.11 [6846]~P108(x68461)+~P13(x68461,f317(f317(f141(x68461),x68462),x68464))+~P1(f317(f317(f319(x68461),x68463),f317(f162(x68461),x68464)))+P1(f317(f317(f224(x68461),x68462),x68463)) % 112.37/112.11 [6936]~P5(x69361)+~P1(f317(f317(f224(x69361),f32(x69361,x69364)),x69363))+P1(f317(f317(f224(x69361),x69362),x69363))+~P1(f317(f317(f319(x69361),x69362),x69364)) % 112.37/112.11 [7082]~P3(x70821)+P1(f317(f317(f277(x70821),x70822),f41(x70821,x70823,x70824)))+~P1(f317(f317(f277(x70821),x70822),x70824))+~P1(f317(f317(f277(x70821),x70822),x70823)) % 112.37/112.11 [7346]~P108(x73461)+E(f317(f317(f91(f906(x73461,a895)),f317(f292(x73461,x73462),x73463)),f317(f292(x73461,x73463),x73464)),f317(f292(x73461,x73462),x73464))+~P1(f317(f317(f224(x73461),x73463),x73464))+~P1(f317(f317(f224(x73461),x73462),x73463)) % 112.37/112.11 [7390]P34(x73901,x73902,x73903)+~E(f750(x73903,x73902,x73901,x73904),x73904)+~P1(f317(x73902,x73904))+~P1(f317(f317(f319(x73901),x73904),f317(f162(x73901),x73903))) % 112.37/112.11 [7391]P34(x73911,x73912,x73913)+~E(f758(x73913,x73912,x73911,x73914),x73914)+~P1(f317(x73912,x73914))+~P1(f317(f317(f319(x73911),x73914),f317(f162(x73911),x73913))) % 112.37/112.11 [7434]~P3(x74341)+~P1(f317(f317(f277(x74341),x74342),f41(x74341,x74343,x74344)))+P1(f317(f317(f277(x74341),x74342),x74343))+~P1(f317(f317(f277(x74341),x74342),x74344)) % 112.37/112.11 [7468]~P108(x74681)+E(f317(f317(f91(f906(x74681,a895)),f317(f292(x74681,x74682),x74683)),f293(x74681,x74683,x74684)),f293(x74681,x74682,x74684))+~P1(f317(f317(f224(x74681),x74683),x74684))+~P1(f317(f317(f224(x74681),x74682),x74683)) % 112.37/112.11 [7530]~P108(x75301)+E(f317(f317(f91(f906(x75301,a895)),f296(x75301,x75302,x75303)),f317(f292(x75301,x75303),x75304)),f296(x75301,x75302,x75304))+~P1(f317(f317(f224(x75301),x75303),x75304))+~P1(f317(f317(f225(x75301),x75302),x75303)) % 112.37/112.11 [7547]~P108(x75471)+E(f317(f317(f91(f906(x75471,a895)),f293(x75471,x75472,x75473)),f296(x75471,x75473,x75474)),f317(f292(x75471,x75472),x75474))+~P1(f317(f317(f224(x75471),x75472),x75473))+~P1(f317(f317(f225(x75471),x75473),x75474)) % 112.37/112.11 [7577]~P108(x75771)+E(f317(f317(f91(f906(x75771,a895)),f296(x75771,x75772,x75773)),f293(x75771,x75773,x75774)),f295(x75771,x75772,x75774))+~P1(f317(f317(f224(x75771),x75773),x75774))+~P1(f317(f317(f225(x75771),x75772),x75773)) % 112.37/112.11 [7578]~P108(x75781)+E(f317(f317(f91(f906(x75781,a895)),f293(x75781,x75782,x75783)),f295(x75781,x75783,x75784)),f293(x75781,x75782,x75784))+~P1(f317(f317(f224(x75781),x75783),x75784))+~P1(f317(f317(f224(x75781),x75782),x75783)) % 112.37/112.11 [7579]~P108(x75791)+E(f317(f317(f91(f906(x75791,a895)),f295(x75791,x75792,x75793)),f296(x75791,x75793,x75794)),f296(x75791,x75792,x75794))+~P1(f317(f317(f224(x75791),x75792),x75793))+~P1(f317(f317(f225(x75791),x75793),x75794)) % 112.37/112.11 [7580]~P108(x75801)+E(f317(f317(f91(f906(x75801,a895)),f295(x75801,x75802,x75803)),f295(x75801,x75803,x75804)),f295(x75801,x75802,x75804))+~P1(f317(f317(f224(x75801),x75803),x75804))+~P1(f317(f317(f224(x75801),x75802),x75803)) % 112.37/112.11 [8370]P24(x83701,x83702,f514(x83703,x83702,x83704,x83701),x83704)+~P1(f317(f29(x83702),x83703))+~P1(f317(f29(x83701),x83704))+~P1(f317(f317(f224(a899),f317(f30(x83701),x83704)),f317(f30(x83702),x83703))) % 112.37/112.11 [8391]P34(x83911,x83912,x83913)+~P1(f317(x83912,x83914))+P1(f317(x83912,f750(x83913,x83912,x83911,x83914)))+~P1(f317(f317(f319(x83911),x83914),f317(f162(x83911),x83913))) % 112.37/112.11 [8392]P34(x83921,x83922,x83923)+~P1(f317(x83922,x83924))+P1(f317(x83922,f758(x83923,x83922,x83921,x83924)))+~P1(f317(f317(f319(x83921),x83924),f317(f162(x83921),x83923))) % 112.37/112.11 [8446]~P75(x84461)+~E(f317(x84463,f432(x84463,x84464,x84462,x84461)),f72(x84461))+E(f317(f317(f317(f60(x84461,x84462,f75(x84461)),x84463),f72(x84461)),x84464),f72(x84461))+~P1(f317(f29(x84462),x84464)) % 112.37/112.11 [8714]~P126(x87141)+~P1(f317(f317(f224(x87141),f2(x87141)),x87143))+P1(f317(f317(f224(x87141),x87142),x87143))+~P1(f317(f317(f224(x87141),f317(f317(f234(x87141),x87142),f317(a102,x87144))),f317(f317(f234(x87141),x87143),f317(a102,x87144)))) % 112.37/112.11 [9032]P34(x90321,x90322,x90323)+~P1(f317(x90322,x90324))+~P1(f317(f317(f319(x90321),x90324),f317(f162(x90321),x90323)))+P1(f317(f317(f319(x90321),f750(x90323,x90322,x90321,x90324)),f317(f162(x90321),x90323))) % 112.37/112.11 [9033]P34(x90331,x90332,x90333)+~P1(f317(x90332,x90334))+~P1(f317(f317(f319(x90331),x90334),f317(f162(x90331),x90333)))+P1(f317(f317(f319(x90331),f758(x90333,x90332,x90331,x90334)),f317(f162(x90331),x90333))) % 112.37/112.11 [9109]~P75(x91091)+E(f317(f317(f317(f60(x91091,x91092,f75(x91091)),x91093),f72(x91091)),x91094),f72(x91091))+~P1(f317(f29(x91092),x91094))+P1(f317(f317(f319(x91092),f432(x91093,x91094,x91092,x91091)),x91094)) % 112.37/112.11 [9611]~P1(f317(f317(f277(a899),x96111),x96113))+~P1(f317(f317(f277(a899),x96111),x96112))+~P1(f317(f317(f277(a899),x96114),x96113))+~P1(f317(f317(f225(f906(a899,a895)),f280(a899,f277(a899),x96111,x96113)),f280(a899,f277(a899),x96112,x96114))) % 112.37/112.11 [9616]~P1(f317(f317(f224(a1),x96164),f2(a1)))+P1(f317(f317(f224(a1),f317(f317(f74(a1),f317(f317(f75(a1),x96161),f41(a1,x96162,x96163))),x96164)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x96163))+~P1(f317(f317(f225(a1),x96161),x96164)) % 112.37/112.11 [10052]~P1(f317(f29(x100521),x100522))+~P1(f317(f317(f319(x100521),x100524),x100522))+~P1(f317(f317(f319(x100521),x100523),x100522))+P1(f317(f317(f225(a899),f317(f30(x100521),f317(f317(f3(f906(x100521,a895)),f317(f317(f3(f906(x100521,a895)),x100522),f317(f317(f299(x100521),x100523),f178(f906(x100521,a895))))),f317(f317(f299(x100521),x100524),f178(f906(x100521,a895)))))),f317(f30(x100521),x100522))) % 112.37/112.11 [6994]~P146(x69943)+~P122(x69943)+P1(f317(x69941,f840(x69942,x69941,x69943)))+~P1(f317(x69941,f317(f317(f75(x69943),x69942),x69944))) % 112.37/112.11 [7054]~P108(x70541)+~P1(f317(f317(f224(x70541),x70542),x70544))+~P1(f317(f317(f224(x70541),x70542),x70543))+P1(f317(f317(f224(x70541),x70542),f317(f317(f228(x70541),x70543),x70544))) % 112.37/112.11 [7057]~P104(x70571)+~P1(f317(f317(f224(x70571),x70572),x70574))+~P1(f317(f317(f224(x70571),x70572),x70573))+P1(f317(f317(f224(x70571),x70572),f317(f317(f92(x70571),x70573),x70574))) % 112.37/112.11 [7058]~P108(x70581)+~P1(f317(f317(f225(x70581),x70582),x70584))+~P1(f317(f317(f225(x70581),x70582),x70583))+P1(f317(f317(f225(x70581),x70582),f317(f317(f228(x70581),x70583),x70584))) % 112.37/112.11 [7059]~P114(x70591)+~P1(f317(f317(f277(x70591),x70592),x70594))+~P1(f317(f317(f277(x70591),x70592),x70593))+P1(f317(f317(f277(x70591),x70592),f317(f317(f3(x70591),x70593),x70594))) % 112.37/112.11 [7060]~P119(x70601)+~P1(f317(f317(f277(x70601),x70602),x70604))+~P1(f317(f317(f277(x70601),x70602),x70603))+P1(f317(f317(f277(x70601),x70602),f317(f317(f74(x70601),x70603),x70604))) % 112.37/112.11 [7080]~P62(x70802)+E(x70801,f2(x70802))+E(f317(f317(f281(x70802),f317(f317(f234(x70802),x70801),x70803)),f317(f317(f234(x70802),x70801),x70804)),f317(f317(f234(x70802),x70801),f317(f317(f3(a899),x70803),x70804)))+~P1(f317(f317(f224(a899),x70804),x70803)) % 112.37/112.11 [7126]~P108(x71261)+~P13(x71261,f317(f317(f141(x71261),x71263),x71264))+P13(x71261,f317(f317(f141(x71261),x71262),f317(f317(f141(x71261),x71263),x71264)))+~P1(f317(f317(f224(x71261),x71262),x71263)) % 112.37/112.11 [7162]~P88(x71621)+~P1(f317(f317(f224(x71621),f2(x71621)),x71624))+~P1(f317(f317(f224(x71621),x71622),x71623))+P1(f317(f317(f224(x71621),x71622),f317(f317(f74(x71621),x71623),x71624))) % 112.37/112.11 [7163]~P88(x71631)+~P1(f317(f317(f224(x71631),f2(x71631)),x71633))+~P1(f317(f317(f224(x71631),x71632),x71634))+P1(f317(f317(f224(x71631),x71632),f317(f317(f74(x71631),x71633),x71634))) % 112.37/112.11 [7164]~P126(x71641)+~P1(f317(f317(f225(x71641),f2(x71641)),x71643))+~P1(f317(f317(f225(x71641),x71642),x71644))+P1(f317(f317(f225(x71641),x71642),f317(f317(f74(x71641),x71643),x71644))) % 112.37/112.11 [7165]~P88(x71651)+~P1(f317(f317(f224(x71651),x71652),x71654))+~P1(f317(f317(f225(x71651),f2(x71651)),x71653))+P1(f317(f317(f225(x71651),x71652),f317(f317(f74(x71651),x71653),x71654))) % 112.37/112.11 [7166]~P88(x71661)+~P1(f317(f317(f224(x71661),f2(x71661)),x71663))+~P1(f317(f317(f225(x71661),x71662),x71664))+P1(f317(f317(f225(x71661),x71662),f317(f317(f74(x71661),x71663),x71664))) % 112.37/112.11 [7207]~P108(x72071)+P1(f317(f317(f224(x72071),x72072),x72073))+P1(f317(f317(f224(x72071),x72072),x72074))+~P1(f317(f317(f224(x72071),x72072),f317(f317(f223(x72071),x72074),x72073))) % 112.37/112.11 [7208]~P108(x72081)+P1(f317(f317(f225(x72081),x72082),x72083))+P1(f317(f317(f225(x72081),x72082),x72084))+~P1(f317(f317(f225(x72081),x72082),f317(f317(f223(x72081),x72084),x72083))) % 112.37/112.11 [7502]~P109(x75022)+~P60(x75021)+~P1(f317(f317(f225(f906(x75021,x75022)),x75023),x75024))+P1(f317(f317(f224(f906(x75021,x75022)),x75023),x75024)) % 112.37/112.11 [7868]~P64(x78681)+~P1(f317(f317(f225(x78681),x78684),f2(x78681)))+~P1(f317(f317(f224(x78681),x78683),f317(f317(f281(x78681),x78682),x78684)))+P1(f317(f317(f224(x78681),x78682),f317(f317(f75(x78681),x78683),x78684))) % 112.37/112.11 [7869]~P64(x78691)+~P1(f317(f317(f225(x78691),x78694),f2(x78691)))+~P1(f317(f317(f224(x78691),x78693),f317(f317(f75(x78691),x78692),x78694)))+P1(f317(f317(f224(x78691),x78692),f317(f317(f281(x78691),x78693),x78694))) % 112.37/112.11 [7870]~P64(x78701)+~P1(f317(f317(f225(x78701),x78704),f2(x78701)))+~P1(f317(f317(f225(x78701),x78703),f317(f317(f281(x78701),x78702),x78704)))+P1(f317(f317(f225(x78701),x78702),f317(f317(f75(x78701),x78703),x78704))) % 112.37/112.11 [7871]~P64(x78711)+~P1(f317(f317(f225(x78711),x78714),f2(x78711)))+~P1(f317(f317(f225(x78711),x78713),f317(f317(f75(x78711),x78712),x78714)))+P1(f317(f317(f225(x78711),x78712),f317(f317(f281(x78711),x78713),x78714))) % 112.37/112.11 [7978]~P111(x79781)+~P1(f317(f317(f224(x79781),x79782),f2(x79781)))+~P1(f317(f317(f224(x79781),x79784),x79783))+P1(f317(f317(f224(x79781),f317(f317(f75(x79781),x79782),x79783)),f317(f317(f75(x79781),x79782),x79784))) % 112.37/112.11 [7979]~P127(x79791)+~P1(f317(f317(f225(x79791),x79792),f2(x79791)))+~P1(f317(f317(f224(x79791),x79794),x79793))+P1(f317(f317(f224(x79791),f317(f317(f75(x79791),x79792),x79793)),f317(f317(f75(x79791),x79792),x79794))) % 112.37/112.11 [7980]~P111(x79801)+~P1(f317(f317(f224(x79801),x79803),f2(x79801)))+~P1(f317(f317(f224(x79801),x79804),x79802))+P1(f317(f317(f224(x79801),f317(f317(f75(x79801),x79802),x79803)),f317(f317(f75(x79801),x79804),x79803))) % 112.37/112.11 [7981]~P63(x79811)+~P1(f317(f317(f224(x79811),x79813),f2(x79811)))+~P1(f317(f317(f224(x79811),x79814),x79812))+P1(f317(f317(f224(x79811),f317(f317(f281(x79811),x79812),x79813)),f317(f317(f281(x79811),x79814),x79813))) % 112.37/112.11 [7985]~P127(x79851)+~P1(f317(f317(f225(x79851),x79853),f2(x79851)))+~P1(f317(f317(f225(x79851),x79854),x79852))+P1(f317(f317(f225(x79851),f317(f317(f75(x79851),x79852),x79853)),f317(f317(f75(x79851),x79854),x79853))) % 112.37/112.11 [7986]~P127(x79861)+~P1(f317(f317(f225(x79861),x79862),f2(x79861)))+~P1(f317(f317(f225(x79861),x79864),x79863))+P1(f317(f317(f225(x79861),f317(f317(f75(x79861),x79862),x79863)),f317(f317(f75(x79861),x79862),x79864))) % 112.37/112.11 [7987]~P64(x79871)+~P1(f317(f317(f225(x79871),x79873),f2(x79871)))+~P1(f317(f317(f225(x79871),x79874),x79872))+P1(f317(f317(f225(x79871),f317(f317(f281(x79871),x79872),x79873)),f317(f317(f281(x79871),x79874),x79873))) % 112.37/112.11 [7988]~P126(x79881)+~P1(f317(f317(f225(x79881),f72(x79881)),x79882))+~P1(f317(f317(f224(a899),x79883),x79884))+P1(f317(f317(f224(x79881),f317(f317(f234(x79881),x79882),x79883)),f317(f317(f234(x79881),x79882),x79884))) % 112.37/112.11 [7989]~P126(x79891)+~P1(f317(f317(f224(x79891),f72(x79891)),x79892))+~P1(f317(f317(f224(a899),x79893),x79894))+P1(f317(f317(f224(x79891),f317(f317(f234(x79891),x79892),x79893)),f317(f317(f234(x79891),x79892),x79894))) % 112.37/112.11 [7991]~P126(x79911)+~P1(f317(f317(f225(x79911),f72(x79911)),x79912))+~P1(f317(f317(f225(a899),x79913),x79914))+P1(f317(f317(f225(x79911),f317(f317(f234(x79911),x79912),x79913)),f317(f317(f234(x79911),x79912),x79914))) % 112.37/112.11 [8018]P1(f317(f317(f225(a899),f2(a899)),f317(x80181,x80182)))+~P1(f317(f29(x80183),x80184))+~P1(f317(f317(f319(x80183),x80182),x80184))+~P1(f317(f317(f225(a899),f2(a899)),f317(f317(f11(x80183,a899),x80181),x80184))) % 112.37/112.11 [8027]~P137(x80271)+~P1(f317(f317(f224(x80271),x80273),x80274))+~P1(f317(f317(f224(x80271),f2(x80271)),x80272))+P1(f317(f317(f224(x80271),f317(f317(f75(x80271),x80272),x80273)),f317(f317(f75(x80271),x80272),x80274))) % 112.37/112.11 [8028]~P136(x80281)+~P1(f317(f317(f224(x80281),x80283),x80284))+~P1(f317(f317(f224(x80281),f2(x80281)),x80282))+P1(f317(f317(f224(x80281),f317(f317(f75(x80281),x80282),x80283)),f317(f317(f75(x80281),x80282),x80284))) % 112.37/112.11 [8029]~P127(x80291)+~P1(f317(f317(f225(x80291),f2(x80291)),x80292))+~P1(f317(f317(f224(x80291),x80293),x80294))+P1(f317(f317(f224(x80291),f317(f317(f75(x80291),x80292),x80293)),f317(f317(f75(x80291),x80292),x80294))) % 112.37/112.11 [8030]~P137(x80301)+~P1(f317(f317(f224(x80301),x80302),x80304))+~P1(f317(f317(f224(x80301),f2(x80301)),x80303))+P1(f317(f317(f224(x80301),f317(f317(f75(x80301),x80302),x80303)),f317(f317(f75(x80301),x80304),x80303))) % 112.37/112.11 [8031]~P63(x80311)+~P1(f317(f317(f224(x80311),x80312),x80314))+~P1(f317(f317(f224(x80311),f2(x80311)),x80313))+P1(f317(f317(f224(x80311),f317(f317(f281(x80311),x80312),x80313)),f317(f317(f281(x80311),x80314),x80313))) % 112.37/112.11 [8032]~P126(x80321)+~P1(f317(f317(f224(x80321),x80322),x80324))+~P1(f317(f317(f224(x80321),f2(x80321)),x80322))+P1(f317(f317(f224(x80321),f317(f317(f234(x80321),x80322),x80323)),f317(f317(f234(x80321),x80324),x80323))) % 112.37/112.11 [8034]~P134(x80341)+~P1(f317(f317(f225(x80341),x80343),x80344))+~P1(f317(f317(f225(x80341),f2(x80341)),x80342))+P1(f317(f317(f225(x80341),f317(f317(f75(x80341),x80342),x80343)),f317(f317(f75(x80341),x80342),x80344))) % 112.37/112.11 [8035]~P120(x80351)+~P1(f317(f317(f225(x80351),x80353),x80354))+~P1(f317(f317(f225(x80351),f2(x80351)),x80352))+P1(f317(f317(f225(x80351),f317(f317(f75(x80351),x80352),x80353)),f317(f317(f75(x80351),x80352),x80354))) % 112.37/112.11 [8036]~P127(x80361)+~P1(f317(f317(f225(x80361),x80362),x80364))+~P1(f317(f317(f225(x80361),f2(x80361)),x80363))+P1(f317(f317(f225(x80361),f317(f317(f75(x80361),x80362),x80363)),f317(f317(f75(x80361),x80364),x80363))) % 112.37/112.11 [8037]~P134(x80371)+~P1(f317(f317(f225(x80371),x80372),x80374))+~P1(f317(f317(f225(x80371),f2(x80371)),x80373))+P1(f317(f317(f225(x80371),f317(f317(f75(x80371),x80372),x80373)),f317(f317(f75(x80371),x80374),x80373))) % 112.37/112.11 [8038]~P127(x80381)+~P1(f317(f317(f225(x80381),x80383),x80384))+~P1(f317(f317(f225(x80381),f2(x80381)),x80382))+P1(f317(f317(f225(x80381),f317(f317(f75(x80381),x80382),x80383)),f317(f317(f75(x80381),x80382),x80384))) % 112.37/112.11 [8039]~P64(x80391)+~P1(f317(f317(f225(x80391),x80392),x80394))+~P1(f317(f317(f225(x80391),f2(x80391)),x80393))+P1(f317(f317(f225(x80391),f317(f317(f281(x80391),x80392),x80393)),f317(f317(f281(x80391),x80394),x80393))) % 112.37/112.11 [8081]~P107(x80812)+P1(f317(f317(f225(f906(x80811,x80812)),x80814),x80813))+~P1(f317(f317(f224(f906(x80811,x80812)),x80814),x80813))+P1(f317(f317(f224(f906(x80811,x80812)),x80813),x80814)) % 112.37/112.11 [8121]P1(f317(f317(f319(x81211),x81212),x81213))+P1(f317(f317(f319(x81211),x81212),x81214))+~P1(f317(f317(f224(f906(x81211,a895)),x81214),x81213))+P1(f317(f317(f225(f906(x81211,a895)),x81214),f317(f317(f299(x81211),x81212),x81213))) % 112.37/112.11 [8232]~P121(x82322)+E(x82321,f2(x82322))+P1(f317(f317(f277(x82322),x82323),x82324))+~P1(f317(f317(f277(x82322),f317(f317(f75(x82322),x82323),x82321)),f317(f317(f75(x82322),x82324),x82321))) % 112.37/112.11 [8233]~P121(x82332)+E(x82331,f2(x82332))+P1(f317(f317(f277(x82332),x82333),x82334))+~P1(f317(f317(f277(x82332),f317(f317(f75(x82332),x82331),x82333)),f317(f317(f75(x82332),x82331),x82334))) % 112.37/112.11 [8282]P1(f317(f317(f319(x82821),x82822),x82823))+P1(f317(f317(f319(x82821),x82822),x82824))+~P1(f317(f317(f225(f906(x82821,a895)),x82824),f317(f317(f299(x82821),x82822),x82823)))+P1(f317(f317(f224(f906(x82821,a895)),x82824),x82823)) % 112.37/112.11 [8347]~P127(x83471)+P1(f317(f317(f225(x83471),x83473),x83472))+P1(f317(f317(f225(x83471),x83472),x83473))+~P1(f317(f317(f225(x83471),f317(f317(f75(x83471),x83474),x83472)),f317(f317(f75(x83471),x83474),x83473))) % 112.37/112.11 [8348]~P127(x83481)+P1(f317(f317(f225(x83481),x83483),x83482))+P1(f317(f317(f225(x83481),x83482),x83483))+~P1(f317(f317(f225(x83481),f317(f317(f75(x83481),x83482),x83484)),f317(f317(f75(x83481),x83483),x83484))) % 112.37/112.11 [8360]~P127(x83601)+P1(f317(f317(f225(x83601),x83604),f2(x83601)))+P1(f317(f317(f225(x83601),x83602),x83603))+~P1(f317(f317(f225(x83601),f317(f317(f75(x83601),x83602),x83604)),f317(f317(f75(x83601),x83603),x83604))) % 112.37/112.11 [8361]~P127(x83611)+P1(f317(f317(f225(x83611),x83614),f2(x83611)))+P1(f317(f317(f225(x83611),x83612),x83613))+~P1(f317(f317(f225(x83611),f317(f317(f75(x83611),x83614),x83612)),f317(f317(f75(x83611),x83614),x83613))) % 112.37/112.11 [8364]~P127(x83641)+P1(f317(f317(f225(x83641),x83642),x83643))+P1(f317(f317(f225(x83641),f2(x83641)),x83644))+~P1(f317(f317(f225(x83641),f317(f317(f75(x83641),x83644),x83643)),f317(f317(f75(x83641),x83644),x83642))) % 112.37/112.11 [8365]~P127(x83651)+P1(f317(f317(f225(x83651),x83652),x83653))+P1(f317(f317(f225(x83651),f2(x83651)),x83654))+~P1(f317(f317(f225(x83651),f317(f317(f75(x83651),x83653),x83654)),f317(f317(f75(x83651),x83652),x83654))) % 112.37/112.11 [8378]~P127(x83781)+P1(f317(f317(f225(x83781),x83782),f2(x83781)))+P1(f317(f317(f225(x83781),f2(x83781)),x83782))+~P1(f317(f317(f225(x83781),f317(f317(f75(x83781),x83783),x83782)),f317(f317(f75(x83781),x83784),x83782))) % 112.37/112.11 [8379]~P127(x83791)+P1(f317(f317(f225(x83791),x83792),f2(x83791)))+P1(f317(f317(f225(x83791),f2(x83791)),x83792))+~P1(f317(f317(f225(x83791),f317(f317(f75(x83791),x83792),x83793)),f317(f317(f75(x83791),x83792),x83794))) % 112.37/112.11 [8408]~P127(x84081)+~P1(f317(f317(f225(x84081),x84084),f2(x84081)))+P1(f317(f317(f224(x84081),x84082),x84083))+~P1(f317(f317(f224(x84081),f317(f317(f75(x84081),x84084),x84083)),f317(f317(f75(x84081),x84084),x84082))) % 112.37/112.11 [8409]~P127(x84091)+~P1(f317(f317(f225(x84091),x84094),f2(x84091)))+P1(f317(f317(f225(x84091),x84092),x84093))+~P1(f317(f317(f225(x84091),f317(f317(f75(x84091),x84094),x84093)),f317(f317(f75(x84091),x84094),x84092))) % 112.37/112.11 [8420]~P126(x84203)+~P1(f317(f317(f225(x84203),f72(x84203)),x84204))+P1(f317(f317(f224(a899),x84201),x84202))+~P1(f317(f317(f224(x84203),f317(f317(f234(x84203),x84204),x84201)),f317(f317(f234(x84203),x84204),x84202))) % 112.37/112.11 [8422]~P126(x84223)+~P1(f317(f317(f225(x84223),f72(x84223)),x84224))+P1(f317(f317(f225(a899),x84221),x84222))+~P1(f317(f317(f225(x84223),f317(f317(f234(x84223),x84224),x84221)),f317(f317(f234(x84223),x84224),x84222))) % 112.37/112.11 [8432]~P127(x84321)+P1(f317(f317(f224(x84321),x84322),x84323))+~P1(f317(f317(f225(x84321),f2(x84321)),x84324))+~P1(f317(f317(f224(x84321),f317(f317(f75(x84321),x84324),x84322)),f317(f317(f75(x84321),x84324),x84323))) % 112.37/112.11 [8433]~P134(x84331)+P1(f317(f317(f224(x84331),x84332),x84333))+~P1(f317(f317(f225(x84331),f2(x84331)),x84334))+~P1(f317(f317(f224(x84331),f317(f317(f75(x84331),x84334),x84332)),f317(f317(f75(x84331),x84334),x84333))) % 112.37/112.11 [8434]~P134(x84341)+P1(f317(f317(f224(x84341),x84342),x84343))+~P1(f317(f317(f225(x84341),f2(x84341)),x84344))+~P1(f317(f317(f224(x84341),f317(f317(f75(x84341),x84342),x84344)),f317(f317(f75(x84341),x84343),x84344))) % 112.37/112.11 [8435]~P127(x84351)+P1(f317(f317(f225(x84351),x84352),x84353))+~P1(f317(f317(f225(x84351),f2(x84351)),x84354))+~P1(f317(f317(f225(x84351),f317(f317(f75(x84351),x84354),x84352)),f317(f317(f75(x84351),x84354),x84353))) % 112.37/112.11 [8436]~P134(x84361)+P1(f317(f317(f225(x84361),x84362),x84363))+~P1(f317(f317(f224(x84361),f2(x84361)),x84364))+~P1(f317(f317(f225(x84361),f317(f317(f75(x84361),x84364),x84362)),f317(f317(f75(x84361),x84364),x84363))) % 112.37/112.11 [8437]~P130(x84371)+P1(f317(f317(f225(x84371),x84372),x84373))+~P1(f317(f317(f224(x84371),f2(x84371)),x84374))+~P1(f317(f317(f225(x84371),f317(f317(f75(x84371),x84374),x84372)),f317(f317(f75(x84371),x84374),x84373))) % 112.37/112.11 [8438]~P126(x84381)+~P1(f317(f317(f224(x84381),f2(x84381)),x84383))+P1(f317(f317(f225(x84381),x84382),x84383))+~P1(f317(f317(f225(x84381),f317(f317(f234(x84381),x84382),x84384)),f317(f317(f234(x84381),x84383),x84384))) % 112.37/112.11 [8439]~P134(x84391)+P1(f317(f317(f225(x84391),x84392),x84393))+~P1(f317(f317(f224(x84391),f2(x84391)),x84394))+~P1(f317(f317(f225(x84391),f317(f317(f75(x84391),x84392),x84394)),f317(f317(f75(x84391),x84393),x84394))) % 112.37/112.11 [8440]~P130(x84401)+P1(f317(f317(f225(x84401),x84402),x84403))+~P1(f317(f317(f224(x84401),f2(x84401)),x84404))+~P1(f317(f317(f225(x84401),f317(f317(f75(x84401),x84402),x84404)),f317(f317(f75(x84401),x84403),x84404))) % 112.37/112.11 [8484]P1(f317(f317(f319(x84841),x84842),x84843))+~P1(f317(f317(f224(f906(x84841,a895)),x84843),x84844))+~P1(f317(f317(f225(f906(x84841,a895)),x84843),x84844))+P1(f317(f317(f225(f906(x84841,a895)),x84843),f317(f317(f299(x84841),x84842),x84844))) % 112.37/112.11 [8517]~P146(x85171)+~P122(x85171)+P1(f317(f317(f277(x85171),x85172),f317(f317(f74(x85171),f840(x85172,x85173,x85171)),f2(x85171))))+~P1(f317(x85173,f317(f317(f75(x85171),x85172),x85174))) % 112.37/112.11 [8864]E(f317(f317(f3(a1),f381(x88641,x88642,x88643,x88644)),f382(x88641,x88642,x88643,x88644)),x88644)+~P1(f317(f317(f225(a1),f2(a1)),x88643))+~P1(f317(f317(f224(a1),x88641),x88644))+P1(f317(f317(f224(a1),x88641),f317(f317(f74(a1),x88644),x88643))) % 112.37/112.11 [8865]E(f317(f317(f3(a1),f386(x88651,x88652,x88653,x88654)),f387(x88651,x88652,x88653,x88654)),x88654)+~P1(f317(f317(f225(a1),f2(a1)),x88653))+~P1(f317(f317(f225(a1),x88651),x88654))+P1(f317(f317(f225(a1),x88651),f317(f317(f74(a1),x88654),x88653))) % 112.37/112.11 [9015]~E(f317(f317(f154(x90151),x90153),f658(x90154,x90153,x90151,x90152)),f317(f317(f154(x90151),x90154),f658(x90154,x90153,x90151,x90152)))+E(f317(f317(f165(x90151),x90152),x90153),f317(f317(f165(x90151),x90152),x90154))+~P1(f317(f317(f224(a899),x90152),f317(f179(f900(x90151)),x90153)))+~P1(f317(f317(f224(a899),x90152),f317(f179(f900(x90151)),x90154))) % 112.37/112.11 [9077]~P1(f317(f317(f225(a1),f2(a1)),x90773))+~P1(f317(f317(f224(a1),x90771),x90774))+P1(f317(f317(f319(a1),f381(x90771,x90772,x90773,x90774)),x90772))+P1(f317(f317(f224(a1),x90771),f317(f317(f74(a1),x90774),x90773))) % 112.37/112.11 [9078]~P1(f317(f317(f225(a1),f2(a1)),x90783))+~P1(f317(f317(f225(a1),x90781),x90784))+P1(f317(f317(f319(a1),f386(x90781,x90782,x90783,x90784)),x90782))+P1(f317(f317(f225(a1),x90781),f317(f317(f74(a1),x90784),x90783))) % 112.37/112.11 [9118]~P108(x91181)+~P1(f317(f29(x91181),x91183))+~P1(f317(f317(f319(x91181),x91184),x91183))+P1(f317(f317(f224(x91181),f317(f317(f59(x91181,x91181,f228(x91181)),x91182),x91183)),f317(f317(f228(x91181),x91184),x91182))) % 112.37/112.11 [9119]~P104(x91191)+~P1(f317(f29(x91191),x91193))+~P1(f317(f317(f319(x91191),x91194),x91193))+P1(f317(f317(f224(x91191),f317(f317(f59(x91191,x91191,f92(x91191)),x91192),x91193)),f317(f317(f92(x91191),x91194),x91192))) % 112.37/112.11 [9163]E(f317(f317(f165(x91631),x91632),x91633),f317(f317(f165(x91631),x91632),x91634))+P1(f317(f317(f225(a899),f658(x91633,x91634,x91631,x91632)),x91632))+~P1(f317(f317(f224(a899),x91632),f317(f179(f900(x91631)),x91633)))+~P1(f317(f317(f224(a899),x91632),f317(f179(f900(x91631)),x91634))) % 112.37/112.11 [9168]~P1(f317(f317(f225(a1),f2(a1)),x91683))+~P1(f317(f317(f224(a1),x91681),x91682))+P1(f317(f317(f319(a1),f382(x91681,x91684,x91683,x91682)),f293(a1,f72(a1),x91683)))+P1(f317(f317(f224(a1),x91681),f317(f317(f74(a1),x91682),x91683))) % 112.37/112.11 [9169]~P1(f317(f317(f225(a1),f2(a1)),x91693))+~P1(f317(f317(f225(a1),x91691),x91692))+P1(f317(f317(f319(a1),f387(x91691,x91694,x91693,x91692)),f293(a1,f72(a1),x91693)))+P1(f317(f317(f225(a1),x91691),f317(f317(f74(a1),x91692),x91693))) % 112.37/112.11 [9495]~P108(x94951)+~P1(f317(f29(x94951),x94954))+P1(f317(f317(f319(x94951),f877(x94952,x94953,x94954,x94951)),x94954))+P1(f317(f317(f224(x94951),f317(f317(f59(x94951,x94951,f223(x94951)),x94952),x94954)),f317(f317(f223(x94951),x94953),x94952))) % 112.37/112.11 [9496]~P98(x94961)+~P1(f317(f29(x94961),x94964))+P1(f317(f317(f319(x94961),f440(x94962,x94963,x94964,x94961)),x94964))+P1(f317(f317(f224(x94961),f317(f317(f59(x94961,x94961,f91(x94961)),x94962),x94964)),f317(f317(f91(x94961),x94963),x94962))) % 112.37/112.11 [9632]~P108(x96321)+~P1(f317(f29(x96321),x96323))+~P1(f317(f317(f224(x96321),f877(x96322,x96324,x96323,x96321)),x96324))+P1(f317(f317(f224(x96321),f317(f317(f59(x96321,x96321,f223(x96321)),x96322),x96323)),f317(f317(f223(x96321),x96324),x96322))) % 112.37/112.11 [9633]~P98(x96331)+~P1(f317(f29(x96331),x96333))+~P1(f317(f317(f224(x96331),f440(x96332,x96334,x96333,x96331)),x96334))+P1(f317(f317(f224(x96331),f317(f317(f59(x96331,x96331,f91(x96331)),x96332),x96333)),f317(f317(f91(x96331),x96334),x96332))) % 112.37/112.11 [9635]~P1(f317(f317(f224(a1),f2(a1)),x96354))+~P1(f317(f317(f225(a1),f2(a1)),x96353))+~P1(f317(f317(f225(a1),x96354),x96351))+P1(f317(f317(f225(a1),f317(f317(f74(a1),f317(f317(f75(a1),x96351),f41(a1,x96352,x96353))),x96354)),f317(f317(f75(a1),x96351),x96353))) % 112.37/112.11 [10024]E(x100241,x100242)+P1(f317(f317(f319(f905(f900(x100243),f900(x100243))),f317(f317(f242(f900(x100243),f900(x100243)),x100242),x100241)),f137(x100243,x100244)))+P1(f317(f317(f319(f905(f900(x100243),f900(x100243))),f317(f317(f242(f900(x100243),f900(x100243)),x100241),x100242)),f137(x100243,x100244)))+~P1(f317(f317(f319(f905(x100243,x100243)),f317(f317(f242(x100243,x100243),f629(x100241,x100242,x100244,x100243)),f631(x100241,x100242,x100244,x100243))),x100244)) % 112.37/112.11 [10025]E(x100251,x100252)+P1(f317(f317(f319(f905(f900(x100253),f900(x100253))),f317(f317(f242(f900(x100253),f900(x100253)),x100252),x100251)),f137(x100253,x100254)))+P1(f317(f317(f319(f905(f900(x100253),f900(x100253))),f317(f317(f242(f900(x100253),f900(x100253)),x100251),x100252)),f137(x100253,x100254)))+~P1(f317(f317(f319(f905(x100253,x100253)),f317(f317(f242(x100253,x100253),f631(x100251,x100252,x100254,x100253)),f629(x100251,x100252,x100254,x100253))),x100254)) % 112.37/112.11 [7568]~P108(x75681)+~P1(f317(f317(f224(x75681),x75683),x75684))+~P1(f317(f317(f224(x75681),x75682),x75684))+P1(f317(f317(f224(x75681),f317(f317(f223(x75681),x75682),x75683)),x75684)) % 112.37/112.11 [7571]~P98(x75711)+~P1(f317(f317(f224(x75711),x75713),x75714))+~P1(f317(f317(f224(x75711),x75712),x75714))+P1(f317(f317(f224(x75711),f317(f317(f91(x75711),x75712),x75713)),x75714)) % 112.37/112.11 [7572]~P108(x75721)+~P1(f317(f317(f225(x75721),x75723),x75724))+~P1(f317(f317(f225(x75721),x75722),x75724))+P1(f317(f317(f225(x75721),f317(f317(f223(x75721),x75722),x75723)),x75724)) % 112.37/112.11 [7811]~P3(x78111)+E(f317(f317(f74(x78111),f317(f317(f31(x78111),x78112),x78113)),f317(f317(f31(x78111),x78114),x78113)),f317(f317(f31(x78111),f317(f317(f74(x78111),x78112),x78114)),x78113))+~P1(f317(f317(f277(x78111),x78113),x78114))+~P1(f317(f317(f277(x78111),x78113),x78112)) % 112.37/112.11 [7894]~E(x78941,x78943)+E(f129(a899,f317(f292(a899,x78941),x78942)),f317(f317(f141(a899),x78943),x78944))+~E(f129(a899,f317(f292(a899,f317(f317(f74(a899),x78941),f72(a899))),x78942)),x78944)+~P1(f317(f317(f225(a899),x78941),x78942)) % 112.37/112.11 [7902]~P108(x79021)+P1(f317(f317(f224(x79021),x79022),x79023))+P1(f317(f317(f224(x79021),x79024),x79023))+~P1(f317(f317(f224(x79021),f317(f317(f228(x79021),x79024),x79022)),x79023)) % 112.37/112.11 [7903]~P108(x79031)+P1(f317(f317(f225(x79031),x79032),x79033))+P1(f317(f317(f225(x79031),x79034),x79033))+~P1(f317(f317(f225(x79031),f317(f317(f228(x79031),x79034),x79032)),x79033)) % 112.37/112.11 [8179]~P63(x81791)+~P1(f317(f317(f225(x81791),f2(x81791)),x81793))+~P1(f317(f317(f224(x81791),x81792),f317(f317(f281(x81791),x81794),x81793)))+P1(f317(f317(f224(x81791),f317(f317(f75(x81791),x81792),x81793)),x81794)) % 112.37/112.11 [8180]~P64(x81801)+~P1(f317(f317(f225(x81801),f2(x81801)),x81803))+~P1(f317(f317(f224(x81801),x81802),f317(f317(f281(x81801),x81804),x81803)))+P1(f317(f317(f224(x81801),f317(f317(f75(x81801),x81802),x81803)),x81804)) % 112.37/112.11 [8181]~P63(x81811)+~P1(f317(f317(f225(x81811),f2(x81811)),x81813))+~P1(f317(f317(f224(x81811),x81812),f317(f317(f75(x81811),x81814),x81813)))+P1(f317(f317(f224(x81811),f317(f317(f281(x81811),x81812),x81813)),x81814)) % 112.37/112.11 [8183]~P64(x81831)+~P1(f317(f317(f225(x81831),f2(x81831)),x81833))+~P1(f317(f317(f224(x81831),x81832),f317(f317(f75(x81831),x81834),x81833)))+P1(f317(f317(f224(x81831),f317(f317(f281(x81831),x81832),x81833)),x81834)) % 112.37/112.11 [8184]~P63(x81841)+~P1(f317(f317(f225(x81841),f2(x81841)),x81843))+~P1(f317(f317(f225(x81841),x81842),f317(f317(f281(x81841),x81844),x81843)))+P1(f317(f317(f225(x81841),f317(f317(f75(x81841),x81842),x81843)),x81844)) % 112.37/112.11 [8185]~P64(x81851)+~P1(f317(f317(f225(x81851),f2(x81851)),x81853))+~P1(f317(f317(f225(x81851),x81852),f317(f317(f281(x81851),x81854),x81853)))+P1(f317(f317(f225(x81851),f317(f317(f75(x81851),x81852),x81853)),x81854)) % 112.37/112.11 [8186]~P63(x81861)+~P1(f317(f317(f225(x81861),f2(x81861)),x81863))+~P1(f317(f317(f225(x81861),x81862),f317(f317(f75(x81861),x81864),x81863)))+P1(f317(f317(f225(x81861),f317(f317(f281(x81861),x81862),x81863)),x81864)) % 112.37/112.11 [8188]~P64(x81881)+~P1(f317(f317(f225(x81881),f2(x81881)),x81883))+~P1(f317(f317(f225(x81881),x81882),f317(f317(f75(x81881),x81884),x81883)))+P1(f317(f317(f225(x81881),f317(f317(f281(x81881),x81882),x81883)),x81884)) % 112.37/112.11 [8317]~P63(x83171)+~P1(f317(f317(f225(x83171),f2(x83171)),x83174))+P1(f317(f317(f224(x83171),x83172),f317(f317(f75(x83171),x83173),x83174)))+~P1(f317(f317(f224(x83171),f317(f317(f281(x83171),x83172),x83174)),x83173)) % 112.37/112.11 [8318]~P63(x83181)+~P1(f317(f317(f225(x83181),f2(x83181)),x83184))+P1(f317(f317(f224(x83181),x83182),f317(f317(f281(x83181),x83183),x83184)))+~P1(f317(f317(f224(x83181),f317(f317(f75(x83181),x83182),x83184)),x83183)) % 112.37/112.11 [8320]~P64(x83201)+~P1(f317(f317(f225(x83201),f2(x83201)),x83204))+P1(f317(f317(f224(x83201),x83202),f317(f317(f75(x83201),x83203),x83204)))+~P1(f317(f317(f224(x83201),f317(f317(f281(x83201),x83202),x83204)),x83203)) % 112.37/112.11 [8321]~P64(x83211)+~P1(f317(f317(f225(x83211),f2(x83211)),x83214))+P1(f317(f317(f224(x83211),x83212),f317(f317(f281(x83211),x83213),x83214)))+~P1(f317(f317(f224(x83211),f317(f317(f75(x83211),x83212),x83214)),x83213)) % 112.37/112.11 [8322]~P63(x83221)+~P1(f317(f317(f225(x83221),f2(x83221)),x83224))+P1(f317(f317(f225(x83221),x83222),f317(f317(f75(x83221),x83223),x83224)))+~P1(f317(f317(f225(x83221),f317(f317(f281(x83221),x83222),x83224)),x83223)) % 112.37/112.11 [8323]~P63(x83231)+~P1(f317(f317(f225(x83231),f2(x83231)),x83234))+P1(f317(f317(f225(x83231),x83232),f317(f317(f281(x83231),x83233),x83234)))+~P1(f317(f317(f225(x83231),f317(f317(f75(x83231),x83232),x83234)),x83233)) % 112.37/112.11 [8325]~P64(x83251)+~P1(f317(f317(f225(x83251),f2(x83251)),x83254))+P1(f317(f317(f225(x83251),x83252),f317(f317(f75(x83251),x83253),x83254)))+~P1(f317(f317(f225(x83251),f317(f317(f281(x83251),x83252),x83254)),x83253)) % 112.37/112.11 [8326]~P64(x83261)+~P1(f317(f317(f225(x83261),f2(x83261)),x83264))+P1(f317(f317(f225(x83261),x83262),f317(f317(f281(x83261),x83263),x83264)))+~P1(f317(f317(f225(x83261),f317(f317(f75(x83261),x83262),x83264)),x83263)) % 112.37/112.11 [8487]~P64(x84871)+~P1(f317(f317(f225(x84871),x84873),f2(x84871)))+~P1(f317(f317(f224(x84871),f317(f317(f281(x84871),x84874),x84873)),x84872))+P1(f317(f317(f224(x84871),f317(f317(f75(x84871),x84872),x84873)),x84874)) % 112.37/112.11 [8488]~P64(x84881)+~P1(f317(f317(f225(x84881),x84883),f2(x84881)))+~P1(f317(f317(f224(x84881),f317(f317(f75(x84881),x84884),x84883)),x84882))+P1(f317(f317(f224(x84881),f317(f317(f281(x84881),x84882),x84883)),x84884)) % 112.37/112.11 [8489]~P64(x84891)+~P1(f317(f317(f225(x84891),x84893),f2(x84891)))+~P1(f317(f317(f225(x84891),f317(f317(f281(x84891),x84894),x84893)),x84892))+P1(f317(f317(f225(x84891),f317(f317(f75(x84891),x84892),x84893)),x84894)) % 112.37/112.11 [8490]~P64(x84901)+~P1(f317(f317(f225(x84901),x84903),f2(x84901)))+~P1(f317(f317(f225(x84901),f317(f317(f75(x84901),x84904),x84903)),x84902))+P1(f317(f317(f225(x84901),f317(f317(f281(x84901),x84902),x84903)),x84904)) % 112.37/112.11 [8502]~P1(f317(x85021,x85024))+~P1(f317(f317(f225(a899),x85022),f317(f317(f75(a899),x85023),f317(a102,x85024))))+P1(f317(x85021,f317(f317(f31(a899),x85022),x85023)))+~P1(f317(f317(f224(a899),f317(f317(f75(a899),x85023),x85024)),x85022)) % 112.37/112.11 [8712]~P108(x87121)+~P1(f317(f29(x87121),x87124))+~P1(f317(f317(f319(x87121),x87122),x87124))+P1(f317(f317(f224(x87121),f317(f317(f223(x87121),x87122),x87123)),f317(f317(f59(x87121,x87121,f223(x87121)),x87123),x87124))) % 112.37/112.11 [8713]~P98(x87131)+~P1(f317(f29(x87131),x87134))+~P1(f317(f317(f319(x87131),x87132),x87134))+P1(f317(f317(f224(x87131),f317(f317(f91(x87131),x87132),x87133)),f317(f317(f59(x87131,x87131,f91(x87131)),x87133),x87134))) % 112.37/112.11 [8866]~P1(f317(f29(x88661),x88662))+E(f317(f30(x88661),f317(f317(f3(f906(x88661,a895)),x88662),f317(f317(f299(x88661),x88663),x88664))),f317(f317(f3(a899),f317(f30(x88661),f317(f317(f3(f906(x88661,a895)),x88662),x88664))),f72(a899)))+P1(f317(f317(f319(x88661),x88663),x88664))+~P1(f317(f317(f319(x88661),x88663),x88662)) % 112.37/112.11 [8943]E(f317(f317(f74(a1),f369(x89431,x89432,x89433,x89434)),f370(x89431,x89432,x89433,x89434)),x89434)+~P1(f317(f317(f225(a1),f2(a1)),x89433))+~P1(f317(f317(f224(a1),x89434),x89431))+P1(f317(f317(f224(a1),f317(f317(f3(a1),x89434),x89433)),x89431)) % 112.37/112.11 [8944]E(f317(f317(f74(a1),f388(x89441,x89442,x89443,x89444)),f389(x89441,x89442,x89443,x89444)),x89444)+~P1(f317(f317(f225(a1),f2(a1)),x89443))+~P1(f317(f317(f225(a1),x89444),x89441))+P1(f317(f317(f225(a1),f317(f317(f3(a1),x89444),x89443)),x89441)) % 112.37/112.11 [9148]~P1(f317(f317(f225(a1),f2(a1)),x91483))+~P1(f317(f317(f224(a1),x91484),x91481))+P1(f317(f317(f319(a1),f369(x91481,x91482,x91483,x91484)),x91482))+P1(f317(f317(f224(a1),f317(f317(f3(a1),x91484),x91483)),x91481)) % 112.37/112.11 [9149]~P1(f317(f317(f225(a1),f2(a1)),x91493))+~P1(f317(f317(f225(a1),x91494),x91491))+P1(f317(f317(f319(a1),f388(x91491,x91492,x91493,x91494)),x91492))+P1(f317(f317(f225(a1),f317(f317(f3(a1),x91494),x91493)),x91491)) % 112.37/112.11 [9235]~P1(f317(f317(f225(a1),f2(a1)),x92352))+~P1(f317(f317(f224(a1),x92351),x92353))+P1(f317(f317(f319(a1),f370(x92353,x92354,x92352,x92351)),f293(a1,f72(a1),x92352)))+P1(f317(f317(f224(a1),f317(f317(f3(a1),x92351),x92352)),x92353)) % 112.37/112.11 [9236]~P1(f317(f317(f225(a1),f2(a1)),x92362))+~P1(f317(f317(f225(a1),x92361),x92363))+P1(f317(f317(f319(a1),f389(x92363,x92364,x92362,x92361)),f293(a1,f72(a1),x92362)))+P1(f317(f317(f225(a1),f317(f317(f3(a1),x92361),x92362)),x92363)) % 112.37/112.11 [9254]~P1(f317(f317(f224(a1),f2(a1)),x92544))+~P1(f317(f317(f225(a1),f2(a1)),x92543))+~P1(f317(f317(f225(a1),x92544),x92541))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),f317(f317(f75(a1),x92541),f41(a1,x92542,x92543))),x92544))) % 112.37/112.11 [9283]E(x92831,x92832)+~P38(x92833,x92834)+~P1(f317(f317(f319(f905(x92833,x92833)),f317(f317(f242(x92833,x92833),x92832),x92831)),x92834))+~P1(f317(f317(f319(f905(x92833,x92833)),f317(f317(f242(x92833,x92833),x92831),x92832)),x92834)) % 112.37/112.11 [9316]~P108(x93161)+~P1(f317(f29(x93161),x93164))+~P1(f317(f317(f224(x93161),x93162),f876(x93163,x93162,x93164,x93161)))+P1(f317(f317(f224(x93161),f317(f317(f228(x93161),x93162),x93163)),f317(f317(f59(x93161,x93161,f228(x93161)),x93163),x93164))) % 112.37/112.11 [9317]~P104(x93171)+~P1(f317(f29(x93171),x93174))+~P1(f317(f317(f224(x93171),x93172),f438(x93173,x93172,x93174,x93171)))+P1(f317(f317(f224(x93171),f317(f317(f92(x93171),x93172),x93173)),f317(f317(f59(x93171,x93171,f92(x93171)),x93173),x93174))) % 112.37/112.11 [9334]~P1(f317(f317(f224(a1),x93344),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x93342))+~P1(f317(f317(f225(a1),x93341),x93344))+P1(f317(f317(f225(a1),f317(f317(f75(a1),x93341),x93342)),f317(f317(f74(a1),f317(f317(f75(a1),x93341),f41(a1,x93343,x93342))),x93344))) % 112.37/112.11 [9360]P1(f317(f29(x93601),x93602))+~P1(f317(f29(x93601),x93603))+~P1(f317(f317(f319(f906(x93601,a895)),x93602),f317(f317(f56(x93601),x93603),x93604)))+~P1(f317(f317(f224(f906(f905(x93601,x93601),a895)),x93604),f317(f317(f244(x93601,x93601),x93603),f317(f18(f906(x93601,a895),x93601),x93603)))) % 112.37/112.11 [9384]~P108(x93841)+~P1(f317(f29(x93841),x93844))+P1(f317(f317(f319(x93841),f876(x93842,x93843,x93844,x93841)),x93844))+P1(f317(f317(f224(x93841),f317(f317(f228(x93841),x93843),x93842)),f317(f317(f59(x93841,x93841,f228(x93841)),x93842),x93844))) % 112.37/112.11 [9385]~P104(x93851)+~P1(f317(f29(x93851),x93854))+P1(f317(f317(f319(x93851),f438(x93852,x93853,x93854,x93851)),x93854))+P1(f317(f317(f224(x93851),f317(f317(f92(x93851),x93853),x93852)),f317(f317(f59(x93851,x93851,f92(x93851)),x93852),x93854))) % 112.37/112.11 [9800]~P1(f317(f29(x98002),x98004))+~P1(f317(f29(x98001),x98003))+~P1(f317(f317(f224(a899),f317(f30(x98002),x98004)),f317(f30(x98001),x98003)))+P1(f317(f317(f224(f906(x98001,a895)),f317(f300(x98002,x98001,f514(x98003,x98001,x98004,x98002)),x98004)),x98003)) % 112.37/112.11 [9436]~P1(f317(f317(f319(x94361),x94362),x94364))+P1(f317(f317(f319(x94361),x94362),x94363))+~P1(f317(f317(f225(f906(x94361,a895)),x94364),f317(f317(f299(x94361),x94362),x94363)))+P1(f317(f317(f225(f906(x94361,a895)),f317(f317(f3(f906(x94361,a895)),x94364),f317(f317(f299(x94361),x94362),f178(f906(x94361,a895))))),x94363)) % 112.37/112.11 [9613]~P1(f317(f317(f319(x96131),x96132),x96134))+P1(f317(f317(f319(x96131),x96132),x96133))+P1(f317(f317(f225(f906(x96131,a895)),x96134),f317(f317(f299(x96131),x96132),x96133)))+~P1(f317(f317(f225(f906(x96131,a895)),f317(f317(f3(f906(x96131,a895)),x96134),f317(f317(f299(x96131),x96132),f178(f906(x96131,a895))))),x96133)) % 112.37/112.11 [9638]P1(f317(f317(f319(x96381),x96382),x96383))+~P1(f317(f317(f224(f906(x96381,a895)),x96384),x96383))+P1(f317(f317(f225(f906(x96381,a895)),x96384),f317(f317(f299(x96381),x96382),x96383)))+~P1(f317(f317(f225(f906(x96381,a895)),f317(f317(f3(f906(x96381,a895)),x96384),f317(f317(f299(x96381),x96382),f178(f906(x96381,a895))))),x96383)) % 112.37/112.11 [9643]~P1(f317(f317(f319(x96431),x96433),x96432))+~P1(f317(f317(f225(f906(x96431,a895)),x96432),x96434))+P1(f317(f317(f225(f906(x96431,a895)),x96432),f317(f317(f299(x96431),x96433),x96434)))+~P1(f317(f317(f225(f906(x96431,a895)),f317(f317(f3(f906(x96431,a895)),x96432),f317(f317(f299(x96431),x96433),f178(f906(x96431,a895))))),x96434)) % 112.37/112.11 [9660]~P1(f317(f317(f224(f906(x96601,a895)),x96602),x96604))+~P1(f317(f317(f225(f906(x96601,a895)),x96602),x96604))+P1(f317(f317(f225(f906(x96601,a895)),x96602),f317(f317(f299(x96601),x96603),x96604)))+~P1(f317(f317(f225(f906(x96601,a895)),f317(f317(f3(f906(x96601,a895)),x96602),f317(f317(f299(x96601),x96603),f178(f906(x96601,a895))))),x96604)) % 112.37/112.11 [9705]~P109(x97052)+~P60(x97051)+~P1(f317(f317(f224(f906(x97051,x97052)),x97053),x97054))+P1(f317(f53(x97051),f317(f317(f20(x97051,x97052,a895),f317(f317(f10(x97052,f906(x97052,a895),x97051),f224(x97052)),x97053)),x97054))) % 112.37/112.11 [9848]~P109(x98482)+~P60(x98481)+P1(f317(f317(f224(f906(x98481,x98482)),x98483),x98484))+~P1(f317(f53(x98481),f317(f317(f20(x98481,x98482,a895),f317(f317(f10(x98482,f906(x98482,a895),x98481),f224(x98482)),x98483)),x98484))) % 112.37/112.11 [10015]E(f317(f317(f154(x100151),f317(f317(f154(f900(x100151)),f169(x100151,x100152)),x100153)),x100154),f317(f317(f154(x100151),f317(f317(f154(f900(x100151)),x100152),x100154)),x100153))+~P1(f317(f317(f225(a899),x100153),f317(f179(f900(f900(x100151))),f169(x100151,x100152))))+~P13(a899,f317(f158(a899),f317(f317(f144(f900(x100151),a899),f179(f900(x100151))),x100152)))+~P1(f317(f317(f225(a899),x100154),f317(f179(f900(f900(x100151))),f317(f126(f900(x100151),f317(f317(f10(a899,a895,f900(x100151)),f317(f225(a899),x100153)),f179(f900(x100151)))),x100152)))) % 112.37/112.11 [10036]~P1(f317(f317(f319(f905(a899,a899)),x100364),x100361))+~P1(f317(f317(f319(f905(f905(a899,a899),f905(a899,a899))),f317(f317(f242(f905(a899,a899),f905(a899,a899)),x100364),x100362)),a26))+~P1(f317(f317(f319(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),x100361),x100363)),a27))+P1(f317(f317(f319(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),x100361),f317(f317(f299(f905(a899,a899)),x100362),x100363))),a27)) % 112.37/112.11 [10037]~P1(f317(f317(f319(f905(a899,a899)),x100374),x100371))+~P1(f317(f317(f319(f905(f905(a899,a899),f905(a899,a899))),f317(f317(f242(f905(a899,a899),f905(a899,a899)),x100374),x100372)),a65))+~P1(f317(f317(f319(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),x100371),x100373)),a66))+P1(f317(f317(f319(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),x100371),f317(f317(f299(f905(a899,a899)),x100372),x100373))),a66)) % 112.37/112.11 [9927]~P109(x99272)+~P60(x99271)+~P1(f317(f317(f225(f906(x99271,x99272)),x99273),x99274))+P1(f317(f52(x99271),f317(f317(f10(a895,a895,x99271),a312),f317(f317(f20(x99271,x99272,a895),f317(f317(f10(x99272,f906(x99272,a895),x99271),a314),x99273)),x99274)))) % 112.37/112.11 [10048]~P1(f317(f317(f319(f905(a899,a899)),x100484),x100483))+~P1(f317(f317(f319(f905(f905(a899,a899),f905(a899,a899))),f317(f317(f242(f905(a899,a899),f905(a899,a899)),x100481),x100484)),a26))+~P1(f317(f317(f319(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),x100482),x100483)),a28))+P1(f317(f317(f319(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),f317(f317(f299(f905(a899,a899)),x100481),x100482)),x100483)),a28)) % 112.37/112.11 [10049]~P1(f317(f317(f319(f905(a899,a899)),x100494),x100493))+~P1(f317(f317(f319(f905(f905(a899,a899),f905(a899,a899))),f317(f317(f242(f905(a899,a899),f905(a899,a899)),x100491),x100494)),a65))+~P1(f317(f317(f319(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),x100492),x100493)),a64))+P1(f317(f317(f319(f905(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895))),f317(f317(f242(f906(f905(a899,a899),a895),f906(f905(a899,a899),a895)),f317(f317(f299(f905(a899,a899)),x100491),x100492)),x100493)),a64)) % 112.37/112.11 [6129]~P7(x61294,x61291)+~P1(f317(f317(x61291,x61292),x61295))+P1(f317(f317(x61291,x61292),x61293))+~P1(f317(f317(x61291,x61295),x61293)) % 112.37/112.11 [6130]~P49(x61304,x61301)+~P1(f317(f317(x61301,x61302),x61305))+P1(f317(f317(x61301,x61302),x61303))+~P1(f317(f317(x61301,x61305),x61303)) % 112.37/112.11 [6131]~P15(x61314,x61311)+~P1(f317(f317(x61311,x61312),x61315))+P1(f317(f317(x61311,x61312),x61313))+~P1(f317(f317(x61311,x61315),x61313)) % 112.37/112.11 [8851]~P7(x88514,x88513)+~P1(f317(x88511,x88515))+P1(f317(x88512,f815(x88512,x88511,x88513,x88514)))+P1(f317(x88511,f814(x88512,x88511,x88513,x88514))) % 112.37/112.11 [9085]~P7(x90854,x90853)+~P1(f317(x90852,x90855))+~P1(f317(x90851,f814(x90851,x90852,x90853,x90854)))+P1(f317(x90851,f815(x90851,x90852,x90853,x90854))) % 112.37/112.11 [9267]~P7(x92674,x92673)+~P1(f317(x92671,x92675))+P1(f317(f317(f319(x92674),f815(x92672,x92671,x92673,x92674)),f260(x92674,x92673)))+P1(f317(x92671,f814(x92672,x92671,x92673,x92674))) % 112.37/112.11 [9393]~P7(x93931,x93934)+~P1(f317(x93933,x93935))+~P1(f317(x93932,f814(x93932,x93933,x93934,x93931)))+P1(f317(f317(f319(x93931),f815(x93932,x93933,x93934,x93931)),f260(x93931,x93934))) % 112.37/112.11 [9694]~P37(x96941,x96944)+P1(f317(f317(f319(f905(f900(x96941),f900(x96941))),f317(f317(f242(f900(x96941),f900(x96941)),x96942),x96943)),f137(x96941,x96944)))+~P1(f317(f317(f319(f905(f900(x96941),f900(x96941))),f317(f317(f242(f900(x96941),f900(x96941)),x96942),x96945)),f137(x96941,x96944)))+~P1(f317(f317(f319(f905(f900(x96941),f900(x96941))),f317(f317(f242(f900(x96941),f900(x96941)),x96945),x96943)),f137(x96941,x96944))) % 112.37/112.11 [5354]~P68(x53545)+E(x53541,x53542)+~E(x53543,x53544)+~E(f317(f317(f3(x53545),x53543),x53544),f317(f317(f3(x53545),x53541),x53542)) % 112.37/112.11 [6245]~P17(x62455,x62451,x62453)+E(f317(f317(x62451,x62452),f317(x62453,x62454)),f317(x62453,x62454))+~P1(f317(f29(x62455),x62454))+~P1(f317(f317(f319(x62455),x62452),x62454)) % 112.37/112.11 [6441]~P79(x64411)+~E(f317(f317(f3(x64411),x64414),x64415),f317(f317(f3(x64411),x64412),x64413))+~P1(f317(f317(f224(x64411),x64414),x64415))+P1(f317(f317(f224(x64411),x64412),x64413)) % 112.37/112.11 [6443]~P79(x64431)+~E(f317(f317(f3(x64431),x64434),x64435),f317(f317(f3(x64431),x64432),x64433))+~P1(f317(f317(f225(x64431),x64434),x64435))+P1(f317(f317(f225(x64431),x64432),x64433)) % 112.37/112.11 [7435]~E(x74352,f317(f317(f141(x74351),x74354),x74355))+P1(f317(f317(f319(f900(x74351)),x74352),f151(x74351,x74353)))+~P1(f317(f317(f319(f900(x74351)),x74355),f151(x74351,x74353)))+~P1(f317(f317(f319(x74351),x74354),x74353)) % 112.37/112.11 [7842]~E(f317(f179(f900(x78421)),x78423),f317(f179(f900(x78422)),x78424))+~E(f317(f317(f144(f905(x78421,x78422),x78422),f246(x78421,x78422)),x78425),x78424)+~E(f317(f317(f144(f905(x78421,x78422),x78421),f241(x78421,x78422)),x78425),x78423)+E(f317(f317(f171(x78421,x78422),x78423),x78424),x78425) % 112.37/112.11 [8175]~P109(x81751)+P1(f317(f317(f225(f906(x81751,a895)),f293(x81751,x81752,x81753)),f293(x81751,x81754,x81755)))+~P1(f317(f317(f224(x81751),x81754),x81755))+P1(f317(f317(f224(x81751),x81752),x81753)) % 112.37/112.11 [8275]~P109(x82751)+P1(f317(f317(f224(f906(x82751,a895)),f293(x82751,x82752,x82753)),f293(x82751,x82754,x82755)))+~P1(f317(f317(f224(x82751),x82753),x82755))+~P1(f317(f317(f224(x82751),x82754),x82752)) % 112.37/112.11 [8394]~P108(x83941)+P1(f317(f317(f224(x83941),x83942),x83943))+P1(f317(f317(f224(x83941),x83944),x83943))+~P1(f317(f317(f224(f906(x83941,a895)),f317(f292(x83941,x83943),x83942)),f317(f292(x83941,x83944),x83945))) % 112.37/112.11 [8395]~P108(x83951)+P1(f317(f317(f224(x83951),x83952),x83953))+P1(f317(f317(f224(x83951),x83952),x83954))+~P1(f317(f317(f224(f906(x83951,a895)),f317(f292(x83951,x83953),x83952)),f317(f292(x83951,x83955),x83954))) % 112.37/112.11 [8629]~P109(x86291)+~P1(f317(f317(f224(f906(x86291,a895)),f293(x86291,x86294,x86292)),f293(x86291,x86295,x86293)))+P1(f317(f317(f224(x86291),x86292),x86293))+~P1(f317(f317(f224(x86291),x86294),x86292)) % 112.37/112.11 [8630]~P109(x86301)+~P1(f317(f317(f225(f906(x86301,a895)),f293(x86301,x86304,x86302)),f293(x86301,x86305,x86303)))+P1(f317(f317(f224(x86301),x86302),x86303))+~P1(f317(f317(f224(x86301),x86304),x86302)) % 112.37/112.11 [8631]~P109(x86311)+~P1(f317(f317(f224(f906(x86311,a895)),f293(x86311,x86313,x86314)),f293(x86311,x86312,x86315)))+P1(f317(f317(f224(x86311),x86312),x86313))+~P1(f317(f317(f224(x86311),x86313),x86314)) % 112.37/112.11 [8632]~P109(x86321)+~P1(f317(f317(f225(f906(x86321,a895)),f293(x86321,x86323,x86324)),f293(x86321,x86322,x86325)))+P1(f317(f317(f224(x86321),x86322),x86323))+~P1(f317(f317(f224(x86321),x86323),x86324)) % 112.37/112.11 [6128]~P17(x61282,x61285,x61283)+E(x61281,f178(f906(x61282,a895)))+~P1(f317(f29(x61282),x61281))+E(f317(x61283,f317(f317(f299(x61282),x61284),x61281)),f317(f317(x61285,x61284),f317(x61283,x61281))) % 112.37/112.11 [6924]~E(x69241,x69242)+~E(f317(f317(f92(f906(x69243,a895)),x69244),x69245),f178(f906(x69243,a895)))+~P1(f317(f317(f319(x69243),x69242),x69245))+~P1(f317(f317(f319(x69243),x69241),x69244)) % 112.37/112.11 [7007]~P18(x70072,x70075,x70071)+~P1(f317(f29(x70072),x70074))+E(f317(x70071,f317(f317(f299(x70072),x70073),x70074)),f317(f317(f59(x70072,x70072,x70075),x70073),x70074))+P1(f317(f317(f319(x70072),x70073),x70074)) % 112.37/112.11 [7076]~P69(x70762)+~P1(f317(f29(x70761),x70765))+E(f317(f317(f8(x70761,x70762),x70763),f317(f317(f299(x70761),x70764),x70765)),f317(f317(f74(x70762),f317(x70763,x70764)),f317(f317(f8(x70761,x70762),x70763),x70765)))+P1(f317(f317(f319(x70761),x70764),x70765)) % 112.37/112.11 [7078]~P75(x70782)+~P1(f317(f29(x70781),x70785))+E(f317(f317(f11(x70781,x70782),x70783),f317(f317(f299(x70781),x70784),x70785)),f317(f317(f75(x70782),f317(x70783,x70784)),f317(f317(f11(x70781,x70782),x70783),x70785)))+P1(f317(f317(f319(x70781),x70784),x70785)) % 112.37/112.11 [7482]~P119(x74821)+~P1(f317(f29(x74824),x74825))+~P1(f317(f317(f319(x74824),x74823),x74825))+P1(f317(f317(f277(x74821),f317(x74822,x74823)),f317(f317(f11(x74824,x74821),x74822),x74825))) % 112.37/112.11 [7581]~P18(x75812,x75815,x75811)+~P1(f317(f29(x75812),x75814))+E(f317(x75811,f317(f317(f299(x75812),x75813),x75814)),x75813)+~E(f317(f317(f3(f906(x75812,a895)),x75814),f317(f317(f299(x75812),x75813),f178(f906(x75812,a895)))),f178(f906(x75812,a895))) % 112.37/112.11 [7915]~P119(x79151)+~P1(f317(f317(f277(x79151),x79152),x79154))+~P1(f317(f317(f224(a899),x79153),x79155))+P1(f317(f317(f277(x79151),f317(f317(f234(x79151),x79152),x79153)),f317(f317(f234(x79151),x79154),x79155))) % 112.37/112.11 [7943]~P3(x79431)+E(f317(f317(f31(x79431),f317(f317(f75(x79431),x79432),x79433)),f317(f317(f75(x79431),x79434),x79435)),f317(f317(f75(x79431),f317(f317(f31(x79431),x79432),x79434)),f317(f317(f31(x79431),x79433),x79435)))+~P1(f317(f317(f277(x79431),x79435),x79433))+~P1(f317(f317(f277(x79431),x79434),x79432)) % 112.37/112.11 [7947]~P85(x79471)+~P1(f317(f317(f224(x79471),x79473),x79475))+~P1(f317(f317(f224(x79471),x79472),x79474))+P1(f317(f317(f224(x79471),f317(f317(f74(x79471),x79472),x79473)),f317(f317(f74(x79471),x79474),x79475))) % 112.37/112.11 [7948]~P108(x79481)+~P1(f317(f317(f224(x79481),x79483),x79485))+~P1(f317(f317(f224(x79481),x79482),x79484))+P1(f317(f317(f224(x79481),f317(f317(f228(x79481),x79482),x79483)),f317(f317(f228(x79481),x79484),x79485))) % 112.37/112.11 [7949]~P108(x79491)+~P1(f317(f317(f224(x79491),x79493),x79495))+~P1(f317(f317(f224(x79491),x79492),x79494))+P1(f317(f317(f224(x79491),f317(f317(f223(x79491),x79492),x79493)),f317(f317(f223(x79491),x79494),x79495))) % 112.37/112.11 [7950]~P98(x79501)+~P1(f317(f317(f224(x79501),x79503),x79505))+~P1(f317(f317(f224(x79501),x79502),x79504))+P1(f317(f317(f224(x79501),f317(f317(f91(x79501),x79502),x79503)),f317(f317(f91(x79501),x79504),x79505))) % 112.37/112.11 [7951]~P104(x79511)+~P1(f317(f317(f224(x79511),x79513),x79515))+~P1(f317(f317(f224(x79511),x79512),x79514))+P1(f317(f317(f224(x79511),f317(f317(f92(x79511),x79512),x79513)),f317(f317(f92(x79511),x79514),x79515))) % 112.37/112.11 [7952]~P83(x79521)+~P1(f317(f317(f224(x79521),x79523),x79525))+~P1(f317(f317(f225(x79521),x79522),x79524))+P1(f317(f317(f225(x79521),f317(f317(f74(x79521),x79522),x79523)),f317(f317(f74(x79521),x79524),x79525))) % 112.37/112.11 [7953]~P83(x79531)+~P1(f317(f317(f224(x79531),x79532),x79534))+~P1(f317(f317(f225(x79531),x79533),x79535))+P1(f317(f317(f225(x79531),f317(f317(f74(x79531),x79532),x79533)),f317(f317(f74(x79531),x79534),x79535))) % 112.37/112.11 [7954]~P83(x79541)+~P1(f317(f317(f225(x79541),x79543),x79545))+~P1(f317(f317(f225(x79541),x79542),x79544))+P1(f317(f317(f225(x79541),f317(f317(f74(x79541),x79542),x79543)),f317(f317(f74(x79541),x79544),x79545))) % 112.37/112.11 [7955]~P119(x79551)+~P1(f317(f317(f277(x79551),x79553),x79555))+~P1(f317(f317(f277(x79551),x79552),x79554))+P1(f317(f317(f277(x79551),f317(f317(f75(x79551),x79552),x79553)),f317(f317(f75(x79551),x79554),x79555))) % 112.37/112.11 [8091]~P143(x80915)+E(x80911,x80912)+E(x80913,x80914)+~E(f317(f317(f74(x80915),f317(f317(f75(x80915),x80913),x80911)),f317(f317(f75(x80915),x80914),x80912)),f317(f317(f74(x80915),f317(f317(f75(x80915),x80913),x80912)),f317(f317(f75(x80915),x80914),x80911))) % 112.37/112.11 [8295]~P108(x82954)+~P1(f317(f127(x82951),x82953))+P1(f317(f317(f319(x82951),x82952),f317(f162(x82951),x82953)))+P1(f317(f127(x82951),f317(f317(f138(x82951,x82954,x82955),x82952),x82953))) % 112.37/112.11 [8441]~P68(x84411)+E(f317(f317(f3(x84411),f317(f317(f8(a899,x84411),x84412),f317(f292(a899,x84413),x84414))),f317(f317(f8(a899,x84411),x84412),f317(f292(a899,x84413),x84415))),f317(f317(f8(a899,x84411),x84412),f317(f292(a899,x84415),x84414)))+~P1(f317(f317(f224(a899),x84415),x84414))+~P1(f317(f317(f224(a899),x84413),x84415)) % 112.37/112.11 [8442]~P69(x84421)+E(f317(f317(f74(x84421),f317(f317(f8(a899,x84421),x84422),f317(f292(a899,x84423),x84424))),f317(f317(f8(a899,x84421),x84422),f317(f292(a899,x84424),x84425))),f317(f317(f8(a899,x84421),x84422),f317(f292(a899,x84423),x84425)))+~P1(f317(f317(f224(a899),x84424),x84425))+~P1(f317(f317(f224(a899),x84423),x84424)) % 112.37/112.11 [8772]~P62(x87722)+E(x87721,f2(x87722))+E(x87723,f2(x87722))+E(f317(f317(f281(x87722),f317(f317(f3(x87722),f317(f317(f75(x87722),x87724),x87721)),f317(f317(f75(x87722),x87725),x87723))),f317(f317(f75(x87722),x87723),x87721)),f317(f317(f3(x87722),f317(f317(f281(x87722),x87724),x87723)),f317(f317(f281(x87722),x87725),x87721))) % 112.37/112.11 [8773]~P62(x87732)+E(x87731,f2(x87732))+E(x87733,f2(x87732))+E(f317(f317(f281(x87732),f317(f317(f74(x87732),f317(f317(f75(x87732),x87734),x87731)),f317(f317(f75(x87732),x87735),x87733))),f317(f317(f75(x87732),x87733),x87731)),f317(f317(f74(x87732),f317(f317(f281(x87732),x87734),x87733)),f317(f317(f281(x87732),x87735),x87731))) % 112.37/112.11 [8782]~E(x87822,f317(x87823,x87821))+E(x87821,f508(x87822,x87823,x87824,x87825))+~P24(x87825,x87824,x87823,f232(f906(x87825,a895)))+~P1(f317(f317(f319(x87824),x87822),f317(f300(x87825,x87824,x87823),f232(f906(x87825,a895))))) % 112.37/112.11 [8999]~P112(x89991)+~P1(f317(f317(f225(x89991),f317(f70(x89991),x89992)),x89994))+P1(f317(f317(f225(x89991),f317(f317(f75(x89991),f317(f70(x89991),x89992)),f317(f70(x89991),x89993))),f317(f317(f75(x89991),x89994),x89995)))+~P1(f317(f317(f225(x89991),f317(f70(x89991),x89993)),x89995)) % 112.37/112.11 [9110]~P24(x91101,x91103,x91105,x91102)+~P1(f317(f29(x91103),x91104))+P1(f317(f317(f224(a899),f317(f30(x91101),x91102)),f317(f30(x91103),x91104)))+~P1(f317(f317(f224(f906(x91103,a895)),f317(f300(x91101,x91103,x91105),x91102)),x91104)) % 112.37/112.11 [9177]~P69(x91772)+~P24(x91771,x91771,x91774,x91775)+~P1(f317(f29(x91771),x91775))+E(f317(f317(f8(x91771,x91772),f317(f67(x91771,x91772,x91771,x91773),x91774)),x91775),f317(f317(f8(x91771,x91772),x91773),f317(f300(x91771,x91771,x91774),x91775))) % 112.37/112.11 [9178]~P75(x91782)+~P24(x91781,x91781,x91784,x91785)+~P1(f317(f29(x91781),x91785))+E(f317(f317(f11(x91781,x91782),f317(f67(x91781,x91782,x91781,x91783),x91784)),x91785),f317(f317(f11(x91781,x91782),x91783),f317(f300(x91781,x91781,x91784),x91785))) % 112.37/112.11 [9296]~P36(x92961,x92962)+~P1(f317(f317(f319(x92961),x92963),x92964))+~P1(f317(f317(f319(x92961),x92965),x92964))+~P1(f317(f317(f319(f905(x92961,x92961)),f317(f317(f242(x92961,x92961),x92965),f587(x92962,x92961,x92964))),x92962)) % 112.37/112.11 [9333]~P24(x93332,x93333,x93335,x93331)+E(x93331,f178(f906(x93332,a895)))+E(f317(f300(x93333,x93332,f510(x93334,x93333,x93332,x93331)),x93334),x93331)+~P1(f317(f317(f224(f906(x93333,a895)),f317(f300(x93332,x93333,x93335),x93331)),x93334)) % 112.37/112.11 [9829]~P108(x98295)+~P5(x98295)+P1(f317(f317(f319(x98291),f478(x98292,x98293,x98291,x98294,x98295)),x98293))+~P1(f317(f317(f225(x98295),x98294),f317(f317(f36(x98291,x98295),x98293),x98292))) % 112.37/112.11 [9834]~P108(x98341)+~P5(x98341)+P1(f317(f317(f225(x98341),x98342),f317(x98343,f478(x98343,x98344,x98345,x98342,x98341))))+~P1(f317(f317(f225(x98341),x98342),f317(f317(f36(x98345,x98341),x98344),x98343))) % 112.37/112.11 [9914]~P70(x99141)+~P1(f317(f61(x99141,x99141,f75(x99141),x99142,x99143),x99145))+P1(f317(f317(f319(x99141),x99142),x99143))+P1(f317(f61(x99141,x99141,f75(x99141),x99144,f317(f317(f299(x99141),x99142),x99143)),f317(f317(f75(x99141),x99144),x99145))) % 112.37/112.11 [10127]~P69(x101272)+~P1(f317(f29(x101271),x101275))+E(f317(f317(f8(x101271,x101272),f317(f317(f9(x101271,x101272,x101272),f317(f317(f20(x101271,x101272,f906(x101272,x101272)),f317(f317(f10(a895,f906(x101272,f906(x101272,x101272)),x101271),f86(x101272)),f317(a314,x101273))),x101274)),f2(x101272))),x101275),f2(x101272))+P1(f317(f317(f319(x101271),x101273),x101275)) % 112.37/112.11 [10128]~P75(x101282)+~P1(f317(f29(x101281),x101285))+E(f317(f317(f11(x101281,x101282),f317(f317(f9(x101281,x101282,x101282),f317(f317(f20(x101281,x101282,f906(x101282,x101282)),f317(f317(f10(a895,f906(x101282,f906(x101282,x101282)),x101281),f86(x101282)),f317(a314,x101283))),x101284)),f72(x101282))),x101285),f72(x101282))+P1(f317(f317(f319(x101281),x101283),x101285)) % 112.37/112.11 [10129]~P69(x101292)+~P1(f317(f29(x101291),x101295))+E(f317(f317(f8(x101291,x101292),f317(f317(f9(x101291,x101292,x101292),f317(f317(f20(x101291,x101292,f906(x101292,x101292)),f317(f317(f10(a895,f906(x101292,f906(x101292,x101292)),x101291),f86(x101292)),f317(a314,x101293))),x101294)),f2(x101292))),x101295),f317(x101294,x101293))+~P1(f317(f317(f319(x101291),x101293),x101295)) % 112.37/112.11 [10130]~P75(x101302)+~P1(f317(f29(x101301),x101305))+E(f317(f317(f11(x101301,x101302),f317(f317(f9(x101301,x101302,x101302),f317(f317(f20(x101301,x101302,f906(x101302,x101302)),f317(f317(f10(a895,f906(x101302,f906(x101302,x101302)),x101301),f86(x101302)),f317(a314,x101303))),x101304)),f72(x101302))),x101305),f317(x101304,x101303))+~P1(f317(f317(f319(x101301),x101303),x101305)) % 112.37/112.11 [10188]~P69(x101882)+~P1(f317(f29(x101881),x101885))+E(f317(f317(f8(x101881,x101882),f317(f317(f9(x101881,x101882,x101882),f317(f317(f20(x101881,x101882,f906(x101882,x101882)),f317(f317(f10(a895,f906(x101882,f906(x101882,x101882)),x101881),f86(x101882)),f317(f317(f9(x101881,x101881,a895),a314),x101883))),x101884)),f2(x101882))),x101885),f2(x101882))+P1(f317(f317(f319(x101881),x101883),x101885)) % 112.37/112.11 [10189]~P75(x101892)+~P1(f317(f29(x101891),x101895))+E(f317(f317(f11(x101891,x101892),f317(f317(f9(x101891,x101892,x101892),f317(f317(f20(x101891,x101892,f906(x101892,x101892)),f317(f317(f10(a895,f906(x101892,f906(x101892,x101892)),x101891),f86(x101892)),f317(f317(f9(x101891,x101891,a895),a314),x101893))),x101894)),f72(x101892))),x101895),f72(x101892))+P1(f317(f317(f319(x101891),x101893),x101895)) % 112.37/112.11 [10191]~P69(x101912)+~P1(f317(f29(x101911),x101915))+E(f317(f317(f8(x101911,x101912),f317(f317(f9(x101911,x101912,x101912),f317(f317(f20(x101911,x101912,f906(x101912,x101912)),f317(f317(f10(a895,f906(x101912,f906(x101912,x101912)),x101911),f86(x101912)),f317(f317(f9(x101911,x101911,a895),a314),x101913))),x101914)),f2(x101912))),x101915),f317(x101914,x101913))+~P1(f317(f317(f319(x101911),x101913),x101915)) % 112.37/112.11 [10192]~P75(x101922)+~P1(f317(f29(x101921),x101925))+E(f317(f317(f11(x101921,x101922),f317(f317(f9(x101921,x101922,x101922),f317(f317(f20(x101921,x101922,f906(x101922,x101922)),f317(f317(f10(a895,f906(x101922,f906(x101922,x101922)),x101921),f86(x101922)),f317(f317(f9(x101921,x101921,a895),a314),x101923))),x101924)),f72(x101922))),x101925),f317(x101924,x101923))+~P1(f317(f317(f319(x101921),x101923),x101925)) % 112.37/112.11 [7946]~P68(x79462)+~P1(f317(f29(x79461),x79464))+E(f317(f317(f8(x79461,x79462),x79463),f317(f317(f3(f906(x79461,a895)),x79464),f317(f317(f299(x79461),x79465),f178(f906(x79461,a895))))),f317(f317(f8(x79461,x79462),x79463),x79464))+P1(f317(f317(f319(x79461),x79465),x79464)) % 112.37/112.11 [8449]~P110(x84492)+~P1(f317(f29(x84491),x84494))+E(f317(f317(f8(x84491,x84492),x84493),f317(f317(f3(f906(x84491,a895)),x84494),f317(f317(f299(x84491),x84495),f178(f906(x84491,a895))))),f317(f317(f3(x84492),f317(f317(f8(x84491,x84492),x84493),x84494)),f317(x84493,x84495)))+~P1(f317(f317(f319(x84491),x84495),x84494)) % 112.37/112.11 [8450]~P68(x84502)+~P1(f317(f29(x84501),x84504))+E(f317(f317(f8(x84501,x84502),x84503),f317(f317(f3(f906(x84501,a895)),x84504),f317(f317(f299(x84501),x84505),f178(f906(x84501,a895))))),f317(f317(f3(x84502),f317(f317(f8(x84501,x84502),x84503),x84504)),f317(x84503,x84505)))+~P1(f317(f317(f319(x84501),x84505),x84504)) % 112.37/112.11 [8462]~P119(x84621)+~P1(f317(f317(f224(a899),x84623),x84625))+~P1(f317(f317(f277(x84621),f317(f317(f234(x84621),x84622),x84625)),x84624))+P1(f317(f317(f277(x84621),f317(f317(f234(x84621),x84622),x84623)),x84624)) % 112.37/112.11 [8480]~P68(x84801)+~P1(f317(f29(x84802),x84804))+E(f317(f317(f3(x84801),f317(f317(f8(x84802,x84801),x84803),x84804)),f317(f317(f8(x84802,x84801),x84803),x84805)),f317(f317(f8(x84802,x84801),x84803),f317(f317(f3(f906(x84802,a895)),x84804),x84805)))+~P1(f317(f317(f224(f906(x84802,a895)),x84805),x84804)) % 112.37/112.11 [8499]P1(f317(f29(x84991),f317(x84992,x84993)))+~P1(f317(f29(x84994),x84995))+~P1(f317(f317(f319(x84994),x84993),x84995))+~P1(f317(f29(x84991),f317(f317(f36(x84994,f906(x84991,a895)),x84995),x84992))) % 112.37/112.11 [8955]~P8(x89551,x89555,x89554)+~E(f317(f275(x89551,x89551,x89554),f317(f317(f299(x89551),x89552),f178(f906(x89551,a895)))),f317(f275(x89551,x89551,x89554),f317(f317(f299(x89551),x89553),f178(f906(x89551,a895)))))+~P1(f317(f317(f319(x89551),x89553),x89555))+P1(f317(f317(f319(f905(x89551,x89551)),f317(f317(f242(x89551,x89551),x89552),x89553)),x89554)) % 112.37/112.11 [9252]~P1(f317(x92521,x92525))+P1(f317(x92521,f397(x92521,x92522,x92523,x92524)))+P1(f317(x92521,f394(x92521,x92522,x92523,x92524)))+~P1(f317(f317(f319(x92524),x92525),f317(f317(f91(f906(x92524,a895)),x92523),x92522))) % 112.37/112.11 [9441]~P1(f317(x94411,x94415))+P1(f317(x94411,f394(x94411,x94412,x94413,x94414)))+P1(f317(f317(f319(x94414),f397(x94411,x94412,x94413,x94414)),x94412))+~P1(f317(f317(f319(x94414),x94415),f317(f317(f91(f906(x94414,a895)),x94413),x94412))) % 112.37/112.11 [9442]~P1(f317(x94421,x94425))+P1(f317(x94421,f397(x94421,x94422,x94423,x94424)))+P1(f317(f317(f319(x94424),f394(x94421,x94422,x94423,x94424)),x94423))+~P1(f317(f317(f319(x94424),x94425),f317(f317(f91(f906(x94424,a895)),x94423),x94422))) % 112.37/112.11 [9446]P1(f317(x94461,x94462))+~P1(f317(x94461,f396(x94461,x94463,x94464,x94465)))+~P1(f317(x94461,f395(x94461,x94463,x94464,x94465)))+~P1(f317(f317(f319(x94465),x94462),f317(f317(f91(f906(x94465,a895)),x94464),x94463))) % 112.37/112.11 [9451]~P37(x94511,x94514)+~P1(f317(f317(f319(f905(x94511,x94511)),f317(f317(f242(x94511,x94511),x94512),x94515)),x94514))+P1(f317(f317(f319(f905(x94511,x94511)),f317(f317(f242(x94511,x94511),x94512),x94513)),x94514))+~P1(f317(f317(f319(f905(x94511,x94511)),f317(f317(f242(x94511,x94511),x94515),x94513)),x94514)) % 112.37/112.11 [9490]E(x94901,x94902)+~P1(f317(f317(f319(f905(x94903,x94903)),f317(f317(f242(x94903,x94903),x94901),x94902)),f297(x94903,x94905)))+P1(f317(f317(f319(x94903),x94901),x94904))+~P1(f317(f317(f224(f906(f905(x94903,x94903),a895)),x94905),f317(f317(f244(x94903,x94903),x94904),f317(f18(f906(x94903,a895),x94903),x94904)))) % 112.37/112.11 [9508]P1(f317(x95081,x95082))+~P1(f317(x95081,f395(x95081,x95084,x95085,x95083)))+P1(f317(f317(f319(x95083),f396(x95081,x95084,x95085,x95083)),x95084))+~P1(f317(f317(f319(x95083),x95082),f317(f317(f91(f906(x95083,a895)),x95085),x95084))) % 112.37/112.11 [9509]P1(f317(x95091,x95092))+~P1(f317(x95091,f396(x95091,x95094,x95095,x95093)))+P1(f317(f317(f319(x95093),f395(x95091,x95094,x95095,x95093)),x95095))+~P1(f317(f317(f319(x95093),x95092),f317(f317(f91(f906(x95093,a895)),x95095),x95094))) % 112.37/112.11 [9577]P1(f317(x95771,x95772))+P1(f317(f317(f319(x95773),f396(x95771,x95774,x95775,x95773)),x95774))+P1(f317(f317(f319(x95773),f395(x95771,x95774,x95775,x95773)),x95775))+~P1(f317(f317(f319(x95773),x95772),f317(f317(f91(f906(x95773,a895)),x95775),x95774))) % 112.37/112.11 [9579]~P1(f317(x95792,x95795))+P1(f317(f317(f319(x95791),f397(x95792,x95793,x95794,x95791)),x95793))+P1(f317(f317(f319(x95791),f394(x95792,x95793,x95794,x95791)),x95794))+~P1(f317(f317(f319(x95791),x95795),f317(f317(f91(f906(x95791,a895)),x95794),x95793))) % 112.37/112.11 [9736]~P8(x97361,x97365,x97364)+~P1(f317(f317(f319(x97361),x97363),x97365))+P1(f317(f317(f319(f905(x97361,x97361)),f317(f317(f242(x97361,x97361),x97362),x97363)),x97364))+~P1(f317(f317(f224(f906(x97361,a895)),f317(f275(x97361,x97361,x97364),f317(f317(f299(x97361),x97363),f178(f906(x97361,a895))))),f317(f275(x97361,x97361,x97364),f317(f317(f299(x97361),x97362),f178(f906(x97361,a895)))))) % 112.37/112.11 [9864]~P108(x98645)+~P5(x98645)+P1(f317(f317(f319(x98641),f480(x98642,x98643,x98644,x98641,x98645)),x98644))+~P1(f317(f317(f225(x98645),f317(f317(f35(x98641,x98645),x98644),x98643)),x98642)) % 112.37/112.11 [9897]~P85(x98975)+~P81(x98975)+P1(f317(f317(f319(x98971),f677(x98972,x98973,x98974,x98971,x98975)),f317(f162(x98971),x98974)))+P1(f317(f317(f224(x98975),f317(f155(x98975),f317(f317(f144(x98971,x98975),x98973),x98974))),f317(f155(x98975),f317(f317(f144(x98971,x98975),x98972),x98974)))) % 112.37/112.11 [10005]~P108(x100051)+~P5(x100051)+P1(f317(f317(f225(x100051),f317(x100052,f480(x100053,x100052,x100054,x100055,x100051))),x100053))+~P1(f317(f317(f225(x100051),f317(f317(f35(x100055,x100051),x100054),x100052)),x100053)) % 112.37/112.11 [10145]~P85(x101451)+~P81(x101451)+~P1(f317(f317(f224(x101451),f317(x101453,f677(x101455,x101453,x101454,x101452,x101451))),f317(x101455,f677(x101455,x101453,x101454,x101452,x101451))))+P1(f317(f317(f224(x101451),f317(f155(x101451),f317(f317(f144(x101452,x101451),x101453),x101454))),f317(f155(x101451),f317(f317(f144(x101452,x101451),x101455),x101454)))) % 112.37/112.11 [8795]~P69(x87951)+~P1(f317(f29(x87954),x87955))+~P1(f317(f317(f319(x87954),x87953),x87955))+E(f317(f317(f74(x87951),f317(x87952,x87953)),f317(f317(f8(x87954,x87951),x87952),f317(f317(f3(f906(x87954,a895)),x87955),f317(f317(f299(x87954),x87953),f178(f906(x87954,a895)))))),f317(f317(f8(x87954,x87951),x87952),x87955)) % 112.37/112.11 [8796]~P75(x87961)+~P1(f317(f29(x87964),x87965))+~P1(f317(f317(f319(x87964),x87963),x87965))+E(f317(f317(f75(x87961),f317(x87962,x87963)),f317(f317(f11(x87964,x87961),x87962),f317(f317(f3(f906(x87964,a895)),x87965),f317(f317(f299(x87964),x87963),f178(f906(x87964,a895)))))),f317(f317(f11(x87964,x87961),x87962),x87965)) % 112.37/112.11 [8856]~P18(x88561,x88564,x88565)+~P1(f317(f29(x88561),x88562))+E(f317(f317(f3(f906(x88561,a895)),x88562),f317(f317(f299(x88561),x88563),f178(f906(x88561,a895)))),f178(f906(x88561,a895)))+E(f317(f317(x88564,x88563),f317(x88565,f317(f317(f3(f906(x88561,a895)),x88562),f317(f317(f299(x88561),x88563),f178(f906(x88561,a895)))))),f317(x88565,f317(f317(f299(x88561),x88563),x88562))) % 112.37/112.11 [9230]~P69(x92301)+~P1(f317(f29(x92302),x92305))+~P1(f317(f29(x92302),x92304))+E(f317(f317(f74(x92301),f317(f317(f8(x92302,x92301),x92303),f317(f317(f91(f906(x92302,a895)),x92304),x92305))),f317(f317(f8(x92302,x92301),x92303),f317(f317(f92(f906(x92302,a895)),x92304),x92305))),f317(f317(f74(x92301),f317(f317(f8(x92302,x92301),x92303),x92304)),f317(f317(f8(x92302,x92301),x92303),x92305))) % 112.37/112.11 [9232]~P75(x92321)+~P1(f317(f29(x92322),x92325))+~P1(f317(f29(x92322),x92324))+E(f317(f317(f75(x92321),f317(f317(f11(x92322,x92321),x92323),f317(f317(f91(f906(x92322,a895)),x92324),x92325))),f317(f317(f11(x92322,x92321),x92323),f317(f317(f92(f906(x92322,a895)),x92324),x92325))),f317(f317(f75(x92321),f317(f317(f11(x92322,x92321),x92323),x92324)),f317(f317(f11(x92322,x92321),x92323),x92325))) % 112.37/112.11 [9373]~P68(x93731)+~P1(f317(f29(x93732),x93735))+~P1(f317(f29(x93732),x93734))+E(f317(f317(f3(x93731),f317(f317(f74(x93731),f317(f317(f8(x93732,x93731),x93733),x93734)),f317(f317(f8(x93732,x93731),x93733),x93735))),f317(f317(f8(x93732,x93731),x93733),f317(f317(f92(f906(x93732,a895)),x93734),x93735))),f317(f317(f8(x93732,x93731),x93733),f317(f317(f91(f906(x93732,a895)),x93734),x93735))) % 112.37/112.11 [9593]~P24(x95931,x95932,x95933,x95935)+~P24(x95931,x95932,x95933,x95934)+P24(x95931,x95932,x95933,f317(f317(f91(f906(x95931,a895)),x95934),x95935))+~E(f317(f317(f92(f906(x95932,a895)),f317(f300(x95931,x95932,x95933),f317(f317(f3(f906(x95931,a895)),x95934),x95935))),f317(f300(x95931,x95932,x95933),f317(f317(f3(f906(x95931,a895)),x95935),x95934))),f178(f906(x95932,a895))) % 112.37/112.11 [9711]E(x97111,f2(a1))+~P1(f317(f317(f225(a1),f2(a1)),x97113))+~P1(f317(f45(x97112,x97111),f317(f317(f242(a1,a1),x97114),x97115)))+P1(f317(f45(x97112,f317(f317(f75(a1),x97111),x97113)),f317(f317(f242(a1,a1),f317(f317(f31(a1),x97114),x97113)),f317(f317(f74(a1),f317(f317(f75(a1),x97111),f41(a1,x97114,x97113))),x97115)))) % 112.37/112.11 [9719]~P1(f317(f317(f225(a899),f2(a899)),x97193))+~P1(f317(f317(f225(a899),f2(a899)),x97192))+~P1(f317(f44(x97191,x97192),f317(f317(f242(a899,a899),x97194),x97195)))+P1(f317(f44(x97191,f317(f317(f75(a899),x97192),x97193)),f317(f317(f242(a899,a899),f317(f317(f31(a899),x97194),x97193)),f317(f317(f74(a899),f317(f317(f75(a899),x97192),f41(a899,x97194,x97193))),x97195)))) % 112.37/112.11 [9768]~P75(x97681)+~P1(f317(f29(x97682),x97685))+~P1(f317(f29(x97682),x97684))+E(f317(f317(f75(x97681),f317(f317(f317(f60(x97681,x97682,f75(x97681)),x97683),f72(x97681)),f317(f317(f91(f906(x97682,a895)),x97684),x97685))),f317(f317(f317(f60(x97681,x97682,f75(x97681)),x97683),f72(x97681)),f317(f317(f92(f906(x97682,a895)),x97684),x97685))),f317(f317(f75(x97681),f317(f317(f317(f60(x97681,x97682,f75(x97681)),x97683),f72(x97681)),x97684)),f317(f317(f317(f60(x97681,x97682,f75(x97681)),x97683),f72(x97681)),x97685))) % 112.37/112.11 [9770]~E(f317(f317(f165(x97701),x97705),x97702),f317(f317(f165(x97701),x97705),x97703))+P1(f317(f317(f319(f905(f900(x97701),f900(x97701))),f317(f317(f242(f900(x97701),f900(x97701)),x97702),x97703)),f137(x97701,x97704)))+~P1(f317(f317(f225(a899),x97705),f317(f317(f228(a899),f317(f179(f900(x97701)),x97702)),f317(f179(f900(x97701)),x97703))))+~P1(f317(f317(f319(f905(x97701,x97701)),f317(f317(f242(x97701,x97701),f317(f317(f154(x97701),x97702),x97705)),f317(f317(f154(x97701),x97703),x97705))),x97704)) % 112.37/112.11 [9886]~P85(x98865)+~P145(x98865)+P1(f317(f317(f319(x98861),f886(x98862,x98863,x98864,x98861,x98865)),x98864))+P1(f317(f317(f224(x98865),f317(f317(f8(x98861,x98865),x98863),x98864)),f317(f317(f75(x98865),f317(f90(x98865),f317(f30(x98861),x98864))),x98862))) % 112.37/112.11 [10063]~P85(x100631)+~P145(x100631)+~P1(f317(f317(f224(x100631),f317(x100633,f886(x100635,x100633,x100634,x100632,x100631))),x100635))+P1(f317(f317(f224(x100631),f317(f317(f8(x100632,x100631),x100633),x100634)),f317(f317(f75(x100631),f317(f90(x100631),f317(f30(x100632),x100634))),x100635))) % 112.37/112.11 [8824]E(f317(f317(f124(x88241),x88242),x88243),f317(f317(f124(x88241),x88244),x88245))+~E(f317(f317(f165(x88241),f317(f179(f900(x88241)),x88242)),x88244),x88242)+~E(f317(f317(f124(x88241),f317(f317(f128(x88241),f317(f179(f900(x88241)),x88242)),x88244)),x88245),x88243)+P1(f317(f317(f224(a899),f317(f179(f900(x88241)),x88244)),f317(f179(f900(x88241)),x88242))) % 112.37/112.11 [8954]E(f317(f317(f124(x89541),x89542),x89543),f317(f317(f124(x89541),x89544),x89545))+~E(f317(f317(f165(x89541),f317(f179(f900(x89541)),x89542)),x89544),x89542)+~E(x89543,f317(f317(f124(x89541),f317(f317(f128(x89541),f317(f179(f900(x89541)),x89542)),x89544)),x89545))+~P1(f317(f317(f224(a899),f317(f179(f900(x89541)),x89542)),f317(f179(f900(x89541)),x89544))) % 112.37/112.11 [10209]~P1(f317(x102095,x102094))+~P1(f317(f29(x102092),f317(f252(x102092),x102095)))+P1(f317(f29(x102091),f317(f252(x102091),f317(f317(f9(x102091,x102092,a895),x102093),x102094))))+~P1(f317(f29(x102091),f317(f252(x102091),f317(f317(f10(f906(x102092,a895),a895,x102091),f81(x102092)),f317(f317(f10(f906(x102092,a895),f906(x102092,a895),x102091),f317(f20(x102092,a895,a895),f317(f317(f10(a895,f906(a895,a895),x102092),a315),x102095))),x102093))))) % 112.37/112.11 [10285]~P1(f317(f29(x102852),x102855))+~P1(f317(f317(f319(x102852),x102854),x102855))+P1(f317(f29(x102851),f317(f252(x102851),f317(f317(f9(x102851,x102852,a895),x102853),x102854))))+~P1(f317(f29(x102851),f317(f252(x102851),f317(f317(f10(f906(x102852,a895),a895,x102851),f81(x102852)),f317(f317(f10(f906(x102852,a895),f906(x102852,a895),x102851),f317(f20(x102852,a895,a895),f317(f317(f10(a895,f906(a895,a895),x102852),a315),f317(f317(f9(x102852,f906(x102852,a895),a895),f319(x102852)),x102855)))),x102853))))) % 112.37/112.11 [8610]~P19(x86105,x86101,x86106,x86102)+E(f317(f67(x86101,x86101,x86101,f317(x86102,x86103)),f317(x86102,x86104)),f317(f67(x86101,x86101,x86101,f317(x86102,x86104)),f317(x86102,x86103)))+~P1(f317(f29(x86105),x86104))+~P1(f317(f29(x86105),x86103)) % 112.37/112.11 [8002]~P24(x80021,x80022,x80024,x80023)+~E(f317(x80024,x80026),x80025)+E(f317(f71(x80021,x80022,x80023,x80024),x80025),x80026)+~P1(f317(f317(f319(x80021),x80026),x80023)) % 112.37/112.11 [8003]~P24(x80031,x80032,x80034,x80033)+~E(f317(x80034,x80036),x80035)+E(f317(f85(x80031,x80032,x80033,x80034),x80035),x80036)+~P1(f317(f317(f319(x80031),x80036),x80033)) % 112.37/112.11 [8196]~P20(x81966,x81961,x81964,x81962)+E(f317(f67(x81961,x81961,x81961,f317(x81962,x81963)),f317(x81964,x81965)),f317(x81962,x81963))+~P1(f317(f29(x81966),x81963))+~P1(f317(f317(f319(x81966),x81965),x81963)) % 112.37/112.11 [9324]E(x93241,x93242)+~E(f317(f85(x93243,x93244,x93245,x93246),x93241),f317(f85(x93243,x93244,x93245,x93246),x93242))+~P1(f317(f317(f319(x93244),x93242),f317(f300(x93243,x93244,x93246),x93245)))+~P1(f317(f317(f319(x93244),x93241),f317(f300(x93243,x93244,x93246),x93245))) % 112.37/112.11 [9425]~P19(x94253,x94251,x94256,x94252)+E(f317(f67(x94251,x94251,x94251,f317(x94252,f317(f317(f3(f906(x94253,a895)),x94254),f317(f317(f299(x94253),x94255),f178(f906(x94253,a895)))))),f317(x94256,x94255)),f317(x94252,x94254))+~P1(f317(f29(x94253),x94254))+~P1(f317(f317(f319(x94253),x94255),x94254)) % 112.37/112.11 [7083]~P4(x70831)+~E(f41(x70831,x70833,x70834),f41(x70831,x70836,x70834))+~E(f41(x70831,x70832,x70834),f41(x70831,x70835,x70834))+E(f41(x70831,f317(f317(f3(x70831),x70832),x70833),x70834),f41(x70831,f317(f317(f3(x70831),x70835),x70836),x70834)) % 112.37/112.11 [7084]~P3(x70841)+~E(f41(x70841,x70843,x70844),f41(x70841,x70846,x70844))+~E(f41(x70841,x70842,x70844),f41(x70841,x70845,x70844))+E(f41(x70841,f317(f317(f74(x70841),x70842),x70843),x70844),f41(x70841,f317(f317(f74(x70841),x70845),x70846),x70844)) % 112.37/112.11 [7085]~P3(x70851)+~E(f41(x70851,x70853,x70854),f41(x70851,x70856,x70854))+~E(f41(x70851,x70852,x70854),f41(x70851,x70855,x70854))+E(f41(x70851,f317(f317(f75(x70851),x70852),x70853),x70854),f41(x70851,f317(f317(f75(x70851),x70855),x70856),x70854)) % 112.37/112.11 [7897]~P16(x78971,x78972,x78973)+~P1(f317(f29(x78971),x78976))+E(f317(f317(f59(x78971,x78972,x78973),x78974),f317(f317(f299(x78971),x78975),x78976)),f317(f317(f59(x78971,x78972,x78973),f317(f317(x78973,x78975),x78974)),x78976))+P1(f317(f317(f319(x78971),x78975),x78976)) % 112.37/112.11 [7961]~P5(x79611)+P1(f317(f317(f224(x79611),x79612),f317(x79613,x79614)))+~P1(f317(f317(f319(x79615),x79614),x79616))+~P1(f317(f317(f224(x79611),x79612),f317(f317(f35(x79615,x79611),x79616),x79613))) % 112.37/112.11 [8118]~P16(x81181,x81182,x81183)+~P1(f317(f29(x81181),x81186))+E(f317(f317(f59(x81181,x81182,x81183),x81184),f317(f317(f299(x81181),x81185),x81186)),f317(f317(x81183,x81185),f317(f317(f59(x81181,x81182,x81183),x81184),x81186)))+P1(f317(f317(f319(x81181),x81185),x81186)) % 112.37/112.11 [8214]~P108(x82143)+~P1(f317(x82142,x82145))+~P13(x82143,f317(f317(f144(x82141,x82143),x82144),x82146))+E(f317(f126(x82141,x82142),f317(f317(f138(x82141,x82143,x82144),x82145),x82146)),f317(f317(f138(x82141,x82143,x82144),x82145),f317(f126(x82141,x82142),x82146))) % 112.37/112.11 [8237]E(x82371,x82372)+E(x82373,f2(a1))+~P1(f317(f45(x82374,x82373),f317(f317(f242(a1,a1),x82375),x82372)))+~P1(f317(f45(x82374,x82373),f317(f317(f242(a1,a1),x82376),x82371))) % 112.37/112.11 [8238]E(x82381,x82382)+E(x82383,f2(a1))+~P1(f317(f45(x82384,x82383),f317(f317(f242(a1,a1),x82382),x82385)))+~P1(f317(f45(x82384,x82383),f317(f317(f242(a1,a1),x82381),x82386))) % 112.37/112.11 [8261]~P19(x82612,x82615,x82616,x82611)+~P1(f317(f29(x82612),x82614))+E(f317(x82611,f317(f317(f299(x82612),x82613),x82614)),f317(f67(x82615,x82615,x82615,f317(x82611,x82614)),f317(x82616,x82613)))+P1(f317(f317(f319(x82612),x82613),x82614)) % 112.37/112.11 [8483]~P20(x84835,x84831,x84836,x84832)+E(f317(f67(x84831,x84831,x84831,f317(x84832,x84833)),f317(x84832,x84834)),f317(x84832,x84833))+~P1(f317(f29(x84835),x84833))+~P1(f317(f317(f224(f906(x84835,a895)),x84834),x84833)) % 112.37/112.11 [9640]~P24(x96401,x96402,x96404,x96403)+~P1(f317(f317(f319(x96402),x96405),f317(f300(x96401,x96402,x96404),x96403)))+P1(f317(f317(f319(x96401),f317(f71(x96401,x96402,x96403,x96404),x96405)),x96406))+~P1(f317(f317(f224(f906(x96401,a895)),x96403),x96406)) % 112.37/112.11 [10016]~P69(x100162)+~E(f579(x100161,x100163,x100165,x100166,x100164,x100162),f580(x100161,x100163,x100165,x100166,x100164,x100162))+~P1(f317(f29(x100164),x100166))+E(f317(f317(f8(x100161,x100162),x100163),f317(f300(x100164,x100161,x100165),x100166)),f317(f317(f8(x100164,x100162),f317(f67(x100161,x100162,x100164,x100163),x100165)),x100166)) % 112.37/112.11 [10044]~P69(x100446)+E(f317(x100441,f579(x100442,x100443,x100441,x100444,x100445,x100446)),f317(x100441,f580(x100442,x100443,x100441,x100444,x100445,x100446)))+E(f317(f317(f8(x100442,x100446),x100443),f317(f300(x100445,x100442,x100441),x100444)),f317(f317(f8(x100445,x100446),f317(f67(x100442,x100446,x100445,x100443),x100441)),x100444))+~P1(f317(f29(x100445),x100444)) % 112.37/112.11 [10095]~P69(x100952)+~E(f317(x100953,f317(x100955,f580(x100951,x100953,x100955,x100956,x100954,x100952))),f2(x100952))+~P1(f317(f29(x100954),x100956))+E(f317(f317(f8(x100951,x100952),x100953),f317(f300(x100954,x100951,x100955),x100956)),f317(f317(f8(x100954,x100952),f317(f67(x100951,x100952,x100954,x100953),x100955)),x100956)) % 112.37/112.11 [10153]~P69(x101532)+~P1(f317(f29(x101534),x101536))+E(f317(f317(f8(x101531,x101532),x101533),f317(f300(x101534,x101531,x101535),x101536)),f317(f317(f8(x101534,x101532),f317(f67(x101531,x101532,x101534,x101533),x101535)),x101536))+P1(f317(f317(f319(x101534),f580(x101531,x101533,x101535,x101536,x101534,x101532)),x101536)) % 112.37/112.11 [10154]~P69(x101542)+~P1(f317(f29(x101544),x101546))+E(f317(f317(f8(x101541,x101542),x101543),f317(f300(x101544,x101541,x101545),x101546)),f317(f317(f8(x101544,x101542),f317(f67(x101541,x101542,x101544,x101543),x101545)),x101546))+P1(f317(f317(f319(x101544),f579(x101541,x101543,x101545,x101546,x101544,x101542)),x101546)) % 112.37/112.11 [10284]~P75(x102841)+~P1(f317(f29(x102842),x102846))+E(f317(f317(f317(f60(x102841,x102842,f75(x102841)),f317(f317(f20(x102842,f906(x102843,a895),x102841),f317(f317(f9(x102842,x102841,f906(f906(x102843,a895),x102841)),f317(f317(f10(f906(x102843,x102841),f906(x102841,f906(f906(x102843,a895),x102841)),x102842),f60(x102841,x102843,f75(x102841))),x102844)),f72(x102841))),x102845)),f72(x102841)),x102846),f317(f317(f317(f60(x102841,f905(x102842,x102843),f75(x102841)),f317(f247(x102842,x102843,x102841),x102844)),f72(x102841)),f317(f317(f244(x102842,x102843),x102846),x102845)))+P1(f317(f317(f319(x102842),f534(x102844,x102845,x102843,x102846,x102842,x102841)),x102846)) % 112.37/112.11 [10306]~P75(x103061)+~P1(f317(f29(x103062),x103066))+E(f317(f317(f317(f60(x103061,x103062,f75(x103061)),f317(f317(f20(x103062,f906(x103063,a895),x103061),f317(f317(f9(x103062,x103061,f906(f906(x103063,a895),x103061)),f317(f317(f10(f906(x103063,x103061),f906(x103061,f906(f906(x103063,a895),x103061)),x103062),f60(x103061,x103063,f75(x103061))),x103064)),f72(x103061))),x103065)),f72(x103061)),x103066),f317(f317(f317(f60(x103061,f905(x103062,x103063),f75(x103061)),f317(f247(x103062,x103063,x103061),x103064)),f72(x103061)),f317(f317(f244(x103062,x103063),x103066),x103065)))+~P1(f317(f29(x103063),f317(x103065,f534(x103064,x103065,x103063,x103066,x103062,x103061)))) % 112.37/112.11 [8393]~P20(x83932,x83935,x83936,x83931)+~P1(f317(f29(x83932),x83934))+~P1(f317(f29(x83932),x83933))+E(f317(x83931,f317(f317(f91(f906(x83932,a895)),x83933),x83934)),f317(f67(x83935,x83935,x83935,f317(x83931,x83933)),f317(x83931,x83934))) % 112.37/112.11 [8611]~P5(x86111)+P1(f317(f317(f224(x86111),f317(x86112,x86113)),x86114))+~P1(f317(f317(f319(x86115),x86113),x86116))+~P1(f317(f317(f224(x86111),f317(f317(f36(x86115,x86111),x86116),x86112)),x86114)) % 112.37/112.11 [9040]~P24(x90402,x90401,x90403,x90406)+E(f317(f317(f3(f906(x90401,a895)),f317(f300(x90402,x90401,x90403),x90404)),f317(f300(x90402,x90401,x90403),x90405)),f317(f300(x90402,x90401,x90403),f317(f317(f3(f906(x90402,a895)),x90404),x90405)))+~P1(f317(f317(f224(f906(x90402,a895)),x90405),x90406))+~P1(f317(f317(f224(f906(x90402,a895)),x90404),x90406)) % 112.37/112.11 [9041]~P24(x90412,x90411,x90413,x90416)+E(f317(f317(f92(f906(x90411,a895)),f317(f300(x90412,x90411,x90413),x90414)),f317(f300(x90412,x90411,x90413),x90415)),f317(f300(x90412,x90411,x90413),f317(f317(f92(f906(x90412,a895)),x90414),x90415)))+~P1(f317(f317(f224(f906(x90412,a895)),x90415),x90416))+~P1(f317(f317(f224(f906(x90412,a895)),x90414),x90416)) % 112.37/112.11 [9298]E(x92981,x92982)+~P54(x92983,x92984,x92985)+~P1(f317(f317(f319(f905(x92983,x92984)),f317(f317(f242(x92983,x92984),x92986),x92982)),x92985))+~P1(f317(f317(f319(f905(x92983,x92984)),f317(f317(f242(x92983,x92984),x92986),x92981)),x92985)) % 112.37/112.11 [10091]~P70(x100911)+~E(f317(x100913,f439(x100914,x100916,x100913,x100915,x100912,x100911)),f317(x100916,f439(x100914,x100916,x100913,x100915,x100912,x100911)))+~P1(f317(f29(x100912),x100915))+E(f317(f317(f317(f60(x100911,x100912,f75(x100911)),x100913),x100914),x100915),f317(f317(f317(f60(x100911,x100912,f75(x100911)),x100916),x100914),x100915)) % 112.37/112.11 [10151]~P70(x101511)+~P1(f317(f29(x101512),x101515))+E(f317(f317(f317(f60(x101511,x101512,f75(x101511)),x101513),x101514),x101515),f317(f317(f317(f60(x101511,x101512,f75(x101511)),x101516),x101514),x101515))+P1(f317(f317(f319(x101512),f439(x101514,x101513,x101516,x101515,x101512,x101511)),x101515)) % 112.37/112.11 [8838]~P70(x88381)+~P1(f317(f29(x88382),x88386))+P1(f317(f317(f319(x88382),x88385),x88386))+E(f317(f317(f317(f60(x88381,x88382,f75(x88381)),x88383),x88384),f317(f317(f299(x88382),x88385),x88386)),f317(f317(f75(x88381),f317(x88383,x88385)),f317(f317(f317(f60(x88381,x88382,f75(x88381)),x88383),x88384),x88386))) % 112.37/112.11 [8891]~P8(x88911,x88916,x88913)+~P11(x88911,f906(x88912,a895),x88913,x88915)+~P1(f317(f317(f319(x88911),x88914),x88916))+E(f317(f317(f36(x88911,f906(x88912,a895)),f317(f275(x88911,x88911,x88913),f317(f317(f299(x88911),x88914),f178(f906(x88911,a895))))),x88915),f317(x88915,x88914)) % 112.37/112.11 [9017]~P16(x90173,x90174,x90171)+~P1(f317(f29(x90173),x90176))+~P1(f317(f317(f319(x90173),x90172),x90176))+E(f317(f317(x90171,x90172),f317(f317(f59(x90173,x90174,x90171),x90175),f317(f317(f3(f906(x90173,a895)),x90176),f317(f317(f299(x90173),x90172),f178(f906(x90173,a895)))))),f317(f317(f59(x90173,x90174,x90171),x90175),x90176)) % 112.37/112.11 [9308]~P19(x93083,x93081,x93086,x93082)+~P1(f317(f29(x93083),x93085))+~P1(f317(f29(x93083),x93084))+E(f317(f67(x93081,x93081,x93081,f317(x93082,f317(f317(f91(f906(x93083,a895)),x93084),x93085))),f317(x93082,f317(f317(f92(f906(x93083,a895)),x93084),x93085))),f317(f67(x93081,x93081,x93081,f317(x93082,x93084)),f317(x93082,x93085))) % 112.37/112.11 [9664]~E(x96643,f317(f317(f149(x96641,x96642),x96645),x96646))+P1(f317(f317(f319(f905(f900(x96641),f900(x96641))),f317(f317(f242(f900(x96641),f900(x96641)),x96642),x96643)),f147(x96641,x96644)))+~P1(f317(f317(f225(a899),x96645),f317(f179(f900(x96641)),x96642)))+~P1(f317(f317(f319(f905(x96641,x96641)),f317(f317(f242(x96641,x96641),f317(f317(f154(x96641),x96642),x96645)),x96646)),x96644)) % 112.37/112.11 [10168]~P69(x101682)+~P1(f317(f29(x101681),x101686))+P1(f317(f317(f319(x101681),f531(x101684,x101685,x101683,x101686,x101681,x101682)),x101686))+E(f317(f317(f8(x101681,x101682),f317(f317(f20(x101681,f906(x101683,a895),x101682),f317(f317(f10(f906(x101683,x101682),f906(f906(x101683,a895),x101682),x101681),f8(x101683,x101682)),x101684)),x101685)),x101686),f317(f317(f8(f905(x101681,x101683),x101682),f317(f247(x101681,x101683,x101682),x101684)),f317(f317(f244(x101681,x101683),x101686),x101685))) % 112.37/112.11 [10169]~P75(x101692)+~P1(f317(f29(x101691),x101696))+P1(f317(f317(f319(x101691),f532(x101694,x101695,x101693,x101696,x101691,x101692)),x101696))+E(f317(f317(f11(x101691,x101692),f317(f317(f20(x101691,f906(x101693,a895),x101692),f317(f317(f10(f906(x101693,x101692),f906(f906(x101693,a895),x101692),x101691),f11(x101693,x101692)),x101694)),x101695)),x101696),f317(f317(f11(f905(x101691,x101693),x101692),f317(f247(x101691,x101693,x101692),x101694)),f317(f317(f244(x101691,x101693),x101696),x101695))) % 112.37/112.11 [10207]~P69(x102072)+~P1(f317(f29(x102071),x102076))+~P1(f317(f29(x102073),f317(x102075,f531(x102074,x102075,x102073,x102076,x102071,x102072))))+E(f317(f317(f8(x102071,x102072),f317(f317(f20(x102071,f906(x102073,a895),x102072),f317(f317(f10(f906(x102073,x102072),f906(f906(x102073,a895),x102072),x102071),f8(x102073,x102072)),x102074)),x102075)),x102076),f317(f317(f8(f905(x102071,x102073),x102072),f317(f247(x102071,x102073,x102072),x102074)),f317(f317(f244(x102071,x102073),x102076),x102075))) % 112.37/112.11 [10208]~P75(x102082)+~P1(f317(f29(x102081),x102086))+~P1(f317(f29(x102083),f317(x102085,f532(x102084,x102085,x102083,x102086,x102081,x102082))))+E(f317(f317(f11(x102081,x102082),f317(f317(f20(x102081,f906(x102083,a895),x102082),f317(f317(f10(f906(x102083,x102082),f906(f906(x102083,a895),x102082),x102081),f11(x102083,x102082)),x102084)),x102085)),x102086),f317(f317(f11(f905(x102081,x102083),x102082),f317(f247(x102081,x102083,x102082),x102084)),f317(f317(f244(x102081,x102083),x102086),x102085))) % 112.37/112.11 [10190]~P75(x101902)+~P1(f317(f29(x101901),x101906))+P1(f317(f317(f319(x101901),x101903),x101906))+E(f317(f317(f11(x101901,x101902),f317(f317(f9(x101901,x101902,x101902),f317(f317(f20(x101901,x101902,f906(x101902,x101902)),f317(f317(f10(a895,f906(x101902,f906(x101902,x101902)),x101901),f86(x101902)),f317(f317(f9(x101901,x101901,a895),a314),x101903))),x101904)),x101905)),x101906),f317(f317(f234(x101902),x101905),f317(f30(x101901),x101906))) % 112.37/112.11 [10193]~P75(x101932)+~P1(f317(f29(x101931),x101936))+~P1(f317(f317(f319(x101931),x101933),x101936))+E(f317(f317(f11(x101931,x101932),f317(f317(f9(x101931,x101932,x101932),f317(f317(f20(x101931,x101932,f906(x101932,x101932)),f317(f317(f10(a895,f906(x101932,f906(x101932,x101932)),x101931),f86(x101932)),f317(f317(f9(x101931,x101931,a895),a314),x101933))),x101934)),x101935)),x101936),f317(f317(f75(x101932),f317(x101934,x101933)),f317(f317(f234(x101932),x101935),f317(f317(f3(a899),f317(f30(x101931),x101936)),f72(a899))))) % 112.37/112.11 [10271]~P1(f317(f29(x102711),x102715))+~P1(f317(f29(x102712),x102713))+P1(f317(f317(f319(x102712),f533(x102716,x102714,x102713,x102712,x102715,x102711)),x102713))+E(f317(f317(f8(x102711,a899),f317(f317(f10(f906(x102712,a895),a899,x102711),f30(x102712)),f317(f317(f10(f906(x102712,a895),f906(x102712,a895),x102711),f252(x102712)),f317(f317(f10(f906(x102712,a895),f906(x102712,a895),x102711),f317(f20(x102712,a895,a895),f317(f317(f10(a895,f906(a895,a895),x102712),a315),f317(f317(f9(x102712,f906(x102712,a895),a895),f319(x102712)),x102713)))),x102714)))),x102715),f317(f317(f75(a899),x102716),f317(f30(x102712),x102713))) % 112.37/112.11 [10272]~P1(f317(f29(x102721),x102725))+~P1(f317(f29(x102722),x102723))+P1(f317(f317(f319(x102722),f538(x102726,x102724,x102723,x102722,x102725,x102721)),x102723))+E(f317(f317(f8(x102721,a899),f317(f317(f10(f906(x102722,a895),a899,x102721),f30(x102722)),f317(f317(f10(f906(x102722,a895),f906(x102722,a895),x102721),f252(x102722)),f317(f317(f10(f906(x102722,a895),f906(x102722,a895),x102721),f317(f20(x102722,a895,a895),f317(f317(f10(a895,f906(a895,a895),x102722),a315),f317(f317(f9(x102722,f906(x102722,a895),a895),f319(x102722)),x102723)))),x102724)))),x102725),f317(f317(f8(x102722,a899),x102726),x102723)) % 112.37/112.11 [10319]~P1(f317(f29(x103192),x103193))+~P1(f317(f29(x103191),x103195))+~E(f317(f30(x103191),f317(f252(x103191),f317(f317(f20(x103191,a895,a895),f317(f317(f10(a895,f906(a895,a895),x103191),a315),f317(f317(f9(x103191,f906(x103191,a895),a895),f319(x103191)),x103195))),f317(f317(f9(x103191,x103192,a895),x103194),f533(x103196,x103194,x103193,x103192,x103195,x103191))))),x103196)+E(f317(f317(f8(x103191,a899),f317(f317(f10(f906(x103192,a895),a899,x103191),f30(x103192)),f317(f317(f10(f906(x103192,a895),f906(x103192,a895),x103191),f252(x103192)),f317(f317(f10(f906(x103192,a895),f906(x103192,a895),x103191),f317(f20(x103192,a895,a895),f317(f317(f10(a895,f906(a895,a895),x103192),a315),f317(f317(f9(x103192,f906(x103192,a895),a895),f319(x103192)),x103193)))),x103194)))),x103195),f317(f317(f75(a899),x103196),f317(f30(x103192),x103193))) % 112.37/112.11 [10321]~P1(f317(f29(x103212),x103213))+~P1(f317(f29(x103211),x103215))+~E(f317(f30(x103211),f317(f252(x103211),f317(f317(f20(x103211,a895,a895),f317(f317(f10(a895,f906(a895,a895),x103211),a315),f317(f317(f9(x103211,f906(x103211,a895),a895),f319(x103211)),x103215))),f317(f317(f9(x103211,x103212,a895),x103214),f538(x103216,x103214,x103213,x103212,x103215,x103211))))),f317(x103216,f538(x103216,x103214,x103213,x103212,x103215,x103211)))+E(f317(f317(f8(x103211,a899),f317(f317(f10(f906(x103212,a895),a899,x103211),f30(x103212)),f317(f317(f10(f906(x103212,a895),f906(x103212,a895),x103211),f252(x103212)),f317(f317(f10(f906(x103212,a895),f906(x103212,a895),x103211),f317(f20(x103212,a895,a895),f317(f317(f10(a895,f906(a895,a895),x103212),a315),f317(f317(f9(x103212,f906(x103212,a895),a895),f319(x103212)),x103213)))),x103214)))),x103215),f317(f317(f8(x103212,a899),x103216),x103213)) % 112.37/112.11 [9942]E(x99421,x99422)+~P16(x99423,x99424,x99425)+~P1(f317(f61(x99423,x99424,x99425,x99426,x99427),x99422))+~P1(f317(f61(x99423,x99424,x99425,x99426,x99427),x99421)) % 112.37/112.11 [9740]P1(f317(x97401,x97402))+~P1(f317(f317(f319(x97407),x97402),f317(x97406,x97404)))+~P1(f317(x97401,f473(x97401,x97406,x97405,x97403,x97407)))+~P1(f317(f317(f319(x97403),x97404),x97405)) % 112.37/112.11 [10182]~P16(x101827,x101826,x101821)+E(f317(f317(x101821,x101822),f481(x101822,x101823,x101824,x101825,x101821,x101826,x101827)),x101823)+~P1(f317(f61(x101827,x101826,x101821,x101825,x101824),x101823))+~P1(f317(f317(f319(x101827),x101822),x101824)) % 112.37/112.11 [10249]~P16(x102491,x102492,x102493)+~P1(f317(f61(x102491,x102492,x102493,x102494,x102495),x102497))+P1(f317(f61(x102491,x102492,x102493,x102494,f317(f317(f3(f906(x102491,a895)),x102495),f317(f317(f299(x102491),x102496),f178(f906(x102491,a895))))),f481(x102496,x102497,x102495,x102494,x102493,x102492,x102491)))+~P1(f317(f317(f319(x102491),x102496),x102495)) % 112.37/112.11 [9380]P25(x93801,x93802,x93803,x93804,x93805)+~P25(x93801,x93802,x93803,x93806,x93807)+~E(f317(f300(x93801,x93802,x93803),x93804),x93805)+~P1(f317(f317(f224(f906(x93801,a895)),x93804),x93806)) % 112.37/112.11 [9631]~P25(x96311,x96312,x96313,x96315,x96317)+~P25(x96311,x96312,x96313,x96314,x96316)+P25(x96311,x96312,x96313,f317(f317(f91(f906(x96311,a895)),x96314),x96315),f317(f317(f91(f906(x96312,a895)),x96316),x96317))+~E(f317(f317(f92(f906(x96312,a895)),x96316),x96317),f178(f906(x96312,a895))) % 112.37/112.11 [9636]~P70(x96361)+~P24(x96365,x96362,x96366,x96367)+~P1(f317(f29(x96365),x96367))+E(f317(f317(f317(f60(x96361,x96362,f75(x96361)),x96363),x96364),f317(f300(x96365,x96362,x96366),x96367)),f317(f317(f317(f60(x96361,x96365,f75(x96361)),f317(f67(x96362,x96361,x96365,x96363),x96366)),x96364),x96367)) % 112.37/112.11 [9763]~E(f317(f317(f299(x97631),x97635),x97636),f317(f317(f299(x97631),x97632),x97633))+~P1(f317(f61(x97631,x97631,x97634,x97632,x97633),x97637))+P1(f317(f317(f319(x97631),x97632),x97633))+P1(f317(f57(x97631,x97634,f317(f317(f299(x97631),x97635),x97636)),x97637)) % 112.37/112.11 [9847]P1(f317(x98471,x98472))+~P1(f317(f317(f319(x98473),x98472),f317(x98474,x98477)))+~P1(f317(f317(f319(x98476),x98477),x98475))+P1(f317(f317(f319(x98473),f473(x98471,x98474,x98475,x98476,x98473)),f317(f317(f36(x98476,f906(x98473,a895)),x98475),x98474))) % 112.37/112.11 [9865]~P24(x98652,x98651,x98655,x98654)+~P24(x98651,x98653,x98656,f317(f300(x98652,x98651,x98655),x98654))+E(f317(f317(f67(x98651,x98652,x98653,f71(x98652,x98651,x98654,x98655)),f71(x98651,x98653,f317(f300(x98652,x98651,x98655),x98654),x98656)),x98657),f317(f71(x98652,x98653,x98654,f317(f67(x98651,x98653,x98652,x98656),x98655)),x98657))+~P1(f317(f317(f319(x98653),x98657),f317(f300(x98651,x98653,x98656),f317(f300(x98652,x98651,x98655),x98654)))) % 112.37/112.11 [9866]~P24(x98662,x98661,x98665,x98664)+~P24(x98661,x98663,x98666,f317(f300(x98662,x98661,x98665),x98664))+E(f317(f317(f67(x98661,x98662,x98663,f85(x98662,x98661,x98664,x98665)),f85(x98661,x98663,f317(f300(x98662,x98661,x98665),x98664),x98666)),x98667),f317(f85(x98662,x98663,x98664,f317(f67(x98661,x98663,x98662,x98666),x98665)),x98667))+~P1(f317(f317(f319(x98663),x98667),f317(f300(x98661,x98663,x98666),f317(f300(x98662,x98661,x98665),x98664)))) % 112.37/112.11 [10183]~P16(x101837,x101836,x101831)+E(f317(f317(x101831,x101832),f543(x101833,x101834,x101832,x101835,x101831,x101836,x101837)),x101833)+P1(f317(f317(f319(x101837),x101832),x101834))+~P1(f317(f61(x101837,x101836,x101831,x101835,f317(f317(f299(x101837),x101832),x101834)),x101833)) % 112.37/112.11 [10248]~P16(x102481,x102484,x102485)+P1(f317(f61(x102481,x102484,x102485,x102486,x102483),f543(x102487,x102483,x102482,x102486,x102485,x102484,x102481)))+P1(f317(f317(f319(x102481),x102482),x102483))+~P1(f317(f61(x102481,x102484,x102485,x102486,f317(f317(f299(x102481),x102482),x102483)),x102487)) % 112.37/112.11 [9924]E(x99241,f2(a1))+~P1(f317(f45(x99243,x99241),f317(f317(f242(a1,a1),x99245),x99247)))+~P1(f317(f45(x99242,x99241),f317(f317(f242(a1,a1),x99244),x99246)))+P1(f317(f45(f317(f317(f74(a1),x99242),x99243),x99241),f317(f317(f242(a1,a1),f317(f317(f74(a1),f317(f317(f74(a1),x99244),x99245)),f317(f317(f31(a1),f317(f317(f74(a1),x99246),x99247)),x99241))),f41(a1,f317(f317(f74(a1),x99246),x99247),x99241)))) % 112.37/112.11 [9926]~P1(f317(f317(f225(a899),f2(a899)),x99263))+~P1(f317(f44(x99262,x99263),f317(f317(f242(a899,a899),x99265),x99267)))+~P1(f317(f44(x99261,x99263),f317(f317(f242(a899,a899),x99264),x99266)))+P1(f317(f44(f317(f317(f74(a899),x99261),x99262),x99263),f317(f317(f242(a899,a899),f317(f317(f74(a899),f317(f317(f74(a899),x99264),x99265)),f317(f317(f31(a899),f317(f317(f74(a899),x99266),x99267)),x99263))),f41(a899,f317(f317(f74(a899),x99266),x99267),x99263)))) % 112.37/112.11 [10318]~P69(x103182)+~P1(f317(f29(x103183),x103185))+~P1(f317(f29(x103181),x103187))+E(f317(f317(f8(x103181,x103182),f317(f317(f20(x103181,f906(x103183,a895),x103182),f317(f317(f10(f906(x103183,x103182),f906(f906(x103183,a895),x103182),x103181),f8(x103183,x103182)),x103184)),f317(f317(f10(f906(x103183,a895),f906(x103183,a895),x103181),f252(x103183)),f317(f317(f10(f906(x103183,a895),f906(x103183,a895),x103181),f317(f20(x103183,a895,a895),f317(f317(f10(a895,f906(a895,a895),x103183),a315),f317(f317(f9(x103183,f906(x103183,a895),a895),f319(x103183)),x103185)))),x103186)))),x103187),f317(f317(f8(x103183,x103182),f317(f317(f20(x103183,f906(x103181,a895),x103182),f317(f317(f10(f906(x103181,x103182),f906(f906(x103181,a895),x103182),x103183),f8(x103181,x103182)),f317(f9(x103181,x103183,x103182),x103184))),f317(f317(f10(f906(x103181,a895),f906(x103181,a895),x103183),f252(x103181)),f317(f317(f10(f906(x103181,a895),f906(x103181,a895),x103183),f317(f20(x103181,a895,a895),f317(f317(f10(a895,f906(a895,a895),x103181),a315),f317(f317(f9(x103181,f906(x103181,a895),a895),f319(x103181)),x103187)))),f317(f9(x103181,x103183,a895),x103186))))),x103185)) % 112.37/112.11 [10269]~P21(x102698,x102697,x102696,x102695,x102691)+~E(f317(x102692,f841(x102694,x102692,x102693,x102691,x102695,x102696,x102697)),f317(x102694,f841(x102694,x102692,x102693,x102691,x102695,x102696,x102697)))+E(f317(f317(x102691,x102692),x102693),f317(f317(x102691,x102694),x102693))+~P1(f317(f29(x102697),x102693)) % 112.37/112.11 [9799]~P22(x97997,x97996,x97991,x97998,x97992,x97994)+E(f317(f317(x97991,f317(x97992,x97993)),f317(x97994,x97995)),f317(x97994,x97995))+~P1(f317(f29(x97996),x97995))+~P1(f317(f317(f319(x97996),x97993),x97995)) % 112.37/112.11 [9803]~P12(x98036,x98031,x98032,x98038,x98033,x98034)+~P8(x98036,x98037,x98038)+P11(x98031,x98032,x98033,f317(x98034,x98035))+~P1(f317(f317(f319(x98036),x98035),x98037)) % 112.37/112.11 [10291]~P21(x102918,x102915,x102917,x102916,x102911)+E(f317(f317(x102911,x102912),x102913),f317(f317(x102911,x102914),x102913))+~P1(f317(f29(x102915),x102913))+P1(f317(f317(f319(x102915),f841(x102912,x102914,x102913,x102911,x102916,x102917,x102915)),x102913)) % 112.37/112.11 [10368]~P1(f317(f317(x103681,x103686),x103685))+P1(f317(f317(x103681,f827(x103681,x103684,x103685,x103686,x103683,x103682,x103687,x103688)),f833(x103681,x103684,x103685,x103686,x103683,x103682,x103687,x103688)))+P1(f317(f317(x103681,x103682),x103683))+~P1(f317(f317(f319(f905(f905(x103688,x103687),f905(x103688,x103687))),f317(f317(f242(f905(x103688,x103687),f905(x103688,x103687)),f317(f317(f242(x103688,x103687),x103682),x103683)),f317(f317(f242(x103688,x103687),x103686),x103685))),f297(f905(x103688,x103687),x103684))) % 112.37/112.11 [10369]~P1(f317(f317(x103691,x103696),x103695))+P1(f317(f317(x103691,f822(x103691,x103694,x103693,x103692,x103695,x103696,x103697,x103698)),f828(x103691,x103694,x103693,x103692,x103695,x103696,x103697,x103698)))+P1(f317(f317(x103691,x103692),x103693))+~P1(f317(f317(f319(f905(f905(x103698,x103697),f905(x103698,x103697))),f317(f317(f242(f905(x103698,x103697),f905(x103698,x103697)),f317(f317(f242(x103698,x103697),x103696),x103695)),f317(f317(f242(x103698,x103697),x103692),x103693))),f297(f905(x103698,x103697),x103694))) % 112.37/112.11 [10379]~P1(f317(f317(x103791,f829(x103791,x103796,x103795,x103794,x103793,x103792,x103797,x103798)),f832(x103791,x103796,x103795,x103794,x103793,x103792,x103797,x103798)))+P1(f317(f317(x103791,x103792),x103793))+~P1(f317(f317(x103791,x103794),x103795))+~P1(f317(f317(f319(f905(f905(x103798,x103797),f905(x103798,x103797))),f317(f317(f242(f905(x103798,x103797),f905(x103798,x103797)),f317(f317(f242(x103798,x103797),x103792),x103793)),f317(f317(f242(x103798,x103797),x103794),x103795))),f297(f905(x103798,x103797),x103796))) % 112.37/112.11 [10380]~P1(f317(f317(x103801,f830(x103801,x103806,x103803,x103802,x103805,x103804,x103807,x103808)),f831(x103801,x103806,x103803,x103802,x103805,x103804,x103807,x103808)))+P1(f317(f317(x103801,x103802),x103803))+~P1(f317(f317(x103801,x103804),x103805))+~P1(f317(f317(f319(f905(f905(x103808,x103807),f905(x103808,x103807))),f317(f317(f242(f905(x103808,x103807),f905(x103808,x103807)),f317(f317(f242(x103808,x103807),x103804),x103805)),f317(f317(f242(x103808,x103807),x103802),x103803))),f297(f905(x103808,x103807),x103806))) % 112.37/112.11 [10393]~P1(f317(f317(x103931,x103936),x103937))+P1(f317(f317(x103931,x103932),x103933))+P1(f317(f317(f319(f905(f905(x103934,x103935),f905(x103934,x103935))),f317(f317(f242(f905(x103934,x103935),f905(x103934,x103935)),f317(f317(f242(x103934,x103935),x103936),x103937)),f317(f317(f242(x103934,x103935),f822(x103931,x103938,x103933,x103932,x103937,x103936,x103935,x103934)),f828(x103931,x103938,x103933,x103932,x103937,x103936,x103935,x103934)))),f297(f905(x103934,x103935),x103938)))+~P1(f317(f317(f319(f905(f905(x103934,x103935),f905(x103934,x103935))),f317(f317(f242(f905(x103934,x103935),f905(x103934,x103935)),f317(f317(f242(x103934,x103935),x103936),x103937)),f317(f317(f242(x103934,x103935),x103932),x103933))),f297(f905(x103934,x103935),x103938))) % 112.37/112.11 [10395]~P1(f317(f317(x103951,x103958),x103957))+P1(f317(f317(x103951,x103952),x103953))+P1(f317(f317(f319(f905(f905(x103954,x103955),f905(x103954,x103955))),f317(f317(f242(f905(x103954,x103955),f905(x103954,x103955)),f317(f317(f242(x103954,x103955),f827(x103951,x103956,x103957,x103958,x103953,x103952,x103955,x103954)),f833(x103951,x103956,x103957,x103958,x103953,x103952,x103955,x103954))),f317(f317(f242(x103954,x103955),x103958),x103957))),f297(f905(x103954,x103955),x103956)))+~P1(f317(f317(f319(f905(f905(x103954,x103955),f905(x103954,x103955))),f317(f317(f242(f905(x103954,x103955),f905(x103954,x103955)),f317(f317(f242(x103954,x103955),x103952),x103953)),f317(f317(f242(x103954,x103955),x103958),x103957))),f297(f905(x103954,x103955),x103956))) % 112.37/112.11 [9408]~P19(x94087,x94081,x94088,x94083)+~P1(f317(f29(x94087),x94085))+~P1(f317(f29(x94087),x94084))+E(f317(f67(x94081,x94081,x94082,f317(x94083,x94084)),f317(f67(x94081,x94081,x94082,f317(x94083,x94085)),x94086)),f317(f67(x94081,x94081,x94082,f317(x94083,x94085)),f317(f67(x94081,x94081,x94082,f317(x94083,x94084)),x94086))) % 112.37/112.11 [9417]~P33(x94171,x94172,x94173,x94174,x94177)+P33(x94171,x94172,x94173,f317(f317(f149(x94171,x94174),x94175),x94176),f317(f317(f149(x94172,x94177),x94175),x94178))+~P1(f317(f317(x94173,x94176),x94178))+~P1(f317(f317(f225(a899),x94175),f317(f179(f900(x94171)),x94174))) % 112.37/112.11 [9418]~P33(x94181,x94182,x94183,x94184,x94187)+P33(x94181,x94182,x94183,f317(f317(f149(x94181,x94184),x94185),x94186),f317(f317(f149(x94182,x94187),x94185),x94188))+~P1(f317(f317(x94183,x94186),x94188))+~P1(f317(f317(f225(a899),x94185),f317(f179(f900(x94182)),x94187))) % 112.37/112.11 [9497]~P24(x94972,x94972,x94975,x94976)+~P21(x94973,x94972,x94977,x94978,x94971)+~P1(f317(f29(x94972),x94976))+E(f317(f317(x94971,f317(f67(x94972,x94973,x94972,x94974),x94975)),x94976),f317(f317(x94971,x94974),f317(f300(x94972,x94972,x94975),x94976))) % 112.37/112.11 [9764]P25(x97641,x97642,x97643,x97644,x97645)+~P25(x97642,x97646,x97647,x97645,x97648)+~P25(x97641,x97646,f317(f67(x97642,x97646,x97641,x97647),x97643),x97644,x97648)+~P1(f317(f317(f224(f906(x97642,a895)),f317(f300(x97641,x97642,x97643),x97644)),x97645)) % 112.37/112.11 [9801]~P23(x98017,x98012,x98015,x98018,x98016,x98011)+~P1(f317(f29(x98012),x98014))+E(f317(x98011,f317(f317(f299(x98012),x98013),x98014)),f317(f317(x98015,f317(x98016,x98013)),f317(x98011,x98014)))+P1(f317(f317(f319(x98012),x98013),x98014)) % 112.37/112.11 [9812]~P22(x98126,x98125,x98121,x98127,x98128,x98122)+E(f317(f317(x98121,f317(x98122,x98123)),f317(x98122,x98124)),f317(x98122,x98124))+~P1(f317(f29(x98125),x98124))+~P1(f317(f317(f224(f906(x98125,a895)),x98123),x98124)) % 112.37/112.11 [9395]P1(f317(f317(f319(f905(f900(x93951),f900(x93951))),f317(f317(f242(f900(x93951),f900(x93951)),x93952),x93953)),f147(x93951,x93954)))+~E(x93953,f317(f317(f124(x93951),x93955),f317(f317(f141(x93951),x93956),x93957)))+~E(x93952,f317(f317(f124(x93951),x93955),f317(f317(f141(x93951),x93958),x93957)))+~P1(f317(f317(f319(f905(x93951,x93951)),f317(f317(f242(x93951,x93951),x93958),x93956)),x93954)) % 112.37/112.11 [9806]~P22(x98066,x98062,x98065,x98067,x98068,x98061)+~P1(f317(f29(x98062),x98064))+~P1(f317(f29(x98062),x98063))+E(f317(x98061,f317(f317(f91(f906(x98062,a895)),x98063),x98064)),f317(f317(x98065,f317(x98061,x98063)),f317(x98061,x98064))) % 112.37/112.11 [10358]~P24(x103584,x103582,x103585,x103588)+E(f317(f317(f35(x103581,f906(x103582,a895)),x103583),f317(f317(f10(f906(x103584,a895),f906(x103582,a895),x103581),f300(x103584,x103582,x103585)),x103586)),f317(f300(x103584,x103582,x103585),f317(f317(f35(x103581,f906(x103584,a895)),x103583),x103586)))+~P1(f317(f317(f319(x103581),x103587),x103583))+P1(f317(f317(f319(x103581),f517(x103587,x103586,x103583,x103581,x103588,x103585,x103582,x103584)),x103583)) % 112.37/112.11 [10384]~P24(x103844,x103842,x103845,x103847)+E(f317(f317(f35(x103841,f906(x103842,a895)),x103843),f317(f317(f10(f906(x103844,a895),f906(x103842,a895),x103841),f300(x103844,x103842,x103845)),x103846)),f317(f300(x103844,x103842,x103845),f317(f317(f35(x103841,f906(x103844,a895)),x103843),x103846)))+~P1(f317(f317(f319(x103841),x103848),x103843))+~P1(f317(f317(f224(f906(x103844,a895)),f317(x103846,f517(x103848,x103846,x103843,x103841,x103847,x103845,x103842,x103844))),x103847)) % 112.37/112.11 [10396]~P1(f317(f317(x103961,x103968),x103967))+P1(f317(f317(x103961,x103962),x103963))+~P1(f317(f317(f319(f905(f905(x103964,x103965),f905(x103964,x103965))),f317(f317(f242(f905(x103964,x103965),f905(x103964,x103965)),f317(f317(f242(x103964,x103965),x103962),x103963)),f317(f317(f242(x103964,x103965),x103968),x103967))),f297(f905(x103964,x103965),x103966)))+P1(f317(f317(f319(f905(f905(x103964,x103965),f905(x103964,x103965))),f317(f317(f242(f905(x103964,x103965),f905(x103964,x103965)),f317(f317(f242(x103964,x103965),f829(x103961,x103966,x103967,x103968,x103963,x103962,x103965,x103964)),f832(x103961,x103966,x103967,x103968,x103963,x103962,x103965,x103964))),f317(f317(f242(x103964,x103965),f827(x103961,x103966,x103967,x103968,x103963,x103962,x103965,x103964)),f833(x103961,x103966,x103967,x103968,x103963,x103962,x103965,x103964)))),x103966)) % 112.37/112.11 [10397]~P1(f317(f317(x103971,x103978),x103977))+P1(f317(f317(x103971,x103972),x103973))+~P1(f317(f317(f319(f905(f905(x103974,x103975),f905(x103974,x103975))),f317(f317(f242(f905(x103974,x103975),f905(x103974,x103975)),f317(f317(f242(x103974,x103975),x103978),x103977)),f317(f317(f242(x103974,x103975),x103972),x103973))),f297(f905(x103974,x103975),x103976)))+P1(f317(f317(f319(f905(f905(x103974,x103975),f905(x103974,x103975))),f317(f317(f242(f905(x103974,x103975),f905(x103974,x103975)),f317(f317(f242(x103974,x103975),f822(x103971,x103976,x103973,x103972,x103977,x103978,x103975,x103974)),f828(x103971,x103976,x103973,x103972,x103977,x103978,x103975,x103974))),f317(f317(f242(x103974,x103975),f830(x103971,x103976,x103973,x103972,x103977,x103978,x103975,x103974)),f831(x103971,x103976,x103973,x103972,x103977,x103978,x103975,x103974)))),x103976)) % 112.37/112.11 [9875]~P23(x98757,x98755,x98751,x98758,x98752,x98754)+~P1(f317(f29(x98755),x98756))+~P1(f317(f317(f319(x98755),x98753),x98756))+E(f317(f317(x98751,f317(x98752,x98753)),f317(x98754,f317(f317(f3(f906(x98755,a895)),x98756),f317(f317(f299(x98755),x98753),f178(f906(x98755,a895)))))),f317(x98754,x98756)) % 112.37/112.11 [9884]~P23(x98846,x98843,x98841,x98847,x98848,x98842)+~P1(f317(f29(x98843),x98845))+~P1(f317(f29(x98843),x98844))+E(f317(f317(x98841,f317(x98842,f317(f317(f91(f906(x98843,a895)),x98844),x98845))),f317(x98842,f317(f317(f92(f906(x98843,a895)),x98844),x98845))),f317(f317(x98841,f317(x98842,x98844)),f317(x98842,x98845))) % 112.37/112.11 [9966]P41(x99661,x99662,x99663,x99664,x99665,f317(f317(x99663,x99666),x99667))+~P41(x99661,x99662,x99663,x99664,f317(f317(f3(f906(x99661,a895)),x99665),f317(f317(f299(x99661),x99668),f178(f906(x99661,a895)))),x99669)+~E(f317(f317(x99663,x99666),x99667),f317(f317(x99663,x99668),x99669))+~P1(f317(f317(f319(x99661),x99668),x99665)) % 112.37/112.11 [9908]~P12(x99086,x99087,x99088,x99089,x990810,x99081)+E(f317(f317(x99081,x99082),x99083),f317(f317(x99081,x99084),x99085))+~P1(f317(f317(f319(f905(x99087,x99087)),f317(f317(f242(x99087,x99087),x99083),x99085)),x990810))+~P1(f317(f317(f319(f905(x99086,x99086)),f317(f317(f242(x99086,x99086),x99082),x99084)),x99089)) % 112.37/112.11 [9501]~P99(x95012)+E(x95011,f178(f906(x95012,a895)))+~P1(f317(f29(x95012),x95011))+P1(f317(f317(f319(x95012),f12(x95012,x95011)),x95011))+~P1(f317(f317(f319(x95012),f317(f317(f91(x95012),f401(x95011,x95012)),f403(x95011,x95012))),f317(f317(f299(x95012),f401(x95011,x95012)),f317(f317(f299(x95012),f403(x95011,x95012)),f178(f906(x95012,a895)))))) % 112.37/112.11 [9502]~P99(x95022)+E(x95021,f178(f906(x95022,a895)))+~P1(f317(f29(x95022),x95021))+P1(f317(f317(f319(x95022),f13(x95022,x95021)),x95021))+~P1(f317(f317(f319(x95022),f317(f317(f92(x95022),f421(x95021,x95022)),f422(x95021,x95022))),f317(f317(f299(x95022),f421(x95021,x95022)),f317(f317(f299(x95022),f422(x95021,x95022)),f178(f906(x95022,a895)))))) % 112.37/112.11 [9533]~P70(x95332)+E(x95331,f178(f906(x95332,a895)))+~P1(f317(f29(x95332),x95331))+P1(f317(f317(f319(x95332),f317(f58(x95332,f75(x95332)),x95331)),x95331))+~P1(f317(f317(f319(x95332),f317(f317(f75(x95332),f724(x95331,x95332)),f736(x95331,x95332))),f317(f317(f299(x95332),f724(x95331,x95332)),f317(f317(f299(x95332),f736(x95331,x95332)),f178(f906(x95332,a895)))))) % 112.37/112.11 [9538]~P108(x95382)+E(x95381,f178(f906(x95382,a895)))+~P1(f317(f29(x95382),x95381))+P1(f317(f317(f319(x95382),f14(x95382,f223(x95382),x95381)),x95381))+~P1(f317(f317(f319(x95382),f317(f317(f223(x95382),f868(x95381,x95382)),f869(x95381,x95382))),f317(f317(f299(x95382),f868(x95381,x95382)),f317(f317(f299(x95382),f869(x95381,x95382)),f178(f906(x95382,a895)))))) % 112.37/112.11 [9539]~P108(x95392)+E(x95391,f178(f906(x95392,a895)))+~P1(f317(f29(x95392),x95391))+P1(f317(f317(f319(x95392),f15(x95392,f228(x95392),x95391)),x95391))+~P1(f317(f317(f319(x95392),f317(f317(f228(x95392),f870(x95391,x95392)),f871(x95391,x95392))),f317(f317(f299(x95392),f870(x95391,x95392)),f317(f317(f299(x95392),f871(x95391,x95392)),f178(f906(x95392,a895)))))) % 112.37/112.11 [6636]~P88(x66362)+E(x66361,f2(x66362))+~E(f317(f317(f74(x66362),x66363),x66361),f2(x66362))+~P1(f317(f317(f224(x66362),f2(x66362)),x66363))+~P1(f317(f317(f224(x66362),f2(x66362)),x66361)) % 112.37/112.11 [6637]~P88(x66372)+E(x66371,f2(x66372))+~E(f317(f317(f74(x66372),x66371),x66373),f2(x66372))+~P1(f317(f317(f224(x66372),f2(x66372)),x66373))+~P1(f317(f317(f224(x66372),f2(x66372)),x66371)) % 112.37/112.11 [7182]~P108(x71822)+~P13(x71822,x71821)+E(x71821,f103(x71822))+~P1(f317(f317(f319(x71822),x71823),f317(f162(x71822),f690(x71821,x71822))))+P1(f317(f317(f224(x71822),f709(x71821,x71822)),x71823)) % 112.37/112.11 [7351]~P108(x73511)+E(f17(x73511,x73512),x73513)+~P1(f317(f29(x73511),x73512))+~P1(f317(f317(f224(x73511),x73513),f853(x73513,x73512,x73511)))+~P1(f317(f317(f319(x73511),x73513),x73512)) % 112.37/112.11 [7384]~P108(x73841)+~P13(x73841,x73842)+~P13(x73841,x73843)+P13(x73841,f317(f317(f124(x73841),x73842),x73843))+P1(f317(f317(f319(x73841),f696(x73843,x73842,x73841)),f317(f162(x73841),x73842))) % 112.37/112.11 [7385]~P108(x73851)+~P13(x73851,x73852)+~P13(x73851,x73853)+P13(x73851,f317(f317(f124(x73851),x73852),x73853))+P1(f317(f317(f319(x73851),f697(x73853,x73852,x73851)),f317(f162(x73851),x73853))) % 112.37/112.11 [7448]~P108(x74481)+E(f16(x74481,x74482),x74483)+~P1(f317(f29(x74481),x74482))+P1(f317(f317(f319(x74481),f854(x74483,x74482,x74481)),x74482))+~P1(f317(f317(f319(x74481),x74483),x74482)) % 112.37/112.11 [7449]~P108(x74491)+E(f17(x74491,x74492),x74493)+~P1(f317(f29(x74491),x74492))+P1(f317(f317(f319(x74491),f853(x74493,x74492,x74491)),x74492))+~P1(f317(f317(f319(x74491),x74493),x74492)) % 112.37/112.11 [8022]~P108(x80221)+E(f16(x80221,x80222),x80223)+~P1(f317(f29(x80221),x80222))+~P1(f317(f317(f319(x80221),x80223),x80222))+~P1(f317(f317(f224(x80221),f854(x80223,x80222,x80221)),x80223)) % 112.37/112.11 [8340]~P108(x83401)+~P13(x83401,x83402)+~P13(x83401,x83403)+P13(x83401,f317(f317(f124(x83401),x83402),x83403))+~P1(f317(f317(f224(x83401),f696(x83403,x83402,x83401)),f697(x83403,x83402,x83401))) % 112.37/112.11 [9133]~P108(x91332)+E(x91331,f178(f906(x91332,a895)))+~E(f317(f317(f223(x91332),f317(x91333,f862(x91331,x91333,x91332))),f317(x91333,f864(x91331,x91333,x91332))),f317(x91333,f317(f317(f223(x91332),f862(x91331,x91333,x91332)),f864(x91331,x91333,x91332))))+E(f16(x91332,f317(f300(x91332,x91332,x91333),x91331)),f317(x91333,f16(x91332,x91331)))+~P1(f317(f29(x91332),x91331)) % 112.37/112.11 [9134]~P108(x91342)+E(x91341,f178(f906(x91342,a895)))+~E(f317(f317(f228(x91342),f317(x91343,f865(x91341,x91343,x91342))),f317(x91343,f866(x91341,x91343,x91342))),f317(x91343,f317(f317(f228(x91342),f865(x91341,x91343,x91342)),f866(x91341,x91343,x91342))))+E(f17(x91342,f317(f300(x91342,x91342,x91343),x91341)),f317(x91343,f17(x91342,x91341)))+~P1(f317(f29(x91342),x91341)) % 112.37/112.11 [9135]~P99(x91352)+E(x91351,f178(f906(x91352,a895)))+~E(f317(f317(f91(x91352),f317(x91353,f402(x91351,x91353,x91352))),f317(x91353,f404(x91351,x91353,x91352))),f317(x91353,f317(f317(f91(x91352),f402(x91351,x91353,x91352)),f404(x91351,x91353,x91352))))+E(f12(x91352,f317(f300(x91352,x91352,x91353),x91351)),f317(x91353,f12(x91352,x91351)))+~P1(f317(f29(x91352),x91351)) % 112.37/112.11 [9136]~P99(x91362)+E(x91361,f178(f906(x91362,a895)))+~E(f317(f317(f92(x91362),f317(x91363,f426(x91361,x91363,x91362))),f317(x91363,f428(x91361,x91363,x91362))),f317(x91363,f317(f317(f92(x91362),f426(x91361,x91363,x91362)),f428(x91361,x91363,x91362))))+E(f13(x91362,f317(f300(x91362,x91362,x91363),x91361)),f317(x91363,f13(x91362,x91361)))+~P1(f317(f29(x91362),x91361)) % 112.37/112.11 [9204]~P108(x92042)+E(x92041,f178(f906(x92042,a895)))+~E(f317(f317(f223(x92042),f317(x92043,f867(x92041,x92043,x92042))),f317(x92043,f872(x92041,x92043,x92042))),f317(x92043,f317(f317(f223(x92042),f867(x92041,x92043,x92042)),f872(x92041,x92043,x92042))))+E(f14(x92042,f223(x92042),f317(f300(x92042,x92042,x92043),x92041)),f317(x92043,f14(x92042,f223(x92042),x92041)))+~P1(f317(f29(x92042),x92041)) % 112.37/112.11 [9205]~P108(x92052)+E(x92051,f178(f906(x92052,a895)))+~E(f317(f317(f228(x92052),f317(x92053,f874(x92051,x92053,x92052))),f317(x92053,f875(x92051,x92053,x92052))),f317(x92053,f317(f317(f228(x92052),f874(x92051,x92053,x92052)),f875(x92051,x92053,x92052))))+E(f15(x92052,f228(x92052),f317(f300(x92052,x92052,x92053),x92051)),f317(x92053,f15(x92052,f228(x92052),x92051)))+~P1(f317(f29(x92052),x92051)) % 112.37/112.11 [6653]~P70(x66532)+E(x66531,f178(f906(x66532,a895)))+~P1(f317(f29(x66532),x66531))+E(f317(f58(x66532,f75(x66532)),f317(f317(f299(x66532),x66533),x66531)),f317(f317(f75(x66532),x66533),f317(f58(x66532,f75(x66532)),x66531)))+P1(f317(f317(f319(x66532),x66533),x66531)) % 112.37/112.11 [7188]~P108(x71882)+E(f317(f317(f228(x71882),f17(x71882,x71881)),f17(x71882,x71883)),f17(x71882,x71883))+E(x71881,f178(f906(x71882,a895)))+~P1(f317(f29(x71882),x71883))+~P1(f317(f317(f224(f906(x71882,a895)),x71881),x71883)) % 112.37/112.11 [7189]~P108(x71892)+E(f317(f317(f223(x71892),f16(x71892,x71891)),f16(x71892,x71893)),f16(x71892,x71893))+E(x71891,f178(f906(x71892,a895)))+~P1(f317(f29(x71892),x71893))+~P1(f317(f317(f224(f906(x71892,a895)),x71891),x71893)) % 112.37/112.11 [7190]~P99(x71902)+E(f317(f317(f91(x71902),f12(x71902,x71901)),f12(x71902,x71903)),f12(x71902,x71903))+E(x71901,f178(f906(x71902,a895)))+~P1(f317(f29(x71902),x71903))+~P1(f317(f317(f224(f906(x71902,a895)),x71901),x71903)) % 112.37/112.11 [7191]~P99(x71912)+E(f317(f317(f92(x71912),f13(x71912,x71911)),f13(x71912,x71913)),f13(x71912,x71913))+E(x71911,f178(f906(x71912,a895)))+~P1(f317(f29(x71912),x71913))+~P1(f317(f317(f224(f906(x71912,a895)),x71911),x71913)) % 112.37/112.11 [7496]~P108(x74962)+E(x74961,f178(f906(x74962,a895)))+~P1(f317(f29(x74962),x74963))+P1(f317(f317(f224(x74962),f16(x74962,x74961)),f16(x74962,x74963)))+~P1(f317(f317(f224(f906(x74962,a895)),x74961),x74963)) % 112.37/112.11 [7497]~P108(x74972)+E(x74971,f178(f906(x74972,a895)))+~P1(f317(f29(x74972),x74973))+P1(f317(f317(f224(x74972),f17(x74972,x74973)),f17(x74972,x74971)))+~P1(f317(f317(f224(f906(x74972,a895)),x74971),x74973)) % 112.37/112.11 [7551]~P108(x75511)+E(f16(x75511,x75512),x75513)+~P1(f317(f29(x75511),x75512))+~E(f317(f317(f3(f906(x75511,a895)),x75512),f317(f317(f299(x75511),x75513),f178(f906(x75511,a895)))),f178(f906(x75511,a895)))+~P1(f317(f317(f319(x75511),x75513),x75512)) % 112.37/112.11 [7552]~P108(x75521)+E(f17(x75521,x75522),x75523)+~P1(f317(f29(x75521),x75522))+~E(f317(f317(f3(f906(x75521,a895)),x75522),f317(f317(f299(x75521),x75523),f178(f906(x75521,a895)))),f178(f906(x75521,a895)))+~P1(f317(f317(f319(x75521),x75523),x75522)) % 112.37/112.11 [7553]~P99(x75531)+E(f12(x75531,x75532),x75533)+~P1(f317(f29(x75531),x75532))+~E(f317(f317(f3(f906(x75531,a895)),x75532),f317(f317(f299(x75531),x75533),f178(f906(x75531,a895)))),f178(f906(x75531,a895)))+~P1(f317(f317(f319(x75531),x75533),x75532)) % 112.37/112.11 [7554]~P99(x75541)+E(f13(x75541,x75542),x75543)+~P1(f317(f29(x75541),x75542))+~E(f317(f317(f3(f906(x75541,a895)),x75542),f317(f317(f299(x75541),x75543),f178(f906(x75541,a895)))),f178(f906(x75541,a895)))+~P1(f317(f317(f319(x75541),x75543),x75542)) % 112.37/112.11 [7650]~P108(x76501)+E(f14(x76501,f223(x76501),x76502),x76503)+~P1(f317(f29(x76501),x76502))+~E(f317(f317(f3(f906(x76501,a895)),x76502),f317(f317(f299(x76501),x76503),f178(f906(x76501,a895)))),f178(f906(x76501,a895)))+~P1(f317(f317(f319(x76501),x76503),x76502)) % 112.37/112.11 [7651]~P108(x76511)+E(f15(x76511,f228(x76511),x76512),x76513)+~P1(f317(f29(x76511),x76512))+~E(f317(f317(f3(f906(x76511,a895)),x76512),f317(f317(f299(x76511),x76513),f178(f906(x76511,a895)))),f178(f906(x76511,a895)))+~P1(f317(f317(f319(x76511),x76513),x76512)) % 112.37/112.11 [7686]~P108(x76862)+E(x76861,f178(f906(x76862,a895)))+~P1(f317(f29(x76862),x76861))+~P1(f317(f317(f224(x76862),x76863),f855(x76863,x76861,x76862)))+P1(f317(f317(f224(x76862),x76863),f317(f58(x76862,f228(x76862)),x76861))) % 112.37/112.11 [7687]~P104(x76872)+E(x76871,f178(f906(x76872,a895)))+~P1(f317(f29(x76872),x76871))+~P1(f317(f317(f224(x76872),x76873),f409(x76873,x76871,x76872)))+P1(f317(f317(f224(x76872),x76873),f317(f58(x76872,f92(x76872)),x76871))) % 112.37/112.11 [7688]~P108(x76882)+E(x76881,f178(f906(x76882,a895)))+~P1(f317(f29(x76882),x76881))+~P1(f317(f317(f225(x76882),x76883),f857(x76883,x76881,x76882)))+P1(f317(f317(f225(x76882),x76883),f317(f58(x76882,f228(x76882)),x76881))) % 112.37/112.11 [7775]~P108(x77752)+E(x77751,f178(f906(x77752,a895)))+~P1(f317(f29(x77752),x77751))+P1(f317(f317(f319(x77752),f855(x77753,x77751,x77752)),x77751))+P1(f317(f317(f224(x77752),x77753),f317(f58(x77752,f228(x77752)),x77751))) % 112.37/112.11 [7776]~P108(x77762)+E(x77761,f178(f906(x77762,a895)))+~P1(f317(f29(x77762),x77761))+P1(f317(f317(f319(x77762),f857(x77763,x77761,x77762)),x77761))+P1(f317(f317(f225(x77762),x77763),f317(f58(x77762,f228(x77762)),x77761))) % 112.37/112.11 [7777]~P104(x77772)+E(x77771,f178(f906(x77772,a895)))+~P1(f317(f29(x77772),x77771))+P1(f317(f317(f319(x77772),f409(x77773,x77771,x77772)),x77771))+P1(f317(f317(f224(x77772),x77773),f317(f58(x77772,f92(x77772)),x77771))) % 112.37/112.11 [7899]~P108(x78992)+E(x78991,f178(f906(x78992,a895)))+E(f317(f317(f228(x78992),f15(x78992,f228(x78992),x78991)),f15(x78992,f228(x78992),x78993)),f15(x78992,f228(x78992),x78993))+~P1(f317(f29(x78992),x78993))+~P1(f317(f317(f224(f906(x78992,a895)),x78991),x78993)) % 112.37/112.11 [7900]~P108(x79002)+E(x79001,f178(f906(x79002,a895)))+E(f317(f317(f223(x79002),f14(x79002,f223(x79002),x79001)),f14(x79002,f223(x79002),x79003)),f14(x79002,f223(x79002),x79003))+~P1(f317(f29(x79002),x79003))+~P1(f317(f317(f224(f906(x79002,a895)),x79001),x79003)) % 112.37/112.11 [8099]~E(f423(x80991,x80993,x80992),f424(x80991,x80993,x80992))+~E(f317(f30(x80992),f425(x80991,x80993,x80992)),x80991)+E(f317(f317(f75(a899),x80991),f317(f30(f906(x80992,a895)),x80993)),f317(f30(x80992),f32(f906(x80992,a895),x80993)))+~P1(f317(f29(x80992),f32(f906(x80992,a895),x80993)))+~P1(f317(f29(f906(x80992,a895)),x80993)) % 112.37/112.11 [8280]~P108(x82802)+E(x82801,f178(f906(x82802,a895)))+~P1(f317(f29(x82802),x82803))+P1(f317(f317(f224(x82802),f317(f58(x82802,f228(x82802)),x82803)),f317(f58(x82802,f228(x82802)),x82801)))+~P1(f317(f317(f224(f906(x82802,a895)),x82801),x82803)) % 112.37/112.11 [8581]~E(f423(x85811,x85813,x85812),f424(x85811,x85813,x85812))+E(f317(f317(f75(a899),x85811),f317(f30(f906(x85812,a895)),x85813)),f317(f30(x85812),f32(f906(x85812,a895),x85813)))+P1(f317(f317(f319(f906(x85812,a895)),f425(x85811,x85813,x85812)),x85813))+~P1(f317(f29(x85812),f32(f906(x85812,a895),x85813)))+~P1(f317(f29(f906(x85812,a895)),x85813)) % 112.37/112.11 [8607]~E(f317(f30(x86072),f425(x86071,x86073,x86072)),x86071)+E(f317(f317(f75(a899),x86071),f317(f30(f906(x86072,a895)),x86073)),f317(f30(x86072),f32(f906(x86072,a895),x86073)))+P1(f317(f317(f319(f906(x86072,a895)),f424(x86071,x86073,x86072)),x86073))+~P1(f317(f29(x86072),f32(f906(x86072,a895),x86073)))+~P1(f317(f29(f906(x86072,a895)),x86073)) % 112.37/112.11 [8608]~E(f317(f30(x86082),f425(x86081,x86083,x86082)),x86081)+E(f317(f317(f75(a899),x86081),f317(f30(f906(x86082,a895)),x86083)),f317(f30(x86082),f32(f906(x86082,a895),x86083)))+P1(f317(f317(f319(f906(x86082,a895)),f423(x86081,x86083,x86082)),x86083))+~P1(f317(f29(x86082),f32(f906(x86082,a895),x86083)))+~P1(f317(f29(f906(x86082,a895)),x86083)) % 112.37/112.11 [8633]~E(f317(f30(x86332),f425(x86331,x86333,x86332)),x86331)+~E(f317(f317(f92(f906(x86332,a895)),f424(x86331,x86333,x86332)),f423(x86331,x86333,x86332)),f178(f906(x86332,a895)))+E(f317(f317(f75(a899),x86331),f317(f30(f906(x86332,a895)),x86333)),f317(f30(x86332),f32(f906(x86332,a895),x86333)))+~P1(f317(f29(f906(x86332,a895)),x86333))+~P1(f317(f29(x86332),f32(f906(x86332,a895),x86333))) % 112.37/112.11 [8897]E(f317(f317(f75(a899),x88971),f317(f30(f906(x88972,a895)),x88973)),f317(f30(x88972),f32(f906(x88972,a895),x88973)))+P1(f317(f317(f319(f906(x88972,a895)),f425(x88971,x88973,x88972)),x88973))+P1(f317(f317(f319(f906(x88972,a895)),f424(x88971,x88973,x88972)),x88973))+~P1(f317(f29(f906(x88972,a895)),x88973))+~P1(f317(f29(x88972),f32(f906(x88972,a895),x88973))) % 112.37/112.11 [8898]E(f317(f317(f75(a899),x88981),f317(f30(f906(x88982,a895)),x88983)),f317(f30(x88982),f32(f906(x88982,a895),x88983)))+P1(f317(f317(f319(f906(x88982,a895)),f425(x88981,x88983,x88982)),x88983))+P1(f317(f317(f319(f906(x88982,a895)),f423(x88981,x88983,x88982)),x88983))+~P1(f317(f29(f906(x88982,a895)),x88983))+~P1(f317(f29(x88982),f32(f906(x88982,a895),x88983))) % 112.37/112.11 [8924]~E(f317(f317(f92(f906(x89242,a895)),f424(x89241,x89243,x89242)),f423(x89241,x89243,x89242)),f178(f906(x89242,a895)))+E(f317(f317(f75(a899),x89241),f317(f30(f906(x89242,a895)),x89243)),f317(f30(x89242),f32(f906(x89242,a895),x89243)))+~P1(f317(f29(f906(x89242,a895)),x89243))+P1(f317(f317(f319(f906(x89242,a895)),f425(x89241,x89243,x89242)),x89243))+~P1(f317(f29(x89242),f32(f906(x89242,a895),x89243))) % 112.37/112.11 [9179]~P97(x91792)+E(x91791,f178(f906(x91792,a895)))+~E(f317(f317(f75(x91792),f317(x91793,f778(x91791,x91793,x91792))),f317(x91793,f788(x91791,x91793,x91792))),f317(x91793,f317(f317(f75(x91792),f778(x91791,x91793,x91792)),f788(x91791,x91793,x91792))))+~P1(f317(f29(x91792),x91791))+E(f317(f58(x91792,f75(x91792)),f317(f300(x91792,x91792,x91793),x91791)),f317(x91793,f317(f58(x91792,f75(x91792)),x91791))) % 112.37/112.11 [10125]P1(f317(f317(x101251,x101252),x101253))+P1(f317(f317(f225(a1),f454(x101251,x101253,x101252)),f455(x101251,x101253,x101252)))+P1(f317(f317(f224(a1),f455(x101251,x101253,x101252)),f2(a1)))+P1(f317(f317(x101251,f454(x101251,x101253,x101252)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f455(x101251,x101253,x101252))))+~P1(f317(f305(f905(a1,a1),a54),f317(f317(f242(a1,a1),x101252),x101253))) % 112.37/112.11 [10131]P1(f317(f317(x101311,x101312),x101313))+P1(f317(f317(f224(a1),f451(x101311,x101313,x101312)),f2(a1)))+P1(f317(f317(x101311,f447(x101311,x101313,x101312)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f451(x101311,x101313,x101312))))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),f447(x101311,x101313,x101312)),f451(x101311,x101313,x101312))))+~P1(f317(f305(f905(a1,a1),a48),f317(f317(f242(a1,a1),x101312),x101313))) % 112.37/112.11 [8071]~P112(x80711)+~P1(f317(f317(f224(x80711),x80712),f72(x80711)))+~P1(f317(f317(f224(x80711),f2(x80711)),x80712))+~P1(f317(f317(f224(x80711),f2(x80711)),x80713))+P1(f317(f317(f224(x80711),f317(f317(f75(x80711),x80712),x80713)),x80713)) % 112.37/112.11 [8072]~P112(x80721)+~P1(f317(f317(f224(x80721),x80723),f72(x80721)))+~P1(f317(f317(f224(x80721),f2(x80721)),x80723))+~P1(f317(f317(f224(x80721),f2(x80721)),x80722))+P1(f317(f317(f224(x80721),f317(f317(f75(x80721),x80722),x80723)),x80722)) % 112.37/112.11 [8426]~P108(x84262)+E(x84261,f178(f906(x84262,a895)))+~P1(f317(f29(x84262),x84261))+P1(f317(f317(f224(x84262),f856(x84263,x84261,x84262)),x84263))+~P1(f317(f317(f224(x84262),f317(f58(x84262,f228(x84262)),x84261)),x84263)) % 112.37/112.11 [8427]~P108(x84272)+E(x84271,f178(f906(x84272,a895)))+~P1(f317(f29(x84272),x84271))+P1(f317(f317(f319(x84272),f856(x84273,x84271,x84272)),x84271))+~P1(f317(f317(f224(x84272),f317(f58(x84272,f228(x84272)),x84271)),x84273)) % 112.37/112.11 [8428]~P108(x84282)+E(x84281,f178(f906(x84282,a895)))+~P1(f317(f29(x84282),x84281))+P1(f317(f317(f319(x84282),f858(x84283,x84281,x84282)),x84281))+~P1(f317(f317(f225(x84282),f317(f58(x84282,f228(x84282)),x84281)),x84283)) % 112.37/112.11 [8429]~P108(x84292)+E(x84291,f178(f906(x84292,a895)))+~P1(f317(f29(x84292),x84291))+P1(f317(f317(f225(x84292),f858(x84293,x84291,x84292)),x84293))+~P1(f317(f317(f225(x84292),f317(f58(x84292,f228(x84292)),x84291)),x84293)) % 112.37/112.11 [8516]~P1(f317(x85161,x85163))+P1(f317(x85161,f383(x85161,x85162)))+P1(f317(x85161,f380(x85161,x85162)))+~P1(f317(f317(f225(a1),f2(a1)),x85162))+P1(f317(x85161,f317(f317(f3(a1),f380(x85161,x85162)),f317(f317(f75(a1),f384(x85161,x85162)),x85162)))) % 112.37/112.11 [8734]~P1(f317(x87341,x87343))+P1(f317(x87341,f380(x87341,x87342)))+~P1(f317(f317(f225(a1),f2(a1)),x87342))+P1(f317(f317(f319(a1),f383(x87341,x87342)),f293(a1,f72(a1),x87342)))+P1(f317(x87341,f317(f317(f3(a1),f380(x87341,x87342)),f317(f317(f75(a1),f384(x87341,x87342)),x87342)))) % 112.37/112.11 [8946]~P1(f317(x89461,x89463))+~P1(f317(x89461,f380(x89461,x89462)))+P1(f317(x89461,f383(x89461,x89462)))+~P1(f317(f317(f225(a1),f2(a1)),x89462))+~P1(f317(x89461,f317(f317(f3(a1),f380(x89461,x89462)),f317(f317(f75(a1),f384(x89461,x89462)),x89462)))) % 112.37/112.11 [9070]~P1(f317(x90701,x90703))+~P1(f317(x90701,f380(x90701,x90702)))+~P1(f317(f317(f225(a1),f2(a1)),x90702))+P1(f317(f317(f319(a1),f383(x90701,x90702)),f293(a1,f72(a1),x90702)))+~P1(f317(x90701,f317(f317(f3(a1),f380(x90701,x90702)),f317(f317(f75(a1),f384(x90701,x90702)),x90702)))) % 112.37/112.11 [8852]~P108(x88521)+~P1(f317(f29(x88521),x88522))+E(f317(f317(f3(f906(x88521,a895)),x88522),f317(f317(f299(x88521),x88523),f178(f906(x88521,a895)))),f178(f906(x88521,a895)))+~P1(f317(f317(f319(x88521),x88523),x88522))+E(f317(f317(f223(x88521),x88523),f16(x88521,f317(f317(f3(f906(x88521,a895)),x88522),f317(f317(f299(x88521),x88523),f178(f906(x88521,a895)))))),f16(x88521,x88522)) % 112.37/112.11 [8853]~P108(x88531)+~P1(f317(f29(x88531),x88532))+E(f317(f317(f3(f906(x88531,a895)),x88532),f317(f317(f299(x88531),x88533),f178(f906(x88531,a895)))),f178(f906(x88531,a895)))+~P1(f317(f317(f319(x88531),x88533),x88532))+E(f317(f317(f228(x88531),x88533),f17(x88531,f317(f317(f3(f906(x88531,a895)),x88532),f317(f317(f299(x88531),x88533),f178(f906(x88531,a895)))))),f17(x88531,x88532)) % 112.37/112.11 [8854]~P99(x88541)+~P1(f317(f29(x88541),x88542))+E(f317(f317(f3(f906(x88541,a895)),x88542),f317(f317(f299(x88541),x88543),f178(f906(x88541,a895)))),f178(f906(x88541,a895)))+~P1(f317(f317(f319(x88541),x88543),x88542))+E(f317(f317(f91(x88541),x88543),f12(x88541,f317(f317(f3(f906(x88541,a895)),x88542),f317(f317(f299(x88541),x88543),f178(f906(x88541,a895)))))),f12(x88541,x88542)) % 112.37/112.11 [8855]~P99(x88551)+~P1(f317(f29(x88551),x88552))+E(f317(f317(f3(f906(x88551,a895)),x88552),f317(f317(f299(x88551),x88553),f178(f906(x88551,a895)))),f178(f906(x88551,a895)))+~P1(f317(f317(f319(x88551),x88553),x88552))+E(f317(f317(f92(x88551),x88553),f13(x88551,f317(f317(f3(f906(x88551,a895)),x88552),f317(f317(f299(x88551),x88553),f178(f906(x88551,a895)))))),f13(x88551,x88552)) % 112.37/112.11 [8917]~P108(x89171)+~P1(f317(f29(x89171),x89172))+E(f317(f317(f3(f906(x89171,a895)),x89172),f317(f317(f299(x89171),x89173),f178(f906(x89171,a895)))),f178(f906(x89171,a895)))+~P1(f317(f317(f319(x89171),x89173),x89172))+E(f317(f317(f223(x89171),x89173),f14(x89171,f223(x89171),f317(f317(f3(f906(x89171,a895)),x89172),f317(f317(f299(x89171),x89173),f178(f906(x89171,a895)))))),f14(x89171,f223(x89171),x89172)) % 112.37/112.11 [8918]~P108(x89181)+~P1(f317(f29(x89181),x89182))+E(f317(f317(f3(f906(x89181,a895)),x89182),f317(f317(f299(x89181),x89183),f178(f906(x89181,a895)))),f178(f906(x89181,a895)))+~P1(f317(f317(f319(x89181),x89183),x89182))+E(f317(f317(f228(x89181),x89183),f15(x89181,f228(x89181),f317(f317(f3(f906(x89181,a895)),x89182),f317(f317(f299(x89181),x89183),f178(f906(x89181,a895)))))),f15(x89181,f228(x89181),x89182)) % 112.37/112.11 [8933]~P108(x89331)+~P1(f317(f29(x89331),x89333))+~P1(f317(f29(x89331),x89332))+E(f317(f317(f92(f906(x89331,a895)),x89332),x89333),f178(f906(x89331,a895)))+E(f317(f317(f228(x89331),f17(x89331,f317(f317(f91(f906(x89331,a895)),x89332),x89333))),f17(x89331,f317(f317(f92(f906(x89331,a895)),x89332),x89333))),f317(f317(f228(x89331),f17(x89331,x89332)),f17(x89331,x89333))) % 112.37/112.11 [8934]~P108(x89341)+~P1(f317(f29(x89341),x89343))+~P1(f317(f29(x89341),x89342))+E(f317(f317(f92(f906(x89341,a895)),x89342),x89343),f178(f906(x89341,a895)))+E(f317(f317(f223(x89341),f16(x89341,f317(f317(f91(f906(x89341,a895)),x89342),x89343))),f16(x89341,f317(f317(f92(f906(x89341,a895)),x89342),x89343))),f317(f317(f223(x89341),f16(x89341,x89342)),f16(x89341,x89343))) % 112.37/112.11 [8935]~P99(x89351)+~P1(f317(f29(x89351),x89353))+~P1(f317(f29(x89351),x89352))+E(f317(f317(f92(f906(x89351,a895)),x89352),x89353),f178(f906(x89351,a895)))+E(f317(f317(f91(x89351),f12(x89351,f317(f317(f91(f906(x89351,a895)),x89352),x89353))),f12(x89351,f317(f317(f92(f906(x89351,a895)),x89352),x89353))),f317(f317(f91(x89351),f12(x89351,x89352)),f12(x89351,x89353))) % 112.37/112.11 [8936]~P99(x89361)+~P1(f317(f29(x89361),x89363))+~P1(f317(f29(x89361),x89362))+E(f317(f317(f92(f906(x89361,a895)),x89362),x89363),f178(f906(x89361,a895)))+E(f317(f317(f92(x89361),f13(x89361,f317(f317(f91(f906(x89361,a895)),x89362),x89363))),f13(x89361,f317(f317(f92(f906(x89361,a895)),x89362),x89363))),f317(f317(f92(x89361),f13(x89361,x89362)),f13(x89361,x89363))) % 112.37/112.11 [9151]~P108(x91511)+~P1(f317(f29(x91511),x91513))+~P1(f317(f29(x91511),x91512))+E(f317(f317(f92(f906(x91511,a895)),x91512),x91513),f178(f906(x91511,a895)))+E(f317(f317(f228(x91511),f15(x91511,f228(x91511),f317(f317(f91(f906(x91511,a895)),x91512),x91513))),f15(x91511,f228(x91511),f317(f317(f92(f906(x91511,a895)),x91512),x91513))),f317(f317(f228(x91511),f15(x91511,f228(x91511),x91512)),f15(x91511,f228(x91511),x91513))) % 112.37/112.11 [9152]~P108(x91521)+~P1(f317(f29(x91521),x91523))+~P1(f317(f29(x91521),x91522))+E(f317(f317(f92(f906(x91521,a895)),x91522),x91523),f178(f906(x91521,a895)))+E(f317(f317(f223(x91521),f14(x91521,f223(x91521),f317(f317(f91(f906(x91521,a895)),x91522),x91523))),f14(x91521,f223(x91521),f317(f317(f92(f906(x91521,a895)),x91522),x91523))),f317(f317(f223(x91521),f14(x91521,f223(x91521),x91522)),f14(x91521,f223(x91521),x91523))) % 112.37/112.11 [9963]~P126(x99633)+E(x99631,x99632)+~P1(f317(f317(f224(x99633),f2(x99633)),x99632))+~P1(f317(f317(f224(x99633),f2(x99633)),x99631))+~E(f317(f317(f234(x99633),x99631),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f234(x99633),x99632),f317(f94(a899),f317(f317(f74(a1),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f3(a1),f317(f317(f74(a1),a77),a77)),a87))))) % 112.37/112.11 [5968]~P3(x59682)+E(x59681,f2(x59682))+~E(f317(f317(f31(x59682),x59683),x59681),x59684)+E(x59683,f317(f317(f75(x59682),x59684),x59681))+~P1(f317(f317(f277(x59682),x59681),x59683)) % 112.37/112.11 [5969]~P3(x59692)+E(x59691,f2(x59692))+~E(x59693,f317(f317(f75(x59692),x59694),x59691))+E(f317(f317(f31(x59692),x59693),x59691),x59694)+~P1(f317(f317(f277(x59692),x59691),x59693)) % 112.37/112.11 [6445]E(f687(x64451,x64452,x64453),x64454)+E(f317(x64451,x64454),f2(a899))+~E(f317(f317(f8(x64453,a899),x64451),x64452),f72(a899))+~P1(f317(f29(x64453),x64452))+~P1(f317(f317(f319(x64453),x64454),x64452)) % 112.37/112.11 [6510]E(f656(x65101,x65102,x65103),x65104)+E(f317(x65101,x65104),f2(a899))+~E(f317(f317(f8(x65103,a899),x65101),x65102),f317(a102,f2(a899)))+~P1(f317(f29(x65103),x65102))+~P1(f317(f317(f319(x65103),x65104),x65102)) % 112.37/112.11 [6622]~P108(x66221)+~P5(x66221)+P1(f317(f317(f225(x66221),x66222),f32(x66221,x66223)))+~P1(f317(f317(f225(x66221),x66222),x66224))+~P1(f317(f317(f319(x66221),x66224),x66223)) % 112.37/112.11 [6799]~P108(x67991)+~P5(x67991)+~P1(f317(f317(f225(x67991),x67994),x67993))+P1(f317(f317(f225(x67991),f33(x67991,x67992)),x67993))+~P1(f317(f317(f319(x67991),x67994),x67992)) % 112.37/112.11 [7067]~P126(x70673)+E(x70671,x70672)+~E(f317(f317(f234(x70673),x70671),f317(a102,x70674)),f317(f317(f234(x70673),x70672),f317(a102,x70674)))+~P1(f317(f317(f224(x70673),f2(x70673)),x70672))+~P1(f317(f317(f224(x70673),f2(x70673)),x70671)) % 112.37/112.11 [7279]~E(f700(x72792,x72793,x72791,x72794),x72794)+~E(f317(x72792,x72794),f72(a899))+E(f317(f317(f8(x72791,a899),x72792),x72793),f72(a899))+~P1(f317(f29(x72791),x72793))+~P1(f317(f317(f319(x72791),x72794),x72793)) % 112.37/112.11 [7286]~P119(x72864)+~P132(x72864)+E(f317(x72861,f569(x72861,x72862,x72863,x72864)),f2(x72864))+~E(f317(f317(f11(x72863,x72864),x72861),x72862),f2(x72864))+~P1(f317(f29(x72863),x72862)) % 112.37/112.11 [7374]~E(f679(x73742,x73743,x73741,x73744),x73744)+~E(f317(x73742,x73744),f317(a102,f2(a899)))+E(f317(f317(f8(x73741,a899),x73742),x73743),f317(a102,f2(a899)))+~P1(f317(f29(x73741),x73743))+~P1(f317(f317(f319(x73741),x73744),x73743)) % 112.37/112.11 [8111]~E(f317(x81112,x81114),f72(a899))+~E(f317(x81112,f700(x81112,x81113,x81111,x81114)),f2(a899))+E(f317(f317(f8(x81111,a899),x81112),x81113),f72(a899))+~P1(f317(f29(x81111),x81113))+~P1(f317(f317(f319(x81111),x81114),x81113)) % 112.37/112.11 [8149]~E(f317(x81492,x81494),f317(a102,f2(a899)))+~E(f317(x81492,f679(x81492,x81493,x81491,x81494)),f2(a899))+E(f317(f317(f8(x81491,a899),x81492),x81493),f317(a102,f2(a899)))+~P1(f317(f29(x81491),x81493))+~P1(f317(f317(f319(x81491),x81494),x81493)) % 112.37/112.11 [8235]~P146(x82352)+~P122(x82352)+~P1(f317(x82351,x82354))+~P1(f317(f317(f277(x82352),x82353),f317(f317(f74(x82352),x82354),f2(x82352))))+P1(f317(x82351,f317(f317(f75(x82352),x82353),f842(x82353,x82351,x82352)))) % 112.37/112.11 [8701]~P108(x87011)+~P13(x87011,x87014)+P13(x87011,x87012)+~E(x87012,f317(f317(f141(x87011),x87013),x87014))+~P1(f317(f317(f224(x87011),x87013),f710(x87012,x87011,x87014,x87013))) % 112.37/112.11 [8738]E(x87381,x87382)+E(f317(f317(f3(a1),f363(x87383,x87382,x87384,x87381)),f364(x87383,x87382,x87384,x87381)),x87381)+~E(f317(f317(f74(a1),x87381),x87384),x87382)+~P1(f317(f317(f225(a1),f2(a1)),x87384))+~P1(f317(f317(f319(a1),x87382),x87383)) % 112.37/112.11 [8739]E(x87391,x87392)+E(f317(f317(f74(a1),f365(x87393,x87392,x87394,x87391)),f366(x87393,x87392,x87394,x87391)),x87391)+~E(f317(f317(f3(a1),x87391),x87394),x87392)+~P1(f317(f317(f225(a1),f2(a1)),x87394))+~P1(f317(f317(f319(a1),x87392),x87393)) % 112.37/112.11 [8931]E(f317(x89311,f330(x89312,x89311,x89313,x89314)),x89312)+P1(f317(f317(f224(a899),x89314),f331(x89312,x89311,x89313,x89314)))+~P1(f317(f317(f224(a1),x89312),f317(x89311,x89313)))+~P1(f317(f317(f225(a899),x89314),x89313))+~P1(f317(f317(f224(a1),f317(x89311,x89314)),x89312)) % 112.37/112.11 [8932]~P108(x89321)+~P13(x89321,x89323)+P13(x89321,x89322)+~E(x89322,f317(f317(f141(x89321),x89324),x89323))+P1(f317(f317(f319(x89321),f710(x89322,x89321,x89323,x89324)),f317(f162(x89321),x89323))) % 112.37/112.11 [8950]~P119(x89504)+~P132(x89504)+~E(f317(f317(f11(x89501,x89504),x89502),x89503),f2(x89504))+~P1(f317(f29(x89501),x89503))+P1(f317(f317(f319(x89501),f569(x89502,x89503,x89501,x89504)),x89503)) % 112.37/112.11 [8988]~E(f317(x89882,x89884),f72(a899))+E(f317(f317(f8(x89881,a899),x89882),x89883),f72(a899))+~P1(f317(f29(x89881),x89883))+~P1(f317(f317(f319(x89881),x89884),x89883))+P1(f317(f317(f319(x89881),f700(x89882,x89883,x89881,x89884)),x89883)) % 112.37/112.11 [9000]E(x90001,x90002)+~E(f317(f317(f74(a1),x90002),x90004),x90001)+~P1(f317(f317(f225(a1),f2(a1)),x90004))+~P1(f317(f317(f319(a1),x90001),x90003))+P1(f317(f317(f319(a1),f363(x90003,x90001,x90004,x90002)),x90003)) % 112.37/112.11 [9001]E(x90011,x90012)+~E(f317(f317(f3(a1),x90012),x90014),x90011)+~P1(f317(f317(f225(a1),f2(a1)),x90014))+~P1(f317(f317(f319(a1),x90011),x90013))+P1(f317(f317(f319(a1),f365(x90013,x90011,x90014,x90012)),x90013)) % 112.37/112.11 [9003]~E(f317(x90032,x90034),f317(a102,f2(a899)))+E(f317(f317(f8(x90031,a899),x90032),x90033),f317(a102,f2(a899)))+~P1(f317(f29(x90031),x90033))+~P1(f317(f317(f319(x90031),x90034),x90033))+P1(f317(f317(f319(x90031),f679(x90032,x90033,x90031,x90034)),x90033)) % 112.37/112.11 [9008]P58(x90082,x90083,x90084,x90081)+E(x90081,f178(f906(x90082,a895)))+~P1(f317(f29(x90082),x90084))+~P1(f317(f29(x90082),x90081))+P1(f317(f317(f319(x90082),f779(x90083,x90081,x90084,x90082)),x90084)) % 112.37/112.11 [9009]P58(x90092,x90093,x90094,x90091)+E(x90091,f178(f906(x90092,a895)))+~P1(f317(f29(x90092),x90094))+~P1(f317(f29(x90092),x90091))+P1(f317(f317(f319(x90092),f515(x90091,x90094,x90093,x90092)),x90094)) % 112.37/112.11 [9010]P58(x90102,x90103,x90104,x90101)+E(x90101,f178(f906(x90102,a895)))+~P1(f317(f29(x90102),x90104))+~P1(f317(f29(x90102),x90101))+P1(f317(f317(f319(x90102),f780(x90101,x90104,x90103,x90102)),x90104)) % 112.37/112.11 [9083]E(x90831,x90832)+~E(f317(f317(f74(a1),x90832),x90834),x90831)+~P1(f317(f317(f225(a1),f2(a1)),x90834))+~P1(f317(f317(f319(a1),x90831),x90833))+P1(f317(f317(f319(a1),f364(x90833,x90831,x90834,x90832)),f293(a1,f72(a1),x90834))) % 112.37/112.11 [9084]E(x90841,x90842)+~E(f317(f317(f3(a1),x90842),x90844),x90841)+~P1(f317(f317(f225(a1),f2(a1)),x90844))+~P1(f317(f317(f319(a1),x90841),x90843))+P1(f317(f317(f319(a1),f366(x90843,x90841,x90844,x90842)),f293(a1,f72(a1),x90844))) % 112.37/112.11 [9157]P1(f317(f317(f224(a899),x91571),f330(x91572,x91573,x91574,x91571)))+~P1(f317(f317(f224(a1),x91572),f317(x91573,x91574)))+P1(f317(f317(f224(a899),x91571),f331(x91572,x91573,x91574,x91571)))+~P1(f317(f317(f225(a899),x91571),x91574))+~P1(f317(f317(f224(a1),f317(x91573,x91571)),x91572)) % 112.37/112.11 [9271]E(f317(x92711,f330(x92712,x92711,x92713,x92714)),x92712)+~P1(f317(f317(f224(a1),x92712),f317(x92711,x92713)))+P1(f317(f317(f225(a899),f331(x92712,x92711,x92713,x92714)),x92713))+~P1(f317(f317(f225(a899),x92714),x92713))+~P1(f317(f317(f224(a1),f317(x92711,x92714)),x92712)) % 112.37/112.11 [9386]~P1(f317(f317(f277(a899),x93864),x93861))+~P1(f317(f317(f277(a899),x93864),x93863))+~P1(f317(f317(f277(a899),x93862),x93861))+P1(f317(f317(f277(a899),x93861),x93862))+P1(f317(f317(f225(f906(a899,a895)),f280(a899,f277(a899),x93863,x93862)),f280(a899,f277(a899),x93864,x93861))) % 112.37/112.11 [9387]~P1(f317(f317(f277(a899),x93872),x93871))+~P1(f317(f317(f277(a899),x93873),x93874))+~P1(f317(f317(f277(a899),x93872),x93874))+P1(f317(f317(f277(a899),x93871),x93872))+P1(f317(f317(f225(f906(a899,a895)),f280(a899,f277(a899),x93871,x93873)),f280(a899,f277(a899),x93872,x93874))) % 112.37/112.11 [9405]~P1(f317(f317(f224(a1),x94052),f317(x94053,x94054)))+P1(f317(f317(f224(a899),x94051),f331(x94052,x94053,x94054,x94051)))+P1(f317(f317(f224(a899),f330(x94052,x94053,x94054,x94051)),x94054))+~P1(f317(f317(f225(a899),x94051),x94054))+~P1(f317(f317(f224(a1),f317(x94053,x94051)),x94052)) % 112.37/112.11 [9406]~P1(f317(f317(f224(a1),x94062),f317(x94063,x94064)))+P1(f317(f317(f224(a899),x94061),f330(x94062,x94063,x94064,x94061)))+P1(f317(f317(f225(a899),f331(x94062,x94063,x94064,x94061)),x94064))+~P1(f317(f317(f225(a899),x94061),x94064))+~P1(f317(f317(f224(a1),f317(x94063,x94061)),x94062)) % 112.37/112.11 [9514]~P1(f317(f317(f224(a1),x95141),f317(x95142,x95143)))+P1(f317(f317(f225(a899),f331(x95141,x95142,x95143,x95144)),x95143))+~P1(f317(f317(f225(a899),x95144),x95143))+~P1(f317(f317(f224(a1),f317(x95142,x95144)),x95141))+P1(f317(f317(f224(a899),f330(x95141,x95142,x95143,x95144)),x95143)) % 112.37/112.11 [9608]E(x96081,f178(f906(x96082,a895)))+~P1(f317(f29(x96082),x96084))+~P1(f317(f29(x96082),x96081))+P1(f317(f317(f319(f905(f906(x96082,a895),f906(x96082,a895))),f317(f317(f242(f906(x96082,a895),f906(x96082,a895)),x96084),x96081)),f309(x96082,x96083)))+P1(f317(f317(f319(x96082),f521(x96083,x96081,x96084,x96082)),x96084)) % 112.37/112.11 [9609]E(x96091,f178(f906(x96092,a895)))+~P1(f317(f29(x96092),x96094))+~P1(f317(f29(x96092),x96091))+P1(f317(f317(f319(f905(f906(x96092,a895),f906(x96092,a895))),f317(f317(f242(f906(x96092,a895),f906(x96092,a895)),x96094),x96091)),f309(x96092,x96093)))+P1(f317(f317(f319(x96092),f592(x96093,x96091,x96094,x96092)),x96094)) % 112.37/112.11 [10286]E(f317(x102861,f330(x102862,x102861,x102863,x102864)),x102862)+~P1(f317(f317(f224(a1),x102862),f317(x102861,x102863)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f3(a1),f317(x102861,f317(f317(f74(a899),f331(x102862,x102861,x102863,x102864)),f72(a899)))),f317(x102861,f331(x102862,x102861,x102863,x102864))))),f72(a1)))+~P1(f317(f317(f225(a899),x102864),x102863))+~P1(f317(f317(f224(a1),f317(x102861,x102864)),x102862)) % 112.37/112.11 [10287]~P1(f317(f317(f224(a1),x102872),f317(x102873,x102874)))+P1(f317(f317(f224(a899),x102871),f330(x102872,x102873,x102874,x102871)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f3(a1),f317(x102873,f317(f317(f74(a899),f331(x102872,x102873,x102874,x102871)),f72(a899)))),f317(x102873,f331(x102872,x102873,x102874,x102871))))),f72(a1)))+~P1(f317(f317(f225(a899),x102871),x102874))+~P1(f317(f317(f224(a1),f317(x102873,x102871)),x102872)) % 112.37/112.11 [10288]~P1(f317(f317(f224(a1),x102881),f317(x102882,x102883)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f3(a1),f317(x102882,f317(f317(f74(a899),f331(x102881,x102882,x102883,x102884)),f72(a899)))),f317(x102882,f331(x102881,x102882,x102883,x102884))))),f72(a1)))+~P1(f317(f317(f225(a899),x102884),x102883))+~P1(f317(f317(f224(a1),f317(x102882,x102884)),x102881))+P1(f317(f317(f224(a899),f330(x102881,x102882,x102883,x102884)),x102883)) % 112.37/112.11 [7337]~P63(x73371)+P1(f317(f317(f225(x73371),x73372),f2(x73371)))+~P1(f317(f317(f224(x73371),x73373),f2(x73371)))+P1(f317(f317(f225(x73371),f2(x73371)),x73372))+P1(f317(f317(f224(x73371),x73373),f317(f317(f281(x73371),x73374),x73372))) % 112.37/112.11 [7338]~P63(x73381)+P1(f317(f317(f225(x73381),x73382),f2(x73381)))+~P1(f317(f317(f225(x73381),x73383),f2(x73381)))+P1(f317(f317(f225(x73381),f2(x73381)),x73382))+P1(f317(f317(f225(x73381),x73383),f317(f317(f281(x73381),x73384),x73382))) % 112.37/112.11 [7587]~P63(x75871)+P1(f317(f317(f224(x75871),x75872),f2(x75871)))+P1(f317(f317(f225(x75871),x75873),f2(x75871)))+P1(f317(f317(f225(x75871),f2(x75871)),x75873))+~P1(f317(f317(f224(x75871),x75872),f317(f317(f281(x75871),x75874),x75873))) % 112.37/112.11 [7588]~P63(x75881)+P1(f317(f317(f225(x75881),x75882),f2(x75881)))+P1(f317(f317(f225(x75881),x75883),f2(x75881)))+P1(f317(f317(f225(x75881),f2(x75881)),x75883))+~P1(f317(f317(f225(x75881),x75882),f317(f317(f281(x75881),x75884),x75883))) % 112.37/112.11 [7707]E(x77071,x77072)+~E(f317(f317(f154(x77073),x77074),x77071),f317(f317(f154(x77073),x77074),x77072))+~P1(f317(f127(x77073),x77074))+~P1(f317(f317(f225(a899),x77072),f317(f179(f900(x77073)),x77074)))+~P1(f317(f317(f225(a899),x77071),f317(f179(f900(x77073)),x77074))) % 112.37/112.11 [8073]~P63(x80731)+~P1(f317(f317(f224(x80731),x80733),f2(x80731)))+P1(f317(f317(f225(x80731),f2(x80731)),x80732))+~P1(f317(f317(f224(x80731),x80734),f317(f317(f75(x80731),x80733),x80732)))+P1(f317(f317(f224(x80731),x80733),f317(f317(f281(x80731),x80734),x80732))) % 112.37/112.11 [8074]~P63(x80741)+~P1(f317(f317(f225(x80741),x80743),f2(x80741)))+P1(f317(f317(f225(x80741),f2(x80741)),x80742))+~P1(f317(f317(f225(x80741),x80744),f317(f317(f75(x80741),x80743),x80742)))+P1(f317(f317(f225(x80741),x80743),f317(f317(f281(x80741),x80744),x80742))) % 112.37/112.11 [8075]~P63(x80751)+~P1(f317(f317(f225(x80751),x80752),f2(x80751)))+P1(f317(f317(f225(x80751),f2(x80751)),x80752))+~P1(f317(f317(f224(x80751),x80754),f317(f317(f75(x80751),x80753),x80752)))+P1(f317(f317(f224(x80751),x80753),f317(f317(f281(x80751),x80754),x80752))) % 112.37/112.11 [8076]~P63(x80761)+~P1(f317(f317(f225(x80761),x80762),f2(x80761)))+P1(f317(f317(f225(x80761),f2(x80761)),x80762))+~P1(f317(f317(f224(x80761),x80764),f317(f317(f281(x80761),x80763),x80762)))+P1(f317(f317(f224(x80761),x80763),f317(f317(f75(x80761),x80764),x80762))) % 112.37/112.11 [8077]~P63(x80771)+~P1(f317(f317(f225(x80771),x80772),f2(x80771)))+P1(f317(f317(f225(x80771),f2(x80771)),x80772))+~P1(f317(f317(f225(x80771),x80774),f317(f317(f75(x80771),x80773),x80772)))+P1(f317(f317(f225(x80771),x80773),f317(f317(f281(x80771),x80774),x80772))) % 112.37/112.11 [8078]~P63(x80781)+~P1(f317(f317(f225(x80781),x80782),f2(x80781)))+P1(f317(f317(f225(x80781),f2(x80781)),x80782))+~P1(f317(f317(f225(x80781),x80784),f317(f317(f281(x80781),x80783),x80782)))+P1(f317(f317(f225(x80781),x80783),f317(f317(f75(x80781),x80784),x80782))) % 112.37/112.11 [8203]~P3(x82031)+~P1(f317(f317(f277(x82031),x82033),x82034))+~P1(f317(f317(f277(x82031),x82033),x82032))+~P1(f317(f317(f277(x82031),x82032),x82034))+P1(f317(f317(f277(x82031),f317(f317(f31(x82031),x82032),x82033)),f317(f317(f31(x82031),x82034),x82033))) % 112.37/112.11 [8218]~P108(x82181)+~P13(x82181,x82182)+~P1(f317(f317(f224(a899),x82183),x82184))+P1(f317(f317(f224(x82181),f317(f317(f154(x82181),x82182),x82183)),f317(f317(f154(x82181),x82182),x82184)))+~P1(f317(f317(f225(a899),x82184),f317(f179(f900(x82181)),x82182))) % 112.37/112.11 [8271]~P126(x82711)+~P1(f317(f317(f224(x82711),x82712),f72(x82711)))+~P1(f317(f317(f224(x82711),f2(x82711)),x82712))+~P1(f317(f317(f224(a899),x82714),x82713))+P1(f317(f317(f224(x82711),f317(f317(f234(x82711),x82712),x82713)),f317(f317(f234(x82711),x82712),x82714))) % 112.37/112.11 [8272]~P126(x82721)+~P1(f317(f317(f225(x82721),x82722),f72(x82721)))+~P1(f317(f317(f225(x82721),f2(x82721)),x82722))+~P1(f317(f317(f225(a899),x82724),x82723))+P1(f317(f317(f225(x82721),f317(f317(f234(x82721),x82722),x82723)),f317(f317(f234(x82721),x82722),x82724))) % 112.37/112.11 [8273]~P126(x82731)+~P1(f317(f317(f224(x82731),f2(x82731)),x82732))+~P1(f317(f317(f225(a899),f2(a899)),x82733))+~P1(f317(f317(f225(x82731),x82732),x82734))+P1(f317(f317(f225(x82731),f317(f317(f234(x82731),x82732),x82733)),f317(f317(f234(x82731),x82734),x82733))) % 112.37/112.11 [8291]~P108(x82911)+~P13(x82911,f317(f158(x82911),x82912))+~P1(f317(f317(f224(a899),x82914),x82913))+P1(f317(f317(f224(x82911),f317(f317(f154(x82911),x82912),x82913)),f317(f317(f154(x82911),x82912),x82914)))+~P1(f317(f317(f225(a899),x82913),f317(f179(f900(x82911)),x82912))) % 112.37/112.11 [8523]~P3(x85231)+P1(f317(f317(f277(x85231),x85232),x85233))+~P1(f317(f317(f277(x85231),x85234),x85233))+~P1(f317(f317(f277(x85231),x85234),x85232))+~P1(f317(f317(f277(x85231),f317(f317(f31(x85231),x85232),x85234)),f317(f317(f31(x85231),x85233),x85234))) % 112.37/112.11 [8538]~P63(x85381)+~P1(f317(f317(f224(x85381),x85382),f2(x85381)))+~P1(f317(f317(f224(x85381),x85383),x85384))+~P1(f317(f317(f225(x85381),f2(x85381)),f317(f317(f75(x85381),x85383),x85384)))+P1(f317(f317(f224(x85381),f317(f317(f281(x85381),x85382),x85383)),f317(f317(f281(x85381),x85382),x85384))) % 112.37/112.11 [8539]~P64(x85391)+~P1(f317(f317(f225(x85391),x85392),f2(x85391)))+~P1(f317(f317(f225(x85391),x85393),x85394))+~P1(f317(f317(f225(x85391),f2(x85391)),f317(f317(f75(x85391),x85393),x85394)))+P1(f317(f317(f225(x85391),f317(f317(f281(x85391),x85392),x85393)),f317(f317(f281(x85391),x85392),x85394))) % 112.37/112.11 [8548]~P64(x85481)+~P1(f317(f317(f224(x85481),x85484),x85483))+~P1(f317(f317(f224(x85481),f2(x85481)),x85482))+~P1(f317(f317(f225(x85481),f2(x85481)),f317(f317(f75(x85481),x85483),x85484)))+P1(f317(f317(f224(x85481),f317(f317(f281(x85481),x85482),x85483)),f317(f317(f281(x85481),x85482),x85484))) % 112.37/112.11 [8549]~P64(x85491)+~P1(f317(f317(f225(x85491),x85494),x85493))+~P1(f317(f317(f225(x85491),f2(x85491)),x85492))+~P1(f317(f317(f225(x85491),f2(x85491)),f317(f317(f75(x85491),x85493),x85494)))+P1(f317(f317(f225(x85491),f317(f317(f281(x85491),x85492),x85493)),f317(f317(f281(x85491),x85492),x85494))) % 112.37/112.11 [8649]P1(f317(x86491,x86492))+~P1(f317(f29(x86494),x86492))+P1(f317(x86491,f893(x86491,x86493,x86492,x86494)))+~P1(f317(x86491,f178(f906(x86494,a895))))+~P1(f317(f317(f224(f906(x86494,a895)),x86492),x86493)) % 112.37/112.11 [8658]P1(f317(x86581,x86582))+P1(f317(f29(x86583),f893(x86581,x86584,x86582,x86583)))+~P1(f317(f29(x86583),x86582))+~P1(f317(x86581,f178(f906(x86583,a895))))+~P1(f317(f317(f224(f906(x86583,a895)),x86582),x86584)) % 112.37/112.11 [8926]E(f317(f317(f74(a1),f367(x89261,x89262,x89263,x89264)),f368(x89261,x89262,x89263,x89264)),x89264)+~P1(f317(f317(f225(a1),f2(a1)),x89263))+~P1(f317(f317(f225(a1),x89262),x89264))+~P1(f317(f317(f319(a1),x89262),x89261))+P1(f317(f317(f225(a1),x89262),f317(f317(f3(a1),x89264),x89263))) % 112.37/112.11 [9139]~P1(f317(f317(f225(a1),f2(a1)),x91393))+~P1(f317(f317(f225(a1),x91392),x91394))+~P1(f317(f317(f319(a1),x91392),x91391))+P1(f317(f317(f319(a1),f367(x91391,x91392,x91393,x91394)),x91391))+P1(f317(f317(f225(a1),x91392),f317(f317(f3(a1),x91394),x91393))) % 112.37/112.11 [9150]P1(f317(x91501,x91502))+~P1(f317(f29(x91503),x91502))+P1(f317(f317(f319(x91503),f884(x91501,x91504,x91502,x91503)),x91504))+~P1(f317(x91501,f178(f906(x91503,a895))))+~P1(f317(f317(f224(f906(x91503,a895)),x91502),x91504)) % 112.37/112.11 [9167]E(f317(f317(f74(a1),f356(x91671,x91672,x91673,x91674)),f357(x91671,x91672,x91673,x91674)),x91674)+~P1(f317(f317(f225(a1),f2(a1)),x91673))+~P1(f317(f317(f224(a1),x91672),x91674))+P1(f317(f317(f224(a1),x91672),f317(f317(f3(a1),x91674),x91673)))+~P1(f317(f317(f319(a1),f317(f317(f3(a1),x91672),f72(a1))),x91671)) % 112.37/112.11 [9221]~P1(f317(f317(f225(a1),f2(a1)),x92213))+~P1(f317(f317(f225(a1),x92211),x92212))+~P1(f317(f317(f319(a1),x92211),x92214))+P1(f317(f317(f319(a1),f368(x92214,x92211,x92213,x92212)),f293(a1,f72(a1),x92213)))+P1(f317(f317(f225(a1),x92211),f317(f317(f3(a1),x92212),x92213))) % 112.37/112.11 [9247]~P69(x92472)+~E(f759(x92473,x92474,x92471,x92472),f760(x92473,x92474,x92471,x92472))+~P1(f317(f29(x92471),f761(x92473,x92474,x92471,x92472)))+E(f317(f317(f8(f906(x92471,a895),x92472),f317(f8(x92471,x92472),x92473)),x92474),f317(f317(f8(x92471,x92472),x92473),f32(f906(x92471,a895),x92474)))+~P1(f317(f29(f906(x92471,a895)),x92474)) % 112.37/112.11 [9251]~P69(x92512)+~E(f317(x92513,f762(x92513,x92514,x92511,x92512)),f2(x92512))+~P1(f317(f29(x92511),f761(x92513,x92514,x92511,x92512)))+E(f317(f317(f8(f906(x92511,a895),x92512),f317(f8(x92511,x92512),x92513)),x92514),f317(f317(f8(x92511,x92512),x92513),f32(f906(x92511,a895),x92514)))+~P1(f317(f29(f906(x92511,a895)),x92514)) % 112.37/112.11 [9315]~P1(f317(f317(f225(a1),f2(a1)),x93153))+~P1(f317(f317(f224(a1),x93152),x93154))+P1(f317(f317(f319(a1),f356(x93151,x93152,x93153,x93154)),x93151))+P1(f317(f317(f224(a1),x93152),f317(f317(f3(a1),x93154),x93153)))+~P1(f317(f317(f319(a1),f317(f317(f3(a1),x93152),f72(a1))),x93151)) % 112.37/112.11 [9361]~P1(f317(f317(f225(a1),f2(a1)),x93613))+~P1(f317(f317(f224(a1),x93611),x93612))+P1(f317(f317(f319(a1),f357(x93614,x93611,x93613,x93612)),f293(a1,f72(a1),x93613)))+P1(f317(f317(f224(a1),x93611),f317(f317(f3(a1),x93612),x93613)))+~P1(f317(f317(f319(a1),f317(f317(f3(a1),x93611),f72(a1))),x93614)) % 112.37/112.11 [9382]~P69(x93822)+~E(f759(x93823,x93824,x93821,x93822),f760(x93823,x93824,x93821,x93822))+E(f317(f317(f8(f906(x93821,a895),x93822),f317(f8(x93821,x93822),x93823)),x93824),f317(f317(f8(x93821,x93822),x93823),f32(f906(x93821,a895),x93824)))+P1(f317(f317(f319(f906(x93821,a895)),f761(x93823,x93824,x93821,x93822)),x93824))+~P1(f317(f29(f906(x93821,a895)),x93824)) % 112.37/112.11 [9389]~P69(x93892)+~E(f317(x93893,f762(x93893,x93894,x93891,x93892)),f2(x93892))+E(f317(f317(f8(f906(x93891,a895),x93892),f317(f8(x93891,x93892),x93893)),x93894),f317(f317(f8(x93891,x93892),x93893),f32(f906(x93891,a895),x93894)))+P1(f317(f317(f319(f906(x93891,a895)),f761(x93893,x93894,x93891,x93892)),x93894))+~P1(f317(f29(f906(x93891,a895)),x93894)) % 112.37/112.11 [9491]~P69(x94912)+~P1(f317(f29(x94911),f761(x94913,x94914,x94911,x94912)))+E(f317(f317(f8(f906(x94911,a895),x94912),f317(f8(x94911,x94912),x94913)),x94914),f317(f317(f8(x94911,x94912),x94913),f32(f906(x94911,a895),x94914)))+P1(f317(f317(f319(f906(x94911,a895)),f760(x94913,x94914,x94911,x94912)),x94914))+~P1(f317(f29(f906(x94911,a895)),x94914)) % 112.37/112.11 [9492]~P69(x94922)+~P1(f317(f29(x94921),f761(x94923,x94924,x94921,x94922)))+E(f317(f317(f8(f906(x94921,a895),x94922),f317(f8(x94921,x94922),x94923)),x94924),f317(f317(f8(x94921,x94922),x94923),f32(f906(x94921,a895),x94924)))+P1(f317(f317(f319(f906(x94921,a895)),f759(x94923,x94924,x94921,x94922)),x94924))+~P1(f317(f29(f906(x94921,a895)),x94924)) % 112.37/112.11 [9572]~P69(x95722)+E(f317(f317(f8(f906(x95721,a895),x95722),f317(f8(x95721,x95722),x95723)),x95724),f317(f317(f8(x95721,x95722),x95723),f32(f906(x95721,a895),x95724)))+P1(f317(f317(f319(f906(x95721,a895)),f761(x95723,x95724,x95721,x95722)),x95724))+P1(f317(f317(f319(f906(x95721,a895)),f760(x95723,x95724,x95721,x95722)),x95724))+~P1(f317(f29(f906(x95721,a895)),x95724)) % 112.37/112.11 [9573]~P69(x95732)+E(f317(f317(f8(f906(x95731,a895),x95732),f317(f8(x95731,x95732),x95733)),x95734),f317(f317(f8(x95731,x95732),x95733),f32(f906(x95731,a895),x95734)))+P1(f317(f317(f319(f906(x95731,a895)),f761(x95733,x95734,x95731,x95732)),x95734))+P1(f317(f317(f319(f906(x95731,a895)),f759(x95733,x95734,x95731,x95732)),x95734))+~P1(f317(f29(f906(x95731,a895)),x95734)) % 112.37/112.11 [9594]~P69(x95942)+P1(f317(f317(f319(x95941),f762(x95943,x95944,x95941,x95942)),f760(x95943,x95944,x95941,x95942)))+~P1(f317(f29(x95941),f761(x95943,x95944,x95941,x95942)))+E(f317(f317(f8(f906(x95941,a895),x95942),f317(f8(x95941,x95942),x95943)),x95944),f317(f317(f8(x95941,x95942),x95943),f32(f906(x95941,a895),x95944)))+~P1(f317(f29(f906(x95941,a895)),x95944)) % 112.37/112.11 [9595]~P69(x95952)+P1(f317(f317(f319(x95951),f762(x95953,x95954,x95951,x95952)),f759(x95953,x95954,x95951,x95952)))+~P1(f317(f29(x95951),f761(x95953,x95954,x95951,x95952)))+E(f317(f317(f8(f906(x95951,a895),x95952),f317(f8(x95951,x95952),x95953)),x95954),f317(f317(f8(x95951,x95952),x95953),f32(f906(x95951,a895),x95954)))+~P1(f317(f29(f906(x95951,a895)),x95954)) % 112.37/112.11 [9612]P1(f317(x96121,x96122))+~P1(f317(f317(f319(x96123),f884(x96121,x96124,x96122,x96123)),f893(x96121,x96124,x96122,x96123)))+~P1(f317(f29(x96123),x96122))+~P1(f317(x96121,f178(f906(x96123,a895))))+~P1(f317(f317(f224(f906(x96123,a895)),x96122),x96124)) % 112.37/112.11 [9649]~P69(x96492)+P1(f317(f317(f319(x96491),f762(x96493,x96494,x96491,x96492)),f760(x96493,x96494,x96491,x96492)))+E(f317(f317(f8(f906(x96491,a895),x96492),f317(f8(x96491,x96492),x96493)),x96494),f317(f317(f8(x96491,x96492),x96493),f32(f906(x96491,a895),x96494)))+P1(f317(f317(f319(f906(x96491,a895)),f761(x96493,x96494,x96491,x96492)),x96494))+~P1(f317(f29(f906(x96491,a895)),x96494)) % 112.37/112.11 [9650]~P69(x96502)+P1(f317(f317(f319(x96501),f762(x96503,x96504,x96501,x96502)),f759(x96503,x96504,x96501,x96502)))+E(f317(f317(f8(f906(x96501,a895),x96502),f317(f8(x96501,x96502),x96503)),x96504),f317(f317(f8(x96501,x96502),x96503),f32(f906(x96501,a895),x96504)))+P1(f317(f317(f319(f906(x96501,a895)),f761(x96503,x96504,x96501,x96502)),x96504))+~P1(f317(f29(f906(x96501,a895)),x96504)) % 112.37/112.11 [9826]P1(f317(x98261,x98262))+~P1(f317(f29(x98263),x98262))+~P1(f317(x98261,f317(f317(f299(x98263),f884(x98261,x98264,x98262,x98263)),f893(x98261,x98264,x98262,x98263))))+~P1(f317(x98261,f178(f906(x98263,a895))))+~P1(f317(f317(f224(f906(x98263,a895)),x98262),x98264)) % 112.37/112.11 [10160]~P109(x101603)+~P48(a899,x101603,f317(f317(f20(a899,f906(a899,a895),f906(a899,a895)),f317(f317(f10(f906(a899,f906(a895,a895)),f906(f906(a899,a895),f906(a899,a895)),a899),f20(a899,a895,a895)),f317(f317(f10(f906(a899,a895),f906(a899,f906(a895,a895)),a899),f317(f10(a895,f906(a895,a895),a899),a315)),f277(a899)))),f317(f317(f10(f906(a899,a895),f906(a899,a895),a899),f317(f10(a895,a895,a899),a312)),f317(f9(a899,a899,a895),f277(a899)))),x101604)+P1(f317(f317(f225(x101603),f317(x101604,x101602)),f317(x101604,x101601)))+~P1(f317(f317(f277(a899),x101602),x101601))+P1(f317(f317(f277(a899),x101601),x101602)) % 112.37/112.11 [7843]~P63(x78431)+P1(f317(f317(f225(x78431),x78432),f2(x78431)))+~P1(f317(f317(f224(x78431),f2(x78431)),x78434))+P1(f317(f317(f225(x78431),f2(x78431)),x78432))+P1(f317(f317(f224(x78431),f317(f317(f281(x78431),x78433),x78432)),x78434)) % 112.37/112.11 [7844]~P63(x78441)+P1(f317(f317(f225(x78441),x78442),f2(x78441)))+P1(f317(f317(f225(x78441),f2(x78441)),x78442))+~P1(f317(f317(f225(x78441),f2(x78441)),x78444))+P1(f317(f317(f225(x78441),f317(f317(f281(x78441),x78443),x78442)),x78444)) % 112.37/112.11 [8124]~P1(f317(f317(f224(a1),x81244),f2(a1)))+~E(x81242,f317(f317(f74(a1),f317(f317(f75(a1),x81241),x81243)),x81244))+P1(f317(f317(f225(a1),f2(a1)),x81241))+~P1(f317(f317(f225(a1),x81241),x81244))+P1(f317(f45(x81242,x81241),f317(f317(f242(a1,a1),x81243),x81244))) % 112.37/112.11 [8158]~P1(f317(x81581,x81584))+P1(f317(x81581,f885(x81582,x81581,x81583)))+~P1(f317(f317(f224(a1),f2(a1)),x81582))+~P1(f317(f317(f225(a1),f2(a1)),x81583))+P1(f317(x81581,f317(f317(f3(a1),x81584),f317(f317(f75(a1),x81582),x81583)))) % 112.37/112.11 [8159]~P1(f317(x81591,x81594))+P1(f317(x81591,f887(x81592,x81591,x81593)))+~P1(f317(f317(f224(a1),f2(a1)),x81592))+~P1(f317(f317(f225(a1),f2(a1)),x81593))+P1(f317(x81591,f317(f317(f74(a1),x81594),f317(f317(f75(a1),x81592),x81593)))) % 112.37/112.11 [8160]~P63(x81601)+P1(f317(f317(f225(x81601),x81602),f2(x81601)))+P1(f317(f317(f225(x81601),f2(x81601)),x81602))+P1(f317(f317(f224(x81601),f2(x81601)),x81603))+~P1(f317(f317(f224(x81601),f317(f317(f281(x81601),x81604),x81602)),x81603)) % 112.37/112.11 [8161]~P63(x81611)+P1(f317(f317(f225(x81611),x81612),f2(x81611)))+P1(f317(f317(f225(x81611),f2(x81611)),x81612))+P1(f317(f317(f225(x81611),f2(x81611)),x81613))+~P1(f317(f317(f225(x81611),f317(f317(f281(x81611),x81614),x81612)),x81613)) % 112.37/112.11 [8213]~E(x82131,f317(f317(f74(a1),f317(f317(f75(a1),x82132),x82133)),x82134))+~P1(f317(f317(f224(a1),f2(a1)),x82134))+~P1(f317(f317(f225(a1),f2(a1)),x82132))+~P1(f317(f317(f225(a1),x82134),x82132))+P1(f317(f45(x82131,x82132),f317(f317(f242(a1,a1),x82133),x82134))) % 112.37/112.11 [8330]~P63(x83301)+P1(f317(f317(f225(x83301),x83302),f2(x83301)))+~P1(f317(f317(f224(x83301),f2(x83301)),x83304))+~P1(f317(f317(f224(x83301),x83303),f317(f317(f75(x83301),x83304),x83302)))+P1(f317(f317(f224(x83301),f317(f317(f281(x83301),x83303),x83302)),x83304)) % 112.37/112.11 [8331]~P63(x83311)+P1(f317(f317(f225(x83311),x83312),f2(x83311)))+~P1(f317(f317(f225(x83311),f2(x83311)),x83314))+~P1(f317(f317(f225(x83311),x83313),f317(f317(f75(x83311),x83314),x83312)))+P1(f317(f317(f225(x83311),f317(f317(f281(x83311),x83313),x83312)),x83314)) % 112.37/112.11 [8416]~P63(x84161)+P1(f317(f317(f225(x84161),x84162),f2(x84161)))+~P1(f317(f317(f224(x84161),x84163),f2(x84161)))+P1(f317(f317(f224(x84161),x84163),f317(f317(f281(x84161),x84164),x84162)))+~P1(f317(f317(f224(x84161),f317(f317(f75(x84161),x84163),x84162)),x84164)) % 112.37/112.11 [8417]~P63(x84171)+P1(f317(f317(f225(x84171),x84172),f2(x84171)))+~P1(f317(f317(f225(x84171),x84173),f2(x84171)))+P1(f317(f317(f225(x84171),x84173),f317(f317(f281(x84171),x84174),x84172)))+~P1(f317(f317(f225(x84171),f317(f317(f75(x84171),x84173),x84172)),x84174)) % 112.37/112.11 [8570]~P63(x85701)+~P1(f317(f317(f225(x85701),x85702),f2(x85701)))+P1(f317(f317(f225(x85701),f2(x85701)),x85702))+~P1(f317(f317(f224(x85701),f317(f317(f281(x85701),x85704),x85702)),x85703))+P1(f317(f317(f224(x85701),f317(f317(f75(x85701),x85703),x85702)),x85704)) % 112.37/112.11 [8571]~P63(x85711)+~P1(f317(f317(f225(x85711),x85712),f2(x85711)))+P1(f317(f317(f225(x85711),f2(x85711)),x85712))+~P1(f317(f317(f224(x85711),f317(f317(f75(x85711),x85714),x85712)),x85713))+P1(f317(f317(f224(x85711),f317(f317(f281(x85711),x85713),x85712)),x85714)) % 112.37/112.11 [8572]~P63(x85721)+~P1(f317(f317(f225(x85721),x85722),f2(x85721)))+P1(f317(f317(f225(x85721),f2(x85721)),x85722))+~P1(f317(f317(f225(x85721),f317(f317(f281(x85721),x85724),x85722)),x85723))+P1(f317(f317(f225(x85721),f317(f317(f75(x85721),x85723),x85722)),x85724)) % 112.37/112.11 [8573]~P63(x85731)+~P1(f317(f317(f225(x85731),x85732),f2(x85731)))+P1(f317(f317(f225(x85731),f2(x85731)),x85732))+~P1(f317(f317(f225(x85731),f317(f317(f75(x85731),x85734),x85732)),x85733))+P1(f317(f317(f225(x85731),f317(f317(f281(x85731),x85733),x85732)),x85734)) % 112.37/112.11 [8589]~P63(x85891)+~P1(f317(f317(f224(x85891),f2(x85891)),x85894))+P1(f317(f317(f225(x85891),f2(x85891)),x85892))+~P1(f317(f317(f224(x85891),f317(f317(f75(x85891),x85894),x85892)),x85893))+P1(f317(f317(f224(x85891),f317(f317(f281(x85891),x85893),x85892)),x85894)) % 112.37/112.11 [8590]~P63(x85901)+~P1(f317(f317(f225(x85901),f2(x85901)),x85904))+P1(f317(f317(f225(x85901),f2(x85901)),x85902))+~P1(f317(f317(f225(x85901),f317(f317(f75(x85901),x85904),x85902)),x85903))+P1(f317(f317(f225(x85901),f317(f317(f281(x85901),x85903),x85902)),x85904)) % 112.37/112.11 [8666]~P63(x86661)+~P1(f317(f317(f225(x86661),x86664),f2(x86661)))+~P1(f317(f317(f224(x86661),x86663),f317(f317(f75(x86661),x86662),x86664)))+P1(f317(f317(f224(x86661),x86662),f317(f317(f281(x86661),x86663),x86664)))+~P1(f317(f317(f224(x86661),f317(f317(f75(x86661),x86662),x86664)),x86663)) % 112.37/112.11 [8667]~P63(x86671)+~P1(f317(f317(f224(x86671),x86672),f2(x86671)))+~P1(f317(f317(f224(x86671),x86673),f317(f317(f75(x86671),x86672),x86674)))+P1(f317(f317(f224(x86671),x86672),f317(f317(f281(x86671),x86673),x86674)))+~P1(f317(f317(f224(x86671),f317(f317(f75(x86671),x86672),x86674)),x86673)) % 112.37/112.11 [8668]~P63(x86681)+~P1(f317(f317(f225(x86681),x86684),f2(x86681)))+~P1(f317(f317(f225(x86681),x86683),f317(f317(f75(x86681),x86682),x86684)))+P1(f317(f317(f225(x86681),x86682),f317(f317(f281(x86681),x86683),x86684)))+~P1(f317(f317(f225(x86681),f317(f317(f75(x86681),x86682),x86684)),x86683)) % 112.37/112.11 [8669]~P63(x86691)+~P1(f317(f317(f225(x86691),x86692),f2(x86691)))+~P1(f317(f317(f225(x86691),x86693),f317(f317(f75(x86691),x86692),x86694)))+P1(f317(f317(f225(x86691),x86692),f317(f317(f281(x86691),x86693),x86694)))+~P1(f317(f317(f225(x86691),f317(f317(f75(x86691),x86692),x86694)),x86693)) % 112.37/112.11 [8791]~P63(x87911)+~P1(f317(f317(f225(x87911),x87913),f2(x87911)))+~P1(f317(f317(f224(x87911),x87912),f317(f317(f75(x87911),x87914),x87913)))+~P1(f317(f317(f224(x87911),f317(f317(f75(x87911),x87914),x87913)),x87912))+P1(f317(f317(f224(x87911),f317(f317(f281(x87911),x87912),x87913)),x87914)) % 112.37/112.11 [8792]~P63(x87921)+~P1(f317(f317(f225(x87921),x87923),f2(x87921)))+~P1(f317(f317(f225(x87921),x87922),f317(f317(f75(x87921),x87924),x87923)))+~P1(f317(f317(f225(x87921),f317(f317(f75(x87921),x87924),x87923)),x87922))+P1(f317(f317(f225(x87921),f317(f317(f281(x87921),x87922),x87923)),x87924)) % 112.37/112.11 [8809]~P63(x88091)+~P1(f317(f317(f224(x88091),f2(x88091)),x88094))+~P1(f317(f317(f224(x88091),x88092),f317(f317(f75(x88091),x88094),x88093)))+~P1(f317(f317(f224(x88091),f317(f317(f75(x88091),x88094),x88093)),x88092))+P1(f317(f317(f224(x88091),f317(f317(f281(x88091),x88092),x88093)),x88094)) % 112.37/112.11 [8810]~P63(x88101)+~P1(f317(f317(f225(x88101),f2(x88101)),x88104))+~P1(f317(f317(f225(x88101),x88102),f317(f317(f75(x88101),x88104),x88103)))+~P1(f317(f317(f225(x88101),f317(f317(f75(x88101),x88104),x88103)),x88102))+P1(f317(f317(f225(x88101),f317(f317(f281(x88101),x88102),x88103)),x88104)) % 112.37/112.11 [8993]E(f317(f317(f3(a1),f371(x89931,x89932,x89933,x89934)),f372(x89931,x89932,x89933,x89934)),x89934)+~P1(f317(f317(f225(a1),f2(a1)),x89933))+~P1(f317(f317(f319(a1),x89932),x89931))+~P1(f317(f317(f225(a1),x89934),x89932))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x89934),x89933)),x89932)) % 112.37/112.11 [9064]~P1(f317(x90641,x90642))+~P1(f317(f317(f224(a1),f2(a1)),x90643))+~P1(f317(f317(f225(a1),f2(a1)),x90644))+~P1(f317(x90641,f317(f317(f3(a1),f885(x90643,x90641,x90644)),x90644)))+P1(f317(x90641,f317(f317(f3(a1),x90642),f317(f317(f75(a1),x90643),x90644)))) % 112.37/112.11 [9065]~P1(f317(x90651,x90652))+~P1(f317(f317(f224(a1),f2(a1)),x90653))+~P1(f317(f317(f225(a1),f2(a1)),x90654))+~P1(f317(x90651,f317(f317(f74(a1),f887(x90653,x90651,x90654)),x90654)))+P1(f317(x90651,f317(f317(f74(a1),x90652),f317(f317(f75(a1),x90653),x90654)))) % 112.37/112.11 [9215]~P1(f317(f317(f225(a1),f2(a1)),x92153))+~P1(f317(f317(f319(a1),x92152),x92151))+~P1(f317(f317(f225(a1),x92154),x92152))+P1(f317(f317(f319(a1),f371(x92151,x92152,x92153,x92154)),x92151))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x92154),x92153)),x92152)) % 112.37/112.11 [9234]E(f317(f317(f3(a1),f358(x92341,x92342,x92343,x92344)),f359(x92341,x92342,x92343,x92344)),x92344)+~P1(f317(f317(f225(a1),f2(a1)),x92343))+~P1(f317(f317(f224(a1),x92344),x92342))+~P1(f317(f317(f319(a1),f317(f317(f74(a1),x92342),f72(a1))),x92341))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x92344),x92343)),x92342)) % 112.37/112.11 [9262]~P1(f317(f317(f225(a1),f2(a1)),x92622))+~P1(f317(f317(f319(a1),x92623),x92624))+~P1(f317(f317(f225(a1),x92621),x92623))+P1(f317(f317(f319(a1),f372(x92624,x92623,x92622,x92621)),f293(a1,f72(a1),x92622)))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x92621),x92622)),x92623)) % 112.37/112.11 [9353]~P1(f317(f317(f225(a1),f2(a1)),x93533))+~P1(f317(f317(f224(a1),x93534),x93532))+P1(f317(f317(f319(a1),f358(x93531,x93532,x93533,x93534)),x93531))+~P1(f317(f317(f319(a1),f317(f317(f74(a1),x93532),f72(a1))),x93531))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x93534),x93533)),x93532)) % 112.37/112.11 [9401]~P1(f317(f317(f225(a1),f2(a1)),x94012))+~P1(f317(f317(f224(a1),x94011),x94013))+P1(f317(f317(f319(a1),f359(x94014,x94013,x94012,x94011)),f293(a1,f72(a1),x94012)))+~P1(f317(f317(f319(a1),f317(f317(f74(a1),x94013),f72(a1))),x94014))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x94011),x94012)),x94013)) % 112.37/112.11 [9704]~P36(x97041,x97043)+~P26(x97041,x97044)+P36(x97041,f317(f317(f91(f906(f905(x97041,x97041),a895)),x97042),x97043))+~P1(f317(f317(f224(f906(f905(x97041,x97041),a895)),x97042),f317(f241(f906(f905(x97041,x97041),a895),f906(f905(x97041,x97041),a895)),x97044)))+~P1(f317(f317(f224(f906(f905(x97041,x97041),a895)),x97043),f317(f246(f906(f905(x97041,x97041),a895),f906(f905(x97041,x97041),a895)),x97044))) % 112.37/112.11 [10094]~P18(x100942,x100944,x100943)+E(x100941,f178(f906(x100942,a895)))+~P1(f317(f29(x100942),x100941))+P1(f317(f317(f319(x100942),f317(x100943,x100941)),x100941))+~P1(f317(f317(f319(x100942),f317(f317(x100944,f335(x100941,x100943,x100944,x100942)),f348(x100941,x100943,x100944,x100942))),f317(f317(f299(x100942),f335(x100941,x100943,x100944,x100942)),f317(f317(f299(x100942),f348(x100941,x100943,x100944,x100942)),f178(f906(x100942,a895)))))) % 112.37/112.11 [10018]~P109(x100182)+~P60(x100181)+~P1(f317(f317(f224(f906(x100181,x100182)),x100183),x100184))+P1(f317(f317(f225(f906(x100181,x100182)),x100183),x100184))+~P1(f317(f52(x100181),f317(f317(f10(a895,a895,x100181),a312),f317(f317(f20(x100181,x100182,a895),f317(f317(f10(x100182,f906(x100182,a895),x100181),a314),x100183)),x100184)))) % 112.37/112.11 [9618]~P54(x96181,x96181,x96184)+P1(f317(f317(f319(f905(x96181,x96181)),f317(f317(f242(x96181,x96181),x96182),x96183)),f297(x96181,x96184)))+P1(f317(f317(f319(f905(x96181,x96181)),f317(f317(f242(x96181,x96181),x96183),x96182)),f297(x96181,x96184)))+~P1(f317(f317(f319(f905(x96181,x96181)),f317(f317(f242(x96181,x96181),x96185),x96182)),f297(x96181,x96184)))+~P1(f317(f317(f319(f905(x96181,x96181)),f317(f317(f242(x96181,x96181),x96185),x96183)),f297(x96181,x96184))) % 112.37/112.11 [5698]E(x56981,f2(a899))+~E(f317(f30(x56982),x56985),x56981)+E(f317(f30(x56982),x56983),f317(a102,x56981))+~E(x56983,f317(f317(f299(x56982),x56984),x56985))+P1(f317(f317(f319(x56982),x56984),x56985)) % 112.37/112.11 [5820]~P62(x58202)+E(x58201,f2(x58202))+E(x58203,f2(x58202))+~E(f317(f317(f281(x58202),x58204),x58203),f317(f317(f281(x58202),x58205),x58201))+E(f317(f317(f75(x58202),x58204),x58201),f317(f317(f75(x58202),x58205),x58203)) % 112.37/112.11 [5821]~P62(x58212)+E(x58211,f2(x58212))+E(x58213,f2(x58212))+~E(f317(f317(f75(x58212),x58214),x58213),f317(f317(f75(x58212),x58215),x58211))+E(f317(f317(f281(x58212),x58214),x58211),f317(f317(f281(x58212),x58215),x58213)) % 112.37/112.11 [5899]~E(f317(f30(x58991),x58995),x58993)+~E(x58995,f178(f906(x58991,a895)))+E(f317(f30(x58991),x58992),f317(a102,x58993))+~E(x58992,f317(f317(f299(x58991),x58994),x58995))+P1(f317(f317(f319(x58991),x58994),x58995)) % 112.37/112.11 [6140]~P119(x61402)+~E(f317(x61403,x61405),f2(x61402))+E(f317(f317(f11(x61401,x61402),x61403),x61404),f2(x61402))+~P1(f317(f29(x61401),x61404))+~P1(f317(f317(f319(x61401),x61405),x61404)) % 112.37/112.11 [6523]~P108(x65233)+E(x65231,x65232)+~E(f317(f292(x65233,x65234),x65231),f317(f292(x65233,x65235),x65232))+~P1(f317(f317(f225(x65233),x65235),x65232))+~P1(f317(f317(f225(x65233),x65234),x65231)) % 112.37/112.11 [6524]~P108(x65243)+E(x65241,x65242)+~E(f317(f292(x65243,x65241),x65244),f317(f292(x65243,x65242),x65245))+~P1(f317(f317(f225(x65243),x65242),x65245))+~P1(f317(f317(f225(x65243),x65241),x65244)) % 112.37/112.11 [7604]~P108(x76041)+~P13(x76041,f317(f317(f124(x76041),x76044),x76045))+~P1(f317(f317(f319(x76041),x76043),f317(f162(x76041),x76045)))+~P1(f317(f317(f319(x76041),x76042),f317(f162(x76041),x76044)))+P1(f317(f317(f224(x76041),x76042),x76043)) % 112.37/112.11 [8703]~P109(x87031)+~P1(f317(f317(f225(f906(x87031,a895)),f293(x87031,x87035,x87032)),f293(x87031,x87034,x87033)))+~P1(f317(f317(f224(x87031),x87035),x87032))+P1(f317(f317(f225(x87031),x87032),x87033))+P1(f317(f317(f225(x87031),x87034),x87035)) % 112.37/112.11 [10137]~P17(x101372,x101375,x101373)+E(x101371,f178(f906(x101372,a895)))+~E(f317(f317(x101375,f317(x101374,f360(x101371,x101374,x101373,x101375,x101372))),f317(x101374,f373(x101371,x101374,x101373,x101375,x101372))),f317(x101374,f317(f317(x101375,f360(x101371,x101374,x101373,x101375,x101372)),f373(x101371,x101374,x101373,x101375,x101372))))+E(f317(x101373,f317(f300(x101372,x101372,x101374),x101371)),f317(x101374,f317(x101373,x101371)))+~P1(f317(f29(x101372),x101371)) % 112.37/112.11 [6520]~P18(x65202,x65205,x65203)+E(x65201,f178(f906(x65202,a895)))+~P1(f317(f29(x65202),x65201))+E(f317(x65203,f317(f317(f299(x65202),x65204),x65201)),f317(f317(x65205,x65204),f317(x65203,x65201)))+P1(f317(f317(f319(x65202),x65204),x65201)) % 112.37/112.11 [7365]~P17(x73652,x73653,x73654)+E(f317(f317(x73653,f317(x73654,x73651)),f317(x73654,x73655)),f317(x73654,x73655))+E(x73651,f178(f906(x73652,a895)))+~P1(f317(f29(x73652),x73655))+~P1(f317(f317(f224(f906(x73652,a895)),x73651),x73655)) % 112.37/112.11 [7742]~P18(x77424,x77425,x77421)+E(f317(x77421,x77422),x77423)+~P1(f317(f29(x77424),x77422))+~E(f317(f317(f3(f906(x77424,a895)),x77422),f317(f317(f299(x77424),x77423),f178(f906(x77424,a895)))),f178(f906(x77424,a895)))+~P1(f317(f317(f319(x77424),x77423),x77422)) % 112.37/112.11 [8624]~P75(x86241)+~P122(x86241)+~P1(f317(f29(x86242),x86245))+P1(f317(f317(f277(x86241),f317(f317(f11(x86242,x86241),x86243),x86244)),f317(f317(f11(x86242,x86241),x86243),x86245)))+~P1(f317(f317(f224(f906(x86242,a895)),x86244),x86245)) % 112.37/112.11 [8673]E(x86731,x86732)+~P8(x86733,x86734,x86735)+E(f317(f317(f92(f906(x86733,a895)),x86731),x86732),f178(f906(x86733,a895)))+~P1(f317(f317(f319(f906(x86733,a895)),x86732),f317(f317(f56(x86733),x86734),x86735)))+~P1(f317(f317(f319(f906(x86733,a895)),x86731),f317(f317(f56(x86733),x86734),x86735))) % 112.37/112.11 [9484]~P69(x94842)+~E(f317(x94843,f816(x94843,x94844,x94845,x94841,x94842)),f2(x94842))+E(f317(f317(f8(x94841,x94842),x94843),x94844),f317(f317(f8(x94841,x94842),x94843),x94845))+~P1(f317(f29(x94841),x94845))+~P1(f317(f317(f224(f906(x94841,a895)),x94844),x94845)) % 112.37/112.11 [9485]~P69(x94852)+~E(f317(x94853,f844(x94853,x94854,x94855,x94851,x94852)),f2(x94852))+E(f317(f317(f8(x94851,x94852),x94853),x94854),f317(f317(f8(x94851,x94852),x94853),x94855))+~P1(f317(f29(x94851),x94855))+~P1(f317(f317(f224(f906(x94851,a895)),x94854),x94855)) % 112.37/112.11 [9486]~P75(x94862)+~E(f317(x94863,f810(x94863,x94864,x94865,x94861,x94862)),f72(x94862))+E(f317(f317(f11(x94861,x94862),x94863),x94864),f317(f317(f11(x94861,x94862),x94863),x94865))+~P1(f317(f29(x94861),x94865))+~P1(f317(f317(f224(f906(x94861,a895)),x94864),x94865)) % 112.37/112.11 [9487]~P75(x94872)+~E(f317(x94873,f817(x94873,x94874,x94875,x94871,x94872)),f72(x94872))+E(f317(f317(f11(x94871,x94872),x94873),x94874),f317(f317(f11(x94871,x94872),x94873),x94875))+~P1(f317(f29(x94871),x94875))+~P1(f317(f317(f224(f906(x94871,a895)),x94874),x94875)) % 112.37/112.11 [9971]~P88(x99711)+~P1(f317(f29(x99712),x99715))+~P1(f317(f317(f224(x99711),f2(x99711)),f317(x99713,f714(x99713,x99714,x99715,x99712,x99711))))+P1(f317(f317(f224(x99711),f317(f317(f8(x99712,x99711),x99713),x99714)),f317(f317(f8(x99712,x99711),x99713),x99715)))+~P1(f317(f317(f224(f906(x99712,a895)),x99714),x99715)) % 112.37/112.11 [7601]E(x76011,f2(a899))+P1(f317(x76012,x76013))+~E(x76014,f317(f317(f74(a899),f317(f317(f75(a899),x76011),x76013)),x76015))+~P1(f317(f317(f225(a899),x76015),x76011))+~P1(f317(x76012,f317(f317(f31(a899),x76014),x76011))) % 112.37/112.11 [7680]E(x76801,f2(a899))+P1(f317(x76802,x76803))+~P1(f317(x76802,f41(a899,x76804,x76801)))+~E(x76804,f317(f317(f74(a899),f317(f317(f75(a899),x76801),x76805)),x76803))+~P1(f317(f317(f225(a899),x76803),x76801)) % 112.37/112.11 [7974]~P62(x79743)+E(f317(x79741,x79742),f2(x79743))+~P1(f317(f29(x79744),x79745))+E(f317(f317(f11(x79744,x79743),x79741),f317(f317(f3(f906(x79744,a895)),x79745),f317(f317(f299(x79744),x79742),f178(f906(x79744,a895))))),f317(f317(f11(x79744,x79743),x79741),x79745))+P1(f317(f317(f319(x79744),x79742),x79745)) % 112.37/112.11 [8371]~P69(x83711)+~P1(f317(f29(x83712),x83715))+~P1(f317(f29(x83712),x83714))+~E(f317(f317(f92(f906(x83712,a895)),x83714),x83715),f178(f906(x83712,a895)))+E(f317(f317(f74(x83711),f317(f317(f8(x83712,x83711),x83713),x83714)),f317(f317(f8(x83712,x83711),x83713),x83715)),f317(f317(f8(x83712,x83711),x83713),f317(f317(f91(f906(x83712,a895)),x83714),x83715))) % 112.37/112.11 [8373]~P75(x83731)+~P1(f317(f29(x83732),x83735))+~P1(f317(f29(x83732),x83734))+~E(f317(f317(f92(f906(x83732,a895)),x83734),x83735),f178(f906(x83732,a895)))+E(f317(f317(f75(x83731),f317(f317(f11(x83732,x83731),x83733),x83734)),f317(f317(f11(x83732,x83731),x83733),x83735)),f317(f317(f11(x83732,x83731),x83733),f317(f317(f91(f906(x83732,a895)),x83734),x83735))) % 112.37/112.11 [8472]~P62(x84723)+E(f317(x84721,x84722),f2(x84723))+~P1(f317(f29(x84724),x84725))+E(f317(f317(f11(x84724,x84723),x84721),f317(f317(f3(f906(x84724,a895)),x84725),f317(f317(f299(x84724),x84722),f178(f906(x84724,a895))))),f317(f317(f281(x84723),f317(f317(f11(x84724,x84723),x84721),x84725)),f317(x84721,x84722)))+~P1(f317(f317(f319(x84724),x84722),x84725)) % 112.37/112.11 [9192]~P8(x91921,x91925,x91924)+~E(f317(f317(f56(x91921),f317(f317(f299(x91921),x91922),f178(f906(x91921,a895)))),x91924),f317(f317(f56(x91921),f317(f317(f299(x91921),x91923),f178(f906(x91921,a895)))),x91924))+~P1(f317(f317(f319(x91921),x91923),x91925))+~P1(f317(f317(f319(x91921),x91922),x91925))+P1(f317(f317(f319(f905(x91921,x91921)),f317(f317(f242(x91921,x91921),x91922),x91923)),x91924)) % 112.37/112.11 [9214]~P8(x92141,x92145,x92143)+E(f317(f317(f56(x92141),f317(f317(f299(x92141),x92142),f178(f906(x92141,a895)))),x92143),f317(f317(f56(x92141),f317(f317(f299(x92141),x92144),f178(f906(x92141,a895)))),x92143))+~P1(f317(f317(f319(x92141),x92144),x92145))+~P1(f317(f317(f319(x92141),x92142),x92145))+~P1(f317(f317(f319(f905(x92141,x92141)),f317(f317(f242(x92141,x92141),x92142),x92144)),x92143)) % 112.37/112.11 [9513]~P75(x95131)+~P1(f317(f29(x95132),x95135))+~P1(f317(f29(x95132),x95134))+~E(f317(f317(f92(f906(x95132,a895)),x95134),x95135),f178(f906(x95132,a895)))+E(f317(f317(f75(x95131),f317(f317(f317(f60(x95131,x95132,f75(x95131)),x95133),f72(x95131)),x95134)),f317(f317(f317(f60(x95131,x95132,f75(x95131)),x95133),f72(x95131)),x95135)),f317(f317(f317(f60(x95131,x95132,f75(x95131)),x95133),f72(x95131)),f317(f317(f91(f906(x95132,a895)),x95134),x95135))) % 112.37/112.11 [9524]~P69(x95241)+~E(f317(x95243,f413(x95243,x95245,x95244,x95242,x95241)),f2(x95241))+~P1(f317(f29(x95242),x95244))+~P1(f317(f29(x95242),x95245))+E(f317(f317(f74(x95241),f317(f317(f8(x95242,x95241),x95243),x95244)),f317(f317(f8(x95242,x95241),x95243),x95245)),f317(f317(f8(x95242,x95241),x95243),f317(f317(f91(f906(x95242,a895)),x95244),x95245))) % 112.37/112.11 [9525]~P69(x95251)+~E(f317(x95253,f417(x95253,x95255,x95254,x95252,x95251)),f2(x95251))+~P1(f317(f29(x95252),x95254))+~P1(f317(f29(x95252),x95255))+E(f317(f317(f74(x95251),f317(f317(f8(x95252,x95251),x95253),x95254)),f317(f317(f8(x95252,x95251),x95253),x95255)),f317(f317(f8(x95252,x95251),x95253),f317(f317(f91(f906(x95252,a895)),x95254),x95255))) % 112.37/112.11 [9526]~P75(x95261)+~E(f317(x95263,f414(x95263,x95265,x95264,x95262,x95261)),f72(x95261))+~P1(f317(f29(x95262),x95264))+~P1(f317(f29(x95262),x95265))+E(f317(f317(f75(x95261),f317(f317(f11(x95262,x95261),x95263),x95264)),f317(f317(f11(x95262,x95261),x95263),x95265)),f317(f317(f11(x95262,x95261),x95263),f317(f317(f91(f906(x95262,a895)),x95264),x95265))) % 112.37/112.11 [9527]~P75(x95271)+~E(f317(x95273,f416(x95273,x95275,x95274,x95272,x95271)),f72(x95271))+~P1(f317(f29(x95272),x95274))+~P1(f317(f29(x95272),x95275))+E(f317(f317(f75(x95271),f317(f317(f11(x95272,x95271),x95273),x95274)),f317(f317(f11(x95272,x95271),x95273),x95275)),f317(f317(f11(x95272,x95271),x95273),f317(f317(f91(f906(x95272,a895)),x95274),x95275))) % 112.37/112.11 [9747]~P75(x97471)+~E(f317(x97473,f429(x97473,x97475,x97474,x97472,x97471)),f72(x97471))+~P1(f317(f29(x97472),x97474))+~P1(f317(f29(x97472),x97475))+E(f317(f317(f75(x97471),f317(f317(f317(f60(x97471,x97472,f75(x97471)),x97473),f72(x97471)),x97474)),f317(f317(f317(f60(x97471,x97472,f75(x97471)),x97473),f72(x97471)),x97475)),f317(f317(f317(f60(x97471,x97472,f75(x97471)),x97473),f72(x97471)),f317(f317(f91(f906(x97472,a895)),x97474),x97475))) % 112.37/112.11 [9858]~P69(x98582)+E(f317(f317(f8(x98581,x98582),x98583),x98584),f317(f317(f8(x98581,x98582),x98583),x98585))+~P1(f317(f29(x98581),x98585))+~P1(f317(f317(f224(f906(x98581,a895)),x98584),x98585))+P1(f317(f317(f319(x98581),f816(x98583,x98584,x98585,x98581,x98582)),f317(f317(f3(f906(x98581,a895)),x98585),x98584))) % 112.37/112.11 [9859]~P69(x98592)+E(f317(f317(f8(x98591,x98592),x98593),x98594),f317(f317(f8(x98591,x98592),x98593),x98595))+~P1(f317(f29(x98591),x98595))+~P1(f317(f317(f224(f906(x98591,a895)),x98594),x98595))+P1(f317(f317(f319(x98591),f844(x98593,x98594,x98595,x98591,x98592)),f317(f317(f3(f906(x98591,a895)),x98595),x98594))) % 112.37/112.11 [9860]~P75(x98602)+E(f317(f317(f11(x98601,x98602),x98603),x98604),f317(f317(f11(x98601,x98602),x98603),x98605))+~P1(f317(f29(x98601),x98605))+~P1(f317(f317(f224(f906(x98601,a895)),x98604),x98605))+P1(f317(f317(f319(x98601),f810(x98603,x98604,x98605,x98601,x98602)),f317(f317(f3(f906(x98601,a895)),x98605),x98604))) % 112.37/112.11 [9861]~P75(x98612)+E(f317(f317(f11(x98611,x98612),x98613),x98614),f317(f317(f11(x98611,x98612),x98613),x98615))+~P1(f317(f29(x98611),x98615))+~P1(f317(f317(f224(f906(x98611,a895)),x98614),x98615))+P1(f317(f317(f319(x98611),f817(x98613,x98614,x98615,x98611,x98612)),f317(f317(f3(f906(x98611,a895)),x98615),x98614))) % 112.37/112.11 [9880]~P69(x98801)+~P1(f317(f29(x98802),x98804))+~P1(f317(f29(x98802),x98805))+E(f317(f317(f74(x98801),f317(f317(f8(x98802,x98801),x98803),x98804)),f317(f317(f8(x98802,x98801),x98803),x98805)),f317(f317(f8(x98802,x98801),x98803),f317(f317(f91(f906(x98802,a895)),x98804),x98805)))+P1(f317(f317(f319(x98802),f413(x98803,x98805,x98804,x98802,x98801)),f317(f317(f92(f906(x98802,a895)),x98804),x98805))) % 112.37/112.11 [9881]~P69(x98811)+~P1(f317(f29(x98812),x98814))+~P1(f317(f29(x98812),x98815))+E(f317(f317(f74(x98811),f317(f317(f8(x98812,x98811),x98813),x98814)),f317(f317(f8(x98812,x98811),x98813),x98815)),f317(f317(f8(x98812,x98811),x98813),f317(f317(f91(f906(x98812,a895)),x98814),x98815)))+P1(f317(f317(f319(x98812),f417(x98813,x98815,x98814,x98812,x98811)),f317(f317(f92(f906(x98812,a895)),x98814),x98815))) % 112.37/112.11 [9882]~P75(x98821)+~P1(f317(f29(x98822),x98824))+~P1(f317(f29(x98822),x98825))+E(f317(f317(f75(x98821),f317(f317(f11(x98822,x98821),x98823),x98824)),f317(f317(f11(x98822,x98821),x98823),x98825)),f317(f317(f11(x98822,x98821),x98823),f317(f317(f91(f906(x98822,a895)),x98824),x98825)))+P1(f317(f317(f319(x98822),f414(x98823,x98825,x98824,x98822,x98821)),f317(f317(f92(f906(x98822,a895)),x98824),x98825))) % 112.37/112.11 [9883]~P75(x98831)+~P1(f317(f29(x98832),x98834))+~P1(f317(f29(x98832),x98835))+E(f317(f317(f75(x98831),f317(f317(f11(x98832,x98831),x98833),x98834)),f317(f317(f11(x98832,x98831),x98833),x98835)),f317(f317(f11(x98832,x98831),x98833),f317(f317(f91(f906(x98832,a895)),x98834),x98835)))+P1(f317(f317(f319(x98832),f416(x98833,x98835,x98834,x98832,x98831)),f317(f317(f92(f906(x98832,a895)),x98834),x98835))) % 112.37/112.11 [9889]~P88(x98895)+~P1(f317(f29(x98891),x98894))+P1(f317(f317(f224(x98895),f317(f317(f8(x98891,x98895),x98892),x98893)),f317(f317(f8(x98891,x98895),x98892),x98894)))+~P1(f317(f317(f224(f906(x98891,a895)),x98893),x98894))+P1(f317(f317(f319(x98891),f714(x98892,x98893,x98894,x98891,x98895)),f317(f317(f3(f906(x98891,a895)),x98894),x98893))) % 112.37/112.11 [9933]~P75(x99331)+~P1(f317(f29(x99332),x99334))+~P1(f317(f29(x99332),x99335))+E(f317(f317(f75(x99331),f317(f317(f317(f60(x99331,x99332,f75(x99331)),x99333),f72(x99331)),x99334)),f317(f317(f317(f60(x99331,x99332,f75(x99331)),x99333),f72(x99331)),x99335)),f317(f317(f317(f60(x99331,x99332,f75(x99331)),x99333),f72(x99331)),f317(f317(f91(f906(x99332,a895)),x99334),x99335)))+P1(f317(f317(f319(x99332),f429(x99333,x99335,x99334,x99332,x99331)),f317(f317(f92(f906(x99332,a895)),x99334),x99335))) % 112.37/112.11 [8882]~P18(x88821,x88824,x88825)+~P1(f317(f29(x88821),x88822))+E(f317(f317(f3(f906(x88821,a895)),x88822),f317(f317(f299(x88821),x88823),f178(f906(x88821,a895)))),f178(f906(x88821,a895)))+~P1(f317(f317(f319(x88821),x88823),x88822))+E(f317(f317(x88824,x88823),f317(x88825,f317(f317(f3(f906(x88821,a895)),x88822),f317(f317(f299(x88821),x88823),f178(f906(x88821,a895)))))),f317(x88825,x88822)) % 112.37/112.11 [8960]~P18(x89601,x89604,x89605)+~P1(f317(f29(x89601),x89603))+~P1(f317(f29(x89601),x89602))+E(f317(f317(f92(f906(x89601,a895)),x89602),x89603),f178(f906(x89601,a895)))+E(f317(f317(x89604,f317(x89605,f317(f317(f91(f906(x89601,a895)),x89602),x89603))),f317(x89605,f317(f317(f92(f906(x89601,a895)),x89602),x89603))),f317(f317(x89604,f317(x89605,x89602)),f317(x89605,x89603))) % 112.37/112.11 [9529]~P1(f317(f317(f224(a1),x95294),f2(a1)))+~P1(f317(f317(f225(a1),x95293),x95295))+P1(f317(f317(f224(a1),x95291),x95292))+~P1(f317(f317(f225(a1),x95293),x95294))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),f317(f317(f75(a1),x95293),x95292)),x95295)),f317(f317(f74(a1),f317(f317(f75(a1),x95293),x95291)),x95294))) % 112.37/112.11 [9531]~P1(f317(f317(f224(a1),f2(a1)),x95315))+P1(f317(f317(f224(a1),x95311),x95312))+~P1(f317(f317(f225(a1),x95313),x95314))+~P1(f317(f317(f225(a1),x95315),x95314))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),f317(f317(f75(a1),x95314),x95311)),x95315)),f317(f317(f74(a1),f317(f317(f75(a1),x95314),x95312)),x95313))) % 112.37/112.11 [9656]~P62(x96565)+E(f317(x96561,f415(x96561,x96562,x96563,x96564,x96565)),f2(x96565))+~P1(f317(f29(x96564),x96563))+~P1(f317(f29(x96564),x96562))+E(f317(f317(f281(x96565),f317(f317(f75(x96565),f317(f317(f11(x96564,x96565),x96561),x96563)),f317(f317(f11(x96564,x96565),x96561),x96562))),f317(f317(f11(x96564,x96565),x96561),f317(f317(f92(f906(x96564,a895)),x96563),x96562))),f317(f317(f11(x96564,x96565),x96561),f317(f317(f91(f906(x96564,a895)),x96563),x96562))) % 112.37/112.11 [9925]~P62(x99251)+~P1(f317(f29(x99252),x99254))+~P1(f317(f29(x99252),x99255))+E(f317(f317(f281(x99251),f317(f317(f75(x99251),f317(f317(f11(x99252,x99251),x99253),x99254)),f317(f317(f11(x99252,x99251),x99253),x99255))),f317(f317(f11(x99252,x99251),x99253),f317(f317(f92(f906(x99252,a895)),x99254),x99255))),f317(f317(f11(x99252,x99251),x99253),f317(f317(f91(f906(x99252,a895)),x99254),x99255)))+P1(f317(f317(f319(x99252),f415(x99253,x99255,x99254,x99252,x99251)),f317(f317(f92(f906(x99252,a895)),x99254),x99255))) % 112.37/112.11 [9233]E(f317(f317(f124(x92331),x92332),x92333),f317(f317(f124(x92331),x92334),x92335))+~E(f317(f317(f165(x92331),f317(f179(f900(x92331)),x92334)),x92332),x92334)+~E(f317(f317(f165(x92331),f317(f179(f900(x92331)),x92332)),x92334),x92332)+~E(x92335,f317(f317(f124(x92331),f317(f317(f128(x92331),f317(f179(f900(x92331)),x92334)),x92332)),x92333))+~E(f317(f317(f124(x92331),f317(f317(f128(x92331),f317(f179(f900(x92331)),x92332)),x92334)),x92335),x92333) % 112.37/112.11 [9653]~P108(x96532)+E(f317(f317(f138(x96531,x96532,x96533),x96534),f160(x96531,x96534,x96535)),x96535)+~P13(x96532,f317(f317(f144(x96531,x96532),x96533),x96535))+~P1(f317(f317(f319(x96531),x96534),f317(f162(x96531),x96535)))+~E(f317(f131(x96531),f317(f126(x96531,f317(f317(f10(x96532,a895,x96531),f317(a314,f317(x96533,x96534))),x96533)),x96535)),x96534) % 112.37/112.11 [9989]~P70(x99891)+~P1(f317(f61(x99891,x99891,f75(x99891),x99892,x99893),x99895))+~P1(f317(f317(f319(x99891),x99894),x99893))+P1(f317(f317(f319(x99891),x99892),x99893))+P1(f317(f61(x99891,x99891,f75(x99891),x99894,f317(f317(f299(x99891),x99892),f317(f317(f3(f906(x99891,a895)),x99893),f317(f317(f299(x99891),x99894),f178(f906(x99891,a895)))))),x99895)) % 112.37/112.11 [7373]E(x73731,x73732)+~P24(x73734,x73735,x73733,x73736)+~E(f317(x73733,x73731),f317(x73733,x73732))+~P1(f317(f317(f319(x73734),x73732),x73736))+~P1(f317(f317(f319(x73734),x73731),x73736)) % 112.37/112.11 [6616]~P143(x66164)+E(x66161,x66162)+~E(x66165,x66166)+E(x66163,f2(x66164))+~E(f317(f317(f74(x66164),x66165),f317(f317(f75(x66164),x66163),x66161)),f317(f317(f74(x66164),x66166),f317(f317(f75(x66164),x66163),x66162))) % 112.37/112.11 [7660]~P108(x76601)+~P5(x76601)+~P1(f317(f317(f225(x76601),x76602),f317(x76605,x76606)))+~P1(f317(f317(f319(x76603),x76606),x76604))+P1(f317(f317(f225(x76601),x76602),f317(f317(f36(x76603,x76601),x76604),x76605))) % 112.37/112.11 [9985]~P24(x99852,x99851,x99853,x99854)+~P24(x99851,x99852,x99856,x99855)+P25(x99851,x99852,f808(x99853,x99854,x99855,x99856,x99852,x99851),x99855,x99854)+~P1(f317(f317(f224(f906(x99852,a895)),f317(f300(x99851,x99852,x99856),x99855)),x99854))+~P1(f317(f317(f224(f906(x99851,a895)),f317(f300(x99852,x99851,x99853),x99854)),x99855)) % 112.37/112.11 [8341]~P108(x83411)+~P5(x83411)+~P1(f317(f317(f225(x83411),f317(x83414,x83416)),x83415))+~P1(f317(f317(f319(x83412),x83416),x83413))+P1(f317(f317(f225(x83411),f317(f317(f35(x83412,x83411),x83413),x83414)),x83415)) % 112.37/112.11 [8596]~P19(x85962,x85965,x85966,x85961)+~P1(f317(f29(x85962),x85964))+~P1(f317(f29(x85962),x85963))+~E(f317(f317(f92(f906(x85962,a895)),x85963),x85964),f178(f906(x85962,a895)))+E(f317(x85961,f317(f317(f91(f906(x85962,a895)),x85963),x85964)),f317(f67(x85965,x85965,x85965,f317(x85961,x85963)),f317(x85961,x85964))) % 112.37/112.11 [10197]~P75(x101971)+~E(f796(x101974,x101975,x101973,x101976,x101972,x101971),f797(x101974,x101975,x101973,x101976,x101972,x101971))+~P1(f317(f29(x101972),x101976))+E(f317(f317(f317(f60(x101971,x101972,f75(x101971)),f317(f317(f10(f906(x101973,a895),x101971,x101972),f317(f317(f60(x101971,x101973,f75(x101971)),x101974),f72(x101971))),x101975)),f72(x101971)),x101976),f317(f317(f317(f60(x101971,x101973,f75(x101971)),x101974),f72(x101971)),f317(f317(f36(x101972,f906(x101973,a895)),x101976),x101975)))+P1(f317(f317(f319(x101972),f795(x101974,x101975,x101973,x101976,x101972,x101971)),x101976)) % 112.37/112.11 [10227]~P75(x102271)+~E(f796(x102274,x102275,x102273,x102276,x102272,x102271),f797(x102274,x102275,x102273,x102276,x102272,x102271))+~P1(f317(f29(x102272),x102276))+E(f317(f317(f317(f60(x102271,x102272,f75(x102271)),f317(f317(f10(f906(x102273,a895),x102271,x102272),f317(f317(f60(x102271,x102273,f75(x102271)),x102274),f72(x102271))),x102275)),f72(x102271)),x102276),f317(f317(f317(f60(x102271,x102273,f75(x102271)),x102274),f72(x102271)),f317(f317(f36(x102272,f906(x102273,a895)),x102276),x102275)))+~P1(f317(f29(x102273),f317(x102275,f795(x102274,x102275,x102273,x102276,x102272,x102271)))) % 112.37/112.11 [10230]~P75(x102301)+~P1(f317(f29(x102302),x102306))+E(f317(f317(f317(f60(x102301,x102302,f75(x102301)),f317(f317(f10(f906(x102303,a895),x102301,x102302),f317(f317(f60(x102301,x102303,f75(x102301)),x102304),f72(x102301))),x102305)),f72(x102301)),x102306),f317(f317(f317(f60(x102301,x102303,f75(x102301)),x102304),f72(x102301)),f317(f317(f36(x102302,f906(x102303,a895)),x102306),x102305)))+P1(f317(f317(f319(x102302),f795(x102304,x102305,x102303,x102306,x102302,x102301)),x102306))+P1(f317(f317(f319(x102302),f797(x102304,x102305,x102303,x102306,x102302,x102301)),x102306)) % 112.37/112.11 [10231]~P75(x102311)+~P1(f317(f29(x102312),x102316))+E(f317(f317(f317(f60(x102311,x102312,f75(x102311)),f317(f317(f10(f906(x102313,a895),x102311,x102312),f317(f317(f60(x102311,x102313,f75(x102311)),x102314),f72(x102311))),x102315)),f72(x102311)),x102316),f317(f317(f317(f60(x102311,x102313,f75(x102311)),x102314),f72(x102311)),f317(f317(f36(x102312,f906(x102313,a895)),x102316),x102315)))+P1(f317(f317(f319(x102312),f795(x102314,x102315,x102313,x102316,x102312,x102311)),x102316))+P1(f317(f317(f319(x102312),f796(x102314,x102315,x102313,x102316,x102312,x102311)),x102316)) % 112.37/112.11 [10250]~P75(x102501)+~P1(f317(f29(x102502),x102506))+E(f317(f317(f317(f60(x102501,x102502,f75(x102501)),f317(f317(f10(f906(x102503,a895),x102501,x102502),f317(f317(f60(x102501,x102503,f75(x102501)),x102504),f72(x102501))),x102505)),f72(x102501)),x102506),f317(f317(f317(f60(x102501,x102503,f75(x102501)),x102504),f72(x102501)),f317(f317(f36(x102502,f906(x102503,a895)),x102506),x102505)))+P1(f317(f317(f319(x102502),f797(x102504,x102505,x102503,x102506,x102502,x102501)),x102506))+~P1(f317(f29(x102503),f317(x102505,f795(x102504,x102505,x102503,x102506,x102502,x102501)))) % 112.37/112.11 [10251]~P75(x102511)+~P1(f317(f29(x102512),x102516))+E(f317(f317(f317(f60(x102511,x102512,f75(x102511)),f317(f317(f10(f906(x102513,a895),x102511,x102512),f317(f317(f60(x102511,x102513,f75(x102511)),x102514),f72(x102511))),x102515)),f72(x102511)),x102516),f317(f317(f317(f60(x102511,x102513,f75(x102511)),x102514),f72(x102511)),f317(f317(f36(x102512,f906(x102513,a895)),x102516),x102515)))+P1(f317(f317(f319(x102512),f796(x102514,x102515,x102513,x102516,x102512,x102511)),x102516))+~P1(f317(f29(x102513),f317(x102515,f795(x102514,x102515,x102513,x102516,x102512,x102511)))) % 112.37/112.11 [10262]~P75(x102621)+~E(f317(f317(f92(f906(x102623,a895)),f317(x102625,f797(x102624,x102625,x102623,x102626,x102622,x102621))),f317(x102625,f796(x102624,x102625,x102623,x102626,x102622,x102621))),f178(f906(x102623,a895)))+~P1(f317(f29(x102622),x102626))+E(f317(f317(f317(f60(x102621,x102622,f75(x102621)),f317(f317(f10(f906(x102623,a895),x102621,x102622),f317(f317(f60(x102621,x102623,f75(x102621)),x102624),f72(x102621))),x102625)),f72(x102621)),x102626),f317(f317(f317(f60(x102621,x102623,f75(x102621)),x102624),f72(x102621)),f317(f317(f36(x102622,f906(x102623,a895)),x102626),x102625)))+P1(f317(f317(f319(x102622),f795(x102624,x102625,x102623,x102626,x102622,x102621)),x102626)) % 112.37/112.11 [10273]~P75(x102731)+~E(f317(f317(f92(f906(x102733,a895)),f317(x102735,f797(x102734,x102735,x102733,x102736,x102732,x102731))),f317(x102735,f796(x102734,x102735,x102733,x102736,x102732,x102731))),f178(f906(x102733,a895)))+~P1(f317(f29(x102732),x102736))+E(f317(f317(f317(f60(x102731,x102732,f75(x102731)),f317(f317(f10(f906(x102733,a895),x102731,x102732),f317(f317(f60(x102731,x102733,f75(x102731)),x102734),f72(x102731))),x102735)),f72(x102731)),x102736),f317(f317(f317(f60(x102731,x102733,f75(x102731)),x102734),f72(x102731)),f317(f317(f36(x102732,f906(x102733,a895)),x102736),x102735)))+~P1(f317(f29(x102733),f317(x102735,f795(x102734,x102735,x102733,x102736,x102732,x102731)))) % 112.37/112.11 [9323]~P122(x93231)+~P118(x93231)+~P1(f317(f317(f277(x93231),x93232),x93235))+~P1(f317(f317(f277(x93231),x93232),f317(f317(f74(x93231),x93233),x93236)))+P1(f317(f317(f277(x93231),x93232),f317(f317(f74(x93231),f317(f317(f3(x93231),x93233),f317(f317(f75(x93231),x93234),x93235))),x93236))) % 112.37/112.11 [9518]~P122(x95181)+~P118(x95181)+~P1(f317(f317(f277(x95181),x95182),x95185))+P1(f317(f317(f277(x95181),x95182),f317(f317(f74(x95181),x95183),x95184)))+~P1(f317(f317(f277(x95181),x95182),f317(f317(f74(x95181),f317(f317(f3(x95181),x95183),f317(f317(f75(x95181),x95186),x95185))),x95184))) % 112.37/112.11 [8930]E(x89301,x89302)+~P56(x89304,x89305,x89306,x89303,x89307)+~E(f317(x89303,x89301),f317(x89303,x89302))+~P1(f317(f317(f319(x89305),x89302),x89307))+~P1(f317(f317(f319(x89305),x89301),x89307)) % 112.37/112.11 [10238]~P1(f317(x102382,x102384))+~E(x102385,f317(f126(x102381,x102382),x102387))+E(f317(f126(x102381,x102382),x102383),f317(f317(f141(x102381),x102384),x102385))+~E(x102383,f317(f317(f124(x102381),x102386),f317(f317(f141(x102381),x102384),x102387)))+P1(f317(x102382,f729(x102385,x102384,x102383,x102382,x102381,x102386,x102387))) % 112.37/112.11 [10239]~P1(f317(x102394,x102392))+~E(x102393,f317(f126(x102391,x102394),x102397))+E(f317(f317(f141(x102391),x102392),x102393),f317(f126(x102391,x102394),x102395))+~E(x102395,f317(f317(f124(x102391),x102396),f317(f317(f141(x102391),x102392),x102397)))+P1(f317(x102394,f730(x102395,x102394,x102393,x102392,x102391,x102396,x102397))) % 112.37/112.11 [10289]~P1(f317(x102892,x102894))+~E(x102895,f317(f126(x102891,x102892),x102897))+E(f317(f126(x102891,x102892),x102893),f317(f317(f141(x102891),x102894),x102895))+~E(x102893,f317(f317(f124(x102891),x102896),f317(f317(f141(x102891),x102894),x102897)))+P1(f317(f317(f319(x102891),f729(x102895,x102894,x102893,x102892,x102891,x102896,x102897)),f317(f162(x102891),x102896))) % 112.37/112.11 [10290]~P1(f317(x102904,x102902))+~E(x102903,f317(f126(x102901,x102904),x102907))+E(f317(f317(f141(x102901),x102902),x102903),f317(f126(x102901,x102904),x102905))+~E(x102905,f317(f317(f124(x102901),x102906),f317(f317(f141(x102901),x102902),x102907)))+P1(f317(f317(f319(x102901),f730(x102905,x102904,x102903,x102902,x102901,x102906,x102907)),f317(f162(x102901),x102906))) % 112.37/112.11 [10294]~P8(x102941,x102947,x102946)+~P11(x102941,f906(x102945,a895),x102946,x102944)+P1(f317(f317(f319(x102941),f503(x102942,x102943,x102944,x102945,x102946,x102947,x102941)),x102947))+~P1(f317(f317(f319(f906(x102941,a895)),x102943),f317(f317(f56(x102941),x102947),x102946)))+P1(f317(f317(f319(f906(x102945,a895)),f317(f317(f36(x102941,f906(x102945,a895)),x102943),x102944)),x102942)) % 112.37/112.11 [10349]~P8(x103492,x103496,x103497)+~P11(x103492,f906(x103491,a895),x103497,x103494)+~P1(f317(f317(f319(f906(x103492,a895)),x103493),f317(f317(f56(x103492),x103496),x103497)))+~P1(f317(f317(f319(f906(x103491,a895)),f317(x103494,f503(x103495,x103493,x103494,x103491,x103497,x103496,x103492))),x103495))+P1(f317(f317(f319(f906(x103491,a895)),f317(f317(f36(x103492,f906(x103491,a895)),x103493),x103494)),x103495)) % 112.37/112.11 [8515]~P75(x85152)+~P24(x85151,x85155,x85158,x85154)+~E(x85153,f317(f67(x85155,x85152,x85151,x85156),x85158))+~E(x85157,f317(f300(x85151,x85155,x85158),x85154))+E(f317(f317(f11(x85151,x85152),x85153),x85154),f317(f317(f11(x85155,x85152),x85156),x85157)) % 112.37/112.11 [10353]~P75(x103532)+~P24(x103535,x103531,x103538,x103537)+~E(f317(x103536,f581(x103533,x103536,x103534,x103537,x103538,x103531,x103535,x103532)),f317(f317(f67(x103531,x103532,x103535,x103533),x103538),f581(x103533,x103536,x103534,x103537,x103538,x103531,x103535,x103532)))+~E(x103534,f317(f300(x103535,x103531,x103538),x103537))+E(f317(f317(f11(x103531,x103532),x103533),x103534),f317(f317(f11(x103535,x103532),x103536),x103537)) % 112.37/112.11 [10356]~P69(x103562)+~P24(x103561,x103565,x103568,x103564)+~E(x103567,f317(f300(x103561,x103565,x103568),x103564))+E(f317(f317(f8(x103561,x103562),x103563),x103564),f317(f317(f8(x103565,x103562),x103566),x103567))+P1(f317(f317(f319(x103561),f595(x103566,x103563,x103567,x103564,x103568,x103565,x103561,x103562)),x103564)) % 112.37/112.11 [10357]~P75(x103572)+~P24(x103571,x103575,x103578,x103574)+~E(x103577,f317(f300(x103571,x103575,x103578),x103574))+E(f317(f317(f11(x103571,x103572),x103573),x103574),f317(f317(f11(x103575,x103572),x103576),x103577))+P1(f317(f317(f319(x103571),f581(x103576,x103573,x103577,x103574,x103578,x103575,x103571,x103572)),x103574)) % 112.37/112.11 [10362]~P69(x103622)+~P24(x103625,x103621,x103628,x103627)+~E(x103624,f317(f300(x103625,x103621,x103628),x103627))+~E(f317(x103626,f595(x103623,x103626,x103624,x103627,x103628,x103621,x103625,x103622)),f317(x103623,f317(x103628,f595(x103623,x103626,x103624,x103627,x103628,x103621,x103625,x103622))))+E(f317(f317(f8(x103621,x103622),x103623),x103624),f317(f317(f8(x103625,x103622),x103626),x103627)) % 112.37/112.11 [9820]~P23(x98206,x98202,x98205,x98207,x98208,x98201)+~P1(f317(f29(x98202),x98204))+~P1(f317(f29(x98202),x98203))+~E(f317(f317(f92(f906(x98202,a895)),x98203),x98204),f178(f906(x98202,a895)))+E(f317(x98201,f317(f317(f91(f906(x98202,a895)),x98203),x98204)),f317(f317(x98205,f317(x98201,x98203)),f317(x98201,x98204))) % 112.37/112.11 [10224]~P23(x102248,x102242,x102245,x102247,x102246,x102241)+~E(f317(x102246,f430(x102244,x102243,x102241,x102246,x102247,x102245,x102242)),x102247)+~P1(f317(f29(x102242),x102243))+~P1(f317(f29(x102242),x102244))+E(f317(x102241,f317(f317(f91(f906(x102242,a895)),x102243),x102244)),f317(f317(x102245,f317(x102241,x102243)),f317(x102241,x102244))) % 112.37/112.11 [10301]~P23(x103018,x103012,x103015,x103017,x103016,x103011)+~P1(f317(f29(x103012),x103013))+~P1(f317(f29(x103012),x103014))+E(f317(x103011,f317(f317(f91(f906(x103012,a895)),x103013),x103014)),f317(f317(x103015,f317(x103011,x103013)),f317(x103011,x103014)))+P1(f317(f317(f319(x103012),f430(x103014,x103013,x103011,x103016,x103017,x103015,x103012)),f317(f317(f92(f906(x103012,a895)),x103013),x103014))) % 112.37/112.11 [9976]~P8(x99764,x99768,x99765)+~P8(x99761,x99769,x99763)+~P12(x99761,x99764,f906(x99762,a895),x99763,x99765,x99767)+P11(x99761,f906(x99762,a895),x99763,f317(f317(f10(f906(x99764,f906(x99762,a895)),f906(x99762,a895),x99761),f317(f36(x99764,f906(x99762,a895)),f317(f275(x99764,x99764,x99765),f317(f317(f299(x99764),x99766),f178(f906(x99764,a895)))))),x99767))+~P1(f317(f317(f319(x99764),x99766),x99768)) % 112.37/112.11 [5495]~P108(x54953)+~P13(x54953,x54951)+E(x54951,f707(x54952,x54953))+~E(f317(f162(x54953),x54951),x54952)+~P1(f317(f29(x54953),x54952))+~P1(f317(f127(x54953),x54951)) % 112.37/112.11 [7364]P15(x73641,x73642)+~E(f317(x73642,f787(x73642)),f317(x73642,f789(x73642)))+~P1(f317(f317(x73642,f787(x73642)),f787(x73642)))+~P1(f317(f317(x73642,f787(x73642)),f789(x73642)))+~P1(f317(f317(x73642,f789(x73642)),f789(x73642)))+~P1(f317(f317(x73642,x73643),x73643)) % 112.37/112.11 [5121]~P132(x51212)+~P133(x51212)+~P144(x51212)+~P115(x51212)+E(x51211,f2(x51212))+~E(f317(f317(f234(x51212),x51211),x51213),f2(x51212)) % 112.37/112.11 [5122]~P132(x51222)+~P133(x51222)+~P144(x51222)+~P115(x51222)+~E(x51221,f2(a899))+~E(f317(f317(f234(x51222),x51223),x51221),f2(x51222)) % 112.37/112.11 [6598]~P88(x65981)+~E(x65983,f2(x65981))+~E(x65982,f2(x65981))+E(f317(f317(f74(x65981),x65982),x65983),f2(x65981))+~P1(f317(f317(f224(x65981),f2(x65981)),x65983))+~P1(f317(f317(f224(x65981),f2(x65981)),x65982)) % 112.37/112.11 [8998]~E(f317(f241(a899,a899),x89983),f2(a899))+~E(x89981,f317(f317(f74(a899),f317(f317(f75(a899),f317(f241(a899,a899),x89983)),x89982)),f317(f246(a899,a899),x89983)))+P1(f317(f44(x89981,x89982),x89983))+~P1(f317(f317(f224(a899),f317(f246(a899,a899),x89983)),f2(a899)))+P1(f317(f317(f225(a899),f2(a899)),x89982))+~P1(f317(f317(f225(a899),x89982),f317(f246(a899,a899),x89983))) % 112.37/112.11 [9006]E(x90061,f2(a899))+~E(x90062,f317(f317(f74(a899),f317(f317(f75(a899),f317(f241(a899,a899),x90063)),x90061)),f317(f246(a899,a899),x90063)))+P1(f317(f44(x90062,x90061),x90063))+~P1(f317(f317(f225(a899),f2(a899)),x90061))+~P1(f317(f317(f224(a899),f2(a899)),f317(f246(a899,a899),x90063)))+~P1(f317(f317(f225(a899),f317(f246(a899,a899),x90063)),x90061)) % 112.37/112.11 [9024]~E(f317(f241(a899,a899),x90243),f2(a899))+~E(x90241,f317(f317(f74(a899),f317(f317(f75(a899),f317(f241(a899,a899),x90243)),x90242)),f317(f246(a899,a899),x90243)))+P1(f317(f44(x90241,x90242),x90243))+~P1(f317(f317(f225(a899),f2(a899)),x90242))+~P1(f317(f317(f224(a899),f2(a899)),f317(f246(a899,a899),x90243)))+~P1(f317(f317(f225(a899),f317(f246(a899,a899),x90243)),x90242)) % 112.37/112.11 [6988]~P108(x69882)+E(x69881,f178(f906(x69882,a895)))+E(x69883,f178(f906(x69882,a895)))+~P1(f317(f29(x69882),x69881))+~P1(f317(f29(x69882),x69883))+E(f16(x69882,f317(f317(f91(f906(x69882,a895)),x69883),x69881)),f317(f317(f223(x69882),f16(x69882,x69883)),f16(x69882,x69881))) % 112.37/112.11 [6989]~P108(x69892)+E(x69891,f178(f906(x69892,a895)))+E(x69893,f178(f906(x69892,a895)))+~P1(f317(f29(x69892),x69891))+~P1(f317(f29(x69892),x69893))+E(f17(x69892,f317(f317(f91(f906(x69892,a895)),x69893),x69891)),f317(f317(f228(x69892),f17(x69892,x69893)),f17(x69892,x69891))) % 112.37/112.11 [6990]~P99(x69902)+E(x69901,f178(f906(x69902,a895)))+E(x69903,f178(f906(x69902,a895)))+~P1(f317(f29(x69902),x69901))+~P1(f317(f29(x69902),x69903))+E(f12(x69902,f317(f317(f91(f906(x69902,a895)),x69903),x69901)),f317(f317(f91(x69902),f12(x69902,x69903)),f12(x69902,x69901))) % 112.37/112.11 [6991]~P99(x69912)+E(x69911,f178(f906(x69912,a895)))+E(x69913,f178(f906(x69912,a895)))+~P1(f317(f29(x69912),x69911))+~P1(f317(f29(x69912),x69913))+E(f13(x69912,f317(f317(f91(f906(x69912,a895)),x69913),x69911)),f317(f317(f92(x69912),f13(x69912,x69913)),f13(x69912,x69911))) % 112.37/112.11 [7634]~P97(x76342)+E(x76341,f178(f906(x76342,a895)))+E(x76343,f178(f906(x76342,a895)))+~P1(f317(f29(x76342),x76341))+~P1(f317(f29(x76342),x76343))+E(f317(f317(f75(x76342),f317(f58(x76342,f75(x76342)),x76343)),f317(f58(x76342,f75(x76342)),x76341)),f317(f58(x76342,f75(x76342)),f317(f317(f91(f906(x76342,a895)),x76343),x76341))) % 112.37/112.11 [7796]~P108(x77962)+E(x77961,f178(f906(x77962,a895)))+E(x77963,f178(f906(x77962,a895)))+~P1(f317(f29(x77962),x77961))+~P1(f317(f29(x77962),x77963))+E(f317(f317(f223(x77962),f14(x77962,f223(x77962),x77963)),f14(x77962,f223(x77962),x77961)),f14(x77962,f223(x77962),f317(f317(f91(f906(x77962,a895)),x77963),x77961))) % 112.37/112.11 [7797]~P108(x77972)+E(x77971,f178(f906(x77972,a895)))+E(x77973,f178(f906(x77972,a895)))+~P1(f317(f29(x77972),x77971))+~P1(f317(f29(x77972),x77973))+E(f317(f317(f228(x77972),f15(x77972,f228(x77972),x77973)),f15(x77972,f228(x77972),x77971)),f15(x77972,f228(x77972),f317(f317(f91(f906(x77972,a895)),x77973),x77971))) % 112.37/112.11 [8831]~P1(f317(x88311,x88313))+P1(f317(x88311,f385(x88311,x88312)))+P1(f317(x88311,f380(x88311,x88312)))+~P1(f317(f317(f225(a1),f2(a1)),x88312))+~P1(f317(f317(f319(a1),x88313),f293(a1,f72(a1),x88312)))+P1(f317(x88311,f317(f317(f3(a1),f380(x88311,x88312)),f317(f317(f75(a1),f384(x88311,x88312)),x88312)))) % 112.37/112.11 [9132]~P1(f317(x91321,x91323))+~P1(f317(x91321,f380(x91321,x91322)))+P1(f317(x91321,f385(x91321,x91322)))+~P1(f317(f317(f225(a1),f2(a1)),x91322))+~P1(f317(f317(f319(a1),x91323),f293(a1,f72(a1),x91322)))+~P1(f317(x91321,f317(f317(f3(a1),f380(x91321,x91322)),f317(f317(f75(a1),f384(x91321,x91322)),x91322)))) % 112.37/112.11 [10389]~P103(x103892)+E(x103891,f178(f906(x103892,a895)))+E(x103893,f178(f906(x103892,a895)))+~P1(f317(f29(x103892),x103891))+~P1(f317(f29(x103892),x103893))+E(f13(x103892,f317(f252(x103892),f317(f317(f10(f906(x103892,a895),a895,x103892),f81(x103892)),f317(f317(f10(f906(x103892,f906(x103892,a895)),f906(x103892,a895),x103892),f317(f10(f906(x103892,a895),a895,x103892),f81(x103892))),f317(f317(f9(x103892,f906(x103892,f906(x103892,a895)),f906(x103892,f906(x103892,a895))),f317(f317(f10(f906(x103892,f906(f906(x103892,a895),f906(x103892,a895))),f906(f906(x103892,f906(x103892,a895)),f906(x103892,f906(x103892,a895))),x103892),f20(x103892,f906(x103892,a895),f906(x103892,a895))),f317(f317(f10(f906(x103892,f906(x103892,f906(a895,a895))),f906(x103892,f906(f906(x103892,a895),f906(x103892,a895))),x103892),f317(f10(f906(x103892,f906(a895,a895)),f906(f906(x103892,a895),f906(x103892,a895)),x103892),f20(x103892,a895,a895))),f317(f317(f10(f906(x103892,f906(x103892,a895)),f906(x103892,f906(x103892,f906(a895,a895))),x103892),f317(f10(f906(x103892,a895),f906(x103892,f906(a895,a895)),x103892),f317(f10(a895,f906(a895,a895),x103892),a315))),f317(f317(f9(x103892,f906(x103892,f906(x103892,x103892)),f906(x103892,f906(x103892,a895))),f317(f317(f10(f906(f906(x103892,x103892),f906(x103892,a895)),f906(f906(x103892,f906(x103892,x103892)),f906(x103892,f906(x103892,a895))),x103892),f10(f906(x103892,x103892),f906(x103892,a895),x103892)),f317(f317(f10(f906(x103892,a895),f906(f906(x103892,x103892),f906(x103892,a895)),x103892),f10(x103892,a895,x103892)),a314))),f91(x103892)))))),f317(f317(f9(x103892,f906(x103892,a895),f906(x103892,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x103892,a895),f906(x103892,a895)),x103892),f10(a895,a895,x103892)),f317(f317(f10(a895,f906(a895,a895),x103892),a315),f317(f317(f9(x103892,f906(x103892,a895),a895),f319(x103892)),x103893)))),f317(f317(f9(x103892,f906(x103892,a895),a895),f319(x103892)),x103891))))))),f317(f317(f91(x103892),f13(x103892,x103893)),f13(x103892,x103891))) % 112.37/112.11 [10390]~P103(x103902)+E(x103901,f178(f906(x103902,a895)))+E(x103903,f178(f906(x103902,a895)))+~P1(f317(f29(x103902),x103901))+~P1(f317(f29(x103902),x103903))+E(f12(x103902,f317(f252(x103902),f317(f317(f10(f906(x103902,a895),a895,x103902),f81(x103902)),f317(f317(f10(f906(x103902,f906(x103902,a895)),f906(x103902,a895),x103902),f317(f10(f906(x103902,a895),a895,x103902),f81(x103902))),f317(f317(f9(x103902,f906(x103902,f906(x103902,a895)),f906(x103902,f906(x103902,a895))),f317(f317(f10(f906(x103902,f906(f906(x103902,a895),f906(x103902,a895))),f906(f906(x103902,f906(x103902,a895)),f906(x103902,f906(x103902,a895))),x103902),f20(x103902,f906(x103902,a895),f906(x103902,a895))),f317(f317(f10(f906(x103902,f906(x103902,f906(a895,a895))),f906(x103902,f906(f906(x103902,a895),f906(x103902,a895))),x103902),f317(f10(f906(x103902,f906(a895,a895)),f906(f906(x103902,a895),f906(x103902,a895)),x103902),f20(x103902,a895,a895))),f317(f317(f10(f906(x103902,f906(x103902,a895)),f906(x103902,f906(x103902,f906(a895,a895))),x103902),f317(f10(f906(x103902,a895),f906(x103902,f906(a895,a895)),x103902),f317(f10(a895,f906(a895,a895),x103902),a315))),f317(f317(f9(x103902,f906(x103902,f906(x103902,x103902)),f906(x103902,f906(x103902,a895))),f317(f317(f10(f906(f906(x103902,x103902),f906(x103902,a895)),f906(f906(x103902,f906(x103902,x103902)),f906(x103902,f906(x103902,a895))),x103902),f10(f906(x103902,x103902),f906(x103902,a895),x103902)),f317(f317(f10(f906(x103902,a895),f906(f906(x103902,x103902),f906(x103902,a895)),x103902),f10(x103902,a895,x103902)),a314))),f92(x103902)))))),f317(f317(f9(x103902,f906(x103902,a895),f906(x103902,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x103902,a895),f906(x103902,a895)),x103902),f10(a895,a895,x103902)),f317(f317(f10(a895,f906(a895,a895),x103902),a315),f317(f317(f9(x103902,f906(x103902,a895),a895),f319(x103902)),x103903)))),f317(f317(f9(x103902,f906(x103902,a895),a895),f319(x103902)),x103901))))))),f317(f317(f92(x103902),f12(x103902,x103903)),f12(x103902,x103901))) % 112.37/112.11 [10391]~P108(x103912)+E(x103911,f178(f906(x103912,a895)))+E(x103913,f178(f906(x103912,a895)))+~P1(f317(f29(x103912),x103911))+~P1(f317(f29(x103912),x103913))+E(f14(x103912,f223(x103912),f317(f252(x103912),f317(f317(f10(f906(x103912,a895),a895,x103912),f81(x103912)),f317(f317(f10(f906(x103912,f906(x103912,a895)),f906(x103912,a895),x103912),f317(f10(f906(x103912,a895),a895,x103912),f81(x103912))),f317(f317(f9(x103912,f906(x103912,f906(x103912,a895)),f906(x103912,f906(x103912,a895))),f317(f317(f10(f906(x103912,f906(f906(x103912,a895),f906(x103912,a895))),f906(f906(x103912,f906(x103912,a895)),f906(x103912,f906(x103912,a895))),x103912),f20(x103912,f906(x103912,a895),f906(x103912,a895))),f317(f317(f10(f906(x103912,f906(x103912,f906(a895,a895))),f906(x103912,f906(f906(x103912,a895),f906(x103912,a895))),x103912),f317(f10(f906(x103912,f906(a895,a895)),f906(f906(x103912,a895),f906(x103912,a895)),x103912),f20(x103912,a895,a895))),f317(f317(f10(f906(x103912,f906(x103912,a895)),f906(x103912,f906(x103912,f906(a895,a895))),x103912),f317(f10(f906(x103912,a895),f906(x103912,f906(a895,a895)),x103912),f317(f10(a895,f906(a895,a895),x103912),a315))),f317(f317(f9(x103912,f906(x103912,f906(x103912,x103912)),f906(x103912,f906(x103912,a895))),f317(f317(f10(f906(f906(x103912,x103912),f906(x103912,a895)),f906(f906(x103912,f906(x103912,x103912)),f906(x103912,f906(x103912,a895))),x103912),f10(f906(x103912,x103912),f906(x103912,a895),x103912)),f317(f317(f10(f906(x103912,a895),f906(f906(x103912,x103912),f906(x103912,a895)),x103912),f10(x103912,a895,x103912)),a314))),f228(x103912)))))),f317(f317(f9(x103912,f906(x103912,a895),f906(x103912,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x103912,a895),f906(x103912,a895)),x103912),f10(a895,a895,x103912)),f317(f317(f10(a895,f906(a895,a895),x103912),a315),f317(f317(f9(x103912,f906(x103912,a895),a895),f319(x103912)),x103913)))),f317(f317(f9(x103912,f906(x103912,a895),a895),f319(x103912)),x103911))))))),f317(f317(f228(x103912),f14(x103912,f223(x103912),x103913)),f14(x103912,f223(x103912),x103911))) % 112.37/112.11 [10392]~P108(x103922)+E(x103921,f178(f906(x103922,a895)))+E(x103923,f178(f906(x103922,a895)))+~P1(f317(f29(x103922),x103921))+~P1(f317(f29(x103922),x103923))+E(f15(x103922,f228(x103922),f317(f252(x103922),f317(f317(f10(f906(x103922,a895),a895,x103922),f81(x103922)),f317(f317(f10(f906(x103922,f906(x103922,a895)),f906(x103922,a895),x103922),f317(f10(f906(x103922,a895),a895,x103922),f81(x103922))),f317(f317(f9(x103922,f906(x103922,f906(x103922,a895)),f906(x103922,f906(x103922,a895))),f317(f317(f10(f906(x103922,f906(f906(x103922,a895),f906(x103922,a895))),f906(f906(x103922,f906(x103922,a895)),f906(x103922,f906(x103922,a895))),x103922),f20(x103922,f906(x103922,a895),f906(x103922,a895))),f317(f317(f10(f906(x103922,f906(x103922,f906(a895,a895))),f906(x103922,f906(f906(x103922,a895),f906(x103922,a895))),x103922),f317(f10(f906(x103922,f906(a895,a895)),f906(f906(x103922,a895),f906(x103922,a895)),x103922),f20(x103922,a895,a895))),f317(f317(f10(f906(x103922,f906(x103922,a895)),f906(x103922,f906(x103922,f906(a895,a895))),x103922),f317(f10(f906(x103922,a895),f906(x103922,f906(a895,a895)),x103922),f317(f10(a895,f906(a895,a895),x103922),a315))),f317(f317(f9(x103922,f906(x103922,f906(x103922,x103922)),f906(x103922,f906(x103922,a895))),f317(f317(f10(f906(f906(x103922,x103922),f906(x103922,a895)),f906(f906(x103922,f906(x103922,x103922)),f906(x103922,f906(x103922,a895))),x103922),f10(f906(x103922,x103922),f906(x103922,a895),x103922)),f317(f317(f10(f906(x103922,a895),f906(f906(x103922,x103922),f906(x103922,a895)),x103922),f10(x103922,a895,x103922)),a314))),f223(x103922)))))),f317(f317(f9(x103922,f906(x103922,a895),f906(x103922,a895)),f317(f317(f10(f906(a895,a895),f906(f906(x103922,a895),f906(x103922,a895)),x103922),f10(a895,a895,x103922)),f317(f317(f10(a895,f906(a895,a895),x103922),a315),f317(f317(f9(x103922,f906(x103922,a895),a895),f319(x103922)),x103923)))),f317(f317(f9(x103922,f906(x103922,a895),a895),f319(x103922)),x103921))))))),f317(f317(f223(x103922),f15(x103922,f228(x103922),x103923)),f15(x103922,f228(x103922),x103921))) % 112.37/112.11 [7320]~P126(x73203)+E(x73201,x73202)+~E(f317(f317(f234(x73203),x73201),x73204),f317(f317(f234(x73203),x73202),x73204))+~P1(f317(f317(f224(x73203),f2(x73203)),x73202))+~P1(f317(f317(f224(x73203),f2(x73203)),x73201))+~P1(f317(f317(f225(a899),f2(a899)),x73204)) % 112.37/112.11 [7593]~P108(x75932)+E(x75931,f178(f906(x75932,a895)))+~P1(f317(f29(x75932),x75931))+~P1(f317(f317(f319(x75932),x75934),x75931))+P1(f317(f317(f224(x75932),x75933),x75934))+~P1(f317(f317(f224(x75932),x75933),f317(f58(x75932,f228(x75932)),x75931))) % 112.37/112.11 [7594]~P104(x75942)+E(x75941,f178(f906(x75942,a895)))+~P1(f317(f29(x75942),x75941))+~P1(f317(f317(f319(x75942),x75944),x75941))+P1(f317(f317(f224(x75942),x75943),x75944))+~P1(f317(f317(f224(x75942),x75943),f317(f58(x75942,f92(x75942)),x75941))) % 112.37/112.11 [7595]~P108(x75952)+E(x75951,f178(f906(x75952,a895)))+~P1(f317(f29(x75952),x75951))+~P1(f317(f317(f319(x75952),x75954),x75951))+P1(f317(f317(f225(x75952),x75953),x75954))+~P1(f317(f317(f225(x75952),x75953),f317(f58(x75952,f228(x75952)),x75951))) % 112.37/112.11 [7500]E(x75001,f2(a1))+E(f317(f317(f31(a1),x75002),x75001),x75003)+~P1(f317(f317(f224(a1),x75004),f2(a1)))+~E(x75002,f317(f317(f74(a1),f317(f317(f75(a1),x75001),x75003)),x75004))+P1(f317(f317(f225(a1),f2(a1)),x75001))+~P1(f317(f317(f225(a1),x75001),x75004)) % 112.37/112.11 [7517]E(f41(a1,x75172,x75171),x75173)+E(x75171,f2(a1))+~P1(f317(f317(f224(a1),x75173),f2(a1)))+~E(x75172,f317(f317(f74(a1),f317(f317(f75(a1),x75171),x75174)),x75173))+P1(f317(f317(f225(a1),f2(a1)),x75171))+~P1(f317(f317(f225(a1),x75171),x75173)) % 112.37/112.11 [7633]E(x76331,f2(a1))+E(f317(f317(f31(a1),x76332),x76331),x76333)+~E(x76332,f317(f317(f74(a1),f317(f317(f75(a1),x76331),x76333)),x76334))+~P1(f317(f317(f224(a1),f2(a1)),x76334))+~P1(f317(f317(f225(a1),f2(a1)),x76331))+~P1(f317(f317(f225(a1),x76334),x76331)) % 112.37/112.11 [7656]E(f41(a1,x76562,x76561),x76563)+E(x76561,f2(a1))+~E(x76562,f317(f317(f74(a1),f317(f317(f75(a1),x76561),x76564)),x76563))+~P1(f317(f317(f224(a1),f2(a1)),x76563))+~P1(f317(f317(f225(a1),f2(a1)),x76561))+~P1(f317(f317(f225(a1),x76563),x76561)) % 112.37/112.11 [7800]~P108(x78002)+E(x78001,f178(f906(x78002,a895)))+~P1(f317(f29(x78002),x78001))+~P1(f317(f317(f319(x78002),x78004),x78001))+~P1(f317(f317(f224(x78002),x78004),x78003))+P1(f317(f317(f224(x78002),f317(f58(x78002,f228(x78002)),x78001)),x78003)) % 112.37/112.11 [7801]~P108(x78012)+E(x78011,f178(f906(x78012,a895)))+~P1(f317(f29(x78012),x78011))+~P1(f317(f317(f225(x78012),x78014),x78013))+~P1(f317(f317(f319(x78012),x78014),x78011))+P1(f317(f317(f225(x78012),f317(f58(x78012,f228(x78012)),x78011)),x78013)) % 112.37/112.11 [8366]~P1(f317(f317(f224(a1),x83664),f2(a1)))+~E(x83661,f317(f317(f74(a1),f317(f317(f75(a1),x83662),x83663)),x83664))+~P1(f317(f317(f224(a1),f2(a1)),x83664))+~P1(f317(f317(f225(a1),x83664),x83662))+~P1(f317(f317(f225(a1),x83662),x83664))+P1(f317(f45(x83661,x83662),f317(f317(f242(a1,a1),x83663),x83664))) % 112.37/112.11 [8535]~P109(x85351)+P1(f317(f317(f225(f906(x85351,a895)),f293(x85351,x85352,x85353)),f293(x85351,x85354,x85355)))+~P1(f317(f317(f224(x85351),x85354),x85352))+~P1(f317(f317(f224(x85351),x85354),x85355))+~P1(f317(f317(f224(x85351),x85353),x85355))+~P1(f317(f317(f225(x85351),x85353),x85355)) % 112.37/112.11 [8536]~P109(x85361)+P1(f317(f317(f225(f906(x85361,a895)),f293(x85361,x85362,x85363)),f293(x85361,x85364,x85365)))+~P1(f317(f317(f224(x85361),x85363),x85365))+~P1(f317(f317(f224(x85361),x85364),x85365))+~P1(f317(f317(f224(x85361),x85364),x85362))+~P1(f317(f317(f225(x85361),x85364),x85362)) % 112.37/112.11 [9397]P58(x93972,x93973,x93974,x93971)+E(x93971,f178(f906(x93972,a895)))+~P1(f317(f29(x93972),x93974))+~P1(f317(f29(x93972),x93971))+~P1(f317(f317(x93973,f515(x93971,x93974,x93973,x93972)),x93975))+~P1(f317(f317(f319(x93972),x93975),x93971)) % 112.37/112.11 [9398]P58(x93982,x93983,x93984,x93981)+E(x93981,f178(f906(x93982,a895)))+~P1(f317(f29(x93982),x93984))+~P1(f317(f29(x93982),x93981))+~P1(f317(f317(x93983,f779(x93983,x93981,x93984,x93982)),x93985))+~P1(f317(f317(f319(x93982),x93985),x93981)) % 112.37/112.11 [9399]P58(x93992,x93993,x93994,x93991)+E(x93991,f178(f906(x93992,a895)))+~P1(f317(f29(x93992),x93994))+~P1(f317(f29(x93992),x93991))+~P1(f317(f317(x93993,f780(x93991,x93994,x93993,x93992)),x93995))+~P1(f317(f317(f319(x93992),x93995),x93991)) % 112.37/112.11 [9547]~E(x95473,x95475)+~P69(x95471)+~P75(x95471)+~P39(x95473)+E(f317(f317(f8(a1,x95471),x95472),x95473),f317(f317(f8(a1,x95471),x95474),x95475))+P1(f317(f317(f224(a1),f2(a1)),f516(x95472,x95474,x95473,x95475,x95471))) % 112.37/112.11 [9548]~E(x95483,x95485)+~P69(x95481)+~P75(x95481)+~P39(x95483)+E(f317(f317(f11(a1,x95481),x95482),x95483),f317(f317(f11(a1,x95481),x95484),x95485))+P1(f317(f317(f224(a1),f2(a1)),f472(x95482,x95484,x95483,x95485,x95481))) % 112.37/112.11 [9730]~E(x97305,x97303)+~P69(x97301)+~P75(x97301)+~P39(x97305)+~E(f317(x97302,f516(x97304,x97302,x97305,x97303,x97301)),f317(x97304,f516(x97304,x97302,x97305,x97303,x97301)))+E(f317(f317(f8(a1,x97301),x97302),x97303),f317(f317(f8(a1,x97301),x97304),x97305)) % 112.37/112.11 [9731]~E(x97315,x97313)+~P69(x97311)+~P75(x97311)+~P39(x97315)+~E(f317(x97312,f472(x97314,x97312,x97315,x97313,x97311)),f317(x97314,f472(x97314,x97312,x97315,x97313,x97311)))+E(f317(f317(f11(a1,x97311),x97312),x97313),f317(f317(f11(a1,x97311),x97314),x97315)) % 112.37/112.11 [9818]~P79(x98183)+E(f317(x98181,x98182),f2(x98183))+~E(f317(f317(f8(x98184,x98183),x98181),x98185),f2(x98183))+~P1(f317(f29(x98184),x98185))+P1(f317(f317(f319(x98184),f462(x98182,x98181,x98185,x98184,x98183)),x98185))+~P1(f317(f317(f319(x98184),x98182),x98185)) % 112.37/112.11 [9947]~P79(x99473)+E(f317(x99471,x99472),f2(x99473))+~E(f317(f317(f8(x99474,x99473),x99471),x99475),f2(x99473))+~P1(f317(f29(x99474),x99475))+~P1(f317(f317(f319(x99474),x99472),x99475))+~P1(f317(f317(f224(x99473),f2(x99473)),f317(x99471,f462(x99472,x99471,x99475,x99474,x99473)))) % 112.37/112.11 [8451]~P137(x84511)+~P1(f317(f317(f224(x84511),x84513),x84515))+~P1(f317(f317(f224(x84511),x84512),x84514))+~P1(f317(f317(f224(x84511),f2(x84511)),x84513))+~P1(f317(f317(f224(x84511),f2(x84511)),x84514))+P1(f317(f317(f224(x84511),f317(f317(f75(x84511),x84512),x84513)),f317(f317(f75(x84511),x84514),x84515))) % 112.37/112.11 [8452]~P137(x84521)+~P1(f317(f317(f224(x84521),x84523),x84525))+~P1(f317(f317(f224(x84521),x84522),x84524))+~P1(f317(f317(f224(x84521),f2(x84521)),x84523))+~P1(f317(f317(f224(x84521),f2(x84521)),x84522))+P1(f317(f317(f224(x84521),f317(f317(f75(x84521),x84522),x84523)),f317(f317(f75(x84521),x84524),x84525))) % 112.37/112.11 [8453]~P64(x84531)+~P1(f317(f317(f225(x84531),f2(x84531)),x84535))+~P1(f317(f317(f224(x84531),x84535),x84533))+~P1(f317(f317(f224(x84531),x84532),x84534))+~P1(f317(f317(f224(x84531),f2(x84531)),x84532))+P1(f317(f317(f224(x84531),f317(f317(f281(x84531),x84532),x84533)),f317(f317(f281(x84531),x84534),x84535))) % 112.37/112.11 [8454]~P134(x84541)+~P1(f317(f317(f224(x84541),x84543),x84545))+~P1(f317(f317(f224(x84541),f2(x84541)),x84542))+~P1(f317(f317(f225(x84541),x84542),x84544))+~P1(f317(f317(f225(x84541),f2(x84541)),x84543))+P1(f317(f317(f225(x84541),f317(f317(f75(x84541),x84542),x84543)),f317(f317(f75(x84541),x84544),x84545))) % 112.37/112.11 [8455]~P134(x84551)+~P1(f317(f317(f224(x84551),x84552),x84554))+~P1(f317(f317(f224(x84551),f2(x84551)),x84553))+~P1(f317(f317(f225(x84551),x84553),x84555))+~P1(f317(f317(f225(x84551),f2(x84551)),x84552))+P1(f317(f317(f225(x84551),f317(f317(f75(x84551),x84552),x84553)),f317(f317(f75(x84551),x84554),x84555))) % 112.37/112.11 [8456]~P134(x84561)+~P1(f317(f317(f224(x84561),f2(x84561)),x84563))+~P1(f317(f317(f224(x84561),f2(x84561)),x84562))+~P1(f317(f317(f225(x84561),x84563),x84565))+~P1(f317(f317(f225(x84561),x84562),x84564))+P1(f317(f317(f225(x84561),f317(f317(f75(x84561),x84562),x84563)),f317(f317(f75(x84561),x84564),x84565))) % 112.37/112.11 [8457]~P134(x84571)+~P1(f317(f317(f224(x84571),f2(x84571)),x84573))+~P1(f317(f317(f225(x84571),x84573),x84575))+~P1(f317(f317(f225(x84571),x84572),x84574))+~P1(f317(f317(f225(x84571),f2(x84571)),x84574))+P1(f317(f317(f225(x84571),f317(f317(f75(x84571),x84572),x84573)),f317(f317(f75(x84571),x84574),x84575))) % 112.37/112.11 [8458]~P64(x84581)+~P1(f317(f317(f224(x84581),x84585),x84583))+~P1(f317(f317(f224(x84581),f2(x84581)),x84582))+~P1(f317(f317(f225(x84581),x84582),x84584))+~P1(f317(f317(f225(x84581),f2(x84581)),x84585))+P1(f317(f317(f225(x84581),f317(f317(f281(x84581),x84582),x84583)),f317(f317(f281(x84581),x84584),x84585))) % 112.37/112.11 [8459]~P64(x84591)+~P1(f317(f317(f224(x84591),x84592),x84594))+~P1(f317(f317(f225(x84591),x84595),x84593))+~P1(f317(f317(f225(x84591),f2(x84591)),x84595))+~P1(f317(f317(f225(x84591),f2(x84591)),x84592))+P1(f317(f317(f225(x84591),f317(f317(f281(x84591),x84592),x84593)),f317(f317(f281(x84591),x84594),x84595))) % 112.37/112.11 [9862]~P69(x98625)+~P83(x98625)+E(x98621,f178(f906(x98622,a895)))+~P1(f317(f29(x98622),x98621))+P1(f317(f317(f319(x98622),f487(x98623,x98624,x98621,x98622,x98625)),x98621))+P1(f317(f317(f225(x98625),f317(f317(f8(x98622,x98625),x98624),x98621)),f317(f317(f8(x98622,x98625),x98623),x98621))) % 112.37/112.11 [9972]~P69(x99721)+~P85(x99721)+~P1(f317(f29(x99722),x99725))+~P1(f317(f317(f224(x99721),f2(x99721)),f317(x99723,f769(x99723,x99724,x99725,x99722,x99721))))+P1(f317(f317(f224(x99721),f317(f317(f8(x99722,x99721),x99723),x99724)),f317(f317(f8(x99722,x99721),x99723),x99725)))+~P1(f317(f317(f224(f906(x99722,a895)),x99724),x99725)) % 112.37/112.11 [10142]~P69(x101423)+~P83(x101423)+E(x101421,f178(f906(x101422,a895)))+~P1(f317(f29(x101422),x101421))+~P1(f317(f317(f225(x101423),f317(x101424,f487(x101425,x101424,x101421,x101422,x101423))),f317(x101425,f487(x101425,x101424,x101421,x101422,x101423))))+P1(f317(f317(f225(x101423),f317(f317(f8(x101422,x101423),x101424),x101421)),f317(f317(f8(x101422,x101423),x101425),x101421))) % 112.37/112.11 [7176]~P17(x71762,x71765,x71764)+E(x71761,f178(f906(x71762,a895)))+E(x71763,f178(f906(x71762,a895)))+~P1(f317(f29(x71762),x71761))+~P1(f317(f29(x71762),x71763))+E(f317(x71764,f317(f317(f91(f906(x71762,a895)),x71763),x71761)),f317(f317(x71765,f317(x71764,x71763)),f317(x71764,x71761))) % 112.37/112.11 [7766]~P148(x77661,x77663,x77664)+P1(f317(x77661,x77662))+~P1(f317(f317(f225(a1),x77664),f2(a1)))+~P1(f317(f317(f224(a1),x77665),f2(a1)))+~E(x77663,f317(f317(f74(a1),f317(f317(f75(a1),x77664),x77662)),x77665))+~P1(f317(f317(f225(a1),x77664),x77665)) % 112.37/112.11 [7767]~P147(x77671,x77673,x77674)+P1(f317(x77671,x77672))+~P1(f317(f317(f225(a1),x77674),f2(a1)))+~P1(f317(f317(f224(a1),x77672),f2(a1)))+~E(x77673,f317(f317(f74(a1),f317(f317(f75(a1),x77674),x77675)),x77672))+~P1(f317(f317(f225(a1),x77674),x77672)) % 112.37/112.11 [7809]~P148(x78091,x78093,x78094)+P1(f317(x78091,x78092))+~E(x78093,f317(f317(f74(a1),f317(f317(f75(a1),x78094),x78092)),x78095))+~P1(f317(f317(f224(a1),f2(a1)),x78095))+~P1(f317(f317(f225(a1),f2(a1)),x78094))+~P1(f317(f317(f225(a1),x78095),x78094)) % 112.37/112.11 [7810]~P147(x78101,x78103,x78104)+P1(f317(x78101,x78102))+~E(x78103,f317(f317(f74(a1),f317(f317(f75(a1),x78104),x78105)),x78102))+~P1(f317(f317(f224(a1),f2(a1)),x78102))+~P1(f317(f317(f225(a1),f2(a1)),x78104))+~P1(f317(f317(f225(a1),x78102),x78104)) % 112.37/112.11 [8744]P1(f317(f317(x87441,x87442),x87443))+~P1(f317(f317(x87441,f317(f317(f31(a1),x87444),x87445)),f41(a1,x87444,x87445)))+~P1(f317(f317(f225(a1),x87445),f2(a1)))+~P1(f317(f317(f224(a1),x87443),f2(a1)))+~E(x87444,f317(f317(f74(a1),f317(f317(f75(a1),x87445),x87442)),x87443))+~P1(f317(f317(f225(a1),x87445),x87443)) % 112.37/112.11 [8753]P1(f317(f317(x87531,x87532),x87533))+~P1(f317(f317(x87531,f317(f317(f31(a1),x87534),x87535)),f41(a1,x87534,x87535)))+~E(x87534,f317(f317(f74(a1),f317(f317(f75(a1),x87535),x87532)),x87533))+~P1(f317(f317(f224(a1),f2(a1)),x87533))+~P1(f317(f317(f225(a1),f2(a1)),x87535))+~P1(f317(f317(f225(a1),x87533),x87535)) % 112.37/112.11 [9014]E(x90141,x90142)+~P55(x90143,x90145,x90144)+~P1(f317(f317(f319(x90143),x90142),x90145))+~P1(f317(f317(f319(x90143),x90141),x90145))+P1(f317(f317(f319(f905(x90143,x90143)),f317(f317(f242(x90143,x90143),x90141),x90142)),x90144))+P1(f317(f317(f319(f905(x90143,x90143)),f317(f317(f242(x90143,x90143),x90142),x90141)),x90144)) % 112.37/112.11 [9890]~P69(x98905)+~P85(x98905)+~P1(f317(f29(x98901),x98904))+P1(f317(f317(f224(x98905),f317(f317(f8(x98901,x98905),x98902),x98903)),f317(f317(f8(x98901,x98905),x98902),x98904)))+~P1(f317(f317(f224(f906(x98901,a895)),x98903),x98904))+P1(f317(f317(f319(x98901),f769(x98902,x98903,x98904,x98901,x98905)),f317(f317(f3(f906(x98901,a895)),x98904),x98903))) % 112.37/112.11 [9980]E(x99801,f178(f906(x99802,a895)))+~P1(f317(f29(x99802),x99803))+~P1(f317(f29(x99802),x99801))+P1(f317(f317(f319(f905(f906(x99802,a895),f906(x99802,a895))),f317(f317(f242(f906(x99802,a895),f906(x99802,a895)),x99803),x99801)),f309(x99802,x99804)))+~P1(f317(f317(f319(x99802),x99805),x99801))+~P1(f317(f317(f319(f905(x99802,x99802)),f317(f317(f242(x99802,x99802),f521(x99804,x99801,x99803,x99802)),x99805)),x99804)) % 112.37/112.11 [9981]E(x99811,f178(f906(x99812,a895)))+~P1(f317(f29(x99812),x99813))+~P1(f317(f29(x99812),x99811))+P1(f317(f317(f319(f905(f906(x99812,a895),f906(x99812,a895))),f317(f317(f242(f906(x99812,a895),f906(x99812,a895)),x99813),x99811)),f309(x99812,x99814)))+~P1(f317(f317(f319(x99812),x99815),x99811))+~P1(f317(f317(f319(f905(x99812,x99812)),f317(f317(f242(x99812,x99812),f592(x99814,x99811,x99813,x99812)),x99815)),x99814)) % 112.37/112.11 [10146]~P79(x101461)+~E(f317(f317(f8(x101465,x101461),x101462),x101466),x101464)+~P1(f317(f29(x101465),x101466))+P1(f317(f317(f319(x101465),f463(x101463,x101464,x101462,x101466,x101465,x101461)),x101466))+P1(f317(f317(f224(x101461),f317(x101462,x101463)),x101464))+~P1(f317(f317(f319(x101465),x101463),x101466)) % 112.37/112.11 [10194]~P79(x101941)+~E(f317(f317(f8(x101945,x101941),x101942),x101946),x101944)+~P1(f317(f29(x101945),x101946))+~P1(f317(f317(f319(x101945),x101943),x101946))+~P1(f317(f317(f224(x101941),f2(x101941)),f317(x101942,f463(x101943,x101944,x101942,x101946,x101945,x101941))))+P1(f317(f317(f224(x101941),f317(x101942,x101943)),x101944)) % 112.37/112.11 [10336]~E(x103365,x103368)+~E(x103364,x103367)+~P107(x103361)+~P69(x103362)+E(f317(f317(f8(x103361,x103362),x103363),f317(f292(x103361,x103364),x103365)),f317(f317(f8(x103361,x103362),x103366),f317(f292(x103361,x103367),x103368)))+P1(f317(f317(f224(x103361),x103364),f441(x103363,x103366,x103365,x103368,x103364,x103367,x103361,x103362))) % 112.37/112.11 [10352]~E(x103527,x103524)+~E(x103528,x103525)+~P107(x103521)+~P69(x103522)+~E(f317(x103523,f441(x103526,x103523,x103528,x103525,x103527,x103524,x103521,x103522)),f317(x103526,f441(x103526,x103523,x103528,x103525,x103527,x103524,x103521,x103522)))+E(f317(f317(f8(x103521,x103522),x103523),f317(f292(x103521,x103524),x103525)),f317(f317(f8(x103521,x103522),x103526),f317(f292(x103521,x103527),x103528))) % 112.37/112.11 [10355]~E(x103554,x103557)+~E(x103555,x103558)+~P107(x103551)+~P69(x103552)+E(f317(f317(f8(x103551,x103552),x103553),f317(f292(x103551,x103554),x103555)),f317(f317(f8(x103551,x103552),x103556),f317(f292(x103551,x103557),x103558)))+P1(f317(f317(f225(x103551),f441(x103553,x103556,x103555,x103558,x103554,x103557,x103551,x103552)),x103555)) % 112.37/112.11 [9987]~P8(x99875,x99879,x99876)+~P8(x99871,x998710,x99873)+~P12(x99871,x99875,f906(x99872,a895),x99873,x99876,x99878)+~P1(f317(f317(f319(x99875),x99877),x99879))+~P1(f317(f317(f319(x99871),x99874),x998710))+E(f317(f317(f36(x99871,f906(x99872,a895)),f317(f275(x99871,x99871,x99873),f317(f317(f299(x99871),x99874),f178(f906(x99871,a895))))),f317(f317(f10(f906(x99875,f906(x99872,a895)),f906(x99872,a895),x99871),f317(f36(x99875,f906(x99872,a895)),f317(f275(x99875,x99875,x99876),f317(f317(f299(x99875),x99877),f178(f906(x99875,a895)))))),x99878)),f317(f317(x99878,x99874),x99877)) % 112.37/112.11 [5668]~P108(x56683)+~P13(x56683,x56682)+~P13(x56683,x56681)+E(x56681,x56682)+~E(f317(f162(x56683),x56681),f317(f162(x56683),x56682))+~P1(f317(f127(x56683),x56682))+~P1(f317(f127(x56683),x56681)) % 112.37/112.11 [4995]~P132(x49952)+~P133(x49952)+~P144(x49952)+~P115(x49952)+~E(x49953,f2(x49952))+E(x49951,f2(a899))+E(f317(f317(f234(x49952),x49953),x49951),f2(x49952)) % 112.37/112.11 [9269]E(x92691,f2(a899))+~E(x92692,f317(f317(f74(a899),f317(f317(f75(a899),f317(f241(a899,a899),x92693)),x92691)),f317(f246(a899,a899),x92693)))+P1(f317(f44(x92692,x92691),x92693))+~P1(f317(f317(f224(a899),f317(f246(a899,a899),x92693)),f2(a899)))+~P1(f317(f317(f224(a899),f2(a899)),f317(f246(a899,a899),x92693)))+~P1(f317(f317(f225(a899),x92691),f317(f246(a899,a899),x92693)))+~P1(f317(f317(f225(a899),f317(f246(a899,a899),x92693)),x92691)) % 112.37/112.11 [9277]~E(f317(f241(a899,a899),x92773),f2(a899))+~E(x92771,f317(f317(f74(a899),f317(f317(f75(a899),f317(f241(a899,a899),x92773)),x92772)),f317(f246(a899,a899),x92773)))+P1(f317(f44(x92771,x92772),x92773))+~P1(f317(f317(f224(a899),f317(f246(a899,a899),x92773)),f2(a899)))+~P1(f317(f317(f224(a899),f2(a899)),f317(f246(a899,a899),x92773)))+~P1(f317(f317(f225(a899),x92772),f317(f246(a899,a899),x92773)))+~P1(f317(f317(f225(a899),f317(f246(a899,a899),x92773)),x92772)) % 112.37/112.11 [8120]~P70(x81202)+E(x81201,f178(f906(x81202,a895)))+E(x81203,f178(f906(x81202,a895)))+~P1(f317(f29(x81202),x81201))+~P1(f317(f29(x81202),x81203))+~E(f317(f317(f92(f906(x81202,a895)),x81203),x81201),f178(f906(x81202,a895)))+E(f317(f317(f75(x81202),f317(f58(x81202,f75(x81202)),x81203)),f317(f58(x81202,f75(x81202)),x81201)),f317(f58(x81202,f75(x81202)),f317(f317(f91(f906(x81202,a895)),x81203),x81201))) % 112.37/112.11 [7905]E(x79051,f2(a1))+E(f317(f317(f31(a1),x79052),x79051),x79053)+~P1(f317(f317(f224(a1),x79054),f2(a1)))+~E(x79052,f317(f317(f74(a1),f317(f317(f75(a1),x79051),x79053)),x79054))+~P1(f317(f317(f224(a1),f2(a1)),x79054))+~P1(f317(f317(f225(a1),x79054),x79051))+~P1(f317(f317(f225(a1),x79051),x79054)) % 112.37/112.11 [7913]E(f41(a1,x79132,x79131),x79133)+E(x79131,f2(a1))+~P1(f317(f317(f224(a1),x79133),f2(a1)))+~E(x79132,f317(f317(f74(a1),f317(f317(f75(a1),x79131),x79134)),x79133))+~P1(f317(f317(f224(a1),f2(a1)),x79133))+~P1(f317(f317(f225(a1),x79133),x79131))+~P1(f317(f317(f225(a1),x79131),x79133)) % 112.37/112.11 [6955]~P3(x69552)+E(x69551,f2(x69552))+E(x69553,f2(x69552))+~E(f317(f317(f31(x69552),x69554),x69553),f317(f317(f31(x69552),x69555),x69551))+E(f317(f317(f75(x69552),x69554),x69551),f317(f317(f75(x69552),x69553),x69555))+~P1(f317(f317(f277(x69552),x69551),x69555))+~P1(f317(f317(f277(x69552),x69553),x69554)) % 112.37/112.11 [6956]~P3(x69562)+E(x69561,f2(x69562))+E(x69563,f2(x69562))+~E(f317(f317(f75(x69562),x69564),x69563),f317(f317(f75(x69562),x69561),x69565))+E(f317(f317(f31(x69562),x69564),x69561),f317(f317(f31(x69562),x69565),x69563))+~P1(f317(f317(f277(x69562),x69561),x69564))+~P1(f317(f317(f277(x69562),x69563),x69565)) % 112.37/112.11 [7819]~P18(x78192,x78195,x78194)+E(x78191,f178(f906(x78192,a895)))+E(x78193,f178(f906(x78192,a895)))+~P1(f317(f29(x78192),x78191))+~P1(f317(f29(x78192),x78193))+~E(f317(f317(f92(f906(x78192,a895)),x78193),x78191),f178(f906(x78192,a895)))+E(f317(x78194,f317(f317(f91(f906(x78192,a895)),x78193),x78191)),f317(f317(x78195,f317(x78194,x78193)),f317(x78194,x78191))) % 112.37/112.11 [9520]~P24(x95203,x95201,x95205,x95204)+~P24(x95201,x95203,x95206,x95202)+E(f317(f30(x95201),x95202),f317(f30(x95203),x95204))+~P1(f317(f29(x95203),x95204))+~P1(f317(f29(x95201),x95202))+~P1(f317(f317(f224(f906(x95203,a895)),f317(f300(x95201,x95203,x95206),x95202)),x95204))+~P1(f317(f317(f224(f906(x95201,a895)),f317(f300(x95203,x95201,x95205),x95204)),x95202)) % 112.37/112.11 [9462]~P1(f317(f317(f225(a1),f317(f317(f74(a1),f317(f317(f75(a1),x94625),x94621)),x94626)),f2(a1)))+~E(f317(f317(f74(a1),f317(f317(f75(a1),x94623),x94622)),x94624),f317(f317(f74(a1),f317(f317(f75(a1),x94625),x94621)),x94626))+~P1(f317(f317(f224(a1),f2(a1)),x94626))+~P1(f317(f317(f225(a1),f2(a1)),x94625))+~P1(f317(f317(f224(a1),x94625),x94623))+~P1(f317(f317(f225(a1),x94624),x94623))+P1(f317(f317(f224(a1),x94621),x94622)) % 112.37/112.11 [9220]~E(f317(f317(f74(a1),f317(f317(f75(a1),x92203),x92201)),x92204),f317(f317(f74(a1),f317(f317(f75(a1),x92205),x92202)),x92206))+~P1(f317(f317(f224(a1),f2(a1)),x92204))+~P1(f317(f317(f225(a1),f2(a1)),x92205))+~P1(f317(f317(f224(a1),x92205),x92203))+~P1(f317(f317(f225(a1),x92206),x92205))+P1(f317(f317(f224(a1),x92201),x92202))+~P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),f317(f317(f75(a1),x92205),x92202)),x92206))) % 112.37/112.11 [9402]~P131(x94021)+~E(f317(f317(f74(x94021),x94022),x94024),f72(x94021))+~P1(f317(f317(f224(x94021),x94025),x94026))+~P1(f317(f317(f224(x94021),x94023),x94026))+~P1(f317(f317(f224(x94021),f2(x94021)),x94024))+~P1(f317(f317(f224(x94021),f2(x94021)),x94022))+P1(f317(f317(f224(x94021),f317(f317(f74(x94021),f317(f317(f75(x94021),x94022),x94023)),f317(f317(f75(x94021),x94024),x94025))),x94026)) % 112.37/112.11 [9403]~P129(x94031)+~E(f317(f317(f74(x94031),x94032),x94034),f72(x94031))+~P1(f317(f317(f224(x94031),f2(x94031)),x94034))+~P1(f317(f317(f224(x94031),f2(x94031)),x94032))+~P1(f317(f317(f225(x94031),x94035),x94036))+~P1(f317(f317(f225(x94031),x94033),x94036))+P1(f317(f317(f225(x94031),f317(f317(f74(x94031),f317(f317(f75(x94031),x94032),x94033)),f317(f317(f75(x94031),x94034),x94035))),x94036)) % 112.37/112.11 [10241]~P8(x102417,x102416,x102415)+E(x102411,x102412)+~P11(x102417,f906(x102414,a895),x102415,x102413)+E(f317(x102413,f502(x102411,x102412,x102413,x102414,x102415,x102416,x102417)),f317(x102413,f501(x102411,x102412,x102413,x102414,x102415,x102416,x102417)))+~E(f317(f317(f36(x102417,f906(x102414,a895)),x102411),x102413),f317(f317(f36(x102417,f906(x102414,a895)),x102412),x102413))+~P1(f317(f317(f319(f906(x102417,a895)),x102412),f317(f317(f56(x102417),x102416),x102415)))+~P1(f317(f317(f319(f906(x102417,a895)),x102411),f317(f317(f56(x102417),x102416),x102415))) % 112.37/112.11 [10292]~P8(x102923,x102927,x102926)+E(x102921,x102922)+~P11(x102923,f906(x102925,a895),x102926,x102924)+~E(f317(f317(f36(x102923,f906(x102925,a895)),x102921),x102924),f317(f317(f36(x102923,f906(x102925,a895)),x102922),x102924))+P1(f317(f317(f319(x102923),f501(x102921,x102922,x102924,x102925,x102926,x102927,x102923)),x102927))+~P1(f317(f317(f319(f906(x102923,a895)),x102922),f317(f317(f56(x102923),x102927),x102926)))+~P1(f317(f317(f319(f906(x102923,a895)),x102921),f317(f317(f56(x102923),x102927),x102926))) % 112.37/112.11 [10293]~P8(x102933,x102937,x102936)+E(x102931,x102932)+~P11(x102933,f906(x102935,a895),x102936,x102934)+~E(f317(f317(f36(x102933,f906(x102935,a895)),x102931),x102934),f317(f317(f36(x102933,f906(x102935,a895)),x102932),x102934))+P1(f317(f317(f319(x102933),f502(x102931,x102932,x102934,x102935,x102936,x102937,x102933)),x102937))+~P1(f317(f317(f319(f906(x102933,a895)),x102932),f317(f317(f56(x102933),x102937),x102936)))+~P1(f317(f317(f319(f906(x102933,a895)),x102931),f317(f317(f56(x102933),x102937),x102936))) % 112.37/112.11 [10371]E(x103711,x103712)+~P8(x103713,x103716,x103717)+~P11(x103713,f906(x103714,a895),x103717,x103715)+~E(f317(f317(f36(x103713,f906(x103714,a895)),x103711),x103715),f317(f317(f36(x103713,f906(x103714,a895)),x103712),x103715))+~P1(f317(f317(f319(f905(x103713,x103713)),f317(f317(f242(x103713,x103713),f501(x103711,x103712,x103715,x103714,x103717,x103716,x103713)),f502(x103711,x103712,x103715,x103714,x103717,x103716,x103713))),x103717))+~P1(f317(f317(f319(f906(x103713,a895)),x103712),f317(f317(f56(x103713),x103716),x103717)))+~P1(f317(f317(f319(f906(x103713,a895)),x103711),f317(f317(f56(x103713),x103716),x103717))) % 112.37/112.11 [9219]~P8(x92191,x92197,x92194)+~E(x92195,x92196)+~P1(f317(f317(f319(x92191),x92193),x92196))+~P1(f317(f317(f319(x92191),x92192),x92195))+~P1(f317(f317(f319(f906(x92191,a895)),x92196),f317(f317(f56(x92191),x92197),x92194)))+~P1(f317(f317(f319(f906(x92191,a895)),x92195),f317(f317(f56(x92191),x92197),x92194)))+P1(f317(f317(f319(f905(x92191,x92191)),f317(f317(f242(x92191,x92191),x92192),x92193)),x92194)) % 112.37/112.11 [9358]E(x93581,x93582)+~P8(x93583,x93584,x93585)+~P1(f317(f317(f319(x93583),x93586),x93582))+~P1(f317(f317(f319(x93583),x93587),x93581))+~P1(f317(f317(f319(f906(x93583,a895)),x93582),f317(f317(f56(x93583),x93584),x93585)))+~P1(f317(f317(f319(f906(x93583,a895)),x93581),f317(f317(f56(x93583),x93584),x93585)))+~P1(f317(f317(f319(f905(x93583,x93583)),f317(f317(f242(x93583,x93583),x93587),x93586)),x93585)) % 112.37/112.11 [10398]~P8(x103989,x103988,x103987)+~P8(x103981,x1039811,x1039810)+~P12(x103981,x103989,f906(x103986,a895),x1039810,x103987,x103985)+P1(f317(f317(f319(x103981),f504(x103982,x103983,x103984,x103985,x103986,x103987,x103988,x103989,x1039810,x1039811,x103981)),x1039811))+~P1(f317(f317(f319(f906(x103989,a895)),x103983),f317(f317(f56(x103989),x103988),x103987)))+~P1(f317(f317(f319(f906(x103981,a895)),x103984),f317(f317(f56(x103981),x1039811),x1039810)))+P1(f317(f317(f319(f906(x103986,a895)),f317(f317(f36(x103981,f906(x103986,a895)),x103984),f317(f317(f10(f906(x103989,f906(x103986,a895)),f906(x103986,a895),x103981),f317(f36(x103989,f906(x103986,a895)),x103983)),x103985))),x103982)) % 112.37/112.11 [10399]~P8(x1039911,x1039910,x103999)+~P8(x103991,x103998,x103997)+~P12(x1039911,x103991,f906(x103996,a895),x103999,x103997,x103995)+P1(f317(f317(f319(x103991),f505(x103992,x103993,x103994,x103995,x103996,x103997,x103998,x103991,x103999,x1039910,x1039911)),x103998))+~P1(f317(f317(f319(f906(x1039911,a895)),x103994),f317(f317(f56(x1039911),x1039910),x103999)))+~P1(f317(f317(f319(f906(x103991,a895)),x103993),f317(f317(f56(x103991),x103998),x103997)))+P1(f317(f317(f319(f906(x103996,a895)),f317(f317(f36(x1039911,f906(x103996,a895)),x103994),f317(f317(f10(f906(x103991,f906(x103996,a895)),f906(x103996,a895),x1039911),f317(f36(x103991,f906(x103996,a895)),x103993)),x103995))),x103992)) % 112.37/112.11 [10400]~P8(x104002,x104008,x104009)+~P8(x104004,x1040010,x1040011)+~P12(x104002,x104004,f906(x104001,a895),x104009,x1040011,x104006)+~P1(f317(f317(f319(f906(x104002,a895)),x104003),f317(f317(f56(x104002),x104008),x104009)))+~P1(f317(f317(f319(f906(x104004,a895)),x104005),f317(f317(f56(x104004),x1040010),x1040011)))+~P1(f317(f317(f319(f906(x104001,a895)),f317(f317(x104006,f504(x104007,x104005,x104003,x104006,x104001,x1040011,x1040010,x104004,x104009,x104008,x104002)),f505(x104007,x104005,x104003,x104006,x104001,x1040011,x1040010,x104004,x104009,x104008,x104002))),x104007))+P1(f317(f317(f319(f906(x104001,a895)),f317(f317(f36(x104002,f906(x104001,a895)),x104003),f317(f317(f10(f906(x104004,f906(x104001,a895)),f906(x104001,a895),x104002),f317(f36(x104004,f906(x104001,a895)),x104005)),x104006))),x104007)) % 112.37/112.11 [9255]E(x92551,x92552)+~P108(x92554)+~P24(x92553,x92554,x92555,f317(f317(f91(f906(x92553,a895)),f317(f162(x92553),x92551)),f317(f162(x92553),x92552)))+~E(f317(f162(x92553),x92551),f317(f162(x92553),x92552))+~P13(x92554,f317(f317(f144(x92553,x92554),x92555),x92552))+~P13(x92554,f317(f317(f144(x92553,x92554),x92555),x92551))+~P1(f317(f127(x92554),f317(f317(f144(x92553,x92554),x92555),x92552)))+~P1(f317(f127(x92554),f317(f317(f144(x92553,x92554),x92555),x92551))) % 112.37/112.11 %EqnAxiom % 112.37/112.11 [1]E(x11,x11) % 112.37/112.11 [2]E(x22,x21)+~E(x21,x22) % 112.37/112.11 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 112.37/112.11 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 112.37/112.11 [5]~E(x51,x52)+E(f3(x51),f3(x52)) % 112.37/112.11 [6]~E(x61,x62)+E(f90(x61),f90(x62)) % 112.37/112.11 [7]~E(x71,x72)+E(f178(x71),f178(x72)) % 112.37/112.11 [8]~E(x81,x82)+E(f317(x81,x83),f317(x82,x83)) % 112.37/112.11 [9]~E(x91,x92)+E(f317(x93,x91),f317(x93,x92)) % 112.37/112.11 [10]~E(x101,x102)+E(f223(x101),f223(x102)) % 112.37/112.11 [11]~E(x111,x112)+E(f91(x111),f91(x112)) % 112.37/112.11 [12]~E(x121,x122)+E(f228(x121),f228(x122)) % 112.37/112.11 [13]~E(x131,x132)+E(f92(x131),f92(x132)) % 112.37/112.11 [14]~E(x141,x142)+E(f93(x141),f93(x142)) % 112.37/112.11 [15]~E(x151,x152)+E(f25(x151),f25(x152)) % 112.37/112.11 [16]~E(x161,x162)+E(f78(x161),f78(x162)) % 112.37/112.11 [17]~E(x171,x172)+E(f20(x171,x173,x174),f20(x172,x173,x174)) % 112.37/112.11 [18]~E(x181,x182)+E(f20(x183,x181,x184),f20(x183,x182,x184)) % 112.37/112.11 [19]~E(x191,x192)+E(f20(x193,x194,x191),f20(x193,x194,x192)) % 112.37/112.11 [20]~E(x201,x202)+E(f906(x201,x203),f906(x202,x203)) % 112.37/112.11 [21]~E(x211,x212)+E(f906(x213,x211),f906(x213,x212)) % 112.37/112.11 [22]~E(x221,x222)+E(f900(x221),f900(x222)) % 112.37/112.11 [23]~E(x231,x232)+E(f72(x231),f72(x232)) % 112.37/112.11 [24]~E(x241,x242)+E(f505(x241,x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412),f505(x242,x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412)) % 112.37/112.11 [25]~E(x251,x252)+E(f505(x253,x251,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512),f505(x253,x252,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512)) % 112.37/112.11 [26]~E(x261,x262)+E(f505(x263,x264,x261,x265,x266,x267,x268,x269,x2610,x2611,x2612),f505(x263,x264,x262,x265,x266,x267,x268,x269,x2610,x2611,x2612)) % 112.37/112.11 [27]~E(x271,x272)+E(f505(x273,x274,x275,x271,x276,x277,x278,x279,x2710,x2711,x2712),f505(x273,x274,x275,x272,x276,x277,x278,x279,x2710,x2711,x2712)) % 112.37/112.11 [28]~E(x281,x282)+E(f505(x283,x284,x285,x286,x281,x287,x288,x289,x2810,x2811,x2812),f505(x283,x284,x285,x286,x282,x287,x288,x289,x2810,x2811,x2812)) % 112.37/112.11 [29]~E(x291,x292)+E(f505(x293,x294,x295,x296,x297,x291,x298,x299,x2910,x2911,x2912),f505(x293,x294,x295,x296,x297,x292,x298,x299,x2910,x2911,x2912)) % 112.37/112.11 [30]~E(x301,x302)+E(f505(x303,x304,x305,x306,x307,x308,x301,x309,x3010,x3011,x3012),f505(x303,x304,x305,x306,x307,x308,x302,x309,x3010,x3011,x3012)) % 112.37/112.11 [31]~E(x311,x312)+E(f505(x313,x314,x315,x316,x317,x318,x319,x311,x3110,x3111,x3112),f505(x313,x314,x315,x316,x317,x318,x319,x312,x3110,x3111,x3112)) % 112.37/112.11 [32]~E(x321,x322)+E(f505(x323,x324,x325,x326,x327,x328,x329,x3210,x321,x3211,x3212),f505(x323,x324,x325,x326,x327,x328,x329,x3210,x322,x3211,x3212)) % 112.37/112.11 [33]~E(x331,x332)+E(f505(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x331,x3312),f505(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x332,x3312)) % 112.37/112.11 [34]~E(x341,x342)+E(f505(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412,x341),f505(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412,x342)) % 112.37/112.11 [35]~E(x351,x352)+E(f252(x351),f252(x352)) % 112.37/112.11 [36]~E(x361,x362)+E(f6(x361),f6(x362)) % 112.37/112.11 [37]~E(x371,x372)+E(f504(x371,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f504(x372,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712)) % 112.37/112.11 [38]~E(x381,x382)+E(f504(x383,x381,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f504(x383,x382,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812)) % 112.37/112.11 [39]~E(x391,x392)+E(f504(x393,x394,x391,x395,x396,x397,x398,x399,x3910,x3911,x3912),f504(x393,x394,x392,x395,x396,x397,x398,x399,x3910,x3911,x3912)) % 112.37/112.11 [40]~E(x401,x402)+E(f504(x403,x404,x405,x401,x406,x407,x408,x409,x4010,x4011,x4012),f504(x403,x404,x405,x402,x406,x407,x408,x409,x4010,x4011,x4012)) % 112.37/112.11 [41]~E(x411,x412)+E(f504(x413,x414,x415,x416,x411,x417,x418,x419,x4110,x4111,x4112),f504(x413,x414,x415,x416,x412,x417,x418,x419,x4110,x4111,x4112)) % 112.37/112.11 [42]~E(x421,x422)+E(f504(x423,x424,x425,x426,x427,x421,x428,x429,x4210,x4211,x4212),f504(x423,x424,x425,x426,x427,x422,x428,x429,x4210,x4211,x4212)) % 112.37/112.11 [43]~E(x431,x432)+E(f504(x433,x434,x435,x436,x437,x438,x431,x439,x4310,x4311,x4312),f504(x433,x434,x435,x436,x437,x438,x432,x439,x4310,x4311,x4312)) % 112.37/112.11 [44]~E(x441,x442)+E(f504(x443,x444,x445,x446,x447,x448,x449,x441,x4410,x4411,x4412),f504(x443,x444,x445,x446,x447,x448,x449,x442,x4410,x4411,x4412)) % 112.37/112.11 [45]~E(x451,x452)+E(f504(x453,x454,x455,x456,x457,x458,x459,x4510,x451,x4511,x4512),f504(x453,x454,x455,x456,x457,x458,x459,x4510,x452,x4511,x4512)) % 112.37/112.11 [46]~E(x461,x462)+E(f504(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x461,x4612),f504(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x462,x4612)) % 112.37/112.11 [47]~E(x471,x472)+E(f504(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x471),f504(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x472)) % 112.37/112.11 [48]~E(x481,x482)+E(f319(x481),f319(x482)) % 112.37/112.11 [49]~E(x491,x492)+E(f101(x491),f101(x492)) % 112.37/112.11 [50]~E(x501,x502)+E(f75(x501),f75(x502)) % 112.37/112.11 [51]~E(x511,x512)+E(f902(x511),f902(x512)) % 112.37/112.11 [52]~E(x521,x522)+E(f94(x521),f94(x522)) % 112.37/112.11 [53]~E(x531,x532)+E(f901(x531),f901(x532)) % 112.37/112.11 [54]~E(x541,x542)+E(f73(x541),f73(x542)) % 112.37/112.11 [55]~E(x551,x552)+E(f299(x551),f299(x552)) % 112.37/112.11 [56]~E(x561,x562)+E(f246(x561,x563),f246(x562,x563)) % 112.37/112.11 [57]~E(x571,x572)+E(f246(x573,x571),f246(x573,x572)) % 112.37/112.11 [58]~E(x581,x582)+E(f29(x581),f29(x582)) % 112.37/112.11 [59]~E(x591,x592)+E(f179(x591),f179(x592)) % 112.37/112.11 [60]~E(x601,x602)+E(f30(x601),f30(x602)) % 112.37/112.11 [61]~E(x611,x612)+E(f281(x611),f281(x612)) % 112.37/112.11 [62]~E(x621,x622)+E(f242(x621,x623),f242(x622,x623)) % 112.37/112.11 [63]~E(x631,x632)+E(f242(x633,x631),f242(x633,x632)) % 112.37/112.11 [64]~E(x641,x642)+E(f162(x641),f162(x642)) % 112.37/112.11 [65]~E(x651,x652)+E(f232(x651),f232(x652)) % 112.37/112.11 [66]~E(x661,x662)+E(f141(x661),f141(x662)) % 112.37/112.11 [67]~E(x671,x672)+E(f74(x671),f74(x672)) % 112.37/112.11 [68]~E(x681,x682)+E(f128(x681),f128(x682)) % 112.37/112.11 [69]~E(x691,x692)+E(f10(x691,x693,x694),f10(x692,x693,x694)) % 112.37/112.11 [70]~E(x701,x702)+E(f10(x703,x701,x704),f10(x703,x702,x704)) % 112.37/112.11 [71]~E(x711,x712)+E(f10(x713,x714,x711),f10(x713,x714,x712)) % 112.37/112.11 [72]~E(x721,x722)+E(f224(x721),f224(x722)) % 112.37/112.11 [73]~E(x731,x732)+E(f154(x731),f154(x732)) % 112.37/112.11 [74]~E(x741,x742)+E(f293(x741,x743,x744),f293(x742,x743,x744)) % 112.37/112.11 [75]~E(x751,x752)+E(f293(x753,x751,x754),f293(x753,x752,x754)) % 112.37/112.11 [76]~E(x761,x762)+E(f293(x763,x764,x761),f293(x763,x764,x762)) % 112.37/112.11 [77]~E(x771,x772)+E(f9(x771,x773,x774),f9(x772,x773,x774)) % 112.37/112.11 [78]~E(x781,x782)+E(f9(x783,x781,x784),f9(x783,x782,x784)) % 112.37/112.11 [79]~E(x791,x792)+E(f9(x793,x794,x791),f9(x793,x794,x792)) % 112.37/112.11 [80]~E(x801,x802)+E(f56(x801),f56(x802)) % 112.37/112.11 [81]~E(x811,x812)+E(f13(x811,x813),f13(x812,x813)) % 112.37/112.11 [82]~E(x821,x822)+E(f13(x823,x821),f13(x823,x822)) % 112.37/112.11 [83]~E(x831,x832)+E(f225(x831),f225(x832)) % 112.37/112.11 [84]~E(x841,x842)+E(f300(x841,x843,x844),f300(x842,x843,x844)) % 112.37/112.11 [85]~E(x851,x852)+E(f300(x853,x851,x854),f300(x853,x852,x854)) % 112.37/112.11 [86]~E(x861,x862)+E(f300(x863,x864,x861),f300(x863,x864,x862)) % 112.37/112.11 [87]~E(x871,x872)+E(f459(x871,x873,x874),f459(x872,x873,x874)) % 112.37/112.11 [88]~E(x881,x882)+E(f459(x883,x881,x884),f459(x883,x882,x884)) % 112.37/112.11 [89]~E(x891,x892)+E(f459(x893,x894,x891),f459(x893,x894,x892)) % 112.37/112.11 [90]~E(x901,x902)+E(f33(x901,x903),f33(x902,x903)) % 112.37/112.11 [91]~E(x911,x912)+E(f33(x913,x911),f33(x913,x912)) % 112.37/112.11 [92]~E(x921,x922)+E(f244(x921,x923),f244(x922,x923)) % 112.37/112.11 [93]~E(x931,x932)+E(f244(x933,x931),f244(x933,x932)) % 112.37/112.11 [94]~E(x941,x942)+E(f905(x941,x943),f905(x942,x943)) % 112.37/112.11 [95]~E(x951,x952)+E(f905(x953,x951),f905(x953,x952)) % 112.37/112.11 [96]~E(x961,x962)+E(f103(x961),f103(x962)) % 112.37/112.11 [97]~E(x971,x972)+E(f84(x971,x973),f84(x972,x973)) % 112.37/112.11 [98]~E(x981,x982)+E(f84(x983,x981),f84(x983,x982)) % 112.37/112.11 [99]~E(x991,x992)+E(f159(x991,x993,x994),f159(x992,x993,x994)) % 112.37/112.11 [100]~E(x1001,x1002)+E(f159(x1003,x1001,x1004),f159(x1003,x1002,x1004)) % 112.37/112.11 [101]~E(x1011,x1012)+E(f159(x1013,x1014,x1011),f159(x1013,x1014,x1012)) % 112.37/112.11 [102]~E(x1021,x1022)+E(f171(x1021,x1023),f171(x1022,x1023)) % 112.37/112.11 [103]~E(x1031,x1032)+E(f171(x1033,x1031),f171(x1033,x1032)) % 112.37/112.11 [104]~E(x1041,x1042)+E(f402(x1041,x1043,x1044),f402(x1042,x1043,x1044)) % 112.37/112.11 [105]~E(x1051,x1052)+E(f402(x1053,x1051,x1054),f402(x1053,x1052,x1054)) % 112.37/112.11 [106]~E(x1061,x1062)+E(f402(x1063,x1064,x1061),f402(x1063,x1064,x1062)) % 112.37/112.11 [107]~E(x1071,x1072)+E(f41(x1071,x1073,x1074),f41(x1072,x1073,x1074)) % 112.37/112.11 [108]~E(x1081,x1082)+E(f41(x1083,x1081,x1084),f41(x1083,x1082,x1084)) % 112.37/112.11 [109]~E(x1091,x1092)+E(f41(x1093,x1094,x1091),f41(x1093,x1094,x1092)) % 112.37/112.11 [110]~E(x1101,x1102)+E(f31(x1101),f31(x1102)) % 112.37/112.11 [111]~E(x1111,x1112)+E(f661(x1111,x1113,x1114,x1115,x1116),f661(x1112,x1113,x1114,x1115,x1116)) % 112.37/112.11 [112]~E(x1121,x1122)+E(f661(x1123,x1121,x1124,x1125,x1126),f661(x1123,x1122,x1124,x1125,x1126)) % 112.37/112.11 [113]~E(x1131,x1132)+E(f661(x1133,x1134,x1131,x1135,x1136),f661(x1133,x1134,x1132,x1135,x1136)) % 112.37/112.11 [114]~E(x1141,x1142)+E(f661(x1143,x1144,x1145,x1141,x1146),f661(x1143,x1144,x1145,x1142,x1146)) % 112.37/112.11 [115]~E(x1151,x1152)+E(f661(x1153,x1154,x1155,x1156,x1151),f661(x1153,x1154,x1155,x1156,x1152)) % 112.37/112.11 [116]~E(x1161,x1162)+E(f127(x1161),f127(x1162)) % 112.37/112.11 [117]~E(x1171,x1172)+E(f67(x1171,x1173,x1174,x1175),f67(x1172,x1173,x1174,x1175)) % 112.37/112.11 [118]~E(x1181,x1182)+E(f67(x1183,x1181,x1184,x1185),f67(x1183,x1182,x1184,x1185)) % 112.37/112.11 [119]~E(x1191,x1192)+E(f67(x1193,x1194,x1191,x1195),f67(x1193,x1194,x1192,x1195)) % 112.37/112.11 [120]~E(x1201,x1202)+E(f67(x1203,x1204,x1205,x1201),f67(x1203,x1204,x1205,x1202)) % 112.37/112.11 [121]~E(x1211,x1212)+E(f144(x1211,x1213),f144(x1212,x1213)) % 112.37/112.11 [122]~E(x1221,x1222)+E(f144(x1223,x1221),f144(x1223,x1222)) % 112.37/112.11 [123]~E(x1231,x1232)+E(f8(x1231,x1233),f8(x1232,x1233)) % 112.37/112.11 [124]~E(x1241,x1242)+E(f8(x1243,x1241),f8(x1243,x1242)) % 112.37/112.11 [125]~E(x1251,x1252)+E(f272(x1251),f272(x1252)) % 112.37/112.11 [126]~E(x1261,x1262)+E(f308(x1261,x1263),f308(x1262,x1263)) % 112.37/112.11 [127]~E(x1271,x1272)+E(f308(x1273,x1271),f308(x1273,x1272)) % 112.37/112.11 [128]~E(x1281,x1282)+E(f42(x1281,x1283),f42(x1282,x1283)) % 112.37/112.11 [129]~E(x1291,x1292)+E(f42(x1293,x1291),f42(x1293,x1292)) % 112.37/112.11 [130]~E(x1301,x1302)+E(f893(x1301,x1303,x1304,x1305),f893(x1302,x1303,x1304,x1305)) % 112.37/112.11 [131]~E(x1311,x1312)+E(f893(x1313,x1311,x1314,x1315),f893(x1313,x1312,x1314,x1315)) % 112.37/112.11 [132]~E(x1321,x1322)+E(f893(x1323,x1324,x1321,x1325),f893(x1323,x1324,x1322,x1325)) % 112.37/112.11 [133]~E(x1331,x1332)+E(f893(x1333,x1334,x1335,x1331),f893(x1333,x1334,x1335,x1332)) % 112.37/112.11 [134]~E(x1341,x1342)+E(f96(x1341),f96(x1342)) % 112.37/112.11 [135]~E(x1351,x1352)+E(f97(x1351),f97(x1352)) % 112.37/112.11 [136]~E(x1361,x1362)+E(f318(x1361),f318(x1362)) % 112.37/112.11 [137]~E(x1371,x1372)+E(f32(x1371,x1373),f32(x1372,x1373)) % 112.37/112.11 [138]~E(x1381,x1382)+E(f32(x1383,x1381),f32(x1383,x1382)) % 112.37/112.11 [139]~E(x1391,x1392)+E(f563(x1391),f563(x1392)) % 112.37/112.11 [140]~E(x1401,x1402)+E(f35(x1401,x1403),f35(x1402,x1403)) % 112.37/112.11 [141]~E(x1411,x1412)+E(f35(x1413,x1411),f35(x1413,x1412)) % 112.37/112.11 [142]~E(x1421,x1422)+E(f675(x1421,x1423,x1424),f675(x1422,x1423,x1424)) % 112.37/112.11 [143]~E(x1431,x1432)+E(f675(x1433,x1431,x1434),f675(x1433,x1432,x1434)) % 112.37/112.11 [144]~E(x1441,x1442)+E(f675(x1443,x1444,x1441),f675(x1443,x1444,x1442)) % 112.37/112.11 [145]~E(x1451,x1452)+E(f231(x1451,x1453),f231(x1452,x1453)) % 112.37/112.11 [146]~E(x1461,x1462)+E(f231(x1463,x1461),f231(x1463,x1462)) % 112.37/112.11 [147]~E(x1471,x1472)+E(f18(x1471,x1473),f18(x1472,x1473)) % 112.37/112.11 [148]~E(x1481,x1482)+E(f18(x1483,x1481),f18(x1483,x1482)) % 112.37/112.11 [149]~E(x1491,x1492)+E(f122(x1491,x1493),f122(x1492,x1493)) % 112.37/112.11 [150]~E(x1501,x1502)+E(f122(x1503,x1501),f122(x1503,x1502)) % 112.37/112.11 [151]~E(x1511,x1512)+E(f807(x1511,x1513,x1514,x1515),f807(x1512,x1513,x1514,x1515)) % 112.37/112.11 [152]~E(x1521,x1522)+E(f807(x1523,x1521,x1524,x1525),f807(x1523,x1522,x1524,x1525)) % 112.37/112.11 [153]~E(x1531,x1532)+E(f807(x1533,x1534,x1531,x1535),f807(x1533,x1534,x1532,x1535)) % 112.37/112.11 [154]~E(x1541,x1542)+E(f807(x1543,x1544,x1545,x1541),f807(x1543,x1544,x1545,x1542)) % 112.37/112.11 [155]~E(x1551,x1552)+E(f151(x1551,x1553),f151(x1552,x1553)) % 112.37/112.11 [156]~E(x1561,x1562)+E(f151(x1563,x1561),f151(x1563,x1562)) % 112.37/112.11 [157]~E(x1571,x1572)+E(f7(x1571),f7(x1572)) % 112.37/112.11 [158]~E(x1581,x1582)+E(f277(x1581),f277(x1582)) % 112.37/112.11 [159]~E(x1591,x1592)+E(f158(x1591),f158(x1592)) % 112.37/112.11 [160]~E(x1601,x1602)+E(f142(x1601,x1603),f142(x1602,x1603)) % 112.37/112.11 [161]~E(x1611,x1612)+E(f142(x1613,x1611),f142(x1613,x1612)) % 112.37/112.11 [162]~E(x1621,x1622)+E(f113(x1621),f113(x1622)) % 112.37/112.11 [163]~E(x1631,x1632)+E(f241(x1631,x1633),f241(x1632,x1633)) % 112.37/112.11 [164]~E(x1641,x1642)+E(f241(x1643,x1641),f241(x1643,x1642)) % 112.37/112.11 [165]~E(x1651,x1652)+E(f168(x1651,x1653),f168(x1652,x1653)) % 112.37/112.11 [166]~E(x1661,x1662)+E(f168(x1663,x1661),f168(x1663,x1662)) % 112.37/112.11 [167]~E(x1671,x1672)+E(f43(x1671,x1673),f43(x1672,x1673)) % 112.37/112.11 [168]~E(x1681,x1682)+E(f43(x1683,x1681),f43(x1683,x1682)) % 112.37/112.11 [169]~E(x1691,x1692)+E(f839(x1691,x1693,x1694),f839(x1692,x1693,x1694)) % 112.37/112.11 [170]~E(x1701,x1702)+E(f839(x1703,x1701,x1704),f839(x1703,x1702,x1704)) % 112.37/112.11 [171]~E(x1711,x1712)+E(f839(x1713,x1714,x1711),f839(x1713,x1714,x1712)) % 112.37/112.11 [172]~E(x1721,x1722)+E(f149(x1721,x1723),f149(x1722,x1723)) % 112.37/112.11 [173]~E(x1731,x1732)+E(f149(x1733,x1731),f149(x1733,x1732)) % 112.37/112.11 [174]~E(x1741,x1742)+E(f407(x1741,x1743,x1744),f407(x1742,x1743,x1744)) % 112.37/112.11 [175]~E(x1751,x1752)+E(f407(x1753,x1751,x1754),f407(x1753,x1752,x1754)) % 112.37/112.11 [176]~E(x1761,x1762)+E(f407(x1763,x1764,x1761),f407(x1763,x1764,x1762)) % 112.37/112.11 [177]~E(x1771,x1772)+E(f233(x1771,x1773,x1774),f233(x1772,x1773,x1774)) % 112.37/112.11 [178]~E(x1781,x1782)+E(f233(x1783,x1781,x1784),f233(x1783,x1782,x1784)) % 112.37/112.11 [179]~E(x1791,x1792)+E(f233(x1793,x1794,x1791),f233(x1793,x1794,x1792)) % 112.37/112.11 [180]~E(x1801,x1802)+E(f129(x1801,x1803),f129(x1802,x1803)) % 112.37/112.11 [181]~E(x1811,x1812)+E(f129(x1813,x1811),f129(x1813,x1812)) % 112.37/112.11 [182]~E(x1821,x1822)+E(f132(x1821,x1823,x1824,x1825),f132(x1822,x1823,x1824,x1825)) % 112.37/112.11 [183]~E(x1831,x1832)+E(f132(x1833,x1831,x1834,x1835),f132(x1833,x1832,x1834,x1835)) % 112.37/112.11 [184]~E(x1841,x1842)+E(f132(x1843,x1844,x1841,x1845),f132(x1843,x1844,x1842,x1845)) % 112.37/112.11 [185]~E(x1851,x1852)+E(f132(x1853,x1854,x1855,x1851),f132(x1853,x1854,x1855,x1852)) % 112.37/112.11 [186]~E(x1861,x1862)+E(f70(x1861),f70(x1862)) % 112.37/112.11 [187]~E(x1871,x1872)+E(f761(x1871,x1873,x1874,x1875),f761(x1872,x1873,x1874,x1875)) % 112.37/112.11 [188]~E(x1881,x1882)+E(f761(x1883,x1881,x1884,x1885),f761(x1883,x1882,x1884,x1885)) % 112.37/112.11 [189]~E(x1891,x1892)+E(f761(x1893,x1894,x1891,x1895),f761(x1893,x1894,x1892,x1895)) % 112.37/112.11 [190]~E(x1901,x1902)+E(f761(x1903,x1904,x1905,x1901),f761(x1903,x1904,x1905,x1902)) % 112.37/112.11 [191]~E(x1911,x1912)+E(f100(x1911),f100(x1912)) % 112.37/112.11 [192]~E(x1921,x1922)+E(f15(x1921,x1923,x1924),f15(x1922,x1923,x1924)) % 112.37/112.11 [193]~E(x1931,x1932)+E(f15(x1933,x1931,x1934),f15(x1933,x1932,x1934)) % 112.37/112.11 [194]~E(x1941,x1942)+E(f15(x1943,x1944,x1941),f15(x1943,x1944,x1942)) % 112.37/112.11 [195]~E(x1951,x1952)+E(f124(x1951),f124(x1952)) % 112.37/112.11 [196]~E(x1961,x1962)+E(f234(x1961),f234(x1962)) % 112.37/112.11 [197]~E(x1971,x1972)+E(f560(x1971,x1973,x1974),f560(x1972,x1973,x1974)) % 112.37/112.11 [198]~E(x1981,x1982)+E(f560(x1983,x1981,x1984),f560(x1983,x1982,x1984)) % 112.37/112.11 [199]~E(x1991,x1992)+E(f560(x1993,x1994,x1991),f560(x1993,x1994,x1992)) % 112.37/112.11 [200]~E(x2001,x2002)+E(f301(x2001,x2003,x2004),f301(x2002,x2003,x2004)) % 112.37/112.11 [201]~E(x2011,x2012)+E(f301(x2013,x2011,x2014),f301(x2013,x2012,x2014)) % 112.37/112.11 [202]~E(x2021,x2022)+E(f301(x2023,x2024,x2021),f301(x2023,x2024,x2022)) % 112.37/112.11 [203]~E(x2031,x2032)+E(f843(x2031,x2033,x2034),f843(x2032,x2033,x2034)) % 112.37/112.11 [204]~E(x2041,x2042)+E(f843(x2043,x2041,x2044),f843(x2043,x2042,x2044)) % 112.37/112.11 [205]~E(x2051,x2052)+E(f843(x2053,x2054,x2051),f843(x2053,x2054,x2052)) % 112.37/112.11 [206]~E(x2061,x2062)+E(f210(x2061,x2063,x2064,x2065),f210(x2062,x2063,x2064,x2065)) % 112.37/112.11 [207]~E(x2071,x2072)+E(f210(x2073,x2071,x2074,x2075),f210(x2073,x2072,x2074,x2075)) % 112.37/112.11 [208]~E(x2081,x2082)+E(f210(x2083,x2084,x2081,x2085),f210(x2083,x2084,x2082,x2085)) % 112.37/112.11 [209]~E(x2091,x2092)+E(f210(x2093,x2094,x2095,x2091),f210(x2093,x2094,x2095,x2092)) % 112.37/112.11 [210]~E(x2101,x2102)+E(f248(x2101,x2103,x2104,x2105,x2106,x2107),f248(x2102,x2103,x2104,x2105,x2106,x2107)) % 112.37/112.11 [211]~E(x2111,x2112)+E(f248(x2113,x2111,x2114,x2115,x2116,x2117),f248(x2113,x2112,x2114,x2115,x2116,x2117)) % 112.37/112.11 [212]~E(x2121,x2122)+E(f248(x2123,x2124,x2121,x2125,x2126,x2127),f248(x2123,x2124,x2122,x2125,x2126,x2127)) % 112.37/112.11 [213]~E(x2131,x2132)+E(f248(x2133,x2134,x2135,x2131,x2136,x2137),f248(x2133,x2134,x2135,x2132,x2136,x2137)) % 112.37/112.11 [214]~E(x2141,x2142)+E(f248(x2143,x2144,x2145,x2146,x2141,x2147),f248(x2143,x2144,x2145,x2146,x2142,x2147)) % 112.37/112.11 [215]~E(x2151,x2152)+E(f248(x2153,x2154,x2155,x2156,x2157,x2151),f248(x2153,x2154,x2155,x2156,x2157,x2152)) % 112.37/112.11 [216]~E(x2161,x2162)+E(f218(x2161,x2163,x2164),f218(x2162,x2163,x2164)) % 112.37/112.11 [217]~E(x2171,x2172)+E(f218(x2173,x2171,x2174),f218(x2173,x2172,x2174)) % 112.37/112.11 [218]~E(x2181,x2182)+E(f218(x2183,x2184,x2181),f218(x2183,x2184,x2182)) % 112.37/112.11 [219]~E(x2191,x2192)+E(f36(x2191,x2193),f36(x2192,x2193)) % 112.37/112.11 [220]~E(x2201,x2202)+E(f36(x2203,x2201),f36(x2203,x2202)) % 112.37/112.11 [221]~E(x2211,x2212)+E(f379(x2211,x2213,x2214),f379(x2212,x2213,x2214)) % 112.37/112.11 [222]~E(x2221,x2222)+E(f379(x2223,x2221,x2224),f379(x2223,x2222,x2224)) % 112.37/112.11 [223]~E(x2231,x2232)+E(f379(x2233,x2234,x2231),f379(x2233,x2234,x2232)) % 112.37/112.11 [224]~E(x2241,x2242)+E(f160(x2241,x2243,x2244),f160(x2242,x2243,x2244)) % 112.37/112.11 [225]~E(x2251,x2252)+E(f160(x2253,x2251,x2254),f160(x2253,x2252,x2254)) % 112.37/112.11 [226]~E(x2261,x2262)+E(f160(x2263,x2264,x2261),f160(x2263,x2264,x2262)) % 112.37/112.11 [227]~E(x2271,x2272)+E(f275(x2271,x2273,x2274),f275(x2272,x2273,x2274)) % 112.37/112.11 [228]~E(x2281,x2282)+E(f275(x2283,x2281,x2284),f275(x2283,x2282,x2284)) % 112.37/112.11 [229]~E(x2291,x2292)+E(f275(x2293,x2294,x2291),f275(x2293,x2294,x2292)) % 112.37/112.11 [230]~E(x2301,x2302)+E(f247(x2301,x2303,x2304),f247(x2302,x2303,x2304)) % 112.37/112.11 [231]~E(x2311,x2312)+E(f247(x2313,x2311,x2314),f247(x2313,x2312,x2314)) % 112.37/112.11 [232]~E(x2321,x2322)+E(f247(x2323,x2324,x2321),f247(x2323,x2324,x2322)) % 112.37/112.11 [233]~E(x2331,x2332)+E(f295(x2331,x2333,x2334),f295(x2332,x2333,x2334)) % 112.37/112.11 [234]~E(x2341,x2342)+E(f295(x2343,x2341,x2344),f295(x2343,x2342,x2344)) % 112.37/112.11 [235]~E(x2351,x2352)+E(f295(x2353,x2354,x2351),f295(x2353,x2354,x2352)) % 112.37/112.11 [236]~E(x2361,x2362)+E(f63(x2361,x2363,x2364),f63(x2362,x2363,x2364)) % 112.37/112.11 [237]~E(x2371,x2372)+E(f63(x2373,x2371,x2374),f63(x2373,x2372,x2374)) % 112.37/112.12 [238]~E(x2381,x2382)+E(f63(x2383,x2384,x2381),f63(x2383,x2384,x2382)) % 112.37/112.12 [239]~E(x2391,x2392)+E(f137(x2391,x2393),f137(x2392,x2393)) % 112.37/112.12 [240]~E(x2401,x2402)+E(f137(x2403,x2401),f137(x2403,x2402)) % 112.37/112.12 [241]~E(x2411,x2412)+E(f759(x2411,x2413,x2414,x2415),f759(x2412,x2413,x2414,x2415)) % 112.37/112.12 [242]~E(x2421,x2422)+E(f759(x2423,x2421,x2424,x2425),f759(x2423,x2422,x2424,x2425)) % 112.37/112.12 [243]~E(x2431,x2432)+E(f759(x2433,x2434,x2431,x2435),f759(x2433,x2434,x2432,x2435)) % 112.37/112.12 [244]~E(x2441,x2442)+E(f759(x2443,x2444,x2445,x2441),f759(x2443,x2444,x2445,x2442)) % 112.37/112.12 [245]~E(x2451,x2452)+E(f280(x2451,x2453,x2454,x2455),f280(x2452,x2453,x2454,x2455)) % 112.37/112.12 [246]~E(x2461,x2462)+E(f280(x2463,x2461,x2464,x2465),f280(x2463,x2462,x2464,x2465)) % 112.37/112.12 [247]~E(x2471,x2472)+E(f280(x2473,x2474,x2471,x2475),f280(x2473,x2474,x2472,x2475)) % 112.37/112.12 [248]~E(x2481,x2482)+E(f280(x2483,x2484,x2485,x2481),f280(x2483,x2484,x2485,x2482)) % 112.37/112.12 [249]~E(x2491,x2492)+E(f240(x2491,x2493,x2494),f240(x2492,x2493,x2494)) % 112.37/112.12 [250]~E(x2501,x2502)+E(f240(x2503,x2501,x2504),f240(x2503,x2502,x2504)) % 112.37/112.12 [251]~E(x2511,x2512)+E(f240(x2513,x2514,x2511),f240(x2513,x2514,x2512)) % 112.37/112.12 [252]~E(x2521,x2522)+E(f104(x2521,x2523),f104(x2522,x2523)) % 112.37/112.12 [253]~E(x2531,x2532)+E(f104(x2533,x2531),f104(x2533,x2532)) % 112.37/112.12 [254]~E(x2541,x2542)+E(f306(x2541,x2543),f306(x2542,x2543)) % 112.37/112.12 [255]~E(x2551,x2552)+E(f306(x2553,x2551),f306(x2553,x2552)) % 112.37/112.12 [256]~E(x2561,x2562)+E(f69(x2561,x2563,x2564,x2565,x2566),f69(x2562,x2563,x2564,x2565,x2566)) % 112.37/112.12 [257]~E(x2571,x2572)+E(f69(x2573,x2571,x2574,x2575,x2576),f69(x2573,x2572,x2574,x2575,x2576)) % 112.37/112.12 [258]~E(x2581,x2582)+E(f69(x2583,x2584,x2581,x2585,x2586),f69(x2583,x2584,x2582,x2585,x2586)) % 112.37/112.12 [259]~E(x2591,x2592)+E(f69(x2593,x2594,x2595,x2591,x2596),f69(x2593,x2594,x2595,x2592,x2596)) % 112.37/112.12 [260]~E(x2601,x2602)+E(f69(x2603,x2604,x2605,x2606,x2601),f69(x2603,x2604,x2605,x2606,x2602)) % 112.37/112.12 [261]~E(x2611,x2612)+E(f330(x2611,x2613,x2614,x2615),f330(x2612,x2613,x2614,x2615)) % 112.37/112.12 [262]~E(x2621,x2622)+E(f330(x2623,x2621,x2624,x2625),f330(x2623,x2622,x2624,x2625)) % 112.37/112.12 [263]~E(x2631,x2632)+E(f330(x2633,x2634,x2631,x2635),f330(x2633,x2634,x2632,x2635)) % 112.37/112.12 [264]~E(x2641,x2642)+E(f330(x2643,x2644,x2645,x2641),f330(x2643,x2644,x2645,x2642)) % 112.37/112.12 [265]~E(x2651,x2652)+E(f304(x2651),f304(x2652)) % 112.37/112.12 [266]~E(x2661,x2662)+E(f181(x2661),f181(x2662)) % 112.37/112.12 [267]~E(x2671,x2672)+E(f81(x2671),f81(x2672)) % 112.37/112.12 [268]~E(x2681,x2682)+E(f105(x2681),f105(x2682)) % 112.37/112.12 [269]~E(x2691,x2692)+E(f904(x2691,x2693),f904(x2692,x2693)) % 112.37/112.12 [270]~E(x2701,x2702)+E(f904(x2703,x2701),f904(x2703,x2702)) % 112.37/112.12 [271]~E(x2711,x2712)+E(f340(x2711,x2713,x2714),f340(x2712,x2713,x2714)) % 112.37/112.12 [272]~E(x2721,x2722)+E(f340(x2723,x2721,x2724),f340(x2723,x2722,x2724)) % 112.37/112.12 [273]~E(x2731,x2732)+E(f340(x2733,x2734,x2731),f340(x2733,x2734,x2732)) % 112.37/112.12 [274]~E(x2741,x2742)+E(f903(x2741,x2743),f903(x2742,x2743)) % 112.37/112.12 [275]~E(x2751,x2752)+E(f903(x2753,x2751),f903(x2753,x2752)) % 112.37/112.12 [276]~E(x2761,x2762)+E(f157(x2761),f157(x2762)) % 112.37/112.12 [277]~E(x2771,x2772)+E(f352(x2771,x2773),f352(x2772,x2773)) % 112.37/112.12 [278]~E(x2781,x2782)+E(f352(x2783,x2781),f352(x2783,x2782)) % 112.37/112.12 [279]~E(x2791,x2792)+E(f155(x2791),f155(x2792)) % 112.37/112.12 [280]~E(x2801,x2802)+E(f196(x2801,x2803,x2804,x2805),f196(x2802,x2803,x2804,x2805)) % 112.37/112.12 [281]~E(x2811,x2812)+E(f196(x2813,x2811,x2814,x2815),f196(x2813,x2812,x2814,x2815)) % 112.37/112.12 [282]~E(x2821,x2822)+E(f196(x2823,x2824,x2821,x2825),f196(x2823,x2824,x2822,x2825)) % 112.37/112.12 [283]~E(x2831,x2832)+E(f196(x2833,x2834,x2835,x2831),f196(x2833,x2834,x2835,x2832)) % 112.37/112.12 [284]~E(x2841,x2842)+E(f161(x2841),f161(x2842)) % 112.37/112.12 [285]~E(x2851,x2852)+E(f195(x2851,x2853,x2854,x2855),f195(x2852,x2853,x2854,x2855)) % 112.37/112.12 [286]~E(x2861,x2862)+E(f195(x2863,x2861,x2864,x2865),f195(x2863,x2862,x2864,x2865)) % 112.37/112.12 [287]~E(x2871,x2872)+E(f195(x2873,x2874,x2871,x2875),f195(x2873,x2874,x2872,x2875)) % 112.37/112.12 [288]~E(x2881,x2882)+E(f195(x2883,x2884,x2885,x2881),f195(x2883,x2884,x2885,x2882)) % 112.37/112.12 [289]~E(x2891,x2892)+E(f117(x2891,x2893,x2894,x2895,x2896),f117(x2892,x2893,x2894,x2895,x2896)) % 112.37/112.12 [290]~E(x2901,x2902)+E(f117(x2903,x2901,x2904,x2905,x2906),f117(x2903,x2902,x2904,x2905,x2906)) % 112.37/112.12 [291]~E(x2911,x2912)+E(f117(x2913,x2914,x2911,x2915,x2916),f117(x2913,x2914,x2912,x2915,x2916)) % 112.37/112.12 [292]~E(x2921,x2922)+E(f117(x2923,x2924,x2925,x2921,x2926),f117(x2923,x2924,x2925,x2922,x2926)) % 112.37/112.12 [293]~E(x2931,x2932)+E(f117(x2933,x2934,x2935,x2936,x2931),f117(x2933,x2934,x2935,x2936,x2932)) % 112.37/112.12 [294]~E(x2941,x2942)+E(f279(x2941,x2943,x2944),f279(x2942,x2943,x2944)) % 112.37/112.12 [295]~E(x2951,x2952)+E(f279(x2953,x2951,x2954),f279(x2953,x2952,x2954)) % 112.37/112.12 [296]~E(x2961,x2962)+E(f279(x2963,x2964,x2961),f279(x2963,x2964,x2962)) % 112.37/112.12 [297]~E(x2971,x2972)+E(f167(x2971,x2973,x2974),f167(x2972,x2973,x2974)) % 112.37/112.12 [298]~E(x2981,x2982)+E(f167(x2983,x2981,x2984),f167(x2983,x2982,x2984)) % 112.37/112.12 [299]~E(x2991,x2992)+E(f167(x2993,x2994,x2991),f167(x2993,x2994,x2992)) % 112.37/112.12 [300]~E(x3001,x3002)+E(f134(x3001,x3003),f134(x3002,x3003)) % 112.37/112.12 [301]~E(x3011,x3012)+E(f134(x3013,x3011),f134(x3013,x3012)) % 112.37/112.12 [302]~E(x3021,x3022)+E(f430(x3021,x3023,x3024,x3025,x3026,x3027,x3028),f430(x3022,x3023,x3024,x3025,x3026,x3027,x3028)) % 112.37/112.12 [303]~E(x3031,x3032)+E(f430(x3033,x3031,x3034,x3035,x3036,x3037,x3038),f430(x3033,x3032,x3034,x3035,x3036,x3037,x3038)) % 112.37/112.12 [304]~E(x3041,x3042)+E(f430(x3043,x3044,x3041,x3045,x3046,x3047,x3048),f430(x3043,x3044,x3042,x3045,x3046,x3047,x3048)) % 112.37/112.12 [305]~E(x3051,x3052)+E(f430(x3053,x3054,x3055,x3051,x3056,x3057,x3058),f430(x3053,x3054,x3055,x3052,x3056,x3057,x3058)) % 112.37/112.12 [306]~E(x3061,x3062)+E(f430(x3063,x3064,x3065,x3066,x3061,x3067,x3068),f430(x3063,x3064,x3065,x3066,x3062,x3067,x3068)) % 112.37/112.12 [307]~E(x3071,x3072)+E(f430(x3073,x3074,x3075,x3076,x3077,x3071,x3078),f430(x3073,x3074,x3075,x3076,x3077,x3072,x3078)) % 112.37/112.12 [308]~E(x3081,x3082)+E(f430(x3083,x3084,x3085,x3086,x3087,x3088,x3081),f430(x3083,x3084,x3085,x3086,x3087,x3088,x3082)) % 112.37/112.12 [309]~E(x3091,x3092)+E(f194(x3091),f194(x3092)) % 112.37/112.12 [310]~E(x3101,x3102)+E(f292(x3101,x3103),f292(x3102,x3103)) % 112.37/112.12 [311]~E(x3111,x3112)+E(f292(x3113,x3111),f292(x3113,x3112)) % 112.37/112.12 [312]~E(x3121,x3122)+E(f509(x3121,x3123,x3124,x3125,x3126),f509(x3122,x3123,x3124,x3125,x3126)) % 112.37/112.12 [313]~E(x3131,x3132)+E(f509(x3133,x3131,x3134,x3135,x3136),f509(x3133,x3132,x3134,x3135,x3136)) % 112.37/112.12 [314]~E(x3141,x3142)+E(f509(x3143,x3144,x3141,x3145,x3146),f509(x3143,x3144,x3142,x3145,x3146)) % 112.37/112.12 [315]~E(x3151,x3152)+E(f509(x3153,x3154,x3155,x3151,x3156),f509(x3153,x3154,x3155,x3152,x3156)) % 112.37/112.12 [316]~E(x3161,x3162)+E(f509(x3163,x3164,x3165,x3166,x3161),f509(x3163,x3164,x3165,x3166,x3162)) % 112.37/112.12 [317]~E(x3171,x3172)+E(f287(x3171,x3173,x3174,x3175,x3176),f287(x3172,x3173,x3174,x3175,x3176)) % 112.37/112.12 [318]~E(x3181,x3182)+E(f287(x3183,x3181,x3184,x3185,x3186),f287(x3183,x3182,x3184,x3185,x3186)) % 112.37/112.12 [319]~E(x3191,x3192)+E(f287(x3193,x3194,x3191,x3195,x3196),f287(x3193,x3194,x3192,x3195,x3196)) % 112.37/112.12 [320]~E(x3201,x3202)+E(f287(x3203,x3204,x3205,x3201,x3206),f287(x3203,x3204,x3205,x3202,x3206)) % 112.37/112.12 [321]~E(x3211,x3212)+E(f287(x3213,x3214,x3215,x3216,x3211),f287(x3213,x3214,x3215,x3216,x3212)) % 112.37/112.12 [322]~E(x3221,x3222)+E(f115(x3221,x3223),f115(x3222,x3223)) % 112.37/112.12 [323]~E(x3231,x3232)+E(f115(x3233,x3231),f115(x3233,x3232)) % 112.37/112.12 [324]~E(x3241,x3242)+E(f847(x3241,x3243,x3244),f847(x3242,x3243,x3244)) % 112.37/112.12 [325]~E(x3251,x3252)+E(f847(x3253,x3251,x3254),f847(x3253,x3252,x3254)) % 112.37/112.12 [326]~E(x3261,x3262)+E(f847(x3263,x3264,x3261),f847(x3263,x3264,x3262)) % 112.37/112.12 [327]~E(x3271,x3272)+E(f845(x3271,x3273,x3274),f845(x3272,x3273,x3274)) % 112.37/112.12 [328]~E(x3281,x3282)+E(f845(x3283,x3281,x3284),f845(x3283,x3282,x3284)) % 112.37/112.12 [329]~E(x3291,x3292)+E(f845(x3293,x3294,x3291),f845(x3293,x3294,x3292)) % 112.37/112.12 [330]~E(x3301,x3302)+E(f838(x3301,x3303,x3304),f838(x3302,x3303,x3304)) % 112.37/112.12 [331]~E(x3311,x3312)+E(f838(x3313,x3311,x3314),f838(x3313,x3312,x3314)) % 112.37/112.12 [332]~E(x3321,x3322)+E(f838(x3323,x3324,x3321),f838(x3323,x3324,x3322)) % 112.37/112.12 [333]~E(x3331,x3332)+E(f309(x3331,x3333),f309(x3332,x3333)) % 112.37/112.12 [334]~E(x3341,x3342)+E(f309(x3343,x3341),f309(x3343,x3342)) % 112.37/112.12 [335]~E(x3351,x3352)+E(f273(x3351),f273(x3352)) % 112.37/112.12 [336]~E(x3361,x3362)+E(f80(x3361,x3363),f80(x3362,x3363)) % 112.37/112.12 [337]~E(x3371,x3372)+E(f80(x3373,x3371),f80(x3373,x3372)) % 112.37/112.12 [338]~E(x3381,x3382)+E(f68(x3381,x3383),f68(x3382,x3383)) % 112.37/112.12 [339]~E(x3391,x3392)+E(f68(x3393,x3391),f68(x3393,x3392)) % 112.37/112.12 [340]~E(x3401,x3402)+E(f298(x3401),f298(x3402)) % 112.37/112.12 [341]~E(x3411,x3412)+E(f427(x3411,x3413,x3414,x3415,x3416,x3417,x3418),f427(x3412,x3413,x3414,x3415,x3416,x3417,x3418)) % 112.37/112.12 [342]~E(x3421,x3422)+E(f427(x3423,x3421,x3424,x3425,x3426,x3427,x3428),f427(x3423,x3422,x3424,x3425,x3426,x3427,x3428)) % 112.37/112.12 [343]~E(x3431,x3432)+E(f427(x3433,x3434,x3431,x3435,x3436,x3437,x3438),f427(x3433,x3434,x3432,x3435,x3436,x3437,x3438)) % 112.37/112.12 [344]~E(x3441,x3442)+E(f427(x3443,x3444,x3445,x3441,x3446,x3447,x3448),f427(x3443,x3444,x3445,x3442,x3446,x3447,x3448)) % 112.37/112.12 [345]~E(x3451,x3452)+E(f427(x3453,x3454,x3455,x3456,x3451,x3457,x3458),f427(x3453,x3454,x3455,x3456,x3452,x3457,x3458)) % 112.37/112.12 [346]~E(x3461,x3462)+E(f427(x3463,x3464,x3465,x3466,x3467,x3461,x3468),f427(x3463,x3464,x3465,x3466,x3467,x3462,x3468)) % 112.37/112.12 [347]~E(x3471,x3472)+E(f427(x3473,x3474,x3475,x3476,x3477,x3478,x3471),f427(x3473,x3474,x3475,x3476,x3477,x3478,x3472)) % 112.37/112.12 [348]~E(x3481,x3482)+E(f153(x3481,x3483,x3484,x3485),f153(x3482,x3483,x3484,x3485)) % 112.37/112.12 [349]~E(x3491,x3492)+E(f153(x3493,x3491,x3494,x3495),f153(x3493,x3492,x3494,x3495)) % 112.37/112.12 [350]~E(x3501,x3502)+E(f153(x3503,x3504,x3501,x3505),f153(x3503,x3504,x3502,x3505)) % 112.37/112.12 [351]~E(x3511,x3512)+E(f153(x3513,x3514,x3515,x3511),f153(x3513,x3514,x3515,x3512)) % 112.37/112.12 [352]~E(x3521,x3522)+E(f434(x3521,x3523,x3524),f434(x3522,x3523,x3524)) % 112.37/112.12 [353]~E(x3531,x3532)+E(f434(x3533,x3531,x3534),f434(x3533,x3532,x3534)) % 112.37/112.12 [354]~E(x3541,x3542)+E(f434(x3543,x3544,x3541),f434(x3543,x3544,x3542)) % 112.37/112.12 [355]~E(x3551,x3552)+E(f38(x3551),f38(x3552)) % 112.37/112.12 [356]~E(x3561,x3562)+E(f58(x3561,x3563),f58(x3562,x3563)) % 112.37/112.12 [357]~E(x3571,x3572)+E(f58(x3573,x3571),f58(x3573,x3572)) % 112.37/112.12 [358]~E(x3581,x3582)+E(f217(x3581,x3583),f217(x3582,x3583)) % 112.37/112.12 [359]~E(x3591,x3592)+E(f217(x3593,x3591),f217(x3593,x3592)) % 112.37/112.12 [360]~E(x3601,x3602)+E(f651(x3601,x3603,x3604,x3605),f651(x3602,x3603,x3604,x3605)) % 112.37/112.12 [361]~E(x3611,x3612)+E(f651(x3613,x3611,x3614,x3615),f651(x3613,x3612,x3614,x3615)) % 112.37/112.12 [362]~E(x3621,x3622)+E(f651(x3623,x3624,x3621,x3625),f651(x3623,x3624,x3622,x3625)) % 112.37/112.12 [363]~E(x3631,x3632)+E(f651(x3633,x3634,x3635,x3631),f651(x3633,x3634,x3635,x3632)) % 112.37/112.12 [364]~E(x3641,x3642)+E(f249(x3641,x3643,x3644,x3645),f249(x3642,x3643,x3644,x3645)) % 112.37/112.12 [365]~E(x3651,x3652)+E(f249(x3653,x3651,x3654,x3655),f249(x3653,x3652,x3654,x3655)) % 112.37/112.12 [366]~E(x3661,x3662)+E(f249(x3663,x3664,x3661,x3665),f249(x3663,x3664,x3662,x3665)) % 112.37/112.12 [367]~E(x3671,x3672)+E(f249(x3673,x3674,x3675,x3671),f249(x3673,x3674,x3675,x3672)) % 112.37/112.12 [368]~E(x3681,x3682)+E(f297(x3681,x3683),f297(x3682,x3683)) % 112.37/112.12 [369]~E(x3691,x3692)+E(f297(x3693,x3691),f297(x3693,x3692)) % 112.37/112.12 [370]~E(x3701,x3702)+E(f296(x3701,x3703,x3704),f296(x3702,x3703,x3704)) % 112.37/112.12 [371]~E(x3711,x3712)+E(f296(x3713,x3711,x3714),f296(x3713,x3712,x3714)) % 112.37/112.12 [372]~E(x3721,x3722)+E(f296(x3723,x3724,x3721),f296(x3723,x3724,x3722)) % 112.37/112.12 [373]~E(x3731,x3732)+E(f767(x3731,x3733,x3734,x3735,x3736,x3737,x3738),f767(x3732,x3733,x3734,x3735,x3736,x3737,x3738)) % 112.37/112.12 [374]~E(x3741,x3742)+E(f767(x3743,x3741,x3744,x3745,x3746,x3747,x3748),f767(x3743,x3742,x3744,x3745,x3746,x3747,x3748)) % 112.37/112.12 [375]~E(x3751,x3752)+E(f767(x3753,x3754,x3751,x3755,x3756,x3757,x3758),f767(x3753,x3754,x3752,x3755,x3756,x3757,x3758)) % 112.37/112.12 [376]~E(x3761,x3762)+E(f767(x3763,x3764,x3765,x3761,x3766,x3767,x3768),f767(x3763,x3764,x3765,x3762,x3766,x3767,x3768)) % 112.37/112.12 [377]~E(x3771,x3772)+E(f767(x3773,x3774,x3775,x3776,x3771,x3777,x3778),f767(x3773,x3774,x3775,x3776,x3772,x3777,x3778)) % 112.37/112.12 [378]~E(x3781,x3782)+E(f767(x3783,x3784,x3785,x3786,x3787,x3781,x3788),f767(x3783,x3784,x3785,x3786,x3787,x3782,x3788)) % 112.37/112.12 [379]~E(x3791,x3792)+E(f767(x3793,x3794,x3795,x3796,x3797,x3798,x3791),f767(x3793,x3794,x3795,x3796,x3797,x3798,x3792)) % 112.37/112.12 [380]~E(x3801,x3802)+E(f14(x3801,x3803,x3804),f14(x3802,x3803,x3804)) % 112.37/112.12 [381]~E(x3811,x3812)+E(f14(x3813,x3811,x3814),f14(x3813,x3812,x3814)) % 112.37/112.12 [382]~E(x3821,x3822)+E(f14(x3823,x3824,x3821),f14(x3823,x3824,x3822)) % 112.37/112.12 [383]~E(x3831,x3832)+E(f109(x3831),f109(x3832)) % 112.37/112.12 [384]~E(x3841,x3842)+E(f110(x3841,x3843),f110(x3842,x3843)) % 112.37/112.12 [385]~E(x3851,x3852)+E(f110(x3853,x3851),f110(x3853,x3852)) % 112.37/112.12 [386]~E(x3861,x3862)+E(f406(x3861,x3863,x3864),f406(x3862,x3863,x3864)) % 112.37/112.12 [387]~E(x3871,x3872)+E(f406(x3873,x3871,x3874),f406(x3873,x3872,x3874)) % 112.37/112.12 [388]~E(x3881,x3882)+E(f406(x3883,x3884,x3881),f406(x3883,x3884,x3882)) % 112.37/112.12 [389]~E(x3891,x3892)+E(f173(x3891,x3893),f173(x3892,x3893)) % 112.37/112.12 [390]~E(x3901,x3902)+E(f173(x3903,x3901),f173(x3903,x3902)) % 112.37/112.12 [391]~E(x3911,x3912)+E(f523(x3911,x3913,x3914,x3915,x3916,x3917),f523(x3912,x3913,x3914,x3915,x3916,x3917)) % 112.37/112.12 [392]~E(x3921,x3922)+E(f523(x3923,x3921,x3924,x3925,x3926,x3927),f523(x3923,x3922,x3924,x3925,x3926,x3927)) % 112.37/112.12 [393]~E(x3931,x3932)+E(f523(x3933,x3934,x3931,x3935,x3936,x3937),f523(x3933,x3934,x3932,x3935,x3936,x3937)) % 112.37/112.12 [394]~E(x3941,x3942)+E(f523(x3943,x3944,x3945,x3941,x3946,x3947),f523(x3943,x3944,x3945,x3942,x3946,x3947)) % 112.37/112.12 [395]~E(x3951,x3952)+E(f523(x3953,x3954,x3955,x3956,x3951,x3957),f523(x3953,x3954,x3955,x3956,x3952,x3957)) % 112.37/112.12 [396]~E(x3961,x3962)+E(f523(x3963,x3964,x3965,x3966,x3967,x3961),f523(x3963,x3964,x3965,x3966,x3967,x3962)) % 112.37/112.12 [397]~E(x3971,x3972)+E(f436(x3971,x3973,x3974),f436(x3972,x3973,x3974)) % 112.37/112.12 [398]~E(x3981,x3982)+E(f436(x3983,x3981,x3984),f436(x3983,x3982,x3984)) % 112.37/112.12 [399]~E(x3991,x3992)+E(f436(x3993,x3994,x3991),f436(x3993,x3994,x3992)) % 112.37/112.12 [400]~E(x4001,x4002)+E(f79(x4001,x4003),f79(x4002,x4003)) % 112.37/112.12 [401]~E(x4011,x4012)+E(f79(x4013,x4011),f79(x4013,x4012)) % 112.37/112.12 [402]~E(x4021,x4022)+E(f512(x4021),f512(x4022)) % 112.37/112.12 [403]~E(x4031,x4032)+E(f324(x4031),f324(x4032)) % 112.37/112.12 [404]~E(x4041,x4042)+E(f826(x4041,x4043,x4044,x4045,x4046,x4047),f826(x4042,x4043,x4044,x4045,x4046,x4047)) % 112.37/112.12 [405]~E(x4051,x4052)+E(f826(x4053,x4051,x4054,x4055,x4056,x4057),f826(x4053,x4052,x4054,x4055,x4056,x4057)) % 112.37/112.12 [406]~E(x4061,x4062)+E(f826(x4063,x4064,x4061,x4065,x4066,x4067),f826(x4063,x4064,x4062,x4065,x4066,x4067)) % 112.37/112.12 [407]~E(x4071,x4072)+E(f826(x4073,x4074,x4075,x4071,x4076,x4077),f826(x4073,x4074,x4075,x4072,x4076,x4077)) % 112.37/112.12 [408]~E(x4081,x4082)+E(f826(x4083,x4084,x4085,x4086,x4081,x4087),f826(x4083,x4084,x4085,x4086,x4082,x4087)) % 112.37/112.12 [409]~E(x4091,x4092)+E(f826(x4093,x4094,x4095,x4096,x4097,x4091),f826(x4093,x4094,x4095,x4096,x4097,x4092)) % 112.37/112.12 [410]~E(x4101,x4102)+E(f143(x4101,x4103),f143(x4102,x4103)) % 112.37/112.12 [411]~E(x4111,x4112)+E(f143(x4113,x4111),f143(x4113,x4112)) % 112.37/112.12 [412]~E(x4121,x4122)+E(f253(x4121,x4123),f253(x4122,x4123)) % 112.37/112.12 [413]~E(x4131,x4132)+E(f253(x4133,x4131),f253(x4133,x4132)) % 112.37/112.12 [414]~E(x4141,x4142)+E(f139(x4141,x4143,x4144,x4145,x4146),f139(x4142,x4143,x4144,x4145,x4146)) % 112.37/112.12 [415]~E(x4151,x4152)+E(f139(x4153,x4151,x4154,x4155,x4156),f139(x4153,x4152,x4154,x4155,x4156)) % 112.37/112.12 [416]~E(x4161,x4162)+E(f139(x4163,x4164,x4161,x4165,x4166),f139(x4163,x4164,x4162,x4165,x4166)) % 112.37/112.12 [417]~E(x4171,x4172)+E(f139(x4173,x4174,x4175,x4171,x4176),f139(x4173,x4174,x4175,x4172,x4176)) % 112.37/112.12 [418]~E(x4181,x4182)+E(f139(x4183,x4184,x4185,x4186,x4181),f139(x4183,x4184,x4185,x4186,x4182)) % 112.37/112.12 [419]~E(x4191,x4192)+E(f695(x4191,x4193,x4194),f695(x4192,x4193,x4194)) % 112.37/112.12 [420]~E(x4201,x4202)+E(f695(x4203,x4201,x4204),f695(x4203,x4202,x4204)) % 112.37/112.12 [421]~E(x4211,x4212)+E(f695(x4213,x4214,x4211),f695(x4213,x4214,x4212)) % 112.37/112.12 [422]~E(x4221,x4222)+E(f150(x4221,x4223),f150(x4222,x4223)) % 112.37/112.12 [423]~E(x4231,x4232)+E(f150(x4233,x4231),f150(x4233,x4232)) % 112.37/112.12 [424]~E(x4241,x4242)+E(f310(x4241,x4243,x4244,x4245),f310(x4242,x4243,x4244,x4245)) % 112.37/112.12 [425]~E(x4251,x4252)+E(f310(x4253,x4251,x4254,x4255),f310(x4253,x4252,x4254,x4255)) % 112.37/112.12 [426]~E(x4261,x4262)+E(f310(x4263,x4264,x4261,x4265),f310(x4263,x4264,x4262,x4265)) % 112.37/112.12 [427]~E(x4271,x4272)+E(f310(x4273,x4274,x4275,x4271),f310(x4273,x4274,x4275,x4272)) % 112.37/112.12 [428]~E(x4281,x4282)+E(f282(x4281,x4283),f282(x4282,x4283)) % 112.37/112.12 [429]~E(x4291,x4292)+E(f282(x4293,x4291),f282(x4293,x4292)) % 112.37/112.12 [430]~E(x4301,x4302)+E(f60(x4301,x4303,x4304),f60(x4302,x4303,x4304)) % 112.37/112.12 [431]~E(x4311,x4312)+E(f60(x4313,x4311,x4314),f60(x4313,x4312,x4314)) % 112.37/112.12 [432]~E(x4321,x4322)+E(f60(x4323,x4324,x4321),f60(x4323,x4324,x4322)) % 112.37/112.12 [433]~E(x4331,x4332)+E(f484(x4331,x4333,x4334,x4335,x4336,x4337,x4338),f484(x4332,x4333,x4334,x4335,x4336,x4337,x4338)) % 112.37/112.12 [434]~E(x4341,x4342)+E(f484(x4343,x4341,x4344,x4345,x4346,x4347,x4348),f484(x4343,x4342,x4344,x4345,x4346,x4347,x4348)) % 112.37/112.12 [435]~E(x4351,x4352)+E(f484(x4353,x4354,x4351,x4355,x4356,x4357,x4358),f484(x4353,x4354,x4352,x4355,x4356,x4357,x4358)) % 112.37/112.12 [436]~E(x4361,x4362)+E(f484(x4363,x4364,x4365,x4361,x4366,x4367,x4368),f484(x4363,x4364,x4365,x4362,x4366,x4367,x4368)) % 112.37/112.12 [437]~E(x4371,x4372)+E(f484(x4373,x4374,x4375,x4376,x4371,x4377,x4378),f484(x4373,x4374,x4375,x4376,x4372,x4377,x4378)) % 112.37/112.12 [438]~E(x4381,x4382)+E(f484(x4383,x4384,x4385,x4386,x4387,x4381,x4388),f484(x4383,x4384,x4385,x4386,x4387,x4382,x4388)) % 112.37/112.12 [439]~E(x4391,x4392)+E(f484(x4393,x4394,x4395,x4396,x4397,x4398,x4391),f484(x4393,x4394,x4395,x4396,x4397,x4398,x4392)) % 112.37/112.12 [440]~E(x4401,x4402)+E(f126(x4401,x4403),f126(x4402,x4403)) % 112.37/112.12 [441]~E(x4411,x4412)+E(f126(x4413,x4411),f126(x4413,x4412)) % 112.37/112.12 [442]~E(x4421,x4422)+E(f147(x4421,x4423),f147(x4422,x4423)) % 112.37/112.12 [443]~E(x4431,x4432)+E(f147(x4433,x4431),f147(x4433,x4432)) % 112.37/112.12 [444]~E(x4441,x4442)+E(f148(x4441,x4443),f148(x4442,x4443)) % 112.37/112.12 [445]~E(x4451,x4452)+E(f148(x4453,x4451),f148(x4453,x4452)) % 112.37/112.12 [446]~E(x4461,x4462)+E(f118(x4461,x4463),f118(x4462,x4463)) % 112.37/112.12 [447]~E(x4471,x4472)+E(f118(x4473,x4471),f118(x4473,x4472)) % 112.37/112.12 [448]~E(x4481,x4482)+E(f145(x4481,x4483,x4484),f145(x4482,x4483,x4484)) % 112.37/112.12 [449]~E(x4491,x4492)+E(f145(x4493,x4491,x4494),f145(x4493,x4492,x4494)) % 112.37/112.12 [450]~E(x4501,x4502)+E(f145(x4503,x4504,x4501),f145(x4503,x4504,x4502)) % 112.37/112.12 [451]~E(x4511,x4512)+E(f254(x4511,x4513),f254(x4512,x4513)) % 112.37/112.12 [452]~E(x4521,x4522)+E(f254(x4523,x4521),f254(x4523,x4522)) % 112.37/112.12 [453]~E(x4531,x4532)+E(f584(x4531,x4533,x4534),f584(x4532,x4533,x4534)) % 112.37/112.12 [454]~E(x4541,x4542)+E(f584(x4543,x4541,x4544),f584(x4543,x4542,x4544)) % 112.37/112.12 [455]~E(x4551,x4552)+E(f584(x4553,x4554,x4551),f584(x4553,x4554,x4552)) % 112.37/112.12 [456]~E(x4561,x4562)+E(f16(x4561,x4563),f16(x4562,x4563)) % 112.37/112.12 [457]~E(x4571,x4572)+E(f16(x4573,x4571),f16(x4573,x4572)) % 112.37/112.12 [458]~E(x4581,x4582)+E(f45(x4581,x4583),f45(x4582,x4583)) % 112.37/112.12 [459]~E(x4591,x4592)+E(f45(x4593,x4591),f45(x4593,x4592)) % 112.37/112.12 [460]~E(x4601,x4602)+E(f828(x4601,x4603,x4604,x4605,x4606,x4607,x4608,x4609),f828(x4602,x4603,x4604,x4605,x4606,x4607,x4608,x4609)) % 112.37/112.12 [461]~E(x4611,x4612)+E(f828(x4613,x4611,x4614,x4615,x4616,x4617,x4618,x4619),f828(x4613,x4612,x4614,x4615,x4616,x4617,x4618,x4619)) % 112.37/112.12 [462]~E(x4621,x4622)+E(f828(x4623,x4624,x4621,x4625,x4626,x4627,x4628,x4629),f828(x4623,x4624,x4622,x4625,x4626,x4627,x4628,x4629)) % 112.37/112.12 [463]~E(x4631,x4632)+E(f828(x4633,x4634,x4635,x4631,x4636,x4637,x4638,x4639),f828(x4633,x4634,x4635,x4632,x4636,x4637,x4638,x4639)) % 112.37/112.12 [464]~E(x4641,x4642)+E(f828(x4643,x4644,x4645,x4646,x4641,x4647,x4648,x4649),f828(x4643,x4644,x4645,x4646,x4642,x4647,x4648,x4649)) % 112.37/112.12 [465]~E(x4651,x4652)+E(f828(x4653,x4654,x4655,x4656,x4657,x4651,x4658,x4659),f828(x4653,x4654,x4655,x4656,x4657,x4652,x4658,x4659)) % 112.37/112.12 [466]~E(x4661,x4662)+E(f828(x4663,x4664,x4665,x4666,x4667,x4668,x4661,x4669),f828(x4663,x4664,x4665,x4666,x4667,x4668,x4662,x4669)) % 112.37/112.12 [467]~E(x4671,x4672)+E(f828(x4673,x4674,x4675,x4676,x4677,x4678,x4679,x4671),f828(x4673,x4674,x4675,x4676,x4677,x4678,x4679,x4672)) % 112.37/112.12 [468]~E(x4681,x4682)+E(f766(x4681,x4683,x4684,x4685,x4686,x4687,x4688),f766(x4682,x4683,x4684,x4685,x4686,x4687,x4688)) % 112.37/112.12 [469]~E(x4691,x4692)+E(f766(x4693,x4691,x4694,x4695,x4696,x4697,x4698),f766(x4693,x4692,x4694,x4695,x4696,x4697,x4698)) % 112.37/112.12 [470]~E(x4701,x4702)+E(f766(x4703,x4704,x4701,x4705,x4706,x4707,x4708),f766(x4703,x4704,x4702,x4705,x4706,x4707,x4708)) % 112.37/112.12 [471]~E(x4711,x4712)+E(f766(x4713,x4714,x4715,x4711,x4716,x4717,x4718),f766(x4713,x4714,x4715,x4712,x4716,x4717,x4718)) % 112.37/112.12 [472]~E(x4721,x4722)+E(f766(x4723,x4724,x4725,x4726,x4721,x4727,x4728),f766(x4723,x4724,x4725,x4726,x4722,x4727,x4728)) % 112.37/112.12 [473]~E(x4731,x4732)+E(f766(x4733,x4734,x4735,x4736,x4737,x4731,x4738),f766(x4733,x4734,x4735,x4736,x4737,x4732,x4738)) % 112.37/112.12 [474]~E(x4741,x4742)+E(f766(x4743,x4744,x4745,x4746,x4747,x4748,x4741),f766(x4743,x4744,x4745,x4746,x4747,x4748,x4742)) % 112.37/112.12 [475]~E(x4751,x4752)+E(f804(x4751,x4753),f804(x4752,x4753)) % 112.37/112.12 [476]~E(x4761,x4762)+E(f804(x4763,x4761),f804(x4763,x4762)) % 112.37/112.12 [477]~E(x4771,x4772)+E(f305(x4771,x4773),f305(x4772,x4773)) % 112.37/112.12 [478]~E(x4781,x4782)+E(f305(x4783,x4781),f305(x4783,x4782)) % 112.37/112.12 [479]~E(x4791,x4792)+E(f769(x4791,x4793,x4794,x4795,x4796),f769(x4792,x4793,x4794,x4795,x4796)) % 112.37/112.12 [480]~E(x4801,x4802)+E(f769(x4803,x4801,x4804,x4805,x4806),f769(x4803,x4802,x4804,x4805,x4806)) % 112.37/112.12 [481]~E(x4811,x4812)+E(f769(x4813,x4814,x4811,x4815,x4816),f769(x4813,x4814,x4812,x4815,x4816)) % 112.37/112.12 [482]~E(x4821,x4822)+E(f769(x4823,x4824,x4825,x4821,x4826),f769(x4823,x4824,x4825,x4822,x4826)) % 112.37/112.12 [483]~E(x4831,x4832)+E(f769(x4833,x4834,x4835,x4836,x4831),f769(x4833,x4834,x4835,x4836,x4832)) % 112.37/112.12 [484]~E(x4841,x4842)+E(f165(x4841),f165(x4842)) % 112.37/112.12 [485]~E(x4851,x4852)+E(f758(x4851,x4853,x4854,x4855),f758(x4852,x4853,x4854,x4855)) % 112.37/112.12 [486]~E(x4861,x4862)+E(f758(x4863,x4861,x4864,x4865),f758(x4863,x4862,x4864,x4865)) % 112.37/112.12 [487]~E(x4871,x4872)+E(f758(x4873,x4874,x4871,x4875),f758(x4873,x4874,x4872,x4875)) % 112.37/112.12 [488]~E(x4881,x4882)+E(f758(x4883,x4884,x4885,x4881),f758(x4883,x4884,x4885,x4882)) % 112.37/112.12 [489]~E(x4891,x4892)+E(f676(x4891,x4893,x4894,x4895,x4896),f676(x4892,x4893,x4894,x4895,x4896)) % 112.37/112.12 [490]~E(x4901,x4902)+E(f676(x4903,x4901,x4904,x4905,x4906),f676(x4903,x4902,x4904,x4905,x4906)) % 112.37/112.12 [491]~E(x4911,x4912)+E(f676(x4913,x4914,x4911,x4915,x4916),f676(x4913,x4914,x4912,x4915,x4916)) % 112.37/112.12 [492]~E(x4921,x4922)+E(f676(x4923,x4924,x4925,x4921,x4926),f676(x4923,x4924,x4925,x4922,x4926)) % 112.37/112.12 [493]~E(x4931,x4932)+E(f676(x4933,x4934,x4935,x4936,x4931),f676(x4933,x4934,x4935,x4936,x4932)) % 112.37/112.12 [494]~E(x4941,x4942)+E(f169(x4941,x4943),f169(x4942,x4943)) % 112.37/112.12 [495]~E(x4951,x4952)+E(f169(x4953,x4951),f169(x4953,x4952)) % 112.37/112.12 [496]~E(x4961,x4962)+E(f256(x4961,x4963),f256(x4962,x4963)) % 112.37/112.12 [497]~E(x4971,x4972)+E(f256(x4973,x4971),f256(x4973,x4972)) % 112.37/112.12 [498]~E(x4981,x4982)+E(f732(x4981,x4983,x4984),f732(x4982,x4983,x4984)) % 112.37/112.12 [499]~E(x4991,x4992)+E(f732(x4993,x4991,x4994),f732(x4993,x4992,x4994)) % 112.37/112.12 [500]~E(x5001,x5002)+E(f732(x5003,x5004,x5001),f732(x5003,x5004,x5002)) % 112.37/112.12 [501]~E(x5011,x5012)+E(f846(x5011,x5013,x5014),f846(x5012,x5013,x5014)) % 112.37/112.12 [502]~E(x5021,x5022)+E(f846(x5023,x5021,x5024),f846(x5023,x5022,x5024)) % 112.37/112.12 [503]~E(x5031,x5032)+E(f846(x5033,x5034,x5031),f846(x5033,x5034,x5032)) % 112.37/112.12 [504]~E(x5041,x5042)+E(f44(x5041,x5043),f44(x5042,x5043)) % 112.37/112.12 [505]~E(x5051,x5052)+E(f44(x5053,x5051),f44(x5053,x5052)) % 112.37/112.12 [506]~E(x5061,x5062)+E(f208(x5061,x5063),f208(x5062,x5063)) % 112.37/112.12 [507]~E(x5071,x5072)+E(f208(x5073,x5071),f208(x5073,x5072)) % 112.37/112.12 [508]~E(x5081,x5082)+E(f130(x5081,x5083,x5084),f130(x5082,x5083,x5084)) % 112.37/112.12 [509]~E(x5091,x5092)+E(f130(x5093,x5091,x5094),f130(x5093,x5092,x5094)) % 112.37/112.12 [510]~E(x5101,x5102)+E(f130(x5103,x5104,x5101),f130(x5103,x5104,x5102)) % 112.37/112.12 [511]~E(x5111,x5112)+E(f76(x5111,x5113),f76(x5112,x5113)) % 112.37/112.12 [512]~E(x5121,x5122)+E(f76(x5123,x5121),f76(x5123,x5122)) % 112.37/112.12 [513]~E(x5131,x5132)+E(f837(x5131,x5133,x5134),f837(x5132,x5133,x5134)) % 112.37/112.12 [514]~E(x5141,x5142)+E(f837(x5143,x5141,x5144),f837(x5143,x5142,x5144)) % 112.37/112.12 [515]~E(x5151,x5152)+E(f837(x5153,x5154,x5151),f837(x5153,x5154,x5152)) % 112.37/112.12 [516]~E(x5161,x5162)+E(f483(x5161,x5163,x5164,x5165,x5166,x5167,x5168),f483(x5162,x5163,x5164,x5165,x5166,x5167,x5168)) % 112.37/112.12 [517]~E(x5171,x5172)+E(f483(x5173,x5171,x5174,x5175,x5176,x5177,x5178),f483(x5173,x5172,x5174,x5175,x5176,x5177,x5178)) % 112.37/112.12 [518]~E(x5181,x5182)+E(f483(x5183,x5184,x5181,x5185,x5186,x5187,x5188),f483(x5183,x5184,x5182,x5185,x5186,x5187,x5188)) % 112.37/112.12 [519]~E(x5191,x5192)+E(f483(x5193,x5194,x5195,x5191,x5196,x5197,x5198),f483(x5193,x5194,x5195,x5192,x5196,x5197,x5198)) % 112.37/112.12 [520]~E(x5201,x5202)+E(f483(x5203,x5204,x5205,x5206,x5201,x5207,x5208),f483(x5203,x5204,x5205,x5206,x5202,x5207,x5208)) % 112.37/112.12 [521]~E(x5211,x5212)+E(f483(x5213,x5214,x5215,x5216,x5217,x5211,x5218),f483(x5213,x5214,x5215,x5216,x5217,x5212,x5218)) % 112.37/112.12 [522]~E(x5221,x5222)+E(f483(x5223,x5224,x5225,x5226,x5227,x5228,x5221),f483(x5223,x5224,x5225,x5226,x5227,x5228,x5222)) % 112.37/112.12 [523]~E(x5231,x5232)+E(f136(x5231,x5233),f136(x5232,x5233)) % 112.37/112.12 [524]~E(x5241,x5242)+E(f136(x5243,x5241),f136(x5243,x5242)) % 112.37/112.12 [525]~E(x5251,x5252)+E(f116(x5251,x5253,x5254),f116(x5252,x5253,x5254)) % 112.37/112.12 [526]~E(x5261,x5262)+E(f116(x5263,x5261,x5264),f116(x5263,x5262,x5264)) % 112.37/112.12 [527]~E(x5271,x5272)+E(f116(x5273,x5274,x5271),f116(x5273,x5274,x5272)) % 112.37/112.12 [528]~E(x5281,x5282)+E(f276(x5281,x5283),f276(x5282,x5283)) % 112.37/112.12 [529]~E(x5291,x5292)+E(f276(x5293,x5291),f276(x5293,x5292)) % 112.37/112.12 [530]~E(x5301,x5302)+E(f481(x5301,x5303,x5304,x5305,x5306,x5307,x5308),f481(x5302,x5303,x5304,x5305,x5306,x5307,x5308)) % 112.37/112.12 [531]~E(x5311,x5312)+E(f481(x5313,x5311,x5314,x5315,x5316,x5317,x5318),f481(x5313,x5312,x5314,x5315,x5316,x5317,x5318)) % 112.37/112.12 [532]~E(x5321,x5322)+E(f481(x5323,x5324,x5321,x5325,x5326,x5327,x5328),f481(x5323,x5324,x5322,x5325,x5326,x5327,x5328)) % 112.37/112.12 [533]~E(x5331,x5332)+E(f481(x5333,x5334,x5335,x5331,x5336,x5337,x5338),f481(x5333,x5334,x5335,x5332,x5336,x5337,x5338)) % 112.37/112.12 [534]~E(x5341,x5342)+E(f481(x5343,x5344,x5345,x5346,x5341,x5347,x5348),f481(x5343,x5344,x5345,x5346,x5342,x5347,x5348)) % 112.37/112.12 [535]~E(x5351,x5352)+E(f481(x5353,x5354,x5355,x5356,x5357,x5351,x5358),f481(x5353,x5354,x5355,x5356,x5357,x5352,x5358)) % 112.37/112.12 [536]~E(x5361,x5362)+E(f481(x5363,x5364,x5365,x5366,x5367,x5368,x5361),f481(x5363,x5364,x5365,x5366,x5367,x5368,x5362)) % 112.37/112.12 [537]~E(x5371,x5372)+E(f373(x5371,x5373,x5374,x5375,x5376),f373(x5372,x5373,x5374,x5375,x5376)) % 112.37/112.12 [538]~E(x5381,x5382)+E(f373(x5383,x5381,x5384,x5385,x5386),f373(x5383,x5382,x5384,x5385,x5386)) % 112.37/112.12 [539]~E(x5391,x5392)+E(f373(x5393,x5394,x5391,x5395,x5396),f373(x5393,x5394,x5392,x5395,x5396)) % 112.37/112.12 [540]~E(x5401,x5402)+E(f373(x5403,x5404,x5405,x5401,x5406),f373(x5403,x5404,x5405,x5402,x5406)) % 112.37/112.12 [541]~E(x5411,x5412)+E(f373(x5413,x5414,x5415,x5416,x5411),f373(x5413,x5414,x5415,x5416,x5412)) % 112.37/112.12 [542]~E(x5421,x5422)+E(f789(x5421),f789(x5422)) % 112.37/112.12 [543]~E(x5431,x5432)+E(f11(x5431,x5433),f11(x5432,x5433)) % 112.37/112.12 [544]~E(x5441,x5442)+E(f11(x5443,x5441),f11(x5443,x5442)) % 112.37/112.12 [545]~E(x5451,x5452)+E(f311(x5451,x5453,x5454),f311(x5452,x5453,x5454)) % 112.37/112.12 [546]~E(x5461,x5462)+E(f311(x5463,x5461,x5464),f311(x5463,x5462,x5464)) % 112.37/112.12 [547]~E(x5471,x5472)+E(f311(x5473,x5474,x5471),f311(x5473,x5474,x5472)) % 112.37/112.12 [548]~E(x5481,x5482)+E(f821(x5481,x5483,x5484,x5485,x5486,x5487),f821(x5482,x5483,x5484,x5485,x5486,x5487)) % 112.37/112.12 [549]~E(x5491,x5492)+E(f821(x5493,x5491,x5494,x5495,x5496,x5497),f821(x5493,x5492,x5494,x5495,x5496,x5497)) % 112.37/112.12 [550]~E(x5501,x5502)+E(f821(x5503,x5504,x5501,x5505,x5506,x5507),f821(x5503,x5504,x5502,x5505,x5506,x5507)) % 112.37/112.12 [551]~E(x5511,x5512)+E(f821(x5513,x5514,x5515,x5511,x5516,x5517),f821(x5513,x5514,x5515,x5512,x5516,x5517)) % 112.37/112.12 [552]~E(x5521,x5522)+E(f821(x5523,x5524,x5525,x5526,x5521,x5527),f821(x5523,x5524,x5525,x5526,x5522,x5527)) % 112.37/112.12 [553]~E(x5531,x5532)+E(f821(x5533,x5534,x5535,x5536,x5537,x5531),f821(x5533,x5534,x5535,x5536,x5537,x5532)) % 112.37/112.12 [554]~E(x5541,x5542)+E(f536(x5541,x5543,x5544,x5545),f536(x5542,x5543,x5544,x5545)) % 112.37/112.12 [555]~E(x5551,x5552)+E(f536(x5553,x5551,x5554,x5555),f536(x5553,x5552,x5554,x5555)) % 112.37/112.12 [556]~E(x5561,x5562)+E(f536(x5563,x5564,x5561,x5565),f536(x5563,x5564,x5562,x5565)) % 112.37/112.12 [557]~E(x5571,x5572)+E(f536(x5573,x5574,x5575,x5571),f536(x5573,x5574,x5575,x5572)) % 112.37/112.12 [558]~E(x5581,x5582)+E(f85(x5581,x5583,x5584,x5585),f85(x5582,x5583,x5584,x5585)) % 112.37/112.12 [559]~E(x5591,x5592)+E(f85(x5593,x5591,x5594,x5595),f85(x5593,x5592,x5594,x5595)) % 112.37/112.12 [560]~E(x5601,x5602)+E(f85(x5603,x5604,x5601,x5605),f85(x5603,x5604,x5602,x5605)) % 112.37/112.12 [561]~E(x5611,x5612)+E(f85(x5613,x5614,x5615,x5611),f85(x5613,x5614,x5615,x5612)) % 112.37/112.12 [562]~E(x5621,x5622)+E(f848(x5621,x5623,x5624),f848(x5622,x5623,x5624)) % 112.37/112.12 [563]~E(x5631,x5632)+E(f848(x5633,x5631,x5634),f848(x5633,x5632,x5634)) % 112.37/112.12 [564]~E(x5641,x5642)+E(f848(x5643,x5644,x5641),f848(x5643,x5644,x5642)) % 112.37/112.12 [565]~E(x5651,x5652)+E(f17(x5651,x5653),f17(x5652,x5653)) % 112.37/112.12 [566]~E(x5661,x5662)+E(f17(x5663,x5661),f17(x5663,x5662)) % 112.37/112.12 [567]~E(x5671,x5672)+E(f723(x5671,x5673,x5674,x5675,x5676),f723(x5672,x5673,x5674,x5675,x5676)) % 112.37/112.12 [568]~E(x5681,x5682)+E(f723(x5683,x5681,x5684,x5685,x5686),f723(x5683,x5682,x5684,x5685,x5686)) % 112.37/112.12 [569]~E(x5691,x5692)+E(f723(x5693,x5694,x5691,x5695,x5696),f723(x5693,x5694,x5692,x5695,x5696)) % 112.37/112.12 [570]~E(x5701,x5702)+E(f723(x5703,x5704,x5705,x5701,x5706),f723(x5703,x5704,x5705,x5702,x5706)) % 112.37/112.12 [571]~E(x5711,x5712)+E(f723(x5713,x5714,x5715,x5716,x5711),f723(x5713,x5714,x5715,x5716,x5712)) % 112.37/112.12 [572]~E(x5721,x5722)+E(f131(x5721),f131(x5722)) % 112.37/112.12 [573]~E(x5731,x5732)+E(f787(x5731),f787(x5732)) % 112.37/112.12 [574]~E(x5741,x5742)+E(f353(x5741,x5743),f353(x5742,x5743)) % 112.37/112.12 [575]~E(x5751,x5752)+E(f353(x5753,x5751),f353(x5753,x5752)) % 112.37/112.12 [576]~E(x5761,x5762)+E(f814(x5761,x5763,x5764,x5765),f814(x5762,x5763,x5764,x5765)) % 112.37/112.12 [577]~E(x5771,x5772)+E(f814(x5773,x5771,x5774,x5775),f814(x5773,x5772,x5774,x5775)) % 112.37/112.12 [578]~E(x5781,x5782)+E(f814(x5783,x5784,x5781,x5785),f814(x5783,x5784,x5782,x5785)) % 112.37/112.12 [579]~E(x5791,x5792)+E(f814(x5793,x5794,x5795,x5791),f814(x5793,x5794,x5795,x5792)) % 112.37/112.12 [580]~E(x5801,x5802)+E(f887(x5801,x5803,x5804),f887(x5802,x5803,x5804)) % 112.37/112.12 [581]~E(x5811,x5812)+E(f887(x5813,x5811,x5814),f887(x5813,x5812,x5814)) % 112.37/112.12 [582]~E(x5821,x5822)+E(f887(x5823,x5824,x5821),f887(x5823,x5824,x5822)) % 112.37/112.12 [583]~E(x5831,x5832)+E(f138(x5831,x5833,x5834),f138(x5832,x5833,x5834)) % 112.37/112.12 [584]~E(x5841,x5842)+E(f138(x5843,x5841,x5844),f138(x5843,x5842,x5844)) % 112.37/112.12 [585]~E(x5851,x5852)+E(f138(x5853,x5854,x5851),f138(x5853,x5854,x5852)) % 112.37/112.12 [586]~E(x5861,x5862)+E(f503(x5861,x5863,x5864,x5865,x5866,x5867,x5868),f503(x5862,x5863,x5864,x5865,x5866,x5867,x5868)) % 112.37/112.12 [587]~E(x5871,x5872)+E(f503(x5873,x5871,x5874,x5875,x5876,x5877,x5878),f503(x5873,x5872,x5874,x5875,x5876,x5877,x5878)) % 112.37/112.12 [588]~E(x5881,x5882)+E(f503(x5883,x5884,x5881,x5885,x5886,x5887,x5888),f503(x5883,x5884,x5882,x5885,x5886,x5887,x5888)) % 112.37/112.12 [589]~E(x5891,x5892)+E(f503(x5893,x5894,x5895,x5891,x5896,x5897,x5898),f503(x5893,x5894,x5895,x5892,x5896,x5897,x5898)) % 112.37/112.12 [590]~E(x5901,x5902)+E(f503(x5903,x5904,x5905,x5906,x5901,x5907,x5908),f503(x5903,x5904,x5905,x5906,x5902,x5907,x5908)) % 112.37/112.12 [591]~E(x5911,x5912)+E(f503(x5913,x5914,x5915,x5916,x5917,x5911,x5918),f503(x5913,x5914,x5915,x5916,x5917,x5912,x5918)) % 112.37/112.12 [592]~E(x5921,x5922)+E(f503(x5923,x5924,x5925,x5926,x5927,x5928,x5921),f503(x5923,x5924,x5925,x5926,x5927,x5928,x5922)) % 112.37/112.12 [593]~E(x5931,x5932)+E(f166(x5931,x5933,x5934),f166(x5932,x5933,x5934)) % 112.37/112.12 [594]~E(x5941,x5942)+E(f166(x5943,x5941,x5944),f166(x5943,x5942,x5944)) % 112.37/112.12 [595]~E(x5951,x5952)+E(f166(x5953,x5954,x5951),f166(x5953,x5954,x5952)) % 112.37/112.12 [596]~E(x5961,x5962)+E(f857(x5961,x5963,x5964),f857(x5962,x5963,x5964)) % 112.37/112.12 [597]~E(x5971,x5972)+E(f857(x5973,x5971,x5974),f857(x5973,x5972,x5974)) % 112.37/112.12 [598]~E(x5981,x5982)+E(f857(x5983,x5984,x5981),f857(x5983,x5984,x5982)) % 112.37/112.12 [599]~E(x5991,x5992)+E(f53(x5991),f53(x5992)) % 112.37/112.12 [600]~E(x6001,x6002)+E(f681(x6001,x6003,x6004,x6005,x6006),f681(x6002,x6003,x6004,x6005,x6006)) % 112.37/112.12 [601]~E(x6011,x6012)+E(f681(x6013,x6011,x6014,x6015,x6016),f681(x6013,x6012,x6014,x6015,x6016)) % 112.37/112.12 [602]~E(x6021,x6022)+E(f681(x6023,x6024,x6021,x6025,x6026),f681(x6023,x6024,x6022,x6025,x6026)) % 112.37/112.12 [603]~E(x6031,x6032)+E(f681(x6033,x6034,x6035,x6031,x6036),f681(x6033,x6034,x6035,x6032,x6036)) % 112.37/112.12 [604]~E(x6041,x6042)+E(f681(x6043,x6044,x6045,x6046,x6041),f681(x6043,x6044,x6045,x6046,x6042)) % 112.37/112.12 [605]~E(x6051,x6052)+E(f202(x6051),f202(x6052)) % 112.37/112.12 [606]~E(x6061,x6062)+E(f452(x6061,x6063,x6064),f452(x6062,x6063,x6064)) % 112.37/112.12 [607]~E(x6071,x6072)+E(f452(x6073,x6071,x6074),f452(x6073,x6072,x6074)) % 112.37/112.12 [608]~E(x6081,x6082)+E(f452(x6083,x6084,x6081),f452(x6083,x6084,x6082)) % 112.37/112.12 [609]~E(x6091,x6092)+E(f284(x6091,x6093,x6094),f284(x6092,x6093,x6094)) % 112.37/112.12 [610]~E(x6101,x6102)+E(f284(x6103,x6101,x6104),f284(x6103,x6102,x6104)) % 112.37/112.12 [611]~E(x6111,x6112)+E(f284(x6113,x6114,x6111),f284(x6113,x6114,x6112)) % 112.37/112.12 [612]~E(x6121,x6122)+E(f59(x6121,x6123,x6124),f59(x6122,x6123,x6124)) % 112.37/112.12 [613]~E(x6131,x6132)+E(f59(x6133,x6131,x6134),f59(x6133,x6132,x6134)) % 112.37/112.12 [614]~E(x6141,x6142)+E(f59(x6143,x6144,x6141),f59(x6143,x6144,x6142)) % 112.37/112.12 [615]~E(x6151,x6152)+E(f170(x6151),f170(x6152)) % 112.37/112.12 [616]~E(x6161,x6162)+E(f380(x6161,x6163),f380(x6162,x6163)) % 112.37/112.12 [617]~E(x6171,x6172)+E(f380(x6173,x6171),f380(x6173,x6172)) % 112.37/112.12 [618]~E(x6181,x6182)+E(f394(x6181,x6183,x6184,x6185),f394(x6182,x6183,x6184,x6185)) % 112.37/112.12 [619]~E(x6191,x6192)+E(f394(x6193,x6191,x6194,x6195),f394(x6193,x6192,x6194,x6195)) % 112.37/112.12 [620]~E(x6201,x6202)+E(f394(x6203,x6204,x6201,x6205),f394(x6203,x6204,x6202,x6205)) % 112.37/112.12 [621]~E(x6211,x6212)+E(f394(x6213,x6214,x6215,x6211),f394(x6213,x6214,x6215,x6212)) % 112.37/112.12 [622]~E(x6221,x6222)+E(f689(x6221,x6223),f689(x6222,x6223)) % 112.37/112.12 [623]~E(x6231,x6232)+E(f689(x6233,x6231),f689(x6233,x6232)) % 112.37/112.12 [624]~E(x6241,x6242)+E(f86(x6241),f86(x6242)) % 112.37/112.12 [625]~E(x6251,x6252)+E(f283(x6251,x6253),f283(x6252,x6253)) % 112.37/112.12 [626]~E(x6261,x6262)+E(f283(x6263,x6261),f283(x6263,x6262)) % 112.37/112.12 [627]~E(x6271,x6272)+E(f204(x6271,x6273),f204(x6272,x6273)) % 112.37/112.12 [628]~E(x6281,x6282)+E(f204(x6283,x6281),f204(x6283,x6282)) % 112.37/112.12 [629]~E(x6291,x6292)+E(f658(x6291,x6293,x6294,x6295),f658(x6292,x6293,x6294,x6295)) % 112.37/112.12 [630]~E(x6301,x6302)+E(f658(x6303,x6301,x6304,x6305),f658(x6303,x6302,x6304,x6305)) % 112.37/112.12 [631]~E(x6311,x6312)+E(f658(x6313,x6314,x6311,x6315),f658(x6313,x6314,x6312,x6315)) % 112.37/112.12 [632]~E(x6321,x6322)+E(f658(x6323,x6324,x6325,x6321),f658(x6323,x6324,x6325,x6322)) % 112.37/112.12 [633]~E(x6331,x6332)+E(f645(x6331,x6333,x6334),f645(x6332,x6333,x6334)) % 112.37/112.12 [634]~E(x6341,x6342)+E(f645(x6343,x6341,x6344),f645(x6343,x6342,x6344)) % 112.37/112.12 [635]~E(x6351,x6352)+E(f645(x6353,x6354,x6351),f645(x6353,x6354,x6352)) % 112.37/112.12 [636]~E(x6361,x6362)+E(f205(x6361,x6363),f205(x6362,x6363)) % 112.37/112.12 [637]~E(x6371,x6372)+E(f205(x6373,x6371),f205(x6373,x6372)) % 112.37/112.12 [638]~E(x6381,x6382)+E(f881(x6381),f881(x6382)) % 112.37/112.12 [639]~E(x6391,x6392)+E(f424(x6391,x6393,x6394),f424(x6392,x6393,x6394)) % 112.37/112.12 [640]~E(x6401,x6402)+E(f424(x6403,x6401,x6404),f424(x6403,x6402,x6404)) % 112.37/112.12 [641]~E(x6411,x6412)+E(f424(x6413,x6414,x6411),f424(x6413,x6414,x6412)) % 112.37/112.12 [642]~E(x6421,x6422)+E(f164(x6421,x6423,x6424),f164(x6422,x6423,x6424)) % 112.37/112.12 [643]~E(x6431,x6432)+E(f164(x6433,x6431,x6434),f164(x6433,x6432,x6434)) % 112.37/112.12 [644]~E(x6441,x6442)+E(f164(x6443,x6444,x6441),f164(x6443,x6444,x6442)) % 112.37/112.12 [645]~E(x6451,x6452)+E(f12(x6451,x6453),f12(x6452,x6453)) % 112.37/112.12 [646]~E(x6461,x6462)+E(f12(x6463,x6461),f12(x6463,x6462)) % 112.37/112.12 [647]~E(x6471,x6472)+E(f890(x6471,x6473),f890(x6472,x6473)) % 112.37/112.12 [648]~E(x6481,x6482)+E(f890(x6483,x6481),f890(x6483,x6482)) % 112.37/112.12 [649]~E(x6491,x6492)+E(f784(x6491,x6493),f784(x6492,x6493)) % 112.37/112.12 [650]~E(x6501,x6502)+E(f784(x6503,x6501),f784(x6503,x6502)) % 112.37/112.12 [651]~E(x6511,x6512)+E(f121(x6511,x6513,x6514,x6515),f121(x6512,x6513,x6514,x6515)) % 112.37/112.12 [652]~E(x6521,x6522)+E(f121(x6523,x6521,x6524,x6525),f121(x6523,x6522,x6524,x6525)) % 112.37/112.12 [653]~E(x6531,x6532)+E(f121(x6533,x6534,x6531,x6535),f121(x6533,x6534,x6532,x6535)) % 112.37/112.12 [654]~E(x6541,x6542)+E(f121(x6543,x6544,x6545,x6541),f121(x6543,x6544,x6545,x6542)) % 112.37/112.12 [655]~E(x6551,x6552)+E(f482(x6551,x6553,x6554,x6555,x6556),f482(x6552,x6553,x6554,x6555,x6556)) % 112.37/112.12 [656]~E(x6561,x6562)+E(f482(x6563,x6561,x6564,x6565,x6566),f482(x6563,x6562,x6564,x6565,x6566)) % 112.37/112.12 [657]~E(x6571,x6572)+E(f482(x6573,x6574,x6571,x6575,x6576),f482(x6573,x6574,x6572,x6575,x6576)) % 112.37/112.12 [658]~E(x6581,x6582)+E(f482(x6583,x6584,x6585,x6581,x6586),f482(x6583,x6584,x6585,x6582,x6586)) % 112.37/112.12 [659]~E(x6591,x6592)+E(f482(x6593,x6594,x6595,x6596,x6591),f482(x6593,x6594,x6595,x6596,x6592)) % 112.37/112.12 [660]~E(x6601,x6602)+E(f39(x6601),f39(x6602)) % 112.37/112.12 [661]~E(x6611,x6612)+E(f82(x6611),f82(x6612)) % 112.37/112.12 [662]~E(x6621,x6622)+E(f764(x6621,x6623,x6624),f764(x6622,x6623,x6624)) % 112.37/112.12 [663]~E(x6631,x6632)+E(f764(x6633,x6631,x6634),f764(x6633,x6632,x6634)) % 112.37/112.12 [664]~E(x6641,x6642)+E(f764(x6643,x6644,x6641),f764(x6643,x6644,x6642)) % 112.37/112.12 [665]~E(x6651,x6652)+E(f502(x6651,x6653,x6654,x6655,x6656,x6657,x6658),f502(x6652,x6653,x6654,x6655,x6656,x6657,x6658)) % 112.37/112.12 [666]~E(x6661,x6662)+E(f502(x6663,x6661,x6664,x6665,x6666,x6667,x6668),f502(x6663,x6662,x6664,x6665,x6666,x6667,x6668)) % 112.37/112.12 [667]~E(x6671,x6672)+E(f502(x6673,x6674,x6671,x6675,x6676,x6677,x6678),f502(x6673,x6674,x6672,x6675,x6676,x6677,x6678)) % 112.37/112.12 [668]~E(x6681,x6682)+E(f502(x6683,x6684,x6685,x6681,x6686,x6687,x6688),f502(x6683,x6684,x6685,x6682,x6686,x6687,x6688)) % 112.37/112.12 [669]~E(x6691,x6692)+E(f502(x6693,x6694,x6695,x6696,x6691,x6697,x6698),f502(x6693,x6694,x6695,x6696,x6692,x6697,x6698)) % 112.37/112.12 [670]~E(x6701,x6702)+E(f502(x6703,x6704,x6705,x6706,x6707,x6701,x6708),f502(x6703,x6704,x6705,x6706,x6707,x6702,x6708)) % 112.37/112.12 [671]~E(x6711,x6712)+E(f502(x6713,x6714,x6715,x6716,x6717,x6718,x6711),f502(x6713,x6714,x6715,x6716,x6717,x6718,x6712)) % 112.37/112.12 [672]~E(x6721,x6722)+E(f736(x6721,x6723),f736(x6722,x6723)) % 112.37/112.12 [673]~E(x6731,x6732)+E(f736(x6733,x6731),f736(x6733,x6732)) % 112.37/112.12 [674]~E(x6741,x6742)+E(f812(x6741,x6743,x6744,x6745),f812(x6742,x6743,x6744,x6745)) % 112.37/112.12 [675]~E(x6751,x6752)+E(f812(x6753,x6751,x6754,x6755),f812(x6753,x6752,x6754,x6755)) % 112.37/112.12 [676]~E(x6761,x6762)+E(f812(x6763,x6764,x6761,x6765),f812(x6763,x6764,x6762,x6765)) % 112.37/112.12 [677]~E(x6771,x6772)+E(f812(x6773,x6774,x6775,x6771),f812(x6773,x6774,x6775,x6772)) % 112.37/112.12 [678]~E(x6781,x6782)+E(f445(x6781,x6783,x6784),f445(x6782,x6783,x6784)) % 112.37/112.12 [679]~E(x6791,x6792)+E(f445(x6793,x6791,x6794),f445(x6793,x6792,x6794)) % 112.37/112.12 [680]~E(x6801,x6802)+E(f445(x6803,x6804,x6801),f445(x6803,x6804,x6802)) % 112.37/112.12 [681]~E(x6811,x6812)+E(f388(x6811,x6813,x6814,x6815),f388(x6812,x6813,x6814,x6815)) % 112.37/112.12 [682]~E(x6821,x6822)+E(f388(x6823,x6821,x6824,x6825),f388(x6823,x6822,x6824,x6825)) % 112.37/112.12 [683]~E(x6831,x6832)+E(f388(x6833,x6834,x6831,x6835),f388(x6833,x6834,x6832,x6835)) % 112.37/112.12 [684]~E(x6841,x6842)+E(f388(x6843,x6844,x6845,x6841),f388(x6843,x6844,x6845,x6842)) % 112.37/112.12 [685]~E(x6851,x6852)+E(f684(x6851,x6853),f684(x6852,x6853)) % 112.37/112.12 [686]~E(x6861,x6862)+E(f684(x6863,x6861),f684(x6863,x6862)) % 112.37/112.12 [687]~E(x6871,x6872)+E(f588(x6871,x6873,x6874),f588(x6872,x6873,x6874)) % 112.37/112.12 [688]~E(x6881,x6882)+E(f588(x6883,x6881,x6884),f588(x6883,x6882,x6884)) % 112.37/112.12 [689]~E(x6891,x6892)+E(f588(x6893,x6894,x6891),f588(x6893,x6894,x6892)) % 112.37/112.12 [690]~E(x6901,x6902)+E(f339(x6901,x6903),f339(x6902,x6903)) % 112.37/112.12 [691]~E(x6911,x6912)+E(f339(x6913,x6911),f339(x6913,x6912)) % 112.37/112.12 [692]~E(x6921,x6922)+E(f733(x6921,x6923,x6924),f733(x6922,x6923,x6924)) % 112.37/112.12 [693]~E(x6931,x6932)+E(f733(x6933,x6931,x6934),f733(x6933,x6932,x6934)) % 112.37/112.12 [694]~E(x6941,x6942)+E(f733(x6943,x6944,x6941),f733(x6943,x6944,x6942)) % 112.37/112.12 [695]~E(x6951,x6952)+E(f700(x6951,x6953,x6954,x6955),f700(x6952,x6953,x6954,x6955)) % 112.37/112.12 [696]~E(x6961,x6962)+E(f700(x6963,x6961,x6964,x6965),f700(x6963,x6962,x6964,x6965)) % 112.37/112.12 [697]~E(x6971,x6972)+E(f700(x6973,x6974,x6971,x6975),f700(x6973,x6974,x6972,x6975)) % 112.37/112.12 [698]~E(x6981,x6982)+E(f700(x6983,x6984,x6985,x6981),f700(x6983,x6984,x6985,x6982)) % 112.37/112.12 [699]~E(x6991,x6992)+E(f263(x6991,x6993,x6994,x6995),f263(x6992,x6993,x6994,x6995)) % 112.37/112.12 [700]~E(x7001,x7002)+E(f263(x7003,x7001,x7004,x7005),f263(x7003,x7002,x7004,x7005)) % 112.37/112.12 [701]~E(x7011,x7012)+E(f263(x7013,x7014,x7011,x7015),f263(x7013,x7014,x7012,x7015)) % 112.37/112.12 [702]~E(x7021,x7022)+E(f263(x7023,x7024,x7025,x7021),f263(x7023,x7024,x7025,x7022)) % 112.37/112.12 [703]~E(x7031,x7032)+E(f334(x7031,x7033,x7034,x7035),f334(x7032,x7033,x7034,x7035)) % 112.37/112.12 [704]~E(x7041,x7042)+E(f334(x7043,x7041,x7044,x7045),f334(x7043,x7042,x7044,x7045)) % 112.37/112.12 [705]~E(x7051,x7052)+E(f334(x7053,x7054,x7051,x7055),f334(x7053,x7054,x7052,x7055)) % 112.37/112.12 [706]~E(x7061,x7062)+E(f334(x7063,x7064,x7065,x7061),f334(x7063,x7064,x7065,x7062)) % 112.37/112.12 [707]~E(x7071,x7072)+E(f238(x7071,x7073),f238(x7072,x7073)) % 112.37/112.12 [708]~E(x7081,x7082)+E(f238(x7083,x7081),f238(x7083,x7082)) % 112.37/112.12 [709]~E(x7091,x7092)+E(f679(x7091,x7093,x7094,x7095),f679(x7092,x7093,x7094,x7095)) % 112.37/112.12 [710]~E(x7101,x7102)+E(f679(x7103,x7101,x7104,x7105),f679(x7103,x7102,x7104,x7105)) % 112.37/112.12 [711]~E(x7111,x7112)+E(f679(x7113,x7114,x7111,x7115),f679(x7113,x7114,x7112,x7115)) % 112.37/112.12 [712]~E(x7121,x7122)+E(f679(x7123,x7124,x7125,x7121),f679(x7123,x7124,x7125,x7122)) % 112.37/112.12 [713]~E(x7131,x7132)+E(f799(x7131),f799(x7132)) % 112.37/112.12 [714]~E(x7141,x7142)+E(f753(x7141,x7143,x7144),f753(x7142,x7143,x7144)) % 112.37/112.12 [715]~E(x7151,x7152)+E(f753(x7153,x7151,x7154),f753(x7153,x7152,x7154)) % 112.37/112.12 [716]~E(x7161,x7162)+E(f753(x7163,x7164,x7161),f753(x7163,x7164,x7162)) % 112.37/112.12 [717]~E(x7171,x7172)+E(f323(x7171),f323(x7172)) % 112.37/112.12 [718]~E(x7181,x7182)+E(f274(x7181,x7183),f274(x7182,x7183)) % 112.37/112.12 [719]~E(x7191,x7192)+E(f274(x7193,x7191),f274(x7193,x7192)) % 112.37/112.12 [720]~E(x7201,x7202)+E(f632(x7201,x7203,x7204),f632(x7202,x7203,x7204)) % 112.37/112.12 [721]~E(x7211,x7212)+E(f632(x7213,x7211,x7214),f632(x7213,x7212,x7214)) % 112.37/112.12 [722]~E(x7221,x7222)+E(f632(x7223,x7224,x7221),f632(x7223,x7224,x7222)) % 112.37/112.12 [723]~E(x7231,x7232)+E(f435(x7231,x7233,x7234),f435(x7232,x7233,x7234)) % 112.37/112.12 [724]~E(x7241,x7242)+E(f435(x7243,x7241,x7244),f435(x7243,x7242,x7244)) % 112.37/112.12 [725]~E(x7251,x7252)+E(f435(x7253,x7254,x7251),f435(x7253,x7254,x7252)) % 112.37/112.12 [726]~E(x7261,x7262)+E(f46(x7261,x7263),f46(x7262,x7263)) % 112.37/112.12 [727]~E(x7271,x7272)+E(f46(x7273,x7271),f46(x7273,x7272)) % 112.37/112.12 [728]~E(x7281,x7282)+E(f501(x7281,x7283,x7284,x7285,x7286,x7287,x7288),f501(x7282,x7283,x7284,x7285,x7286,x7287,x7288)) % 112.37/112.12 [729]~E(x7291,x7292)+E(f501(x7293,x7291,x7294,x7295,x7296,x7297,x7298),f501(x7293,x7292,x7294,x7295,x7296,x7297,x7298)) % 112.37/112.12 [730]~E(x7301,x7302)+E(f501(x7303,x7304,x7301,x7305,x7306,x7307,x7308),f501(x7303,x7304,x7302,x7305,x7306,x7307,x7308)) % 112.37/112.12 [731]~E(x7311,x7312)+E(f501(x7313,x7314,x7315,x7311,x7316,x7317,x7318),f501(x7313,x7314,x7315,x7312,x7316,x7317,x7318)) % 112.37/112.12 [732]~E(x7321,x7322)+E(f501(x7323,x7324,x7325,x7326,x7321,x7327,x7328),f501(x7323,x7324,x7325,x7326,x7322,x7327,x7328)) % 112.37/112.12 [733]~E(x7331,x7332)+E(f501(x7333,x7334,x7335,x7336,x7337,x7331,x7338),f501(x7333,x7334,x7335,x7336,x7337,x7332,x7338)) % 112.37/112.12 [734]~E(x7341,x7342)+E(f501(x7343,x7344,x7345,x7346,x7347,x7348,x7341),f501(x7343,x7344,x7345,x7346,x7347,x7348,x7342)) % 112.37/112.12 [735]~E(x7351,x7352)+E(f849(x7351,x7353,x7354),f849(x7352,x7353,x7354)) % 112.37/112.12 [736]~E(x7361,x7362)+E(f849(x7363,x7361,x7364),f849(x7363,x7362,x7364)) % 112.37/112.12 [737]~E(x7371,x7372)+E(f849(x7373,x7374,x7371),f849(x7373,x7374,x7372)) % 112.37/112.12 [738]~E(x7381,x7382)+E(f822(x7381,x7383,x7384,x7385,x7386,x7387,x7388,x7389),f822(x7382,x7383,x7384,x7385,x7386,x7387,x7388,x7389)) % 112.37/112.12 [739]~E(x7391,x7392)+E(f822(x7393,x7391,x7394,x7395,x7396,x7397,x7398,x7399),f822(x7393,x7392,x7394,x7395,x7396,x7397,x7398,x7399)) % 112.37/112.12 [740]~E(x7401,x7402)+E(f822(x7403,x7404,x7401,x7405,x7406,x7407,x7408,x7409),f822(x7403,x7404,x7402,x7405,x7406,x7407,x7408,x7409)) % 112.37/112.12 [741]~E(x7411,x7412)+E(f822(x7413,x7414,x7415,x7411,x7416,x7417,x7418,x7419),f822(x7413,x7414,x7415,x7412,x7416,x7417,x7418,x7419)) % 112.37/112.12 [742]~E(x7421,x7422)+E(f822(x7423,x7424,x7425,x7426,x7421,x7427,x7428,x7429),f822(x7423,x7424,x7425,x7426,x7422,x7427,x7428,x7429)) % 112.37/112.12 [743]~E(x7431,x7432)+E(f822(x7433,x7434,x7435,x7436,x7437,x7431,x7438,x7439),f822(x7433,x7434,x7435,x7436,x7437,x7432,x7438,x7439)) % 112.37/112.12 [744]~E(x7441,x7442)+E(f822(x7443,x7444,x7445,x7446,x7447,x7448,x7441,x7449),f822(x7443,x7444,x7445,x7446,x7447,x7448,x7442,x7449)) % 112.37/112.12 [745]~E(x7451,x7452)+E(f822(x7453,x7454,x7455,x7456,x7457,x7458,x7459,x7451),f822(x7453,x7454,x7455,x7456,x7457,x7458,x7459,x7452)) % 112.37/112.12 [746]~E(x7461,x7462)+E(f156(x7461,x7463,x7464),f156(x7462,x7463,x7464)) % 112.37/112.12 [747]~E(x7471,x7472)+E(f156(x7473,x7471,x7474),f156(x7473,x7472,x7474)) % 112.37/112.12 [748]~E(x7481,x7482)+E(f156(x7483,x7484,x7481),f156(x7483,x7484,x7482)) % 112.37/112.12 [749]~E(x7491,x7492)+E(f260(x7491,x7493),f260(x7492,x7493)) % 112.37/112.12 [750]~E(x7501,x7502)+E(f260(x7503,x7501),f260(x7503,x7502)) % 112.37/112.12 [751]~E(x7511,x7512)+E(f841(x7511,x7513,x7514,x7515,x7516,x7517,x7518),f841(x7512,x7513,x7514,x7515,x7516,x7517,x7518)) % 112.37/112.12 [752]~E(x7521,x7522)+E(f841(x7523,x7521,x7524,x7525,x7526,x7527,x7528),f841(x7523,x7522,x7524,x7525,x7526,x7527,x7528)) % 112.37/112.12 [753]~E(x7531,x7532)+E(f841(x7533,x7534,x7531,x7535,x7536,x7537,x7538),f841(x7533,x7534,x7532,x7535,x7536,x7537,x7538)) % 112.37/112.12 [754]~E(x7541,x7542)+E(f841(x7543,x7544,x7545,x7541,x7546,x7547,x7548),f841(x7543,x7544,x7545,x7542,x7546,x7547,x7548)) % 112.37/112.12 [755]~E(x7551,x7552)+E(f841(x7553,x7554,x7555,x7556,x7551,x7557,x7558),f841(x7553,x7554,x7555,x7556,x7552,x7557,x7558)) % 112.37/112.12 [756]~E(x7561,x7562)+E(f841(x7563,x7564,x7565,x7566,x7567,x7561,x7568),f841(x7563,x7564,x7565,x7566,x7567,x7562,x7568)) % 112.37/112.12 [757]~E(x7571,x7572)+E(f841(x7573,x7574,x7575,x7576,x7577,x7578,x7571),f841(x7573,x7574,x7575,x7576,x7577,x7578,x7572)) % 112.37/112.12 [758]~E(x7581,x7582)+E(f755(x7581,x7583,x7584,x7585,x7586),f755(x7582,x7583,x7584,x7585,x7586)) % 112.37/112.12 [759]~E(x7591,x7592)+E(f755(x7593,x7591,x7594,x7595,x7596),f755(x7593,x7592,x7594,x7595,x7596)) % 112.37/112.12 [760]~E(x7601,x7602)+E(f755(x7603,x7604,x7601,x7605,x7606),f755(x7603,x7604,x7602,x7605,x7606)) % 112.37/112.12 [761]~E(x7611,x7612)+E(f755(x7613,x7614,x7615,x7611,x7616),f755(x7613,x7614,x7615,x7612,x7616)) % 112.37/112.12 [762]~E(x7621,x7622)+E(f755(x7623,x7624,x7625,x7626,x7621),f755(x7623,x7624,x7625,x7626,x7622)) % 112.37/112.12 [763]~E(x7631,x7632)+E(f776(x7631,x7633,x7634),f776(x7632,x7633,x7634)) % 112.37/112.12 [764]~E(x7641,x7642)+E(f776(x7643,x7641,x7644),f776(x7643,x7642,x7644)) % 112.37/112.12 [765]~E(x7651,x7652)+E(f776(x7653,x7654,x7651),f776(x7653,x7654,x7652)) % 112.37/112.12 [766]~E(x7661,x7662)+E(f180(x7661,x7663,x7664,x7665),f180(x7662,x7663,x7664,x7665)) % 112.37/112.12 [767]~E(x7671,x7672)+E(f180(x7673,x7671,x7674,x7675),f180(x7673,x7672,x7674,x7675)) % 112.37/112.12 [768]~E(x7681,x7682)+E(f180(x7683,x7684,x7681,x7685),f180(x7683,x7684,x7682,x7685)) % 112.37/112.12 [769]~E(x7691,x7692)+E(f180(x7693,x7694,x7695,x7691),f180(x7693,x7694,x7695,x7692)) % 112.37/112.12 [770]~E(x7701,x7702)+E(f61(x7701,x7703,x7704,x7705,x7706),f61(x7702,x7703,x7704,x7705,x7706)) % 112.37/112.12 [771]~E(x7711,x7712)+E(f61(x7713,x7711,x7714,x7715,x7716),f61(x7713,x7712,x7714,x7715,x7716)) % 112.37/112.12 [772]~E(x7721,x7722)+E(f61(x7723,x7724,x7721,x7725,x7726),f61(x7723,x7724,x7722,x7725,x7726)) % 112.37/112.12 [773]~E(x7731,x7732)+E(f61(x7733,x7734,x7735,x7731,x7736),f61(x7733,x7734,x7735,x7732,x7736)) % 112.37/112.12 [774]~E(x7741,x7742)+E(f61(x7743,x7744,x7745,x7746,x7741),f61(x7743,x7744,x7745,x7746,x7742)) % 112.37/112.12 [775]~E(x7751,x7752)+E(f52(x7751),f52(x7752)) % 112.37/112.12 [776]~E(x7761,x7762)+E(f451(x7761,x7763,x7764),f451(x7762,x7763,x7764)) % 112.37/112.12 [777]~E(x7771,x7772)+E(f451(x7773,x7771,x7774),f451(x7773,x7772,x7774)) % 112.37/112.12 [778]~E(x7781,x7782)+E(f451(x7783,x7784,x7781),f451(x7783,x7784,x7782)) % 112.37/112.12 [779]~E(x7791,x7792)+E(f471(x7791,x7793,x7794,x7795),f471(x7792,x7793,x7794,x7795)) % 112.37/112.12 [780]~E(x7801,x7802)+E(f471(x7803,x7801,x7804,x7805),f471(x7803,x7802,x7804,x7805)) % 112.37/112.12 [781]~E(x7811,x7812)+E(f471(x7813,x7814,x7811,x7815),f471(x7813,x7814,x7812,x7815)) % 112.37/112.12 [782]~E(x7821,x7822)+E(f471(x7823,x7824,x7825,x7821),f471(x7823,x7824,x7825,x7822)) % 112.37/112.12 [783]~E(x7831,x7832)+E(f175(x7831,x7833,x7834,x7835),f175(x7832,x7833,x7834,x7835)) % 112.37/112.12 [784]~E(x7841,x7842)+E(f175(x7843,x7841,x7844,x7845),f175(x7843,x7842,x7844,x7845)) % 112.37/112.12 [785]~E(x7851,x7852)+E(f175(x7853,x7854,x7851,x7855),f175(x7853,x7854,x7852,x7855)) % 112.37/112.12 [786]~E(x7861,x7862)+E(f175(x7863,x7864,x7865,x7861),f175(x7863,x7864,x7865,x7862)) % 112.37/112.12 [787]~E(x7871,x7872)+E(f730(x7871,x7873,x7874,x7875,x7876,x7877,x7878),f730(x7872,x7873,x7874,x7875,x7876,x7877,x7878)) % 112.37/112.12 [788]~E(x7881,x7882)+E(f730(x7883,x7881,x7884,x7885,x7886,x7887,x7888),f730(x7883,x7882,x7884,x7885,x7886,x7887,x7888)) % 112.37/112.12 [789]~E(x7891,x7892)+E(f730(x7893,x7894,x7891,x7895,x7896,x7897,x7898),f730(x7893,x7894,x7892,x7895,x7896,x7897,x7898)) % 112.37/112.12 [790]~E(x7901,x7902)+E(f730(x7903,x7904,x7905,x7901,x7906,x7907,x7908),f730(x7903,x7904,x7905,x7902,x7906,x7907,x7908)) % 112.37/112.12 [791]~E(x7911,x7912)+E(f730(x7913,x7914,x7915,x7916,x7911,x7917,x7918),f730(x7913,x7914,x7915,x7916,x7912,x7917,x7918)) % 112.37/112.12 [792]~E(x7921,x7922)+E(f730(x7923,x7924,x7925,x7926,x7927,x7921,x7928),f730(x7923,x7924,x7925,x7926,x7927,x7922,x7928)) % 112.37/112.12 [793]~E(x7931,x7932)+E(f730(x7933,x7934,x7935,x7936,x7937,x7938,x7931),f730(x7933,x7934,x7935,x7936,x7937,x7938,x7932)) % 112.37/112.12 [794]~E(x7941,x7942)+E(f492(x7941),f492(x7942)) % 112.37/112.12 [795]~E(x7951,x7952)+E(f286(x7951,x7953,x7954),f286(x7952,x7953,x7954)) % 112.37/112.12 [796]~E(x7961,x7962)+E(f286(x7963,x7961,x7964),f286(x7963,x7962,x7964)) % 112.37/112.12 [797]~E(x7971,x7972)+E(f286(x7973,x7974,x7971),f286(x7973,x7974,x7972)) % 112.37/112.12 [798]~E(x7981,x7982)+E(f690(x7981,x7983),f690(x7982,x7983)) % 112.37/112.12 [799]~E(x7991,x7992)+E(f690(x7993,x7991),f690(x7993,x7992)) % 112.37/112.12 [800]~E(x8001,x8002)+E(f615(x8001,x8003,x8004,x8005,x8006),f615(x8002,x8003,x8004,x8005,x8006)) % 112.37/112.12 [801]~E(x8011,x8012)+E(f615(x8013,x8011,x8014,x8015,x8016),f615(x8013,x8012,x8014,x8015,x8016)) % 112.37/112.12 [802]~E(x8021,x8022)+E(f615(x8023,x8024,x8021,x8025,x8026),f615(x8023,x8024,x8022,x8025,x8026)) % 112.37/112.12 [803]~E(x8031,x8032)+E(f615(x8033,x8034,x8035,x8031,x8036),f615(x8033,x8034,x8035,x8032,x8036)) % 112.37/112.12 [804]~E(x8041,x8042)+E(f615(x8043,x8044,x8045,x8046,x8041),f615(x8043,x8044,x8045,x8046,x8042)) % 112.37/112.12 [805]~E(x8051,x8052)+E(f331(x8051,x8053,x8054,x8055),f331(x8052,x8053,x8054,x8055)) % 112.37/112.12 [806]~E(x8061,x8062)+E(f331(x8063,x8061,x8064,x8065),f331(x8063,x8062,x8064,x8065)) % 112.37/112.12 [807]~E(x8071,x8072)+E(f331(x8073,x8074,x8071,x8075),f331(x8073,x8074,x8072,x8075)) % 112.37/112.12 [808]~E(x8081,x8082)+E(f331(x8083,x8084,x8085,x8081),f331(x8083,x8084,x8085,x8082)) % 112.37/112.12 [809]~E(x8091,x8092)+E(f348(x8091,x8093,x8094,x8095),f348(x8092,x8093,x8094,x8095)) % 112.37/112.12 [810]~E(x8101,x8102)+E(f348(x8103,x8101,x8104,x8105),f348(x8103,x8102,x8104,x8105)) % 112.37/112.12 [811]~E(x8111,x8112)+E(f348(x8113,x8114,x8111,x8115),f348(x8113,x8114,x8112,x8115)) % 112.37/112.12 [812]~E(x8121,x8122)+E(f348(x8123,x8124,x8125,x8121),f348(x8123,x8124,x8125,x8122)) % 112.37/112.12 [813]~E(x8131,x8132)+E(f715(x8131,x8133,x8134,x8135,x8136,x8137,x8138,x8139),f715(x8132,x8133,x8134,x8135,x8136,x8137,x8138,x8139)) % 112.37/112.12 [814]~E(x8141,x8142)+E(f715(x8143,x8141,x8144,x8145,x8146,x8147,x8148,x8149),f715(x8143,x8142,x8144,x8145,x8146,x8147,x8148,x8149)) % 112.37/112.12 [815]~E(x8151,x8152)+E(f715(x8153,x8154,x8151,x8155,x8156,x8157,x8158,x8159),f715(x8153,x8154,x8152,x8155,x8156,x8157,x8158,x8159)) % 112.37/112.12 [816]~E(x8161,x8162)+E(f715(x8163,x8164,x8165,x8161,x8166,x8167,x8168,x8169),f715(x8163,x8164,x8165,x8162,x8166,x8167,x8168,x8169)) % 112.37/112.12 [817]~E(x8171,x8172)+E(f715(x8173,x8174,x8175,x8176,x8171,x8177,x8178,x8179),f715(x8173,x8174,x8175,x8176,x8172,x8177,x8178,x8179)) % 112.37/112.12 [818]~E(x8181,x8182)+E(f715(x8183,x8184,x8185,x8186,x8187,x8181,x8188,x8189),f715(x8183,x8184,x8185,x8186,x8187,x8182,x8188,x8189)) % 112.37/112.12 [819]~E(x8191,x8192)+E(f715(x8193,x8194,x8195,x8196,x8197,x8198,x8191,x8199),f715(x8193,x8194,x8195,x8196,x8197,x8198,x8192,x8199)) % 112.37/112.12 [820]~E(x8201,x8202)+E(f715(x8203,x8204,x8205,x8206,x8207,x8208,x8209,x8201),f715(x8203,x8204,x8205,x8206,x8207,x8208,x8209,x8202)) % 112.37/112.12 [821]~E(x8211,x8212)+E(f344(x8211,x8213,x8214),f344(x8212,x8213,x8214)) % 112.37/112.12 [822]~E(x8221,x8222)+E(f344(x8223,x8221,x8224),f344(x8223,x8222,x8224)) % 112.37/112.12 [823]~E(x8231,x8232)+E(f344(x8233,x8234,x8231),f344(x8233,x8234,x8232)) % 112.37/112.12 [824]~E(x8241,x8242)+E(f291(x8241),f291(x8242)) % 112.37/112.12 [825]~E(x8251,x8252)+E(f569(x8251,x8253,x8254,x8255),f569(x8252,x8253,x8254,x8255)) % 112.37/112.12 [826]~E(x8261,x8262)+E(f569(x8263,x8261,x8264,x8265),f569(x8263,x8262,x8264,x8265)) % 112.37/112.12 [827]~E(x8271,x8272)+E(f569(x8273,x8274,x8271,x8275),f569(x8273,x8274,x8272,x8275)) % 112.37/112.12 [828]~E(x8281,x8282)+E(f569(x8283,x8284,x8285,x8281),f569(x8283,x8284,x8285,x8282)) % 112.37/112.12 [829]~E(x8291,x8292)+E(f447(x8291,x8293,x8294),f447(x8292,x8293,x8294)) % 112.37/112.12 [830]~E(x8301,x8302)+E(f447(x8303,x8301,x8304),f447(x8303,x8302,x8304)) % 112.37/112.12 [831]~E(x8311,x8312)+E(f447(x8313,x8314,x8311),f447(x8313,x8314,x8312)) % 112.37/112.12 [832]~E(x8321,x8322)+E(f625(x8321,x8323,x8324,x8325,x8326),f625(x8322,x8323,x8324,x8325,x8326)) % 112.37/112.12 [833]~E(x8331,x8332)+E(f625(x8333,x8331,x8334,x8335,x8336),f625(x8333,x8332,x8334,x8335,x8336)) % 112.37/112.12 [834]~E(x8341,x8342)+E(f625(x8343,x8344,x8341,x8345,x8346),f625(x8343,x8344,x8342,x8345,x8346)) % 112.37/112.12 [835]~E(x8351,x8352)+E(f625(x8353,x8354,x8355,x8351,x8356),f625(x8353,x8354,x8355,x8352,x8356)) % 112.37/112.12 [836]~E(x8361,x8362)+E(f625(x8363,x8364,x8365,x8366,x8361),f625(x8363,x8364,x8365,x8366,x8362)) % 112.37/112.12 [837]~E(x8371,x8372)+E(f493(x8371),f493(x8372)) % 112.37/112.12 [838]~E(x8381,x8382)+E(f357(x8381,x8383,x8384,x8385),f357(x8382,x8383,x8384,x8385)) % 112.37/112.12 [839]~E(x8391,x8392)+E(f357(x8393,x8391,x8394,x8395),f357(x8393,x8392,x8394,x8395)) % 112.37/112.12 [840]~E(x8401,x8402)+E(f357(x8403,x8404,x8401,x8405),f357(x8403,x8404,x8402,x8405)) % 112.37/112.12 [841]~E(x8411,x8412)+E(f357(x8413,x8414,x8415,x8411),f357(x8413,x8414,x8415,x8412)) % 112.37/112.12 [842]~E(x8421,x8422)+E(f729(x8421,x8423,x8424,x8425,x8426,x8427,x8428),f729(x8422,x8423,x8424,x8425,x8426,x8427,x8428)) % 112.37/112.12 [843]~E(x8431,x8432)+E(f729(x8433,x8431,x8434,x8435,x8436,x8437,x8438),f729(x8433,x8432,x8434,x8435,x8436,x8437,x8438)) % 112.37/112.12 [844]~E(x8441,x8442)+E(f729(x8443,x8444,x8441,x8445,x8446,x8447,x8448),f729(x8443,x8444,x8442,x8445,x8446,x8447,x8448)) % 112.37/112.12 [845]~E(x8451,x8452)+E(f729(x8453,x8454,x8455,x8451,x8456,x8457,x8458),f729(x8453,x8454,x8455,x8452,x8456,x8457,x8458)) % 112.37/112.12 [846]~E(x8461,x8462)+E(f729(x8463,x8464,x8465,x8466,x8461,x8467,x8468),f729(x8463,x8464,x8465,x8466,x8462,x8467,x8468)) % 112.37/112.12 [847]~E(x8471,x8472)+E(f729(x8473,x8474,x8475,x8476,x8477,x8471,x8478),f729(x8473,x8474,x8475,x8476,x8477,x8472,x8478)) % 112.37/112.12 [848]~E(x8481,x8482)+E(f729(x8483,x8484,x8485,x8486,x8487,x8488,x8481),f729(x8483,x8484,x8485,x8486,x8487,x8488,x8482)) % 112.37/112.12 [849]~E(x8491,x8492)+E(f264(x8491,x8493,x8494),f264(x8492,x8493,x8494)) % 112.37/112.12 [850]~E(x8501,x8502)+E(f264(x8503,x8501,x8504),f264(x8503,x8502,x8504)) % 112.37/112.12 [851]~E(x8511,x8512)+E(f264(x8513,x8514,x8511),f264(x8513,x8514,x8512)) % 112.37/112.12 [852]~E(x8521,x8522)+E(f188(x8521,x8523,x8524,x8525),f188(x8522,x8523,x8524,x8525)) % 112.37/112.12 [853]~E(x8531,x8532)+E(f188(x8533,x8531,x8534,x8535),f188(x8533,x8532,x8534,x8535)) % 112.37/112.12 [854]~E(x8541,x8542)+E(f188(x8543,x8544,x8541,x8545),f188(x8543,x8544,x8542,x8545)) % 112.37/112.12 [855]~E(x8551,x8552)+E(f188(x8553,x8554,x8555,x8551),f188(x8553,x8554,x8555,x8552)) % 112.37/112.12 [856]~E(x8561,x8562)+E(f364(x8561,x8563,x8564,x8565),f364(x8562,x8563,x8564,x8565)) % 112.37/112.12 [857]~E(x8571,x8572)+E(f364(x8573,x8571,x8574,x8575),f364(x8573,x8572,x8574,x8575)) % 112.37/112.12 [858]~E(x8581,x8582)+E(f364(x8583,x8584,x8581,x8585),f364(x8583,x8584,x8582,x8585)) % 112.37/112.12 [859]~E(x8591,x8592)+E(f364(x8593,x8594,x8595,x8591),f364(x8593,x8594,x8595,x8592)) % 112.37/112.12 [860]~E(x8601,x8602)+E(f811(x8601,x8603,x8604),f811(x8602,x8603,x8604)) % 112.37/112.12 [861]~E(x8611,x8612)+E(f811(x8613,x8611,x8614),f811(x8613,x8612,x8614)) % 112.37/112.12 [862]~E(x8621,x8622)+E(f811(x8623,x8624,x8621),f811(x8623,x8624,x8622)) % 112.37/112.12 [863]~E(x8631,x8632)+E(f682(x8631,x8633,x8634,x8635,x8636),f682(x8632,x8633,x8634,x8635,x8636)) % 112.37/112.12 [864]~E(x8641,x8642)+E(f682(x8643,x8641,x8644,x8645,x8646),f682(x8643,x8642,x8644,x8645,x8646)) % 112.37/112.12 [865]~E(x8651,x8652)+E(f682(x8653,x8654,x8651,x8655,x8656),f682(x8653,x8654,x8652,x8655,x8656)) % 112.37/112.12 [866]~E(x8661,x8662)+E(f682(x8663,x8664,x8665,x8661,x8666),f682(x8663,x8664,x8665,x8662,x8666)) % 112.37/112.12 [867]~E(x8671,x8672)+E(f682(x8673,x8674,x8675,x8676,x8671),f682(x8673,x8674,x8675,x8676,x8672)) % 112.37/112.12 [868]~E(x8681,x8682)+E(f278(x8681,x8683),f278(x8682,x8683)) % 112.37/112.12 [869]~E(x8691,x8692)+E(f278(x8693,x8691),f278(x8693,x8692)) % 112.37/112.12 [870]~E(x8701,x8702)+E(f419(x8701,x8703,x8704),f419(x8702,x8703,x8704)) % 112.37/112.12 [871]~E(x8711,x8712)+E(f419(x8713,x8711,x8714),f419(x8713,x8712,x8714)) % 112.37/112.12 [872]~E(x8721,x8722)+E(f419(x8723,x8724,x8721),f419(x8723,x8724,x8722)) % 112.37/112.12 [873]~E(x8731,x8732)+E(f425(x8731,x8733,x8734),f425(x8732,x8733,x8734)) % 112.37/112.12 [874]~E(x8741,x8742)+E(f425(x8743,x8741,x8744),f425(x8743,x8742,x8744)) % 112.37/112.12 [875]~E(x8751,x8752)+E(f425(x8753,x8754,x8751),f425(x8753,x8754,x8752)) % 112.37/112.12 [876]~E(x8761,x8762)+E(f325(x8761),f325(x8762)) % 112.37/112.12 [877]~E(x8771,x8772)+E(f176(x8771),f176(x8772)) % 112.37/112.12 [878]~E(x8781,x8782)+E(f386(x8781,x8783,x8784,x8785),f386(x8782,x8783,x8784,x8785)) % 112.37/112.12 [879]~E(x8791,x8792)+E(f386(x8793,x8791,x8794,x8795),f386(x8793,x8792,x8794,x8795)) % 112.37/112.12 [880]~E(x8801,x8802)+E(f386(x8803,x8804,x8801,x8805),f386(x8803,x8804,x8802,x8805)) % 112.37/112.12 [881]~E(x8811,x8812)+E(f386(x8813,x8814,x8815,x8811),f386(x8813,x8814,x8815,x8812)) % 112.37/112.12 [882]~E(x8821,x8822)+E(f410(x8821,x8823,x8824),f410(x8822,x8823,x8824)) % 112.37/112.12 [883]~E(x8831,x8832)+E(f410(x8833,x8831,x8834),f410(x8833,x8832,x8834)) % 112.37/112.12 [884]~E(x8841,x8842)+E(f410(x8843,x8844,x8841),f410(x8843,x8844,x8842)) % 112.37/112.12 [885]~E(x8851,x8852)+E(f438(x8851,x8853,x8854,x8855),f438(x8852,x8853,x8854,x8855)) % 112.37/112.12 [886]~E(x8861,x8862)+E(f438(x8863,x8861,x8864,x8865),f438(x8863,x8862,x8864,x8865)) % 112.37/112.12 [887]~E(x8871,x8872)+E(f438(x8873,x8874,x8871,x8875),f438(x8873,x8874,x8872,x8875)) % 112.37/112.12 [888]~E(x8881,x8882)+E(f438(x8883,x8884,x8885,x8881),f438(x8883,x8884,x8885,x8882)) % 112.37/112.12 [889]~E(x8891,x8892)+E(f663(x8891,x8893,x8894,x8895,x8896),f663(x8892,x8893,x8894,x8895,x8896)) % 112.37/112.12 [890]~E(x8901,x8902)+E(f663(x8903,x8901,x8904,x8905,x8906),f663(x8903,x8902,x8904,x8905,x8906)) % 112.37/112.12 [891]~E(x8911,x8912)+E(f663(x8913,x8914,x8911,x8915,x8916),f663(x8913,x8914,x8912,x8915,x8916)) % 112.37/112.12 [892]~E(x8921,x8922)+E(f663(x8923,x8924,x8925,x8921,x8926),f663(x8923,x8924,x8925,x8922,x8926)) % 112.37/112.12 [893]~E(x8931,x8932)+E(f663(x8933,x8934,x8935,x8936,x8931),f663(x8933,x8934,x8935,x8936,x8932)) % 112.37/112.12 [894]~E(x8941,x8942)+E(f192(x8941,x8943),f192(x8942,x8943)) % 112.37/112.12 [895]~E(x8951,x8952)+E(f192(x8953,x8951),f192(x8953,x8952)) % 112.37/112.12 [896]~E(x8961,x8962)+E(f850(x8961,x8963,x8964,x8965),f850(x8962,x8963,x8964,x8965)) % 112.37/112.12 [897]~E(x8971,x8972)+E(f850(x8973,x8971,x8974,x8975),f850(x8973,x8972,x8974,x8975)) % 112.37/112.12 [898]~E(x8981,x8982)+E(f850(x8983,x8984,x8981,x8985),f850(x8983,x8984,x8982,x8985)) % 112.37/112.12 [899]~E(x8991,x8992)+E(f850(x8993,x8994,x8995,x8991),f850(x8993,x8994,x8995,x8992)) % 112.37/112.12 [900]~E(x9001,x9002)+E(f469(x9001,x9003,x9004,x9005,x9006),f469(x9002,x9003,x9004,x9005,x9006)) % 112.37/112.12 [901]~E(x9011,x9012)+E(f469(x9013,x9011,x9014,x9015,x9016),f469(x9013,x9012,x9014,x9015,x9016)) % 112.37/112.12 [902]~E(x9021,x9022)+E(f469(x9023,x9024,x9021,x9025,x9026),f469(x9023,x9024,x9022,x9025,x9026)) % 112.37/112.12 [903]~E(x9031,x9032)+E(f469(x9033,x9034,x9035,x9031,x9036),f469(x9033,x9034,x9035,x9032,x9036)) % 112.37/112.12 [904]~E(x9041,x9042)+E(f469(x9043,x9044,x9045,x9046,x9041),f469(x9043,x9044,x9045,x9046,x9042)) % 112.37/112.12 [905]~E(x9051,x9052)+E(f294(x9051),f294(x9052)) % 112.37/112.12 [906]~E(x9061,x9062)+E(f506(x9061,x9063,x9064,x9065),f506(x9062,x9063,x9064,x9065)) % 112.37/112.12 [907]~E(x9071,x9072)+E(f506(x9073,x9071,x9074,x9075),f506(x9073,x9072,x9074,x9075)) % 112.37/112.12 [908]~E(x9081,x9082)+E(f506(x9083,x9084,x9081,x9085),f506(x9083,x9084,x9082,x9085)) % 112.37/112.12 [909]~E(x9091,x9092)+E(f506(x9093,x9094,x9095,x9091),f506(x9093,x9094,x9095,x9092)) % 112.37/112.12 [910]~E(x9101,x9102)+E(f182(x9101,x9103),f182(x9102,x9103)) % 112.37/112.12 [911]~E(x9111,x9112)+E(f182(x9113,x9111),f182(x9113,x9112)) % 112.37/112.12 [912]~E(x9121,x9122)+E(f114(x9121),f114(x9122)) % 112.37/112.12 [913]~E(x9131,x9132)+E(f111(x9131,x9133),f111(x9132,x9133)) % 112.37/112.12 [914]~E(x9141,x9142)+E(f111(x9143,x9141),f111(x9143,x9142)) % 112.37/112.12 [915]~E(x9151,x9152)+E(f55(x9151,x9153,x9154,x9155),f55(x9152,x9153,x9154,x9155)) % 112.37/112.12 [916]~E(x9161,x9162)+E(f55(x9163,x9161,x9164,x9165),f55(x9163,x9162,x9164,x9165)) % 112.37/112.12 [917]~E(x9171,x9172)+E(f55(x9173,x9174,x9171,x9175),f55(x9173,x9174,x9172,x9175)) % 112.37/112.12 [918]~E(x9181,x9182)+E(f55(x9183,x9184,x9185,x9181),f55(x9183,x9184,x9185,x9182)) % 112.37/112.12 [919]~E(x9191,x9192)+E(f657(x9191,x9193,x9194),f657(x9192,x9193,x9194)) % 112.37/112.12 [920]~E(x9201,x9202)+E(f657(x9203,x9201,x9204),f657(x9203,x9202,x9204)) % 112.37/112.12 [921]~E(x9211,x9212)+E(f657(x9213,x9214,x9211),f657(x9213,x9214,x9212)) % 112.37/112.12 [922]~E(x9221,x9222)+E(f561(x9221,x9223,x9224,x9225),f561(x9222,x9223,x9224,x9225)) % 112.37/112.12 [923]~E(x9231,x9232)+E(f561(x9233,x9231,x9234,x9235),f561(x9233,x9232,x9234,x9235)) % 112.37/112.12 [924]~E(x9241,x9242)+E(f561(x9243,x9244,x9241,x9245),f561(x9243,x9244,x9242,x9245)) % 112.37/112.12 [925]~E(x9251,x9252)+E(f561(x9253,x9254,x9255,x9251),f561(x9253,x9254,x9255,x9252)) % 112.37/112.12 [926]~E(x9261,x9262)+E(f874(x9261,x9263,x9264),f874(x9262,x9263,x9264)) % 112.37/112.12 [927]~E(x9271,x9272)+E(f874(x9273,x9271,x9274),f874(x9273,x9272,x9274)) % 112.37/112.12 [928]~E(x9281,x9282)+E(f874(x9283,x9284,x9281),f874(x9283,x9284,x9282)) % 112.37/112.12 [929]~E(x9291,x9292)+E(f57(x9291,x9293,x9294),f57(x9292,x9293,x9294)) % 112.37/112.12 [930]~E(x9301,x9302)+E(f57(x9303,x9301,x9304),f57(x9303,x9302,x9304)) % 112.37/112.12 [931]~E(x9311,x9312)+E(f57(x9313,x9314,x9311),f57(x9313,x9314,x9312)) % 112.37/112.12 [932]~E(x9321,x9322)+E(f455(x9321,x9323,x9324),f455(x9322,x9323,x9324)) % 112.37/112.12 [933]~E(x9331,x9332)+E(f455(x9333,x9331,x9334),f455(x9333,x9332,x9334)) % 112.37/112.12 [934]~E(x9341,x9342)+E(f455(x9343,x9344,x9341),f455(x9343,x9344,x9342)) % 112.37/112.12 [935]~E(x9351,x9352)+E(f815(x9351,x9353,x9354,x9355),f815(x9352,x9353,x9354,x9355)) % 112.37/112.12 [936]~E(x9361,x9362)+E(f815(x9363,x9361,x9364,x9365),f815(x9363,x9362,x9364,x9365)) % 112.37/112.12 [937]~E(x9371,x9372)+E(f815(x9373,x9374,x9371,x9375),f815(x9373,x9374,x9372,x9375)) % 112.37/112.12 [938]~E(x9381,x9382)+E(f815(x9383,x9384,x9385,x9381),f815(x9383,x9384,x9385,x9382)) % 112.37/112.12 [939]~E(x9391,x9392)+E(f290(x9391,x9393,x9394,x9395,x9396),f290(x9392,x9393,x9394,x9395,x9396)) % 112.37/112.12 [940]~E(x9401,x9402)+E(f290(x9403,x9401,x9404,x9405,x9406),f290(x9403,x9402,x9404,x9405,x9406)) % 112.37/112.12 [941]~E(x9411,x9412)+E(f290(x9413,x9414,x9411,x9415,x9416),f290(x9413,x9414,x9412,x9415,x9416)) % 112.37/112.12 [942]~E(x9421,x9422)+E(f290(x9423,x9424,x9425,x9421,x9426),f290(x9423,x9424,x9425,x9422,x9426)) % 112.37/112.12 [943]~E(x9431,x9432)+E(f290(x9433,x9434,x9435,x9436,x9431),f290(x9433,x9434,x9435,x9436,x9432)) % 112.37/112.12 [944]~E(x9441,x9442)+E(f383(x9441,x9443),f383(x9442,x9443)) % 112.37/112.12 [945]~E(x9451,x9452)+E(f383(x9453,x9451),f383(x9453,x9452)) % 112.37/112.12 [946]~E(x9461,x9462)+E(f432(x9461,x9463,x9464,x9465),f432(x9462,x9463,x9464,x9465)) % 112.37/112.12 [947]~E(x9471,x9472)+E(f432(x9473,x9471,x9474,x9475),f432(x9473,x9472,x9474,x9475)) % 112.37/112.12 [948]~E(x9481,x9482)+E(f432(x9483,x9484,x9481,x9485),f432(x9483,x9484,x9482,x9485)) % 112.37/112.12 [949]~E(x9491,x9492)+E(f432(x9493,x9494,x9495,x9491),f432(x9493,x9494,x9495,x9492)) % 112.37/112.12 [950]~E(x9501,x9502)+E(f795(x9501,x9503,x9504,x9505,x9506,x9507),f795(x9502,x9503,x9504,x9505,x9506,x9507)) % 112.37/112.12 [951]~E(x9511,x9512)+E(f795(x9513,x9511,x9514,x9515,x9516,x9517),f795(x9513,x9512,x9514,x9515,x9516,x9517)) % 112.37/112.12 [952]~E(x9521,x9522)+E(f795(x9523,x9524,x9521,x9525,x9526,x9527),f795(x9523,x9524,x9522,x9525,x9526,x9527)) % 112.37/112.12 [953]~E(x9531,x9532)+E(f795(x9533,x9534,x9535,x9531,x9536,x9537),f795(x9533,x9534,x9535,x9532,x9536,x9537)) % 112.37/112.12 [954]~E(x9541,x9542)+E(f795(x9543,x9544,x9545,x9546,x9541,x9547),f795(x9543,x9544,x9545,x9546,x9542,x9547)) % 112.37/112.12 [955]~E(x9551,x9552)+E(f795(x9553,x9554,x9555,x9556,x9557,x9551),f795(x9553,x9554,x9555,x9556,x9557,x9552)) % 112.37/112.12 [956]~E(x9561,x9562)+E(f437(x9561,x9563,x9564),f437(x9562,x9563,x9564)) % 112.37/112.12 [957]~E(x9571,x9572)+E(f437(x9573,x9571,x9574),f437(x9573,x9572,x9574)) % 112.37/112.12 [958]~E(x9581,x9582)+E(f437(x9583,x9584,x9581),f437(x9583,x9584,x9582)) % 112.37/112.12 [959]~E(x9591,x9592)+E(f193(x9591,x9593,x9594),f193(x9592,x9593,x9594)) % 112.37/112.12 [960]~E(x9601,x9602)+E(f193(x9603,x9601,x9604),f193(x9603,x9602,x9604)) % 112.37/112.12 [961]~E(x9611,x9612)+E(f193(x9613,x9614,x9611),f193(x9613,x9614,x9612)) % 112.37/112.12 [962]~E(x9621,x9622)+E(f361(x9621,x9623,x9624),f361(x9622,x9623,x9624)) % 112.37/112.12 [963]~E(x9631,x9632)+E(f361(x9633,x9631,x9634),f361(x9633,x9632,x9634)) % 112.37/112.12 [964]~E(x9641,x9642)+E(f361(x9643,x9644,x9641),f361(x9643,x9644,x9642)) % 112.37/112.12 [965]~E(x9651,x9652)+E(f656(x9651,x9653,x9654),f656(x9652,x9653,x9654)) % 112.37/112.12 [966]~E(x9661,x9662)+E(f656(x9663,x9661,x9664),f656(x9663,x9662,x9664)) % 112.37/112.12 [967]~E(x9671,x9672)+E(f656(x9673,x9674,x9671),f656(x9673,x9674,x9672)) % 112.37/112.12 [968]~E(x9681,x9682)+E(f648(x9681,x9683),f648(x9682,x9683)) % 112.37/112.12 [969]~E(x9691,x9692)+E(f648(x9693,x9691),f648(x9693,x9692)) % 112.37/112.12 [970]~E(x9701,x9702)+E(f106(x9701,x9703,x9704),f106(x9702,x9703,x9704)) % 112.37/112.12 [971]~E(x9711,x9712)+E(f106(x9713,x9711,x9714),f106(x9713,x9712,x9714)) % 112.37/112.12 [972]~E(x9721,x9722)+E(f106(x9723,x9724,x9721),f106(x9723,x9724,x9722)) % 112.37/112.12 [973]~E(x9731,x9732)+E(f186(x9731,x9733,x9734,x9735),f186(x9732,x9733,x9734,x9735)) % 112.37/112.12 [974]~E(x9741,x9742)+E(f186(x9743,x9741,x9744,x9745),f186(x9743,x9742,x9744,x9745)) % 112.37/112.12 [975]~E(x9751,x9752)+E(f186(x9753,x9754,x9751,x9755),f186(x9753,x9754,x9752,x9755)) % 112.37/112.12 [976]~E(x9761,x9762)+E(f186(x9763,x9764,x9765,x9761),f186(x9763,x9764,x9765,x9762)) % 112.37/112.12 [977]~E(x9771,x9772)+E(f491(x9771,x9773,x9774,x9775,x9776),f491(x9772,x9773,x9774,x9775,x9776)) % 112.37/112.12 [978]~E(x9781,x9782)+E(f491(x9783,x9781,x9784,x9785,x9786),f491(x9783,x9782,x9784,x9785,x9786)) % 112.37/112.12 [979]~E(x9791,x9792)+E(f491(x9793,x9794,x9791,x9795,x9796),f491(x9793,x9794,x9792,x9795,x9796)) % 112.37/112.12 [980]~E(x9801,x9802)+E(f491(x9803,x9804,x9805,x9801,x9806),f491(x9803,x9804,x9805,x9802,x9806)) % 112.37/112.12 [981]~E(x9811,x9812)+E(f491(x9813,x9814,x9815,x9816,x9811),f491(x9813,x9814,x9815,x9816,x9812)) % 112.37/112.12 [982]~E(x9821,x9822)+E(f724(x9821,x9823),f724(x9822,x9823)) % 112.37/112.12 [983]~E(x9831,x9832)+E(f724(x9833,x9831),f724(x9833,x9832)) % 112.37/112.12 [984]~E(x9841,x9842)+E(f359(x9841,x9843,x9844,x9845),f359(x9842,x9843,x9844,x9845)) % 112.37/112.12 [985]~E(x9851,x9852)+E(f359(x9853,x9851,x9854,x9855),f359(x9853,x9852,x9854,x9855)) % 112.37/112.12 [986]~E(x9861,x9862)+E(f359(x9863,x9864,x9861,x9865),f359(x9863,x9864,x9862,x9865)) % 112.37/112.12 [987]~E(x9871,x9872)+E(f359(x9873,x9874,x9875,x9871),f359(x9873,x9874,x9875,x9872)) % 112.37/112.12 [988]~E(x9881,x9882)+E(f51(x9881,x9883,x9884),f51(x9882,x9883,x9884)) % 112.37/112.12 [989]~E(x9891,x9892)+E(f51(x9893,x9891,x9894),f51(x9893,x9892,x9894)) % 112.37/112.12 [990]~E(x9901,x9902)+E(f51(x9903,x9904,x9901),f51(x9903,x9904,x9902)) % 112.37/112.12 [991]~E(x9911,x9912)+E(f605(x9911,x9913,x9914),f605(x9912,x9913,x9914)) % 112.37/112.12 [992]~E(x9921,x9922)+E(f605(x9923,x9921,x9924),f605(x9923,x9922,x9924)) % 112.37/112.12 [993]~E(x9931,x9932)+E(f605(x9933,x9934,x9931),f605(x9933,x9934,x9932)) % 112.37/112.12 [994]~E(x9941,x9942)+E(f270(x9941,x9943,x9944,x9945),f270(x9942,x9943,x9944,x9945)) % 112.37/112.12 [995]~E(x9951,x9952)+E(f270(x9953,x9951,x9954,x9955),f270(x9953,x9952,x9954,x9955)) % 112.37/112.12 [996]~E(x9961,x9962)+E(f270(x9963,x9964,x9961,x9965),f270(x9963,x9964,x9962,x9965)) % 112.37/112.12 [997]~E(x9971,x9972)+E(f270(x9973,x9974,x9975,x9971),f270(x9973,x9974,x9975,x9972)) % 112.37/112.12 [998]~E(x9981,x9982)+E(f342(x9981,x9983,x9984),f342(x9982,x9983,x9984)) % 112.37/112.12 [999]~E(x9991,x9992)+E(f342(x9993,x9991,x9994),f342(x9993,x9992,x9994)) % 112.37/112.12 [1000]~E(x10001,x10002)+E(f342(x10003,x10004,x10001),f342(x10003,x10004,x10002)) % 112.37/112.12 [1001]~E(x10011,x10012)+E(f135(x10011,x10013),f135(x10012,x10013)) % 112.37/112.12 [1002]~E(x10021,x10022)+E(f135(x10023,x10021),f135(x10023,x10022)) % 112.37/112.12 [1003]~E(x10031,x10032)+E(f257(x10031),f257(x10032)) % 112.37/112.12 [1004]~E(x10041,x10042)+E(f762(x10041,x10043,x10044,x10045),f762(x10042,x10043,x10044,x10045)) % 112.37/112.12 [1005]~E(x10051,x10052)+E(f762(x10053,x10051,x10054,x10055),f762(x10053,x10052,x10054,x10055)) % 112.37/112.12 [1006]~E(x10061,x10062)+E(f762(x10063,x10064,x10061,x10065),f762(x10063,x10064,x10062,x10065)) % 112.37/112.12 [1007]~E(x10071,x10072)+E(f762(x10073,x10074,x10075,x10071),f762(x10073,x10074,x10075,x10072)) % 112.37/112.12 [1008]~E(x10081,x10082)+E(f718(x10081,x10083,x10084,x10085,x10086),f718(x10082,x10083,x10084,x10085,x10086)) % 112.37/112.12 [1009]~E(x10091,x10092)+E(f718(x10093,x10091,x10094,x10095,x10096),f718(x10093,x10092,x10094,x10095,x10096)) % 112.37/112.12 [1010]~E(x10101,x10102)+E(f718(x10103,x10104,x10101,x10105,x10106),f718(x10103,x10104,x10102,x10105,x10106)) % 112.37/112.12 [1011]~E(x10111,x10112)+E(f718(x10113,x10114,x10115,x10111,x10116),f718(x10113,x10114,x10115,x10112,x10116)) % 112.37/112.12 [1012]~E(x10121,x10122)+E(f718(x10123,x10124,x10125,x10126,x10121),f718(x10123,x10124,x10125,x10126,x10122)) % 112.37/112.12 [1013]~E(x10131,x10132)+E(f783(x10131,x10133),f783(x10132,x10133)) % 112.37/112.12 [1014]~E(x10141,x10142)+E(f783(x10143,x10141),f783(x10143,x10142)) % 112.37/112.12 [1015]~E(x10151,x10152)+E(f384(x10151,x10153),f384(x10152,x10153)) % 112.37/112.12 [1016]~E(x10161,x10162)+E(f384(x10163,x10161),f384(x10163,x10162)) % 112.37/112.12 [1017]~E(x10171,x10172)+E(f49(x10171,x10173),f49(x10172,x10173)) % 112.37/112.12 [1018]~E(x10181,x10182)+E(f49(x10183,x10181),f49(x10183,x10182)) % 112.37/112.12 [1019]~E(x10191,x10192)+E(f401(x10191,x10193),f401(x10192,x10193)) % 112.37/112.12 [1020]~E(x10201,x10202)+E(f401(x10203,x10201),f401(x10203,x10202)) % 112.37/112.12 [1021]~E(x10211,x10212)+E(f376(x10211,x10213,x10214),f376(x10212,x10213,x10214)) % 112.37/112.12 [1022]~E(x10221,x10222)+E(f376(x10223,x10221,x10224),f376(x10223,x10222,x10224)) % 112.37/112.12 [1023]~E(x10231,x10232)+E(f376(x10233,x10234,x10231),f376(x10233,x10234,x10232)) % 112.37/112.12 [1024]~E(x10241,x10242)+E(f288(x10241,x10243,x10244),f288(x10242,x10243,x10244)) % 112.37/112.12 [1025]~E(x10251,x10252)+E(f288(x10253,x10251,x10254),f288(x10253,x10252,x10254)) % 112.37/112.12 [1026]~E(x10261,x10262)+E(f288(x10263,x10264,x10261),f288(x10263,x10264,x10262)) % 112.37/112.12 [1027]~E(x10271,x10272)+E(f546(x10271,x10273,x10274,x10275),f546(x10272,x10273,x10274,x10275)) % 112.37/112.12 [1028]~E(x10281,x10282)+E(f546(x10283,x10281,x10284,x10285),f546(x10283,x10282,x10284,x10285)) % 112.37/112.12 [1029]~E(x10291,x10292)+E(f546(x10293,x10294,x10291,x10295),f546(x10293,x10294,x10292,x10295)) % 112.37/112.12 [1030]~E(x10301,x10302)+E(f546(x10303,x10304,x10305,x10301),f546(x10303,x10304,x10305,x10302)) % 112.37/112.12 [1031]~E(x10311,x10312)+E(f490(x10311,x10313,x10314,x10315),f490(x10312,x10313,x10314,x10315)) % 112.37/112.12 [1032]~E(x10321,x10322)+E(f490(x10323,x10321,x10324,x10325),f490(x10323,x10322,x10324,x10325)) % 112.37/112.12 [1033]~E(x10331,x10332)+E(f490(x10333,x10334,x10331,x10335),f490(x10333,x10334,x10332,x10335)) % 112.37/112.12 [1034]~E(x10341,x10342)+E(f490(x10343,x10344,x10345,x10341),f490(x10343,x10344,x10345,x10342)) % 112.37/112.12 [1035]~E(x10351,x10352)+E(f327(x10351,x10353,x10354),f327(x10352,x10353,x10354)) % 112.37/112.12 [1036]~E(x10361,x10362)+E(f327(x10363,x10361,x10364),f327(x10363,x10362,x10364)) % 112.37/112.12 [1037]~E(x10371,x10372)+E(f327(x10373,x10374,x10371),f327(x10373,x10374,x10372)) % 112.37/112.12 [1038]~E(x10381,x10382)+E(f422(x10381,x10383),f422(x10382,x10383)) % 112.37/112.12 [1039]~E(x10391,x10392)+E(f422(x10393,x10391),f422(x10393,x10392)) % 112.37/112.12 [1040]~E(x10401,x10402)+E(f258(x10401,x10403),f258(x10402,x10403)) % 112.37/112.12 [1041]~E(x10411,x10412)+E(f258(x10413,x10411),f258(x10413,x10412)) % 112.37/112.12 [1042]~E(x10421,x10422)+E(f146(x10421,x10423,x10424,x10425),f146(x10422,x10423,x10424,x10425)) % 112.37/112.12 [1043]~E(x10431,x10432)+E(f146(x10433,x10431,x10434,x10435),f146(x10433,x10432,x10434,x10435)) % 112.37/112.12 [1044]~E(x10441,x10442)+E(f146(x10443,x10444,x10441,x10445),f146(x10443,x10444,x10442,x10445)) % 112.37/112.12 [1045]~E(x10451,x10452)+E(f146(x10453,x10454,x10455,x10451),f146(x10453,x10454,x10455,x10452)) % 112.37/112.12 [1046]~E(x10461,x10462)+E(f515(x10461,x10463,x10464,x10465),f515(x10462,x10463,x10464,x10465)) % 112.37/112.12 [1047]~E(x10471,x10472)+E(f515(x10473,x10471,x10474,x10475),f515(x10473,x10472,x10474,x10475)) % 112.37/112.12 [1048]~E(x10481,x10482)+E(f515(x10483,x10484,x10481,x10485),f515(x10483,x10484,x10482,x10485)) % 112.37/112.12 [1049]~E(x10491,x10492)+E(f515(x10493,x10494,x10495,x10491),f515(x10493,x10494,x10495,x10492)) % 112.37/112.12 [1050]~E(x10501,x10502)+E(f721(x10501,x10503),f721(x10502,x10503)) % 112.37/112.12 [1051]~E(x10511,x10512)+E(f721(x10513,x10511),f721(x10513,x10512)) % 112.37/112.12 [1052]~E(x10521,x10522)+E(f647(x10521,x10523),f647(x10522,x10523)) % 112.37/112.12 [1053]~E(x10531,x10532)+E(f647(x10533,x10531),f647(x10533,x10532)) % 112.37/112.12 [1054]~E(x10541,x10542)+E(f597(x10541,x10543,x10544),f597(x10542,x10543,x10544)) % 112.37/112.12 [1055]~E(x10551,x10552)+E(f597(x10553,x10551,x10554),f597(x10553,x10552,x10554)) % 112.37/112.12 [1056]~E(x10561,x10562)+E(f597(x10563,x10564,x10561),f597(x10563,x10564,x10562)) % 112.37/112.12 [1057]~E(x10571,x10572)+E(f796(x10571,x10573,x10574,x10575,x10576,x10577),f796(x10572,x10573,x10574,x10575,x10576,x10577)) % 112.37/112.12 [1058]~E(x10581,x10582)+E(f796(x10583,x10581,x10584,x10585,x10586,x10587),f796(x10583,x10582,x10584,x10585,x10586,x10587)) % 112.37/112.12 [1059]~E(x10591,x10592)+E(f796(x10593,x10594,x10591,x10595,x10596,x10597),f796(x10593,x10594,x10592,x10595,x10596,x10597)) % 112.37/112.12 [1060]~E(x10601,x10602)+E(f796(x10603,x10604,x10605,x10601,x10606,x10607),f796(x10603,x10604,x10605,x10602,x10606,x10607)) % 112.37/112.12 [1061]~E(x10611,x10612)+E(f796(x10613,x10614,x10615,x10616,x10611,x10617),f796(x10613,x10614,x10615,x10616,x10612,x10617)) % 112.37/112.12 [1062]~E(x10621,x10622)+E(f796(x10623,x10624,x10625,x10626,x10627,x10621),f796(x10623,x10624,x10625,x10626,x10627,x10622)) % 112.37/112.12 [1063]~E(x10631,x10632)+E(f659(x10631,x10633,x10634),f659(x10632,x10633,x10634)) % 112.37/112.12 [1064]~E(x10641,x10642)+E(f659(x10643,x10641,x10644),f659(x10643,x10642,x10644)) % 112.37/112.12 [1065]~E(x10651,x10652)+E(f659(x10653,x10654,x10651),f659(x10653,x10654,x10652)) % 112.37/112.12 [1066]~E(x10661,x10662)+E(f390(x10661,x10663,x10664),f390(x10662,x10663,x10664)) % 112.37/112.12 [1067]~E(x10671,x10672)+E(f390(x10673,x10671,x10674),f390(x10673,x10672,x10674)) % 112.37/112.12 [1068]~E(x10681,x10682)+E(f390(x10683,x10684,x10681),f390(x10683,x10684,x10682)) % 112.37/112.12 [1069]~E(x10691,x10692)+E(f408(x10691,x10693,x10694),f408(x10692,x10693,x10694)) % 112.37/112.12 [1070]~E(x10701,x10702)+E(f408(x10703,x10701,x10704),f408(x10703,x10702,x10704)) % 112.37/112.12 [1071]~E(x10711,x10712)+E(f408(x10713,x10714,x10711),f408(x10713,x10714,x10712)) % 112.37/112.12 [1072]~E(x10721,x10722)+E(f495(x10721,x10723,x10724,x10725),f495(x10722,x10723,x10724,x10725)) % 112.37/112.12 [1073]~E(x10731,x10732)+E(f495(x10733,x10731,x10734,x10735),f495(x10733,x10732,x10734,x10735)) % 112.37/112.12 [1074]~E(x10741,x10742)+E(f495(x10743,x10744,x10741,x10745),f495(x10743,x10744,x10742,x10745)) % 112.37/112.12 [1075]~E(x10751,x10752)+E(f495(x10753,x10754,x10755,x10751),f495(x10753,x10754,x10755,x10752)) % 112.37/112.12 [1076]~E(x10761,x10762)+E(f638(x10761,x10763,x10764,x10765,x10766),f638(x10762,x10763,x10764,x10765,x10766)) % 112.37/112.12 [1077]~E(x10771,x10772)+E(f638(x10773,x10771,x10774,x10775,x10776),f638(x10773,x10772,x10774,x10775,x10776)) % 112.37/112.12 [1078]~E(x10781,x10782)+E(f638(x10783,x10784,x10781,x10785,x10786),f638(x10783,x10784,x10782,x10785,x10786)) % 112.37/112.12 [1079]~E(x10791,x10792)+E(f638(x10793,x10794,x10795,x10791,x10796),f638(x10793,x10794,x10795,x10792,x10796)) % 112.37/112.12 [1080]~E(x10801,x10802)+E(f638(x10803,x10804,x10805,x10806,x10801),f638(x10803,x10804,x10805,x10806,x10802)) % 112.37/112.12 [1081]~E(x10811,x10812)+E(f541(x10811,x10813,x10814,x10815,x10816,x10817,x10818,x10819),f541(x10812,x10813,x10814,x10815,x10816,x10817,x10818,x10819)) % 112.37/112.12 [1082]~E(x10821,x10822)+E(f541(x10823,x10821,x10824,x10825,x10826,x10827,x10828,x10829),f541(x10823,x10822,x10824,x10825,x10826,x10827,x10828,x10829)) % 112.37/112.12 [1083]~E(x10831,x10832)+E(f541(x10833,x10834,x10831,x10835,x10836,x10837,x10838,x10839),f541(x10833,x10834,x10832,x10835,x10836,x10837,x10838,x10839)) % 112.37/112.12 [1084]~E(x10841,x10842)+E(f541(x10843,x10844,x10845,x10841,x10846,x10847,x10848,x10849),f541(x10843,x10844,x10845,x10842,x10846,x10847,x10848,x10849)) % 112.37/112.12 [1085]~E(x10851,x10852)+E(f541(x10853,x10854,x10855,x10856,x10851,x10857,x10858,x10859),f541(x10853,x10854,x10855,x10856,x10852,x10857,x10858,x10859)) % 112.37/112.12 [1086]~E(x10861,x10862)+E(f541(x10863,x10864,x10865,x10866,x10867,x10861,x10868,x10869),f541(x10863,x10864,x10865,x10866,x10867,x10862,x10868,x10869)) % 112.37/112.12 [1087]~E(x10871,x10872)+E(f541(x10873,x10874,x10875,x10876,x10877,x10878,x10871,x10879),f541(x10873,x10874,x10875,x10876,x10877,x10878,x10872,x10879)) % 112.37/112.12 [1088]~E(x10881,x10882)+E(f541(x10883,x10884,x10885,x10886,x10887,x10888,x10889,x10881),f541(x10883,x10884,x10885,x10886,x10887,x10888,x10889,x10882)) % 112.37/112.12 [1089]~E(x10891,x10892)+E(f199(x10891,x10893,x10894,x10895),f199(x10892,x10893,x10894,x10895)) % 112.37/112.12 [1090]~E(x10901,x10902)+E(f199(x10903,x10901,x10904,x10905),f199(x10903,x10902,x10904,x10905)) % 112.37/112.12 [1091]~E(x10911,x10912)+E(f199(x10913,x10914,x10911,x10915),f199(x10913,x10914,x10912,x10915)) % 112.37/112.12 [1092]~E(x10921,x10922)+E(f199(x10923,x10924,x10925,x10921),f199(x10923,x10924,x10925,x10922)) % 112.37/112.12 [1093]~E(x10931,x10932)+E(f463(x10931,x10933,x10934,x10935,x10936,x10937),f463(x10932,x10933,x10934,x10935,x10936,x10937)) % 112.37/112.12 [1094]~E(x10941,x10942)+E(f463(x10943,x10941,x10944,x10945,x10946,x10947),f463(x10943,x10942,x10944,x10945,x10946,x10947)) % 112.37/112.12 [1095]~E(x10951,x10952)+E(f463(x10953,x10954,x10951,x10955,x10956,x10957),f463(x10953,x10954,x10952,x10955,x10956,x10957)) % 112.37/112.12 [1096]~E(x10961,x10962)+E(f463(x10963,x10964,x10965,x10961,x10966,x10967),f463(x10963,x10964,x10965,x10962,x10966,x10967)) % 112.37/112.12 [1097]~E(x10971,x10972)+E(f463(x10973,x10974,x10975,x10976,x10971,x10977),f463(x10973,x10974,x10975,x10976,x10972,x10977)) % 112.37/112.12 [1098]~E(x10981,x10982)+E(f463(x10983,x10984,x10985,x10986,x10987,x10981),f463(x10983,x10984,x10985,x10986,x10987,x10982)) % 112.37/112.12 [1099]~E(x10991,x10992)+E(f713(x10991,x10993),f713(x10992,x10993)) % 112.37/112.12 [1100]~E(x11001,x11002)+E(f713(x11003,x11001),f713(x11003,x11002)) % 112.37/112.12 [1101]~E(x11011,x11012)+E(f633(x11011,x11013,x11014),f633(x11012,x11013,x11014)) % 112.37/112.12 [1102]~E(x11021,x11022)+E(f633(x11023,x11021,x11024),f633(x11023,x11022,x11024)) % 112.37/112.12 [1103]~E(x11031,x11032)+E(f633(x11033,x11034,x11031),f633(x11033,x11034,x11032)) % 112.37/112.12 [1104]~E(x11041,x11042)+E(f303(x11041,x11043,x11044,x11045),f303(x11042,x11043,x11044,x11045)) % 112.37/112.12 [1105]~E(x11051,x11052)+E(f303(x11053,x11051,x11054,x11055),f303(x11053,x11052,x11054,x11055)) % 112.37/112.12 [1106]~E(x11061,x11062)+E(f303(x11063,x11064,x11061,x11065),f303(x11063,x11064,x11062,x11065)) % 112.37/112.12 [1107]~E(x11071,x11072)+E(f303(x11073,x11074,x11075,x11071),f303(x11073,x11074,x11075,x11072)) % 112.37/112.12 [1108]~E(x11081,x11082)+E(f289(x11081,x11083,x11084,x11085),f289(x11082,x11083,x11084,x11085)) % 112.37/112.12 [1109]~E(x11091,x11092)+E(f289(x11093,x11091,x11094,x11095),f289(x11093,x11092,x11094,x11095)) % 112.37/112.12 [1110]~E(x11101,x11102)+E(f289(x11103,x11104,x11101,x11105),f289(x11103,x11104,x11102,x11105)) % 112.37/112.12 [1111]~E(x11111,x11112)+E(f289(x11113,x11114,x11115,x11111),f289(x11113,x11114,x11115,x11112)) % 112.37/112.12 [1112]~E(x11121,x11122)+E(f454(x11121,x11123,x11124),f454(x11122,x11123,x11124)) % 112.37/112.12 [1113]~E(x11131,x11132)+E(f454(x11133,x11131,x11134),f454(x11133,x11132,x11134)) % 112.37/112.12 [1114]~E(x11141,x11142)+E(f454(x11143,x11144,x11141),f454(x11143,x11144,x11142)) % 112.37/112.12 [1115]~E(x11151,x11152)+E(f752(x11151,x11153,x11154,x11155),f752(x11152,x11153,x11154,x11155)) % 112.37/112.12 [1116]~E(x11161,x11162)+E(f752(x11163,x11161,x11164,x11165),f752(x11163,x11162,x11164,x11165)) % 112.37/112.12 [1117]~E(x11171,x11172)+E(f752(x11173,x11174,x11171,x11175),f752(x11173,x11174,x11172,x11175)) % 112.37/112.12 [1118]~E(x11181,x11182)+E(f752(x11183,x11184,x11185,x11181),f752(x11183,x11184,x11185,x11182)) % 112.37/112.12 [1119]~E(x11191,x11192)+E(f487(x11191,x11193,x11194,x11195,x11196),f487(x11192,x11193,x11194,x11195,x11196)) % 112.37/112.12 [1120]~E(x11201,x11202)+E(f487(x11203,x11201,x11204,x11205,x11206),f487(x11203,x11202,x11204,x11205,x11206)) % 112.37/112.12 [1121]~E(x11211,x11212)+E(f487(x11213,x11214,x11211,x11215,x11216),f487(x11213,x11214,x11212,x11215,x11216)) % 112.37/112.12 [1122]~E(x11221,x11222)+E(f487(x11223,x11224,x11225,x11221,x11226),f487(x11223,x11224,x11225,x11222,x11226)) % 112.37/112.12 [1123]~E(x11231,x11232)+E(f487(x11233,x11234,x11235,x11236,x11231),f487(x11233,x11234,x11235,x11236,x11232)) % 112.37/112.12 [1124]~E(x11241,x11242)+E(f107(x11241,x11243,x11244),f107(x11242,x11243,x11244)) % 112.37/112.12 [1125]~E(x11251,x11252)+E(f107(x11253,x11251,x11254),f107(x11253,x11252,x11254)) % 112.37/112.12 [1126]~E(x11261,x11262)+E(f107(x11263,x11264,x11261),f107(x11263,x11264,x11262)) % 112.37/112.12 [1127]~E(x11271,x11272)+E(f213(x11271,x11273,x11274,x11275,x11276),f213(x11272,x11273,x11274,x11275,x11276)) % 112.37/112.12 [1128]~E(x11281,x11282)+E(f213(x11283,x11281,x11284,x11285,x11286),f213(x11283,x11282,x11284,x11285,x11286)) % 112.37/112.12 [1129]~E(x11291,x11292)+E(f213(x11293,x11294,x11291,x11295,x11296),f213(x11293,x11294,x11292,x11295,x11296)) % 112.37/112.12 [1130]~E(x11301,x11302)+E(f213(x11303,x11304,x11305,x11301,x11306),f213(x11303,x11304,x11305,x11302,x11306)) % 112.37/112.12 [1131]~E(x11311,x11312)+E(f213(x11313,x11314,x11315,x11316,x11311),f213(x11313,x11314,x11315,x11316,x11312)) % 112.37/112.12 [1132]~E(x11321,x11322)+E(f472(x11321,x11323,x11324,x11325,x11326),f472(x11322,x11323,x11324,x11325,x11326)) % 112.37/112.12 [1133]~E(x11331,x11332)+E(f472(x11333,x11331,x11334,x11335,x11336),f472(x11333,x11332,x11334,x11335,x11336)) % 112.37/112.12 [1134]~E(x11341,x11342)+E(f472(x11343,x11344,x11341,x11345,x11346),f472(x11343,x11344,x11342,x11345,x11346)) % 112.37/112.12 [1135]~E(x11351,x11352)+E(f472(x11353,x11354,x11355,x11351,x11356),f472(x11353,x11354,x11355,x11352,x11356)) % 112.37/112.12 [1136]~E(x11361,x11362)+E(f472(x11363,x11364,x11365,x11366,x11361),f472(x11363,x11364,x11365,x11366,x11362)) % 112.37/112.12 [1137]~E(x11371,x11372)+E(f133(x11371,x11373),f133(x11372,x11373)) % 112.37/112.12 [1138]~E(x11381,x11382)+E(f133(x11383,x11381),f133(x11383,x11382)) % 112.37/112.12 [1139]~E(x11391,x11392)+E(f608(x11391,x11393,x11394,x11395,x11396),f608(x11392,x11393,x11394,x11395,x11396)) % 112.37/112.12 [1140]~E(x11401,x11402)+E(f608(x11403,x11401,x11404,x11405,x11406),f608(x11403,x11402,x11404,x11405,x11406)) % 112.37/112.12 [1141]~E(x11411,x11412)+E(f608(x11413,x11414,x11411,x11415,x11416),f608(x11413,x11414,x11412,x11415,x11416)) % 112.37/112.12 [1142]~E(x11421,x11422)+E(f608(x11423,x11424,x11425,x11421,x11426),f608(x11423,x11424,x11425,x11422,x11426)) % 112.37/112.12 [1143]~E(x11431,x11432)+E(f608(x11433,x11434,x11435,x11436,x11431),f608(x11433,x11434,x11435,x11436,x11432)) % 112.37/112.12 [1144]~E(x11441,x11442)+E(f641(x11441,x11443,x11444,x11445),f641(x11442,x11443,x11444,x11445)) % 112.37/112.12 [1145]~E(x11451,x11452)+E(f641(x11453,x11451,x11454,x11455),f641(x11453,x11452,x11454,x11455)) % 112.37/112.12 [1146]~E(x11461,x11462)+E(f641(x11463,x11464,x11461,x11465),f641(x11463,x11464,x11462,x11465)) % 112.37/112.12 [1147]~E(x11471,x11472)+E(f641(x11473,x11474,x11475,x11471),f641(x11473,x11474,x11475,x11472)) % 112.37/112.12 [1148]~E(x11481,x11482)+E(f722(x11481,x11483,x11484,x11485),f722(x11482,x11483,x11484,x11485)) % 112.37/112.12 [1149]~E(x11491,x11492)+E(f722(x11493,x11491,x11494,x11495),f722(x11493,x11492,x11494,x11495)) % 112.37/112.12 [1150]~E(x11501,x11502)+E(f722(x11503,x11504,x11501,x11505),f722(x11503,x11504,x11502,x11505)) % 112.37/112.12 [1151]~E(x11511,x11512)+E(f722(x11513,x11514,x11515,x11511),f722(x11513,x11514,x11515,x11512)) % 112.37/112.12 [1152]~E(x11521,x11522)+E(f860(x11521,x11523),f860(x11522,x11523)) % 112.37/112.12 [1153]~E(x11531,x11532)+E(f860(x11533,x11531),f860(x11533,x11532)) % 112.37/112.12 [1154]~E(x11541,x11542)+E(f694(x11541,x11543,x11544),f694(x11542,x11543,x11544)) % 112.37/112.12 [1155]~E(x11551,x11552)+E(f694(x11553,x11551,x11554),f694(x11553,x11552,x11554)) % 112.37/112.12 [1156]~E(x11561,x11562)+E(f694(x11563,x11564,x11561),f694(x11563,x11564,x11562)) % 112.37/112.12 [1157]~E(x11571,x11572)+E(f829(x11571,x11573,x11574,x11575,x11576,x11577,x11578,x11579),f829(x11572,x11573,x11574,x11575,x11576,x11577,x11578,x11579)) % 112.37/112.12 [1158]~E(x11581,x11582)+E(f829(x11583,x11581,x11584,x11585,x11586,x11587,x11588,x11589),f829(x11583,x11582,x11584,x11585,x11586,x11587,x11588,x11589)) % 112.37/112.12 [1159]~E(x11591,x11592)+E(f829(x11593,x11594,x11591,x11595,x11596,x11597,x11598,x11599),f829(x11593,x11594,x11592,x11595,x11596,x11597,x11598,x11599)) % 112.37/112.12 [1160]~E(x11601,x11602)+E(f829(x11603,x11604,x11605,x11601,x11606,x11607,x11608,x11609),f829(x11603,x11604,x11605,x11602,x11606,x11607,x11608,x11609)) % 112.37/112.12 [1161]~E(x11611,x11612)+E(f829(x11613,x11614,x11615,x11616,x11611,x11617,x11618,x11619),f829(x11613,x11614,x11615,x11616,x11612,x11617,x11618,x11619)) % 112.37/112.12 [1162]~E(x11621,x11622)+E(f829(x11623,x11624,x11625,x11626,x11627,x11621,x11628,x11629),f829(x11623,x11624,x11625,x11626,x11627,x11622,x11628,x11629)) % 112.37/112.12 [1163]~E(x11631,x11632)+E(f829(x11633,x11634,x11635,x11636,x11637,x11638,x11631,x11639),f829(x11633,x11634,x11635,x11636,x11637,x11638,x11632,x11639)) % 112.37/112.12 [1164]~E(x11641,x11642)+E(f829(x11643,x11644,x11645,x11646,x11647,x11648,x11649,x11641),f829(x11643,x11644,x11645,x11646,x11647,x11648,x11649,x11642)) % 112.37/112.12 [1165]~E(x11651,x11652)+E(f709(x11651,x11653),f709(x11652,x11653)) % 112.37/112.12 [1166]~E(x11661,x11662)+E(f709(x11663,x11661),f709(x11663,x11662)) % 112.37/112.12 [1167]~E(x11671,x11672)+E(f50(x11671,x11673),f50(x11672,x11673)) % 112.37/112.12 [1168]~E(x11681,x11682)+E(f50(x11683,x11681),f50(x11683,x11682)) % 112.37/112.12 [1169]~E(x11691,x11692)+E(f742(x11691,x11693,x11694),f742(x11692,x11693,x11694)) % 112.37/112.12 [1170]~E(x11701,x11702)+E(f742(x11703,x11701,x11704),f742(x11703,x11702,x11704)) % 112.37/112.12 [1171]~E(x11711,x11712)+E(f742(x11713,x11714,x11711),f742(x11713,x11714,x11712)) % 112.37/112.12 [1172]~E(x11721,x11722)+E(f450(x11721,x11723,x11724),f450(x11722,x11723,x11724)) % 112.37/112.12 [1173]~E(x11731,x11732)+E(f450(x11733,x11731,x11734),f450(x11733,x11732,x11734)) % 112.37/112.12 [1174]~E(x11741,x11742)+E(f450(x11743,x11744,x11741),f450(x11743,x11744,x11742)) % 112.37/112.12 [1175]~E(x11751,x11752)+E(f522(x11751,x11753,x11754,x11755,x11756),f522(x11752,x11753,x11754,x11755,x11756)) % 112.37/112.12 [1176]~E(x11761,x11762)+E(f522(x11763,x11761,x11764,x11765,x11766),f522(x11763,x11762,x11764,x11765,x11766)) % 112.37/112.12 [1177]~E(x11771,x11772)+E(f522(x11773,x11774,x11771,x11775,x11776),f522(x11773,x11774,x11772,x11775,x11776)) % 112.37/112.12 [1178]~E(x11781,x11782)+E(f522(x11783,x11784,x11785,x11781,x11786),f522(x11783,x11784,x11785,x11782,x11786)) % 112.37/112.12 [1179]~E(x11791,x11792)+E(f522(x11793,x11794,x11795,x11796,x11791),f522(x11793,x11794,x11795,x11796,x11792)) % 112.37/112.12 [1180]~E(x11801,x11802)+E(f420(x11801,x11803,x11804),f420(x11802,x11803,x11804)) % 112.37/112.12 [1181]~E(x11811,x11812)+E(f420(x11813,x11811,x11814),f420(x11813,x11812,x11814)) % 112.37/112.12 [1182]~E(x11821,x11822)+E(f420(x11823,x11824,x11821),f420(x11823,x11824,x11822)) % 112.37/112.12 [1183]~E(x11831,x11832)+E(f189(x11831,x11833),f189(x11832,x11833)) % 112.37/112.12 [1184]~E(x11841,x11842)+E(f189(x11843,x11841),f189(x11843,x11842)) % 112.37/112.12 [1185]~E(x11851,x11852)+E(f460(x11851,x11853,x11854),f460(x11852,x11853,x11854)) % 112.37/112.12 [1186]~E(x11861,x11862)+E(f460(x11863,x11861,x11864),f460(x11863,x11862,x11864)) % 112.37/112.12 [1187]~E(x11871,x11872)+E(f460(x11873,x11874,x11871),f460(x11873,x11874,x11872)) % 112.37/112.12 [1188]~E(x11881,x11882)+E(f119(x11881),f119(x11882)) % 112.37/112.12 [1189]~E(x11891,x11892)+E(f792(x11891,x11893,x11894),f792(x11892,x11893,x11894)) % 112.37/112.12 [1190]~E(x11901,x11902)+E(f792(x11903,x11901,x11904),f792(x11903,x11902,x11904)) % 112.37/112.12 [1191]~E(x11911,x11912)+E(f792(x11913,x11914,x11911),f792(x11913,x11914,x11912)) % 112.37/112.12 [1192]~E(x11921,x11922)+E(f836(x11921,x11923,x11924),f836(x11922,x11923,x11924)) % 112.37/112.12 [1193]~E(x11931,x11932)+E(f836(x11933,x11931,x11934),f836(x11933,x11932,x11934)) % 112.37/112.12 [1194]~E(x11941,x11942)+E(f836(x11943,x11944,x11941),f836(x11943,x11944,x11942)) % 112.37/112.12 [1195]~E(x11951,x11952)+E(f516(x11951,x11953,x11954,x11955,x11956),f516(x11952,x11953,x11954,x11955,x11956)) % 112.37/112.12 [1196]~E(x11961,x11962)+E(f516(x11963,x11961,x11964,x11965,x11966),f516(x11963,x11962,x11964,x11965,x11966)) % 112.37/112.12 [1197]~E(x11971,x11972)+E(f516(x11973,x11974,x11971,x11975,x11976),f516(x11973,x11974,x11972,x11975,x11976)) % 112.37/112.12 [1198]~E(x11981,x11982)+E(f516(x11983,x11984,x11985,x11981,x11986),f516(x11983,x11984,x11985,x11982,x11986)) % 112.37/112.12 [1199]~E(x11991,x11992)+E(f516(x11993,x11994,x11995,x11996,x11991),f516(x11993,x11994,x11995,x11996,x11992)) % 112.37/112.12 [1200]~E(x12001,x12002)+E(f245(x12001,x12003,x12004,x12005),f245(x12002,x12003,x12004,x12005)) % 112.37/112.12 [1201]~E(x12011,x12012)+E(f245(x12013,x12011,x12014,x12015),f245(x12013,x12012,x12014,x12015)) % 112.37/112.12 [1202]~E(x12021,x12022)+E(f245(x12023,x12024,x12021,x12025),f245(x12023,x12024,x12022,x12025)) % 112.37/112.12 [1203]~E(x12031,x12032)+E(f245(x12033,x12034,x12035,x12031),f245(x12033,x12034,x12035,x12032)) % 112.37/112.12 [1204]~E(x12041,x12042)+E(f499(x12041,x12043,x12044),f499(x12042,x12043,x12044)) % 112.37/112.12 [1205]~E(x12051,x12052)+E(f499(x12053,x12051,x12054),f499(x12053,x12052,x12054)) % 112.37/112.12 [1206]~E(x12061,x12062)+E(f499(x12063,x12064,x12061),f499(x12063,x12064,x12062)) % 112.37/112.12 [1207]~E(x12071,x12072)+E(f883(x12071,x12073),f883(x12072,x12073)) % 112.37/112.12 [1208]~E(x12081,x12082)+E(f883(x12083,x12081),f883(x12083,x12082)) % 112.37/112.12 [1209]~E(x12091,x12092)+E(f550(x12091,x12093),f550(x12092,x12093)) % 112.37/112.12 [1210]~E(x12101,x12102)+E(f550(x12103,x12101),f550(x12103,x12102)) % 112.37/112.12 [1211]~E(x12111,x12112)+E(f572(x12111,x12113,x12114),f572(x12112,x12113,x12114)) % 112.37/112.12 [1212]~E(x12121,x12122)+E(f572(x12123,x12121,x12124),f572(x12123,x12122,x12124)) % 112.37/112.12 [1213]~E(x12131,x12132)+E(f572(x12133,x12134,x12131),f572(x12133,x12134,x12132)) % 112.37/112.12 [1214]~E(x12141,x12142)+E(f581(x12141,x12143,x12144,x12145,x12146,x12147,x12148,x12149),f581(x12142,x12143,x12144,x12145,x12146,x12147,x12148,x12149)) % 112.37/112.12 [1215]~E(x12151,x12152)+E(f581(x12153,x12151,x12154,x12155,x12156,x12157,x12158,x12159),f581(x12153,x12152,x12154,x12155,x12156,x12157,x12158,x12159)) % 112.37/112.12 [1216]~E(x12161,x12162)+E(f581(x12163,x12164,x12161,x12165,x12166,x12167,x12168,x12169),f581(x12163,x12164,x12162,x12165,x12166,x12167,x12168,x12169)) % 112.37/112.12 [1217]~E(x12171,x12172)+E(f581(x12173,x12174,x12175,x12171,x12176,x12177,x12178,x12179),f581(x12173,x12174,x12175,x12172,x12176,x12177,x12178,x12179)) % 112.37/112.12 [1218]~E(x12181,x12182)+E(f581(x12183,x12184,x12185,x12186,x12181,x12187,x12188,x12189),f581(x12183,x12184,x12185,x12186,x12182,x12187,x12188,x12189)) % 112.37/112.12 [1219]~E(x12191,x12192)+E(f581(x12193,x12194,x12195,x12196,x12197,x12191,x12198,x12199),f581(x12193,x12194,x12195,x12196,x12197,x12192,x12198,x12199)) % 112.37/112.12 [1220]~E(x12201,x12202)+E(f581(x12203,x12204,x12205,x12206,x12207,x12208,x12201,x12209),f581(x12203,x12204,x12205,x12206,x12207,x12208,x12202,x12209)) % 112.37/112.12 [1221]~E(x12211,x12212)+E(f581(x12213,x12214,x12215,x12216,x12217,x12218,x12219,x12211),f581(x12213,x12214,x12215,x12216,x12217,x12218,x12219,x12212)) % 112.37/112.12 [1222]~E(x12221,x12222)+E(f336(x12221,x12223),f336(x12222,x12223)) % 112.37/112.12 [1223]~E(x12231,x12232)+E(f336(x12233,x12231),f336(x12233,x12232)) % 112.37/112.12 [1224]~E(x12241,x12242)+E(f532(x12241,x12243,x12244,x12245,x12246,x12247),f532(x12242,x12243,x12244,x12245,x12246,x12247)) % 112.37/112.12 [1225]~E(x12251,x12252)+E(f532(x12253,x12251,x12254,x12255,x12256,x12257),f532(x12253,x12252,x12254,x12255,x12256,x12257)) % 112.37/112.12 [1226]~E(x12261,x12262)+E(f532(x12263,x12264,x12261,x12265,x12266,x12267),f532(x12263,x12264,x12262,x12265,x12266,x12267)) % 112.37/112.12 [1227]~E(x12271,x12272)+E(f532(x12273,x12274,x12275,x12271,x12276,x12277),f532(x12273,x12274,x12275,x12272,x12276,x12277)) % 112.37/112.12 [1228]~E(x12281,x12282)+E(f532(x12283,x12284,x12285,x12286,x12281,x12287),f532(x12283,x12284,x12285,x12286,x12282,x12287)) % 112.37/112.12 [1229]~E(x12291,x12292)+E(f532(x12293,x12294,x12295,x12296,x12297,x12291),f532(x12293,x12294,x12295,x12296,x12297,x12292)) % 112.37/112.12 [1230]~E(x12301,x12302)+E(f642(x12301,x12303,x12304),f642(x12302,x12303,x12304)) % 112.37/112.12 [1231]~E(x12311,x12312)+E(f642(x12313,x12311,x12314),f642(x12313,x12312,x12314)) % 112.37/112.12 [1232]~E(x12321,x12322)+E(f642(x12323,x12324,x12321),f642(x12323,x12324,x12322)) % 112.37/112.12 [1233]~E(x12331,x12332)+E(f870(x12331,x12333),f870(x12332,x12333)) % 112.37/112.12 [1234]~E(x12341,x12342)+E(f870(x12343,x12341),f870(x12343,x12342)) % 112.37/112.12 [1235]~E(x12351,x12352)+E(f163(x12351,x12353,x12354),f163(x12352,x12353,x12354)) % 112.37/112.12 [1236]~E(x12361,x12362)+E(f163(x12363,x12361,x12364),f163(x12363,x12362,x12364)) % 112.37/112.12 [1237]~E(x12371,x12372)+E(f163(x12373,x12374,x12371),f163(x12373,x12374,x12372)) % 112.37/112.12 [1238]~E(x12381,x12382)+E(f875(x12381,x12383,x12384),f875(x12382,x12383,x12384)) % 112.37/112.12 [1239]~E(x12391,x12392)+E(f875(x12393,x12391,x12394),f875(x12393,x12392,x12394)) % 112.37/112.12 [1240]~E(x12401,x12402)+E(f875(x12403,x12404,x12401),f875(x12403,x12404,x12402)) % 112.37/112.12 [1241]~E(x12411,x12412)+E(f691(x12411,x12413),f691(x12412,x12413)) % 112.37/112.12 [1242]~E(x12421,x12422)+E(f691(x12423,x12421),f691(x12423,x12422)) % 112.37/112.12 [1243]~E(x12431,x12432)+E(f197(x12431,x12433,x12434,x12435,x12436,x12437,x12438),f197(x12432,x12433,x12434,x12435,x12436,x12437,x12438)) % 112.37/112.12 [1244]~E(x12441,x12442)+E(f197(x12443,x12441,x12444,x12445,x12446,x12447,x12448),f197(x12443,x12442,x12444,x12445,x12446,x12447,x12448)) % 112.37/112.12 [1245]~E(x12451,x12452)+E(f197(x12453,x12454,x12451,x12455,x12456,x12457,x12458),f197(x12453,x12454,x12452,x12455,x12456,x12457,x12458)) % 112.37/112.12 [1246]~E(x12461,x12462)+E(f197(x12463,x12464,x12465,x12461,x12466,x12467,x12468),f197(x12463,x12464,x12465,x12462,x12466,x12467,x12468)) % 112.37/112.12 [1247]~E(x12471,x12472)+E(f197(x12473,x12474,x12475,x12476,x12471,x12477,x12478),f197(x12473,x12474,x12475,x12476,x12472,x12477,x12478)) % 112.37/112.12 [1248]~E(x12481,x12482)+E(f197(x12483,x12484,x12485,x12486,x12487,x12481,x12488),f197(x12483,x12484,x12485,x12486,x12487,x12482,x12488)) % 112.37/112.12 [1249]~E(x12491,x12492)+E(f197(x12493,x12494,x12495,x12496,x12497,x12498,x12491),f197(x12493,x12494,x12495,x12496,x12497,x12498,x12492)) % 112.37/112.12 [1250]~E(x12501,x12502)+E(f226(x12501,x12503),f226(x12502,x12503)) % 112.37/112.12 [1251]~E(x12511,x12512)+E(f226(x12513,x12511),f226(x12513,x12512)) % 112.37/112.12 [1252]~E(x12521,x12522)+E(f772(x12521,x12523,x12524,x12525,x12526,x12527,x12528),f772(x12522,x12523,x12524,x12525,x12526,x12527,x12528)) % 112.37/112.12 [1253]~E(x12531,x12532)+E(f772(x12533,x12531,x12534,x12535,x12536,x12537,x12538),f772(x12533,x12532,x12534,x12535,x12536,x12537,x12538)) % 112.37/112.12 [1254]~E(x12541,x12542)+E(f772(x12543,x12544,x12541,x12545,x12546,x12547,x12548),f772(x12543,x12544,x12542,x12545,x12546,x12547,x12548)) % 112.37/112.12 [1255]~E(x12551,x12552)+E(f772(x12553,x12554,x12555,x12551,x12556,x12557,x12558),f772(x12553,x12554,x12555,x12552,x12556,x12557,x12558)) % 112.37/112.12 [1256]~E(x12561,x12562)+E(f772(x12563,x12564,x12565,x12566,x12561,x12567,x12568),f772(x12563,x12564,x12565,x12566,x12562,x12567,x12568)) % 112.37/112.12 [1257]~E(x12571,x12572)+E(f772(x12573,x12574,x12575,x12576,x12577,x12571,x12578),f772(x12573,x12574,x12575,x12576,x12577,x12572,x12578)) % 112.37/112.12 [1258]~E(x12581,x12582)+E(f772(x12583,x12584,x12585,x12586,x12587,x12588,x12581),f772(x12583,x12584,x12585,x12586,x12587,x12588,x12582)) % 112.37/112.12 [1259]~E(x12591,x12592)+E(f462(x12591,x12593,x12594,x12595,x12596),f462(x12592,x12593,x12594,x12595,x12596)) % 112.37/112.12 [1260]~E(x12601,x12602)+E(f462(x12603,x12601,x12604,x12605,x12606),f462(x12603,x12602,x12604,x12605,x12606)) % 112.37/112.12 [1261]~E(x12611,x12612)+E(f462(x12613,x12614,x12611,x12615,x12616),f462(x12613,x12614,x12612,x12615,x12616)) % 112.37/112.12 [1262]~E(x12621,x12622)+E(f462(x12623,x12624,x12625,x12621,x12626),f462(x12623,x12624,x12625,x12622,x12626)) % 112.37/112.12 [1263]~E(x12631,x12632)+E(f462(x12633,x12634,x12635,x12636,x12631),f462(x12633,x12634,x12635,x12636,x12632)) % 112.37/112.12 [1264]~E(x12641,x12642)+E(f395(x12641,x12643,x12644,x12645),f395(x12642,x12643,x12644,x12645)) % 112.37/112.12 [1265]~E(x12651,x12652)+E(f395(x12653,x12651,x12654,x12655),f395(x12653,x12652,x12654,x12655)) % 112.37/112.12 [1266]~E(x12661,x12662)+E(f395(x12663,x12664,x12661,x12665),f395(x12663,x12664,x12662,x12665)) % 112.37/112.12 [1267]~E(x12671,x12672)+E(f395(x12673,x12674,x12675,x12671),f395(x12673,x12674,x12675,x12672)) % 112.37/112.12 [1268]~E(x12681,x12682)+E(f574(x12681,x12683,x12684),f574(x12682,x12683,x12684)) % 112.37/112.12 [1269]~E(x12691,x12692)+E(f574(x12693,x12691,x12694),f574(x12693,x12692,x12694)) % 112.37/112.12 [1270]~E(x12701,x12702)+E(f574(x12703,x12704,x12701),f574(x12703,x12704,x12702)) % 112.37/112.12 [1271]~E(x12711,x12712)+E(f488(x12711,x12713,x12714),f488(x12712,x12713,x12714)) % 112.37/112.12 [1272]~E(x12721,x12722)+E(f488(x12723,x12721,x12724),f488(x12723,x12722,x12724)) % 112.37/112.12 [1273]~E(x12731,x12732)+E(f488(x12733,x12734,x12731),f488(x12733,x12734,x12732)) % 112.37/112.12 [1274]~E(x12741,x12742)+E(f727(x12741,x12743,x12744,x12745,x12746),f727(x12742,x12743,x12744,x12745,x12746)) % 112.37/112.12 [1275]~E(x12751,x12752)+E(f727(x12753,x12751,x12754,x12755,x12756),f727(x12753,x12752,x12754,x12755,x12756)) % 112.37/112.12 [1276]~E(x12761,x12762)+E(f727(x12763,x12764,x12761,x12765,x12766),f727(x12763,x12764,x12762,x12765,x12766)) % 112.37/112.12 [1277]~E(x12771,x12772)+E(f727(x12773,x12774,x12775,x12771,x12776),f727(x12773,x12774,x12775,x12772,x12776)) % 112.37/112.12 [1278]~E(x12781,x12782)+E(f727(x12783,x12784,x12785,x12786,x12781),f727(x12783,x12784,x12785,x12786,x12782)) % 112.37/112.12 [1279]~E(x12791,x12792)+E(f517(x12791,x12793,x12794,x12795,x12796,x12797,x12798,x12799),f517(x12792,x12793,x12794,x12795,x12796,x12797,x12798,x12799)) % 112.37/112.12 [1280]~E(x12801,x12802)+E(f517(x12803,x12801,x12804,x12805,x12806,x12807,x12808,x12809),f517(x12803,x12802,x12804,x12805,x12806,x12807,x12808,x12809)) % 112.37/112.12 [1281]~E(x12811,x12812)+E(f517(x12813,x12814,x12811,x12815,x12816,x12817,x12818,x12819),f517(x12813,x12814,x12812,x12815,x12816,x12817,x12818,x12819)) % 112.37/112.12 [1282]~E(x12821,x12822)+E(f517(x12823,x12824,x12825,x12821,x12826,x12827,x12828,x12829),f517(x12823,x12824,x12825,x12822,x12826,x12827,x12828,x12829)) % 112.37/112.12 [1283]~E(x12831,x12832)+E(f517(x12833,x12834,x12835,x12836,x12831,x12837,x12838,x12839),f517(x12833,x12834,x12835,x12836,x12832,x12837,x12838,x12839)) % 112.37/112.12 [1284]~E(x12841,x12842)+E(f517(x12843,x12844,x12845,x12846,x12847,x12841,x12848,x12849),f517(x12843,x12844,x12845,x12846,x12847,x12842,x12848,x12849)) % 112.37/112.12 [1285]~E(x12851,x12852)+E(f517(x12853,x12854,x12855,x12856,x12857,x12858,x12851,x12859),f517(x12853,x12854,x12855,x12856,x12857,x12858,x12852,x12859)) % 112.37/112.12 [1286]~E(x12861,x12862)+E(f517(x12863,x12864,x12865,x12866,x12867,x12868,x12869,x12861),f517(x12863,x12864,x12865,x12866,x12867,x12868,x12869,x12862)) % 112.37/112.12 [1287]~E(x12871,x12872)+E(f423(x12871,x12873,x12874),f423(x12872,x12873,x12874)) % 112.37/112.12 [1288]~E(x12881,x12882)+E(f423(x12883,x12881,x12884),f423(x12883,x12882,x12884)) % 112.37/112.12 [1289]~E(x12891,x12892)+E(f423(x12893,x12894,x12891),f423(x12893,x12894,x12892)) % 112.37/112.12 [1290]~E(x12901,x12902)+E(f712(x12901,x12903),f712(x12902,x12903)) % 112.37/112.12 [1291]~E(x12911,x12912)+E(f712(x12913,x12911),f712(x12913,x12912)) % 112.37/112.12 [1292]~E(x12921,x12922)+E(f220(x12921,x12923,x12924),f220(x12922,x12923,x12924)) % 112.37/112.12 [1293]~E(x12931,x12932)+E(f220(x12933,x12931,x12934),f220(x12933,x12932,x12934)) % 112.37/112.12 [1294]~E(x12941,x12942)+E(f220(x12943,x12944,x12941),f220(x12943,x12944,x12942)) % 112.37/112.12 [1295]~E(x12951,x12952)+E(f622(x12951,x12953),f622(x12952,x12953)) % 112.37/112.12 [1296]~E(x12961,x12962)+E(f622(x12963,x12961),f622(x12963,x12962)) % 112.37/112.12 [1297]~E(x12971,x12972)+E(f140(x12971,x12973,x12974,x12975),f140(x12972,x12973,x12974,x12975)) % 112.37/112.12 [1298]~E(x12981,x12982)+E(f140(x12983,x12981,x12984,x12985),f140(x12983,x12982,x12984,x12985)) % 112.37/112.12 [1299]~E(x12991,x12992)+E(f140(x12993,x12994,x12991,x12995),f140(x12993,x12994,x12992,x12995)) % 112.37/112.12 [1300]~E(x13001,x13002)+E(f140(x13003,x13004,x13005,x13001),f140(x13003,x13004,x13005,x13002)) % 112.37/112.12 [1301]~E(x13011,x13012)+E(f548(x13011,x13013,x13014,x13015),f548(x13012,x13013,x13014,x13015)) % 112.37/112.12 [1302]~E(x13021,x13022)+E(f548(x13023,x13021,x13024,x13025),f548(x13023,x13022,x13024,x13025)) % 112.37/112.12 [1303]~E(x13031,x13032)+E(f548(x13033,x13034,x13031,x13035),f548(x13033,x13034,x13032,x13035)) % 112.37/112.12 [1304]~E(x13041,x13042)+E(f548(x13043,x13044,x13045,x13041),f548(x13043,x13044,x13045,x13042)) % 112.37/112.12 [1305]~E(x13051,x13052)+E(f473(x13051,x13053,x13054,x13055,x13056),f473(x13052,x13053,x13054,x13055,x13056)) % 112.37/112.12 [1306]~E(x13061,x13062)+E(f473(x13063,x13061,x13064,x13065,x13066),f473(x13063,x13062,x13064,x13065,x13066)) % 112.37/112.12 [1307]~E(x13071,x13072)+E(f473(x13073,x13074,x13071,x13075,x13076),f473(x13073,x13074,x13072,x13075,x13076)) % 112.37/112.12 [1308]~E(x13081,x13082)+E(f473(x13083,x13084,x13085,x13081,x13086),f473(x13083,x13084,x13085,x13082,x13086)) % 112.37/112.12 [1309]~E(x13091,x13092)+E(f473(x13093,x13094,x13095,x13096,x13091),f473(x13093,x13094,x13095,x13096,x13092)) % 112.37/112.12 [1310]~E(x13101,x13102)+E(f529(x13101,x13103,x13104,x13105),f529(x13102,x13103,x13104,x13105)) % 112.37/112.12 [1311]~E(x13111,x13112)+E(f529(x13113,x13111,x13114,x13115),f529(x13113,x13112,x13114,x13115)) % 112.37/112.12 [1312]~E(x13121,x13122)+E(f529(x13123,x13124,x13121,x13125),f529(x13123,x13124,x13122,x13125)) % 112.37/112.12 [1313]~E(x13131,x13132)+E(f529(x13133,x13134,x13135,x13131),f529(x13133,x13134,x13135,x13132)) % 112.37/112.12 [1314]~E(x13141,x13142)+E(f508(x13141,x13143,x13144,x13145),f508(x13142,x13143,x13144,x13145)) % 112.37/112.12 [1315]~E(x13151,x13152)+E(f508(x13153,x13151,x13154,x13155),f508(x13153,x13152,x13154,x13155)) % 112.37/112.12 [1316]~E(x13161,x13162)+E(f508(x13163,x13164,x13161,x13165),f508(x13163,x13164,x13162,x13165)) % 112.37/112.12 [1317]~E(x13171,x13172)+E(f508(x13173,x13174,x13175,x13171),f508(x13173,x13174,x13175,x13172)) % 112.37/112.12 [1318]~E(x13181,x13182)+E(f381(x13181,x13183,x13184,x13185),f381(x13182,x13183,x13184,x13185)) % 112.37/112.12 [1319]~E(x13191,x13192)+E(f381(x13193,x13191,x13194,x13195),f381(x13193,x13192,x13194,x13195)) % 112.37/112.12 [1320]~E(x13201,x13202)+E(f381(x13203,x13204,x13201,x13205),f381(x13203,x13204,x13202,x13205)) % 112.37/112.12 [1321]~E(x13211,x13212)+E(f381(x13213,x13214,x13215,x13211),f381(x13213,x13214,x13215,x13212)) % 112.37/112.12 [1322]~E(x13221,x13222)+E(f174(x13221,x13223,x13224),f174(x13222,x13223,x13224)) % 112.37/112.12 [1323]~E(x13231,x13232)+E(f174(x13233,x13231,x13234),f174(x13233,x13232,x13234)) % 112.37/112.12 [1324]~E(x13241,x13242)+E(f174(x13243,x13244,x13241),f174(x13243,x13244,x13242)) % 112.37/112.12 [1325]~E(x13251,x13252)+E(f360(x13251,x13253,x13254,x13255,x13256),f360(x13252,x13253,x13254,x13255,x13256)) % 112.37/112.12 [1326]~E(x13261,x13262)+E(f360(x13263,x13261,x13264,x13265,x13266),f360(x13263,x13262,x13264,x13265,x13266)) % 112.37/112.12 [1327]~E(x13271,x13272)+E(f360(x13273,x13274,x13271,x13275,x13276),f360(x13273,x13274,x13272,x13275,x13276)) % 112.37/112.12 [1328]~E(x13281,x13282)+E(f360(x13283,x13284,x13285,x13281,x13286),f360(x13283,x13284,x13285,x13282,x13286)) % 112.37/112.12 [1329]~E(x13291,x13292)+E(f360(x13293,x13294,x13295,x13296,x13291),f360(x13293,x13294,x13295,x13296,x13292)) % 112.37/112.12 [1330]~E(x13301,x13302)+E(f802(x13301,x13303,x13304),f802(x13302,x13303,x13304)) % 112.37/112.12 [1331]~E(x13311,x13312)+E(f802(x13313,x13311,x13314),f802(x13313,x13312,x13314)) % 112.37/112.12 [1332]~E(x13321,x13322)+E(f802(x13323,x13324,x13321),f802(x13323,x13324,x13322)) % 112.37/112.12 [1333]~E(x13331,x13332)+E(f534(x13331,x13333,x13334,x13335,x13336,x13337),f534(x13332,x13333,x13334,x13335,x13336,x13337)) % 112.37/112.12 [1334]~E(x13341,x13342)+E(f534(x13343,x13341,x13344,x13345,x13346,x13347),f534(x13343,x13342,x13344,x13345,x13346,x13347)) % 112.37/112.12 [1335]~E(x13351,x13352)+E(f534(x13353,x13354,x13351,x13355,x13356,x13357),f534(x13353,x13354,x13352,x13355,x13356,x13357)) % 112.37/112.12 [1336]~E(x13361,x13362)+E(f534(x13363,x13364,x13365,x13361,x13366,x13367),f534(x13363,x13364,x13365,x13362,x13366,x13367)) % 112.37/112.12 [1337]~E(x13371,x13372)+E(f534(x13373,x13374,x13375,x13376,x13371,x13377),f534(x13373,x13374,x13375,x13376,x13372,x13377)) % 112.37/112.12 [1338]~E(x13381,x13382)+E(f534(x13383,x13384,x13385,x13386,x13387,x13381),f534(x13383,x13384,x13385,x13386,x13387,x13382)) % 112.37/112.12 [1339]~E(x13391,x13392)+E(f885(x13391,x13393,x13394),f885(x13392,x13393,x13394)) % 112.37/112.12 [1340]~E(x13401,x13402)+E(f885(x13403,x13401,x13404),f885(x13403,x13402,x13404)) % 112.37/112.12 [1341]~E(x13411,x13412)+E(f885(x13413,x13414,x13411),f885(x13413,x13414,x13412)) % 112.37/112.12 [1342]~E(x13421,x13422)+E(f614(x13421,x13423,x13424,x13425,x13426),f614(x13422,x13423,x13424,x13425,x13426)) % 112.37/112.12 [1343]~E(x13431,x13432)+E(f614(x13433,x13431,x13434,x13435,x13436),f614(x13433,x13432,x13434,x13435,x13436)) % 112.37/112.12 [1344]~E(x13441,x13442)+E(f614(x13443,x13444,x13441,x13445,x13446),f614(x13443,x13444,x13442,x13445,x13446)) % 112.37/112.12 [1345]~E(x13451,x13452)+E(f614(x13453,x13454,x13455,x13451,x13456),f614(x13453,x13454,x13455,x13452,x13456)) % 112.37/112.12 [1346]~E(x13461,x13462)+E(f614(x13463,x13464,x13465,x13466,x13461),f614(x13463,x13464,x13465,x13466,x13462)) % 112.37/112.12 [1347]~E(x13471,x13472)+E(f191(x13471),f191(x13472)) % 112.37/112.12 [1348]~E(x13481,x13482)+E(f568(x13481,x13483),f568(x13482,x13483)) % 112.37/112.12 [1349]~E(x13491,x13492)+E(f568(x13493,x13491),f568(x13493,x13492)) % 112.37/112.12 [1350]~E(x13501,x13502)+E(f489(x13501,x13503,x13504,x13505),f489(x13502,x13503,x13504,x13505)) % 112.37/112.12 [1351]~E(x13511,x13512)+E(f489(x13513,x13511,x13514,x13515),f489(x13513,x13512,x13514,x13515)) % 112.37/112.12 [1352]~E(x13521,x13522)+E(f489(x13523,x13524,x13521,x13525),f489(x13523,x13524,x13522,x13525)) % 112.37/112.12 [1353]~E(x13531,x13532)+E(f489(x13533,x13534,x13535,x13531),f489(x13533,x13534,x13535,x13532)) % 112.37/112.12 [1354]~E(x13541,x13542)+E(f528(x13541,x13543),f528(x13542,x13543)) % 112.37/112.12 [1355]~E(x13551,x13552)+E(f528(x13553,x13551),f528(x13553,x13552)) % 112.37/112.12 [1356]~E(x13561,x13562)+E(f479(x13561,x13563,x13564,x13565,x13566),f479(x13562,x13563,x13564,x13565,x13566)) % 112.37/112.12 [1357]~E(x13571,x13572)+E(f479(x13573,x13571,x13574,x13575,x13576),f479(x13573,x13572,x13574,x13575,x13576)) % 112.37/112.12 [1358]~E(x13581,x13582)+E(f479(x13583,x13584,x13581,x13585,x13586),f479(x13583,x13584,x13582,x13585,x13586)) % 112.37/112.12 [1359]~E(x13591,x13592)+E(f479(x13593,x13594,x13595,x13591,x13596),f479(x13593,x13594,x13595,x13592,x13596)) % 112.37/112.12 [1360]~E(x13601,x13602)+E(f479(x13603,x13604,x13605,x13606,x13601),f479(x13603,x13604,x13605,x13606,x13602)) % 112.37/112.12 [1361]~E(x13611,x13612)+E(f329(x13611,x13613,x13614),f329(x13612,x13613,x13614)) % 112.37/112.12 [1362]~E(x13621,x13622)+E(f329(x13623,x13621,x13624),f329(x13623,x13622,x13624)) % 112.37/112.12 [1363]~E(x13631,x13632)+E(f329(x13633,x13634,x13631),f329(x13633,x13634,x13632)) % 112.37/112.12 [1364]~E(x13641,x13642)+E(f771(x13641,x13643,x13644,x13645,x13646,x13647,x13648),f771(x13642,x13643,x13644,x13645,x13646,x13647,x13648)) % 112.37/112.12 [1365]~E(x13651,x13652)+E(f771(x13653,x13651,x13654,x13655,x13656,x13657,x13658),f771(x13653,x13652,x13654,x13655,x13656,x13657,x13658)) % 112.37/112.12 [1366]~E(x13661,x13662)+E(f771(x13663,x13664,x13661,x13665,x13666,x13667,x13668),f771(x13663,x13664,x13662,x13665,x13666,x13667,x13668)) % 112.37/112.12 [1367]~E(x13671,x13672)+E(f771(x13673,x13674,x13675,x13671,x13676,x13677,x13678),f771(x13673,x13674,x13675,x13672,x13676,x13677,x13678)) % 112.37/112.12 [1368]~E(x13681,x13682)+E(f771(x13683,x13684,x13685,x13686,x13681,x13687,x13688),f771(x13683,x13684,x13685,x13686,x13682,x13687,x13688)) % 112.37/112.12 [1369]~E(x13691,x13692)+E(f771(x13693,x13694,x13695,x13696,x13697,x13691,x13698),f771(x13693,x13694,x13695,x13696,x13697,x13692,x13698)) % 112.37/112.12 [1370]~E(x13701,x13702)+E(f771(x13703,x13704,x13705,x13706,x13707,x13708,x13701),f771(x13703,x13704,x13705,x13706,x13707,x13708,x13702)) % 112.37/112.12 [1371]~E(x13711,x13712)+E(f265(x13711,x13713),f265(x13712,x13713)) % 112.37/112.12 [1372]~E(x13721,x13722)+E(f265(x13723,x13721),f265(x13723,x13722)) % 112.37/112.12 [1373]~E(x13731,x13732)+E(f19(x13731,x13733,x13734,x13735),f19(x13732,x13733,x13734,x13735)) % 112.37/112.12 [1374]~E(x13741,x13742)+E(f19(x13743,x13741,x13744,x13745),f19(x13743,x13742,x13744,x13745)) % 112.37/112.12 [1375]~E(x13751,x13752)+E(f19(x13753,x13754,x13751,x13755),f19(x13753,x13754,x13752,x13755)) % 112.37/112.12 [1376]~E(x13761,x13762)+E(f19(x13763,x13764,x13765,x13761),f19(x13763,x13764,x13765,x13762)) % 112.37/112.12 [1377]~E(x13771,x13772)+E(f583(x13771,x13773,x13774),f583(x13772,x13773,x13774)) % 112.37/112.12 [1378]~E(x13781,x13782)+E(f583(x13783,x13781,x13784),f583(x13783,x13782,x13784)) % 112.37/112.12 [1379]~E(x13791,x13792)+E(f583(x13793,x13794,x13791),f583(x13793,x13794,x13792)) % 112.37/112.12 [1380]~E(x13801,x13802)+E(f794(x13801,x13803,x13804,x13805,x13806),f794(x13802,x13803,x13804,x13805,x13806)) % 112.37/112.12 [1381]~E(x13811,x13812)+E(f794(x13813,x13811,x13814,x13815,x13816),f794(x13813,x13812,x13814,x13815,x13816)) % 112.37/112.12 [1382]~E(x13821,x13822)+E(f794(x13823,x13824,x13821,x13825,x13826),f794(x13823,x13824,x13822,x13825,x13826)) % 112.37/112.12 [1383]~E(x13831,x13832)+E(f794(x13833,x13834,x13835,x13831,x13836),f794(x13833,x13834,x13835,x13832,x13836)) % 112.37/112.12 [1384]~E(x13841,x13842)+E(f794(x13843,x13844,x13845,x13846,x13841),f794(x13843,x13844,x13845,x13846,x13842)) % 112.37/112.12 [1385]~E(x13851,x13852)+E(f416(x13851,x13853,x13854,x13855,x13856),f416(x13852,x13853,x13854,x13855,x13856)) % 112.37/112.12 [1386]~E(x13861,x13862)+E(f416(x13863,x13861,x13864,x13865,x13866),f416(x13863,x13862,x13864,x13865,x13866)) % 112.37/112.12 [1387]~E(x13871,x13872)+E(f416(x13873,x13874,x13871,x13875,x13876),f416(x13873,x13874,x13872,x13875,x13876)) % 112.37/112.12 [1388]~E(x13881,x13882)+E(f416(x13883,x13884,x13885,x13881,x13886),f416(x13883,x13884,x13885,x13882,x13886)) % 112.37/112.12 [1389]~E(x13891,x13892)+E(f416(x13893,x13894,x13895,x13896,x13891),f416(x13893,x13894,x13895,x13896,x13892)) % 112.37/112.12 [1390]~E(x13901,x13902)+E(f259(x13901,x13903),f259(x13902,x13903)) % 112.37/112.12 [1391]~E(x13911,x13912)+E(f259(x13913,x13911),f259(x13913,x13912)) % 112.37/112.12 [1392]~E(x13921,x13922)+E(f606(x13921,x13923,x13924),f606(x13922,x13923,x13924)) % 112.37/112.12 [1393]~E(x13931,x13932)+E(f606(x13933,x13931,x13934),f606(x13933,x13932,x13934)) % 112.37/112.12 [1394]~E(x13941,x13942)+E(f606(x13943,x13944,x13941),f606(x13943,x13944,x13942)) % 112.37/112.12 [1395]~E(x13951,x13952)+E(f497(x13951),f497(x13952)) % 112.37/112.12 [1396]~E(x13961,x13962)+E(f856(x13961,x13963,x13964),f856(x13962,x13963,x13964)) % 112.37/112.12 [1397]~E(x13971,x13972)+E(f856(x13973,x13971,x13974),f856(x13973,x13972,x13974)) % 112.37/112.12 [1398]~E(x13981,x13982)+E(f856(x13983,x13984,x13981),f856(x13983,x13984,x13982)) % 112.37/112.12 [1399]~E(x13991,x13992)+E(f377(x13991,x13993),f377(x13992,x13993)) % 112.37/112.12 [1400]~E(x14001,x14002)+E(f377(x14003,x14001),f377(x14003,x14002)) % 112.37/112.12 [1401]~E(x14011,x14012)+E(f801(x14011,x14013),f801(x14012,x14013)) % 112.37/112.12 [1402]~E(x14021,x14022)+E(f801(x14023,x14021),f801(x14023,x14022)) % 112.37/112.12 [1403]~E(x14031,x14032)+E(f697(x14031,x14033,x14034),f697(x14032,x14033,x14034)) % 112.37/112.12 [1404]~E(x14041,x14042)+E(f697(x14043,x14041,x14044),f697(x14043,x14042,x14044)) % 112.37/112.12 [1405]~E(x14051,x14052)+E(f697(x14053,x14054,x14051),f697(x14053,x14054,x14052)) % 112.37/112.12 [1406]~E(x14061,x14062)+E(f596(x14061,x14063,x14064),f596(x14062,x14063,x14064)) % 112.37/112.12 [1407]~E(x14071,x14072)+E(f596(x14073,x14071,x14074),f596(x14073,x14072,x14074)) % 112.37/112.12 [1408]~E(x14081,x14082)+E(f596(x14083,x14084,x14081),f596(x14083,x14084,x14082)) % 112.37/112.12 [1409]~E(x14091,x14092)+E(f635(x14091,x14093,x14094,x14095,x14096),f635(x14092,x14093,x14094,x14095,x14096)) % 112.37/112.12 [1410]~E(x14101,x14102)+E(f635(x14103,x14101,x14104,x14105,x14106),f635(x14103,x14102,x14104,x14105,x14106)) % 112.37/112.12 [1411]~E(x14111,x14112)+E(f635(x14113,x14114,x14111,x14115,x14116),f635(x14113,x14114,x14112,x14115,x14116)) % 112.37/112.12 [1412]~E(x14121,x14122)+E(f635(x14123,x14124,x14125,x14121,x14126),f635(x14123,x14124,x14125,x14122,x14126)) % 112.37/112.12 [1413]~E(x14131,x14132)+E(f635(x14133,x14134,x14135,x14136,x14131),f635(x14133,x14134,x14135,x14136,x14132)) % 112.37/112.12 [1414]~E(x14141,x14142)+E(f644(x14141,x14143,x14144),f644(x14142,x14143,x14144)) % 112.37/112.12 [1415]~E(x14151,x14152)+E(f644(x14153,x14151,x14154),f644(x14153,x14152,x14154)) % 112.37/112.12 [1416]~E(x14161,x14162)+E(f644(x14163,x14164,x14161),f644(x14163,x14164,x14162)) % 112.37/112.12 [1417]~E(x14171,x14172)+E(f746(x14171,x14173,x14174),f746(x14172,x14173,x14174)) % 112.37/112.12 [1418]~E(x14181,x14182)+E(f746(x14183,x14181,x14184),f746(x14183,x14182,x14184)) % 112.37/112.12 [1419]~E(x14191,x14192)+E(f746(x14193,x14194,x14191),f746(x14193,x14194,x14192)) % 112.37/112.12 [1420]~E(x14201,x14202)+E(f867(x14201,x14203,x14204),f867(x14202,x14203,x14204)) % 112.37/112.12 [1421]~E(x14211,x14212)+E(f867(x14213,x14211,x14214),f867(x14213,x14212,x14214)) % 112.37/112.12 [1422]~E(x14221,x14222)+E(f867(x14223,x14224,x14221),f867(x14223,x14224,x14222)) % 112.37/112.12 [1423]~E(x14231,x14232)+E(f543(x14231,x14233,x14234,x14235,x14236,x14237,x14238),f543(x14232,x14233,x14234,x14235,x14236,x14237,x14238)) % 112.37/112.12 [1424]~E(x14241,x14242)+E(f543(x14243,x14241,x14244,x14245,x14246,x14247,x14248),f543(x14243,x14242,x14244,x14245,x14246,x14247,x14248)) % 112.37/112.12 [1425]~E(x14251,x14252)+E(f543(x14253,x14254,x14251,x14255,x14256,x14257,x14258),f543(x14253,x14254,x14252,x14255,x14256,x14257,x14258)) % 112.37/112.12 [1426]~E(x14261,x14262)+E(f543(x14263,x14264,x14265,x14261,x14266,x14267,x14268),f543(x14263,x14264,x14265,x14262,x14266,x14267,x14268)) % 112.37/112.12 [1427]~E(x14271,x14272)+E(f543(x14273,x14274,x14275,x14276,x14271,x14277,x14278),f543(x14273,x14274,x14275,x14276,x14272,x14277,x14278)) % 112.37/112.12 [1428]~E(x14281,x14282)+E(f543(x14283,x14284,x14285,x14286,x14287,x14281,x14288),f543(x14283,x14284,x14285,x14286,x14287,x14282,x14288)) % 112.37/112.12 [1429]~E(x14291,x14292)+E(f543(x14293,x14294,x14295,x14296,x14297,x14298,x14291),f543(x14293,x14294,x14295,x14296,x14297,x14298,x14292)) % 112.37/112.12 [1430]~E(x14301,x14302)+E(f610(x14301,x14303),f610(x14302,x14303)) % 112.37/112.12 [1431]~E(x14311,x14312)+E(f610(x14313,x14311),f610(x14313,x14312)) % 112.37/112.12 [1432]~E(x14321,x14322)+E(f227(x14321,x14323),f227(x14322,x14323)) % 112.37/112.12 [1433]~E(x14331,x14332)+E(f227(x14333,x14331),f227(x14333,x14332)) % 112.37/112.12 [1434]~E(x14341,x14342)+E(f399(x14341,x14343),f399(x14342,x14343)) % 112.37/112.12 [1435]~E(x14351,x14352)+E(f399(x14353,x14351),f399(x14353,x14352)) % 112.37/112.12 [1436]~E(x14361,x14362)+E(f649(x14361,x14363,x14364,x14365),f649(x14362,x14363,x14364,x14365)) % 112.37/112.12 [1437]~E(x14371,x14372)+E(f649(x14373,x14371,x14374,x14375),f649(x14373,x14372,x14374,x14375)) % 112.37/112.12 [1438]~E(x14381,x14382)+E(f649(x14383,x14384,x14381,x14385),f649(x14383,x14384,x14382,x14385)) % 112.37/112.12 [1439]~E(x14391,x14392)+E(f649(x14393,x14394,x14395,x14391),f649(x14393,x14394,x14395,x14392)) % 112.37/112.12 [1440]~E(x14401,x14402)+E(f786(x14401,x14403),f786(x14402,x14403)) % 112.37/112.12 [1441]~E(x14411,x14412)+E(f786(x14413,x14411),f786(x14413,x14412)) % 112.37/112.12 [1442]~E(x14421,x14422)+E(f739(x14421,x14423,x14424),f739(x14422,x14423,x14424)) % 112.37/112.12 [1443]~E(x14431,x14432)+E(f739(x14433,x14431,x14434),f739(x14433,x14432,x14434)) % 112.37/112.12 [1444]~E(x14441,x14442)+E(f739(x14443,x14444,x14441),f739(x14443,x14444,x14442)) % 112.37/112.12 [1445]~E(x14451,x14452)+E(f579(x14451,x14453,x14454,x14455,x14456,x14457),f579(x14452,x14453,x14454,x14455,x14456,x14457)) % 112.37/112.12 [1446]~E(x14461,x14462)+E(f579(x14463,x14461,x14464,x14465,x14466,x14467),f579(x14463,x14462,x14464,x14465,x14466,x14467)) % 112.37/112.12 [1447]~E(x14471,x14472)+E(f579(x14473,x14474,x14471,x14475,x14476,x14477),f579(x14473,x14474,x14472,x14475,x14476,x14477)) % 112.37/112.12 [1448]~E(x14481,x14482)+E(f579(x14483,x14484,x14485,x14481,x14486,x14487),f579(x14483,x14484,x14485,x14482,x14486,x14487)) % 112.37/112.12 [1449]~E(x14491,x14492)+E(f579(x14493,x14494,x14495,x14496,x14491,x14497),f579(x14493,x14494,x14495,x14496,x14492,x14497)) % 112.37/112.12 [1450]~E(x14501,x14502)+E(f579(x14503,x14504,x14505,x14506,x14507,x14501),f579(x14503,x14504,x14505,x14506,x14507,x14502)) % 112.37/112.12 [1451]~E(x14511,x14512)+E(f206(x14511,x14513),f206(x14512,x14513)) % 112.37/112.12 [1452]~E(x14521,x14522)+E(f206(x14523,x14521),f206(x14523,x14522)) % 112.37/112.12 [1453]~E(x14531,x14532)+E(f810(x14531,x14533,x14534,x14535,x14536),f810(x14532,x14533,x14534,x14535,x14536)) % 112.37/112.12 [1454]~E(x14541,x14542)+E(f810(x14543,x14541,x14544,x14545,x14546),f810(x14543,x14542,x14544,x14545,x14546)) % 112.37/112.12 [1455]~E(x14551,x14552)+E(f810(x14553,x14554,x14551,x14555,x14556),f810(x14553,x14554,x14552,x14555,x14556)) % 112.37/112.12 [1456]~E(x14561,x14562)+E(f810(x14563,x14564,x14565,x14561,x14566),f810(x14563,x14564,x14565,x14562,x14566)) % 112.37/112.12 [1457]~E(x14571,x14572)+E(f810(x14573,x14574,x14575,x14576,x14571),f810(x14573,x14574,x14575,x14576,x14572)) % 112.37/112.12 [1458]~E(x14581,x14582)+E(f778(x14581,x14583,x14584),f778(x14582,x14583,x14584)) % 112.37/112.12 [1459]~E(x14591,x14592)+E(f778(x14593,x14591,x14594),f778(x14593,x14592,x14594)) % 112.37/112.12 [1460]~E(x14601,x14602)+E(f778(x14603,x14604,x14601),f778(x14603,x14604,x14602)) % 112.37/112.12 [1461]~E(x14611,x14612)+E(f617(x14611,x14613,x14614,x14615,x14616),f617(x14612,x14613,x14614,x14615,x14616)) % 112.37/112.12 [1462]~E(x14621,x14622)+E(f617(x14623,x14621,x14624,x14625,x14626),f617(x14623,x14622,x14624,x14625,x14626)) % 112.37/112.12 [1463]~E(x14631,x14632)+E(f617(x14633,x14634,x14631,x14635,x14636),f617(x14633,x14634,x14632,x14635,x14636)) % 112.37/112.12 [1464]~E(x14641,x14642)+E(f617(x14643,x14644,x14645,x14641,x14646),f617(x14643,x14644,x14645,x14642,x14646)) % 112.37/112.12 [1465]~E(x14651,x14652)+E(f617(x14653,x14654,x14655,x14656,x14651),f617(x14653,x14654,x14655,x14656,x14652)) % 112.37/112.12 [1466]~E(x14661,x14662)+E(f271(x14661),f271(x14662)) % 112.37/112.12 [1467]~E(x14671,x14672)+E(f719(x14671,x14673),f719(x14672,x14673)) % 112.37/112.12 [1468]~E(x14681,x14682)+E(f719(x14683,x14681),f719(x14683,x14682)) % 112.37/112.12 [1469]~E(x14691,x14692)+E(f356(x14691,x14693,x14694,x14695),f356(x14692,x14693,x14694,x14695)) % 112.37/112.12 [1470]~E(x14701,x14702)+E(f356(x14703,x14701,x14704,x14705),f356(x14703,x14702,x14704,x14705)) % 112.37/112.12 [1471]~E(x14711,x14712)+E(f356(x14713,x14714,x14711,x14715),f356(x14713,x14714,x14712,x14715)) % 112.37/112.12 [1472]~E(x14721,x14722)+E(f356(x14723,x14724,x14725,x14721),f356(x14723,x14724,x14725,x14722)) % 112.37/112.12 [1473]~E(x14731,x14732)+E(f831(x14731,x14733,x14734,x14735,x14736,x14737,x14738,x14739),f831(x14732,x14733,x14734,x14735,x14736,x14737,x14738,x14739)) % 112.37/112.12 [1474]~E(x14741,x14742)+E(f831(x14743,x14741,x14744,x14745,x14746,x14747,x14748,x14749),f831(x14743,x14742,x14744,x14745,x14746,x14747,x14748,x14749)) % 112.37/112.12 [1475]~E(x14751,x14752)+E(f831(x14753,x14754,x14751,x14755,x14756,x14757,x14758,x14759),f831(x14753,x14754,x14752,x14755,x14756,x14757,x14758,x14759)) % 112.37/112.12 [1476]~E(x14761,x14762)+E(f831(x14763,x14764,x14765,x14761,x14766,x14767,x14768,x14769),f831(x14763,x14764,x14765,x14762,x14766,x14767,x14768,x14769)) % 112.37/112.12 [1477]~E(x14771,x14772)+E(f831(x14773,x14774,x14775,x14776,x14771,x14777,x14778,x14779),f831(x14773,x14774,x14775,x14776,x14772,x14777,x14778,x14779)) % 112.37/112.12 [1478]~E(x14781,x14782)+E(f831(x14783,x14784,x14785,x14786,x14787,x14781,x14788,x14789),f831(x14783,x14784,x14785,x14786,x14787,x14782,x14788,x14789)) % 112.37/112.12 [1479]~E(x14791,x14792)+E(f831(x14793,x14794,x14795,x14796,x14797,x14798,x14791,x14799),f831(x14793,x14794,x14795,x14796,x14797,x14798,x14792,x14799)) % 112.37/112.12 [1480]~E(x14801,x14802)+E(f831(x14803,x14804,x14805,x14806,x14807,x14808,x14809,x14801),f831(x14803,x14804,x14805,x14806,x14807,x14808,x14809,x14802)) % 112.37/112.12 [1481]~E(x14811,x14812)+E(f833(x14811,x14813,x14814,x14815,x14816,x14817,x14818,x14819),f833(x14812,x14813,x14814,x14815,x14816,x14817,x14818,x14819)) % 112.37/112.12 [1482]~E(x14821,x14822)+E(f833(x14823,x14821,x14824,x14825,x14826,x14827,x14828,x14829),f833(x14823,x14822,x14824,x14825,x14826,x14827,x14828,x14829)) % 112.37/112.12 [1483]~E(x14831,x14832)+E(f833(x14833,x14834,x14831,x14835,x14836,x14837,x14838,x14839),f833(x14833,x14834,x14832,x14835,x14836,x14837,x14838,x14839)) % 112.37/112.12 [1484]~E(x14841,x14842)+E(f833(x14843,x14844,x14845,x14841,x14846,x14847,x14848,x14849),f833(x14843,x14844,x14845,x14842,x14846,x14847,x14848,x14849)) % 112.37/112.12 [1485]~E(x14851,x14852)+E(f833(x14853,x14854,x14855,x14856,x14851,x14857,x14858,x14859),f833(x14853,x14854,x14855,x14856,x14852,x14857,x14858,x14859)) % 112.37/112.12 [1486]~E(x14861,x14862)+E(f833(x14863,x14864,x14865,x14866,x14867,x14861,x14868,x14869),f833(x14863,x14864,x14865,x14866,x14867,x14862,x14868,x14869)) % 112.37/112.12 [1487]~E(x14871,x14872)+E(f833(x14873,x14874,x14875,x14876,x14877,x14878,x14871,x14879),f833(x14873,x14874,x14875,x14876,x14877,x14878,x14872,x14879)) % 112.37/112.12 [1488]~E(x14881,x14882)+E(f833(x14883,x14884,x14885,x14886,x14887,x14888,x14889,x14881),f833(x14883,x14884,x14885,x14886,x14887,x14888,x14889,x14882)) % 112.37/112.12 [1489]~E(x14891,x14892)+E(f404(x14891,x14893,x14894),f404(x14892,x14893,x14894)) % 112.37/112.12 [1490]~E(x14901,x14902)+E(f404(x14903,x14901,x14904),f404(x14903,x14902,x14904)) % 112.37/112.12 [1491]~E(x14911,x14912)+E(f404(x14913,x14914,x14911),f404(x14913,x14914,x14912)) % 112.37/112.12 [1492]~E(x14921,x14922)+E(f853(x14921,x14923,x14924),f853(x14922,x14923,x14924)) % 112.37/112.12 [1493]~E(x14931,x14932)+E(f853(x14933,x14931,x14934),f853(x14933,x14932,x14934)) % 112.37/112.12 [1494]~E(x14941,x14942)+E(f853(x14943,x14944,x14941),f853(x14943,x14944,x14942)) % 112.37/112.12 [1495]~E(x14951,x14952)+E(f586(x14951,x14953),f586(x14952,x14953)) % 112.37/112.12 [1496]~E(x14961,x14962)+E(f586(x14963,x14961),f586(x14963,x14962)) % 112.37/112.12 [1497]~E(x14971,x14972)+E(f640(x14971,x14973,x14974),f640(x14972,x14973,x14974)) % 112.37/112.12 [1498]~E(x14981,x14982)+E(f640(x14983,x14981,x14984),f640(x14983,x14982,x14984)) % 112.37/112.12 [1499]~E(x14991,x14992)+E(f640(x14993,x14994,x14991),f640(x14993,x14994,x14992)) % 112.37/112.12 [1500]~E(x15001,x15002)+E(f262(x15001,x15003),f262(x15002,x15003)) % 112.37/112.12 [1501]~E(x15011,x15012)+E(f262(x15013,x15011),f262(x15013,x15012)) % 112.37/112.12 [1502]~E(x15021,x15022)+E(f403(x15021,x15023),f403(x15022,x15023)) % 112.37/112.12 [1503]~E(x15031,x15032)+E(f403(x15033,x15031),f403(x15033,x15032)) % 112.37/112.12 [1504]~E(x15041,x15042)+E(f576(x15041,x15043,x15044,x15045,x15046,x15047),f576(x15042,x15043,x15044,x15045,x15046,x15047)) % 112.37/112.12 [1505]~E(x15051,x15052)+E(f576(x15053,x15051,x15054,x15055,x15056,x15057),f576(x15053,x15052,x15054,x15055,x15056,x15057)) % 112.37/112.12 [1506]~E(x15061,x15062)+E(f576(x15063,x15064,x15061,x15065,x15066,x15067),f576(x15063,x15064,x15062,x15065,x15066,x15067)) % 112.37/112.12 [1507]~E(x15071,x15072)+E(f576(x15073,x15074,x15075,x15071,x15076,x15077),f576(x15073,x15074,x15075,x15072,x15076,x15077)) % 112.37/112.12 [1508]~E(x15081,x15082)+E(f576(x15083,x15084,x15085,x15086,x15081,x15087),f576(x15083,x15084,x15085,x15086,x15082,x15087)) % 112.37/112.12 [1509]~E(x15091,x15092)+E(f576(x15093,x15094,x15095,x15096,x15097,x15091),f576(x15093,x15094,x15095,x15096,x15097,x15092)) % 112.37/112.12 [1510]~E(x15101,x15102)+E(f108(x15101,x15103,x15104),f108(x15102,x15103,x15104)) % 112.37/112.12 [1511]~E(x15111,x15112)+E(f108(x15113,x15111,x15114),f108(x15113,x15112,x15114)) % 112.37/112.12 [1512]~E(x15121,x15122)+E(f108(x15123,x15124,x15121),f108(x15123,x15124,x15122)) % 112.37/112.12 [1513]~E(x15131,x15132)+E(f696(x15131,x15133,x15134),f696(x15132,x15133,x15134)) % 112.37/112.12 [1514]~E(x15141,x15142)+E(f696(x15143,x15141,x15144),f696(x15143,x15142,x15144)) % 112.37/112.12 [1515]~E(x15151,x15152)+E(f696(x15153,x15154,x15151),f696(x15153,x15154,x15152)) % 112.37/112.12 [1516]~E(x15161,x15162)+E(f711(x15161,x15163),f711(x15162,x15163)) % 112.37/112.12 [1517]~E(x15171,x15172)+E(f711(x15173,x15171),f711(x15173,x15172)) % 112.37/112.12 [1518]~E(x15181,x15182)+E(f580(x15181,x15183,x15184,x15185,x15186,x15187),f580(x15182,x15183,x15184,x15185,x15186,x15187)) % 112.37/112.12 [1519]~E(x15191,x15192)+E(f580(x15193,x15191,x15194,x15195,x15196,x15197),f580(x15193,x15192,x15194,x15195,x15196,x15197)) % 112.37/112.12 [1520]~E(x15201,x15202)+E(f580(x15203,x15204,x15201,x15205,x15206,x15207),f580(x15203,x15204,x15202,x15205,x15206,x15207)) % 112.37/112.12 [1521]~E(x15211,x15212)+E(f580(x15213,x15214,x15215,x15211,x15216,x15217),f580(x15213,x15214,x15215,x15212,x15216,x15217)) % 112.37/112.12 [1522]~E(x15221,x15222)+E(f580(x15223,x15224,x15225,x15226,x15221,x15227),f580(x15223,x15224,x15225,x15226,x15222,x15227)) % 112.37/112.12 [1523]~E(x15231,x15232)+E(f580(x15233,x15234,x15235,x15236,x15237,x15231),f580(x15233,x15234,x15235,x15236,x15237,x15232)) % 112.37/112.12 [1524]~E(x15241,x15242)+E(f243(x15241,x15243,x15244,x15245,x15246),f243(x15242,x15243,x15244,x15245,x15246)) % 112.37/112.12 [1525]~E(x15251,x15252)+E(f243(x15253,x15251,x15254,x15255,x15256),f243(x15253,x15252,x15254,x15255,x15256)) % 112.37/112.12 [1526]~E(x15261,x15262)+E(f243(x15263,x15264,x15261,x15265,x15266),f243(x15263,x15264,x15262,x15265,x15266)) % 112.37/112.12 [1527]~E(x15271,x15272)+E(f243(x15273,x15274,x15275,x15271,x15276),f243(x15273,x15274,x15275,x15272,x15276)) % 112.37/112.12 [1528]~E(x15281,x15282)+E(f243(x15283,x15284,x15285,x15286,x15281),f243(x15283,x15284,x15285,x15286,x15282)) % 112.37/112.12 [1529]~E(x15291,x15292)+E(f797(x15291,x15293,x15294,x15295,x15296,x15297),f797(x15292,x15293,x15294,x15295,x15296,x15297)) % 112.37/112.12 [1530]~E(x15301,x15302)+E(f797(x15303,x15301,x15304,x15305,x15306,x15307),f797(x15303,x15302,x15304,x15305,x15306,x15307)) % 112.37/112.12 [1531]~E(x15311,x15312)+E(f797(x15313,x15314,x15311,x15315,x15316,x15317),f797(x15313,x15314,x15312,x15315,x15316,x15317)) % 112.37/112.12 [1532]~E(x15321,x15322)+E(f797(x15323,x15324,x15325,x15321,x15326,x15327),f797(x15323,x15324,x15325,x15322,x15326,x15327)) % 112.37/112.12 [1533]~E(x15331,x15332)+E(f797(x15333,x15334,x15335,x15336,x15331,x15337),f797(x15333,x15334,x15335,x15336,x15332,x15337)) % 112.37/112.12 [1534]~E(x15341,x15342)+E(f797(x15343,x15344,x15345,x15346,x15347,x15341),f797(x15343,x15344,x15345,x15346,x15347,x15342)) % 112.37/112.12 [1535]~E(x15351,x15352)+E(f748(x15351,x15353,x15354),f748(x15352,x15353,x15354)) % 112.37/112.12 [1536]~E(x15361,x15362)+E(f748(x15363,x15361,x15364),f748(x15363,x15362,x15364)) % 112.37/112.12 [1537]~E(x15371,x15372)+E(f748(x15373,x15374,x15371),f748(x15373,x15374,x15372)) % 112.37/112.12 [1538]~E(x15381,x15382)+E(f888(x15381,x15383),f888(x15382,x15383)) % 112.37/112.12 [1539]~E(x15391,x15392)+E(f888(x15393,x15391),f888(x15393,x15392)) % 112.37/112.12 [1540]~E(x15401,x15402)+E(f385(x15401,x15403),f385(x15402,x15403)) % 112.37/112.12 [1541]~E(x15411,x15412)+E(f385(x15413,x15411),f385(x15413,x15412)) % 112.37/112.12 [1542]~E(x15421,x15422)+E(f577(x15421,x15423,x15424,x15425,x15426,x15427),f577(x15422,x15423,x15424,x15425,x15426,x15427)) % 112.37/112.12 [1543]~E(x15431,x15432)+E(f577(x15433,x15431,x15434,x15435,x15436,x15437),f577(x15433,x15432,x15434,x15435,x15436,x15437)) % 112.37/112.12 [1544]~E(x15441,x15442)+E(f577(x15443,x15444,x15441,x15445,x15446,x15447),f577(x15443,x15444,x15442,x15445,x15446,x15447)) % 112.37/112.12 [1545]~E(x15451,x15452)+E(f577(x15453,x15454,x15455,x15451,x15456,x15457),f577(x15453,x15454,x15455,x15452,x15456,x15457)) % 112.37/112.12 [1546]~E(x15461,x15462)+E(f577(x15463,x15464,x15465,x15466,x15461,x15467),f577(x15463,x15464,x15465,x15466,x15462,x15467)) % 112.37/112.12 [1547]~E(x15471,x15472)+E(f577(x15473,x15474,x15475,x15476,x15477,x15471),f577(x15473,x15474,x15475,x15476,x15477,x15472)) % 112.37/112.12 [1548]~E(x15481,x15482)+E(f466(x15481,x15483,x15484,x15485),f466(x15482,x15483,x15484,x15485)) % 112.37/112.12 [1549]~E(x15491,x15492)+E(f466(x15493,x15491,x15494,x15495),f466(x15493,x15492,x15494,x15495)) % 112.37/112.12 [1550]~E(x15501,x15502)+E(f466(x15503,x15504,x15501,x15505),f466(x15503,x15504,x15502,x15505)) % 112.37/112.12 [1551]~E(x15511,x15512)+E(f466(x15513,x15514,x15515,x15511),f466(x15513,x15514,x15515,x15512)) % 112.37/112.12 [1552]~E(x15521,x15522)+E(f760(x15521,x15523,x15524,x15525),f760(x15522,x15523,x15524,x15525)) % 112.37/112.12 [1553]~E(x15531,x15532)+E(f760(x15533,x15531,x15534,x15535),f760(x15533,x15532,x15534,x15535)) % 112.37/112.12 [1554]~E(x15541,x15542)+E(f760(x15543,x15544,x15541,x15545),f760(x15543,x15544,x15542,x15545)) % 112.37/112.12 [1555]~E(x15551,x15552)+E(f760(x15553,x15554,x15555,x15551),f760(x15553,x15554,x15555,x15552)) % 112.37/112.12 [1556]~E(x15561,x15562)+E(f665(x15561,x15563,x15564,x15565),f665(x15562,x15563,x15564,x15565)) % 112.37/112.12 [1557]~E(x15571,x15572)+E(f665(x15573,x15571,x15574,x15575),f665(x15573,x15572,x15574,x15575)) % 112.37/112.12 [1558]~E(x15581,x15582)+E(f665(x15583,x15584,x15581,x15585),f665(x15583,x15584,x15582,x15585)) % 112.37/112.12 [1559]~E(x15591,x15592)+E(f665(x15593,x15594,x15595,x15591),f665(x15593,x15594,x15595,x15592)) % 112.37/112.12 [1560]~E(x15601,x15602)+E(f871(x15601,x15603),f871(x15602,x15603)) % 112.37/112.12 [1561]~E(x15611,x15612)+E(f871(x15613,x15611),f871(x15613,x15612)) % 112.37/112.12 [1562]~E(x15621,x15622)+E(f558(x15621,x15623,x15624),f558(x15622,x15623,x15624)) % 112.37/112.12 [1563]~E(x15631,x15632)+E(f558(x15633,x15631,x15634),f558(x15633,x15632,x15634)) % 112.37/112.12 [1564]~E(x15641,x15642)+E(f558(x15643,x15644,x15641),f558(x15643,x15644,x15642)) % 112.37/112.12 [1565]~E(x15651,x15652)+E(f626(x15651,x15653,x15654,x15655,x15656,x15657),f626(x15652,x15653,x15654,x15655,x15656,x15657)) % 112.37/112.12 [1566]~E(x15661,x15662)+E(f626(x15663,x15661,x15664,x15665,x15666,x15667),f626(x15663,x15662,x15664,x15665,x15666,x15667)) % 112.37/112.12 [1567]~E(x15671,x15672)+E(f626(x15673,x15674,x15671,x15675,x15676,x15677),f626(x15673,x15674,x15672,x15675,x15676,x15677)) % 112.37/112.12 [1568]~E(x15681,x15682)+E(f626(x15683,x15684,x15685,x15681,x15686,x15687),f626(x15683,x15684,x15685,x15682,x15686,x15687)) % 112.37/112.12 [1569]~E(x15691,x15692)+E(f626(x15693,x15694,x15695,x15696,x15691,x15697),f626(x15693,x15694,x15695,x15696,x15692,x15697)) % 112.37/112.12 [1570]~E(x15701,x15702)+E(f626(x15703,x15704,x15705,x15706,x15707,x15701),f626(x15703,x15704,x15705,x15706,x15707,x15702)) % 112.37/112.12 [1571]~E(x15711,x15712)+E(f824(x15711,x15713,x15714,x15715,x15716,x15717,x15718),f824(x15712,x15713,x15714,x15715,x15716,x15717,x15718)) % 112.37/112.12 [1572]~E(x15721,x15722)+E(f824(x15723,x15721,x15724,x15725,x15726,x15727,x15728),f824(x15723,x15722,x15724,x15725,x15726,x15727,x15728)) % 112.37/112.12 [1573]~E(x15731,x15732)+E(f824(x15733,x15734,x15731,x15735,x15736,x15737,x15738),f824(x15733,x15734,x15732,x15735,x15736,x15737,x15738)) % 112.37/112.12 [1574]~E(x15741,x15742)+E(f824(x15743,x15744,x15745,x15741,x15746,x15747,x15748),f824(x15743,x15744,x15745,x15742,x15746,x15747,x15748)) % 112.37/112.12 [1575]~E(x15751,x15752)+E(f824(x15753,x15754,x15755,x15756,x15751,x15757,x15758),f824(x15753,x15754,x15755,x15756,x15752,x15757,x15758)) % 112.37/112.12 [1576]~E(x15761,x15762)+E(f824(x15763,x15764,x15765,x15766,x15767,x15761,x15768),f824(x15763,x15764,x15765,x15766,x15767,x15762,x15768)) % 112.37/112.12 [1577]~E(x15771,x15772)+E(f824(x15773,x15774,x15775,x15776,x15777,x15778,x15771),f824(x15773,x15774,x15775,x15776,x15777,x15778,x15772)) % 112.37/112.12 [1578]~E(x15781,x15782)+E(f816(x15781,x15783,x15784,x15785,x15786),f816(x15782,x15783,x15784,x15785,x15786)) % 112.37/112.12 [1579]~E(x15791,x15792)+E(f816(x15793,x15791,x15794,x15795,x15796),f816(x15793,x15792,x15794,x15795,x15796)) % 112.37/112.12 [1580]~E(x15801,x15802)+E(f816(x15803,x15804,x15801,x15805,x15806),f816(x15803,x15804,x15802,x15805,x15806)) % 112.37/112.12 [1581]~E(x15811,x15812)+E(f816(x15813,x15814,x15815,x15811,x15816),f816(x15813,x15814,x15815,x15812,x15816)) % 112.37/112.12 [1582]~E(x15821,x15822)+E(f816(x15823,x15824,x15825,x15826,x15821),f816(x15823,x15824,x15825,x15826,x15822)) % 112.37/112.12 [1583]~E(x15831,x15832)+E(f735(x15831,x15833,x15834),f735(x15832,x15833,x15834)) % 112.37/112.12 [1584]~E(x15841,x15842)+E(f735(x15843,x15841,x15844),f735(x15843,x15842,x15844)) % 112.37/112.12 [1585]~E(x15851,x15852)+E(f735(x15853,x15854,x15851),f735(x15853,x15854,x15852)) % 112.37/112.12 [1586]~E(x15861,x15862)+E(f366(x15861,x15863,x15864,x15865),f366(x15862,x15863,x15864,x15865)) % 112.37/112.12 [1587]~E(x15871,x15872)+E(f366(x15873,x15871,x15874,x15875),f366(x15873,x15872,x15874,x15875)) % 112.37/112.12 [1588]~E(x15881,x15882)+E(f366(x15883,x15884,x15881,x15885),f366(x15883,x15884,x15882,x15885)) % 112.37/112.12 [1589]~E(x15891,x15892)+E(f366(x15893,x15894,x15895,x15891),f366(x15893,x15894,x15895,x15892)) % 112.37/112.12 [1590]~E(x15901,x15902)+E(f494(x15901),f494(x15902)) % 112.37/112.12 [1591]~E(x15911,x15912)+E(f666(x15911,x15913,x15914,x15915),f666(x15912,x15913,x15914,x15915)) % 112.37/112.12 [1592]~E(x15921,x15922)+E(f666(x15923,x15921,x15924,x15925),f666(x15923,x15922,x15924,x15925)) % 112.37/112.12 [1593]~E(x15931,x15932)+E(f666(x15933,x15934,x15931,x15935),f666(x15933,x15934,x15932,x15935)) % 112.37/112.12 [1594]~E(x15941,x15942)+E(f666(x15943,x15944,x15945,x15941),f666(x15943,x15944,x15945,x15942)) % 112.37/112.12 [1595]~E(x15951,x15952)+E(f559(x15951,x15953,x15954),f559(x15952,x15953,x15954)) % 112.37/112.12 [1596]~E(x15961,x15962)+E(f559(x15963,x15961,x15964),f559(x15963,x15962,x15964)) % 112.37/112.12 [1597]~E(x15971,x15972)+E(f559(x15973,x15974,x15971),f559(x15973,x15974,x15972)) % 112.37/112.12 [1598]~E(x15981,x15982)+E(f326(x15981),f326(x15982)) % 112.37/112.12 [1599]~E(x15991,x15992)+E(f553(x15991,x15993,x15994),f553(x15992,x15993,x15994)) % 112.37/112.12 [1600]~E(x16001,x16002)+E(f553(x16003,x16001,x16004),f553(x16003,x16002,x16004)) % 112.37/112.12 [1601]~E(x16011,x16012)+E(f553(x16013,x16014,x16011),f553(x16013,x16014,x16012)) % 112.37/112.12 [1602]~E(x16021,x16022)+E(f677(x16021,x16023,x16024,x16025,x16026),f677(x16022,x16023,x16024,x16025,x16026)) % 112.37/112.12 [1603]~E(x16031,x16032)+E(f677(x16033,x16031,x16034,x16035,x16036),f677(x16033,x16032,x16034,x16035,x16036)) % 112.37/112.12 [1604]~E(x16041,x16042)+E(f677(x16043,x16044,x16041,x16045,x16046),f677(x16043,x16044,x16042,x16045,x16046)) % 112.37/112.12 [1605]~E(x16051,x16052)+E(f677(x16053,x16054,x16055,x16051,x16056),f677(x16053,x16054,x16055,x16052,x16056)) % 112.37/112.12 [1606]~E(x16061,x16062)+E(f677(x16063,x16064,x16065,x16066,x16061),f677(x16063,x16064,x16065,x16066,x16062)) % 112.37/112.12 [1607]~E(x16071,x16072)+E(f790(x16071,x16073),f790(x16072,x16073)) % 112.37/112.12 [1608]~E(x16081,x16082)+E(f790(x16083,x16081),f790(x16083,x16082)) % 112.37/112.12 [1609]~E(x16091,x16092)+E(f476(x16091,x16093,x16094,x16095,x16096),f476(x16092,x16093,x16094,x16095,x16096)) % 112.37/112.12 [1610]~E(x16101,x16102)+E(f476(x16103,x16101,x16104,x16105,x16106),f476(x16103,x16102,x16104,x16105,x16106)) % 112.37/112.12 [1611]~E(x16111,x16112)+E(f476(x16113,x16114,x16111,x16115,x16116),f476(x16113,x16114,x16112,x16115,x16116)) % 112.37/112.12 [1612]~E(x16121,x16122)+E(f476(x16123,x16124,x16125,x16121,x16126),f476(x16123,x16124,x16125,x16122,x16126)) % 112.37/112.12 [1613]~E(x16131,x16132)+E(f476(x16133,x16134,x16135,x16136,x16131),f476(x16133,x16134,x16135,x16136,x16132)) % 112.37/112.12 [1614]~E(x16141,x16142)+E(f556(x16141,x16143,x16144,x16145),f556(x16142,x16143,x16144,x16145)) % 112.37/112.12 [1615]~E(x16151,x16152)+E(f556(x16153,x16151,x16154,x16155),f556(x16153,x16152,x16154,x16155)) % 112.37/112.12 [1616]~E(x16161,x16162)+E(f556(x16163,x16164,x16161,x16165),f556(x16163,x16164,x16162,x16165)) % 112.37/112.12 [1617]~E(x16171,x16172)+E(f556(x16173,x16174,x16175,x16171),f556(x16173,x16174,x16175,x16172)) % 112.37/112.12 [1618]~E(x16181,x16182)+E(f507(x16181,x16183,x16184,x16185),f507(x16182,x16183,x16184,x16185)) % 112.37/112.12 [1619]~E(x16191,x16192)+E(f507(x16193,x16191,x16194,x16195),f507(x16193,x16192,x16194,x16195)) % 112.37/112.12 [1620]~E(x16201,x16202)+E(f507(x16203,x16204,x16201,x16205),f507(x16203,x16204,x16202,x16205)) % 112.37/112.12 [1621]~E(x16211,x16212)+E(f507(x16213,x16214,x16215,x16211),f507(x16213,x16214,x16215,x16212)) % 112.37/112.12 [1622]~E(x16221,x16222)+E(f825(x16221,x16223,x16224,x16225,x16226,x16227),f825(x16222,x16223,x16224,x16225,x16226,x16227)) % 112.37/112.12 [1623]~E(x16231,x16232)+E(f825(x16233,x16231,x16234,x16235,x16236,x16237),f825(x16233,x16232,x16234,x16235,x16236,x16237)) % 112.37/112.12 [1624]~E(x16241,x16242)+E(f825(x16243,x16244,x16241,x16245,x16246,x16247),f825(x16243,x16244,x16242,x16245,x16246,x16247)) % 112.37/112.12 [1625]~E(x16251,x16252)+E(f825(x16253,x16254,x16255,x16251,x16256,x16257),f825(x16253,x16254,x16255,x16252,x16256,x16257)) % 112.37/112.12 [1626]~E(x16261,x16262)+E(f825(x16263,x16264,x16265,x16266,x16261,x16267),f825(x16263,x16264,x16265,x16266,x16262,x16267)) % 112.37/112.12 [1627]~E(x16271,x16272)+E(f825(x16273,x16274,x16275,x16276,x16277,x16271),f825(x16273,x16274,x16275,x16276,x16277,x16272)) % 112.37/112.12 [1628]~E(x16281,x16282)+E(f859(x16281,x16283),f859(x16282,x16283)) % 112.37/112.12 [1629]~E(x16291,x16292)+E(f859(x16293,x16291),f859(x16293,x16292)) % 112.37/112.12 [1630]~E(x16301,x16302)+E(f809(x16301,x16303,x16304,x16305,x16306),f809(x16302,x16303,x16304,x16305,x16306)) % 112.37/112.12 [1631]~E(x16311,x16312)+E(f809(x16313,x16311,x16314,x16315,x16316),f809(x16313,x16312,x16314,x16315,x16316)) % 112.37/112.12 [1632]~E(x16321,x16322)+E(f809(x16323,x16324,x16321,x16325,x16326),f809(x16323,x16324,x16322,x16325,x16326)) % 112.37/112.12 [1633]~E(x16331,x16332)+E(f809(x16333,x16334,x16335,x16331,x16336),f809(x16333,x16334,x16335,x16332,x16336)) % 112.37/112.12 [1634]~E(x16341,x16342)+E(f809(x16343,x16344,x16345,x16346,x16341),f809(x16343,x16344,x16345,x16346,x16342)) % 112.37/112.12 [1635]~E(x16351,x16352)+E(f726(x16351,x16353,x16354,x16355,x16356),f726(x16352,x16353,x16354,x16355,x16356)) % 112.37/112.12 [1636]~E(x16361,x16362)+E(f726(x16363,x16361,x16364,x16365,x16366),f726(x16363,x16362,x16364,x16365,x16366)) % 112.37/112.12 [1637]~E(x16371,x16372)+E(f726(x16373,x16374,x16371,x16375,x16376),f726(x16373,x16374,x16372,x16375,x16376)) % 112.37/112.12 [1638]~E(x16381,x16382)+E(f726(x16383,x16384,x16385,x16381,x16386),f726(x16383,x16384,x16385,x16382,x16386)) % 112.37/112.12 [1639]~E(x16391,x16392)+E(f726(x16393,x16394,x16395,x16396,x16391),f726(x16393,x16394,x16395,x16396,x16392)) % 112.37/112.12 [1640]~E(x16401,x16402)+E(f526(x16401,x16403),f526(x16402,x16403)) % 112.37/112.12 [1641]~E(x16411,x16412)+E(f526(x16413,x16411),f526(x16413,x16412)) % 112.37/112.12 [1642]~E(x16421,x16422)+E(f239(x16421,x16423,x16424),f239(x16422,x16423,x16424)) % 112.37/112.12 [1643]~E(x16431,x16432)+E(f239(x16433,x16431,x16434),f239(x16433,x16432,x16434)) % 112.37/112.12 [1644]~E(x16441,x16442)+E(f239(x16443,x16444,x16441),f239(x16443,x16444,x16442)) % 112.37/112.12 [1645]~E(x16451,x16452)+E(f370(x16451,x16453,x16454,x16455),f370(x16452,x16453,x16454,x16455)) % 112.37/112.12 [1646]~E(x16461,x16462)+E(f370(x16463,x16461,x16464,x16465),f370(x16463,x16462,x16464,x16465)) % 112.37/112.12 [1647]~E(x16471,x16472)+E(f370(x16473,x16474,x16471,x16475),f370(x16473,x16474,x16472,x16475)) % 112.37/112.12 [1648]~E(x16481,x16482)+E(f370(x16483,x16484,x16485,x16481),f370(x16483,x16484,x16485,x16482)) % 112.37/112.12 [1649]~E(x16491,x16492)+E(f701(x16491,x16493,x16494),f701(x16492,x16493,x16494)) % 112.37/112.12 [1650]~E(x16501,x16502)+E(f701(x16503,x16501,x16504),f701(x16503,x16502,x16504)) % 112.37/112.12 [1651]~E(x16511,x16512)+E(f701(x16513,x16514,x16511),f701(x16513,x16514,x16512)) % 112.37/112.12 [1652]~E(x16521,x16522)+E(f785(x16521,x16523),f785(x16522,x16523)) % 112.37/112.12 [1653]~E(x16531,x16532)+E(f785(x16533,x16531),f785(x16533,x16532)) % 112.37/112.12 [1654]~E(x16541,x16542)+E(f513(x16541,x16543,x16544),f513(x16542,x16543,x16544)) % 112.37/112.12 [1655]~E(x16551,x16552)+E(f513(x16553,x16551,x16554),f513(x16553,x16552,x16554)) % 112.37/112.12 [1656]~E(x16561,x16562)+E(f513(x16563,x16564,x16561),f513(x16563,x16564,x16562)) % 112.37/112.12 [1657]~E(x16571,x16572)+E(f710(x16571,x16573,x16574,x16575),f710(x16572,x16573,x16574,x16575)) % 112.37/112.12 [1658]~E(x16581,x16582)+E(f710(x16583,x16581,x16584,x16585),f710(x16583,x16582,x16584,x16585)) % 112.37/112.12 [1659]~E(x16591,x16592)+E(f710(x16593,x16594,x16591,x16595),f710(x16593,x16594,x16592,x16595)) % 112.37/112.12 [1660]~E(x16601,x16602)+E(f710(x16603,x16604,x16605,x16601),f710(x16603,x16604,x16605,x16602)) % 112.37/112.12 [1661]~E(x16611,x16612)+E(f703(x16611,x16613),f703(x16612,x16613)) % 112.37/112.12 [1662]~E(x16621,x16622)+E(f703(x16623,x16621),f703(x16623,x16622)) % 112.37/112.12 [1663]~E(x16631,x16632)+E(f590(x16631,x16633,x16634,x16635,x16636,x16637),f590(x16632,x16633,x16634,x16635,x16636,x16637)) % 112.37/112.12 [1664]~E(x16641,x16642)+E(f590(x16643,x16641,x16644,x16645,x16646,x16647),f590(x16643,x16642,x16644,x16645,x16646,x16647)) % 112.37/112.12 [1665]~E(x16651,x16652)+E(f590(x16653,x16654,x16651,x16655,x16656,x16657),f590(x16653,x16654,x16652,x16655,x16656,x16657)) % 112.37/112.12 [1666]~E(x16661,x16662)+E(f590(x16663,x16664,x16665,x16661,x16666,x16667),f590(x16663,x16664,x16665,x16662,x16666,x16667)) % 112.37/112.12 [1667]~E(x16671,x16672)+E(f590(x16673,x16674,x16675,x16676,x16671,x16677),f590(x16673,x16674,x16675,x16676,x16672,x16677)) % 112.37/112.12 [1668]~E(x16681,x16682)+E(f590(x16683,x16684,x16685,x16686,x16687,x16681),f590(x16683,x16684,x16685,x16686,x16687,x16682)) % 112.37/112.12 [1669]~E(x16691,x16692)+E(f441(x16691,x16693,x16694,x16695,x16696,x16697,x16698,x16699),f441(x16692,x16693,x16694,x16695,x16696,x16697,x16698,x16699)) % 112.37/112.12 [1670]~E(x16701,x16702)+E(f441(x16703,x16701,x16704,x16705,x16706,x16707,x16708,x16709),f441(x16703,x16702,x16704,x16705,x16706,x16707,x16708,x16709)) % 112.37/112.12 [1671]~E(x16711,x16712)+E(f441(x16713,x16714,x16711,x16715,x16716,x16717,x16718,x16719),f441(x16713,x16714,x16712,x16715,x16716,x16717,x16718,x16719)) % 112.37/112.12 [1672]~E(x16721,x16722)+E(f441(x16723,x16724,x16725,x16721,x16726,x16727,x16728,x16729),f441(x16723,x16724,x16725,x16722,x16726,x16727,x16728,x16729)) % 112.37/112.12 [1673]~E(x16731,x16732)+E(f441(x16733,x16734,x16735,x16736,x16731,x16737,x16738,x16739),f441(x16733,x16734,x16735,x16736,x16732,x16737,x16738,x16739)) % 112.37/112.12 [1674]~E(x16741,x16742)+E(f441(x16743,x16744,x16745,x16746,x16747,x16741,x16748,x16749),f441(x16743,x16744,x16745,x16746,x16747,x16742,x16748,x16749)) % 112.37/112.12 [1675]~E(x16751,x16752)+E(f441(x16753,x16754,x16755,x16756,x16757,x16758,x16751,x16759),f441(x16753,x16754,x16755,x16756,x16757,x16758,x16752,x16759)) % 112.37/112.12 [1676]~E(x16761,x16762)+E(f441(x16763,x16764,x16765,x16766,x16767,x16768,x16769,x16761),f441(x16763,x16764,x16765,x16766,x16767,x16768,x16769,x16762)) % 112.37/112.12 [1677]~E(x16771,x16772)+E(f365(x16771,x16773,x16774,x16775),f365(x16772,x16773,x16774,x16775)) % 112.37/112.12 [1678]~E(x16781,x16782)+E(f365(x16783,x16781,x16784,x16785),f365(x16783,x16782,x16784,x16785)) % 112.37/112.12 [1679]~E(x16791,x16792)+E(f365(x16793,x16794,x16791,x16795),f365(x16793,x16794,x16792,x16795)) % 112.37/112.12 [1680]~E(x16801,x16802)+E(f365(x16803,x16804,x16805,x16801),f365(x16803,x16804,x16805,x16802)) % 112.37/112.12 [1681]~E(x16811,x16812)+E(f393(x16811,x16813,x16814,x16815),f393(x16812,x16813,x16814,x16815)) % 112.37/112.12 [1682]~E(x16821,x16822)+E(f393(x16823,x16821,x16824,x16825),f393(x16823,x16822,x16824,x16825)) % 112.37/112.12 [1683]~E(x16831,x16832)+E(f393(x16833,x16834,x16831,x16835),f393(x16833,x16834,x16832,x16835)) % 112.37/112.12 [1684]~E(x16841,x16842)+E(f393(x16843,x16844,x16845,x16841),f393(x16843,x16844,x16845,x16842)) % 112.37/112.12 [1685]~E(x16851,x16852)+E(f830(x16851,x16853,x16854,x16855,x16856,x16857,x16858,x16859),f830(x16852,x16853,x16854,x16855,x16856,x16857,x16858,x16859)) % 112.37/112.12 [1686]~E(x16861,x16862)+E(f830(x16863,x16861,x16864,x16865,x16866,x16867,x16868,x16869),f830(x16863,x16862,x16864,x16865,x16866,x16867,x16868,x16869)) % 112.37/112.12 [1687]~E(x16871,x16872)+E(f830(x16873,x16874,x16871,x16875,x16876,x16877,x16878,x16879),f830(x16873,x16874,x16872,x16875,x16876,x16877,x16878,x16879)) % 112.37/112.12 [1688]~E(x16881,x16882)+E(f830(x16883,x16884,x16885,x16881,x16886,x16887,x16888,x16889),f830(x16883,x16884,x16885,x16882,x16886,x16887,x16888,x16889)) % 112.37/112.12 [1689]~E(x16891,x16892)+E(f830(x16893,x16894,x16895,x16896,x16891,x16897,x16898,x16899),f830(x16893,x16894,x16895,x16896,x16892,x16897,x16898,x16899)) % 112.37/112.12 [1690]~E(x16901,x16902)+E(f830(x16903,x16904,x16905,x16906,x16907,x16901,x16908,x16909),f830(x16903,x16904,x16905,x16906,x16907,x16902,x16908,x16909)) % 112.37/112.12 [1691]~E(x16911,x16912)+E(f830(x16913,x16914,x16915,x16916,x16917,x16918,x16911,x16919),f830(x16913,x16914,x16915,x16916,x16917,x16918,x16912,x16919)) % 112.37/112.12 [1692]~E(x16921,x16922)+E(f830(x16923,x16924,x16925,x16926,x16927,x16928,x16929,x16921),f830(x16923,x16924,x16925,x16926,x16927,x16928,x16929,x16922)) % 112.37/112.12 [1693]~E(x16931,x16932)+E(f367(x16931,x16933,x16934,x16935),f367(x16932,x16933,x16934,x16935)) % 112.37/112.12 [1694]~E(x16941,x16942)+E(f367(x16943,x16941,x16944,x16945),f367(x16943,x16942,x16944,x16945)) % 112.37/112.12 [1695]~E(x16951,x16952)+E(f367(x16953,x16954,x16951,x16955),f367(x16953,x16954,x16952,x16955)) % 112.37/112.12 [1696]~E(x16961,x16962)+E(f367(x16963,x16964,x16965,x16961),f367(x16963,x16964,x16965,x16962)) % 112.37/112.12 [1697]~E(x16971,x16972)+E(f813(x16971,x16973,x16974,x16975),f813(x16972,x16973,x16974,x16975)) % 112.37/112.12 [1698]~E(x16981,x16982)+E(f813(x16983,x16981,x16984,x16985),f813(x16983,x16982,x16984,x16985)) % 112.37/112.12 [1699]~E(x16991,x16992)+E(f813(x16993,x16994,x16991,x16995),f813(x16993,x16994,x16992,x16995)) % 112.37/112.12 [1700]~E(x17001,x17002)+E(f813(x17003,x17004,x17005,x17001),f813(x17003,x17004,x17005,x17002)) % 112.37/112.12 [1701]~E(x17011,x17012)+E(f777(x17011,x17013,x17014),f777(x17012,x17013,x17014)) % 112.37/112.12 [1702]~E(x17021,x17022)+E(f777(x17023,x17021,x17024),f777(x17023,x17022,x17024)) % 112.37/112.12 [1703]~E(x17031,x17032)+E(f777(x17033,x17034,x17031),f777(x17033,x17034,x17032)) % 112.37/112.12 [1704]~E(x17041,x17042)+E(f389(x17041,x17043,x17044,x17045),f389(x17042,x17043,x17044,x17045)) % 112.37/112.12 [1705]~E(x17051,x17052)+E(f389(x17053,x17051,x17054,x17055),f389(x17053,x17052,x17054,x17055)) % 112.37/112.12 [1706]~E(x17061,x17062)+E(f389(x17063,x17064,x17061,x17065),f389(x17063,x17064,x17062,x17065)) % 112.37/112.12 [1707]~E(x17071,x17072)+E(f389(x17073,x17074,x17075,x17071),f389(x17073,x17074,x17075,x17072)) % 112.37/112.12 [1708]~E(x17081,x17082)+E(f125(x17081),f125(x17082)) % 112.37/112.12 [1709]~E(x17091,x17092)+E(f655(x17091,x17093,x17094),f655(x17092,x17093,x17094)) % 112.37/112.12 [1710]~E(x17101,x17102)+E(f655(x17103,x17101,x17104),f655(x17103,x17102,x17104)) % 112.37/112.12 [1711]~E(x17111,x17112)+E(f655(x17113,x17114,x17111),f655(x17113,x17114,x17112)) % 112.37/112.12 [1712]~E(x17121,x17122)+E(f542(x17121,x17123,x17124,x17125,x17126,x17127,x17128,x17129),f542(x17122,x17123,x17124,x17125,x17126,x17127,x17128,x17129)) % 112.37/112.12 [1713]~E(x17131,x17132)+E(f542(x17133,x17131,x17134,x17135,x17136,x17137,x17138,x17139),f542(x17133,x17132,x17134,x17135,x17136,x17137,x17138,x17139)) % 112.37/112.12 [1714]~E(x17141,x17142)+E(f542(x17143,x17144,x17141,x17145,x17146,x17147,x17148,x17149),f542(x17143,x17144,x17142,x17145,x17146,x17147,x17148,x17149)) % 112.37/112.12 [1715]~E(x17151,x17152)+E(f542(x17153,x17154,x17155,x17151,x17156,x17157,x17158,x17159),f542(x17153,x17154,x17155,x17152,x17156,x17157,x17158,x17159)) % 112.37/112.12 [1716]~E(x17161,x17162)+E(f542(x17163,x17164,x17165,x17166,x17161,x17167,x17168,x17169),f542(x17163,x17164,x17165,x17166,x17162,x17167,x17168,x17169)) % 112.37/112.12 [1717]~E(x17171,x17172)+E(f542(x17173,x17174,x17175,x17176,x17177,x17171,x17178,x17179),f542(x17173,x17174,x17175,x17176,x17177,x17172,x17178,x17179)) % 112.37/112.12 [1718]~E(x17181,x17182)+E(f542(x17183,x17184,x17185,x17186,x17187,x17188,x17181,x17189),f542(x17183,x17184,x17185,x17186,x17187,x17188,x17182,x17189)) % 112.37/112.12 [1719]~E(x17191,x17192)+E(f542(x17193,x17194,x17195,x17196,x17197,x17198,x17199,x17191),f542(x17193,x17194,x17195,x17196,x17197,x17198,x17199,x17192)) % 112.37/112.12 [1720]~E(x17201,x17202)+E(f750(x17201,x17203,x17204,x17205),f750(x17202,x17203,x17204,x17205)) % 112.37/112.12 [1721]~E(x17211,x17212)+E(f750(x17213,x17211,x17214,x17215),f750(x17213,x17212,x17214,x17215)) % 112.37/112.12 [1722]~E(x17221,x17222)+E(f750(x17223,x17224,x17221,x17225),f750(x17223,x17224,x17222,x17225)) % 112.37/112.12 [1723]~E(x17231,x17232)+E(f750(x17233,x17234,x17235,x17231),f750(x17233,x17234,x17235,x17232)) % 112.37/112.12 [1724]~E(x17241,x17242)+E(f688(x17241,x17243),f688(x17242,x17243)) % 112.37/112.12 [1725]~E(x17251,x17252)+E(f688(x17253,x17251),f688(x17253,x17252)) % 112.37/112.12 [1726]~E(x17261,x17262)+E(f71(x17261,x17263,x17264,x17265),f71(x17262,x17263,x17264,x17265)) % 112.37/112.12 [1727]~E(x17271,x17272)+E(f71(x17273,x17271,x17274,x17275),f71(x17273,x17272,x17274,x17275)) % 112.37/112.12 [1728]~E(x17281,x17282)+E(f71(x17283,x17284,x17281,x17285),f71(x17283,x17284,x17282,x17285)) % 112.37/112.12 [1729]~E(x17291,x17292)+E(f71(x17293,x17294,x17295,x17291),f71(x17293,x17294,x17295,x17292)) % 112.37/112.12 [1730]~E(x17301,x17302)+E(f743(x17301,x17303,x17304),f743(x17302,x17303,x17304)) % 112.37/112.12 [1731]~E(x17311,x17312)+E(f743(x17313,x17311,x17314),f743(x17313,x17312,x17314)) % 112.37/112.12 [1732]~E(x17321,x17322)+E(f743(x17323,x17324,x17321),f743(x17323,x17324,x17322)) % 112.37/112.12 [1733]~E(x17331,x17332)+E(f671(x17331,x17333,x17334,x17335,x17336),f671(x17332,x17333,x17334,x17335,x17336)) % 112.37/112.12 [1734]~E(x17341,x17342)+E(f671(x17343,x17341,x17344,x17345,x17346),f671(x17343,x17342,x17344,x17345,x17346)) % 112.37/112.12 [1735]~E(x17351,x17352)+E(f671(x17353,x17354,x17351,x17355,x17356),f671(x17353,x17354,x17352,x17355,x17356)) % 112.37/112.12 [1736]~E(x17361,x17362)+E(f671(x17363,x17364,x17365,x17361,x17366),f671(x17363,x17364,x17365,x17362,x17366)) % 112.37/112.12 [1737]~E(x17371,x17372)+E(f671(x17373,x17374,x17375,x17376,x17371),f671(x17373,x17374,x17375,x17376,x17372)) % 112.37/112.12 [1738]~E(x17381,x17382)+E(f387(x17381,x17383,x17384,x17385),f387(x17382,x17383,x17384,x17385)) % 112.37/112.12 [1739]~E(x17391,x17392)+E(f387(x17393,x17391,x17394,x17395),f387(x17393,x17392,x17394,x17395)) % 112.37/112.12 [1740]~E(x17401,x17402)+E(f387(x17403,x17404,x17401,x17405),f387(x17403,x17404,x17402,x17405)) % 112.37/112.12 [1741]~E(x17411,x17412)+E(f387(x17413,x17414,x17415,x17411),f387(x17413,x17414,x17415,x17412)) % 112.37/112.12 [1742]~E(x17421,x17422)+E(f670(x17421,x17423,x17424,x17425),f670(x17422,x17423,x17424,x17425)) % 112.37/112.12 [1743]~E(x17431,x17432)+E(f670(x17433,x17431,x17434,x17435),f670(x17433,x17432,x17434,x17435)) % 112.37/112.12 [1744]~E(x17441,x17442)+E(f670(x17443,x17444,x17441,x17445),f670(x17443,x17444,x17442,x17445)) % 112.37/112.12 [1745]~E(x17451,x17452)+E(f670(x17453,x17454,x17455,x17451),f670(x17453,x17454,x17455,x17452)) % 112.37/112.12 [1746]~E(x17461,x17462)+E(f683(x17461,x17463,x17464,x17465,x17466),f683(x17462,x17463,x17464,x17465,x17466)) % 112.37/112.12 [1747]~E(x17471,x17472)+E(f683(x17473,x17471,x17474,x17475,x17476),f683(x17473,x17472,x17474,x17475,x17476)) % 112.37/112.12 [1748]~E(x17481,x17482)+E(f683(x17483,x17484,x17481,x17485,x17486),f683(x17483,x17484,x17482,x17485,x17486)) % 112.37/112.12 [1749]~E(x17491,x17492)+E(f683(x17493,x17494,x17495,x17491,x17496),f683(x17493,x17494,x17495,x17492,x17496)) % 112.37/112.12 [1750]~E(x17501,x17502)+E(f683(x17503,x17504,x17505,x17506,x17501),f683(x17503,x17504,x17505,x17506,x17502)) % 112.37/112.12 [1751]~E(x17511,x17512)+E(f62(x17511,x17513,x17514),f62(x17512,x17513,x17514)) % 112.37/112.12 [1752]~E(x17521,x17522)+E(f62(x17523,x17521,x17524),f62(x17523,x17522,x17524)) % 112.37/112.12 [1753]~E(x17531,x17532)+E(f62(x17533,x17534,x17531),f62(x17533,x17534,x17532)) % 112.37/112.12 [1754]~E(x17541,x17542)+E(f444(x17541,x17543,x17544),f444(x17542,x17543,x17544)) % 112.37/112.12 [1755]~E(x17551,x17552)+E(f444(x17553,x17551,x17554),f444(x17553,x17552,x17554)) % 112.37/112.12 [1756]~E(x17561,x17562)+E(f444(x17563,x17564,x17561),f444(x17563,x17564,x17562)) % 112.37/112.12 [1757]~E(x17571,x17572)+E(f539(x17571,x17573,x17574,x17575,x17576),f539(x17572,x17573,x17574,x17575,x17576)) % 112.37/112.12 [1758]~E(x17581,x17582)+E(f539(x17583,x17581,x17584,x17585,x17586),f539(x17583,x17582,x17584,x17585,x17586)) % 112.37/112.12 [1759]~E(x17591,x17592)+E(f539(x17593,x17594,x17591,x17595,x17596),f539(x17593,x17594,x17592,x17595,x17596)) % 112.37/112.12 [1760]~E(x17601,x17602)+E(f539(x17603,x17604,x17605,x17601,x17606),f539(x17603,x17604,x17605,x17602,x17606)) % 112.37/112.12 [1761]~E(x17611,x17612)+E(f539(x17613,x17614,x17615,x17616,x17611),f539(x17613,x17614,x17615,x17616,x17612)) % 112.37/112.12 [1762]~E(x17621,x17622)+E(f734(x17621,x17623,x17624,x17625),f734(x17622,x17623,x17624,x17625)) % 112.37/112.12 [1763]~E(x17631,x17632)+E(f734(x17633,x17631,x17634,x17635),f734(x17633,x17632,x17634,x17635)) % 112.37/112.12 [1764]~E(x17641,x17642)+E(f734(x17643,x17644,x17641,x17645),f734(x17643,x17644,x17642,x17645)) % 112.37/112.12 [1765]~E(x17651,x17652)+E(f734(x17653,x17654,x17655,x17651),f734(x17653,x17654,x17655,x17652)) % 112.37/112.12 [1766]~E(x17661,x17662)+E(f868(x17661,x17663),f868(x17662,x17663)) % 112.37/112.12 [1767]~E(x17671,x17672)+E(f868(x17673,x17671),f868(x17673,x17672)) % 112.37/112.12 [1768]~E(x17681,x17682)+E(f593(x17681,x17683,x17684,x17685,x17686),f593(x17682,x17683,x17684,x17685,x17686)) % 112.37/112.12 [1769]~E(x17691,x17692)+E(f593(x17693,x17691,x17694,x17695,x17696),f593(x17693,x17692,x17694,x17695,x17696)) % 112.37/112.12 [1770]~E(x17701,x17702)+E(f593(x17703,x17704,x17701,x17705,x17706),f593(x17703,x17704,x17702,x17705,x17706)) % 112.37/112.12 [1771]~E(x17711,x17712)+E(f593(x17713,x17714,x17715,x17711,x17716),f593(x17713,x17714,x17715,x17712,x17716)) % 112.37/112.12 [1772]~E(x17721,x17722)+E(f593(x17723,x17724,x17725,x17726,x17721),f593(x17723,x17724,x17725,x17726,x17722)) % 112.37/112.12 [1773]~E(x17731,x17732)+E(f578(x17731,x17733,x17734,x17735,x17736,x17737),f578(x17732,x17733,x17734,x17735,x17736,x17737)) % 112.37/112.12 [1774]~E(x17741,x17742)+E(f578(x17743,x17741,x17744,x17745,x17746,x17747),f578(x17743,x17742,x17744,x17745,x17746,x17747)) % 112.37/112.12 [1775]~E(x17751,x17752)+E(f578(x17753,x17754,x17751,x17755,x17756,x17757),f578(x17753,x17754,x17752,x17755,x17756,x17757)) % 112.37/112.12 [1776]~E(x17761,x17762)+E(f578(x17763,x17764,x17765,x17761,x17766,x17767),f578(x17763,x17764,x17765,x17762,x17766,x17767)) % 112.37/112.12 [1777]~E(x17771,x17772)+E(f578(x17773,x17774,x17775,x17776,x17771,x17777),f578(x17773,x17774,x17775,x17776,x17772,x17777)) % 112.37/112.12 [1778]~E(x17781,x17782)+E(f578(x17783,x17784,x17785,x17786,x17787,x17781),f578(x17783,x17784,x17785,x17786,x17787,x17782)) % 112.37/112.12 [1779]~E(x17791,x17792)+E(f575(x17791,x17793,x17794,x17795,x17796,x17797),f575(x17792,x17793,x17794,x17795,x17796,x17797)) % 112.37/112.12 [1780]~E(x17801,x17802)+E(f575(x17803,x17801,x17804,x17805,x17806,x17807),f575(x17803,x17802,x17804,x17805,x17806,x17807)) % 112.37/112.12 [1781]~E(x17811,x17812)+E(f575(x17813,x17814,x17811,x17815,x17816,x17817),f575(x17813,x17814,x17812,x17815,x17816,x17817)) % 112.37/112.12 [1782]~E(x17821,x17822)+E(f575(x17823,x17824,x17825,x17821,x17826,x17827),f575(x17823,x17824,x17825,x17822,x17826,x17827)) % 112.37/112.12 [1783]~E(x17831,x17832)+E(f575(x17833,x17834,x17835,x17836,x17831,x17837),f575(x17833,x17834,x17835,x17836,x17832,x17837)) % 112.37/112.12 [1784]~E(x17841,x17842)+E(f575(x17843,x17844,x17845,x17846,x17847,x17841),f575(x17843,x17844,x17845,x17846,x17847,x17842)) % 112.37/112.12 [1785]~E(x17851,x17852)+E(f668(x17851,x17853,x17854),f668(x17852,x17853,x17854)) % 112.37/112.12 [1786]~E(x17861,x17862)+E(f668(x17863,x17861,x17864),f668(x17863,x17862,x17864)) % 112.37/112.12 [1787]~E(x17871,x17872)+E(f668(x17873,x17874,x17871),f668(x17873,x17874,x17872)) % 112.37/112.12 [1788]~E(x17881,x17882)+E(f538(x17881,x17883,x17884,x17885,x17886,x17887),f538(x17882,x17883,x17884,x17885,x17886,x17887)) % 112.37/112.12 [1789]~E(x17891,x17892)+E(f538(x17893,x17891,x17894,x17895,x17896,x17897),f538(x17893,x17892,x17894,x17895,x17896,x17897)) % 112.37/112.12 [1790]~E(x17901,x17902)+E(f538(x17903,x17904,x17901,x17905,x17906,x17907),f538(x17903,x17904,x17902,x17905,x17906,x17907)) % 112.37/112.12 [1791]~E(x17911,x17912)+E(f538(x17913,x17914,x17915,x17911,x17916,x17917),f538(x17913,x17914,x17915,x17912,x17916,x17917)) % 112.37/112.12 [1792]~E(x17921,x17922)+E(f538(x17923,x17924,x17925,x17926,x17921,x17927),f538(x17923,x17924,x17925,x17926,x17922,x17927)) % 112.37/112.12 [1793]~E(x17931,x17932)+E(f538(x17933,x17934,x17935,x17936,x17937,x17931),f538(x17933,x17934,x17935,x17936,x17937,x17932)) % 112.37/112.12 [1794]~E(x17941,x17942)+E(f269(x17941,x17943,x17944,x17945),f269(x17942,x17943,x17944,x17945)) % 112.37/112.12 [1795]~E(x17951,x17952)+E(f269(x17953,x17951,x17954,x17955),f269(x17953,x17952,x17954,x17955)) % 112.37/112.12 [1796]~E(x17961,x17962)+E(f269(x17963,x17964,x17961,x17965),f269(x17963,x17964,x17962,x17965)) % 112.37/112.12 [1797]~E(x17971,x17972)+E(f269(x17973,x17974,x17975,x17971),f269(x17973,x17974,x17975,x17972)) % 112.37/112.12 [1798]~E(x17981,x17982)+E(f628(x17981,x17983,x17984,x17985,x17986,x17987),f628(x17982,x17983,x17984,x17985,x17986,x17987)) % 112.37/112.12 [1799]~E(x17991,x17992)+E(f628(x17993,x17991,x17994,x17995,x17996,x17997),f628(x17993,x17992,x17994,x17995,x17996,x17997)) % 112.37/112.12 [1800]~E(x18001,x18002)+E(f628(x18003,x18004,x18001,x18005,x18006,x18007),f628(x18003,x18004,x18002,x18005,x18006,x18007)) % 112.37/112.12 [1801]~E(x18011,x18012)+E(f628(x18013,x18014,x18015,x18011,x18016,x18017),f628(x18013,x18014,x18015,x18012,x18016,x18017)) % 112.37/112.12 [1802]~E(x18021,x18022)+E(f628(x18023,x18024,x18025,x18026,x18021,x18027),f628(x18023,x18024,x18025,x18026,x18022,x18027)) % 112.37/112.12 [1803]~E(x18031,x18032)+E(f628(x18033,x18034,x18035,x18036,x18037,x18031),f628(x18033,x18034,x18035,x18036,x18037,x18032)) % 112.37/112.12 [1804]~E(x18041,x18042)+E(f704(x18041,x18043,x18044),f704(x18042,x18043,x18044)) % 112.37/112.12 [1805]~E(x18051,x18052)+E(f704(x18053,x18051,x18054),f704(x18053,x18052,x18054)) % 112.37/112.12 [1806]~E(x18061,x18062)+E(f704(x18063,x18064,x18061),f704(x18063,x18064,x18062)) % 112.37/112.12 [1807]~E(x18071,x18072)+E(f184(x18071,x18073),f184(x18072,x18073)) % 112.37/112.12 [1808]~E(x18081,x18082)+E(f184(x18083,x18081),f184(x18083,x18082)) % 112.37/112.12 [1809]~E(x18091,x18092)+E(f343(x18091,x18093,x18094),f343(x18092,x18093,x18094)) % 112.37/112.12 [1810]~E(x18101,x18102)+E(f343(x18103,x18101,x18104),f343(x18103,x18102,x18104)) % 112.37/112.12 [1811]~E(x18111,x18112)+E(f343(x18113,x18114,x18111),f343(x18113,x18114,x18112)) % 112.37/112.12 [1812]~E(x18121,x18122)+E(f266(x18121,x18123,x18124,x18125),f266(x18122,x18123,x18124,x18125)) % 112.37/112.12 [1813]~E(x18131,x18132)+E(f266(x18133,x18131,x18134,x18135),f266(x18133,x18132,x18134,x18135)) % 112.37/112.12 [1814]~E(x18141,x18142)+E(f266(x18143,x18144,x18141,x18145),f266(x18143,x18144,x18142,x18145)) % 112.37/112.12 [1815]~E(x18151,x18152)+E(f266(x18153,x18154,x18155,x18151),f266(x18153,x18154,x18155,x18152)) % 112.37/112.12 [1816]~E(x18161,x18162)+E(f21(x18161,x18163,x18164,x18165),f21(x18162,x18163,x18164,x18165)) % 112.37/112.12 [1817]~E(x18171,x18172)+E(f21(x18173,x18171,x18174,x18175),f21(x18173,x18172,x18174,x18175)) % 112.37/112.12 [1818]~E(x18181,x18182)+E(f21(x18183,x18184,x18181,x18185),f21(x18183,x18184,x18182,x18185)) % 112.37/112.12 [1819]~E(x18191,x18192)+E(f21(x18193,x18194,x18195,x18191),f21(x18193,x18194,x18195,x18192)) % 112.37/112.12 [1820]~E(x18201,x18202)+E(f530(x18201,x18203,x18204,x18205),f530(x18202,x18203,x18204,x18205)) % 112.37/112.12 [1821]~E(x18211,x18212)+E(f530(x18213,x18211,x18214,x18215),f530(x18213,x18212,x18214,x18215)) % 112.37/112.12 [1822]~E(x18221,x18222)+E(f530(x18223,x18224,x18221,x18225),f530(x18223,x18224,x18222,x18225)) % 112.37/112.12 [1823]~E(x18231,x18232)+E(f530(x18233,x18234,x18235,x18231),f530(x18233,x18234,x18235,x18232)) % 112.37/112.12 [1824]~E(x18241,x18242)+E(f477(x18241,x18243,x18244,x18245,x18246),f477(x18242,x18243,x18244,x18245,x18246)) % 112.37/112.12 [1825]~E(x18251,x18252)+E(f477(x18253,x18251,x18254,x18255,x18256),f477(x18253,x18252,x18254,x18255,x18256)) % 112.37/112.12 [1826]~E(x18261,x18262)+E(f477(x18263,x18264,x18261,x18265,x18266),f477(x18263,x18264,x18262,x18265,x18266)) % 112.37/112.12 [1827]~E(x18271,x18272)+E(f477(x18273,x18274,x18275,x18271,x18276),f477(x18273,x18274,x18275,x18272,x18276)) % 112.37/112.12 [1828]~E(x18281,x18282)+E(f477(x18283,x18284,x18285,x18286,x18281),f477(x18283,x18284,x18285,x18286,x18282)) % 112.37/112.12 [1829]~E(x18291,x18292)+E(f680(x18291,x18293,x18294,x18295),f680(x18292,x18293,x18294,x18295)) % 112.37/112.12 [1830]~E(x18301,x18302)+E(f680(x18303,x18301,x18304,x18305),f680(x18303,x18302,x18304,x18305)) % 112.37/112.12 [1831]~E(x18311,x18312)+E(f680(x18313,x18314,x18311,x18315),f680(x18313,x18314,x18312,x18315)) % 112.37/112.12 [1832]~E(x18321,x18322)+E(f680(x18323,x18324,x18325,x18321),f680(x18323,x18324,x18325,x18322)) % 112.37/112.12 [1833]~E(x18331,x18332)+E(f474(x18331,x18333,x18334,x18335,x18336),f474(x18332,x18333,x18334,x18335,x18336)) % 112.37/112.12 [1834]~E(x18341,x18342)+E(f474(x18343,x18341,x18344,x18345,x18346),f474(x18343,x18342,x18344,x18345,x18346)) % 112.37/112.12 [1835]~E(x18351,x18352)+E(f474(x18353,x18354,x18351,x18355,x18356),f474(x18353,x18354,x18352,x18355,x18356)) % 112.37/112.12 [1836]~E(x18361,x18362)+E(f474(x18363,x18364,x18365,x18361,x18366),f474(x18363,x18364,x18365,x18362,x18366)) % 112.37/112.12 [1837]~E(x18371,x18372)+E(f474(x18373,x18374,x18375,x18376,x18371),f474(x18373,x18374,x18375,x18376,x18372)) % 112.37/112.12 [1838]~E(x18381,x18382)+E(f392(x18381,x18383),f392(x18382,x18383)) % 112.37/112.12 [1839]~E(x18391,x18392)+E(f392(x18393,x18391),f392(x18393,x18392)) % 112.37/112.12 [1840]~E(x18401,x18402)+E(f720(x18401,x18403,x18404),f720(x18402,x18403,x18404)) % 112.37/112.12 [1841]~E(x18411,x18412)+E(f720(x18413,x18411,x18414),f720(x18413,x18412,x18414)) % 112.37/112.12 [1842]~E(x18421,x18422)+E(f720(x18423,x18424,x18421),f720(x18423,x18424,x18422)) % 112.37/112.12 [1843]~E(x18431,x18432)+E(f362(x18431,x18433,x18434),f362(x18432,x18433,x18434)) % 112.37/112.12 [1844]~E(x18441,x18442)+E(f362(x18443,x18441,x18444),f362(x18443,x18442,x18444)) % 112.37/112.12 [1845]~E(x18451,x18452)+E(f362(x18453,x18454,x18451),f362(x18453,x18454,x18452)) % 112.37/112.12 [1846]~E(x18461,x18462)+E(f630(x18461,x18463),f630(x18462,x18463)) % 112.37/112.12 [1847]~E(x18471,x18472)+E(f630(x18473,x18471),f630(x18473,x18472)) % 112.37/112.12 [1848]~E(x18481,x18482)+E(f673(x18481,x18483,x18484),f673(x18482,x18483,x18484)) % 112.37/112.12 [1849]~E(x18491,x18492)+E(f673(x18493,x18491,x18494),f673(x18493,x18492,x18494)) % 112.37/112.12 [1850]~E(x18501,x18502)+E(f673(x18503,x18504,x18501),f673(x18503,x18504,x18502)) % 112.37/112.12 [1851]~E(x18511,x18512)+E(f687(x18511,x18513,x18514),f687(x18512,x18513,x18514)) % 112.37/112.12 [1852]~E(x18521,x18522)+E(f687(x18523,x18521,x18524),f687(x18523,x18522,x18524)) % 112.37/112.12 [1853]~E(x18531,x18532)+E(f687(x18533,x18534,x18531),f687(x18533,x18534,x18532)) % 112.37/112.12 [1854]~E(x18541,x18542)+E(f415(x18541,x18543,x18544,x18545,x18546),f415(x18542,x18543,x18544,x18545,x18546)) % 112.37/112.12 [1855]~E(x18551,x18552)+E(f415(x18553,x18551,x18554,x18555,x18556),f415(x18553,x18552,x18554,x18555,x18556)) % 112.37/112.12 [1856]~E(x18561,x18562)+E(f415(x18563,x18564,x18561,x18565,x18566),f415(x18563,x18564,x18562,x18565,x18566)) % 112.37/112.12 [1857]~E(x18571,x18572)+E(f415(x18573,x18574,x18575,x18571,x18576),f415(x18573,x18574,x18575,x18572,x18576)) % 112.37/112.12 [1858]~E(x18581,x18582)+E(f415(x18583,x18584,x18585,x18586,x18581),f415(x18583,x18584,x18585,x18586,x18582)) % 112.37/112.12 [1859]~E(x18591,x18592)+E(f768(x18591,x18593,x18594,x18595),f768(x18592,x18593,x18594,x18595)) % 112.37/112.12 [1860]~E(x18601,x18602)+E(f768(x18603,x18601,x18604,x18605),f768(x18603,x18602,x18604,x18605)) % 112.37/112.12 [1861]~E(x18611,x18612)+E(f768(x18613,x18614,x18611,x18615),f768(x18613,x18614,x18612,x18615)) % 112.37/112.12 [1862]~E(x18621,x18622)+E(f768(x18623,x18624,x18625,x18621),f768(x18623,x18624,x18625,x18622)) % 112.37/112.12 [1863]~E(x18631,x18632)+E(f480(x18631,x18633,x18634,x18635,x18636),f480(x18632,x18633,x18634,x18635,x18636)) % 112.37/112.12 [1864]~E(x18641,x18642)+E(f480(x18643,x18641,x18644,x18645,x18646),f480(x18643,x18642,x18644,x18645,x18646)) % 112.37/112.12 [1865]~E(x18651,x18652)+E(f480(x18653,x18654,x18651,x18655,x18656),f480(x18653,x18654,x18652,x18655,x18656)) % 112.37/112.12 [1866]~E(x18661,x18662)+E(f480(x18663,x18664,x18665,x18661,x18666),f480(x18663,x18664,x18665,x18662,x18666)) % 112.37/112.12 [1867]~E(x18671,x18672)+E(f480(x18673,x18674,x18675,x18676,x18671),f480(x18673,x18674,x18675,x18676,x18672)) % 112.37/112.12 [1868]~E(x18681,x18682)+E(f518(x18681,x18683,x18684,x18685,x18686),f518(x18682,x18683,x18684,x18685,x18686)) % 112.37/112.12 [1869]~E(x18691,x18692)+E(f518(x18693,x18691,x18694,x18695,x18696),f518(x18693,x18692,x18694,x18695,x18696)) % 112.37/112.12 [1870]~E(x18701,x18702)+E(f518(x18703,x18704,x18701,x18705,x18706),f518(x18703,x18704,x18702,x18705,x18706)) % 112.37/112.12 [1871]~E(x18711,x18712)+E(f518(x18713,x18714,x18715,x18711,x18716),f518(x18713,x18714,x18715,x18712,x18716)) % 112.37/112.12 [1872]~E(x18721,x18722)+E(f518(x18723,x18724,x18725,x18726,x18721),f518(x18723,x18724,x18725,x18726,x18722)) % 112.37/112.12 [1873]~E(x18731,x18732)+E(f600(x18731,x18733),f600(x18732,x18733)) % 112.37/112.12 [1874]~E(x18741,x18742)+E(f600(x18743,x18741),f600(x18743,x18742)) % 112.37/112.12 [1875]~E(x18751,x18752)+E(f268(x18751),f268(x18752)) % 112.37/112.12 [1876]~E(x18761,x18762)+E(f886(x18761,x18763,x18764,x18765,x18766),f886(x18762,x18763,x18764,x18765,x18766)) % 112.37/112.12 [1877]~E(x18771,x18772)+E(f886(x18773,x18771,x18774,x18775,x18776),f886(x18773,x18772,x18774,x18775,x18776)) % 112.37/112.12 [1878]~E(x18781,x18782)+E(f886(x18783,x18784,x18781,x18785,x18786),f886(x18783,x18784,x18782,x18785,x18786)) % 112.37/112.12 [1879]~E(x18791,x18792)+E(f886(x18793,x18794,x18795,x18791,x18796),f886(x18793,x18794,x18795,x18792,x18796)) % 112.37/112.12 [1880]~E(x18801,x18802)+E(f886(x18803,x18804,x18805,x18806,x18801),f886(x18803,x18804,x18805,x18806,x18802)) % 112.37/112.12 [1881]~E(x18811,x18812)+E(f667(x18811,x18813,x18814),f667(x18812,x18813,x18814)) % 112.37/112.12 [1882]~E(x18821,x18822)+E(f667(x18823,x18821,x18824),f667(x18823,x18822,x18824)) % 112.37/112.12 [1883]~E(x18831,x18832)+E(f667(x18833,x18834,x18831),f667(x18833,x18834,x18832)) % 112.37/112.12 [1884]~E(x18841,x18842)+E(f500(x18841,x18843,x18844,x18845,x18846),f500(x18842,x18843,x18844,x18845,x18846)) % 112.37/112.12 [1885]~E(x18851,x18852)+E(f500(x18853,x18851,x18854,x18855,x18856),f500(x18853,x18852,x18854,x18855,x18856)) % 112.37/112.12 [1886]~E(x18861,x18862)+E(f500(x18863,x18864,x18861,x18865,x18866),f500(x18863,x18864,x18862,x18865,x18866)) % 112.37/112.12 [1887]~E(x18871,x18872)+E(f500(x18873,x18874,x18875,x18871,x18876),f500(x18873,x18874,x18875,x18872,x18876)) % 112.37/112.12 [1888]~E(x18881,x18882)+E(f500(x18883,x18884,x18885,x18886,x18881),f500(x18883,x18884,x18885,x18886,x18882)) % 112.37/112.12 [1889]~E(x18891,x18892)+E(f629(x18891,x18893,x18894,x18895),f629(x18892,x18893,x18894,x18895)) % 112.37/112.12 [1890]~E(x18901,x18902)+E(f629(x18903,x18901,x18904,x18905),f629(x18903,x18902,x18904,x18905)) % 112.37/112.12 [1891]~E(x18911,x18912)+E(f629(x18913,x18914,x18911,x18915),f629(x18913,x18914,x18912,x18915)) % 112.37/112.12 [1892]~E(x18921,x18922)+E(f629(x18923,x18924,x18925,x18921),f629(x18923,x18924,x18925,x18922)) % 112.37/112.12 [1893]~E(x18931,x18932)+E(f654(x18931,x18933,x18934),f654(x18932,x18933,x18934)) % 112.37/112.12 [1894]~E(x18941,x18942)+E(f654(x18943,x18941,x18944),f654(x18943,x18942,x18944)) % 112.37/112.12 [1895]~E(x18951,x18952)+E(f654(x18953,x18954,x18951),f654(x18953,x18954,x18952)) % 112.37/112.12 [1896]~E(x18961,x18962)+E(f602(x18961,x18963,x18964),f602(x18962,x18963,x18964)) % 112.37/112.12 [1897]~E(x18971,x18972)+E(f602(x18973,x18971,x18974),f602(x18973,x18972,x18974)) % 112.37/112.12 [1898]~E(x18981,x18982)+E(f602(x18983,x18984,x18981),f602(x18983,x18984,x18982)) % 112.37/112.12 [1899]~E(x18991,x18992)+E(f819(x18991,x18993,x18994),f819(x18992,x18993,x18994)) % 112.37/112.12 [1900]~E(x19001,x19002)+E(f819(x19003,x19001,x19004),f819(x19003,x19002,x19004)) % 112.37/112.12 [1901]~E(x19011,x19012)+E(f819(x19013,x19014,x19011),f819(x19013,x19014,x19012)) % 112.37/112.12 [1902]~E(x19021,x19022)+E(f611(x19021,x19023,x19024,x19025,x19026),f611(x19022,x19023,x19024,x19025,x19026)) % 112.37/112.12 [1903]~E(x19031,x19032)+E(f611(x19033,x19031,x19034,x19035,x19036),f611(x19033,x19032,x19034,x19035,x19036)) % 112.37/112.12 [1904]~E(x19041,x19042)+E(f611(x19043,x19044,x19041,x19045,x19046),f611(x19043,x19044,x19042,x19045,x19046)) % 112.37/112.12 [1905]~E(x19051,x19052)+E(f611(x19053,x19054,x19055,x19051,x19056),f611(x19053,x19054,x19055,x19052,x19056)) % 112.37/112.12 [1906]~E(x19061,x19062)+E(f611(x19063,x19064,x19065,x19066,x19061),f611(x19063,x19064,x19065,x19066,x19062)) % 112.37/112.12 [1907]~E(x19071,x19072)+E(f613(x19071,x19073,x19074,x19075,x19076),f613(x19072,x19073,x19074,x19075,x19076)) % 112.37/112.12 [1908]~E(x19081,x19082)+E(f613(x19083,x19081,x19084,x19085,x19086),f613(x19083,x19082,x19084,x19085,x19086)) % 112.37/112.12 [1909]~E(x19091,x19092)+E(f613(x19093,x19094,x19091,x19095,x19096),f613(x19093,x19094,x19092,x19095,x19096)) % 112.37/112.12 [1910]~E(x19101,x19102)+E(f613(x19103,x19104,x19105,x19101,x19106),f613(x19103,x19104,x19105,x19102,x19106)) % 112.37/112.12 [1911]~E(x19111,x19112)+E(f613(x19113,x19114,x19115,x19116,x19111),f613(x19113,x19114,x19115,x19116,x19112)) % 112.37/112.12 [1912]~E(x19121,x19122)+E(f368(x19121,x19123,x19124,x19125),f368(x19122,x19123,x19124,x19125)) % 112.37/112.12 [1913]~E(x19131,x19132)+E(f368(x19133,x19131,x19134,x19135),f368(x19133,x19132,x19134,x19135)) % 112.37/112.12 [1914]~E(x19141,x19142)+E(f368(x19143,x19144,x19141,x19145),f368(x19143,x19144,x19142,x19145)) % 112.37/112.12 [1915]~E(x19151,x19152)+E(f368(x19153,x19154,x19155,x19151),f368(x19153,x19154,x19155,x19152)) % 112.37/112.12 [1916]~E(x19161,x19162)+E(f235(x19161,x19163,x19164),f235(x19162,x19163,x19164)) % 112.37/112.12 [1917]~E(x19171,x19172)+E(f235(x19173,x19171,x19174),f235(x19173,x19172,x19174)) % 112.37/112.12 [1918]~E(x19181,x19182)+E(f235(x19183,x19184,x19181),f235(x19183,x19184,x19182)) % 112.37/112.12 [1919]~E(x19191,x19192)+E(f421(x19191,x19193),f421(x19192,x19193)) % 112.37/112.12 [1920]~E(x19201,x19202)+E(f421(x19203,x19201),f421(x19203,x19202)) % 112.37/112.12 [1921]~E(x19211,x19212)+E(f549(x19211,x19213),f549(x19212,x19213)) % 112.37/112.12 [1922]~E(x19221,x19222)+E(f549(x19223,x19221),f549(x19223,x19222)) % 112.37/112.12 [1923]~E(x19231,x19232)+E(f152(x19231,x19233),f152(x19232,x19233)) % 112.37/112.12 [1924]~E(x19241,x19242)+E(f152(x19243,x19241),f152(x19243,x19242)) % 112.37/112.12 [1925]~E(x19251,x19252)+E(f653(x19251,x19253),f653(x19252,x19253)) % 112.37/112.12 [1926]~E(x19261,x19262)+E(f653(x19263,x19261),f653(x19263,x19262)) % 112.37/112.12 [1927]~E(x19271,x19272)+E(f612(x19271,x19273,x19274,x19275),f612(x19272,x19273,x19274,x19275)) % 112.37/112.12 [1928]~E(x19281,x19282)+E(f612(x19283,x19281,x19284,x19285),f612(x19283,x19282,x19284,x19285)) % 112.37/112.12 [1929]~E(x19291,x19292)+E(f612(x19293,x19294,x19291,x19295),f612(x19293,x19294,x19292,x19295)) % 112.37/112.12 [1930]~E(x19301,x19302)+E(f612(x19303,x19304,x19305,x19301),f612(x19303,x19304,x19305,x19302)) % 112.37/112.12 [1931]~E(x19311,x19312)+E(f863(x19311,x19313),f863(x19312,x19313)) % 112.37/112.12 [1932]~E(x19321,x19322)+E(f863(x19323,x19321),f863(x19323,x19322)) % 112.37/112.12 [1933]~E(x19331,x19332)+E(f470(x19331,x19333),f470(x19332,x19333)) % 112.37/112.12 [1934]~E(x19341,x19342)+E(f470(x19343,x19341),f470(x19343,x19342)) % 112.37/112.12 [1935]~E(x19351,x19352)+E(f878(x19351),f878(x19352)) % 112.37/112.12 [1936]~E(x19361,x19362)+E(f872(x19361,x19363,x19364),f872(x19362,x19363,x19364)) % 112.37/112.12 [1937]~E(x19371,x19372)+E(f872(x19373,x19371,x19374),f872(x19373,x19372,x19374)) % 112.37/112.12 [1938]~E(x19381,x19382)+E(f872(x19383,x19384,x19381),f872(x19383,x19384,x19382)) % 112.37/112.12 [1939]~E(x19391,x19392)+E(f757(x19391,x19393,x19394,x19395),f757(x19392,x19393,x19394,x19395)) % 112.37/112.12 [1940]~E(x19401,x19402)+E(f757(x19403,x19401,x19404,x19405),f757(x19403,x19402,x19404,x19405)) % 112.37/112.12 [1941]~E(x19411,x19412)+E(f757(x19413,x19414,x19411,x19415),f757(x19413,x19414,x19412,x19415)) % 112.37/112.12 [1942]~E(x19421,x19422)+E(f757(x19423,x19424,x19425,x19421),f757(x19423,x19424,x19425,x19422)) % 112.37/112.12 [1943]~E(x19431,x19432)+E(f889(x19431),f889(x19432)) % 112.37/112.12 [1944]~E(x19441,x19442)+E(f731(x19441,x19443),f731(x19442,x19443)) % 112.37/112.12 [1945]~E(x19451,x19452)+E(f731(x19453,x19451),f731(x19453,x19452)) % 112.37/112.12 [1946]~E(x19461,x19462)+E(f555(x19461,x19463,x19464,x19465),f555(x19462,x19463,x19464,x19465)) % 112.37/112.12 [1947]~E(x19471,x19472)+E(f555(x19473,x19471,x19474,x19475),f555(x19473,x19472,x19474,x19475)) % 112.37/112.12 [1948]~E(x19481,x19482)+E(f555(x19483,x19484,x19481,x19485),f555(x19483,x19484,x19482,x19485)) % 112.37/112.12 [1949]~E(x19491,x19492)+E(f555(x19493,x19494,x19495,x19491),f555(x19493,x19494,x19495,x19492)) % 112.37/112.12 [1950]~E(x19501,x19502)+E(f456(x19501,x19503,x19504),f456(x19502,x19503,x19504)) % 112.37/112.12 [1951]~E(x19511,x19512)+E(f456(x19513,x19511,x19514),f456(x19513,x19512,x19514)) % 112.37/112.12 [1952]~E(x19521,x19522)+E(f456(x19523,x19524,x19521),f456(x19523,x19524,x19522)) % 112.37/112.12 [1953]~E(x19531,x19532)+E(f780(x19531,x19533,x19534,x19535),f780(x19532,x19533,x19534,x19535)) % 112.37/112.12 [1954]~E(x19541,x19542)+E(f780(x19543,x19541,x19544,x19545),f780(x19543,x19542,x19544,x19545)) % 112.37/112.12 [1955]~E(x19551,x19552)+E(f780(x19553,x19554,x19551,x19555),f780(x19553,x19554,x19552,x19555)) % 112.37/112.12 [1956]~E(x19561,x19562)+E(f780(x19563,x19564,x19565,x19561),f780(x19563,x19564,x19565,x19562)) % 112.37/112.12 [1957]~E(x19571,x19572)+E(f442(x19571,x19573,x19574),f442(x19572,x19573,x19574)) % 112.37/112.12 [1958]~E(x19581,x19582)+E(f442(x19583,x19581,x19584),f442(x19583,x19582,x19584)) % 112.37/112.12 [1959]~E(x19591,x19592)+E(f442(x19593,x19594,x19591),f442(x19593,x19594,x19592)) % 112.37/112.12 [1960]~E(x19601,x19602)+E(f652(x19601,x19603),f652(x19602,x19603)) % 112.37/112.12 [1961]~E(x19611,x19612)+E(f652(x19613,x19611),f652(x19613,x19612)) % 112.37/112.12 [1962]~E(x19621,x19622)+E(f717(x19621,x19623,x19624,x19625),f717(x19622,x19623,x19624,x19625)) % 112.37/112.12 [1963]~E(x19631,x19632)+E(f717(x19633,x19631,x19634,x19635),f717(x19633,x19632,x19634,x19635)) % 112.37/112.12 [1964]~E(x19641,x19642)+E(f717(x19643,x19644,x19641,x19645),f717(x19643,x19644,x19642,x19645)) % 112.37/112.12 [1965]~E(x19651,x19652)+E(f717(x19653,x19654,x19655,x19651),f717(x19653,x19654,x19655,x19652)) % 112.37/112.12 [1966]~E(x19661,x19662)+E(f911(x19661),f911(x19662)) % 112.37/112.12 [1967]~E(x19671,x19672)+E(f706(x19671,x19673,x19674,x19675),f706(x19672,x19673,x19674,x19675)) % 112.37/112.12 [1968]~E(x19681,x19682)+E(f706(x19683,x19681,x19684,x19685),f706(x19683,x19682,x19684,x19685)) % 112.37/112.12 [1969]~E(x19691,x19692)+E(f706(x19693,x19694,x19691,x19695),f706(x19693,x19694,x19692,x19695)) % 112.37/112.12 [1970]~E(x19701,x19702)+E(f706(x19703,x19704,x19705,x19701),f706(x19703,x19704,x19705,x19702)) % 112.37/112.12 [1971]~E(x19711,x19712)+E(f754(x19711,x19713,x19714),f754(x19712,x19713,x19714)) % 112.37/112.12 [1972]~E(x19721,x19722)+E(f754(x19723,x19721,x19724),f754(x19723,x19722,x19724)) % 112.37/112.12 [1973]~E(x19731,x19732)+E(f754(x19733,x19734,x19731),f754(x19733,x19734,x19732)) % 112.37/112.12 [1974]~E(x19741,x19742)+E(f433(x19741,x19743,x19744,x19745,x19746,x19747,x19748),f433(x19742,x19743,x19744,x19745,x19746,x19747,x19748)) % 112.37/112.12 [1975]~E(x19751,x19752)+E(f433(x19753,x19751,x19754,x19755,x19756,x19757,x19758),f433(x19753,x19752,x19754,x19755,x19756,x19757,x19758)) % 112.37/112.12 [1976]~E(x19761,x19762)+E(f433(x19763,x19764,x19761,x19765,x19766,x19767,x19768),f433(x19763,x19764,x19762,x19765,x19766,x19767,x19768)) % 112.37/112.12 [1977]~E(x19771,x19772)+E(f433(x19773,x19774,x19775,x19771,x19776,x19777,x19778),f433(x19773,x19774,x19775,x19772,x19776,x19777,x19778)) % 112.37/112.12 [1978]~E(x19781,x19782)+E(f433(x19783,x19784,x19785,x19786,x19781,x19787,x19788),f433(x19783,x19784,x19785,x19786,x19782,x19787,x19788)) % 112.37/112.12 [1979]~E(x19791,x19792)+E(f433(x19793,x19794,x19795,x19796,x19797,x19791,x19798),f433(x19793,x19794,x19795,x19796,x19797,x19792,x19798)) % 112.37/112.12 [1980]~E(x19801,x19802)+E(f433(x19803,x19804,x19805,x19806,x19807,x19808,x19801),f433(x19803,x19804,x19805,x19806,x19807,x19808,x19802)) % 112.37/112.12 [1981]~E(x19811,x19812)+E(f120(x19811,x19813,x19814,x19815),f120(x19812,x19813,x19814,x19815)) % 112.37/112.12 [1982]~E(x19821,x19822)+E(f120(x19823,x19821,x19824,x19825),f120(x19823,x19822,x19824,x19825)) % 112.37/112.12 [1983]~E(x19831,x19832)+E(f120(x19833,x19834,x19831,x19835),f120(x19833,x19834,x19832,x19835)) % 112.37/112.12 [1984]~E(x19841,x19842)+E(f120(x19843,x19844,x19845,x19841),f120(x19843,x19844,x19845,x19842)) % 112.37/112.12 [1985]~E(x19851,x19852)+E(f564(x19851),f564(x19852)) % 112.37/112.12 [1986]~E(x19861,x19862)+E(f565(x19861,x19863),f565(x19862,x19863)) % 112.37/112.12 [1987]~E(x19871,x19872)+E(f565(x19873,x19871),f565(x19873,x19872)) % 112.37/112.12 [1988]~E(x19881,x19882)+E(f861(x19881,x19883),f861(x19882,x19883)) % 112.37/112.12 [1989]~E(x19891,x19892)+E(f861(x19893,x19891),f861(x19893,x19892)) % 112.37/112.12 [1990]~E(x19901,x19902)+E(f866(x19901,x19903,x19904),f866(x19902,x19903,x19904)) % 112.37/112.12 [1991]~E(x19911,x19912)+E(f866(x19913,x19911,x19914),f866(x19913,x19912,x19914)) % 112.37/112.12 [1992]~E(x19921,x19922)+E(f866(x19923,x19924,x19921),f866(x19923,x19924,x19922)) % 112.37/112.12 [1993]~E(x19931,x19932)+E(f345(x19931,x19933,x19934),f345(x19932,x19933,x19934)) % 112.37/112.12 [1994]~E(x19941,x19942)+E(f345(x19943,x19941,x19944),f345(x19943,x19942,x19944)) % 112.37/112.12 [1995]~E(x19951,x19952)+E(f345(x19953,x19954,x19951),f345(x19953,x19954,x19952)) % 112.37/112.12 [1996]~E(x19961,x19962)+E(f355(x19961,x19963,x19964),f355(x19962,x19963,x19964)) % 112.37/112.12 [1997]~E(x19971,x19972)+E(f355(x19973,x19971,x19974),f355(x19973,x19972,x19974)) % 112.37/112.12 [1998]~E(x19981,x19982)+E(f355(x19983,x19984,x19981),f355(x19983,x19984,x19982)) % 112.37/112.12 [1999]~E(x19991,x19992)+E(f609(x19991,x19993,x19994,x19995,x19996),f609(x19992,x19993,x19994,x19995,x19996)) % 112.37/112.12 [2000]~E(x20001,x20002)+E(f609(x20003,x20001,x20004,x20005,x20006),f609(x20003,x20002,x20004,x20005,x20006)) % 112.37/112.12 [2001]~E(x20011,x20012)+E(f609(x20013,x20014,x20011,x20015,x20016),f609(x20013,x20014,x20012,x20015,x20016)) % 112.37/112.12 [2002]~E(x20021,x20022)+E(f609(x20023,x20024,x20025,x20021,x20026),f609(x20023,x20024,x20025,x20022,x20026)) % 112.37/112.12 [2003]~E(x20031,x20032)+E(f609(x20033,x20034,x20035,x20036,x20031),f609(x20033,x20034,x20035,x20036,x20032)) % 112.37/112.12 [2004]~E(x20041,x20042)+E(f458(x20041,x20043,x20044),f458(x20042,x20043,x20044)) % 112.37/112.12 [2005]~E(x20051,x20052)+E(f458(x20053,x20051,x20054),f458(x20053,x20052,x20054)) % 112.37/112.12 [2006]~E(x20061,x20062)+E(f458(x20063,x20064,x20061),f458(x20063,x20064,x20062)) % 112.37/112.12 [2007]~E(x20071,x20072)+E(f740(x20071,x20073,x20074),f740(x20072,x20073,x20074)) % 112.37/112.12 [2008]~E(x20081,x20082)+E(f740(x20083,x20081,x20084),f740(x20083,x20082,x20084)) % 112.37/112.12 [2009]~E(x20091,x20092)+E(f740(x20093,x20094,x20091),f740(x20093,x20094,x20092)) % 112.37/112.12 [2010]~E(x20101,x20102)+E(f832(x20101,x20103,x20104,x20105,x20106,x20107,x20108,x20109),f832(x20102,x20103,x20104,x20105,x20106,x20107,x20108,x20109)) % 112.37/112.12 [2011]~E(x20111,x20112)+E(f832(x20113,x20111,x20114,x20115,x20116,x20117,x20118,x20119),f832(x20113,x20112,x20114,x20115,x20116,x20117,x20118,x20119)) % 112.37/112.12 [2012]~E(x20121,x20122)+E(f832(x20123,x20124,x20121,x20125,x20126,x20127,x20128,x20129),f832(x20123,x20124,x20122,x20125,x20126,x20127,x20128,x20129)) % 112.37/112.12 [2013]~E(x20131,x20132)+E(f832(x20133,x20134,x20135,x20131,x20136,x20137,x20138,x20139),f832(x20133,x20134,x20135,x20132,x20136,x20137,x20138,x20139)) % 112.37/112.12 [2014]~E(x20141,x20142)+E(f832(x20143,x20144,x20145,x20146,x20141,x20147,x20148,x20149),f832(x20143,x20144,x20145,x20146,x20142,x20147,x20148,x20149)) % 112.37/112.12 [2015]~E(x20151,x20152)+E(f832(x20153,x20154,x20155,x20156,x20157,x20151,x20158,x20159),f832(x20153,x20154,x20155,x20156,x20157,x20152,x20158,x20159)) % 112.37/112.12 [2016]~E(x20161,x20162)+E(f832(x20163,x20164,x20165,x20166,x20167,x20168,x20161,x20169),f832(x20163,x20164,x20165,x20166,x20167,x20168,x20162,x20169)) % 112.37/112.12 [2017]~E(x20171,x20172)+E(f832(x20173,x20174,x20175,x20176,x20177,x20178,x20179,x20171),f832(x20173,x20174,x20175,x20176,x20177,x20178,x20179,x20172)) % 112.37/112.12 [2018]~E(x20181,x20182)+E(f623(x20181,x20183,x20184,x20185),f623(x20182,x20183,x20184,x20185)) % 112.37/112.12 [2019]~E(x20191,x20192)+E(f623(x20193,x20191,x20194,x20195),f623(x20193,x20192,x20194,x20195)) % 112.37/112.12 [2020]~E(x20201,x20202)+E(f623(x20203,x20204,x20201,x20205),f623(x20203,x20204,x20202,x20205)) % 112.37/112.12 [2021]~E(x20211,x20212)+E(f623(x20213,x20214,x20215,x20211),f623(x20213,x20214,x20215,x20212)) % 112.37/112.12 [2022]~E(x20221,x20222)+E(f664(x20221,x20223,x20224,x20225),f664(x20222,x20223,x20224,x20225)) % 112.37/112.12 [2023]~E(x20231,x20232)+E(f664(x20233,x20231,x20234,x20235),f664(x20233,x20232,x20234,x20235)) % 112.37/112.12 [2024]~E(x20241,x20242)+E(f664(x20243,x20244,x20241,x20245),f664(x20243,x20244,x20242,x20245)) % 112.37/112.12 [2025]~E(x20251,x20252)+E(f664(x20253,x20254,x20255,x20251),f664(x20253,x20254,x20255,x20252)) % 112.37/112.12 [2026]~E(x20261,x20262)+E(f496(x20261,x20263,x20264,x20265,x20266),f496(x20262,x20263,x20264,x20265,x20266)) % 112.37/112.12 [2027]~E(x20271,x20272)+E(f496(x20273,x20271,x20274,x20275,x20276),f496(x20273,x20272,x20274,x20275,x20276)) % 112.37/112.12 [2028]~E(x20281,x20282)+E(f496(x20283,x20284,x20281,x20285,x20286),f496(x20283,x20284,x20282,x20285,x20286)) % 112.37/112.12 [2029]~E(x20291,x20292)+E(f496(x20293,x20294,x20295,x20291,x20296),f496(x20293,x20294,x20295,x20292,x20296)) % 112.37/112.12 [2030]~E(x20301,x20302)+E(f496(x20303,x20304,x20305,x20306,x20301),f496(x20303,x20304,x20305,x20306,x20302)) % 112.37/112.12 [2031]~E(x20311,x20312)+E(f485(x20311,x20313,x20314,x20315,x20316),f485(x20312,x20313,x20314,x20315,x20316)) % 112.37/112.12 [2032]~E(x20321,x20322)+E(f485(x20323,x20321,x20324,x20325,x20326),f485(x20323,x20322,x20324,x20325,x20326)) % 112.37/112.12 [2033]~E(x20331,x20332)+E(f485(x20333,x20334,x20331,x20335,x20336),f485(x20333,x20334,x20332,x20335,x20336)) % 112.37/112.12 [2034]~E(x20341,x20342)+E(f485(x20343,x20344,x20345,x20341,x20346),f485(x20343,x20344,x20345,x20342,x20346)) % 112.37/112.12 [2035]~E(x20351,x20352)+E(f485(x20353,x20354,x20355,x20356,x20351),f485(x20353,x20354,x20355,x20356,x20352)) % 112.37/112.12 [2036]~E(x20361,x20362)+E(f514(x20361,x20363,x20364,x20365),f514(x20362,x20363,x20364,x20365)) % 112.37/112.12 [2037]~E(x20371,x20372)+E(f514(x20373,x20371,x20374,x20375),f514(x20373,x20372,x20374,x20375)) % 112.37/112.12 [2038]~E(x20381,x20382)+E(f514(x20383,x20384,x20381,x20385),f514(x20383,x20384,x20382,x20385)) % 112.37/112.12 [2039]~E(x20391,x20392)+E(f514(x20393,x20394,x20395,x20391),f514(x20393,x20394,x20395,x20392)) % 112.37/112.12 [2040]~E(x20401,x20402)+E(f627(x20401,x20403,x20404,x20405,x20406,x20407),f627(x20402,x20403,x20404,x20405,x20406,x20407)) % 112.37/112.12 [2041]~E(x20411,x20412)+E(f627(x20413,x20411,x20414,x20415,x20416,x20417),f627(x20413,x20412,x20414,x20415,x20416,x20417)) % 112.37/112.12 [2042]~E(x20421,x20422)+E(f627(x20423,x20424,x20421,x20425,x20426,x20427),f627(x20423,x20424,x20422,x20425,x20426,x20427)) % 112.37/112.12 [2043]~E(x20431,x20432)+E(f627(x20433,x20434,x20435,x20431,x20436,x20437),f627(x20433,x20434,x20435,x20432,x20436,x20437)) % 112.37/112.12 [2044]~E(x20441,x20442)+E(f627(x20443,x20444,x20445,x20446,x20441,x20447),f627(x20443,x20444,x20445,x20446,x20442,x20447)) % 112.37/112.12 [2045]~E(x20451,x20452)+E(f627(x20453,x20454,x20455,x20456,x20457,x20451),f627(x20453,x20454,x20455,x20456,x20457,x20452)) % 112.37/112.12 [2046]~E(x20461,x20462)+E(f631(x20461,x20463,x20464,x20465),f631(x20462,x20463,x20464,x20465)) % 112.37/112.12 [2047]~E(x20471,x20472)+E(f631(x20473,x20471,x20474,x20475),f631(x20473,x20472,x20474,x20475)) % 112.37/112.12 [2048]~E(x20481,x20482)+E(f631(x20483,x20484,x20481,x20485),f631(x20483,x20484,x20482,x20485)) % 112.37/112.12 [2049]~E(x20491,x20492)+E(f631(x20493,x20494,x20495,x20491),f631(x20493,x20494,x20495,x20492)) % 112.37/112.12 [2050]~E(x20501,x20502)+E(f236(x20501,x20503,x20504,x20505,x20506,x20507),f236(x20502,x20503,x20504,x20505,x20506,x20507)) % 112.37/112.12 [2051]~E(x20511,x20512)+E(f236(x20513,x20511,x20514,x20515,x20516,x20517),f236(x20513,x20512,x20514,x20515,x20516,x20517)) % 112.37/112.12 [2052]~E(x20521,x20522)+E(f236(x20523,x20524,x20521,x20525,x20526,x20527),f236(x20523,x20524,x20522,x20525,x20526,x20527)) % 112.37/112.12 [2053]~E(x20531,x20532)+E(f236(x20533,x20534,x20535,x20531,x20536,x20537),f236(x20533,x20534,x20535,x20532,x20536,x20537)) % 112.37/112.12 [2054]~E(x20541,x20542)+E(f236(x20543,x20544,x20545,x20546,x20541,x20547),f236(x20543,x20544,x20545,x20546,x20542,x20547)) % 112.37/112.12 [2055]~E(x20551,x20552)+E(f236(x20553,x20554,x20555,x20556,x20557,x20551),f236(x20553,x20554,x20555,x20556,x20557,x20552)) % 112.37/112.12 [2056]~E(x20561,x20562)+E(f707(x20561,x20563),f707(x20562,x20563)) % 112.37/112.12 [2057]~E(x20571,x20572)+E(f707(x20573,x20571),f707(x20573,x20572)) % 112.37/112.12 [2058]~E(x20581,x20582)+E(f873(x20581,x20583,x20584,x20585),f873(x20582,x20583,x20584,x20585)) % 112.37/112.12 [2059]~E(x20591,x20592)+E(f873(x20593,x20591,x20594,x20595),f873(x20593,x20592,x20594,x20595)) % 112.37/112.12 [2060]~E(x20601,x20602)+E(f873(x20603,x20604,x20601,x20605),f873(x20603,x20604,x20602,x20605)) % 112.37/112.12 [2061]~E(x20611,x20612)+E(f873(x20613,x20614,x20615,x20611),f873(x20613,x20614,x20615,x20612)) % 112.37/112.12 [2062]~E(x20621,x20622)+E(f834(x20621,x20623,x20624,x20625,x20626,x20627),f834(x20622,x20623,x20624,x20625,x20626,x20627)) % 112.37/112.12 [2063]~E(x20631,x20632)+E(f834(x20633,x20631,x20634,x20635,x20636,x20637),f834(x20633,x20632,x20634,x20635,x20636,x20637)) % 112.37/112.12 [2064]~E(x20641,x20642)+E(f834(x20643,x20644,x20641,x20645,x20646,x20647),f834(x20643,x20644,x20642,x20645,x20646,x20647)) % 112.37/112.12 [2065]~E(x20651,x20652)+E(f834(x20653,x20654,x20655,x20651,x20656,x20657),f834(x20653,x20654,x20655,x20652,x20656,x20657)) % 112.37/112.12 [2066]~E(x20661,x20662)+E(f834(x20663,x20664,x20665,x20666,x20661,x20667),f834(x20663,x20664,x20665,x20666,x20662,x20667)) % 112.37/112.12 [2067]~E(x20671,x20672)+E(f834(x20673,x20674,x20675,x20676,x20677,x20671),f834(x20673,x20674,x20675,x20676,x20677,x20672)) % 112.37/112.12 [2068]~E(x20681,x20682)+E(f744(x20681,x20683,x20684),f744(x20682,x20683,x20684)) % 112.37/112.12 [2069]~E(x20691,x20692)+E(f744(x20693,x20691,x20694),f744(x20693,x20692,x20694)) % 112.37/112.12 [2070]~E(x20701,x20702)+E(f744(x20703,x20704,x20701),f744(x20703,x20704,x20702)) % 112.37/112.12 [2071]~E(x20711,x20712)+E(f869(x20711,x20713),f869(x20712,x20713)) % 112.37/112.12 [2072]~E(x20721,x20722)+E(f869(x20723,x20721),f869(x20723,x20722)) % 112.37/112.12 [2073]~E(x20731,x20732)+E(f798(x20731,x20733),f798(x20732,x20733)) % 112.37/112.12 [2074]~E(x20741,x20742)+E(f798(x20743,x20741),f798(x20743,x20742)) % 112.37/112.12 [2075]~E(x20751,x20752)+E(f884(x20751,x20753,x20754,x20755),f884(x20752,x20753,x20754,x20755)) % 112.37/112.12 [2076]~E(x20761,x20762)+E(f884(x20763,x20761,x20764,x20765),f884(x20763,x20762,x20764,x20765)) % 112.37/112.12 [2077]~E(x20771,x20772)+E(f884(x20773,x20774,x20771,x20775),f884(x20773,x20774,x20772,x20775)) % 112.37/112.12 [2078]~E(x20781,x20782)+E(f884(x20783,x20784,x20785,x20781),f884(x20783,x20784,x20785,x20782)) % 112.37/112.12 [2079]~E(x20791,x20792)+E(f662(x20791,x20793,x20794,x20795,x20796),f662(x20792,x20793,x20794,x20795,x20796)) % 112.37/112.12 [2080]~E(x20801,x20802)+E(f662(x20803,x20801,x20804,x20805,x20806),f662(x20803,x20802,x20804,x20805,x20806)) % 112.37/112.12 [2081]~E(x20811,x20812)+E(f662(x20813,x20814,x20811,x20815,x20816),f662(x20813,x20814,x20812,x20815,x20816)) % 112.37/112.12 [2082]~E(x20821,x20822)+E(f662(x20823,x20824,x20825,x20821,x20826),f662(x20823,x20824,x20825,x20822,x20826)) % 112.37/112.12 [2083]~E(x20831,x20832)+E(f662(x20833,x20834,x20835,x20836,x20831),f662(x20833,x20834,x20835,x20836,x20832)) % 112.37/112.12 [2084]~E(x20841,x20842)+E(f607(x20841,x20843,x20844,x20845,x20846),f607(x20842,x20843,x20844,x20845,x20846)) % 112.37/112.12 [2085]~E(x20851,x20852)+E(f607(x20853,x20851,x20854,x20855,x20856),f607(x20853,x20852,x20854,x20855,x20856)) % 112.37/112.12 [2086]~E(x20861,x20862)+E(f607(x20863,x20864,x20861,x20865,x20866),f607(x20863,x20864,x20862,x20865,x20866)) % 112.37/112.12 [2087]~E(x20871,x20872)+E(f607(x20873,x20874,x20875,x20871,x20876),f607(x20873,x20874,x20875,x20872,x20876)) % 112.37/112.12 [2088]~E(x20881,x20882)+E(f607(x20883,x20884,x20885,x20886,x20881),f607(x20883,x20884,x20885,x20886,x20882)) % 112.37/112.12 [2089]~E(x20891,x20892)+E(f391(x20891,x20893,x20894,x20895),f391(x20892,x20893,x20894,x20895)) % 112.37/112.12 [2090]~E(x20901,x20902)+E(f391(x20903,x20901,x20904,x20905),f391(x20903,x20902,x20904,x20905)) % 112.37/112.12 [2091]~E(x20911,x20912)+E(f391(x20913,x20914,x20911,x20915),f391(x20913,x20914,x20912,x20915)) % 112.37/112.12 [2092]~E(x20921,x20922)+E(f391(x20923,x20924,x20925,x20921),f391(x20923,x20924,x20925,x20922)) % 112.37/112.12 [2093]~E(x20931,x20932)+E(f396(x20931,x20933,x20934,x20935),f396(x20932,x20933,x20934,x20935)) % 112.37/112.12 [2094]~E(x20941,x20942)+E(f396(x20943,x20941,x20944,x20945),f396(x20943,x20942,x20944,x20945)) % 112.37/112.12 [2095]~E(x20951,x20952)+E(f396(x20953,x20954,x20951,x20955),f396(x20953,x20954,x20952,x20955)) % 112.37/112.12 [2096]~E(x20961,x20962)+E(f396(x20963,x20964,x20965,x20961),f396(x20963,x20964,x20965,x20962)) % 112.37/112.12 [2097]~E(x20971,x20972)+E(f751(x20971,x20973,x20974,x20975),f751(x20972,x20973,x20974,x20975)) % 112.37/112.12 [2098]~E(x20981,x20982)+E(f751(x20983,x20981,x20984,x20985),f751(x20983,x20982,x20984,x20985)) % 112.37/112.12 [2099]~E(x20991,x20992)+E(f751(x20993,x20994,x20991,x20995),f751(x20993,x20994,x20992,x20995)) % 112.37/112.12 [2100]~E(x21001,x21002)+E(f751(x21003,x21004,x21005,x21001),f751(x21003,x21004,x21005,x21002)) % 112.37/112.12 [2101]~E(x21011,x21012)+E(f369(x21011,x21013,x21014,x21015),f369(x21012,x21013,x21014,x21015)) % 112.37/112.12 [2102]~E(x21021,x21022)+E(f369(x21023,x21021,x21024,x21025),f369(x21023,x21022,x21024,x21025)) % 112.37/112.12 [2103]~E(x21031,x21032)+E(f369(x21033,x21034,x21031,x21035),f369(x21033,x21034,x21032,x21035)) % 112.37/112.12 [2104]~E(x21041,x21042)+E(f369(x21043,x21044,x21045,x21041),f369(x21043,x21044,x21045,x21042)) % 112.37/112.12 [2105]~E(x21051,x21052)+E(f693(x21051,x21053,x21054),f693(x21052,x21053,x21054)) % 112.37/112.12 [2106]~E(x21061,x21062)+E(f693(x21063,x21061,x21064),f693(x21063,x21062,x21064)) % 112.37/112.12 [2107]~E(x21071,x21072)+E(f693(x21073,x21074,x21071),f693(x21073,x21074,x21072)) % 112.37/112.12 [2108]~E(x21081,x21082)+E(f417(x21081,x21083,x21084,x21085,x21086),f417(x21082,x21083,x21084,x21085,x21086)) % 112.37/112.12 [2109]~E(x21091,x21092)+E(f417(x21093,x21091,x21094,x21095,x21096),f417(x21093,x21092,x21094,x21095,x21096)) % 112.37/112.12 [2110]~E(x21101,x21102)+E(f417(x21103,x21104,x21101,x21105,x21106),f417(x21103,x21104,x21102,x21105,x21106)) % 112.37/112.12 [2111]~E(x21111,x21112)+E(f417(x21113,x21114,x21115,x21111,x21116),f417(x21113,x21114,x21115,x21112,x21116)) % 112.37/112.12 [2112]~E(x21121,x21122)+E(f417(x21123,x21124,x21125,x21126,x21121),f417(x21123,x21124,x21125,x21126,x21122)) % 112.37/112.12 [2113]~E(x21131,x21132)+E(f250(x21131,x21133,x21134,x21135,x21136),f250(x21132,x21133,x21134,x21135,x21136)) % 112.37/112.12 [2114]~E(x21141,x21142)+E(f250(x21143,x21141,x21144,x21145,x21146),f250(x21143,x21142,x21144,x21145,x21146)) % 112.37/112.12 [2115]~E(x21151,x21152)+E(f250(x21153,x21154,x21151,x21155,x21156),f250(x21153,x21154,x21152,x21155,x21156)) % 112.37/112.12 [2116]~E(x21161,x21162)+E(f250(x21163,x21164,x21165,x21161,x21166),f250(x21163,x21164,x21165,x21162,x21166)) % 112.37/112.12 [2117]~E(x21171,x21172)+E(f250(x21173,x21174,x21175,x21176,x21171),f250(x21173,x21174,x21175,x21176,x21172)) % 112.37/112.12 [2118]~E(x21181,x21182)+E(f349(x21181,x21183,x21184),f349(x21182,x21183,x21184)) % 112.37/112.12 [2119]~E(x21191,x21192)+E(f349(x21193,x21191,x21194),f349(x21193,x21192,x21194)) % 112.37/112.12 [2120]~E(x21201,x21202)+E(f349(x21203,x21204,x21201),f349(x21203,x21204,x21202)) % 112.37/112.12 [2121]~E(x21211,x21212)+E(f705(x21211,x21213,x21214,x21215),f705(x21212,x21213,x21214,x21215)) % 112.37/112.12 [2122]~E(x21221,x21222)+E(f705(x21223,x21221,x21224,x21225),f705(x21223,x21222,x21224,x21225)) % 112.37/112.12 [2123]~E(x21231,x21232)+E(f705(x21233,x21234,x21231,x21235),f705(x21233,x21234,x21232,x21235)) % 112.37/112.12 [2124]~E(x21241,x21242)+E(f705(x21243,x21244,x21245,x21241),f705(x21243,x21244,x21245,x21242)) % 112.37/112.12 [2125]~E(x21251,x21252)+E(f465(x21251,x21253,x21254,x21255),f465(x21252,x21253,x21254,x21255)) % 112.37/112.12 [2126]~E(x21261,x21262)+E(f465(x21263,x21261,x21264,x21265),f465(x21263,x21262,x21264,x21265)) % 112.37/112.12 [2127]~E(x21271,x21272)+E(f465(x21273,x21274,x21271,x21275),f465(x21273,x21274,x21272,x21275)) % 112.37/112.12 [2128]~E(x21281,x21282)+E(f465(x21283,x21284,x21285,x21281),f465(x21283,x21284,x21285,x21282)) % 112.37/112.12 [2129]~E(x21291,x21292)+E(f443(x21291,x21293,x21294),f443(x21292,x21293,x21294)) % 112.37/112.12 [2130]~E(x21301,x21302)+E(f443(x21303,x21301,x21304),f443(x21303,x21302,x21304)) % 112.37/112.12 [2131]~E(x21311,x21312)+E(f443(x21313,x21314,x21311),f443(x21313,x21314,x21312)) % 112.37/112.12 [2132]~E(x21321,x21322)+E(f698(x21321,x21323),f698(x21322,x21323)) % 112.37/112.12 [2133]~E(x21331,x21332)+E(f698(x21333,x21331),f698(x21333,x21332)) % 112.37/112.12 [2134]~E(x21341,x21342)+E(f397(x21341,x21343,x21344,x21345),f397(x21342,x21343,x21344,x21345)) % 112.37/112.12 [2135]~E(x21351,x21352)+E(f397(x21353,x21351,x21354,x21355),f397(x21353,x21352,x21354,x21355)) % 112.37/112.12 [2136]~E(x21361,x21362)+E(f397(x21363,x21364,x21361,x21365),f397(x21363,x21364,x21362,x21365)) % 112.37/112.12 [2137]~E(x21371,x21372)+E(f397(x21373,x21374,x21375,x21371),f397(x21373,x21374,x21375,x21372)) % 112.37/112.12 [2138]~E(x21381,x21382)+E(f756(x21381,x21383,x21384),f756(x21382,x21383,x21384)) % 112.37/112.12 [2139]~E(x21391,x21392)+E(f756(x21393,x21391,x21394),f756(x21393,x21392,x21394)) % 112.37/112.12 [2140]~E(x21401,x21402)+E(f756(x21403,x21404,x21401),f756(x21403,x21404,x21402)) % 112.37/112.12 [2141]~E(x21411,x21412)+E(f201(x21411,x21413,x21414,x21415,x21416,x21417,x21418),f201(x21412,x21413,x21414,x21415,x21416,x21417,x21418)) % 112.37/112.12 [2142]~E(x21421,x21422)+E(f201(x21423,x21421,x21424,x21425,x21426,x21427,x21428),f201(x21423,x21422,x21424,x21425,x21426,x21427,x21428)) % 112.37/112.12 [2143]~E(x21431,x21432)+E(f201(x21433,x21434,x21431,x21435,x21436,x21437,x21438),f201(x21433,x21434,x21432,x21435,x21436,x21437,x21438)) % 112.37/112.12 [2144]~E(x21441,x21442)+E(f201(x21443,x21444,x21445,x21441,x21446,x21447,x21448),f201(x21443,x21444,x21445,x21442,x21446,x21447,x21448)) % 112.37/112.12 [2145]~E(x21451,x21452)+E(f201(x21453,x21454,x21455,x21456,x21451,x21457,x21458),f201(x21453,x21454,x21455,x21456,x21452,x21457,x21458)) % 112.37/112.12 [2146]~E(x21461,x21462)+E(f201(x21463,x21464,x21465,x21466,x21467,x21461,x21468),f201(x21463,x21464,x21465,x21466,x21467,x21462,x21468)) % 112.37/112.12 [2147]~E(x21471,x21472)+E(f201(x21473,x21474,x21475,x21476,x21477,x21478,x21471),f201(x21473,x21474,x21475,x21476,x21477,x21478,x21472)) % 112.37/112.12 [2148]~E(x21481,x21482)+E(f468(x21481,x21483,x21484,x21485,x21486),f468(x21482,x21483,x21484,x21485,x21486)) % 112.37/112.12 [2149]~E(x21491,x21492)+E(f468(x21493,x21491,x21494,x21495,x21496),f468(x21493,x21492,x21494,x21495,x21496)) % 112.37/112.12 [2150]~E(x21501,x21502)+E(f468(x21503,x21504,x21501,x21505,x21506),f468(x21503,x21504,x21502,x21505,x21506)) % 112.37/112.12 [2151]~E(x21511,x21512)+E(f468(x21513,x21514,x21515,x21511,x21516),f468(x21513,x21514,x21515,x21512,x21516)) % 112.37/112.12 [2152]~E(x21521,x21522)+E(f468(x21523,x21524,x21525,x21526,x21521),f468(x21523,x21524,x21525,x21526,x21522)) % 112.37/112.12 [2153]~E(x21531,x21532)+E(f864(x21531,x21533,x21534),f864(x21532,x21533,x21534)) % 112.37/112.12 [2154]~E(x21541,x21542)+E(f864(x21543,x21541,x21544),f864(x21543,x21542,x21544)) % 112.37/112.12 [2155]~E(x21551,x21552)+E(f864(x21553,x21554,x21551),f864(x21553,x21554,x21552)) % 112.37/112.12 [2156]~E(x21561,x21562)+E(f285(x21561,x21563,x21564),f285(x21562,x21563,x21564)) % 112.37/112.12 [2157]~E(x21571,x21572)+E(f285(x21573,x21571,x21574),f285(x21573,x21572,x21574)) % 112.37/112.12 [2158]~E(x21581,x21582)+E(f285(x21583,x21584,x21581),f285(x21583,x21584,x21582)) % 112.37/112.12 [2159]~E(x21591,x21592)+E(f544(x21591,x21593),f544(x21592,x21593)) % 112.37/112.12 [2160]~E(x21601,x21602)+E(f544(x21603,x21601),f544(x21603,x21602)) % 112.37/112.12 [2161]~E(x21611,x21612)+E(f267(x21611,x21613,x21614,x21615),f267(x21612,x21613,x21614,x21615)) % 112.37/112.12 [2162]~E(x21621,x21622)+E(f267(x21623,x21621,x21624,x21625),f267(x21623,x21622,x21624,x21625)) % 112.37/112.12 [2163]~E(x21631,x21632)+E(f267(x21633,x21634,x21631,x21635),f267(x21633,x21634,x21632,x21635)) % 112.37/112.12 [2164]~E(x21641,x21642)+E(f267(x21643,x21644,x21645,x21641),f267(x21643,x21644,x21645,x21642)) % 112.37/112.12 [2165]~E(x21651,x21652)+E(f545(x21651,x21653),f545(x21652,x21653)) % 112.37/112.12 [2166]~E(x21661,x21662)+E(f545(x21663,x21661),f545(x21663,x21662)) % 112.37/112.12 [2167]~E(x21671,x21672)+E(f557(x21671,x21673,x21674,x21675),f557(x21672,x21673,x21674,x21675)) % 112.37/112.12 [2168]~E(x21681,x21682)+E(f557(x21683,x21681,x21684,x21685),f557(x21683,x21682,x21684,x21685)) % 112.37/112.12 [2169]~E(x21691,x21692)+E(f557(x21693,x21694,x21691,x21695),f557(x21693,x21694,x21692,x21695)) % 112.37/112.12 [2170]~E(x21701,x21702)+E(f557(x21703,x21704,x21705,x21701),f557(x21703,x21704,x21705,x21702)) % 112.37/112.12 [2171]~E(x21711,x21712)+E(f892(x21711,x21713,x21714),f892(x21712,x21713,x21714)) % 112.37/112.12 [2172]~E(x21721,x21722)+E(f892(x21723,x21721,x21724),f892(x21723,x21722,x21724)) % 112.37/112.12 [2173]~E(x21731,x21732)+E(f892(x21733,x21734,x21731),f892(x21733,x21734,x21732)) % 112.37/112.12 [2174]~E(x21741,x21742)+E(f222(x21741,x21743),f222(x21742,x21743)) % 112.37/112.12 [2175]~E(x21751,x21752)+E(f222(x21753,x21751),f222(x21753,x21752)) % 112.37/112.12 [2176]~E(x21761,x21762)+E(f876(x21761,x21763,x21764,x21765),f876(x21762,x21763,x21764,x21765)) % 112.37/112.12 [2177]~E(x21771,x21772)+E(f876(x21773,x21771,x21774,x21775),f876(x21773,x21772,x21774,x21775)) % 112.37/112.12 [2178]~E(x21781,x21782)+E(f876(x21783,x21784,x21781,x21785),f876(x21783,x21784,x21782,x21785)) % 112.37/112.12 [2179]~E(x21791,x21792)+E(f876(x21793,x21794,x21795,x21791),f876(x21793,x21794,x21795,x21792)) % 112.37/112.12 [2180]~E(x21801,x21802)+E(f589(x21801,x21803,x21804),f589(x21802,x21803,x21804)) % 112.37/112.12 [2181]~E(x21811,x21812)+E(f589(x21813,x21811,x21814),f589(x21813,x21812,x21814)) % 112.37/112.12 [2182]~E(x21821,x21822)+E(f589(x21823,x21824,x21821),f589(x21823,x21824,x21822)) % 112.37/112.12 [2183]~E(x21831,x21832)+E(f882(x21831,x21833),f882(x21832,x21833)) % 112.37/112.12 [2184]~E(x21841,x21842)+E(f882(x21843,x21841),f882(x21843,x21842)) % 112.37/112.12 [2185]~E(x21851,x21852)+E(f692(x21851,x21853),f692(x21852,x21853)) % 112.37/112.12 [2186]~E(x21861,x21862)+E(f692(x21863,x21861),f692(x21863,x21862)) % 112.37/112.12 [2187]~E(x21871,x21872)+E(f618(x21871,x21873,x21874,x21875,x21876),f618(x21872,x21873,x21874,x21875,x21876)) % 112.37/112.12 [2188]~E(x21881,x21882)+E(f618(x21883,x21881,x21884,x21885,x21886),f618(x21883,x21882,x21884,x21885,x21886)) % 112.37/112.12 [2189]~E(x21891,x21892)+E(f618(x21893,x21894,x21891,x21895,x21896),f618(x21893,x21894,x21892,x21895,x21896)) % 112.37/112.12 [2190]~E(x21901,x21902)+E(f618(x21903,x21904,x21905,x21901,x21906),f618(x21903,x21904,x21905,x21902,x21906)) % 112.37/112.12 [2191]~E(x21911,x21912)+E(f618(x21913,x21914,x21915,x21916,x21911),f618(x21913,x21914,x21915,x21916,x21912)) % 112.37/112.12 [2192]~E(x21921,x21922)+E(f599(x21921,x21923),f599(x21922,x21923)) % 112.37/112.12 [2193]~E(x21931,x21932)+E(f599(x21933,x21931),f599(x21933,x21932)) % 112.37/112.12 [2194]~E(x21941,x21942)+E(f567(x21941,x21943),f567(x21942,x21943)) % 112.37/112.12 [2195]~E(x21951,x21952)+E(f567(x21953,x21951),f567(x21953,x21952)) % 112.37/112.12 [2196]~E(x21961,x21962)+E(f351(x21961,x21963),f351(x21962,x21963)) % 112.37/112.12 [2197]~E(x21971,x21972)+E(f351(x21973,x21971),f351(x21973,x21972)) % 112.37/112.12 [2198]~E(x21981,x21982)+E(f817(x21981,x21983,x21984,x21985,x21986),f817(x21982,x21983,x21984,x21985,x21986)) % 112.37/112.12 [2199]~E(x21991,x21992)+E(f817(x21993,x21991,x21994,x21995,x21996),f817(x21993,x21992,x21994,x21995,x21996)) % 112.37/112.12 [2200]~E(x22001,x22002)+E(f817(x22003,x22004,x22001,x22005,x22006),f817(x22003,x22004,x22002,x22005,x22006)) % 112.37/112.12 [2201]~E(x22011,x22012)+E(f817(x22013,x22014,x22015,x22011,x22016),f817(x22013,x22014,x22015,x22012,x22016)) % 112.37/112.12 [2202]~E(x22021,x22022)+E(f817(x22023,x22024,x22025,x22026,x22021),f817(x22023,x22024,x22025,x22026,x22022)) % 112.37/112.12 [2203]~E(x22031,x22032)+E(f358(x22031,x22033,x22034,x22035),f358(x22032,x22033,x22034,x22035)) % 112.37/112.12 [2204]~E(x22041,x22042)+E(f358(x22043,x22041,x22044,x22045),f358(x22043,x22042,x22044,x22045)) % 112.37/112.12 [2205]~E(x22051,x22052)+E(f358(x22053,x22054,x22051,x22055),f358(x22053,x22054,x22052,x22055)) % 112.37/112.12 [2206]~E(x22061,x22062)+E(f358(x22063,x22064,x22065,x22061),f358(x22063,x22064,x22065,x22062)) % 112.37/112.12 [2207]~E(x22071,x22072)+E(f375(x22071,x22073),f375(x22072,x22073)) % 112.37/112.12 [2208]~E(x22081,x22082)+E(f375(x22083,x22081),f375(x22083,x22082)) % 112.37/112.12 [2209]~E(x22091,x22092)+E(f413(x22091,x22093,x22094,x22095,x22096),f413(x22092,x22093,x22094,x22095,x22096)) % 112.37/112.12 [2210]~E(x22101,x22102)+E(f413(x22103,x22101,x22104,x22105,x22106),f413(x22103,x22102,x22104,x22105,x22106)) % 112.37/112.12 [2211]~E(x22111,x22112)+E(f413(x22113,x22114,x22111,x22115,x22116),f413(x22113,x22114,x22112,x22115,x22116)) % 112.37/112.12 [2212]~E(x22121,x22122)+E(f413(x22123,x22124,x22125,x22121,x22126),f413(x22123,x22124,x22125,x22122,x22126)) % 112.37/112.12 [2213]~E(x22131,x22132)+E(f413(x22133,x22134,x22135,x22136,x22131),f413(x22133,x22134,x22135,x22136,x22132)) % 112.37/112.12 [2214]~E(x22141,x22142)+E(f346(x22141,x22143,x22144),f346(x22142,x22143,x22144)) % 112.37/112.12 [2215]~E(x22151,x22152)+E(f346(x22153,x22151,x22154),f346(x22153,x22152,x22154)) % 112.37/112.12 [2216]~E(x22161,x22162)+E(f346(x22163,x22164,x22161),f346(x22163,x22164,x22162)) % 112.37/112.12 [2217]~E(x22171,x22172)+E(f552(x22171,x22173,x22174,x22175),f552(x22172,x22173,x22174,x22175)) % 112.37/112.12 [2218]~E(x22181,x22182)+E(f552(x22183,x22181,x22184,x22185),f552(x22183,x22182,x22184,x22185)) % 112.37/112.12 [2219]~E(x22191,x22192)+E(f552(x22193,x22194,x22191,x22195),f552(x22193,x22194,x22192,x22195)) % 112.37/112.12 [2220]~E(x22201,x22202)+E(f552(x22203,x22204,x22205,x22201),f552(x22203,x22204,x22205,x22202)) % 112.37/112.12 [2221]~E(x22211,x22212)+E(f650(x22211,x22213,x22214,x22215),f650(x22212,x22213,x22214,x22215)) % 112.37/112.12 [2222]~E(x22221,x22222)+E(f650(x22223,x22221,x22224,x22225),f650(x22223,x22222,x22224,x22225)) % 112.37/112.12 [2223]~E(x22231,x22232)+E(f650(x22233,x22234,x22231,x22235),f650(x22233,x22234,x22232,x22235)) % 112.37/112.12 [2224]~E(x22241,x22242)+E(f650(x22243,x22244,x22245,x22241),f650(x22243,x22244,x22245,x22242)) % 112.37/112.12 [2225]~E(x22251,x22252)+E(f453(x22251,x22253,x22254,x22255),f453(x22252,x22253,x22254,x22255)) % 112.37/112.12 [2226]~E(x22261,x22262)+E(f453(x22263,x22261,x22264,x22265),f453(x22263,x22262,x22264,x22265)) % 112.37/112.12 [2227]~E(x22271,x22272)+E(f453(x22273,x22274,x22271,x22275),f453(x22273,x22274,x22272,x22275)) % 112.37/112.12 [2228]~E(x22281,x22282)+E(f453(x22283,x22284,x22285,x22281),f453(x22283,x22284,x22285,x22282)) % 112.37/112.12 [2229]~E(x22291,x22292)+E(f788(x22291,x22293,x22294),f788(x22292,x22293,x22294)) % 112.37/112.12 [2230]~E(x22301,x22302)+E(f788(x22303,x22301,x22304),f788(x22303,x22302,x22304)) % 112.37/112.12 [2231]~E(x22311,x22312)+E(f788(x22313,x22314,x22311),f788(x22313,x22314,x22312)) % 112.37/112.12 [2232]~E(x22321,x22322)+E(f200(x22321,x22323,x22324,x22325),f200(x22322,x22323,x22324,x22325)) % 112.37/112.12 [2233]~E(x22331,x22332)+E(f200(x22333,x22331,x22334,x22335),f200(x22333,x22332,x22334,x22335)) % 112.37/112.12 [2234]~E(x22341,x22342)+E(f200(x22343,x22344,x22341,x22345),f200(x22343,x22344,x22342,x22345)) % 112.37/112.12 [2235]~E(x22351,x22352)+E(f200(x22353,x22354,x22355,x22351),f200(x22353,x22354,x22355,x22352)) % 112.37/112.12 [2236]~E(x22361,x22362)+E(f562(x22361,x22363,x22364,x22365),f562(x22362,x22363,x22364,x22365)) % 112.37/112.12 [2237]~E(x22371,x22372)+E(f562(x22373,x22371,x22374,x22375),f562(x22373,x22372,x22374,x22375)) % 112.37/112.12 [2238]~E(x22381,x22382)+E(f562(x22383,x22384,x22381,x22385),f562(x22383,x22384,x22382,x22385)) % 112.37/112.12 [2239]~E(x22391,x22392)+E(f562(x22393,x22394,x22395,x22391),f562(x22393,x22394,x22395,x22392)) % 112.37/112.12 [2240]~E(x22401,x22402)+E(f547(x22401,x22403,x22404),f547(x22402,x22403,x22404)) % 112.37/112.12 [2241]~E(x22411,x22412)+E(f547(x22413,x22411,x22414),f547(x22413,x22412,x22414)) % 112.37/112.12 [2242]~E(x22421,x22422)+E(f547(x22423,x22424,x22421),f547(x22423,x22424,x22422)) % 112.37/112.12 [2243]~E(x22431,x22432)+E(f302(x22431,x22433),f302(x22432,x22433)) % 112.37/112.12 [2244]~E(x22441,x22442)+E(f302(x22443,x22441),f302(x22443,x22442)) % 112.37/112.12 [2245]~E(x22451,x22452)+E(f566(x22451,x22453),f566(x22452,x22453)) % 112.37/112.12 [2246]~E(x22461,x22462)+E(f566(x22463,x22461),f566(x22463,x22462)) % 112.37/112.12 [2247]~E(x22471,x22472)+E(f844(x22471,x22473,x22474,x22475,x22476),f844(x22472,x22473,x22474,x22475,x22476)) % 112.37/112.12 [2248]~E(x22481,x22482)+E(f844(x22483,x22481,x22484,x22485,x22486),f844(x22483,x22482,x22484,x22485,x22486)) % 112.37/112.12 [2249]~E(x22491,x22492)+E(f844(x22493,x22494,x22491,x22495,x22496),f844(x22493,x22494,x22492,x22495,x22496)) % 112.37/112.12 [2250]~E(x22501,x22502)+E(f844(x22503,x22504,x22505,x22501,x22506),f844(x22503,x22504,x22505,x22502,x22506)) % 112.37/112.12 [2251]~E(x22511,x22512)+E(f844(x22513,x22514,x22515,x22516,x22511),f844(x22513,x22514,x22515,x22516,x22512)) % 112.37/112.12 [2252]~E(x22521,x22522)+E(f34(x22521),f34(x22522)) % 112.37/112.12 [2253]~E(x22531,x22532)+E(f592(x22531,x22533,x22534,x22535),f592(x22532,x22533,x22534,x22535)) % 112.37/112.12 [2254]~E(x22541,x22542)+E(f592(x22543,x22541,x22544,x22545),f592(x22543,x22542,x22544,x22545)) % 112.37/112.12 [2255]~E(x22551,x22552)+E(f592(x22553,x22554,x22551,x22555),f592(x22553,x22554,x22552,x22555)) % 112.37/112.12 [2256]~E(x22561,x22562)+E(f592(x22563,x22564,x22565,x22561),f592(x22563,x22564,x22565,x22562)) % 112.37/112.12 [2257]~E(x22571,x22572)+E(f620(x22571,x22573,x22574,x22575),f620(x22572,x22573,x22574,x22575)) % 112.37/112.12 [2258]~E(x22581,x22582)+E(f620(x22583,x22581,x22584,x22585),f620(x22583,x22582,x22584,x22585)) % 112.37/112.12 [2259]~E(x22591,x22592)+E(f620(x22593,x22594,x22591,x22595),f620(x22593,x22594,x22592,x22595)) % 112.37/112.12 [2260]~E(x22601,x22602)+E(f620(x22603,x22604,x22605,x22601),f620(x22603,x22604,x22605,x22602)) % 112.37/112.12 [2261]~E(x22611,x22612)+E(f714(x22611,x22613,x22614,x22615,x22616),f714(x22612,x22613,x22614,x22615,x22616)) % 112.37/112.12 [2262]~E(x22621,x22622)+E(f714(x22623,x22621,x22624,x22625,x22626),f714(x22623,x22622,x22624,x22625,x22626)) % 112.37/112.12 [2263]~E(x22631,x22632)+E(f714(x22633,x22634,x22631,x22635,x22636),f714(x22633,x22634,x22632,x22635,x22636)) % 112.37/112.12 [2264]~E(x22641,x22642)+E(f714(x22643,x22644,x22645,x22641,x22646),f714(x22643,x22644,x22645,x22642,x22646)) % 112.37/112.12 [2265]~E(x22651,x22652)+E(f714(x22653,x22654,x22655,x22656,x22651),f714(x22653,x22654,x22655,x22656,x22652)) % 112.37/112.12 [2266]~E(x22661,x22662)+E(f412(x22661,x22663),f412(x22662,x22663)) % 112.37/112.12 [2267]~E(x22671,x22672)+E(f412(x22673,x22671),f412(x22673,x22672)) % 112.37/112.12 [2268]~E(x22681,x22682)+E(f594(x22681,x22683,x22684),f594(x22682,x22683,x22684)) % 112.37/112.12 [2269]~E(x22691,x22692)+E(f594(x22693,x22691,x22694),f594(x22693,x22692,x22694)) % 112.37/112.12 [2270]~E(x22701,x22702)+E(f594(x22703,x22704,x22701),f594(x22703,x22704,x22702)) % 112.37/112.12 [2271]~E(x22711,x22712)+E(f382(x22711,x22713,x22714,x22715),f382(x22712,x22713,x22714,x22715)) % 112.37/112.12 [2272]~E(x22721,x22722)+E(f382(x22723,x22721,x22724,x22725),f382(x22723,x22722,x22724,x22725)) % 112.37/112.12 [2273]~E(x22731,x22732)+E(f382(x22733,x22734,x22731,x22735),f382(x22733,x22734,x22732,x22735)) % 112.37/112.12 [2274]~E(x22741,x22742)+E(f382(x22743,x22744,x22745,x22741),f382(x22743,x22744,x22745,x22742)) % 112.37/112.12 [2275]~E(x22751,x22752)+E(f591(x22751,x22753,x22754),f591(x22752,x22753,x22754)) % 112.37/112.12 [2276]~E(x22761,x22762)+E(f591(x22763,x22761,x22764),f591(x22763,x22762,x22764)) % 112.37/112.12 [2277]~E(x22771,x22772)+E(f591(x22773,x22774,x22771),f591(x22773,x22774,x22772)) % 112.37/112.12 [2278]~E(x22781,x22782)+E(f634(x22781,x22783,x22784,x22785),f634(x22782,x22783,x22784,x22785)) % 112.37/112.12 [2279]~E(x22791,x22792)+E(f634(x22793,x22791,x22794,x22795),f634(x22793,x22792,x22794,x22795)) % 112.37/112.12 [2280]~E(x22801,x22802)+E(f634(x22803,x22804,x22801,x22805),f634(x22803,x22804,x22802,x22805)) % 112.37/112.12 [2281]~E(x22811,x22812)+E(f634(x22813,x22814,x22815,x22811),f634(x22813,x22814,x22815,x22812)) % 112.37/112.12 [2282]~E(x22821,x22822)+E(f198(x22821),f198(x22822)) % 112.37/112.12 [2283]~E(x22831,x22832)+E(f770(x22831,x22833),f770(x22832,x22833)) % 112.37/112.12 [2284]~E(x22841,x22842)+E(f770(x22843,x22841),f770(x22843,x22842)) % 112.37/112.12 [2285]~E(x22851,x22852)+E(f439(x22851,x22853,x22854,x22855,x22856,x22857),f439(x22852,x22853,x22854,x22855,x22856,x22857)) % 112.37/112.12 [2286]~E(x22861,x22862)+E(f439(x22863,x22861,x22864,x22865,x22866,x22867),f439(x22863,x22862,x22864,x22865,x22866,x22867)) % 112.37/112.12 [2287]~E(x22871,x22872)+E(f439(x22873,x22874,x22871,x22875,x22876,x22877),f439(x22873,x22874,x22872,x22875,x22876,x22877)) % 112.37/112.12 [2288]~E(x22881,x22882)+E(f439(x22883,x22884,x22885,x22881,x22886,x22887),f439(x22883,x22884,x22885,x22882,x22886,x22887)) % 112.37/112.12 [2289]~E(x22891,x22892)+E(f439(x22893,x22894,x22895,x22896,x22891,x22897),f439(x22893,x22894,x22895,x22896,x22892,x22897)) % 112.37/112.12 [2290]~E(x22901,x22902)+E(f439(x22903,x22904,x22905,x22906,x22907,x22901),f439(x22903,x22904,x22905,x22906,x22907,x22902)) % 112.37/112.12 [2291]~E(x22911,x22912)+E(f521(x22911,x22913,x22914,x22915),f521(x22912,x22913,x22914,x22915)) % 112.37/112.12 [2292]~E(x22921,x22922)+E(f521(x22923,x22921,x22924,x22925),f521(x22923,x22922,x22924,x22925)) % 112.37/112.12 [2293]~E(x22931,x22932)+E(f521(x22933,x22934,x22931,x22935),f521(x22933,x22934,x22932,x22935)) % 112.37/112.12 [2294]~E(x22941,x22942)+E(f521(x22943,x22944,x22945,x22941),f521(x22943,x22944,x22945,x22942)) % 112.37/112.12 [2295]~E(x22951,x22952)+E(f537(x22951,x22953,x22954,x22955,x22956),f537(x22952,x22953,x22954,x22955,x22956)) % 112.37/112.12 [2296]~E(x22961,x22962)+E(f537(x22963,x22961,x22964,x22965,x22966),f537(x22963,x22962,x22964,x22965,x22966)) % 112.37/112.12 [2297]~E(x22971,x22972)+E(f537(x22973,x22974,x22971,x22975,x22976),f537(x22973,x22974,x22972,x22975,x22976)) % 112.37/112.12 [2298]~E(x22981,x22982)+E(f537(x22983,x22984,x22985,x22981,x22986),f537(x22983,x22984,x22985,x22982,x22986)) % 112.37/112.12 [2299]~E(x22991,x22992)+E(f537(x22993,x22994,x22995,x22996,x22991),f537(x22993,x22994,x22995,x22996,x22992)) % 112.37/112.12 [2300]~E(x23001,x23002)+E(f779(x23001,x23003,x23004,x23005),f779(x23002,x23003,x23004,x23005)) % 112.37/112.12 [2301]~E(x23011,x23012)+E(f779(x23013,x23011,x23014,x23015),f779(x23013,x23012,x23014,x23015)) % 112.37/112.12 [2302]~E(x23021,x23022)+E(f779(x23023,x23024,x23021,x23025),f779(x23023,x23024,x23022,x23025)) % 112.37/112.12 [2303]~E(x23031,x23032)+E(f779(x23033,x23034,x23035,x23031),f779(x23033,x23034,x23035,x23032)) % 112.37/112.12 [2304]~E(x23041,x23042)+E(f639(x23041,x23043,x23044),f639(x23042,x23043,x23044)) % 112.37/112.12 [2305]~E(x23051,x23052)+E(f639(x23053,x23051,x23054),f639(x23053,x23052,x23054)) % 112.37/112.12 [2306]~E(x23061,x23062)+E(f639(x23063,x23064,x23061),f639(x23063,x23064,x23062)) % 112.37/112.12 [2307]~E(x23071,x23072)+E(f347(x23071,x23073,x23074),f347(x23072,x23073,x23074)) % 112.37/112.12 [2308]~E(x23081,x23082)+E(f347(x23083,x23081,x23084),f347(x23083,x23082,x23084)) % 112.37/112.12 [2309]~E(x23091,x23092)+E(f347(x23093,x23094,x23091),f347(x23093,x23094,x23092)) % 112.37/112.12 [2310]~E(x23101,x23102)+E(f862(x23101,x23103,x23104),f862(x23102,x23103,x23104)) % 112.37/112.12 [2311]~E(x23111,x23112)+E(f862(x23113,x23111,x23114),f862(x23113,x23112,x23114)) % 112.37/112.12 [2312]~E(x23121,x23122)+E(f862(x23123,x23124,x23121),f862(x23123,x23124,x23122)) % 112.37/112.12 [2313]~E(x23131,x23132)+E(f448(x23131,x23133),f448(x23132,x23133)) % 112.37/112.12 [2314]~E(x23141,x23142)+E(f448(x23143,x23141),f448(x23143,x23142)) % 112.37/112.12 [2315]~E(x23151,x23152)+E(f774(x23151,x23153),f774(x23152,x23153)) % 112.37/112.12 [2316]~E(x23161,x23162)+E(f774(x23163,x23161),f774(x23163,x23162)) % 112.37/112.12 [2317]~E(x23171,x23172)+E(f808(x23171,x23173,x23174,x23175,x23176,x23177),f808(x23172,x23173,x23174,x23175,x23176,x23177)) % 112.37/112.12 [2318]~E(x23181,x23182)+E(f808(x23183,x23181,x23184,x23185,x23186,x23187),f808(x23183,x23182,x23184,x23185,x23186,x23187)) % 112.37/112.12 [2319]~E(x23191,x23192)+E(f808(x23193,x23194,x23191,x23195,x23196,x23197),f808(x23193,x23194,x23192,x23195,x23196,x23197)) % 112.37/112.12 [2320]~E(x23201,x23202)+E(f808(x23203,x23204,x23205,x23201,x23206,x23207),f808(x23203,x23204,x23205,x23202,x23206,x23207)) % 112.37/112.12 [2321]~E(x23211,x23212)+E(f808(x23213,x23214,x23215,x23216,x23211,x23217),f808(x23213,x23214,x23215,x23216,x23212,x23217)) % 112.37/112.12 [2322]~E(x23221,x23222)+E(f808(x23223,x23224,x23225,x23226,x23227,x23221),f808(x23223,x23224,x23225,x23226,x23227,x23222)) % 112.37/112.12 [2323]~E(x23231,x23232)+E(f603(x23231,x23233,x23234),f603(x23232,x23233,x23234)) % 112.37/112.12 [2324]~E(x23241,x23242)+E(f603(x23243,x23241,x23244),f603(x23243,x23242,x23244)) % 112.37/112.12 [2325]~E(x23251,x23252)+E(f603(x23253,x23254,x23251),f603(x23253,x23254,x23252)) % 112.37/112.12 [2326]~E(x23261,x23262)+E(f255(x23261,x23263,x23264),f255(x23262,x23263,x23264)) % 112.37/112.12 [2327]~E(x23271,x23272)+E(f255(x23273,x23271,x23274),f255(x23273,x23272,x23274)) % 112.37/112.12 [2328]~E(x23281,x23282)+E(f255(x23283,x23284,x23281),f255(x23283,x23284,x23282)) % 112.37/112.12 [2329]~E(x23291,x23292)+E(f738(x23291,x23293,x23294),f738(x23292,x23293,x23294)) % 112.37/112.12 [2330]~E(x23301,x23302)+E(f738(x23303,x23301,x23304),f738(x23303,x23302,x23304)) % 112.37/112.12 [2331]~E(x23311,x23312)+E(f738(x23313,x23314,x23311),f738(x23313,x23314,x23312)) % 112.37/112.12 [2332]~E(x23321,x23322)+E(f571(x23321,x23323,x23324,x23325),f571(x23322,x23323,x23324,x23325)) % 112.37/112.12 [2333]~E(x23331,x23332)+E(f571(x23333,x23331,x23334,x23335),f571(x23333,x23332,x23334,x23335)) % 112.37/112.12 [2334]~E(x23341,x23342)+E(f571(x23343,x23344,x23341,x23345),f571(x23343,x23344,x23342,x23345)) % 112.37/112.12 [2335]~E(x23351,x23352)+E(f571(x23353,x23354,x23355,x23351),f571(x23353,x23354,x23355,x23352)) % 112.37/112.12 [2336]~E(x23361,x23362)+E(f237(x23361,x23363,x23364),f237(x23362,x23363,x23364)) % 112.37/112.12 [2337]~E(x23371,x23372)+E(f237(x23373,x23371,x23374),f237(x23373,x23372,x23374)) % 112.37/112.12 [2338]~E(x23381,x23382)+E(f237(x23383,x23384,x23381),f237(x23383,x23384,x23382)) % 112.37/112.12 [2339]~E(x23391,x23392)+E(f877(x23391,x23393,x23394,x23395),f877(x23392,x23393,x23394,x23395)) % 112.37/112.12 [2340]~E(x23401,x23402)+E(f877(x23403,x23401,x23404,x23405),f877(x23403,x23402,x23404,x23405)) % 112.37/112.12 [2341]~E(x23411,x23412)+E(f877(x23413,x23414,x23411,x23415),f877(x23413,x23414,x23412,x23415)) % 112.37/112.12 [2342]~E(x23421,x23422)+E(f877(x23423,x23424,x23425,x23421),f877(x23423,x23424,x23425,x23422)) % 112.37/112.12 [2343]~E(x23431,x23432)+E(f409(x23431,x23433,x23434),f409(x23432,x23433,x23434)) % 112.37/112.12 [2344]~E(x23441,x23442)+E(f409(x23443,x23441,x23444),f409(x23443,x23442,x23444)) % 112.37/112.12 [2345]~E(x23451,x23452)+E(f409(x23453,x23454,x23451),f409(x23453,x23454,x23452)) % 112.37/112.12 [2346]~E(x23461,x23462)+E(f428(x23461,x23463,x23464),f428(x23462,x23463,x23464)) % 112.37/112.12 [2347]~E(x23471,x23472)+E(f428(x23473,x23471,x23474),f428(x23473,x23472,x23474)) % 112.37/112.12 [2348]~E(x23481,x23482)+E(f428(x23483,x23484,x23481),f428(x23483,x23484,x23482)) % 112.37/112.12 [2349]~E(x23491,x23492)+E(f372(x23491,x23493,x23494,x23495),f372(x23492,x23493,x23494,x23495)) % 112.37/112.12 [2350]~E(x23501,x23502)+E(f372(x23503,x23501,x23504,x23505),f372(x23503,x23502,x23504,x23505)) % 112.37/112.12 [2351]~E(x23511,x23512)+E(f372(x23513,x23514,x23511,x23515),f372(x23513,x23514,x23512,x23515)) % 112.37/112.12 [2352]~E(x23521,x23522)+E(f372(x23523,x23524,x23525,x23521),f372(x23523,x23524,x23525,x23522)) % 112.37/112.12 [2353]~E(x23531,x23532)+E(f371(x23531,x23533,x23534,x23535),f371(x23532,x23533,x23534,x23535)) % 112.37/112.12 [2354]~E(x23541,x23542)+E(f371(x23543,x23541,x23544,x23545),f371(x23543,x23542,x23544,x23545)) % 112.37/112.12 [2355]~E(x23551,x23552)+E(f371(x23553,x23554,x23551,x23555),f371(x23553,x23554,x23552,x23555)) % 112.37/112.12 [2356]~E(x23561,x23562)+E(f371(x23563,x23564,x23565,x23561),f371(x23563,x23564,x23565,x23562)) % 112.37/112.12 [2357]~E(x23571,x23572)+E(f341(x23571,x23573,x23574),f341(x23572,x23573,x23574)) % 112.37/112.12 [2358]~E(x23581,x23582)+E(f341(x23583,x23581,x23584),f341(x23583,x23582,x23584)) % 112.37/112.12 [2359]~E(x23591,x23592)+E(f341(x23593,x23594,x23591),f341(x23593,x23594,x23592)) % 112.37/112.12 [2360]~E(x23601,x23602)+E(f660(x23601,x23603,x23604,x23605,x23606),f660(x23602,x23603,x23604,x23605,x23606)) % 112.37/112.12 [2361]~E(x23611,x23612)+E(f660(x23613,x23611,x23614,x23615,x23616),f660(x23613,x23612,x23614,x23615,x23616)) % 112.37/112.12 [2362]~E(x23621,x23622)+E(f660(x23623,x23624,x23621,x23625,x23626),f660(x23623,x23624,x23622,x23625,x23626)) % 112.37/112.12 [2363]~E(x23631,x23632)+E(f660(x23633,x23634,x23635,x23631,x23636),f660(x23633,x23634,x23635,x23632,x23636)) % 112.37/112.12 [2364]~E(x23641,x23642)+E(f660(x23643,x23644,x23645,x23646,x23641),f660(x23643,x23644,x23645,x23646,x23642)) % 112.37/112.12 [2365]~E(x23651,x23652)+E(f486(x23651,x23653,x23654,x23655,x23656),f486(x23652,x23653,x23654,x23655,x23656)) % 112.37/112.12 [2366]~E(x23661,x23662)+E(f486(x23663,x23661,x23664,x23665,x23666),f486(x23663,x23662,x23664,x23665,x23666)) % 112.37/112.12 [2367]~E(x23671,x23672)+E(f486(x23673,x23674,x23671,x23675,x23676),f486(x23673,x23674,x23672,x23675,x23676)) % 112.37/112.12 [2368]~E(x23681,x23682)+E(f486(x23683,x23684,x23685,x23681,x23686),f486(x23683,x23684,x23685,x23682,x23686)) % 112.37/112.12 [2369]~E(x23691,x23692)+E(f486(x23693,x23694,x23695,x23696,x23691),f486(x23693,x23694,x23695,x23696,x23692)) % 112.37/112.12 [2370]~E(x23701,x23702)+E(f405(x23701,x23703,x23704),f405(x23702,x23703,x23704)) % 112.37/112.12 [2371]~E(x23711,x23712)+E(f405(x23713,x23711,x23714),f405(x23713,x23712,x23714)) % 112.37/112.12 [2372]~E(x23721,x23722)+E(f405(x23723,x23724,x23721),f405(x23723,x23724,x23722)) % 112.37/112.12 [2373]~E(x23731,x23732)+E(f669(x23731,x23733),f669(x23732,x23733)) % 112.37/112.12 [2374]~E(x23741,x23742)+E(f669(x23743,x23741),f669(x23743,x23742)) % 112.37/112.12 [2375]~E(x23751,x23752)+E(f511(x23751,x23753,x23754,x23755,x23756),f511(x23752,x23753,x23754,x23755,x23756)) % 112.37/112.12 [2376]~E(x23761,x23762)+E(f511(x23763,x23761,x23764,x23765,x23766),f511(x23763,x23762,x23764,x23765,x23766)) % 112.37/112.12 [2377]~E(x23771,x23772)+E(f511(x23773,x23774,x23771,x23775,x23776),f511(x23773,x23774,x23772,x23775,x23776)) % 112.37/112.12 [2378]~E(x23781,x23782)+E(f511(x23783,x23784,x23785,x23781,x23786),f511(x23783,x23784,x23785,x23782,x23786)) % 112.37/112.12 [2379]~E(x23791,x23792)+E(f511(x23793,x23794,x23795,x23796,x23791),f511(x23793,x23794,x23795,x23796,x23792)) % 112.37/112.12 [2380]~E(x23801,x23802)+E(f457(x23801,x23803,x23804,x23805,x23806),f457(x23802,x23803,x23804,x23805,x23806)) % 112.37/112.12 [2381]~E(x23811,x23812)+E(f457(x23813,x23811,x23814,x23815,x23816),f457(x23813,x23812,x23814,x23815,x23816)) % 112.37/112.12 [2382]~E(x23821,x23822)+E(f457(x23823,x23824,x23821,x23825,x23826),f457(x23823,x23824,x23822,x23825,x23826)) % 112.37/112.12 [2383]~E(x23831,x23832)+E(f457(x23833,x23834,x23835,x23831,x23836),f457(x23833,x23834,x23835,x23832,x23836)) % 112.37/112.12 [2384]~E(x23841,x23842)+E(f457(x23843,x23844,x23845,x23846,x23841),f457(x23843,x23844,x23845,x23846,x23842)) % 112.37/112.12 [2385]~E(x23851,x23852)+E(f880(x23851),f880(x23852)) % 112.37/112.12 [2386]~E(x23861,x23862)+E(f570(x23861,x23863),f570(x23862,x23863)) % 112.37/112.12 [2387]~E(x23871,x23872)+E(f570(x23873,x23871),f570(x23873,x23872)) % 112.37/112.12 [2388]~E(x23881,x23882)+E(f573(x23881,x23883,x23884),f573(x23882,x23883,x23884)) % 112.37/112.12 [2389]~E(x23891,x23892)+E(f573(x23893,x23891,x23894),f573(x23893,x23892,x23894)) % 112.37/112.12 [2390]~E(x23901,x23902)+E(f573(x23903,x23904,x23901),f573(x23903,x23904,x23902)) % 112.37/112.12 [2391]~E(x23911,x23912)+E(f595(x23911,x23913,x23914,x23915,x23916,x23917,x23918,x23919),f595(x23912,x23913,x23914,x23915,x23916,x23917,x23918,x23919)) % 112.37/112.12 [2392]~E(x23921,x23922)+E(f595(x23923,x23921,x23924,x23925,x23926,x23927,x23928,x23929),f595(x23923,x23922,x23924,x23925,x23926,x23927,x23928,x23929)) % 112.37/112.12 [2393]~E(x23931,x23932)+E(f595(x23933,x23934,x23931,x23935,x23936,x23937,x23938,x23939),f595(x23933,x23934,x23932,x23935,x23936,x23937,x23938,x23939)) % 112.37/112.12 [2394]~E(x23941,x23942)+E(f595(x23943,x23944,x23945,x23941,x23946,x23947,x23948,x23949),f595(x23943,x23944,x23945,x23942,x23946,x23947,x23948,x23949)) % 112.37/112.12 [2395]~E(x23951,x23952)+E(f595(x23953,x23954,x23955,x23956,x23951,x23957,x23958,x23959),f595(x23953,x23954,x23955,x23956,x23952,x23957,x23958,x23959)) % 112.37/112.12 [2396]~E(x23961,x23962)+E(f595(x23963,x23964,x23965,x23966,x23967,x23961,x23968,x23969),f595(x23963,x23964,x23965,x23966,x23967,x23962,x23968,x23969)) % 112.37/112.12 [2397]~E(x23971,x23972)+E(f595(x23973,x23974,x23975,x23976,x23977,x23978,x23971,x23979),f595(x23973,x23974,x23975,x23976,x23977,x23978,x23972,x23979)) % 112.37/112.12 [2398]~E(x23981,x23982)+E(f595(x23983,x23984,x23985,x23986,x23987,x23988,x23989,x23981),f595(x23983,x23984,x23985,x23986,x23987,x23988,x23989,x23982)) % 112.37/112.12 [2399]~E(x23991,x23992)+E(f261(x23991,x23993,x23994,x23995),f261(x23992,x23993,x23994,x23995)) % 112.37/112.12 [2400]~E(x24001,x24002)+E(f261(x24003,x24001,x24004,x24005),f261(x24003,x24002,x24004,x24005)) % 112.37/112.12 [2401]~E(x24011,x24012)+E(f261(x24013,x24014,x24011,x24015),f261(x24013,x24014,x24012,x24015)) % 112.37/112.12 [2402]~E(x24021,x24022)+E(f261(x24023,x24024,x24025,x24021),f261(x24023,x24024,x24025,x24022)) % 112.37/112.12 [2403]~E(x24031,x24032)+E(f646(x24031,x24033,x24034,x24035),f646(x24032,x24033,x24034,x24035)) % 112.37/112.12 [2404]~E(x24041,x24042)+E(f646(x24043,x24041,x24044,x24045),f646(x24043,x24042,x24044,x24045)) % 112.37/112.12 [2405]~E(x24051,x24052)+E(f646(x24053,x24054,x24051,x24055),f646(x24053,x24054,x24052,x24055)) % 112.37/112.12 [2406]~E(x24061,x24062)+E(f646(x24063,x24064,x24065,x24061),f646(x24063,x24064,x24065,x24062)) % 112.37/112.12 [2407]~E(x24071,x24072)+E(f400(x24071,x24073,x24074),f400(x24072,x24073,x24074)) % 112.37/112.12 [2408]~E(x24081,x24082)+E(f400(x24083,x24081,x24084),f400(x24083,x24082,x24084)) % 112.37/112.12 [2409]~E(x24091,x24092)+E(f400(x24093,x24094,x24091),f400(x24093,x24094,x24092)) % 112.37/112.12 [2410]~E(x24101,x24102)+E(f354(x24101,x24103,x24104),f354(x24102,x24103,x24104)) % 112.37/112.12 [2411]~E(x24111,x24112)+E(f354(x24113,x24111,x24114),f354(x24113,x24112,x24114)) % 112.37/112.12 [2412]~E(x24121,x24122)+E(f354(x24123,x24124,x24121),f354(x24123,x24124,x24122)) % 112.37/112.12 [2413]~E(x24131,x24132)+E(f185(x24131,x24133,x24134,x24135),f185(x24132,x24133,x24134,x24135)) % 112.37/112.12 [2414]~E(x24141,x24142)+E(f185(x24143,x24141,x24144,x24145),f185(x24143,x24142,x24144,x24145)) % 112.37/112.12 [2415]~E(x24151,x24152)+E(f185(x24153,x24154,x24151,x24155),f185(x24153,x24154,x24152,x24155)) % 112.37/112.12 [2416]~E(x24161,x24162)+E(f185(x24163,x24164,x24165,x24161),f185(x24163,x24164,x24165,x24162)) % 112.37/112.12 [2417]~E(x24171,x24172)+E(f335(x24171,x24173,x24174,x24175),f335(x24172,x24173,x24174,x24175)) % 112.37/112.12 [2418]~E(x24181,x24182)+E(f335(x24183,x24181,x24184,x24185),f335(x24183,x24182,x24184,x24185)) % 112.37/112.12 [2419]~E(x24191,x24192)+E(f335(x24193,x24194,x24191,x24195),f335(x24193,x24194,x24192,x24195)) % 112.37/112.12 [2420]~E(x24201,x24202)+E(f335(x24203,x24204,x24205,x24201),f335(x24203,x24204,x24205,x24202)) % 112.37/112.12 [2421]~E(x24211,x24212)+E(f702(x24211,x24213,x24214,x24215,x24216),f702(x24212,x24213,x24214,x24215,x24216)) % 112.37/112.12 [2422]~E(x24221,x24222)+E(f702(x24223,x24221,x24224,x24225,x24226),f702(x24223,x24222,x24224,x24225,x24226)) % 112.37/112.12 [2423]~E(x24231,x24232)+E(f702(x24233,x24234,x24231,x24235,x24236),f702(x24233,x24234,x24232,x24235,x24236)) % 112.37/112.12 [2424]~E(x24241,x24242)+E(f702(x24243,x24244,x24245,x24241,x24246),f702(x24243,x24244,x24245,x24242,x24246)) % 112.37/112.12 [2425]~E(x24251,x24252)+E(f702(x24253,x24254,x24255,x24256,x24251),f702(x24253,x24254,x24255,x24256,x24252)) % 112.37/112.12 [2426]~E(x24261,x24262)+E(f321(x24261,x24263,x24264,x24265),f321(x24262,x24263,x24264,x24265)) % 112.37/112.12 [2427]~E(x24271,x24272)+E(f321(x24273,x24271,x24274,x24275),f321(x24273,x24272,x24274,x24275)) % 112.37/112.12 [2428]~E(x24281,x24282)+E(f321(x24283,x24284,x24281,x24285),f321(x24283,x24284,x24282,x24285)) % 112.37/112.12 [2429]~E(x24291,x24292)+E(f321(x24293,x24294,x24295,x24291),f321(x24293,x24294,x24295,x24292)) % 112.37/112.12 [2430]~E(x24301,x24302)+E(f708(x24301,x24303),f708(x24302,x24303)) % 112.37/112.12 [2431]~E(x24311,x24312)+E(f708(x24313,x24311),f708(x24313,x24312)) % 112.37/112.12 [2432]~E(x24321,x24322)+E(f855(x24321,x24323,x24324),f855(x24322,x24323,x24324)) % 112.37/112.12 [2433]~E(x24331,x24332)+E(f855(x24333,x24331,x24334),f855(x24333,x24332,x24334)) % 112.37/112.12 [2434]~E(x24341,x24342)+E(f855(x24343,x24344,x24341),f855(x24343,x24344,x24342)) % 112.37/112.12 [2435]~E(x24351,x24352)+E(f585(x24351,x24353),f585(x24352,x24353)) % 112.37/112.12 [2436]~E(x24361,x24362)+E(f585(x24363,x24361),f585(x24363,x24362)) % 112.37/112.12 [2437]~E(x24371,x24372)+E(f478(x24371,x24373,x24374,x24375,x24376),f478(x24372,x24373,x24374,x24375,x24376)) % 112.37/112.12 [2438]~E(x24381,x24382)+E(f478(x24383,x24381,x24384,x24385,x24386),f478(x24383,x24382,x24384,x24385,x24386)) % 112.37/112.12 [2439]~E(x24391,x24392)+E(f478(x24393,x24394,x24391,x24395,x24396),f478(x24393,x24394,x24392,x24395,x24396)) % 112.37/112.12 [2440]~E(x24401,x24402)+E(f478(x24403,x24404,x24405,x24401,x24406),f478(x24403,x24404,x24405,x24402,x24406)) % 112.37/112.12 [2441]~E(x24411,x24412)+E(f478(x24413,x24414,x24415,x24416,x24411),f478(x24413,x24414,x24415,x24416,x24412)) % 112.37/112.12 [2442]~E(x24421,x24422)+E(f363(x24421,x24423,x24424,x24425),f363(x24422,x24423,x24424,x24425)) % 112.37/112.12 [2443]~E(x24431,x24432)+E(f363(x24433,x24431,x24434,x24435),f363(x24433,x24432,x24434,x24435)) % 112.37/112.12 [2444]~E(x24441,x24442)+E(f363(x24443,x24444,x24441,x24445),f363(x24443,x24444,x24442,x24445)) % 112.37/112.12 [2445]~E(x24451,x24452)+E(f363(x24453,x24454,x24455,x24451),f363(x24453,x24454,x24455,x24452)) % 112.37/112.12 [2446]~E(x24461,x24462)+E(f510(x24461,x24463,x24464,x24465),f510(x24462,x24463,x24464,x24465)) % 112.37/112.12 [2447]~E(x24471,x24472)+E(f510(x24473,x24471,x24474,x24475),f510(x24473,x24472,x24474,x24475)) % 112.37/112.12 [2448]~E(x24481,x24482)+E(f510(x24483,x24484,x24481,x24485),f510(x24483,x24484,x24482,x24485)) % 112.37/112.12 [2449]~E(x24491,x24492)+E(f510(x24493,x24494,x24495,x24491),f510(x24493,x24494,x24495,x24492)) % 112.37/112.12 [2450]~E(x24501,x24502)+E(f791(x24501),f791(x24502)) % 112.37/112.12 [2451]~E(x24511,x24512)+E(f686(x24511,x24513,x24514),f686(x24512,x24513,x24514)) % 112.37/112.12 [2452]~E(x24521,x24522)+E(f686(x24523,x24521,x24524),f686(x24523,x24522,x24524)) % 112.37/112.12 [2453]~E(x24531,x24532)+E(f686(x24533,x24534,x24531),f686(x24533,x24534,x24532)) % 112.37/112.12 [2454]~E(x24541,x24542)+E(f616(x24541,x24543,x24544,x24545,x24546),f616(x24542,x24543,x24544,x24545,x24546)) % 112.37/112.12 [2455]~E(x24551,x24552)+E(f616(x24553,x24551,x24554,x24555,x24556),f616(x24553,x24552,x24554,x24555,x24556)) % 112.37/112.12 [2456]~E(x24561,x24562)+E(f616(x24563,x24564,x24561,x24565,x24566),f616(x24563,x24564,x24562,x24565,x24566)) % 112.37/112.12 [2457]~E(x24571,x24572)+E(f616(x24573,x24574,x24575,x24571,x24576),f616(x24573,x24574,x24575,x24572,x24576)) % 112.37/112.12 [2458]~E(x24581,x24582)+E(f616(x24583,x24584,x24585,x24586,x24581),f616(x24583,x24584,x24585,x24586,x24582)) % 112.37/112.12 [2459]~E(x24591,x24592)+E(f221(x24591,x24593,x24594,x24595),f221(x24592,x24593,x24594,x24595)) % 112.37/112.12 [2460]~E(x24601,x24602)+E(f221(x24603,x24601,x24604,x24605),f221(x24603,x24602,x24604,x24605)) % 112.37/112.12 [2461]~E(x24611,x24612)+E(f221(x24613,x24614,x24611,x24615),f221(x24613,x24614,x24612,x24615)) % 112.37/112.12 [2462]~E(x24621,x24622)+E(f221(x24623,x24624,x24625,x24621),f221(x24623,x24624,x24625,x24622)) % 112.37/112.12 [2463]~E(x24631,x24632)+E(f636(x24631,x24633,x24634,x24635,x24636),f636(x24632,x24633,x24634,x24635,x24636)) % 112.37/112.12 [2464]~E(x24641,x24642)+E(f636(x24643,x24641,x24644,x24645,x24646),f636(x24643,x24642,x24644,x24645,x24646)) % 112.37/112.12 [2465]~E(x24651,x24652)+E(f636(x24653,x24654,x24651,x24655,x24656),f636(x24653,x24654,x24652,x24655,x24656)) % 112.37/112.12 [2466]~E(x24661,x24662)+E(f636(x24663,x24664,x24665,x24661,x24666),f636(x24663,x24664,x24665,x24662,x24666)) % 112.37/112.12 [2467]~E(x24671,x24672)+E(f636(x24673,x24674,x24675,x24676,x24671),f636(x24673,x24674,x24675,x24676,x24672)) % 112.37/112.12 [2468]~E(x24681,x24682)+E(f378(x24681,x24683,x24684),f378(x24682,x24683,x24684)) % 112.37/112.12 [2469]~E(x24691,x24692)+E(f378(x24693,x24691,x24694),f378(x24693,x24692,x24694)) % 112.37/112.12 [2470]~E(x24701,x24702)+E(f378(x24703,x24704,x24701),f378(x24703,x24704,x24702)) % 112.37/112.12 [2471]~E(x24711,x24712)+E(f533(x24711,x24713,x24714,x24715,x24716,x24717),f533(x24712,x24713,x24714,x24715,x24716,x24717)) % 112.37/112.12 [2472]~E(x24721,x24722)+E(f533(x24723,x24721,x24724,x24725,x24726,x24727),f533(x24723,x24722,x24724,x24725,x24726,x24727)) % 112.37/112.12 [2473]~E(x24731,x24732)+E(f533(x24733,x24734,x24731,x24735,x24736,x24737),f533(x24733,x24734,x24732,x24735,x24736,x24737)) % 112.37/112.12 [2474]~E(x24741,x24742)+E(f533(x24743,x24744,x24745,x24741,x24746,x24747),f533(x24743,x24744,x24745,x24742,x24746,x24747)) % 112.37/112.12 [2475]~E(x24751,x24752)+E(f533(x24753,x24754,x24755,x24756,x24751,x24757),f533(x24753,x24754,x24755,x24756,x24752,x24757)) % 112.37/112.12 [2476]~E(x24761,x24762)+E(f533(x24763,x24764,x24765,x24766,x24767,x24761),f533(x24763,x24764,x24765,x24766,x24767,x24762)) % 112.37/112.12 [2477]~E(x24771,x24772)+E(f851(x24771,x24773,x24774,x24775,x24776),f851(x24772,x24773,x24774,x24775,x24776)) % 112.37/112.12 [2478]~E(x24781,x24782)+E(f851(x24783,x24781,x24784,x24785,x24786),f851(x24783,x24782,x24784,x24785,x24786)) % 112.37/112.12 [2479]~E(x24791,x24792)+E(f851(x24793,x24794,x24791,x24795,x24796),f851(x24793,x24794,x24792,x24795,x24796)) % 112.37/112.12 [2480]~E(x24801,x24802)+E(f851(x24803,x24804,x24805,x24801,x24806),f851(x24803,x24804,x24805,x24802,x24806)) % 112.37/112.12 [2481]~E(x24811,x24812)+E(f851(x24813,x24814,x24815,x24816,x24811),f851(x24813,x24814,x24815,x24816,x24812)) % 112.37/112.12 [2482]~E(x24821,x24822)+E(f728(x24821,x24823,x24824,x24825,x24826),f728(x24822,x24823,x24824,x24825,x24826)) % 112.37/112.12 [2483]~E(x24831,x24832)+E(f728(x24833,x24831,x24834,x24835,x24836),f728(x24833,x24832,x24834,x24835,x24836)) % 112.37/112.12 [2484]~E(x24841,x24842)+E(f728(x24843,x24844,x24841,x24845,x24846),f728(x24843,x24844,x24842,x24845,x24846)) % 112.37/112.12 [2485]~E(x24851,x24852)+E(f728(x24853,x24854,x24855,x24851,x24856),f728(x24853,x24854,x24855,x24852,x24856)) % 112.37/112.12 [2486]~E(x24861,x24862)+E(f728(x24863,x24864,x24865,x24866,x24861),f728(x24863,x24864,x24865,x24866,x24862)) % 112.37/112.12 [2487]~E(x24871,x24872)+E(f858(x24871,x24873,x24874),f858(x24872,x24873,x24874)) % 112.37/112.12 [2488]~E(x24881,x24882)+E(f858(x24883,x24881,x24884),f858(x24883,x24882,x24884)) % 112.37/112.12 [2489]~E(x24891,x24892)+E(f858(x24893,x24894,x24891),f858(x24893,x24894,x24892)) % 112.37/112.12 [2490]~E(x24901,x24902)+E(f865(x24901,x24903,x24904),f865(x24902,x24903,x24904)) % 112.37/112.12 [2491]~E(x24911,x24912)+E(f865(x24913,x24911,x24914),f865(x24913,x24912,x24914)) % 112.37/112.12 [2492]~E(x24921,x24922)+E(f865(x24923,x24924,x24921),f865(x24923,x24924,x24922)) % 112.37/112.12 [2493]~E(x24931,x24932)+E(f619(x24931,x24933,x24934,x24935,x24936),f619(x24932,x24933,x24934,x24935,x24936)) % 112.37/112.12 [2494]~E(x24941,x24942)+E(f619(x24943,x24941,x24944,x24945,x24946),f619(x24943,x24942,x24944,x24945,x24946)) % 112.37/112.12 [2495]~E(x24951,x24952)+E(f619(x24953,x24954,x24951,x24955,x24956),f619(x24953,x24954,x24952,x24955,x24956)) % 112.37/112.12 [2496]~E(x24961,x24962)+E(f619(x24963,x24964,x24965,x24961,x24966),f619(x24963,x24964,x24965,x24962,x24966)) % 112.37/112.12 [2497]~E(x24971,x24972)+E(f619(x24973,x24974,x24975,x24976,x24971),f619(x24973,x24974,x24975,x24976,x24972)) % 112.37/112.12 [2498]~E(x24981,x24982)+E(f773(x24981,x24983),f773(x24982,x24983)) % 112.37/112.12 [2499]~E(x24991,x24992)+E(f773(x24993,x24991),f773(x24993,x24992)) % 112.37/112.12 [2500]~E(x25001,x25002)+E(f531(x25001,x25003,x25004,x25005,x25006,x25007),f531(x25002,x25003,x25004,x25005,x25006,x25007)) % 112.37/112.12 [2501]~E(x25011,x25012)+E(f531(x25013,x25011,x25014,x25015,x25016,x25017),f531(x25013,x25012,x25014,x25015,x25016,x25017)) % 112.37/112.12 [2502]~E(x25021,x25022)+E(f531(x25023,x25024,x25021,x25025,x25026,x25027),f531(x25023,x25024,x25022,x25025,x25026,x25027)) % 112.37/112.12 [2503]~E(x25031,x25032)+E(f531(x25033,x25034,x25035,x25031,x25036,x25037),f531(x25033,x25034,x25035,x25032,x25036,x25037)) % 112.37/112.12 [2504]~E(x25041,x25042)+E(f531(x25043,x25044,x25045,x25046,x25041,x25047),f531(x25043,x25044,x25045,x25046,x25042,x25047)) % 112.37/112.12 [2505]~E(x25051,x25052)+E(f531(x25053,x25054,x25055,x25056,x25057,x25051),f531(x25053,x25054,x25055,x25056,x25057,x25052)) % 112.37/112.12 [2506]~E(x25061,x25062)+E(f498(x25061,x25063,x25064,x25065),f498(x25062,x25063,x25064,x25065)) % 112.37/112.12 [2507]~E(x25071,x25072)+E(f498(x25073,x25071,x25074,x25075),f498(x25073,x25072,x25074,x25075)) % 112.37/112.12 [2508]~E(x25081,x25082)+E(f498(x25083,x25084,x25081,x25085),f498(x25083,x25084,x25082,x25085)) % 112.37/112.12 [2509]~E(x25091,x25092)+E(f498(x25093,x25094,x25095,x25091),f498(x25093,x25094,x25095,x25092)) % 112.37/112.12 [2510]~E(x25101,x25102)+E(f820(x25101,x25103,x25104),f820(x25102,x25103,x25104)) % 112.37/112.12 [2511]~E(x25111,x25112)+E(f820(x25113,x25111,x25114),f820(x25113,x25112,x25114)) % 112.37/112.12 [2512]~E(x25121,x25122)+E(f820(x25123,x25124,x25121),f820(x25123,x25124,x25122)) % 112.37/112.12 [2513]~E(x25131,x25132)+E(f823(x25131,x25133,x25134,x25135,x25136,x25137,x25138),f823(x25132,x25133,x25134,x25135,x25136,x25137,x25138)) % 112.37/112.12 [2514]~E(x25141,x25142)+E(f823(x25143,x25141,x25144,x25145,x25146,x25147,x25148),f823(x25143,x25142,x25144,x25145,x25146,x25147,x25148)) % 112.37/112.12 [2515]~E(x25151,x25152)+E(f823(x25153,x25154,x25151,x25155,x25156,x25157,x25158),f823(x25153,x25154,x25152,x25155,x25156,x25157,x25158)) % 112.37/112.12 [2516]~E(x25161,x25162)+E(f823(x25163,x25164,x25165,x25161,x25166,x25167,x25168),f823(x25163,x25164,x25165,x25162,x25166,x25167,x25168)) % 112.37/112.12 [2517]~E(x25171,x25172)+E(f823(x25173,x25174,x25175,x25176,x25171,x25177,x25178),f823(x25173,x25174,x25175,x25176,x25172,x25177,x25178)) % 112.37/112.12 [2518]~E(x25181,x25182)+E(f823(x25183,x25184,x25185,x25186,x25187,x25181,x25188),f823(x25183,x25184,x25185,x25186,x25187,x25182,x25188)) % 112.37/112.12 [2519]~E(x25191,x25192)+E(f823(x25193,x25194,x25195,x25196,x25197,x25198,x25191),f823(x25193,x25194,x25195,x25196,x25197,x25198,x25192)) % 112.37/112.12 [2520]~E(x25201,x25202)+E(f725(x25201,x25203,x25204,x25205,x25206),f725(x25202,x25203,x25204,x25205,x25206)) % 112.37/112.12 [2521]~E(x25211,x25212)+E(f725(x25213,x25211,x25214,x25215,x25216),f725(x25213,x25212,x25214,x25215,x25216)) % 112.37/112.12 [2522]~E(x25221,x25222)+E(f725(x25223,x25224,x25221,x25225,x25226),f725(x25223,x25224,x25222,x25225,x25226)) % 112.37/112.12 [2523]~E(x25231,x25232)+E(f725(x25233,x25234,x25235,x25231,x25236),f725(x25233,x25234,x25235,x25232,x25236)) % 112.37/112.12 [2524]~E(x25241,x25242)+E(f725(x25243,x25244,x25245,x25246,x25241),f725(x25243,x25244,x25245,x25246,x25242)) % 112.37/112.12 [2525]~E(x25251,x25252)+E(f426(x25251,x25253,x25254),f426(x25252,x25253,x25254)) % 112.37/112.12 [2526]~E(x25261,x25262)+E(f426(x25263,x25261,x25264),f426(x25263,x25262,x25264)) % 112.37/112.12 [2527]~E(x25271,x25272)+E(f426(x25273,x25274,x25271),f426(x25273,x25274,x25272)) % 112.37/112.12 [2528]~E(x25281,x25282)+E(f621(x25281,x25283,x25284),f621(x25282,x25283,x25284)) % 112.37/112.12 [2529]~E(x25291,x25292)+E(f621(x25293,x25291,x25294),f621(x25293,x25292,x25294)) % 112.37/112.12 [2530]~E(x25301,x25302)+E(f621(x25303,x25304,x25301),f621(x25303,x25304,x25302)) % 112.37/112.12 [2531]~E(x25311,x25312)+E(f775(x25311,x25313,x25314,x25315),f775(x25312,x25313,x25314,x25315)) % 112.37/112.12 [2532]~E(x25321,x25322)+E(f775(x25323,x25321,x25324,x25325),f775(x25323,x25322,x25324,x25325)) % 112.37/112.12 [2533]~E(x25331,x25332)+E(f775(x25333,x25334,x25331,x25335),f775(x25333,x25334,x25332,x25335)) % 112.37/112.12 [2534]~E(x25341,x25342)+E(f775(x25343,x25344,x25345,x25341),f775(x25343,x25344,x25345,x25342)) % 112.37/112.12 [2535]~E(x25351,x25352)+E(f431(x25351,x25353,x25354),f431(x25352,x25353,x25354)) % 112.37/112.12 [2536]~E(x25361,x25362)+E(f431(x25363,x25361,x25364),f431(x25363,x25362,x25364)) % 112.37/112.12 [2537]~E(x25371,x25372)+E(f431(x25373,x25374,x25371),f431(x25373,x25374,x25372)) % 112.37/112.12 [2538]~E(x25381,x25382)+E(f852(x25381,x25383),f852(x25382,x25383)) % 112.37/112.12 [2539]~E(x25391,x25392)+E(f852(x25393,x25391),f852(x25393,x25392)) % 112.37/112.12 [2540]~E(x25401,x25402)+E(f745(x25401,x25403,x25404),f745(x25402,x25403,x25404)) % 112.37/112.12 [2541]~E(x25411,x25412)+E(f745(x25413,x25411,x25414),f745(x25413,x25412,x25414)) % 112.37/112.12 [2542]~E(x25421,x25422)+E(f745(x25423,x25424,x25421),f745(x25423,x25424,x25422)) % 112.37/112.12 [2543]~E(x25431,x25432)+E(f782(x25431),f782(x25432)) % 112.37/112.12 [2544]~E(x25441,x25442)+E(f582(x25441),f582(x25442)) % 112.37/112.12 [2545]~E(x25451,x25452)+E(f333(x25451,x25453,x25454,x25455),f333(x25452,x25453,x25454,x25455)) % 112.37/112.12 [2546]~E(x25461,x25462)+E(f333(x25463,x25461,x25464,x25465),f333(x25463,x25462,x25464,x25465)) % 112.37/112.12 [2547]~E(x25471,x25472)+E(f333(x25473,x25474,x25471,x25475),f333(x25473,x25474,x25472,x25475)) % 112.37/112.12 [2548]~E(x25481,x25482)+E(f333(x25483,x25484,x25485,x25481),f333(x25483,x25484,x25485,x25482)) % 112.37/112.12 [2549]~E(x25491,x25492)+E(f551(x25491,x25493,x25494),f551(x25492,x25493,x25494)) % 112.37/112.12 [2550]~E(x25501,x25502)+E(f551(x25503,x25501,x25504),f551(x25503,x25502,x25504)) % 112.37/112.12 [2551]~E(x25511,x25512)+E(f551(x25513,x25514,x25511),f551(x25513,x25514,x25512)) % 112.37/112.12 [2552]~E(x25521,x25522)+E(f803(x25521,x25523,x25524),f803(x25522,x25523,x25524)) % 112.37/112.12 [2553]~E(x25531,x25532)+E(f803(x25533,x25531,x25534),f803(x25533,x25532,x25534)) % 112.37/112.12 [2554]~E(x25541,x25542)+E(f803(x25543,x25544,x25541),f803(x25543,x25544,x25542)) % 112.37/112.12 [2555]~E(x25551,x25552)+E(f793(x25551,x25553),f793(x25552,x25553)) % 112.37/112.12 [2556]~E(x25561,x25562)+E(f793(x25563,x25561),f793(x25563,x25562)) % 112.37/112.12 [2557]~E(x25571,x25572)+E(f854(x25571,x25573,x25574),f854(x25572,x25573,x25574)) % 112.37/112.12 [2558]~E(x25581,x25582)+E(f854(x25583,x25581,x25584),f854(x25583,x25582,x25584)) % 112.37/112.12 [2559]~E(x25591,x25592)+E(f854(x25593,x25594,x25591),f854(x25593,x25594,x25592)) % 112.37/112.12 [2560]~E(x25601,x25602)+E(f716(x25601,x25603),f716(x25602,x25603)) % 112.37/112.12 [2561]~E(x25611,x25612)+E(f716(x25613,x25611),f716(x25613,x25612)) % 112.37/112.12 [2562]~E(x25621,x25622)+E(f37(x25621),f37(x25622)) % 112.37/112.12 [2563]~E(x25631,x25632)+E(f840(x25631,x25633,x25634),f840(x25632,x25633,x25634)) % 112.37/112.12 [2564]~E(x25641,x25642)+E(f840(x25643,x25641,x25644),f840(x25643,x25642,x25644)) % 112.37/112.12 [2565]~E(x25651,x25652)+E(f840(x25653,x25654,x25651),f840(x25653,x25654,x25652)) % 112.37/112.12 [2566]~E(x25661,x25662)+E(f398(x25661,x25663,x25664),f398(x25662,x25663,x25664)) % 112.37/112.12 [2567]~E(x25671,x25672)+E(f398(x25673,x25671,x25674),f398(x25673,x25672,x25674)) % 112.37/112.12 [2568]~E(x25681,x25682)+E(f398(x25683,x25684,x25681),f398(x25683,x25684,x25682)) % 112.37/112.12 [2569]~E(x25691,x25692)+E(f749(x25691,x25693,x25694),f749(x25692,x25693,x25694)) % 112.37/112.12 [2570]~E(x25701,x25702)+E(f749(x25703,x25701,x25704),f749(x25703,x25702,x25704)) % 112.37/112.12 [2571]~E(x25711,x25712)+E(f749(x25713,x25714,x25711),f749(x25713,x25714,x25712)) % 112.37/112.12 [2572]~E(x25721,x25722)+E(f891(x25721),f891(x25722)) % 112.37/112.12 [2573]~E(x25731,x25732)+E(f637(x25731,x25733,x25734,x25735,x25736),f637(x25732,x25733,x25734,x25735,x25736)) % 112.37/112.12 [2574]~E(x25741,x25742)+E(f637(x25743,x25741,x25744,x25745,x25746),f637(x25743,x25742,x25744,x25745,x25746)) % 112.37/112.12 [2575]~E(x25751,x25752)+E(f637(x25753,x25754,x25751,x25755,x25756),f637(x25753,x25754,x25752,x25755,x25756)) % 112.37/112.12 [2576]~E(x25761,x25762)+E(f637(x25763,x25764,x25765,x25761,x25766),f637(x25763,x25764,x25765,x25762,x25766)) % 112.37/112.12 [2577]~E(x25771,x25772)+E(f637(x25773,x25774,x25775,x25776,x25771),f637(x25773,x25774,x25775,x25776,x25772)) % 112.37/112.12 [2578]~E(x25781,x25782)+E(f540(x25781,x25783,x25784,x25785),f540(x25782,x25783,x25784,x25785)) % 112.37/112.12 [2579]~E(x25791,x25792)+E(f540(x25793,x25791,x25794,x25795),f540(x25793,x25792,x25794,x25795)) % 112.37/112.12 [2580]~E(x25801,x25802)+E(f540(x25803,x25804,x25801,x25805),f540(x25803,x25804,x25802,x25805)) % 112.37/112.12 [2581]~E(x25811,x25812)+E(f540(x25813,x25814,x25815,x25811),f540(x25813,x25814,x25815,x25812)) % 112.37/112.12 [2582]~E(x25821,x25822)+E(f524(x25821),f524(x25822)) % 112.37/112.12 [2583]~E(x25831,x25832)+E(f187(x25831,x25833,x25834,x25835),f187(x25832,x25833,x25834,x25835)) % 112.37/112.12 [2584]~E(x25841,x25842)+E(f187(x25843,x25841,x25844,x25845),f187(x25843,x25842,x25844,x25845)) % 112.37/112.12 [2585]~E(x25851,x25852)+E(f187(x25853,x25854,x25851,x25855),f187(x25853,x25854,x25852,x25855)) % 112.37/112.12 [2586]~E(x25861,x25862)+E(f187(x25863,x25864,x25865,x25861),f187(x25863,x25864,x25865,x25862)) % 112.37/112.12 [2587]~E(x25871,x25872)+E(f674(x25871,x25873,x25874),f674(x25872,x25873,x25874)) % 112.37/112.12 [2588]~E(x25881,x25882)+E(f674(x25883,x25881,x25884),f674(x25883,x25882,x25884)) % 112.37/112.12 [2589]~E(x25891,x25892)+E(f674(x25893,x25894,x25891),f674(x25893,x25894,x25892)) % 112.37/112.12 [2590]~E(x25901,x25902)+E(f601(x25901,x25903,x25904,x25905,x25906),f601(x25902,x25903,x25904,x25905,x25906)) % 112.37/112.12 [2591]~E(x25911,x25912)+E(f601(x25913,x25911,x25914,x25915,x25916),f601(x25913,x25912,x25914,x25915,x25916)) % 112.37/112.12 [2592]~E(x25921,x25922)+E(f601(x25923,x25924,x25921,x25925,x25926),f601(x25923,x25924,x25922,x25925,x25926)) % 112.37/112.12 [2593]~E(x25931,x25932)+E(f601(x25933,x25934,x25935,x25931,x25936),f601(x25933,x25934,x25935,x25932,x25936)) % 112.37/112.12 [2594]~E(x25941,x25942)+E(f601(x25943,x25944,x25945,x25946,x25941),f601(x25943,x25944,x25945,x25946,x25942)) % 112.37/112.12 [2595]~E(x25951,x25952)+E(f251(x25951,x25953,x25954,x25955,x25956),f251(x25952,x25953,x25954,x25955,x25956)) % 112.37/112.12 [2596]~E(x25961,x25962)+E(f251(x25963,x25961,x25964,x25965,x25966),f251(x25963,x25962,x25964,x25965,x25966)) % 112.37/112.12 [2597]~E(x25971,x25972)+E(f251(x25973,x25974,x25971,x25975,x25976),f251(x25973,x25974,x25972,x25975,x25976)) % 112.37/112.12 [2598]~E(x25981,x25982)+E(f251(x25983,x25984,x25985,x25981,x25986),f251(x25983,x25984,x25985,x25982,x25986)) % 112.37/112.12 [2599]~E(x25991,x25992)+E(f251(x25993,x25994,x25995,x25996,x25991),f251(x25993,x25994,x25995,x25996,x25992)) % 112.37/112.12 [2600]~E(x26001,x26002)+E(f827(x26001,x26003,x26004,x26005,x26006,x26007,x26008,x26009),f827(x26002,x26003,x26004,x26005,x26006,x26007,x26008,x26009)) % 112.37/112.12 [2601]~E(x26011,x26012)+E(f827(x26013,x26011,x26014,x26015,x26016,x26017,x26018,x26019),f827(x26013,x26012,x26014,x26015,x26016,x26017,x26018,x26019)) % 112.37/112.12 [2602]~E(x26021,x26022)+E(f827(x26023,x26024,x26021,x26025,x26026,x26027,x26028,x26029),f827(x26023,x26024,x26022,x26025,x26026,x26027,x26028,x26029)) % 112.37/112.12 [2603]~E(x26031,x26032)+E(f827(x26033,x26034,x26035,x26031,x26036,x26037,x26038,x26039),f827(x26033,x26034,x26035,x26032,x26036,x26037,x26038,x26039)) % 112.37/112.12 [2604]~E(x26041,x26042)+E(f827(x26043,x26044,x26045,x26046,x26041,x26047,x26048,x26049),f827(x26043,x26044,x26045,x26046,x26042,x26047,x26048,x26049)) % 112.37/112.12 [2605]~E(x26051,x26052)+E(f827(x26053,x26054,x26055,x26056,x26057,x26051,x26058,x26059),f827(x26053,x26054,x26055,x26056,x26057,x26052,x26058,x26059)) % 112.37/112.12 [2606]~E(x26061,x26062)+E(f827(x26063,x26064,x26065,x26066,x26067,x26068,x26061,x26069),f827(x26063,x26064,x26065,x26066,x26067,x26068,x26062,x26069)) % 112.37/112.12 [2607]~E(x26071,x26072)+E(f827(x26073,x26074,x26075,x26076,x26077,x26078,x26079,x26071),f827(x26073,x26074,x26075,x26076,x26077,x26078,x26079,x26072)) % 112.37/112.12 [2608]~E(x26081,x26082)+E(f643(x26081,x26083,x26084),f643(x26082,x26083,x26084)) % 112.37/112.12 [2609]~E(x26091,x26092)+E(f643(x26093,x26091,x26094),f643(x26093,x26092,x26094)) % 112.37/112.12 [2610]~E(x26101,x26102)+E(f643(x26103,x26104,x26101),f643(x26103,x26104,x26102)) % 112.37/112.12 [2611]~E(x26111,x26112)+E(f322(x26111),f322(x26112)) % 112.37/112.12 [2612]~E(x26121,x26122)+E(f685(x26121,x26123,x26124),f685(x26122,x26123,x26124)) % 112.37/112.12 [2613]~E(x26131,x26132)+E(f685(x26133,x26131,x26134),f685(x26133,x26132,x26134)) % 112.37/112.12 [2614]~E(x26141,x26142)+E(f685(x26143,x26144,x26141),f685(x26143,x26144,x26142)) % 112.37/112.12 [2615]~E(x26151,x26152)+E(f525(x26151,x26153),f525(x26152,x26153)) % 112.37/112.12 [2616]~E(x26161,x26162)+E(f525(x26163,x26161),f525(x26163,x26162)) % 112.37/112.12 [2617]~E(x26171,x26172)+E(f464(x26171,x26173,x26174,x26175),f464(x26172,x26173,x26174,x26175)) % 112.37/112.12 [2618]~E(x26181,x26182)+E(f464(x26183,x26181,x26184,x26185),f464(x26183,x26182,x26184,x26185)) % 112.37/112.12 [2619]~E(x26191,x26192)+E(f464(x26193,x26194,x26191,x26195),f464(x26193,x26194,x26192,x26195)) % 112.37/112.12 [2620]~E(x26201,x26202)+E(f464(x26203,x26204,x26205,x26201),f464(x26203,x26204,x26205,x26202)) % 112.37/112.12 [2621]~E(x26211,x26212)+E(f818(x26211,x26213,x26214,x26215,x26216),f818(x26212,x26213,x26214,x26215,x26216)) % 112.37/112.12 [2622]~E(x26221,x26222)+E(f818(x26223,x26221,x26224,x26225,x26226),f818(x26223,x26222,x26224,x26225,x26226)) % 112.37/112.12 [2623]~E(x26231,x26232)+E(f818(x26233,x26234,x26231,x26235,x26236),f818(x26233,x26234,x26232,x26235,x26236)) % 112.37/112.12 [2624]~E(x26241,x26242)+E(f818(x26243,x26244,x26245,x26241,x26246),f818(x26243,x26244,x26245,x26242,x26246)) % 112.37/112.12 [2625]~E(x26251,x26252)+E(f818(x26253,x26254,x26255,x26256,x26251),f818(x26253,x26254,x26255,x26256,x26252)) % 112.37/112.12 [2626]~E(x26261,x26262)+E(f678(x26261,x26263),f678(x26262,x26263)) % 112.37/112.12 [2627]~E(x26271,x26272)+E(f678(x26273,x26271),f678(x26273,x26272)) % 112.37/112.12 [2628]~E(x26281,x26282)+E(f350(x26281,x26283),f350(x26282,x26283)) % 112.37/112.12 [2629]~E(x26291,x26292)+E(f350(x26293,x26291),f350(x26293,x26292)) % 112.37/112.12 [2630]~E(x26301,x26302)+E(f835(x26301,x26303,x26304,x26305,x26306,x26307),f835(x26302,x26303,x26304,x26305,x26306,x26307)) % 112.37/112.12 [2631]~E(x26311,x26312)+E(f835(x26313,x26311,x26314,x26315,x26316,x26317),f835(x26313,x26312,x26314,x26315,x26316,x26317)) % 112.37/112.12 [2632]~E(x26321,x26322)+E(f835(x26323,x26324,x26321,x26325,x26326,x26327),f835(x26323,x26324,x26322,x26325,x26326,x26327)) % 112.37/112.12 [2633]~E(x26331,x26332)+E(f835(x26333,x26334,x26335,x26331,x26336,x26337),f835(x26333,x26334,x26335,x26332,x26336,x26337)) % 112.37/112.12 [2634]~E(x26341,x26342)+E(f835(x26343,x26344,x26345,x26346,x26341,x26347),f835(x26343,x26344,x26345,x26346,x26342,x26347)) % 112.37/112.12 [2635]~E(x26351,x26352)+E(f835(x26353,x26354,x26355,x26356,x26357,x26351),f835(x26353,x26354,x26355,x26356,x26357,x26352)) % 112.37/112.12 [2636]~E(x26361,x26362)+E(f598(x26361,x26363),f598(x26362,x26363)) % 112.37/112.12 [2637]~E(x26371,x26372)+E(f598(x26373,x26371),f598(x26373,x26372)) % 112.37/112.12 [2638]~E(x26381,x26382)+E(f414(x26381,x26383,x26384,x26385,x26386),f414(x26382,x26383,x26384,x26385,x26386)) % 112.37/112.12 [2639]~E(x26391,x26392)+E(f414(x26393,x26391,x26394,x26395,x26396),f414(x26393,x26392,x26394,x26395,x26396)) % 112.37/112.12 [2640]~E(x26401,x26402)+E(f414(x26403,x26404,x26401,x26405,x26406),f414(x26403,x26404,x26402,x26405,x26406)) % 112.37/112.12 [2641]~E(x26411,x26412)+E(f414(x26413,x26414,x26415,x26411,x26416),f414(x26413,x26414,x26415,x26412,x26416)) % 112.37/112.12 [2642]~E(x26421,x26422)+E(f414(x26423,x26424,x26425,x26426,x26421),f414(x26423,x26424,x26425,x26426,x26422)) % 112.37/112.12 [2643]~E(x26431,x26432)+E(f467(x26431,x26433,x26434,x26435,x26436),f467(x26432,x26433,x26434,x26435,x26436)) % 112.37/112.12 [2644]~E(x26441,x26442)+E(f467(x26443,x26441,x26444,x26445,x26446),f467(x26443,x26442,x26444,x26445,x26446)) % 112.37/112.12 [2645]~E(x26451,x26452)+E(f467(x26453,x26454,x26451,x26455,x26456),f467(x26453,x26454,x26452,x26455,x26456)) % 112.37/112.12 [2646]~E(x26461,x26462)+E(f467(x26463,x26464,x26465,x26461,x26466),f467(x26463,x26464,x26465,x26462,x26466)) % 112.37/112.12 [2647]~E(x26471,x26472)+E(f467(x26473,x26474,x26475,x26476,x26471),f467(x26473,x26474,x26475,x26476,x26472)) % 112.37/112.12 [2648]~E(x26481,x26482)+E(f535(x26481,x26483,x26484,x26485,x26486),f535(x26482,x26483,x26484,x26485,x26486)) % 112.37/112.12 [2649]~E(x26491,x26492)+E(f535(x26493,x26491,x26494,x26495,x26496),f535(x26493,x26492,x26494,x26495,x26496)) % 112.37/112.12 [2650]~E(x26501,x26502)+E(f535(x26503,x26504,x26501,x26505,x26506),f535(x26503,x26504,x26502,x26505,x26506)) % 112.37/112.12 [2651]~E(x26511,x26512)+E(f535(x26513,x26514,x26515,x26511,x26516),f535(x26513,x26514,x26515,x26512,x26516)) % 112.37/112.12 [2652]~E(x26521,x26522)+E(f535(x26523,x26524,x26525,x26526,x26521),f535(x26523,x26524,x26525,x26526,x26522)) % 112.37/112.12 [2653]~E(x26531,x26532)+E(f741(x26531,x26533,x26534),f741(x26532,x26533,x26534)) % 112.37/112.12 [2654]~E(x26541,x26542)+E(f741(x26543,x26541,x26544),f741(x26543,x26542,x26544)) % 112.37/112.12 [2655]~E(x26551,x26552)+E(f741(x26553,x26554,x26551),f741(x26553,x26554,x26552)) % 112.37/112.12 [2656]~E(x26561,x26562)+E(f216(x26561,x26563,x26564,x26565,x26566),f216(x26562,x26563,x26564,x26565,x26566)) % 112.37/112.12 [2657]~E(x26571,x26572)+E(f216(x26573,x26571,x26574,x26575,x26576),f216(x26573,x26572,x26574,x26575,x26576)) % 112.37/112.12 [2658]~E(x26581,x26582)+E(f216(x26583,x26584,x26581,x26585,x26586),f216(x26583,x26584,x26582,x26585,x26586)) % 112.37/112.12 [2659]~E(x26591,x26592)+E(f216(x26593,x26594,x26595,x26591,x26596),f216(x26593,x26594,x26595,x26592,x26596)) % 112.37/112.12 [2660]~E(x26601,x26602)+E(f216(x26603,x26604,x26605,x26606,x26601),f216(x26603,x26604,x26605,x26606,x26602)) % 112.37/112.12 [2661]~E(x26611,x26612)+E(f699(x26611,x26613,x26614),f699(x26612,x26613,x26614)) % 112.37/112.12 [2662]~E(x26621,x26622)+E(f699(x26623,x26621,x26624),f699(x26623,x26622,x26624)) % 112.37/112.12 [2663]~E(x26631,x26632)+E(f699(x26633,x26634,x26631),f699(x26633,x26634,x26632)) % 112.37/112.12 [2664]~E(x26641,x26642)+E(f520(x26641,x26643,x26644,x26645),f520(x26642,x26643,x26644,x26645)) % 112.37/112.12 [2665]~E(x26651,x26652)+E(f520(x26653,x26651,x26654,x26655),f520(x26653,x26652,x26654,x26655)) % 112.37/112.12 [2666]~E(x26661,x26662)+E(f520(x26663,x26664,x26661,x26665),f520(x26663,x26664,x26662,x26665)) % 112.37/112.12 [2667]~E(x26671,x26672)+E(f520(x26673,x26674,x26675,x26671),f520(x26673,x26674,x26675,x26672)) % 112.37/112.12 [2668]~E(x26681,x26682)+E(f418(x26681,x26683,x26684),f418(x26682,x26683,x26684)) % 112.37/112.12 [2669]~E(x26691,x26692)+E(f418(x26693,x26691,x26694),f418(x26693,x26692,x26694)) % 112.37/112.12 [2670]~E(x26701,x26702)+E(f418(x26703,x26704,x26701),f418(x26703,x26704,x26702)) % 112.37/112.12 [2671]~E(x26711,x26712)+E(f429(x26711,x26713,x26714,x26715,x26716),f429(x26712,x26713,x26714,x26715,x26716)) % 112.37/112.12 [2672]~E(x26721,x26722)+E(f429(x26723,x26721,x26724,x26725,x26726),f429(x26723,x26722,x26724,x26725,x26726)) % 112.37/112.12 [2673]~E(x26731,x26732)+E(f429(x26733,x26734,x26731,x26735,x26736),f429(x26733,x26734,x26732,x26735,x26736)) % 112.37/112.12 [2674]~E(x26741,x26742)+E(f429(x26743,x26744,x26745,x26741,x26746),f429(x26743,x26744,x26745,x26742,x26746)) % 112.37/112.12 [2675]~E(x26751,x26752)+E(f429(x26753,x26754,x26755,x26756,x26751),f429(x26753,x26754,x26755,x26756,x26752)) % 112.37/112.12 [2676]~E(x26761,x26762)+E(f23(x26761,x26763),f23(x26762,x26763)) % 112.37/112.12 [2677]~E(x26771,x26772)+E(f23(x26773,x26771),f23(x26773,x26772)) % 112.37/112.12 [2678]~E(x26781,x26782)+E(f781(x26781,x26783,x26784,x26785,x26786),f781(x26782,x26783,x26784,x26785,x26786)) % 112.37/112.12 [2679]~E(x26791,x26792)+E(f781(x26793,x26791,x26794,x26795,x26796),f781(x26793,x26792,x26794,x26795,x26796)) % 112.37/112.12 [2680]~E(x26801,x26802)+E(f781(x26803,x26804,x26801,x26805,x26806),f781(x26803,x26804,x26802,x26805,x26806)) % 112.37/112.12 [2681]~E(x26811,x26812)+E(f781(x26813,x26814,x26815,x26811,x26816),f781(x26813,x26814,x26815,x26812,x26816)) % 112.37/112.12 [2682]~E(x26821,x26822)+E(f781(x26823,x26824,x26825,x26826,x26821),f781(x26823,x26824,x26825,x26826,x26822)) % 112.37/112.12 [2683]~E(x26831,x26832)+E(f763(x26831),f763(x26832)) % 112.37/112.12 [2684]~E(x26841,x26842)+E(f519(x26841,x26843),f519(x26842,x26843)) % 112.37/112.12 [2685]~E(x26851,x26852)+E(f519(x26853,x26851),f519(x26853,x26852)) % 112.37/112.12 [2686]~E(x26861,x26862)+E(f328(x26861,x26863,x26864),f328(x26862,x26863,x26864)) % 112.37/112.12 [2687]~E(x26871,x26872)+E(f328(x26873,x26871,x26874),f328(x26873,x26872,x26874)) % 112.37/112.12 [2688]~E(x26881,x26882)+E(f328(x26883,x26884,x26881),f328(x26883,x26884,x26882)) % 112.37/112.12 [2689]~E(x26891,x26892)+E(f461(x26891,x26893,x26894),f461(x26892,x26893,x26894)) % 112.37/112.12 [2690]~E(x26901,x26902)+E(f461(x26903,x26901,x26904),f461(x26903,x26902,x26904)) % 112.37/112.12 [2691]~E(x26911,x26912)+E(f461(x26913,x26914,x26911),f461(x26913,x26914,x26912)) % 112.37/112.12 [2692]~E(x26921,x26922)+E(f805(x26921,x26923),f805(x26922,x26923)) % 112.37/112.12 [2693]~E(x26931,x26932)+E(f805(x26933,x26931),f805(x26933,x26932)) % 112.37/112.12 [2694]~E(x26941,x26942)+E(f737(x26941,x26943,x26944),f737(x26942,x26943,x26944)) % 112.37/112.12 [2695]~E(x26951,x26952)+E(f737(x26953,x26951,x26954),f737(x26953,x26952,x26954)) % 112.37/112.12 [2696]~E(x26961,x26962)+E(f737(x26963,x26964,x26961),f737(x26963,x26964,x26962)) % 112.37/112.12 [2697]~E(x26971,x26972)+E(f475(x26971,x26973,x26974,x26975,x26976),f475(x26972,x26973,x26974,x26975,x26976)) % 112.37/112.12 [2698]~E(x26981,x26982)+E(f475(x26983,x26981,x26984,x26985,x26986),f475(x26983,x26982,x26984,x26985,x26986)) % 112.37/112.12 [2699]~E(x26991,x26992)+E(f475(x26993,x26994,x26991,x26995,x26996),f475(x26993,x26994,x26992,x26995,x26996)) % 112.37/112.12 [2700]~E(x27001,x27002)+E(f475(x27003,x27004,x27005,x27001,x27006),f475(x27003,x27004,x27005,x27002,x27006)) % 112.37/112.12 [2701]~E(x27011,x27012)+E(f475(x27013,x27014,x27015,x27016,x27011),f475(x27013,x27014,x27015,x27016,x27012)) % 112.37/112.12 [2702]~E(x27021,x27022)+E(f212(x27021,x27023,x27024),f212(x27022,x27023,x27024)) % 112.37/112.12 [2703]~E(x27031,x27032)+E(f212(x27033,x27031,x27034),f212(x27033,x27032,x27034)) % 112.37/112.12 [2704]~E(x27041,x27042)+E(f212(x27043,x27044,x27041),f212(x27043,x27044,x27042)) % 112.37/112.12 [2705]~E(x27051,x27052)+E(f554(x27051,x27053),f554(x27052,x27053)) % 112.37/112.12 [2706]~E(x27061,x27062)+E(f554(x27063,x27061),f554(x27063,x27062)) % 112.37/112.12 [2707]~E(x27071,x27072)+E(f374(x27071,x27073),f374(x27072,x27073)) % 112.37/112.12 [2708]~E(x27081,x27082)+E(f374(x27083,x27081),f374(x27083,x27082)) % 112.37/112.12 [2709]~E(x27091,x27092)+E(f112(x27091,x27093,x27094,x27095),f112(x27092,x27093,x27094,x27095)) % 112.37/112.12 [2710]~E(x27101,x27102)+E(f112(x27103,x27101,x27104,x27105),f112(x27103,x27102,x27104,x27105)) % 112.37/112.12 [2711]~E(x27111,x27112)+E(f112(x27113,x27114,x27111,x27115),f112(x27113,x27114,x27112,x27115)) % 112.37/112.12 [2712]~E(x27121,x27122)+E(f112(x27123,x27124,x27125,x27121),f112(x27123,x27124,x27125,x27122)) % 112.37/112.12 [2713]~E(x27131,x27132)+E(f440(x27131,x27133,x27134,x27135),f440(x27132,x27133,x27134,x27135)) % 112.37/112.12 [2714]~E(x27141,x27142)+E(f440(x27143,x27141,x27144,x27145),f440(x27143,x27142,x27144,x27145)) % 112.37/112.12 [2715]~E(x27151,x27152)+E(f440(x27153,x27154,x27151,x27155),f440(x27153,x27154,x27152,x27155)) % 112.37/112.12 [2716]~E(x27161,x27162)+E(f440(x27163,x27164,x27165,x27161),f440(x27163,x27164,x27165,x27162)) % 112.37/112.12 [2717]~E(x27171,x27172)+E(f337(x27171,x27173),f337(x27172,x27173)) % 112.37/112.12 [2718]~E(x27181,x27182)+E(f337(x27183,x27181),f337(x27183,x27182)) % 112.37/112.12 [2719]~E(x27191,x27192)+E(f672(x27191,x27193,x27194),f672(x27192,x27193,x27194)) % 112.37/112.12 [2720]~E(x27201,x27202)+E(f672(x27203,x27201,x27204),f672(x27203,x27202,x27204)) % 112.37/112.12 [2721]~E(x27211,x27212)+E(f672(x27213,x27214,x27211),f672(x27213,x27214,x27212)) % 112.37/112.12 [2722]~E(x27221,x27222)+E(f587(x27221,x27223,x27224),f587(x27222,x27223,x27224)) % 112.37/112.12 [2723]~E(x27231,x27232)+E(f587(x27233,x27231,x27234),f587(x27233,x27232,x27234)) % 112.37/112.12 [2724]~E(x27241,x27242)+E(f587(x27243,x27244,x27241),f587(x27243,x27244,x27242)) % 112.37/112.12 [2725]~E(x27251,x27252)+E(f800(x27251,x27253),f800(x27252,x27253)) % 112.37/112.12 [2726]~E(x27261,x27262)+E(f800(x27263,x27261),f800(x27263,x27262)) % 112.37/112.12 [2727]~E(x27271,x27272)+E(f765(x27271,x27273),f765(x27272,x27273)) % 112.37/112.12 [2728]~E(x27281,x27282)+E(f765(x27283,x27281),f765(x27283,x27282)) % 112.37/112.12 [2729]~E(x27291,x27292)+E(f214(x27291,x27293,x27294,x27295,x27296),f214(x27292,x27293,x27294,x27295,x27296)) % 112.37/112.12 [2730]~E(x27301,x27302)+E(f214(x27303,x27301,x27304,x27305,x27306),f214(x27303,x27302,x27304,x27305,x27306)) % 112.37/112.12 [2731]~E(x27311,x27312)+E(f214(x27313,x27314,x27311,x27315,x27316),f214(x27313,x27314,x27312,x27315,x27316)) % 112.37/112.12 [2732]~E(x27321,x27322)+E(f214(x27323,x27324,x27325,x27321,x27326),f214(x27323,x27324,x27325,x27322,x27326)) % 112.37/112.12 [2733]~E(x27331,x27332)+E(f214(x27333,x27334,x27335,x27336,x27331),f214(x27333,x27334,x27335,x27336,x27332)) % 112.37/112.12 [2734]~E(x27341,x27342)+E(f842(x27341,x27343,x27344),f842(x27342,x27343,x27344)) % 112.37/112.12 [2735]~E(x27351,x27352)+E(f842(x27353,x27351,x27354),f842(x27353,x27352,x27354)) % 112.37/112.12 [2736]~E(x27361,x27362)+E(f842(x27363,x27364,x27361),f842(x27363,x27364,x27362)) % 112.37/112.12 [2737]~E(x27371,x27372)+E(f338(x27371),f338(x27372)) % 112.37/112.12 [2738]~E(x27381,x27382)+E(f604(x27381,x27383,x27384),f604(x27382,x27383,x27384)) % 112.37/112.12 [2739]~E(x27391,x27392)+E(f604(x27393,x27391,x27394),f604(x27393,x27392,x27394)) % 112.37/112.12 [2740]~E(x27401,x27402)+E(f604(x27403,x27404,x27401),f604(x27403,x27404,x27402)) % 112.37/112.12 [2741]~E(x27411,x27412)+E(f449(x27411,x27413,x27414),f449(x27412,x27413,x27414)) % 112.37/112.12 [2742]~E(x27421,x27422)+E(f449(x27423,x27421,x27424),f449(x27423,x27422,x27424)) % 112.37/112.12 [2743]~E(x27431,x27432)+E(f449(x27433,x27434,x27431),f449(x27433,x27434,x27432)) % 112.37/112.12 [2744]~E(x27441,x27442)+E(f527(x27441,x27443),f527(x27442,x27443)) % 112.37/112.12 [2745]~E(x27451,x27452)+E(f527(x27453,x27451),f527(x27453,x27452)) % 112.37/112.12 [2746]~E(x27461,x27462)+E(f40(x27461),f40(x27462)) % 112.37/112.12 [2747]~E(x27471,x27472)+E(f219(x27471,x27473,x27474,x27475),f219(x27472,x27473,x27474,x27475)) % 112.37/112.12 [2748]~E(x27481,x27482)+E(f219(x27483,x27481,x27484,x27485),f219(x27483,x27482,x27484,x27485)) % 112.37/112.12 [2749]~E(x27491,x27492)+E(f219(x27493,x27494,x27491,x27495),f219(x27493,x27494,x27492,x27495)) % 112.37/112.12 [2750]~E(x27501,x27502)+E(f219(x27503,x27504,x27505,x27501),f219(x27503,x27504,x27505,x27502)) % 112.37/112.12 [2751]~E(x27511,x27512)+E(f190(x27511),f190(x27512)) % 112.37/112.12 [2752]~E(x27521,x27522)+E(f411(x27521,x27523,x27524),f411(x27522,x27523,x27524)) % 112.37/112.12 [2753]~E(x27531,x27532)+E(f411(x27533,x27531,x27534),f411(x27533,x27532,x27534)) % 112.37/112.12 [2754]~E(x27541,x27542)+E(f411(x27543,x27544,x27541),f411(x27543,x27544,x27542)) % 112.37/112.12 [2755]~E(x27551,x27552)+E(f747(x27551,x27553,x27554),f747(x27552,x27553,x27554)) % 112.37/112.12 [2756]~E(x27561,x27562)+E(f747(x27563,x27561,x27564),f747(x27563,x27562,x27564)) % 112.37/112.12 [2757]~E(x27571,x27572)+E(f747(x27573,x27574,x27571),f747(x27573,x27574,x27572)) % 112.37/112.12 [2758]~E(x27581,x27582)+E(f332(x27581),f332(x27582)) % 112.37/112.12 [2759]~E(x27591,x27592)+E(f215(x27591,x27593,x27594,x27595,x27596),f215(x27592,x27593,x27594,x27595,x27596)) % 112.37/112.12 [2760]~E(x27601,x27602)+E(f215(x27603,x27601,x27604,x27605,x27606),f215(x27603,x27602,x27604,x27605,x27606)) % 112.37/112.12 [2761]~E(x27611,x27612)+E(f215(x27613,x27614,x27611,x27615,x27616),f215(x27613,x27614,x27612,x27615,x27616)) % 112.37/112.12 [2762]~E(x27621,x27622)+E(f215(x27623,x27624,x27625,x27621,x27626),f215(x27623,x27624,x27625,x27622,x27626)) % 112.37/112.12 [2763]~E(x27631,x27632)+E(f215(x27633,x27634,x27635,x27636,x27631),f215(x27633,x27634,x27635,x27636,x27632)) % 112.37/112.12 [2764]~E(x27641,x27642)+E(f446(x27641,x27643,x27644),f446(x27642,x27643,x27644)) % 112.37/112.12 [2765]~E(x27651,x27652)+E(f446(x27653,x27651,x27654),f446(x27653,x27652,x27654)) % 112.37/112.12 [2766]~E(x27661,x27662)+E(f446(x27663,x27664,x27661),f446(x27663,x27664,x27662)) % 112.37/112.12 [2767]~E(x27671,x27672)+E(f806(x27671,x27673),f806(x27672,x27673)) % 112.37/112.12 [2768]~E(x27681,x27682)+E(f806(x27683,x27681),f806(x27683,x27682)) % 112.37/112.12 [2769]~E(x27691,x27692)+E(f624(x27691,x27693,x27694,x27695),f624(x27692,x27693,x27694,x27695)) % 112.37/112.12 [2770]~E(x27701,x27702)+E(f624(x27703,x27701,x27704,x27705),f624(x27703,x27702,x27704,x27705)) % 112.37/112.12 [2771]~E(x27711,x27712)+E(f624(x27713,x27714,x27711,x27715),f624(x27713,x27714,x27712,x27715)) % 112.37/112.12 [2772]~E(x27721,x27722)+E(f624(x27723,x27724,x27725,x27721),f624(x27723,x27724,x27725,x27722)) % 112.37/112.12 [2773]~E(x27731,x27732)+E(f879(x27731),f879(x27732)) % 112.37/112.12 [2774]~P1(x27741)+P1(x27742)+~E(x27741,x27742) % 112.37/112.12 [2775]~P2(x27751)+P2(x27752)+~E(x27751,x27752) % 112.37/112.12 [2776]P13(x27762,x27763)+~E(x27761,x27762)+~P13(x27761,x27763) % 112.37/112.12 [2777]P13(x27773,x27772)+~E(x27771,x27772)+~P13(x27773,x27771) % 112.37/112.12 [2778]~P65(x27781)+P65(x27782)+~E(x27781,x27782) % 112.37/112.12 [2779]~P108(x27791)+P108(x27792)+~E(x27791,x27792) % 112.37/112.12 [2780]~P3(x27801)+P3(x27802)+~E(x27801,x27802) % 112.37/112.12 [2781]~P112(x27811)+P112(x27812)+~E(x27811,x27812) % 112.37/112.12 [2782]~P66(x27821)+P66(x27822)+~E(x27821,x27822) % 112.37/112.12 [2783]~P98(x27831)+P98(x27832)+~E(x27831,x27832) % 112.37/112.12 [2784]~P107(x27841)+P107(x27842)+~E(x27841,x27842) % 112.37/112.12 [2785]~P63(x27851)+P63(x27852)+~E(x27851,x27852) % 112.37/112.12 [2786]~P109(x27861)+P109(x27862)+~E(x27861,x27862) % 112.37/112.12 [2787]~P127(x27871)+P127(x27872)+~E(x27871,x27872) % 112.37/112.12 [2788]~P4(x27881)+P4(x27882)+~E(x27881,x27882) % 112.37/112.12 [2789]~P94(x27891)+P94(x27892)+~E(x27891,x27892) % 112.37/112.12 [2790]P58(x27902,x27903,x27904,x27905)+~E(x27901,x27902)+~P58(x27901,x27903,x27904,x27905) % 112.37/112.12 [2791]P58(x27913,x27912,x27914,x27915)+~E(x27911,x27912)+~P58(x27913,x27911,x27914,x27915) % 112.37/112.12 [2792]P58(x27923,x27924,x27922,x27925)+~E(x27921,x27922)+~P58(x27923,x27924,x27921,x27925) % 112.37/112.12 [2793]P58(x27933,x27934,x27935,x27932)+~E(x27931,x27932)+~P58(x27933,x27934,x27935,x27931) % 112.37/112.12 [2794]P24(x27942,x27943,x27944,x27945)+~E(x27941,x27942)+~P24(x27941,x27943,x27944,x27945) % 112.37/112.12 [2795]P24(x27953,x27952,x27954,x27955)+~E(x27951,x27952)+~P24(x27953,x27951,x27954,x27955) % 112.37/112.12 [2796]P24(x27963,x27964,x27962,x27965)+~E(x27961,x27962)+~P24(x27963,x27964,x27961,x27965) % 112.37/112.12 [2797]P24(x27973,x27974,x27975,x27972)+~E(x27971,x27972)+~P24(x27973,x27974,x27975,x27971) % 112.37/112.12 [2798]~P126(x27981)+P126(x27982)+~E(x27981,x27982) % 112.37/112.12 [2799]~P93(x27991)+P93(x27992)+~E(x27991,x27992) % 112.37/112.12 [2800]~P134(x28001)+P134(x28002)+~E(x28001,x28002) % 112.37/112.12 [2801]~P67(x28011)+P67(x28012)+~E(x28011,x28012) % 112.37/112.12 [2802]~P104(x28021)+P104(x28022)+~E(x28021,x28022) % 112.37/112.12 [2803]~P105(x28031)+P105(x28032)+~E(x28031,x28032) % 112.37/112.12 [2804]~P64(x28041)+P64(x28042)+~E(x28041,x28042) % 112.37/112.12 [2805]~P79(x28051)+P79(x28052)+~E(x28051,x28052) % 112.37/112.12 [2806]~P68(x28061)+P68(x28062)+~E(x28061,x28062) % 112.37/112.12 [2807]~P110(x28071)+P110(x28072)+~E(x28071,x28072) % 112.37/112.12 [2808]~P69(x28081)+P69(x28082)+~E(x28081,x28082) % 112.37/112.12 [2809]~P39(x28091)+P39(x28092)+~E(x28091,x28092) % 112.37/112.12 [2810]P147(x28102,x28103,x28104)+~E(x28101,x28102)+~P147(x28101,x28103,x28104) % 112.37/112.12 [2811]P147(x28113,x28112,x28114)+~E(x28111,x28112)+~P147(x28113,x28111,x28114) % 112.37/112.12 [2812]P147(x28123,x28124,x28122)+~E(x28121,x28122)+~P147(x28123,x28124,x28121) % 112.37/112.12 [2813]~P83(x28131)+P83(x28132)+~E(x28131,x28132) % 112.37/112.12 [2814]P8(x28142,x28143,x28144)+~E(x28141,x28142)+~P8(x28141,x28143,x28144) % 112.37/112.12 [2815]P8(x28153,x28152,x28154)+~E(x28151,x28152)+~P8(x28153,x28151,x28154) % 112.37/112.12 [2816]P8(x28163,x28164,x28162)+~E(x28161,x28162)+~P8(x28163,x28164,x28161) % 112.37/112.12 [2817]~P5(x28171)+P5(x28172)+~E(x28171,x28172) % 112.37/112.12 [2818]~P70(x28181)+P70(x28182)+~E(x28181,x28182) % 112.37/112.12 [2819]P17(x28192,x28193,x28194)+~E(x28191,x28192)+~P17(x28191,x28193,x28194) % 112.37/112.12 [2820]P17(x28203,x28202,x28204)+~E(x28201,x28202)+~P17(x28203,x28201,x28204) % 112.37/112.12 [2821]P17(x28213,x28214,x28212)+~E(x28211,x28212)+~P17(x28213,x28214,x28211) % 112.37/112.12 [2822]P18(x28222,x28223,x28224)+~E(x28221,x28222)+~P18(x28221,x28223,x28224) % 112.37/112.12 [2823]P18(x28233,x28232,x28234)+~E(x28231,x28232)+~P18(x28233,x28231,x28234) % 112.37/112.12 [2824]P18(x28243,x28244,x28242)+~E(x28241,x28242)+~P18(x28243,x28244,x28241) % 112.37/112.12 [2825]~P80(x28251)+P80(x28252)+~E(x28251,x28252) % 112.37/112.12 [2826]~P145(x28261)+P145(x28262)+~E(x28261,x28262) % 112.37/112.12 [2827]~P92(x28271)+P92(x28272)+~E(x28271,x28272) % 112.37/112.12 [2828]~P75(x28281)+P75(x28282)+~E(x28281,x28282) % 112.37/112.12 [2829]P27(x28292,x28293)+~E(x28291,x28292)+~P27(x28291,x28293) % 112.37/112.12 [2830]P27(x28303,x28302)+~E(x28301,x28302)+~P27(x28303,x28301) % 112.37/112.12 [2831]P38(x28312,x28313)+~E(x28311,x28312)+~P38(x28311,x28313) % 112.37/112.12 [2832]P38(x28323,x28322)+~E(x28321,x28322)+~P38(x28323,x28321) % 112.37/112.12 [2833]~P82(x28331)+P82(x28332)+~E(x28331,x28332) % 112.37/112.12 [2834]P32(x28342,x28343,x28344)+~E(x28341,x28342)+~P32(x28341,x28343,x28344) % 112.37/112.12 [2835]P32(x28353,x28352,x28354)+~E(x28351,x28352)+~P32(x28353,x28351,x28354) % 112.37/112.12 [2836]P32(x28363,x28364,x28362)+~E(x28361,x28362)+~P32(x28363,x28364,x28361) % 112.37/112.12 [2837]P14(x28372,x28373,x28374)+~E(x28371,x28372)+~P14(x28371,x28373,x28374) % 112.37/112.12 [2838]P14(x28383,x28382,x28384)+~E(x28381,x28382)+~P14(x28383,x28381,x28384) % 112.37/112.12 [2839]P14(x28393,x28394,x28392)+~E(x28391,x28392)+~P14(x28393,x28394,x28391) % 112.37/112.12 [2840]~P71(x28401)+P71(x28402)+~E(x28401,x28402) % 112.37/112.12 [2841]P54(x28412,x28413,x28414)+~E(x28411,x28412)+~P54(x28411,x28413,x28414) % 112.37/112.12 [2842]P54(x28423,x28422,x28424)+~E(x28421,x28422)+~P54(x28423,x28421,x28424) % 112.37/112.12 [2843]P54(x28433,x28434,x28432)+~E(x28431,x28432)+~P54(x28433,x28434,x28431) % 112.37/112.12 [2844]~P99(x28441)+P99(x28442)+~E(x28441,x28442) % 112.37/112.12 [2845]~P72(x28451)+P72(x28452)+~E(x28451,x28452) % 112.37/112.12 [2846]P57(x28462,x28463)+~E(x28461,x28462)+~P57(x28461,x28463) % 112.37/112.12 [2847]P57(x28473,x28472)+~E(x28471,x28472)+~P57(x28473,x28471) % 112.37/112.12 [2848]~P121(x28481)+P121(x28482)+~E(x28481,x28482) % 112.37/112.12 [2849]~P73(x28491)+P73(x28492)+~E(x28491,x28492) % 112.37/112.12 [2850]P36(x28502,x28503)+~E(x28501,x28502)+~P36(x28501,x28503) % 112.37/112.12 [2851]P36(x28513,x28512)+~E(x28511,x28512)+~P36(x28513,x28511) % 112.37/112.12 [2852]~P128(x28521)+P128(x28522)+~E(x28521,x28522) % 112.37/112.12 [2853]~P84(x28531)+P84(x28532)+~E(x28531,x28532) % 112.37/112.12 [2854]P31(x28542,x28543,x28544,x28545)+~E(x28541,x28542)+~P31(x28541,x28543,x28544,x28545) % 112.37/112.12 [2855]P31(x28553,x28552,x28554,x28555)+~E(x28551,x28552)+~P31(x28553,x28551,x28554,x28555) % 112.37/112.12 [2856]P31(x28563,x28564,x28562,x28565)+~E(x28561,x28562)+~P31(x28563,x28564,x28561,x28565) % 112.37/112.12 [2857]P31(x28573,x28574,x28575,x28572)+~E(x28571,x28572)+~P31(x28573,x28574,x28575,x28571) % 112.37/112.12 [2858]~P96(x28581)+P96(x28582)+~E(x28581,x28582) % 112.37/112.12 [2859]~P85(x28591)+P85(x28592)+~E(x28591,x28592) % 112.37/112.12 [2860]P33(x28602,x28603,x28604,x28605,x28606)+~E(x28601,x28602)+~P33(x28601,x28603,x28604,x28605,x28606) % 112.37/112.12 [2861]P33(x28613,x28612,x28614,x28615,x28616)+~E(x28611,x28612)+~P33(x28613,x28611,x28614,x28615,x28616) % 112.37/112.12 [2862]P33(x28623,x28624,x28622,x28625,x28626)+~E(x28621,x28622)+~P33(x28623,x28624,x28621,x28625,x28626) % 112.37/112.12 [2863]P33(x28633,x28634,x28635,x28632,x28636)+~E(x28631,x28632)+~P33(x28633,x28634,x28635,x28631,x28636) % 112.37/112.12 [2864]P33(x28643,x28644,x28645,x28646,x28642)+~E(x28641,x28642)+~P33(x28643,x28644,x28645,x28646,x28641) % 112.37/112.12 [2865]P150(x28652,x28653)+~E(x28651,x28652)+~P150(x28651,x28653) % 112.37/112.12 [2866]P150(x28663,x28662)+~E(x28661,x28662)+~P150(x28663,x28661) % 112.37/112.12 [2867]~P76(x28671)+P76(x28672)+~E(x28671,x28672) % 112.37/112.12 [2868]~P111(x28681)+P111(x28682)+~E(x28681,x28682) % 112.37/112.12 [2869]~P81(x28691)+P81(x28692)+~E(x28691,x28692) % 112.37/112.12 [2870]~P113(x28701)+P113(x28702)+~E(x28701,x28702) % 112.37/112.12 [2871]P30(x28712,x28713,x28714)+~E(x28711,x28712)+~P30(x28711,x28713,x28714) % 112.37/112.12 [2872]P30(x28723,x28722,x28724)+~E(x28721,x28722)+~P30(x28723,x28721,x28724) % 112.37/112.12 [2873]P30(x28733,x28734,x28732)+~E(x28731,x28732)+~P30(x28733,x28734,x28731) % 112.37/112.12 [2874]P52(x28742,x28743,x28744)+~E(x28741,x28742)+~P52(x28741,x28743,x28744) % 112.37/112.12 [2875]P52(x28753,x28752,x28754)+~E(x28751,x28752)+~P52(x28753,x28751,x28754) % 112.37/112.12 [2876]P52(x28763,x28764,x28762)+~E(x28761,x28762)+~P52(x28763,x28764,x28761) % 112.37/112.12 [2877]~P139(x28771)+P139(x28772)+~E(x28771,x28772) % 112.37/112.12 [2878]~P143(x28781)+P143(x28782)+~E(x28781,x28782) % 112.37/112.12 [2879]~P60(x28791)+P60(x28792)+~E(x28791,x28792) % 112.37/112.12 [2880]~P130(x28801)+P130(x28802)+~E(x28801,x28802) % 112.37/112.12 [2881]P37(x28812,x28813)+~E(x28811,x28812)+~P37(x28811,x28813) % 112.37/112.12 [2882]P37(x28823,x28822)+~E(x28821,x28822)+~P37(x28823,x28821) % 112.37/112.12 [2883]~P61(x28831)+P61(x28832)+~E(x28831,x28832) % 112.37/112.12 [2884]~P119(x28841)+P119(x28842)+~E(x28841,x28842) % 112.37/112.12 [2885]~P141(x28851)+P141(x28852)+~E(x28851,x28852) % 112.37/112.12 [2886]~P86(x28861)+P86(x28862)+~E(x28861,x28862) % 112.37/112.12 [2887]P15(x28872,x28873)+~E(x28871,x28872)+~P15(x28871,x28873) % 112.37/112.12 [2888]P15(x28883,x28882)+~E(x28881,x28882)+~P15(x28883,x28881) % 112.37/112.12 [2889]~P88(x28891)+P88(x28892)+~E(x28891,x28892) % 112.37/112.12 [2890]~P129(x28901)+P129(x28902)+~E(x28901,x28902) % 112.37/112.12 [2891]~P132(x28911)+P132(x28912)+~E(x28911,x28912) % 112.37/112.12 [2892]~P6(x28921)+P6(x28922)+~E(x28921,x28922) % 112.37/112.12 [2893]~P102(x28931)+P102(x28932)+~E(x28931,x28932) % 112.37/112.12 [2894]~P87(x28941)+P87(x28942)+~E(x28941,x28942) % 112.37/112.12 [2895]~P115(x28951)+P115(x28952)+~E(x28951,x28952) % 112.37/112.12 [2896]P51(x28962,x28963)+~E(x28961,x28962)+~P51(x28961,x28963) % 112.37/112.12 [2897]P51(x28973,x28972)+~E(x28971,x28972)+~P51(x28973,x28971) % 112.37/112.12 [2898]~P77(x28981)+P77(x28982)+~E(x28981,x28982) % 112.37/112.12 [2899]P16(x28992,x28993,x28994)+~E(x28991,x28992)+~P16(x28991,x28993,x28994) % 112.37/112.12 [2900]P16(x29003,x29002,x29004)+~E(x29001,x29002)+~P16(x29003,x29001,x29004) % 112.37/112.12 [2901]P16(x29013,x29014,x29012)+~E(x29011,x29012)+~P16(x29013,x29014,x29011) % 112.37/112.12 [2902]~P136(x29021)+P136(x29022)+~E(x29021,x29022) % 112.37/112.12 [2903]P25(x29032,x29033,x29034,x29035,x29036)+~E(x29031,x29032)+~P25(x29031,x29033,x29034,x29035,x29036) % 112.37/112.12 [2904]P25(x29043,x29042,x29044,x29045,x29046)+~E(x29041,x29042)+~P25(x29043,x29041,x29044,x29045,x29046) % 112.37/112.12 [2905]P25(x29053,x29054,x29052,x29055,x29056)+~E(x29051,x29052)+~P25(x29053,x29054,x29051,x29055,x29056) % 112.37/112.12 [2906]P25(x29063,x29064,x29065,x29062,x29066)+~E(x29061,x29062)+~P25(x29063,x29064,x29065,x29061,x29066) % 112.37/112.12 [2907]P25(x29073,x29074,x29075,x29076,x29072)+~E(x29071,x29072)+~P25(x29073,x29074,x29075,x29076,x29071) % 112.37/112.12 [2908]~P133(x29081)+P133(x29082)+~E(x29081,x29082) % 112.37/112.12 [2909]P20(x29092,x29093,x29094,x29095)+~E(x29091,x29092)+~P20(x29091,x29093,x29094,x29095) % 112.37/112.12 [2910]P20(x29103,x29102,x29104,x29105)+~E(x29101,x29102)+~P20(x29103,x29101,x29104,x29105) % 112.37/112.12 [2911]P20(x29113,x29114,x29112,x29115)+~E(x29111,x29112)+~P20(x29113,x29114,x29111,x29115) % 112.37/112.12 [2912]P20(x29123,x29124,x29125,x29122)+~E(x29121,x29122)+~P20(x29123,x29124,x29125,x29121) % 112.37/112.12 [2913]~P35(x29131)+P35(x29132)+~E(x29131,x29132) % 112.37/112.12 [2914]~P140(x29141)+P140(x29142)+~E(x29141,x29142) % 112.37/112.12 [2915]~P144(x29151)+P144(x29152)+~E(x29151,x29152) % 112.37/112.12 [2916]P59(x29162,x29163)+~E(x29161,x29162)+~P59(x29161,x29163) % 112.37/112.12 [2917]P59(x29173,x29172)+~E(x29171,x29172)+~P59(x29173,x29171) % 112.37/112.12 [2918]P56(x29182,x29183,x29184,x29185,x29186)+~E(x29181,x29182)+~P56(x29181,x29183,x29184,x29185,x29186) % 112.37/112.12 [2919]P56(x29193,x29192,x29194,x29195,x29196)+~E(x29191,x29192)+~P56(x29193,x29191,x29194,x29195,x29196) % 112.37/112.12 [2920]P56(x29203,x29204,x29202,x29205,x29206)+~E(x29201,x29202)+~P56(x29203,x29204,x29201,x29205,x29206) % 112.37/112.12 [2921]P56(x29213,x29214,x29215,x29212,x29216)+~E(x29211,x29212)+~P56(x29213,x29214,x29215,x29211,x29216) % 112.37/112.12 [2922]P56(x29223,x29224,x29225,x29226,x29222)+~E(x29221,x29222)+~P56(x29223,x29224,x29225,x29226,x29221) % 112.37/112.12 [2923]~P146(x29231)+P146(x29232)+~E(x29231,x29232) % 112.37/112.12 [2924]P42(x29242,x29243)+~E(x29241,x29242)+~P42(x29241,x29243) % 112.37/112.12 [2925]P42(x29253,x29252)+~E(x29251,x29252)+~P42(x29253,x29251) % 112.37/112.12 [2926]~P123(x29261)+P123(x29262)+~E(x29261,x29262) % 112.37/112.12 [2927]~P135(x29271)+P135(x29272)+~E(x29271,x29272) % 112.37/112.12 [2928]~P62(x29281)+P62(x29282)+~E(x29281,x29282) % 112.37/112.12 [2929]P148(x29292,x29293,x29294)+~E(x29291,x29292)+~P148(x29291,x29293,x29294) % 112.37/112.12 [2930]P148(x29303,x29302,x29304)+~E(x29301,x29302)+~P148(x29303,x29301,x29304) % 112.37/112.12 [2931]P148(x29313,x29314,x29312)+~E(x29311,x29312)+~P148(x29313,x29314,x29311) % 112.37/112.12 [2932]~P137(x29321)+P137(x29322)+~E(x29321,x29322) % 112.37/112.12 [2933]P19(x29332,x29333,x29334,x29335)+~E(x29331,x29332)+~P19(x29331,x29333,x29334,x29335) % 112.37/112.12 [2934]P19(x29343,x29342,x29344,x29345)+~E(x29341,x29342)+~P19(x29343,x29341,x29344,x29345) % 112.37/112.12 [2935]P19(x29353,x29354,x29352,x29355)+~E(x29351,x29352)+~P19(x29353,x29354,x29351,x29355) % 112.37/112.12 [2936]P19(x29363,x29364,x29365,x29362)+~E(x29361,x29362)+~P19(x29363,x29364,x29365,x29361) % 112.37/112.12 [2937]P34(x29372,x29373,x29374)+~E(x29371,x29372)+~P34(x29371,x29373,x29374) % 112.37/112.12 [2938]P34(x29383,x29382,x29384)+~E(x29381,x29382)+~P34(x29383,x29381,x29384) % 112.37/112.12 [2939]P34(x29393,x29394,x29392)+~E(x29391,x29392)+~P34(x29393,x29394,x29391) % 112.37/112.12 [2940]P23(x29402,x29403,x29404,x29405,x29406,x29407)+~E(x29401,x29402)+~P23(x29401,x29403,x29404,x29405,x29406,x29407) % 112.37/112.12 [2941]P23(x29413,x29412,x29414,x29415,x29416,x29417)+~E(x29411,x29412)+~P23(x29413,x29411,x29414,x29415,x29416,x29417) % 112.37/112.12 [2942]P23(x29423,x29424,x29422,x29425,x29426,x29427)+~E(x29421,x29422)+~P23(x29423,x29424,x29421,x29425,x29426,x29427) % 112.37/112.12 [2943]P23(x29433,x29434,x29435,x29432,x29436,x29437)+~E(x29431,x29432)+~P23(x29433,x29434,x29435,x29431,x29436,x29437) % 112.37/112.12 [2944]P23(x29443,x29444,x29445,x29446,x29442,x29447)+~E(x29441,x29442)+~P23(x29443,x29444,x29445,x29446,x29441,x29447) % 112.37/112.12 [2945]P23(x29453,x29454,x29455,x29456,x29457,x29452)+~E(x29451,x29452)+~P23(x29453,x29454,x29455,x29456,x29457,x29451) % 112.37/112.12 [2946]~P125(x29461)+P125(x29462)+~E(x29461,x29462) % 112.37/112.12 [2947]~P114(x29471)+P114(x29472)+~E(x29471,x29472) % 112.37/112.12 [2948]~P142(x29481)+P142(x29482)+~E(x29481,x29482) % 112.37/112.12 [2949]~P138(x29491)+P138(x29492)+~E(x29491,x29492) % 112.37/112.12 [2950]P7(x29502,x29503)+~E(x29501,x29502)+~P7(x29501,x29503) % 112.37/112.13 [2951]P7(x29513,x29512)+~E(x29511,x29512)+~P7(x29513,x29511) % 112.37/112.13 [2952]P55(x29522,x29523,x29524)+~E(x29521,x29522)+~P55(x29521,x29523,x29524) % 112.37/112.13 [2953]P55(x29533,x29532,x29534)+~E(x29531,x29532)+~P55(x29533,x29531,x29534) % 112.37/112.13 [2954]P55(x29543,x29544,x29542)+~E(x29541,x29542)+~P55(x29543,x29544,x29541) % 112.37/112.13 [2955]~P122(x29551)+P122(x29552)+~E(x29551,x29552) % 112.37/112.13 [2956]~P120(x29561)+P120(x29562)+~E(x29561,x29562) % 112.37/112.13 [2957]P41(x29572,x29573,x29574,x29575,x29576,x29577)+~E(x29571,x29572)+~P41(x29571,x29573,x29574,x29575,x29576,x29577) % 112.37/112.13 [2958]P41(x29583,x29582,x29584,x29585,x29586,x29587)+~E(x29581,x29582)+~P41(x29583,x29581,x29584,x29585,x29586,x29587) % 112.37/112.13 [2959]P41(x29593,x29594,x29592,x29595,x29596,x29597)+~E(x29591,x29592)+~P41(x29593,x29594,x29591,x29595,x29596,x29597) % 112.37/112.13 [2960]P41(x29603,x29604,x29605,x29602,x29606,x29607)+~E(x29601,x29602)+~P41(x29603,x29604,x29605,x29601,x29606,x29607) % 112.37/112.13 [2961]P41(x29613,x29614,x29615,x29616,x29612,x29617)+~E(x29611,x29612)+~P41(x29613,x29614,x29615,x29616,x29611,x29617) % 112.37/112.13 [2962]P41(x29623,x29624,x29625,x29626,x29627,x29622)+~E(x29621,x29622)+~P41(x29623,x29624,x29625,x29626,x29627,x29621) % 112.37/112.13 [2963]P49(x29632,x29633)+~E(x29631,x29632)+~P49(x29631,x29633) % 112.37/112.13 [2964]P49(x29643,x29642)+~E(x29641,x29642)+~P49(x29643,x29641) % 112.37/112.13 [2965]P11(x29652,x29653,x29654,x29655)+~E(x29651,x29652)+~P11(x29651,x29653,x29654,x29655) % 112.37/112.13 [2966]P11(x29663,x29662,x29664,x29665)+~E(x29661,x29662)+~P11(x29663,x29661,x29664,x29665) % 112.37/112.13 [2967]P11(x29673,x29674,x29672,x29675)+~E(x29671,x29672)+~P11(x29673,x29674,x29671,x29675) % 112.37/112.13 [2968]P11(x29683,x29684,x29685,x29682)+~E(x29681,x29682)+~P11(x29683,x29684,x29685,x29681) % 112.37/112.13 [2969]P50(x29692,x29693)+~E(x29691,x29692)+~P50(x29691,x29693) % 112.37/112.13 [2970]P50(x29703,x29702)+~E(x29701,x29702)+~P50(x29703,x29701) % 112.37/112.13 [2971]P12(x29712,x29713,x29714,x29715,x29716,x29717)+~E(x29711,x29712)+~P12(x29711,x29713,x29714,x29715,x29716,x29717) % 112.37/112.13 [2972]P12(x29723,x29722,x29724,x29725,x29726,x29727)+~E(x29721,x29722)+~P12(x29723,x29721,x29724,x29725,x29726,x29727) % 112.37/112.13 [2973]P12(x29733,x29734,x29732,x29735,x29736,x29737)+~E(x29731,x29732)+~P12(x29733,x29734,x29731,x29735,x29736,x29737) % 112.37/112.13 [2974]P12(x29743,x29744,x29745,x29742,x29746,x29747)+~E(x29741,x29742)+~P12(x29743,x29744,x29745,x29741,x29746,x29747) % 112.37/112.13 [2975]P12(x29753,x29754,x29755,x29756,x29752,x29757)+~E(x29751,x29752)+~P12(x29753,x29754,x29755,x29756,x29751,x29757) % 112.37/112.13 [2976]P12(x29763,x29764,x29765,x29766,x29767,x29762)+~E(x29761,x29762)+~P12(x29763,x29764,x29765,x29766,x29767,x29761) % 112.37/112.13 [2977]~P131(x29771)+P131(x29772)+~E(x29771,x29772) % 112.37/112.13 [2978]P26(x29782,x29783)+~E(x29781,x29782)+~P26(x29781,x29783) % 112.37/112.13 [2979]P26(x29793,x29792)+~E(x29791,x29792)+~P26(x29793,x29791) % 112.37/112.13 [2980]~P90(x29801)+P90(x29802)+~E(x29801,x29802) % 112.37/112.13 [2981]~P100(x29811)+P100(x29812)+~E(x29811,x29812) % 112.37/112.13 [2982]P47(x29822,x29823,x29824)+~E(x29821,x29822)+~P47(x29821,x29823,x29824) % 112.37/112.13 [2983]P47(x29833,x29832,x29834)+~E(x29831,x29832)+~P47(x29833,x29831,x29834) % 112.37/112.13 [2984]P47(x29843,x29844,x29842)+~E(x29841,x29842)+~P47(x29843,x29844,x29841) % 112.37/112.13 [2985]~P97(x29851)+P97(x29852)+~E(x29851,x29852) % 112.37/112.13 [2986]P28(x29862,x29863,x29864)+~E(x29861,x29862)+~P28(x29861,x29863,x29864) % 112.37/112.13 [2987]P28(x29873,x29872,x29874)+~E(x29871,x29872)+~P28(x29873,x29871,x29874) % 112.37/112.13 [2988]P28(x29883,x29884,x29882)+~E(x29881,x29882)+~P28(x29883,x29884,x29881) % 112.37/112.13 [2989]~P95(x29891)+P95(x29892)+~E(x29891,x29892) % 112.37/112.13 [2990]~P103(x29901)+P103(x29902)+~E(x29901,x29902) % 112.37/112.13 [2991]P53(x29912,x29913)+~E(x29911,x29912)+~P53(x29911,x29913) % 112.37/112.13 [2992]P53(x29923,x29922)+~E(x29921,x29922)+~P53(x29923,x29921) % 112.37/112.13 [2993]P10(x29932,x29933,x29934,x29935,x29936)+~E(x29931,x29932)+~P10(x29931,x29933,x29934,x29935,x29936) % 112.37/112.13 [2994]P10(x29943,x29942,x29944,x29945,x29946)+~E(x29941,x29942)+~P10(x29943,x29941,x29944,x29945,x29946) % 112.37/112.13 [2995]P10(x29953,x29954,x29952,x29955,x29956)+~E(x29951,x29952)+~P10(x29953,x29954,x29951,x29955,x29956) % 112.37/112.13 [2996]P10(x29963,x29964,x29965,x29962,x29966)+~E(x29961,x29962)+~P10(x29963,x29964,x29965,x29961,x29966) % 112.37/112.13 [2997]P10(x29973,x29974,x29975,x29976,x29972)+~E(x29971,x29972)+~P10(x29973,x29974,x29975,x29976,x29971) % 112.37/112.13 [2998]~P101(x29981)+P101(x29982)+~E(x29981,x29982) % 112.37/112.13 [2999]~P118(x29991)+P118(x29992)+~E(x29991,x29992) % 112.37/112.13 [3000]P40(x30002,x30003,x30004,x30005)+~E(x30001,x30002)+~P40(x30001,x30003,x30004,x30005) % 112.37/112.13 [3001]P40(x30013,x30012,x30014,x30015)+~E(x30011,x30012)+~P40(x30013,x30011,x30014,x30015) % 112.37/112.13 [3002]P40(x30023,x30024,x30022,x30025)+~E(x30021,x30022)+~P40(x30023,x30024,x30021,x30025) % 112.37/112.13 [3003]P40(x30033,x30034,x30035,x30032)+~E(x30031,x30032)+~P40(x30033,x30034,x30035,x30031) % 112.37/112.13 [3004]P43(x30042,x30043)+~E(x30041,x30042)+~P43(x30041,x30043) % 112.37/112.13 [3005]P43(x30053,x30052)+~E(x30051,x30052)+~P43(x30053,x30051) % 112.37/112.13 [3006]P48(x30062,x30063,x30064,x30065)+~E(x30061,x30062)+~P48(x30061,x30063,x30064,x30065) % 112.37/112.13 [3007]P48(x30073,x30072,x30074,x30075)+~E(x30071,x30072)+~P48(x30073,x30071,x30074,x30075) % 112.37/112.13 [3008]P48(x30083,x30084,x30082,x30085)+~E(x30081,x30082)+~P48(x30083,x30084,x30081,x30085) % 112.37/112.13 [3009]P48(x30093,x30094,x30095,x30092)+~E(x30091,x30092)+~P48(x30093,x30094,x30095,x30091) % 112.37/112.13 [3010]~P89(x30101)+P89(x30102)+~E(x30101,x30102) % 112.37/112.13 [3011]~P106(x30111)+P106(x30112)+~E(x30111,x30112) % 112.37/112.13 [3012]~P149(x30121)+P149(x30122)+~E(x30121,x30122) % 112.37/112.13 [3013]P22(x30132,x30133,x30134,x30135,x30136,x30137)+~E(x30131,x30132)+~P22(x30131,x30133,x30134,x30135,x30136,x30137) % 112.37/112.13 [3014]P22(x30143,x30142,x30144,x30145,x30146,x30147)+~E(x30141,x30142)+~P22(x30143,x30141,x30144,x30145,x30146,x30147) % 112.37/112.13 [3015]P22(x30153,x30154,x30152,x30155,x30156,x30157)+~E(x30151,x30152)+~P22(x30153,x30154,x30151,x30155,x30156,x30157) % 112.37/112.13 [3016]P22(x30163,x30164,x30165,x30162,x30166,x30167)+~E(x30161,x30162)+~P22(x30163,x30164,x30165,x30161,x30166,x30167) % 112.37/112.13 [3017]P22(x30173,x30174,x30175,x30176,x30172,x30177)+~E(x30171,x30172)+~P22(x30173,x30174,x30175,x30176,x30171,x30177) % 112.37/112.13 [3018]P22(x30183,x30184,x30185,x30186,x30187,x30182)+~E(x30181,x30182)+~P22(x30183,x30184,x30185,x30186,x30187,x30181) % 112.37/112.13 [3019]P46(x30192,x30193,x30194)+~E(x30191,x30192)+~P46(x30191,x30193,x30194) % 112.37/112.13 [3020]P46(x30203,x30202,x30204)+~E(x30201,x30202)+~P46(x30203,x30201,x30204) % 112.37/112.13 [3021]P46(x30213,x30214,x30212)+~E(x30211,x30212)+~P46(x30213,x30214,x30211) % 112.37/112.13 [3022]~P74(x30221)+P74(x30222)+~E(x30221,x30222) % 112.37/112.13 [3023]P29(x30232,x30233,x30234)+~E(x30231,x30232)+~P29(x30231,x30233,x30234) % 112.37/112.13 [3024]P29(x30243,x30242,x30244)+~E(x30241,x30242)+~P29(x30243,x30241,x30244) % 112.37/112.13 [3025]P29(x30253,x30254,x30252)+~E(x30251,x30252)+~P29(x30253,x30254,x30251) % 112.37/112.13 [3026]~P116(x30261)+P116(x30262)+~E(x30261,x30262) % 112.37/112.13 [3027]~P78(x30271)+P78(x30272)+~E(x30271,x30272) % 112.37/112.13 [3028]P21(x30282,x30283,x30284,x30285,x30286)+~E(x30281,x30282)+~P21(x30281,x30283,x30284,x30285,x30286) % 112.37/112.13 [3029]P21(x30293,x30292,x30294,x30295,x30296)+~E(x30291,x30292)+~P21(x30293,x30291,x30294,x30295,x30296) % 112.37/112.13 [3030]P21(x30303,x30304,x30302,x30305,x30306)+~E(x30301,x30302)+~P21(x30303,x30304,x30301,x30305,x30306) % 112.37/112.13 [3031]P21(x30313,x30314,x30315,x30312,x30316)+~E(x30311,x30312)+~P21(x30313,x30314,x30315,x30311,x30316) % 112.37/112.13 [3032]P21(x30323,x30324,x30325,x30326,x30322)+~E(x30321,x30322)+~P21(x30323,x30324,x30325,x30326,x30321) % 112.37/112.13 [3033]~P124(x30331)+P124(x30332)+~E(x30331,x30332) % 112.37/112.13 [3034]~P117(x30341)+P117(x30342)+~E(x30341,x30342) % 112.37/112.13 [3035]P9(x30352,x30353,x30354)+~E(x30351,x30352)+~P9(x30351,x30353,x30354) % 112.37/112.13 [3036]P9(x30363,x30362,x30364)+~E(x30361,x30362)+~P9(x30363,x30361,x30364) % 112.37/112.13 [3037]P9(x30373,x30374,x30372)+~E(x30371,x30372)+~P9(x30373,x30374,x30371) % 112.37/112.13 [3038]P45(x30382,x30383)+~E(x30381,x30382)+~P45(x30381,x30383) % 112.37/112.13 [3039]P45(x30393,x30392)+~E(x30391,x30392)+~P45(x30393,x30391) % 112.37/112.13 [3040]~P91(x30401)+P91(x30402)+~E(x30401,x30402) % 112.37/112.13 [3041]~P44(x30411)+P44(x30412)+~E(x30411,x30412) % 112.37/112.13 % 112.37/112.13 %------------------------------------------- % 112.37/112.16 cnf(10404,plain, % 112.37/112.16 (~E(f317(a102,x104041),x104041)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(10414,plain, % 112.37/112.16 (~E(f317(a102,x104141),x104141)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(10427,plain, % 112.37/112.16 (~E(f317(a102,x104271),x104271)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(10432,plain, % 112.37/112.16 (~P1(f317(f317(f162(x104321),f103(x104321)),x104322))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(10435,plain, % 112.37/112.16 (~P1(f317(f317(f162(x104351),f103(x104351)),x104352))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(10438,plain, % 112.37/112.16 (~E(f317(a102,x104381),x104381)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(10441,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x104411),f2(a899)))), % 112.37/112.16 inference(rename_variables,[],[4615])). % 112.37/112.16 cnf(10444,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x104441),f2(a899)))), % 112.37/112.16 inference(rename_variables,[],[4615])). % 112.37/112.16 cnf(10461,plain, % 112.37/112.16 (~P1(f317(f317(f224(a899),f317(a102,x104611)),x104611))), % 112.37/112.16 inference(rename_variables,[],[4619])). % 112.37/112.16 cnf(10464,plain, % 112.37/112.16 (~E(f317(f317(f141(x104641),x104642),x104643),x104643)), % 112.37/112.16 inference(rename_variables,[],[4591])). % 112.37/112.16 cnf(10470,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x104701),f2(a899)))), % 112.37/112.16 inference(rename_variables,[],[4615])). % 112.37/112.16 cnf(10473,plain, % 112.37/112.16 (E(f317(f274(x104731,x104731),f253(x104731,x104732)),x104732)), % 112.37/112.16 inference(rename_variables,[],[3398])). % 112.37/112.16 cnf(10476,plain, % 112.37/112.16 (E(f317(f274(x104761,x104761),f253(x104761,x104762)),x104762)), % 112.37/112.16 inference(rename_variables,[],[3398])). % 112.37/112.16 cnf(10481,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x104811),x104811))), % 112.37/112.16 inference(rename_variables,[],[4611])). % 112.37/112.16 cnf(10486,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),f317(f317(f74(a899),x104861),x104862)),x104862))), % 112.37/112.16 inference(rename_variables,[],[4633])). % 112.37/112.16 cnf(10489,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),f317(f317(f74(a899),x104891),x104892)),x104892))), % 112.37/112.16 inference(rename_variables,[],[4633])). % 112.37/112.16 cnf(10510,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x105101),x105101))), % 112.37/112.16 inference(rename_variables,[],[4611])). % 112.37/112.16 cnf(10513,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),f41(a899,x105131,x105132)),x105131))), % 112.37/112.16 inference(rename_variables,[],[3886])). % 112.37/112.16 cnf(10534,plain, % 112.37/112.16 (E(f317(f30(a899),f317(f272(a899),x105341)),x105341)), % 112.37/112.16 inference(rename_variables,[],[3332])). % 112.37/112.16 cnf(10542,plain, % 112.37/112.16 (~E(f317(a102,x105421),x105421)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(10547,plain, % 112.37/112.16 (~E(f317(a102,x105471),x105471)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(10550,plain, % 112.37/112.16 (~E(f317(a102,x105501),x105501)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(10555,plain, % 112.37/112.16 (P1(f317(f317(f225(a899),x105551),f317(a102,x105551)))), % 112.37/112.16 inference(rename_variables,[],[3504])). % 112.37/112.16 cnf(10564,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x105641),x105641))), % 112.37/112.16 inference(rename_variables,[],[3438])). % 112.37/112.16 cnf(10571,plain, % 112.37/112.16 (E(f317(f274(x105711,x105711),f253(x105711,x105712)),x105712)), % 112.37/112.16 inference(rename_variables,[],[3398])). % 112.37/112.16 cnf(10574,plain, % 112.37/112.16 (E(f317(f274(x105741,x105741),f253(x105741,x105742)),x105742)), % 112.37/112.16 inference(rename_variables,[],[3398])). % 112.37/112.16 cnf(10591,plain, % 112.37/112.16 (P1(f317(f317(f224(a1),x105911),x105911))), % 112.37/112.16 inference(rename_variables,[],[3439])). % 112.37/112.16 cnf(10596,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x105961),f2(a899)))), % 112.37/112.16 inference(rename_variables,[],[4615])). % 112.37/112.16 cnf(10599,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x105991,a895)),x105992),f232(f906(x105991,a895))))), % 112.37/112.16 inference(rename_variables,[],[3812])). % 112.37/112.16 cnf(10604,plain, % 112.37/112.16 (~P1(f317(f317(f162(x106041),f103(x106041)),x106042))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(10633,plain, % 112.37/112.16 (~E(f317(f317(f141(x106331),x106332),x106333),x106333)), % 112.37/112.16 inference(rename_variables,[],[4591])). % 112.37/112.16 cnf(10636,plain, % 112.37/112.16 (~E(f317(a102,x106361),f2(a899))), % 112.37/112.16 inference(rename_variables,[],[4584])). % 112.37/112.16 cnf(10647,plain, % 112.37/112.16 (P1(f317(f317(f224(a1),x106471),x106471))), % 112.37/112.16 inference(rename_variables,[],[3439])). % 112.37/112.16 cnf(10652,plain, % 112.37/112.16 (~E(f317(a102,x106521),x106521)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(10655,plain, % 112.37/112.16 (~P1(f317(f317(f178(f906(x106551,f906(x106552,a895))),x106553),x106554))), % 112.37/112.16 inference(rename_variables,[],[4636])). % 112.37/112.16 cnf(10662,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x106621),x106621))), % 112.37/112.16 inference(rename_variables,[],[3438])). % 112.37/112.16 cnf(10675,plain, % 112.37/112.16 (P1(f317(f317(f225(a899),x106751),f317(a102,x106751)))), % 112.37/112.16 inference(rename_variables,[],[3504])). % 112.37/112.16 cnf(10696,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x106961,a895)),x106962),f232(f906(x106961,a895))))), % 112.37/112.16 inference(rename_variables,[],[3812])). % 112.37/112.16 cnf(10699,plain, % 112.37/112.16 (~P1(f317(f317(f162(x106991),f103(x106991)),x106992))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(10722,plain, % 112.37/112.16 (~P1(f317(f317(f162(x107221),f103(x107221)),x107222))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(10729,plain, % 112.37/112.16 (~P1(f317(f317(f162(x107291),f103(x107291)),x107292))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(10740,plain, % 112.37/112.16 (~E(f317(a102,x107401),f2(a899))), % 112.37/112.16 inference(rename_variables,[],[4584])). % 112.37/112.16 cnf(10745,plain, % 112.37/112.16 (P1(f317(f317(f319(x107451),x107452),f232(f906(x107451,a895))))), % 112.37/112.16 inference(rename_variables,[],[3587])). % 112.37/112.16 cnf(10752,plain, % 112.37/112.16 (~P1(f317(f317(f162(x107521),f103(x107521)),x107522))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(10757,plain, % 112.37/112.16 (P1(f317(f317(f225(a899),x107571),f317(a102,x107571)))), % 112.37/112.16 inference(rename_variables,[],[3504])). % 112.37/112.16 cnf(10760,plain, % 112.37/112.16 (~P1(f317(f317(f162(x107601),f103(x107601)),x107602))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(10763,plain, % 112.37/112.16 (~P1(f317(f317(f162(x107631),f103(x107631)),x107632))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(10766,plain, % 112.37/112.16 (~P1(f317(f57(x107661,x107662,f178(f906(x107661,a895))),x107663))), % 112.37/112.16 inference(rename_variables,[],[4632])). % 112.37/112.16 cnf(10769,plain, % 112.37/112.16 (~P1(f317(f57(x107691,x107692,f178(f906(x107691,a895))),x107693))), % 112.37/112.16 inference(rename_variables,[],[4632])). % 112.37/112.16 cnf(10772,plain, % 112.37/112.16 (~P1(f317(f317(f178(f906(x107721,f906(x107722,a895))),x107723),x107724))), % 112.37/112.16 inference(rename_variables,[],[4636])). % 112.37/112.16 cnf(10775,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x107751),f2(a899)))), % 112.37/112.16 inference(rename_variables,[],[4615])). % 112.37/112.16 cnf(10780,plain, % 112.37/112.16 (~P1(f317(f317(f162(x107801),f103(x107801)),x107802))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(10791,plain, % 112.37/112.16 (~E(f317(a102,x107911),x107911)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(10816,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x108161),x108161))), % 112.37/112.16 inference(rename_variables,[],[3438])). % 112.37/112.16 cnf(10819,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x108191),f317(f317(f75(a899),x108191),x108191)))), % 112.37/112.16 inference(rename_variables,[],[3696])). % 112.37/112.16 cnf(10822,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x108221),f317(f317(f75(a899),x108221),x108221)))), % 112.37/112.16 inference(rename_variables,[],[3696])). % 112.37/112.16 cnf(10825,plain, % 112.37/112.16 (P1(f317(f317(f225(a899),x108251),f317(a102,f317(f317(f74(a899),x108252),x108251))))), % 112.37/112.16 inference(rename_variables,[],[3879])). % 112.37/112.16 cnf(10830,plain, % 112.37/112.16 (P1(f317(f317(f225(a899),x108301),f317(a102,x108301)))), % 112.37/112.16 inference(rename_variables,[],[3504])). % 112.37/112.16 cnf(10833,plain, % 112.37/112.16 (P1(f317(f317(f225(a899),x108331),f317(a102,x108331)))), % 112.37/112.16 inference(rename_variables,[],[3504])). % 112.37/112.16 cnf(10836,plain, % 112.37/112.16 (P1(f317(f317(f319(x108361),x108362),f232(f906(x108361,a895))))), % 112.37/112.16 inference(rename_variables,[],[3587])). % 112.37/112.16 cnf(10855,plain, % 112.37/112.16 (~P1(f317(f317(f224(a899),f317(a102,x108551)),x108551))), % 112.37/112.16 inference(rename_variables,[],[4619])). % 112.37/112.16 cnf(10858,plain, % 112.37/112.16 (~P1(f317(f317(f224(a899),f317(a102,x108581)),x108581))), % 112.37/112.16 inference(rename_variables,[],[4619])). % 112.37/112.16 cnf(10861,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),f317(f317(f74(a899),x108611),x108612)),x108612))), % 112.37/112.16 inference(rename_variables,[],[4633])). % 112.37/112.16 cnf(10864,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),f317(f317(f74(a899),x108641),x108642)),x108642))), % 112.37/112.16 inference(rename_variables,[],[4633])). % 112.37/112.16 cnf(10867,plain, % 112.37/112.16 (P1(f317(f232(f906(x108671,a895)),x108672))), % 112.37/112.16 inference(rename_variables,[],[3497])). % 112.37/112.16 cnf(10870,plain, % 112.37/112.16 (E(f317(f30(a899),f317(f272(a899),x108701)),x108701)), % 112.37/112.16 inference(rename_variables,[],[3332])). % 112.37/112.16 cnf(10873,plain, % 112.37/112.16 (P1(f317(f317(f225(a899),x108731),f317(a102,x108731)))), % 112.37/112.16 inference(rename_variables,[],[3504])). % 112.37/112.16 cnf(10880,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x108801),x108801))), % 112.37/112.16 inference(rename_variables,[],[3438])). % 112.37/112.16 cnf(10885,plain, % 112.37/112.16 (P1(f317(f317(f224(a1),x108851),x108851))), % 112.37/112.16 inference(rename_variables,[],[3439])). % 112.37/112.16 cnf(10888,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x108881,a895)),f317(f162(x108881),f317(f126(x108881,x108882),x108883))),f317(f162(x108881),x108883)))), % 112.37/112.16 inference(rename_variables,[],[4072])). % 112.37/112.16 cnf(10897,plain, % 112.37/112.16 (E(f317(f274(x108971,x108971),f253(x108971,x108972)),x108972)), % 112.37/112.16 inference(rename_variables,[],[3398])). % 112.37/112.16 cnf(10900,plain, % 112.37/112.16 (P1(f317(f232(f906(x109001,a895)),x109002))), % 112.37/112.16 inference(rename_variables,[],[3497])). % 112.37/112.16 cnf(10903,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),f2(a899)),x109031))), % 112.37/112.16 inference(rename_variables,[],[3459])). % 112.37/112.16 cnf(10906,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x109061,a895)),f178(f906(x109061,a895))),x109062))), % 112.37/112.16 inference(rename_variables,[],[3878])). % 112.37/112.16 cnf(10909,plain, % 112.37/112.16 (P1(f317(f232(f906(x109091,a895)),x109092))), % 112.37/112.16 inference(rename_variables,[],[3497])). % 112.37/112.16 cnf(10912,plain, % 112.37/112.16 (P1(f317(f232(f906(x109121,a895)),x109122))), % 112.37/112.16 inference(rename_variables,[],[3497])). % 112.37/112.16 cnf(10915,plain, % 112.37/112.16 (P1(f317(f232(f906(x109151,a895)),x109152))), % 112.37/112.16 inference(rename_variables,[],[3497])). % 112.37/112.16 cnf(10918,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x109181),f317(f317(f75(a899),x109181),x109181)))), % 112.37/112.16 inference(rename_variables,[],[3696])). % 112.37/112.16 cnf(10958,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x109581),x109581))), % 112.37/112.16 inference(rename_variables,[],[3438])). % 112.37/112.16 cnf(10971,plain, % 112.37/112.16 (~P1(f317(f317(f162(x109711),f103(x109711)),x109712))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(10978,plain, % 112.37/112.16 (P1(f317(f317(f225(a899),x109781),f317(a102,x109781)))), % 112.37/112.16 inference(rename_variables,[],[3504])). % 112.37/112.16 cnf(10981,plain, % 112.37/112.16 (P1(f317(f317(f224(a1),x109811),x109811))), % 112.37/112.16 inference(rename_variables,[],[3439])). % 112.37/112.16 cnf(10986,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x109861),f2(a899)))), % 112.37/112.16 inference(rename_variables,[],[4615])). % 112.37/112.16 cnf(11001,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x110011),f2(a899)))), % 112.37/112.16 inference(rename_variables,[],[4615])). % 112.37/112.16 cnf(11004,plain, % 112.37/112.16 (~P1(f317(f317(f225(f906(x110041,a895)),x110042),f178(f906(x110041,a895))))), % 112.37/112.16 inference(rename_variables,[],[4630])). % 112.37/112.16 cnf(11007,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x110071),x110071))), % 112.37/112.16 inference(rename_variables,[],[3438])). % 112.37/112.16 cnf(11010,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x110101),x110101))), % 112.37/112.16 inference(rename_variables,[],[3438])). % 112.37/112.16 cnf(11025,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x110251),x110251))), % 112.37/112.16 inference(rename_variables,[],[4611])). % 112.37/112.16 cnf(11034,plain, % 112.37/112.16 (~P1(f317(f317(f319(x110341),x110342),f178(f906(x110341,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11041,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x110411),x110411))), % 112.37/112.16 inference(rename_variables,[],[3438])). % 112.37/112.16 cnf(11044,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x110441,a895)),f317(f300(x110442,x110441,x110443),f317(f301(x110442,x110441,x110443),x110444))),x110444))), % 112.37/112.16 inference(rename_variables,[],[4299])). % 112.37/112.16 cnf(11053,plain, % 112.37/112.16 (E(f317(f300(x110531,x110531,f7(x110531)),x110532),x110532)), % 112.37/112.16 inference(rename_variables,[],[3493])). % 112.37/112.16 cnf(11058,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),f2(a899)),x110581))), % 112.37/112.16 inference(rename_variables,[],[3459])). % 112.37/112.16 cnf(11061,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x110611),x110611))), % 112.37/112.16 inference(rename_variables,[],[3438])). % 112.37/112.16 cnf(11064,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x110641),x110641))), % 112.37/112.16 inference(rename_variables,[],[4611])). % 112.37/112.16 cnf(11073,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x110731),x110731))), % 112.37/112.16 inference(rename_variables,[],[4611])). % 112.37/112.16 cnf(11084,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x110841),f317(f317(f75(a899),x110841),x110841)))), % 112.37/112.16 inference(rename_variables,[],[3696])). % 112.37/112.16 cnf(11090,plain, % 112.37/112.16 (P1(f317(f317(f225(a899),x110901),f317(a102,f317(f317(f74(a899),x110902),x110901))))), % 112.37/112.16 inference(rename_variables,[],[3879])). % 112.37/112.16 cnf(11097,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x110971),x110971))), % 112.37/112.16 inference(rename_variables,[],[3438])). % 112.37/112.16 cnf(11100,plain, % 112.37/112.16 (P1(f317(f317(f224(a1),x111001),x111001))), % 112.37/112.16 inference(rename_variables,[],[3439])). % 112.37/112.16 cnf(11103,plain, % 112.37/112.16 (~E(f317(a102,x111031),x111031)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11108,plain, % 112.37/112.16 (P1(f317(f317(f319(x111081),x111082),f232(f906(x111081,a895))))), % 112.37/112.16 inference(rename_variables,[],[3587])). % 112.37/112.16 cnf(11115,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x111151),f2(a899)))), % 112.37/112.16 inference(rename_variables,[],[4615])). % 112.37/112.16 cnf(11130,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),f2(a899)),x111301))), % 112.37/112.16 inference(rename_variables,[],[3459])). % 112.37/112.16 cnf(11137,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x111371),x111371))), % 112.37/112.16 inference(rename_variables,[],[3438])). % 112.37/112.16 cnf(11146,plain, % 112.37/112.16 (~P1(f317(f317(f319(x111461),x111462),f178(f906(x111461,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11154,plain, % 112.37/112.16 (P1(f317(f317(f319(x111541),x111542),f232(f906(x111541,a895))))), % 112.37/112.16 inference(rename_variables,[],[3587])). % 112.37/112.16 cnf(11157,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(f900(x111571),f900(x111571))),f317(f317(f242(f900(x111571),f900(x111571)),x111572),f103(x111571))),f135(x111571,x111573)))), % 112.37/112.16 inference(rename_variables,[],[4638])). % 112.37/112.16 cnf(11167,plain, % 112.37/112.16 (~P1(f317(f317(f319(x111671),x111672),f178(f906(x111671,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11170,plain, % 112.37/112.16 (~P1(f317(f317(f319(x111701),x111702),f178(f906(x111701,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11173,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x111731,a895)),x111732),f317(f317(f299(x111731),x111733),x111732)))), % 112.37/112.16 inference(rename_variables,[],[3876])). % 112.37/112.16 cnf(11176,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),x111761),x111761))), % 112.37/112.16 inference(rename_variables,[],[3438])). % 112.37/112.16 cnf(11179,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x111791,a895)),x111792),f317(f317(f299(x111791),x111793),x111792)))), % 112.37/112.16 inference(rename_variables,[],[3876])). % 112.37/112.16 cnf(11182,plain, % 112.37/112.16 (E(f317(f300(x111821,x111821,f7(x111821)),x111822),x111822)), % 112.37/112.16 inference(rename_variables,[],[3493])). % 112.37/112.16 cnf(11197,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x111971,a895)),x111972),f317(f317(f299(x111971),x111973),x111972)))), % 112.37/112.16 inference(rename_variables,[],[3876])). % 112.37/112.16 cnf(11208,plain, % 112.37/112.16 (~E(f317(a102,x112081),f2(a899))), % 112.37/112.16 inference(rename_variables,[],[4584])). % 112.37/112.16 cnf(11211,plain, % 112.37/112.16 (~P1(f317(f317(f162(x112111),f103(x112111)),x112112))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(11224,plain, % 112.37/112.16 (P1(f317(f317(f225(a899),x112241),f317(a102,x112241)))), % 112.37/112.16 inference(rename_variables,[],[3504])). % 112.37/112.16 cnf(11234,plain, % 112.37/112.16 (~E(f317(f300(x112341,f906(x112341,a895),x112342),x112343),f317(f298(x112341),x112343))), % 112.37/112.16 inference(rename_variables,[],[4620])). % 112.37/112.16 cnf(11237,plain, % 112.37/112.16 (~P1(f317(f317(f319(x112371),x112372),f178(f906(x112371,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11240,plain, % 112.37/112.16 (~P1(f317(f317(f319(x112401),x112402),f178(f906(x112401,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11243,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(x112431,x112431)),f317(f317(f242(x112431,x112431),x112432),x112433)),f143(x112431,f103(f906(x112431,a899)))))), % 112.37/112.16 inference(rename_variables,[],[4637])). % 112.37/112.16 cnf(11246,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(x112461,x112461)),f317(f317(f242(x112461,x112461),x112462),x112463)),f143(x112461,f103(f906(x112461,a899)))))), % 112.37/112.16 inference(rename_variables,[],[4637])). % 112.37/112.16 cnf(11251,plain, % 112.37/112.16 (~P1(f317(f317(f319(x112511),x112512),f178(f906(x112511,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11254,plain, % 112.37/112.16 (P1(f317(f317(f319(f905(x112541,x112541)),f317(f317(f242(x112541,x112541),x112542),x112542)),f297(x112541,x112543)))), % 112.37/112.16 inference(rename_variables,[],[4063])). % 112.37/112.16 cnf(11257,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x112571,a895)),x112572),f232(f906(x112571,a895))))), % 112.37/112.16 inference(rename_variables,[],[3812])). % 112.37/112.16 cnf(11260,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x112601,a895)),f317(f162(x112601),f166(x112601,x112602,x112603))),f317(f162(x112601),x112602)))), % 112.37/112.16 inference(rename_variables,[],[4119])). % 112.37/112.16 cnf(11276,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x112761,a895)),f178(f906(x112761,a895))),x112762))), % 112.37/112.16 inference(rename_variables,[],[3878])). % 112.37/112.16 cnf(11287,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(f900(x112871),f900(x112871))),f317(f317(f242(f900(x112871),f900(x112871)),x112872),f103(x112871))),f137(x112871,x112873)))), % 112.37/112.16 inference(rename_variables,[],[4639])). % 112.37/112.16 cnf(11298,plain, % 112.37/112.16 (~E(f317(a102,x112981),x112981)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11301,plain, % 112.37/112.16 (~E(f317(a102,x113011),x113011)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11308,plain, % 112.37/112.16 (~E(f317(a102,x113081),f2(a899))), % 112.37/112.16 inference(rename_variables,[],[4584])). % 112.37/112.16 cnf(11313,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x113131,a895)),x113132),x113132))), % 112.37/112.16 inference(rename_variables,[],[3727])). % 112.37/112.16 cnf(11320,plain, % 112.37/112.16 (~E(f317(a102,x113201),x113201)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11323,plain, % 112.37/112.16 (~E(f317(a102,x113231),x113231)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11328,plain, % 112.37/112.16 (P24(x113281,x113281,f7(x113281),x113282)), % 112.37/112.16 inference(rename_variables,[],[3671])). % 112.37/112.16 cnf(11333,plain, % 112.37/112.16 (~E(f317(f300(x113331,f906(x113331,a895),x113332),x113333),f317(f298(x113331),x113333))), % 112.37/112.16 inference(rename_variables,[],[4620])). % 112.37/112.16 cnf(11340,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x113401,a895)),x113402),f232(f906(x113401,a895))))), % 112.37/112.16 inference(rename_variables,[],[3812])). % 112.37/112.16 cnf(11356,plain, % 112.37/112.16 (~P1(f317(f317(f319(x113561),x113562),f178(f906(x113561,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11359,plain, % 112.37/112.16 (~P1(f317(f317(f224(a899),f317(a102,x113591)),x113591))), % 112.37/112.16 inference(rename_variables,[],[4619])). % 112.37/112.16 cnf(11364,plain, % 112.37/112.16 (~P1(f317(f317(f319(x113641),x113642),f178(f906(x113641,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11375,plain, % 112.37/112.16 (~P1(f317(f317(f224(a899),f317(a102,x113751)),x113751))), % 112.37/112.16 inference(rename_variables,[],[4619])). % 112.37/112.16 cnf(11378,plain, % 112.37/112.16 (~P1(f317(f317(f319(x113781),x113782),f178(f906(x113781,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11387,plain, % 112.37/112.16 (P1(f317(f317(f319(f905(x113871,x113871)),f317(f317(f242(x113871,x113871),x113872),x113872)),f297(x113871,x113873)))), % 112.37/112.16 inference(rename_variables,[],[4063])). % 112.37/112.16 cnf(11390,plain, % 112.37/112.16 (P1(f317(f317(f319(x113901),x113902),f232(f906(x113901,a895))))), % 112.37/112.16 inference(rename_variables,[],[3587])). % 112.37/112.16 cnf(11393,plain, % 112.37/112.16 (P1(f317(f317(f319(x113931),x113932),f232(f906(x113931,a895))))), % 112.37/112.16 inference(rename_variables,[],[3587])). % 112.37/112.16 cnf(11400,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(f900(x114001),f900(x114001))),f317(f317(f242(f900(x114001),f900(x114001)),x114002),f103(x114001))),f135(x114001,x114003)))), % 112.37/112.16 inference(rename_variables,[],[4638])). % 112.37/112.16 cnf(11403,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(f900(x114031),f900(x114031))),f317(f317(f242(f900(x114031),f900(x114031)),x114032),f103(x114031))),f137(x114031,x114033)))), % 112.37/112.16 inference(rename_variables,[],[4639])). % 112.37/112.16 cnf(11406,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(f900(x114061),f900(x114061))),f317(f317(f242(f900(x114061),f900(x114061)),x114062),f103(x114061))),f147(x114061,x114063)))), % 112.37/112.16 inference(rename_variables,[],[4640])). % 112.37/112.16 cnf(11411,plain, % 112.37/112.16 (~P1(f317(f317(f225(f906(x114111,a895)),x114112),f178(f906(x114111,a895))))), % 112.37/112.16 inference(rename_variables,[],[4630])). % 112.37/112.16 cnf(11414,plain, % 112.37/112.16 (~P1(f317(f317(f319(x114141),x114142),f178(f906(x114141,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11419,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x114191,a895)),x114192),f232(f906(x114191,a895))))), % 112.37/112.16 inference(rename_variables,[],[3812])). % 112.37/112.16 cnf(11426,plain, % 112.37/112.16 (~P1(f317(f317(f162(x114261),f103(x114261)),x114262))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(11431,plain, % 112.37/112.16 (~P1(f317(f317(f319(x114311),x114312),f178(f906(x114311,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11434,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(x114341,x114341)),f317(f317(f242(x114341,x114341),x114342),x114343)),f143(x114341,f103(f906(x114341,a899)))))), % 112.37/112.16 inference(rename_variables,[],[4637])). % 112.37/112.16 cnf(11437,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x114371,a895)),x114372),x114372))), % 112.37/112.16 inference(rename_variables,[],[3727])). % 112.37/112.16 cnf(11440,plain, % 112.37/112.16 (~P1(f317(f317(f319(x114401),x114402),f178(f906(x114401,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11443,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x114431,a895)),f178(f906(x114431,a895))),x114432))), % 112.37/112.16 inference(rename_variables,[],[3878])). % 112.37/112.16 cnf(11446,plain, % 112.37/112.16 (P1(f317(f317(f319(f905(x114461,x114461)),f317(f317(f242(x114461,x114461),x114462),x114462)),f297(x114461,x114463)))), % 112.37/112.16 inference(rename_variables,[],[4063])). % 112.37/112.16 cnf(11457,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(f900(x114571),f900(x114571))),f317(f317(f242(f900(x114571),f900(x114571)),x114572),f103(x114571))),f147(x114571,x114573)))), % 112.37/112.16 inference(rename_variables,[],[4640])). % 112.37/112.16 cnf(11464,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(f900(x114641),f900(x114641))),f317(f317(f242(f900(x114641),f900(x114641)),f103(x114641)),x114642)),f135(x114641,x114643)))), % 112.37/112.16 inference(rename_variables,[],[4642])). % 112.37/112.16 cnf(11472,plain, % 112.37/112.16 (P1(f317(f317(f319(x114721),x114722),f232(f906(x114721,a895))))), % 112.37/112.16 inference(rename_variables,[],[3587])). % 112.37/112.16 cnf(11477,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x114771,a895)),f178(f906(x114771,a895))),x114772))), % 112.37/112.16 inference(rename_variables,[],[3878])). % 112.37/112.16 cnf(11480,plain, % 112.37/112.16 (~P1(f317(f317(f319(x114801),x114802),f178(f906(x114801,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11483,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x114831,a895)),x114832),f232(f906(x114831,a895))))), % 112.37/112.16 inference(rename_variables,[],[3812])). % 112.37/112.16 cnf(11488,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x114881,a895)),f178(f906(x114881,a895))),x114882))), % 112.37/112.16 inference(rename_variables,[],[3878])). % 112.37/112.16 cnf(11501,plain, % 112.37/112.16 (P1(f317(f232(f906(x115011,a895)),x115012))), % 112.37/112.16 inference(rename_variables,[],[3497])). % 112.37/112.16 cnf(11509,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(f900(x115091),f900(x115091))),f317(f317(f242(f900(x115091),f900(x115091)),x115092),f103(x115091))),f135(x115091,x115093)))), % 112.37/112.16 inference(rename_variables,[],[4638])). % 112.37/112.16 cnf(11512,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(f900(x115121),f900(x115121))),f317(f317(f242(f900(x115121),f900(x115121)),x115122),f103(x115121))),f137(x115121,x115123)))), % 112.37/112.16 inference(rename_variables,[],[4639])). % 112.37/112.16 cnf(11515,plain, % 112.37/112.16 (~E(f317(f317(f141(x115151),x115152),x115153),x115153)), % 112.37/112.16 inference(rename_variables,[],[4591])). % 112.37/112.16 cnf(11518,plain, % 112.37/112.16 (~E(f317(a102,x115181),x115181)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11521,plain, % 112.37/112.16 (~P1(f317(f317(f319(x115211),x115212),f178(f906(x115211,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11526,plain, % 112.37/112.16 (~P1(f317(f317(f319(x115261),x115262),f178(f906(x115261,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11529,plain, % 112.37/112.16 (~P1(f317(f317(f319(x115291),x115292),f178(f906(x115291,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11532,plain, % 112.37/112.16 (P1(f317(f317(f319(f905(f900(x115321),f900(x115321))),f317(f317(f242(f900(x115321),f900(x115321)),x115322),x115322)),f148(x115321,f297(x115321,x115323))))), % 112.37/112.16 inference(rename_variables,[],[4196])). % 112.37/112.16 cnf(11535,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(f900(x115351),f900(x115351))),f317(f317(f242(f900(x115351),f900(x115351)),x115352),f103(x115351))),f135(x115351,x115353)))), % 112.37/112.16 inference(rename_variables,[],[4638])). % 112.37/112.16 cnf(11545,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(x115451,x115451)),f317(f317(f242(x115451,x115451),x115452),x115453)),f143(x115451,f103(f906(x115451,a899)))))), % 112.37/112.16 inference(rename_variables,[],[4637])). % 112.37/112.16 cnf(11548,plain, % 112.37/112.16 (~P1(f317(f317(f319(x115481),x115482),f178(f906(x115481,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11551,plain, % 112.37/112.16 (~P1(f317(f317(f319(x115511),x115512),f178(f906(x115511,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11554,plain, % 112.37/112.16 (P1(f317(f317(f319(x115541),x115542),f232(f906(x115541,a895))))), % 112.37/112.16 inference(rename_variables,[],[3587])). % 112.37/112.16 cnf(11557,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x115571),f2(a899)))), % 112.37/112.16 inference(rename_variables,[],[4615])). % 112.37/112.16 cnf(11562,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(x115621,x115621)),f317(f317(f242(x115621,x115621),x115622),x115623)),f143(x115621,f103(f906(x115621,a899)))))), % 112.37/112.16 inference(rename_variables,[],[4637])). % 112.37/112.16 cnf(11571,plain, % 112.37/112.16 (~E(f317(f300(x115711,f906(x115711,a895),x115712),x115713),f317(f298(x115711),x115713))), % 112.37/112.16 inference(rename_variables,[],[4620])). % 112.37/112.16 cnf(11574,plain, % 112.37/112.16 (~E(f317(f300(x115741,f906(x115741,a895),x115742),x115743),f317(f298(x115741),x115743))), % 112.37/112.16 inference(rename_variables,[],[4620])). % 112.37/112.16 cnf(11579,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(f900(x115791),f900(x115791))),f317(f317(f242(f900(x115791),f900(x115791)),x115792),f103(x115791))),f135(x115791,x115793)))), % 112.37/112.16 inference(rename_variables,[],[4638])). % 112.37/112.16 cnf(11585,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(f900(x115851),f900(x115851))),f317(f317(f242(f900(x115851),f900(x115851)),x115852),f103(x115851))),f135(x115851,x115853)))), % 112.37/112.16 inference(rename_variables,[],[4638])). % 112.37/112.16 cnf(11588,plain, % 112.37/112.16 (~P1(f317(f317(f319(x115881),x115882),f178(f906(x115881,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11593,plain, % 112.37/112.16 (~P1(f317(f317(f319(x115931),x115932),f178(f906(x115931,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11596,plain, % 112.37/112.16 (~P1(f317(f317(f319(x115961),x115962),f178(f906(x115961,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11599,plain, % 112.37/112.16 (~P1(f317(f317(f319(x115991),x115992),f178(f906(x115991,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11602,plain, % 112.37/112.16 (~P1(f317(f317(f319(x116021),x116022),f178(f906(x116021,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11605,plain, % 112.37/112.16 (P1(f317(f317(f319(x116051),f317(x116052,x116053)),f317(f300(x116054,x116051,x116052),f232(f906(x116054,a895)))))), % 112.37/112.16 inference(rename_variables,[],[4029])). % 112.37/112.16 cnf(11608,plain, % 112.37/112.16 (~P1(f317(f317(f319(f905(x116081,x116081)),f317(f317(f242(x116081,x116081),x116082),x116083)),f143(x116081,f103(f906(x116081,a899)))))), % 112.37/112.16 inference(rename_variables,[],[4637])). % 112.37/112.16 cnf(11616,plain, % 112.37/112.16 (E(f104(x116161,f103(x116161)),f103(x116161))), % 112.37/112.16 inference(rename_variables,[],[3283])). % 112.37/112.16 cnf(11619,plain, % 112.37/112.16 (~E(f317(a102,x116191),x116191)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11626,plain, % 112.37/112.16 (~E(f317(a102,x116261),x116261)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11631,plain, % 112.37/112.16 (E(f317(f274(x116311,x116311),f253(x116311,x116312)),x116312)), % 112.37/112.16 inference(rename_variables,[],[3398])). % 112.37/112.16 cnf(11634,plain, % 112.37/112.16 (E(f317(f274(x116341,x116341),f253(x116341,x116342)),x116342)), % 112.37/112.16 inference(rename_variables,[],[3398])). % 112.37/112.16 cnf(11640,plain, % 112.37/112.16 (~E(f317(a102,x116401),x116401)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11645,plain, % 112.37/112.16 (~E(f317(f317(f74(a1),x116451),x116451),a87)), % 112.37/112.16 inference(rename_variables,[],[4589])). % 112.37/112.16 cnf(11652,plain, % 112.37/112.16 (E(f317(f317(f3(a899),f2(a899)),x116521),f2(a899))), % 112.37/112.16 inference(rename_variables,[],[3354])). % 112.37/112.16 cnf(11655,plain, % 112.37/112.16 (P1(f317(f317(f224(f906(x116551,a895)),x116552),f232(f906(x116551,a895))))), % 112.37/112.16 inference(rename_variables,[],[3812])). % 112.37/112.16 cnf(11662,plain, % 112.37/112.16 (E(f317(f317(f74(a1),f317(f317(f75(a1),x116621),f317(f317(f31(a1),x116622),x116621))),f41(a1,x116622,x116621)),x116622)), % 112.37/112.16 inference(rename_variables,[],[3979])). % 112.37/112.16 cnf(11686,plain, % 112.37/112.16 (~E(f317(a102,x116861),x116861)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11689,plain, % 112.37/112.16 (~E(f317(a102,x116891),x116891)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11715,plain, % 112.37/112.16 (~P1(f317(f317(f162(x117151),f103(x117151)),x117152))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(11721,plain, % 112.37/112.16 (P1(f317(f317(f225(a899),f2(a899)),f317(a102,x117211)))), % 112.37/112.16 inference(rename_variables,[],[3516])). % 112.37/112.16 cnf(11722,plain, % 112.37/112.16 (~E(f317(a102,x117221),x117221)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11725,plain, % 112.37/112.16 (P1(f317(f317(f319(x117251),x117252),f232(f906(x117251,a895))))), % 112.37/112.16 inference(rename_variables,[],[3587])). % 112.37/112.16 cnf(11737,plain, % 112.37/112.16 (~E(f317(a102,x117371),x117371)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11740,plain, % 112.37/112.16 (P1(f317(f317(f224(a1),x117401),x117401))), % 112.37/112.16 inference(rename_variables,[],[3439])). % 112.37/112.16 cnf(11747,plain, % 112.37/112.16 (P1(f317(f61(x117471,x117472,x117473,x117474,f178(f906(x117471,a895))),x117474))), % 112.37/112.16 inference(rename_variables,[],[4338])). % 112.37/112.16 cnf(11748,plain, % 112.37/112.16 (E(f317(f274(x117481,x117481),f253(x117481,x117482)),x117482)), % 112.37/112.16 inference(rename_variables,[],[3398])). % 112.37/112.16 cnf(11761,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),f317(f317(f74(a899),x117611),x117612)),x117612))), % 112.37/112.16 inference(rename_variables,[],[4633])). % 112.37/112.16 cnf(11764,plain, % 112.37/112.16 (~P1(f317(f317(f225(a1),f317(f90(a1),x117641)),f2(a1)))), % 112.37/112.16 inference(rename_variables,[],[4626])). % 112.37/112.16 cnf(11787,plain, % 112.37/112.16 (E(f317(f274(x117871,x117871),f253(x117871,x117872)),x117872)), % 112.37/112.16 inference(rename_variables,[],[3398])). % 112.37/112.16 cnf(11792,plain, % 112.37/112.16 (E(f317(f274(x117921,x117921),f253(x117921,x117922)),x117922)), % 112.37/112.16 inference(rename_variables,[],[3398])). % 112.37/112.16 cnf(11795,plain, % 112.37/112.16 (~P1(f317(f317(f225(a1),f317(f90(a1),x117951)),f2(a1)))), % 112.37/112.16 inference(rename_variables,[],[4626])). % 112.37/112.16 cnf(11800,plain, % 112.37/112.16 (~E(f317(a102,x118001),x118001)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11809,plain, % 112.37/112.16 (~P1(f317(f317(f162(x118091),f103(x118091)),x118092))), % 112.37/112.16 inference(rename_variables,[],[4618])). % 112.37/112.16 cnf(11832,plain, % 112.37/112.16 (~P1(f317(f317(f225(a1),f317(f90(a1),x118321)),f2(a1)))), % 112.37/112.16 inference(rename_variables,[],[4626])). % 112.37/112.16 cnf(11835,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),x118351),f2(a899)))), % 112.37/112.16 inference(rename_variables,[],[4615])). % 112.37/112.16 cnf(11836,plain, % 112.37/112.16 (P1(f317(f317(f225(a899),x118361),f317(a102,x118361)))), % 112.37/112.16 inference(rename_variables,[],[3504])). % 112.37/112.16 cnf(11839,plain, % 112.37/112.16 (~P1(f317(f317(f225(a1),f317(f90(a1),x118391)),f2(a1)))), % 112.37/112.16 inference(rename_variables,[],[4626])). % 112.37/112.16 cnf(11842,plain, % 112.37/112.16 (~P1(f317(f317(f319(x118421),x118422),f178(f906(x118421,a895))))), % 112.37/112.16 inference(rename_variables,[],[4622])). % 112.37/112.16 cnf(11843,plain, % 112.37/112.16 (P1(f317(f317(f319(f906(x118431,a895)),x118432),f317(f298(x118431),x118432)))), % 112.37/112.16 inference(rename_variables,[],[3795])). % 112.37/112.16 cnf(11858,plain, % 112.37/112.16 (~P1(f317(f317(f224(a899),f317(a102,x118581)),x118581))), % 112.37/112.16 inference(rename_variables,[],[4619])). % 112.37/112.16 cnf(11859,plain, % 112.37/112.16 (~E(f317(a102,x118591),x118591)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11869,plain, % 112.37/112.16 (~P1(f317(f317(f225(a899),f317(f317(f74(a899),x118691),x118692)),x118691))), % 112.37/112.16 inference(rename_variables,[],[4634])). % 112.37/112.16 cnf(11872,plain, % 112.37/112.16 (~P1(f317(f317(f225(a1),f317(f90(a1),x118721)),f2(a1)))), % 112.37/112.16 inference(rename_variables,[],[4626])). % 112.37/112.16 cnf(11875,plain, % 112.37/112.16 (~E(f317(a102,x118751),x118751)), % 112.37/112.16 inference(rename_variables,[],[4578])). % 112.37/112.16 cnf(11888,plain, % 112.37/112.16 (P1(f317(f317(f319(x118881),x118882),f317(f317(f299(x118881),x118882),x118883)))), % 112.37/112.16 inference(rename_variables,[],[3743])). % 112.37/112.16 cnf(11889,plain, % 112.37/112.16 (~P1(f317(f317(f224(a1),f2(a1)),f317(f73(a1),f317(f90(a1),f317(a102,x118891)))))), % 112.37/112.16 inference(rename_variables,[],[4635])). % 112.37/112.16 cnf(11892,plain, % 112.37/112.16 (P1(f317(f317(f225(a899),f317(f317(f3(a899),x118921),x118922)),f317(a102,x118921)))), % 112.37/112.16 inference(rename_variables,[],[3881])). % 112.37/112.16 cnf(11895,plain, % 112.37/112.16 (P1(f317(f317(f224(a899),f41(a899,x118951,x118952)),x118951))), % 112.37/112.16 inference(rename_variables,[],[3886])). % 112.37/112.16 cnf(11901,plain, % 112.37/112.16 (E(f317(f274(x119011,x119011),f253(x119011,x119012)),x119012)), % 112.37/112.16 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(11906,plain, % 112.37/112.17 (E(f317(f317(f124(x119061),f159(x119061,x119062,x119063)),f159(x119061,x119064,x119063)),f317(f317(f124(x119061),f159(x119061,x119064,x119063)),f159(x119061,x119062,x119063)))), % 112.37/112.17 inference(rename_variables,[],[3993])). % 112.37/112.17 cnf(11911,plain, % 112.37/112.17 (~P1(f317(f317(f224(a899),f317(a102,x119111)),x119111))), % 112.37/112.17 inference(rename_variables,[],[4619])). % 112.37/112.17 cnf(11920,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x119201),x119201))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(11923,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),f41(a899,x119231,x119232)),x119231))), % 112.37/112.17 inference(rename_variables,[],[3886])). % 112.37/112.17 cnf(11924,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),f2(a899)),x119241))), % 112.37/112.17 inference(rename_variables,[],[3459])). % 112.37/112.17 cnf(11941,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x119411),x119411))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(11944,plain, % 112.37/112.17 (P1(f317(f317(f319(x119441),f317(x119442,x119443)),f317(f300(x119444,x119441,x119442),f232(f906(x119444,a895)))))), % 112.37/112.17 inference(rename_variables,[],[4029])). % 112.37/112.17 cnf(11945,plain, % 112.37/112.17 (~P1(f317(f317(f224(a899),f317(a102,x119451)),x119451))), % 112.37/112.17 inference(rename_variables,[],[4619])). % 112.37/112.17 cnf(11948,plain, % 112.37/112.17 (P1(f317(f317(f319(x119481),f317(x119482,x119483)),f317(f300(x119484,x119481,x119482),f232(f906(x119484,a895)))))), % 112.37/112.17 inference(rename_variables,[],[4029])). % 112.37/112.17 cnf(11949,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),f317(f317(f74(a899),x119491),x119492)),x119492))), % 112.37/112.17 inference(rename_variables,[],[4633])). % 112.37/112.17 cnf(11954,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),f317(f317(f74(a899),x119541),x119542)),x119541))), % 112.37/112.17 inference(rename_variables,[],[4634])). % 112.37/112.17 cnf(11957,plain, % 112.37/112.17 (~P1(f317(f317(f162(x119571),f103(x119571)),x119572))), % 112.37/112.17 inference(rename_variables,[],[4618])). % 112.37/112.17 cnf(11960,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x119601),x119601))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(11968,plain, % 112.37/112.17 (~P34(x119681,x119682,f103(x119681))), % 112.37/112.17 inference(rename_variables,[],[4598])). % 112.37/112.17 cnf(11971,plain, % 112.37/112.17 (P1(f317(f317(f319(x119711),x119712),f232(f906(x119711,a895))))), % 112.37/112.17 inference(rename_variables,[],[3587])). % 112.37/112.17 cnf(11972,plain, % 112.37/112.17 (~P1(f317(f317(f224(a899),f317(a102,x119721)),x119721))), % 112.37/112.17 inference(rename_variables,[],[4619])). % 112.37/112.17 cnf(11985,plain, % 112.37/112.17 (~P1(f317(f317(f319(x119851),x119852),f178(f906(x119851,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(11988,plain, % 112.37/112.17 (E(f317(f317(f18(x119881,x119882),x119883),x119884),x119883)), % 112.37/112.17 inference(rename_variables,[],[3429])). % 112.37/112.17 cnf(11991,plain, % 112.37/112.17 (E(f317(f317(f18(x119911,x119912),x119913),x119914),x119913)), % 112.37/112.17 inference(rename_variables,[],[3429])). % 112.37/112.17 cnf(12003,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),f2(a899)),f317(a102,x120031)))), % 112.37/112.17 inference(rename_variables,[],[3516])). % 112.37/112.17 cnf(12006,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x120061),x120061))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12011,plain, % 112.37/112.17 (P1(f317(f29(x120111),f317(f162(x120111),x120112)))), % 112.37/112.17 inference(rename_variables,[],[3478])). % 112.37/112.17 cnf(12014,plain, % 112.37/112.17 (P1(f317(f29(x120141),f317(f162(x120141),x120142)))), % 112.37/112.17 inference(rename_variables,[],[3478])). % 112.37/112.17 cnf(12017,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),f317(f73(a1),f317(f90(a1),x120171))),f317(f90(a1),x120172)))), % 112.37/112.17 inference(rename_variables,[],[3910])). % 112.37/112.17 cnf(12020,plain, % 112.37/112.17 (~P1(f317(f317(f319(x120201),x120202),f178(f906(x120201,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12041,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x120411),x120411))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(12044,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x120441),f317(a102,x120441)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(12047,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x120471),x120471))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(12058,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x120581),x120581))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(12061,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x120611),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(12066,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x120661),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(12075,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),f2(a899)),x120751))), % 112.37/112.17 inference(rename_variables,[],[3459])). % 112.37/112.17 cnf(12076,plain, % 112.37/112.17 (~P1(f317(f317(f224(a899),f317(a102,x120761)),x120761))), % 112.37/112.17 inference(rename_variables,[],[4619])). % 112.37/112.17 cnf(12079,plain, % 112.37/112.17 (~P1(f317(f317(f162(x120791),f103(x120791)),x120792))), % 112.37/112.17 inference(rename_variables,[],[4618])). % 112.37/112.17 cnf(12082,plain, % 112.37/112.17 (~P1(f317(f317(f162(x120821),f103(x120821)),x120822))), % 112.37/112.17 inference(rename_variables,[],[4618])). % 112.37/112.17 cnf(12090,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x120901),f317(a102,x120901)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(12105,plain, % 112.37/112.17 (~P1(f317(f317(f224(a899),f317(a102,x121051)),x121051))), % 112.37/112.17 inference(rename_variables,[],[4619])). % 112.37/112.17 cnf(12108,plain, % 112.37/112.17 (~P1(f317(f317(f224(a899),f317(a102,x121081)),x121081))), % 112.37/112.17 inference(rename_variables,[],[4619])). % 112.37/112.17 cnf(12111,plain, % 112.37/112.17 (~P1(f317(f317(f224(a899),f317(a102,x121111)),x121111))), % 112.37/112.17 inference(rename_variables,[],[4619])). % 112.37/112.17 cnf(12114,plain, % 112.37/112.17 (~P1(f317(f317(f224(a899),f317(a102,x121141)),x121141))), % 112.37/112.17 inference(rename_variables,[],[4619])). % 112.37/112.17 cnf(12117,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x121171),x121171))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12120,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x121201),x121201))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12123,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x121231),x121231))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12126,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x121261),x121261))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12143,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x121431),x121431))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12146,plain, % 112.37/112.17 (P24(a899,a899,a102,x121461)), % 112.37/112.17 inference(rename_variables,[],[3639])). % 112.37/112.17 cnf(12149,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x121491),x121491))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(12160,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x121601),x121601))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(12163,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(f905(f900(x121631),f900(x121631)),a895)),f148(x121631,x121632)),f297(f900(x121631),f147(x121631,x121632))))), % 112.37/112.17 inference(rename_variables,[],[4124])). % 112.37/112.17 cnf(12170,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x121701),f317(a102,x121701)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(12173,plain, % 112.37/112.17 (P1(f317(f317(f319(f906(x121731,a895)),x121732),f317(f298(x121731),x121732)))), % 112.37/112.17 inference(rename_variables,[],[3795])). % 112.37/112.17 cnf(12174,plain, % 112.37/112.17 (~E(f317(a102,x121741),x121741)), % 112.37/112.17 inference(rename_variables,[],[4578])). % 112.37/112.17 cnf(12179,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x121791),x121791))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(12184,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x121841),x121841))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(12195,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x121951,a895)),x121952),f317(f317(f299(x121951),x121953),x121952)))), % 112.37/112.17 inference(rename_variables,[],[3876])). % 112.37/112.17 cnf(12198,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x121981),x121981))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12199,plain, % 112.37/112.17 (~E(f317(a102,x121991),x121991)), % 112.37/112.17 inference(rename_variables,[],[4578])). % 112.37/112.17 cnf(12212,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x122121),x122121))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12213,plain, % 112.37/112.17 (~E(f317(a102,x122131),x122131)), % 112.37/112.17 inference(rename_variables,[],[4578])). % 112.37/112.17 cnf(12216,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x122161),x122161))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12219,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x122191),x122191))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12222,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x122221),x122221))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12225,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x122251),x122251))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12228,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x122281),x122281))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(12231,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x122311),x122311))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12234,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x122341),x122341))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12235,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x122351),f317(a102,x122351)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(12242,plain, % 112.37/112.17 (~E(f317(a102,x122421),x122421)), % 112.37/112.17 inference(rename_variables,[],[4578])). % 112.37/112.17 cnf(12247,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x122471),x122471))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12248,plain, % 112.37/112.17 (~E(f317(a102,x122481),x122481)), % 112.37/112.17 inference(rename_variables,[],[4578])). % 112.37/112.17 cnf(12251,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x122511),x122511))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(12268,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x122681),x122681))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(12273,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),f2(a899)),x122731))), % 112.37/112.17 inference(rename_variables,[],[3459])). % 112.37/112.17 cnf(12289,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x122891),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(12292,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x122921),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(12295,plain, % 112.37/112.17 (~P1(f317(f317(f319(x122951),x122952),f178(f906(x122951,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12298,plain, % 112.37/112.17 (~P1(f317(f317(f319(x122981),x122982),f178(f906(x122981,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12301,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x123011),x123011))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12304,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x123041),x123041))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12307,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x123071),x123071))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12310,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x123101),x123101))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12313,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x123131),f317(a102,x123131)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(12320,plain, % 112.37/112.17 (P1(f317(f317(f319(f906(x123201,a895)),x123202),f317(f298(x123201),x123202)))), % 112.37/112.17 inference(rename_variables,[],[3795])). % 112.37/112.17 cnf(12325,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x123251,a895)),x123252),f317(f317(f299(x123251),x123253),x123252)))), % 112.37/112.17 inference(rename_variables,[],[3876])). % 112.37/112.17 cnf(12332,plain, % 112.37/112.17 (~P1(f317(f317(f319(x123321),x123322),f178(f906(x123321,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12341,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x123411,a895)),x123412),f232(f906(x123411,a895))))), % 112.37/112.17 inference(rename_variables,[],[3812])). % 112.37/112.17 cnf(12342,plain, % 112.37/112.17 (~E(f317(a102,x123421),x123421)), % 112.37/112.17 inference(rename_variables,[],[4578])). % 112.37/112.17 cnf(12348,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x123481),f317(a102,x123481)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(12357,plain, % 112.37/112.17 (E(f317(f274(x123571,x123571),f253(x123571,x123572)),x123572)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(12368,plain, % 112.37/112.17 (~P1(f317(f317(f224(a899),f317(a102,x123681)),x123681))), % 112.37/112.17 inference(rename_variables,[],[4619])). % 112.37/112.17 cnf(12369,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x123691),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(12374,plain, % 112.37/112.17 (P1(f317(f29(x123741),f178(f906(x123741,a895))))), % 112.37/112.17 inference(rename_variables,[],[3512])). % 112.37/112.17 cnf(12375,plain, % 112.37/112.17 (~P1(f317(f317(f319(x123751),x123752),f178(f906(x123751,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12384,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x123841,a895)),f317(f162(x123841),f166(x123841,x123842,x123843))),f317(f162(x123841),x123842)))), % 112.37/112.17 inference(rename_variables,[],[4119])). % 112.37/112.17 cnf(12387,plain, % 112.37/112.17 (P24(x123871,x123871,f7(x123871),x123872)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(12392,plain, % 112.37/112.17 (P1(f317(f317(f319(f906(x123921,a895)),x123922),f317(f298(x123921),x123922)))), % 112.37/112.17 inference(rename_variables,[],[3795])). % 112.37/112.17 cnf(12399,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x123991),x123991))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12402,plain, % 112.37/112.17 (~P1(f317(f317(f319(x124021),x124022),f178(f906(x124021,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12405,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x124051,a895)),x124052),f317(f317(f299(x124051),x124053),x124052)))), % 112.37/112.17 inference(rename_variables,[],[3876])). % 112.37/112.17 cnf(12406,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x124061,a895)),x124062),f232(f906(x124061,a895))))), % 112.37/112.17 inference(rename_variables,[],[3812])). % 112.37/112.17 cnf(12413,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x124131),x124131))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12416,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x124161),x124161))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12419,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x124191),x124191))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12422,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x124221),x124221))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12425,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x124251),f317(a102,x124251)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(12428,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x124281),f317(a102,x124281)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(12431,plain, % 112.37/112.17 (P1(f317(f317(f277(a899),x124311),x124311))), % 112.37/112.17 inference(rename_variables,[],[3440])). % 112.37/112.17 cnf(12434,plain, % 112.37/112.17 (P1(f317(f317(f277(a899),x124341),x124341))), % 112.37/112.17 inference(rename_variables,[],[3440])). % 112.37/112.17 cnf(12437,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x124371,a895)),x124372),x124372))), % 112.37/112.17 inference(rename_variables,[],[3727])). % 112.37/112.17 cnf(12444,plain, % 112.37/112.17 (P1(f317(f317(f319(f906(x124441,a895)),x124442),f317(f298(x124441),x124442)))), % 112.37/112.17 inference(rename_variables,[],[3795])). % 112.37/112.17 cnf(12453,plain, % 112.37/112.17 (~E(f317(a102,x124531),x124531)), % 112.37/112.17 inference(rename_variables,[],[4578])). % 112.37/112.17 cnf(12454,plain, % 112.37/112.17 (E(f317(f300(x124541,x124541,f7(x124541)),x124542),x124542)), % 112.37/112.17 inference(rename_variables,[],[3493])). % 112.37/112.17 cnf(12457,plain, % 112.37/112.17 (P31(x124571,x124572,f103(x124571),f103(x124571))), % 112.37/112.17 inference(rename_variables,[],[3680])). % 112.37/112.17 cnf(12460,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x124601,a895)),f317(f162(x124601),f166(x124601,x124602,x124603))),f317(f162(x124601),x124602)))), % 112.37/112.17 inference(rename_variables,[],[4119])). % 112.37/112.17 cnf(12461,plain, % 112.37/112.17 (P1(f317(f29(x124611),f317(f162(x124611),x124612)))), % 112.37/112.17 inference(rename_variables,[],[3478])). % 112.37/112.17 cnf(12472,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x124721),x124721))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12475,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x124751),x124751))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12480,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),f2(a899)),x124801))), % 112.37/112.17 inference(rename_variables,[],[3459])). % 112.37/112.17 cnf(12489,plain, % 112.37/112.17 (P13(a899,f317(f158(a899),f317(f317(f144(f900(x124891),a899),f179(f900(x124891))),f169(x124891,x124892))))), % 112.37/112.17 inference(rename_variables,[],[3989])). % 112.37/112.17 cnf(12492,plain, % 112.37/112.17 (P24(x124921,x124921,f7(x124921),x124922)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(12495,plain, % 112.37/112.17 (P24(x124951,x124951,f7(x124951),x124952)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(12498,plain, % 112.37/112.17 (P1(f317(f317(f319(f900(x124981)),f103(x124981)),f151(x124981,x124982)))), % 112.37/112.17 inference(rename_variables,[],[3631])). % 112.37/112.17 cnf(12501,plain, % 112.37/112.17 (~P1(f317(f317(f178(f906(x125011,f906(x125012,a895))),x125013),x125014))), % 112.37/112.17 inference(rename_variables,[],[4636])). % 112.37/112.17 cnf(12506,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x125061),x125061))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12507,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),f2(a899)),x125071))), % 112.37/112.17 inference(rename_variables,[],[3459])). % 112.37/112.17 cnf(12510,plain, % 112.37/112.17 (~P1(f317(f317(f178(f906(x125101,f906(x125102,a895))),x125103),x125104))), % 112.37/112.17 inference(rename_variables,[],[4636])). % 112.37/112.17 cnf(12513,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(f905(f900(x125131),f900(x125131)),a895)),f148(x125131,x125132)),f297(f900(x125131),f147(x125131,x125132))))), % 112.37/112.17 inference(rename_variables,[],[4124])). % 112.37/112.17 cnf(12519,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x125191,a895)),f317(f300(x125192,x125191,x125193),f317(f301(x125192,x125191,x125193),x125194))),x125194))), % 112.37/112.17 inference(rename_variables,[],[4299])). % 112.37/112.17 cnf(12522,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x125221,a895)),f317(f162(x125221),f166(x125221,x125222,x125223))),f317(f162(x125221),x125222)))), % 112.37/112.17 inference(rename_variables,[],[4119])). % 112.37/112.17 cnf(12523,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x125231,a895)),f317(f162(x125231),f317(f126(x125231,x125232),x125233))),f317(f162(x125231),x125233)))), % 112.37/112.17 inference(rename_variables,[],[4072])). % 112.37/112.17 cnf(12526,plain, % 112.37/112.17 (~P1(f317(f317(f225(f906(x125261,a895)),x125262),f178(f906(x125261,a895))))), % 112.37/112.17 inference(rename_variables,[],[4630])). % 112.37/112.17 cnf(12534,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x125341,a895)),f317(f300(x125342,x125341,x125343),f317(f301(x125342,x125341,x125343),x125344))),x125344))), % 112.37/112.17 inference(rename_variables,[],[4299])). % 112.37/112.17 cnf(12539,plain, % 112.37/112.17 (P1(f317(f317(f319(f900(x125391)),f103(x125391)),f151(x125391,x125392)))), % 112.37/112.17 inference(rename_variables,[],[3631])). % 112.37/112.17 cnf(12542,plain, % 112.37/112.17 (~P1(f317(f317(f319(f905(f900(x125421),f900(x125421))),f317(f317(f242(f900(x125421),f900(x125421)),x125422),f103(x125421))),f135(x125421,x125423)))), % 112.37/112.17 inference(rename_variables,[],[4638])). % 112.37/112.17 cnf(12545,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x125451),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(12548,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x125481,a895)),x125482),x125482))), % 112.37/112.17 inference(rename_variables,[],[3727])). % 112.37/112.17 cnf(12551,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x125511,a895)),f178(f906(x125511,a895))),x125512))), % 112.37/112.17 inference(rename_variables,[],[3878])). % 112.37/112.17 cnf(12554,plain, % 112.37/112.17 (~P1(f317(f317(f319(x125541),x125542),f178(f906(x125541,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12557,plain, % 112.37/112.17 (~P1(f317(f317(f178(f906(x125571,f906(x125572,a895))),x125573),x125574))), % 112.37/112.17 inference(rename_variables,[],[4636])). % 112.37/112.17 cnf(12560,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x125601,a895)),f317(f300(x125602,x125601,x125603),f317(f301(x125602,x125601,x125603),x125604))),x125604))), % 112.37/112.17 inference(rename_variables,[],[4299])). % 112.37/112.17 cnf(12561,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x125611,a895)),x125612),x125612))), % 112.37/112.17 inference(rename_variables,[],[3727])). % 112.37/112.17 cnf(12566,plain, % 112.37/112.17 (E(f317(f274(x125661,x125661),f253(x125661,x125662)),x125662)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(12569,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x125691,a895)),f317(f162(x125691),f166(x125691,x125692,x125693))),f317(f162(x125691),x125692)))), % 112.37/112.17 inference(rename_variables,[],[4119])). % 112.37/112.17 cnf(12570,plain, % 112.37/112.17 (P1(f317(f29(x125701),f317(f162(x125701),x125702)))), % 112.37/112.17 inference(rename_variables,[],[3478])). % 112.37/112.17 cnf(12573,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x125731),x125731))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12576,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x125761),x125761))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12579,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x125791),x125791))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12590,plain, % 112.37/112.17 (P24(x125901,x125901,f7(x125901),x125902)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(12598,plain, % 112.37/112.17 (~P1(f317(f317(f319(x125981),x125982),f178(f906(x125981,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12601,plain, % 112.37/112.17 (P1(f317(f317(f319(f905(x126011,x126011)),f317(f317(f242(x126011,x126011),x126012),x126012)),f297(x126011,x126013)))), % 112.37/112.17 inference(rename_variables,[],[4063])). % 112.37/112.17 cnf(12604,plain, % 112.37/112.17 (~P1(f317(f317(f319(x126041),x126042),f178(f906(x126041,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12607,plain, % 112.37/112.17 (P1(f317(f317(f319(f905(x126071,x126071)),f317(f317(f242(x126071,x126071),x126072),x126072)),f297(x126071,x126073)))), % 112.37/112.17 inference(rename_variables,[],[4063])). % 112.37/112.17 cnf(12617,plain, % 112.37/112.17 (~E(f317(f317(f141(x126171),x126172),x126173),x126173)), % 112.37/112.17 inference(rename_variables,[],[4591])). % 112.37/112.17 cnf(12624,plain, % 112.37/112.17 (P1(f317(f317(f319(x126241),x126242),f232(f906(x126241,a895))))), % 112.37/112.17 inference(rename_variables,[],[3587])). % 112.37/112.17 cnf(12625,plain, % 112.37/112.17 (~E(f317(a102,x126251),x126251)), % 112.37/112.17 inference(rename_variables,[],[4578])). % 112.37/112.17 cnf(12628,plain, % 112.37/112.17 (P1(f317(f317(f319(f900(x126281)),f103(x126281)),f151(x126281,x126282)))), % 112.37/112.17 inference(rename_variables,[],[3631])). % 112.37/112.17 cnf(12629,plain, % 112.37/112.17 (~E(f317(f317(f141(x126291),x126292),x126293),f103(x126291))), % 112.37/112.17 inference(rename_variables,[],[4594])). % 112.37/112.17 cnf(12632,plain, % 112.37/112.17 (P24(x126321,x126321,f7(x126321),x126322)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(12635,plain, % 112.37/112.17 (P1(f317(f317(f319(x126351),f317(x126352,x126353)),f317(f300(x126354,x126351,x126352),f232(f906(x126354,a895)))))), % 112.37/112.17 inference(rename_variables,[],[4029])). % 112.37/112.17 cnf(12636,plain, % 112.37/112.17 (P24(x126361,x126361,f7(x126361),x126362)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(12639,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x126391,a895)),f178(f906(x126391,a895))),x126392))), % 112.37/112.17 inference(rename_variables,[],[3878])). % 112.37/112.17 cnf(12640,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x126401,a895)),x126402),x126402))), % 112.37/112.17 inference(rename_variables,[],[3727])). % 112.37/112.17 cnf(12643,plain, % 112.37/112.17 (P1(f317(f317(f319(x126431),f317(x126432,x126433)),f317(f300(x126434,x126431,x126432),f232(f906(x126434,a895)))))), % 112.37/112.17 inference(rename_variables,[],[4029])). % 112.37/112.17 cnf(12644,plain, % 112.37/112.17 (P24(x126441,x126441,f7(x126441),x126442)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(12647,plain, % 112.37/112.17 (P1(f317(f317(f319(f905(f900(x126471),f900(x126471))),f317(f317(f242(f900(x126471),f900(x126471)),f103(x126471)),f103(x126471))),f148(x126471,x126472)))), % 112.37/112.17 inference(rename_variables,[],[4203])). % 112.37/112.17 cnf(12651,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x126511),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(12657,plain, % 112.37/112.17 (E(f317(f317(f124(x126571),x126572),f103(x126571)),x126572)), % 112.37/112.17 inference(rename_variables,[],[3369])). % 112.37/112.17 cnf(12658,plain, % 112.37/112.17 (~E(f317(f317(f141(x126581),x126582),x126583),x126583)), % 112.37/112.17 inference(rename_variables,[],[4591])). % 112.37/112.17 cnf(12661,plain, % 112.37/112.17 (E(f317(f317(f124(x126611),x126612),f103(x126611)),x126612)), % 112.37/112.17 inference(rename_variables,[],[3369])). % 112.37/112.17 cnf(12662,plain, % 112.37/112.17 (~E(f317(f317(f141(x126621),x126622),x126623),x126623)), % 112.37/112.17 inference(rename_variables,[],[4591])). % 112.37/112.17 cnf(12665,plain, % 112.37/112.17 (E(f317(f317(f124(x126651),x126652),f103(x126651)),x126652)), % 112.37/112.17 inference(rename_variables,[],[3369])). % 112.37/112.17 cnf(12672,plain, % 112.37/112.17 (P51(x126721,f253(x126721,x126722))), % 112.37/112.17 inference(rename_variables,[],[3311])). % 112.37/112.17 cnf(12675,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x126751,a895)),f317(f162(x126751),f317(f126(x126751,x126752),x126753))),f317(f162(x126751),x126753)))), % 112.37/112.17 inference(rename_variables,[],[4072])). % 112.37/112.17 cnf(12676,plain, % 112.37/112.17 (E(f317(f300(x126761,x126761,f7(x126761)),x126762),x126762)), % 112.37/112.17 inference(rename_variables,[],[3493])). % 112.37/112.17 cnf(12681,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x126811,a895)),x126812),f232(f906(x126811,a895))))), % 112.37/112.17 inference(rename_variables,[],[3812])). % 112.37/112.17 cnf(12685,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x126851),x126851))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12686,plain, % 112.37/112.17 (~E(f317(a102,x126861),x126861)), % 112.37/112.17 inference(rename_variables,[],[4578])). % 112.37/112.17 cnf(12689,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x126891,a895)),f178(f906(x126891,a895))),x126892))), % 112.37/112.17 inference(rename_variables,[],[3878])). % 112.37/112.17 cnf(12692,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x126921),x126921))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12695,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x126951,a895)),x126952),x126952))), % 112.37/112.17 inference(rename_variables,[],[3727])). % 112.37/112.17 cnf(12700,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x127001,a895)),x127002),f317(f317(f299(x127001),x127003),x127002)))), % 112.37/112.17 inference(rename_variables,[],[3876])). % 112.37/112.17 cnf(12703,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x127031,a895)),x127032),x127032))), % 112.37/112.17 inference(rename_variables,[],[3727])). % 112.37/112.17 cnf(12704,plain, % 112.37/112.17 (~P1(f317(f317(f319(x127041),x127042),f178(f906(x127041,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12707,plain, % 112.37/112.17 (~P1(f317(f317(f319(x127071),x127072),f178(f906(x127071,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12716,plain, % 112.37/112.17 (P24(x127161,x127161,f7(x127161),x127162)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(12719,plain, % 112.37/112.17 (E(f317(f179(f900(x127191)),f159(x127191,x127192,x127193)),x127192)), % 112.37/112.17 inference(rename_variables,[],[3503])). % 112.37/112.17 cnf(12722,plain, % 112.37/112.17 (P25(x127221,x127221,f25(x127221),x127222,x127222)), % 112.37/112.17 inference(rename_variables,[],[4087])). % 112.37/112.17 cnf(12725,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x127251),x127251))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12726,plain, % 112.37/112.17 (P1(f317(f232(f906(x127261,a895)),x127262))), % 112.37/112.17 inference(rename_variables,[],[3497])). % 112.37/112.17 cnf(12729,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x127291,a895)),f178(f906(x127291,a895))),x127292))), % 112.37/112.17 inference(rename_variables,[],[3878])). % 112.37/112.17 cnf(12732,plain, % 112.37/112.17 (~P1(f317(f317(f319(x127321),x127322),f178(f906(x127321,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12735,plain, % 112.37/112.17 (P1(f317(f317(f319(x127351),f317(x127352,x127353)),f317(f300(x127354,x127351,x127352),f232(f906(x127354,a895)))))), % 112.37/112.17 inference(rename_variables,[],[4029])). % 112.37/112.17 cnf(12736,plain, % 112.37/112.17 (P1(f317(f317(f319(f905(x127361,x127361)),f317(f317(f242(x127361,x127361),x127362),x127362)),f297(x127361,x127363)))), % 112.37/112.17 inference(rename_variables,[],[4063])). % 112.37/112.17 cnf(12739,plain, % 112.37/112.17 (P1(f317(f317(f319(f905(x127391,x127391)),f317(f317(f242(x127391,x127391),x127392),x127392)),f297(x127391,x127393)))), % 112.37/112.17 inference(rename_variables,[],[4063])). % 112.37/112.17 cnf(12742,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x127421),x127421))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(12743,plain, % 112.37/112.17 (P1(f317(f232(f906(x127431,a895)),x127432))), % 112.37/112.17 inference(rename_variables,[],[3497])). % 112.37/112.17 cnf(12746,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x127461,a895)),x127462),f232(f906(x127461,a895))))), % 112.37/112.17 inference(rename_variables,[],[3812])). % 112.37/112.17 cnf(12747,plain, % 112.37/112.17 (P25(x127471,x127471,f25(x127471),x127472,x127472)), % 112.37/112.17 inference(rename_variables,[],[4087])). % 112.37/112.17 cnf(12750,plain, % 112.37/112.17 (P1(f317(f29(x127501),f317(f162(x127501),x127502)))), % 112.37/112.17 inference(rename_variables,[],[3478])). % 112.37/112.17 cnf(12760,plain, % 112.37/112.17 (~P1(f317(f317(f178(f906(x127601,f906(x127602,a895))),x127603),x127604))), % 112.37/112.17 inference(rename_variables,[],[4636])). % 112.37/112.17 cnf(12766,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x127661,a895)),x127662),f232(f906(x127661,a895))))), % 112.37/112.17 inference(rename_variables,[],[3812])). % 112.37/112.17 cnf(12769,plain, % 112.37/112.17 (P1(f317(f317(f319(f905(x127691,x127691)),f317(f317(f242(x127691,x127691),x127692),x127692)),f297(x127691,x127693)))), % 112.37/112.17 inference(rename_variables,[],[4063])). % 112.37/112.17 cnf(12772,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),f317(f317(f74(a899),x127721),x127722)),x127722))), % 112.37/112.17 inference(rename_variables,[],[4633])). % 112.37/112.17 cnf(12773,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x127731),f317(a102,x127731)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(12776,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x127761,a895)),x127762),f232(f906(x127761,a895))))), % 112.37/112.17 inference(rename_variables,[],[3812])). % 112.37/112.17 cnf(12779,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x127791,a895)),f178(f906(x127791,a895))),x127792))), % 112.37/112.17 inference(rename_variables,[],[3878])). % 112.37/112.17 cnf(12782,plain, % 112.37/112.17 (E(f317(f274(x127821,x127821),f253(x127821,x127822)),x127822)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(12793,plain, % 112.37/112.17 (~P1(f317(f317(f319(x127931),x127932),f178(f906(x127931,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12794,plain, % 112.37/112.17 (P1(f317(f317(f319(f905(f900(x127941),f900(x127941))),f317(f317(f242(f900(x127941),f900(x127941)),f103(x127941)),f103(x127941))),f148(x127941,x127942)))), % 112.37/112.17 inference(rename_variables,[],[4203])). % 112.37/112.17 cnf(12799,plain, % 112.37/112.17 (~P1(f317(f317(f319(x127991),x127992),f178(f906(x127991,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12804,plain, % 112.37/112.17 (P30(x128041,x128042,f103(x128041))), % 112.37/112.17 inference(rename_variables,[],[3374])). % 112.37/112.17 cnf(12807,plain, % 112.37/112.17 (E(f317(f179(f900(x128071)),f159(x128071,x128072,x128073)),x128072)), % 112.37/112.17 inference(rename_variables,[],[3503])). % 112.37/112.17 cnf(12810,plain, % 112.37/112.17 (~P1(f317(f317(f319(x128101),x128102),f178(f906(x128101,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12816,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x128161),x128161))), % 112.37/112.17 inference(rename_variables,[],[4611])). % 112.37/112.17 cnf(12819,plain, % 112.37/112.17 (P1(f317(f317(f319(x128191),x128192),f232(f906(x128191,a895))))), % 112.37/112.17 inference(rename_variables,[],[3587])). % 112.37/112.17 cnf(12823,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x128231,a895)),x128232),x128232))), % 112.37/112.17 inference(rename_variables,[],[3727])). % 112.37/112.17 cnf(12826,plain, % 112.37/112.17 (~P1(f317(f317(f319(x128261),x128262),f178(f906(x128261,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(12829,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),f2(a1)),f317(f317(f234(a1),f317(f70(a1),x128291)),x128292)))), % 112.37/112.17 inference(rename_variables,[],[3909])). % 112.37/112.17 cnf(12832,plain, % 112.37/112.17 (~E(f317(a102,x128321),x128321)), % 112.37/112.17 inference(rename_variables,[],[4578])). % 112.37/112.17 cnf(12834,plain, % 112.37/112.17 (E(f317(f274(x128341,x128341),f253(x128341,x128342)),x128342)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(12836,plain, % 112.37/112.17 (E(f317(f274(x128361,x128361),f253(x128361,x128362)),x128362)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(12840,plain, % 112.37/112.17 (E(f317(f274(x128401,x128401),f253(x128401,x128402)),x128402)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(12842,plain, % 112.37/112.17 (P24(x128421,x128421,f7(x128421),x128422)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(12844,plain, % 112.37/112.17 (P24(x128441,x128441,f7(x128441),x128442)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(12851,plain, % 112.37/112.17 (E(f317(f274(x128511,x128511),f253(x128511,x128512)),x128512)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(12853,plain, % 112.37/112.17 (E(f317(f274(x128531,x128531),f253(x128531,x128532)),x128532)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(12855,plain, % 112.37/112.17 (E(f317(f274(x128551,x128551),f253(x128551,x128552)),x128552)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(12862,plain, % 112.37/112.17 (E(f178(f906(f905(x128621,x128621),a895)),f253(x128621,f178(f906(x128621,a895))))), % 112.37/112.17 inference(rename_variables,[],[3507])). % 112.37/112.17 cnf(12864,plain, % 112.37/112.17 (E(f317(f274(x128641,x128641),f253(x128641,x128642)),x128642)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(12871,plain, % 112.37/112.17 (P14(x128711,f906(x128711,a895),f299(x128711))), % 112.37/112.17 inference(rename_variables,[],[3411])). % 112.37/112.17 cnf(12875,plain, % 112.37/112.17 (P54(x128751,x128751,f253(x128751,x128752))), % 112.37/112.17 inference(rename_variables,[],[3408])). % 112.37/112.17 cnf(12881,plain, % 112.37/112.17 (P36(x128811,f143(x128811,x128812))), % 112.37/112.17 inference(rename_variables,[],[3307])). % 112.37/112.17 cnf(12885,plain, % 112.37/112.17 (P31(x128851,x128852,f103(x128851),f103(x128851))), % 112.37/112.17 inference(rename_variables,[],[3680])). % 112.37/112.17 cnf(12887,plain, % 112.37/112.17 (P31(x128871,x128872,f103(x128871),f103(x128871))), % 112.37/112.17 inference(rename_variables,[],[3680])). % 112.37/112.17 cnf(12899,plain, % 112.37/112.17 (E(f317(f274(x128991,x128991),f253(x128991,x128992)),x128992)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(12905,plain, % 112.37/112.17 (P52(x129051,x129052,f253(x129051,x129052))), % 112.37/112.17 inference(rename_variables,[],[3407])). % 112.37/112.17 cnf(12907,plain, % 112.37/112.17 (P52(x129071,x129072,f253(x129071,x129072))), % 112.37/112.17 inference(rename_variables,[],[3407])). % 112.37/112.17 cnf(12909,plain, % 112.37/112.17 (P52(x129091,x129092,f253(x129091,x129092))), % 112.37/112.17 inference(rename_variables,[],[3407])). % 112.37/112.17 cnf(12911,plain, % 112.37/112.17 (P37(x129111,f253(x129111,x129112))), % 112.37/112.17 inference(rename_variables,[],[3308])). % 112.37/112.17 cnf(12915,plain, % 112.37/112.17 (E(f317(f274(x129151,x129151),f253(x129151,x129152)),x129152)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(12917,plain, % 112.37/112.17 (P51(x129171,f253(x129171,x129172))), % 112.37/112.17 inference(rename_variables,[],[3311])). % 112.37/112.17 cnf(12922,plain, % 112.37/112.17 (P25(x129221,x129221,f25(x129221),x129222,x129222)), % 112.37/112.17 inference(rename_variables,[],[4087])). % 112.37/112.17 cnf(12924,plain, % 112.37/112.17 (P25(x129241,x129241,f25(x129241),x129242,x129242)), % 112.37/112.17 inference(rename_variables,[],[4087])). % 112.37/112.17 cnf(12926,plain, % 112.37/112.17 (P25(x129261,x129261,f25(x129261),x129262,x129262)), % 112.37/112.17 inference(rename_variables,[],[4087])). % 112.37/112.17 cnf(12944,plain, % 112.37/112.17 (P55(x129441,f178(f906(x129441,a895)),x129442)), % 112.37/112.17 inference(rename_variables,[],[3457])). % 112.37/112.17 cnf(12948,plain, % 112.37/112.17 (P41(x129481,x129482,x129483,x129484,f178(f906(x129481,a895)),x129484)), % 112.37/112.17 inference(rename_variables,[],[4360])). % 112.37/112.17 cnf(12959,plain, % 112.37/112.17 (E(f178(f906(f905(x129591,x129591),a895)),f253(x129591,f178(f906(x129591,a895))))), % 112.37/112.17 inference(rename_variables,[],[3507])). % 112.37/112.17 cnf(12966,plain, % 112.37/112.17 (E(f317(f274(x129661,x129661),f253(x129661,x129662)),x129662)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(12978,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x129781),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(12987,plain, % 112.37/112.17 (~P1(f317(f317(f225(a1),f317(f90(a1),x129871)),f317(f73(a1),f317(f90(a1),x129872))))), % 112.37/112.17 inference(rename_variables,[],[4631])). % 112.37/112.17 cnf(12997,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x129971),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(13000,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x130001),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(13003,plain, % 112.37/112.17 (P1(f317(f29(a899),f295(a899,x130031,x130032)))), % 112.37/112.17 inference(rename_variables,[],[3642])). % 112.37/112.17 cnf(13006,plain, % 112.37/112.17 (P1(f317(f29(a899),f295(a899,x130061,x130062)))), % 112.37/112.17 inference(rename_variables,[],[3642])). % 112.37/112.17 cnf(13009,plain, % 112.37/112.17 (P1(f317(f29(a899),f295(a899,x130091,x130092)))), % 112.37/112.17 inference(rename_variables,[],[3642])). % 112.37/112.17 cnf(13012,plain, % 112.37/112.17 (P1(f317(f29(a899),f295(a899,x130121,x130122)))), % 112.37/112.17 inference(rename_variables,[],[3642])). % 112.37/112.17 cnf(13019,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),f317(f73(a1),f317(f90(a1),x130191))),f317(f90(a1),x130192)))), % 112.37/112.17 inference(rename_variables,[],[3910])). % 112.37/112.17 cnf(13024,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x130241),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(13025,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x130251),x130251))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(13032,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x130321),f317(a102,x130321)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(13037,plain, % 112.37/112.17 (~E(f317(a102,x130371),f2(a899))), % 112.37/112.17 inference(rename_variables,[],[4584])). % 112.37/112.17 cnf(13042,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x130421),x130421))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(13045,plain, % 112.37/112.17 (P1(f317(f29(a899),f295(a899,x130451,x130452)))), % 112.37/112.17 inference(rename_variables,[],[3642])). % 112.37/112.17 cnf(13048,plain, % 112.37/112.17 (P1(f317(f29(a899),f295(a899,x130481,x130482)))), % 112.37/112.17 inference(rename_variables,[],[3642])). % 112.37/112.17 cnf(13051,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x130511),x130511))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(13068,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),f41(a899,x130681,x130682)),x130681))), % 112.37/112.17 inference(rename_variables,[],[3886])). % 112.37/112.17 cnf(13073,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x130731),f317(a102,x130731)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(13076,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x130761),f317(a102,x130761)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(13077,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x130771),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(13086,plain, % 112.37/112.17 (~P1(f317(f317(f225(a1),f317(f90(a1),x130861)),f2(a1)))), % 112.37/112.17 inference(rename_variables,[],[4626])). % 112.37/112.17 cnf(13087,plain, % 112.37/112.17 (P1(f317(f232(f906(x130871,a895)),x130872))), % 112.37/112.17 inference(rename_variables,[],[3497])). % 112.37/112.17 cnf(13090,plain, % 112.37/112.17 (~P1(f317(f317(f225(a1),f317(f90(a1),x130901)),f2(a1)))), % 112.37/112.17 inference(rename_variables,[],[4626])). % 112.37/112.17 cnf(13091,plain, % 112.37/112.17 (P1(f317(f232(f906(x130911,a895)),x130912))), % 112.37/112.17 inference(rename_variables,[],[3497])). % 112.37/112.17 cnf(13094,plain, % 112.37/112.17 (P1(f317(f232(f906(x130941,a895)),x130942))), % 112.37/112.17 inference(rename_variables,[],[3497])). % 112.37/112.17 cnf(13097,plain, % 112.37/112.17 (P1(f317(f232(f906(x130971,a895)),x130972))), % 112.37/112.17 inference(rename_variables,[],[3497])). % 112.37/112.17 cnf(13105,plain, % 112.37/112.17 (~P1(f317(f317(f319(x131051),x131052),f178(f906(x131051,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(13106,plain, % 112.37/112.17 (P1(f317(f29(x131061),f178(f906(x131061,a895))))), % 112.37/112.17 inference(rename_variables,[],[3512])). % 112.37/112.17 cnf(13109,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x131091),x131091))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(13118,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),f2(a899)),x131181))), % 112.37/112.17 inference(rename_variables,[],[3459])). % 112.37/112.17 cnf(13121,plain, % 112.37/112.17 (~P1(f317(f317(f319(x131211),x131212),f178(f906(x131211,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(13124,plain, % 112.37/112.17 (~P1(f317(f317(f319(x131241),x131242),f178(f906(x131241,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(13129,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x131291),x131291))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(13137,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x131371),f317(a102,x131371)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(13140,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x131401),x131401))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(13145,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x131451),x131451))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(13148,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x131481),x131481))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(13151,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x131511),x131511))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(13154,plain, % 112.37/112.17 (E(f317(f317(f3(f906(x131541,a895)),f178(f906(x131541,a895))),x131542),f178(f906(x131541,a895)))), % 112.37/112.17 inference(rename_variables,[],[3698])). % 112.37/112.17 cnf(13155,plain, % 112.37/112.17 (P1(f317(f29(x131551),f178(f906(x131551,a895))))), % 112.37/112.17 inference(rename_variables,[],[3512])). % 112.37/112.17 cnf(13158,plain, % 112.37/112.17 (E(f317(f317(f3(f906(x131581,a895)),f178(f906(x131581,a895))),x131582),f178(f906(x131581,a895)))), % 112.37/112.17 inference(rename_variables,[],[3698])). % 112.37/112.17 cnf(13159,plain, % 112.37/112.17 (P1(f317(f29(x131591),f178(f906(x131591,a895))))), % 112.37/112.17 inference(rename_variables,[],[3512])). % 112.37/112.17 cnf(13162,plain, % 112.37/112.17 (E(f317(f317(f3(f906(x131621,a895)),f178(f906(x131621,a895))),x131622),f178(f906(x131621,a895)))), % 112.37/112.17 inference(rename_variables,[],[3698])). % 112.37/112.17 cnf(13163,plain, % 112.37/112.17 (P1(f317(f29(x131631),f178(f906(x131631,a895))))), % 112.37/112.17 inference(rename_variables,[],[3512])). % 112.37/112.17 cnf(13166,plain, % 112.37/112.17 (E(f317(f317(f3(f906(x131661,a895)),f178(f906(x131661,a895))),x131662),f178(f906(x131661,a895)))), % 112.37/112.17 inference(rename_variables,[],[3698])). % 112.37/112.17 cnf(13167,plain, % 112.37/112.17 (P1(f317(f29(x131671),f178(f906(x131671,a895))))), % 112.37/112.17 inference(rename_variables,[],[3512])). % 112.37/112.17 cnf(13171,plain, % 112.37/112.17 (E(f317(f274(x131711,x131711),f253(x131711,x131712)),x131712)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(13176,plain, % 112.37/112.17 (E(f317(f317(f3(f906(x131761,a895)),f178(f906(x131761,a895))),x131762),f178(f906(x131761,a895)))), % 112.37/112.17 inference(rename_variables,[],[3698])). % 112.37/112.17 cnf(13177,plain, % 112.37/112.17 (P1(f317(f29(x131771),f178(f906(x131771,a895))))), % 112.37/112.17 inference(rename_variables,[],[3512])). % 112.37/112.17 cnf(13181,plain, % 112.37/112.17 (P1(f317(f29(x131811),f178(f906(x131811,a895))))), % 112.37/112.17 inference(rename_variables,[],[3512])). % 112.37/112.17 cnf(13184,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x131841),x131841))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(13188,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x131881),x131881))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(13195,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x131951),x131951))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(13208,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x132081),x132081))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(13221,plain, % 112.37/112.17 (~P1(f317(f317(f319(x132211),x132212),f178(f906(x132211,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(13232,plain, % 112.37/112.17 (P1(f317(f317(f319(x132321),x132322),f232(f906(x132321,a895))))), % 112.37/112.17 inference(rename_variables,[],[3587])). % 112.37/112.17 cnf(13233,plain, % 112.37/112.17 (E(f317(f182(x132331,x132332),x132333),f111(x132331,x132332))), % 112.37/112.17 inference(rename_variables,[],[3352])). % 112.37/112.17 cnf(13236,plain, % 112.37/112.17 (P1(f317(f317(f319(x132361),f317(x132362,x132363)),f317(f300(x132364,x132361,x132362),f232(f906(x132364,a895)))))), % 112.37/112.17 inference(rename_variables,[],[4029])). % 112.37/112.17 cnf(13240,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x132401,a895)),x132402),f232(f906(x132401,a895))))), % 112.37/112.17 inference(rename_variables,[],[3812])). % 112.37/112.17 cnf(13243,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x132431,a895)),x132432),x132432))), % 112.37/112.17 inference(rename_variables,[],[3727])). % 112.37/112.17 cnf(13249,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x132491),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(13250,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x132501),x132501))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(13254,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x132541),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(13255,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x132551),x132551))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(13260,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x132601),x132601))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(13267,plain, % 112.37/112.17 (E(f317(f317(f18(x132671,x132672),x132673),x132674),x132673)), % 112.37/112.17 inference(rename_variables,[],[3429])). % 112.37/112.17 cnf(13272,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x132721,a895)),f317(f162(x132721),f166(x132721,x132722,x132723))),f317(f162(x132721),x132722)))), % 112.37/112.17 inference(rename_variables,[],[4119])). % 112.37/112.17 cnf(13279,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x132791),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(13280,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x132801),x132801))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(13284,plain, % 112.37/112.17 (~P1(f317(f317(f225(a899),x132841),f2(a899)))), % 112.37/112.17 inference(rename_variables,[],[4615])). % 112.37/112.17 cnf(13285,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),x132851),x132851))), % 112.37/112.17 inference(rename_variables,[],[3439])). % 112.37/112.17 cnf(13290,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x132901),x132901))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(13293,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),x132931),x132931))), % 112.37/112.17 inference(rename_variables,[],[3438])). % 112.37/112.17 cnf(13296,plain, % 112.37/112.17 (~P1(f317(f317(f224(a899),f317(a102,x132961)),x132961))), % 112.37/112.17 inference(rename_variables,[],[4619])). % 112.37/112.17 cnf(13302,plain, % 112.37/112.17 (P1(f317(f317(f319(x133021),f317(x133022,x133023)),f317(f300(x133024,x133021,x133022),f232(f906(x133024,a895)))))), % 112.37/112.17 inference(rename_variables,[],[4029])). % 112.37/112.17 cnf(13303,plain, % 112.37/112.17 (P24(x133031,x133031,f7(x133031),x133032)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(13308,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x133081,a895)),x133082),f232(f906(x133081,a895))))), % 112.37/112.17 inference(rename_variables,[],[3812])). % 112.37/112.17 cnf(13309,plain, % 112.37/112.17 (P24(x133091,x133091,f7(x133091),x133092)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(13313,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x133131,a895)),x133132),f232(f906(x133131,a895))))), % 112.37/112.17 inference(rename_variables,[],[3812])). % 112.37/112.17 cnf(13314,plain, % 112.37/112.17 (P24(x133141,x133141,f7(x133141),x133142)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(13318,plain, % 112.37/112.17 (P24(x133181,x133181,f7(x133181),x133182)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(13321,plain, % 112.37/112.17 (~P1(f317(f317(f225(f906(x133211,a895)),x133212),f178(f906(x133211,a895))))), % 112.37/112.17 inference(rename_variables,[],[4630])). % 112.37/112.17 cnf(13324,plain, % 112.37/112.17 (P24(x133241,x133241,f7(x133241),x133242)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(13327,plain, % 112.37/112.17 (P24(x133271,x133271,f7(x133271),x133272)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(13333,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x133331,a895)),x133332),f232(f906(x133331,a895))))), % 112.37/112.17 inference(rename_variables,[],[3812])). % 112.37/112.17 cnf(13338,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x133381,a895)),f178(f906(x133381,a895))),x133382))), % 112.37/112.17 inference(rename_variables,[],[3878])). % 112.37/112.17 cnf(13342,plain, % 112.37/112.17 (E(f317(f274(x133421,x133421),f253(x133421,x133422)),x133422)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(13346,plain, % 112.37/112.17 (~P1(f317(f317(f319(x133461),x133462),f178(f906(x133461,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(13351,plain, % 112.37/112.17 (P24(x133511,x133511,f7(x133511),x133512)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(13354,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x133541,a895)),x133542),f232(f906(x133541,a895))))), % 112.37/112.17 inference(rename_variables,[],[3812])). % 112.37/112.17 cnf(13362,plain, % 112.37/112.17 (E(f317(f317(f18(x133621,x133622),x133623),x133624),x133623)), % 112.37/112.17 inference(rename_variables,[],[3429])). % 112.37/112.17 cnf(13365,plain, % 112.37/112.17 (~P1(f317(f317(f319(x133651),x133652),f178(f906(x133651,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(13368,plain, % 112.37/112.17 (~P1(f317(f317(f319(x133681),x133682),f178(f906(x133681,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(13373,plain, % 112.37/112.17 (~E(f317(a102,x133731),x133731)), % 112.37/112.17 inference(rename_variables,[],[4578])). % 112.37/112.17 cnf(13379,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x133791),f317(a102,x133791)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(13380,plain, % 112.37/112.17 (~E(f317(a102,x133801),x133801)), % 112.37/112.17 inference(rename_variables,[],[4578])). % 112.37/112.17 cnf(13383,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x133831),f317(a102,f317(f317(f74(a899),x133832),x133831))))), % 112.37/112.17 inference(rename_variables,[],[3879])). % 112.37/112.17 cnf(13384,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),x133841),f317(a102,x133841)))), % 112.37/112.17 inference(rename_variables,[],[3504])). % 112.37/112.17 cnf(13393,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),f2(a1)),f317(f90(a1),x133931)))), % 112.37/112.17 inference(rename_variables,[],[3536])). % 112.37/112.17 cnf(13396,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),f2(a899)),x133961))), % 112.37/112.17 inference(rename_variables,[],[3459])). % 112.37/112.17 cnf(13400,plain, % 112.37/112.17 (~E(f317(a102,x134001),f2(a899))), % 112.37/112.17 inference(rename_variables,[],[4584])). % 112.37/112.17 cnf(13403,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x134031,a895)),f317(f162(x134031),f166(x134031,x134032,x134033))),f317(f162(x134031),x134032)))), % 112.37/112.17 inference(rename_variables,[],[4119])). % 112.37/112.17 cnf(13408,plain, % 112.37/112.17 (~P1(f317(f317(f319(x134081),x134082),f178(f906(x134081,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(13411,plain, % 112.37/112.17 (P1(f317(f29(a899),f295(a899,x134111,x134112)))), % 112.37/112.17 inference(rename_variables,[],[3642])). % 112.37/112.17 cnf(13412,plain, % 112.37/112.17 (E(f317(f317(f223(a899),f317(a102,x134121)),f317(a102,x134122)),f317(a102,f317(f317(f223(a899),x134121),x134122)))), % 112.37/112.17 inference(rename_variables,[],[3606])). % 112.37/112.17 cnf(13415,plain, % 112.37/112.17 (P1(f317(f29(a899),f295(a899,x134151,x134152)))), % 112.37/112.17 inference(rename_variables,[],[3642])). % 112.37/112.17 cnf(13416,plain, % 112.37/112.17 (E(f317(f317(f228(a899),f317(a102,x134161)),f317(a102,x134162)),f317(a102,f317(f317(f228(a899),x134161),x134162)))), % 112.37/112.17 inference(rename_variables,[],[3605])). % 112.37/112.17 cnf(13419,plain, % 112.37/112.17 (P1(f317(f29(a899),f295(a899,x134191,x134192)))), % 112.37/112.17 inference(rename_variables,[],[3642])). % 112.37/112.17 cnf(13428,plain, % 112.37/112.17 (~P1(f317(f317(f319(x134281),x134282),f178(f906(x134281,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(13429,plain, % 112.37/112.17 (E(f317(f317(f18(x134291,x134292),x134293),x134294),x134293)), % 112.37/112.17 inference(rename_variables,[],[3429])). % 112.37/112.17 cnf(13432,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x134321,a895)),f317(f162(x134321),f317(f126(x134321,x134322),x134323))),f317(f162(x134321),x134323)))), % 112.37/112.17 inference(rename_variables,[],[4072])). % 112.37/112.17 cnf(13433,plain, % 112.37/112.17 (E(f317(f317(f18(x134331,x134332),x134333),x134334),x134333)), % 112.37/112.17 inference(rename_variables,[],[3429])). % 112.37/112.17 cnf(13436,plain, % 112.37/112.17 (P1(f317(f317(f224(f906(x134361,a895)),f317(f162(x134361),f317(f317(f165(x134361),x134362),x134363))),f317(f162(x134361),x134363)))), % 112.37/112.17 inference(rename_variables,[],[4114])). % 112.37/112.17 cnf(13437,plain, % 112.37/112.17 (E(f317(f317(f18(x134371,x134372),x134373),x134374),x134373)), % 112.37/112.17 inference(rename_variables,[],[3429])). % 112.37/112.17 cnf(13441,plain, % 112.37/112.17 (E(f317(f317(f18(x134411,x134412),x134413),x134414),x134413)), % 112.37/112.17 inference(rename_variables,[],[3429])). % 112.37/112.17 cnf(13454,plain, % 112.37/112.17 (P1(f317(f317(f224(a1),f2(a1)),f317(f90(a1),x134541)))), % 112.37/112.17 inference(rename_variables,[],[3536])). % 112.37/112.17 cnf(13459,plain, % 112.37/112.17 (P24(x134591,x134591,f7(x134591),x134592)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(13462,plain, % 112.37/112.17 (~P1(f317(f317(f319(x134621),x134622),f178(f906(x134621,a895))))), % 112.37/112.17 inference(rename_variables,[],[4622])). % 112.37/112.17 cnf(13463,plain, % 112.37/112.17 (E(f317(f274(x134631,x134631),f253(x134631,x134632)),x134632)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(13464,plain, % 112.37/112.17 (P24(x134641,x134641,f7(x134641),x134642)), % 112.37/112.17 inference(rename_variables,[],[3671])). % 112.37/112.17 cnf(13468,plain, % 112.37/112.17 (E(f317(f274(x134681,x134681),f253(x134681,x134682)),x134682)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(13482,plain, % 112.37/112.17 (P1(f317(f317(f224(a899),f2(a899)),x134821))), % 112.37/112.17 inference(rename_variables,[],[3459])). % 112.37/112.17 cnf(13483,plain, % 112.37/112.17 (P1(f317(f317(f225(a899),f2(a899)),f317(a102,x134831)))), % 112.37/112.17 inference(rename_variables,[],[3516])). % 112.37/112.17 cnf(13484,plain, % 112.37/112.17 (E(f317(f274(x134841,x134841),f253(x134841,x134842)),x134842)), % 112.37/112.17 inference(rename_variables,[],[3398])). % 112.37/112.17 cnf(13599,plain, % 112.37/112.17 ($false), % 112.37/112.17 inference(scs_inference,[],[4641,4087,12722,12747,12922,12924,12926,3671,11328,12387,12492,12495,12590,12632,12636,12644,12716,12842,12844,13303,13309,13314,13318,13324,13327,13351,13459,13464,3680,12457,12885,12887,3687,3407,12905,12907,12909,3408,12875,3374,12804,4597,4598,11968,4360,12948,3411,12871,3250,3307,12881,3308,12911,3309,3310,3311,12672,12917,4596,3729,4578,10404,10414,10427,10438,10542,10547,10550,10652,10791,11103,11298,11301,11320,11323,11518,11619,11626,11640,11686,11689,11722,11737,11800,11859,11875,12174,12199,12213,12242,12248,12342,12453,12625,12686,12832,13373,13380,3492,3457,12944,3639,12146,3358,4584,10636,10740,11208,11308,13037,13400,3049,3050,3054,3055,3058,3059,3061,3062,3063,3069,3070,3071,3072,3073,3075,3078,3084,3093,3099,3103,3105,3107,3114,3117,3120,3121,3123,3132,3140,3141,3144,3152,3155,3164,3166,3169,3173,3174,3176,3177,3184,3185,3186,3193,3197,3198,3199,3200,3205,3210,3211,3219,3229,3234,3306,4576,3768,3993,11906,3283,11616,3420,3395,3398,10473,10476,10571,10574,10897,11631,11634,11748,11787,11792,11901,12357,12566,12782,12834,12836,12840,12851,12853,12855,12864,12899,12915,12966,13171,13342,13463,13468,13484,3369,12657,12661,12665,3375,3384,3888,4189,3352,13233,3503,12719,12807,3272,3273,4265,3633,3979,11662,3337,3269,3297,3748,3292,3491,4096,3987,3810,3278,3279,3260,3900,3317,3493,11053,11182,12454,12676,3368,4061,4591,10464,10633,11515,12617,12658,12662,4594,12629,3429,11988,11991,13267,13362,13429,13433,13437,13441,4019,4620,11234,11333,11571,11574,3403,3829,3424,3540,3754,3532,4600,3507,12862,12959,3332,10534,10870,3333,4609,3592,3325,3251,3354,11652,4203,12647,12794,4063,11254,11387,11446,12601,12607,12736,12739,12769,4638,11157,11400,11509,11535,11579,11585,12542,4639,11287,11403,11512,4640,11406,11457,4642,11464,4643,3353,3631,12498,12539,12628,3794,3580,4474,4475,3615,3652,4589,11645,3772,3731,3774,3943,3698,13154,13158,13162,13166,13176,3989,12489,3617,3871,3504,10555,10675,10757,10830,10833,10873,10978,11224,11836,12044,12090,12170,12235,12313,12348,12425,12428,12773,13032,13073,13076,13137,13379,13384,3881,11892,3422,3516,11721,12003,13483,3693,4615,10441,10444,10470,10596,10775,10986,11001,11115,11557,11835,12061,12066,12289,12292,12369,12545,12651,12978,12997,13000,13024,13077,13249,13254,13279,13284,4626,11764,11795,11832,11839,11872,13086,13090,3868,3640,3642,13003,13006,13009,13012,13045,13048,13411,13415,13419,4011,3605,13416,3606,13412,3466,3468,3441,4612,3331,3296,4586,3820,4125,3624,4627,4196,11532,3753,3478,12011,12014,12461,12570,12750,4618,10432,10435,10604,10699,10722,10729,10752,10760,10763,10780,10971,11211,11426,11715,11809,11957,12079,12082,4165,4124,12163,12513,4072,10888,12523,12675,13432,4114,13436,4119,11260,12384,12460,12522,12569,13272,13403,4120,3795,11843,12173,12320,12392,12444,4153,3812,10599,10696,11257,11340,11419,11483,11655,12341,12406,12681,12746,12766,12776,13240,13308,13313,13333,13354,4630,11004,11411,12526,13321,3438,10564,10662,10816,10880,10958,11007,11010,11041,11061,11097,11137,11176,11960,12006,12143,12198,12216,12219,12222,12225,12399,12413,12416,12419,12422,12506,12573,12692,12742,13025,13051,13109,13129,13140,13145,13148,13151,13184,13195,13260,13290,13293,3439,10591,10647,10885,10981,11100,11740,12041,12047,12058,12149,12160,12179,12184,12228,12251,12268,13042,13188,13208,13250,13255,13280,13285,3440,12431,12434,3512,12374,13106,13155,13159,13163,13167,13177,13181,4611,10481,10510,11025,11064,11073,11920,11941,12117,12120,12123,12126,12212,12231,12234,12247,12301,12304,12307,12310,12472,12475,12576,12579,12685,12725,12816,3587,10745,10836,11108,11154,11390,11393,11472,11554,11725,11971,12624,12819,13232,4622,11034,11146,11167,11170,11237,11240,11251,11356,11364,11378,11414,11431,11440,11480,11521,11526,11529,11548,11551,11588,11593,11596,11599,11602,11842,11985,12020,12295,12298,12332,12375,12402,12554,12598,12604,12704,12707,12732,12793,12799,12810,12826,13105,13121,13124,13221,13346,13365,13368,13408,13428,13462,3497,10867,10900,10909,10912,10915,11501,12726,12743,13087,13091,13094,13097,3536,13393,13454,3529,3947,3886,10513,11895,11923,13068,4619,10461,10855,10858,11359,11375,11858,11911,11945,11972,12076,12105,12108,12111,12114,12368,13296,3459,10903,11058,11130,11924,12075,12273,12480,12507,13118,13396,13482,3910,12017,13019,4244,3646,4616,3921,3955,4603,4606,4607,3414,3419,4605,3418,4604,4367,4411,3743,11888,4338,11747,4632,10766,10769,4637,11243,11246,11434,11545,11562,11608,4029,11605,11944,11948,12635,12643,12735,13236,13302,3876,11173,11179,11197,12195,12325,12405,12700,3727,11313,11437,12437,12548,12561,12640,12695,12703,12823,13243,4201,3878,10906,11276,11443,11477,11488,12551,12639,12689,12729,12779,13338,3588,3696,10819,10822,10918,11084,3695,4635,11889,4631,12987,4636,10655,10772,12501,12510,12557,12760,4299,11044,12519,12534,12560,4207,3909,12829,3854,3855,4633,10486,10489,10861,10864,11761,11949,12772,4634,11869,11954,3879,10825,11090,13383,3880,4139,4650,4676,4731,4735,4759,4774,4781,4783,4819,482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% 112.37/112.17 ['proof']). % 112.37/112.17 % SZS output end Proof % 112.37/112.17 % Total time :82.930000s %------------------------------------------------------------------------------