%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW207+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n014.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 18:06:23 EDT 2024 % Result : Theorem 7.54s 7.63s % Output : CNFRefutation 7.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SWW207+1 : TPTP v8.2.0. Released v5.2.0. % 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n014.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Jun 19 06:48:39 EDT 2024 % 0.13/0.34 % CPUTime : % 0.20/0.57 start to proof:theBenchmark % 7.47/7.56 %------------------------------------------- % 7.47/7.56 % File :CSE---1.7 % 7.47/7.56 % Problem :theBenchmark % 7.47/7.56 % Transform :cnf % 7.47/7.56 % Format :tptp:raw % 7.47/7.56 % Command :java -jar mcs_scs.jar %d %s % 7.47/7.56 % 7.47/7.56 % Result :Theorem 5.980000s % 7.47/7.56 % Output :CNFRefutation 5.980000s % 7.47/7.56 %------------------------------------------- % 7.47/7.56 %------------------------------------------------------------------------------ % 7.47/7.56 % File : SWW207+1 : TPTP v8.2.0. Released v5.2.0. % 7.47/7.56 % Domain : Software Verification % 7.47/7.56 % Problem : Fundamental Theorem of Algebra 436793, 1000 axioms selected % 7.47/7.56 % Version : Especial. % 7.47/7.56 % English : % 7.47/7.56 % 7.47/7.56 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 7.47/7.56 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 7.47/7.56 % Source : [Bla11] % 7.47/7.56 % Names : fta_436793.1000.p [Bla11] % 7.47/7.56 % 7.47/7.56 % Status : Theorem % 7.47/7.56 % Rating : 0.53 v8.2.0, 0.50 v8.1.0, 0.56 v7.4.0, 0.47 v7.3.0, 0.55 v7.2.0, 0.52 v7.1.0, 0.48 v7.0.0, 0.60 v6.4.0, 0.58 v6.3.0, 0.54 v6.2.0, 0.60 v6.1.0, 0.77 v6.0.0, 0.70 v5.5.0, 0.74 v5.4.0, 0.79 v5.3.0, 0.81 v5.2.0 % 7.47/7.56 % Syntax : Number of formulae : 1269 ( 428 unt; 0 def) % 7.47/7.56 % Number of atoms : 2891 ( 732 equ) % 7.47/7.56 % Maximal formula atoms : 13 ( 2 avg) % 7.47/7.56 % Number of connectives : 1773 ( 151 ~; 57 |; 113 &) % 7.47/7.56 % ( 216 <=>;1236 =>; 0 <=; 0 <~>) % 7.47/7.56 % Maximal formula depth : 13 ( 4 avg) % 7.47/7.56 % Maximal term depth : 10 ( 2 avg) % 7.47/7.56 % Number of predicates : 78 ( 77 usr; 0 prp; 1-2 aty) % 7.47/7.56 % Number of functors : 52 ( 52 usr; 12 con; 0-5 aty) % 7.47/7.56 % Number of variables : 2668 (2625 !; 43 ?) % 7.47/7.56 % SPC : FOF_THM_RFO_SEQ % 7.47/7.56 % 7.47/7.56 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 7.47/7.56 % 2011-03-01 11:30:43 % 7.47/7.56 %------------------------------------------------------------------------------ % 7.47/7.56 %----Relevant facts (997) % 7.47/7.56 fof(fact_ext,axiom, % 7.47/7.56 ! [V_gb_2,V_fa_2] : % 7.47/7.56 ( ! [B_x] : hAPP(V_fa_2,B_x) = hAPP(V_gb_2,B_x) % 7.47/7.56 => V_fa_2 = V_gb_2 ) ). % 7.47/7.56 % 7.47/7.56 fof(fact_f_I1_J,axiom, % 7.47/7.56 c_SEQ_Osubseq(v_f____) ). % 7.47/7.56 % 7.47/7.56 fof(fact_g_I1_J,axiom, % 7.47/7.56 c_SEQ_Osubseq(v_ga____) ). % 7.47/7.56 % 7.47/7.56 fof(fact_rp,axiom, % 7.47/7.56 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ). % 7.47/7.56 % 7.47/7.56 fof(fact_abs__not__less__zero,axiom, % 7.47/7.56 ! [V_a,T_a] : % 7.47/7.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.47/7.56 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 7.47/7.56 % 7.47/7.56 fof(fact_zero__less__abs__iff,axiom, % 7.47/7.56 ! [V_a_2,T_a] : % 7.47/7.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.47/7.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2))) % 7.47/7.56 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.47/7.56 % 7.47/7.56 fof(fact_abs__of__pos,axiom, % 7.47/7.56 ! [V_a,T_a] : % 7.47/7.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.47/7.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.47/7.56 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ). % 7.47/7.56 % 7.47/7.56 fof(fact_abs__ge__zero,axiom, % 7.47/7.56 ! [V_a,T_a] : % 7.47/7.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.47/7.56 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a))) ) ). % 7.47/7.56 % 7.47/7.56 fof(fact_abs__le__zero__iff,axiom, % 7.47/7.56 ! [V_a_2,T_a] : % 7.47/7.56 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.47/7.56 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 7.47/7.57 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_abs__of__nonneg,axiom, % 7.47/7.57 ! [V_a,T_a] : % 7.47/7.57 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.47/7.57 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_order__refl,axiom, % 7.47/7.57 ! [V_x,T_a] : % 7.47/7.57 ( class_Orderings_Opreorder(T_a) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_assms,axiom, % 7.47/7.57 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r)) ). % 7.47/7.57 % 7.47/7.57 fof(fact_real__less__def,axiom, % 7.47/7.57 ! [V_y_2,V_x_2] : % 7.47/7.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) % 7.47/7.57 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) % 7.47/7.57 & V_x_2 != V_y_2 ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_less__eq__real__def,axiom, % 7.47/7.57 ! [V_y_2,V_x_2] : % 7.47/7.57 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) % 7.47/7.57 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) % 7.47/7.57 | V_x_2 = V_y_2 ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_abs__ge__self,axiom, % 7.47/7.57 ! [V_a,T_a] : % 7.47/7.57 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a))) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_abs__le__D1,axiom, % 7.47/7.57 ! [V_b,V_a,T_a] : % 7.47/7.57 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_b)) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact__096cmod_A_Is_A0_J_A_060_061_Ar_096,axiom, % 7.47/7.57 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)) ). % 7.47/7.57 % 7.47/7.57 fof(fact_zero__reorient,axiom, % 7.47/7.57 ! [V_x_2,T_a] : % 7.47/7.57 ( class_Groups_Ozero(T_a) % 7.47/7.57 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 7.47/7.57 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_linorder__le__cases,axiom, % 7.47/7.57 ! [V_y,V_x,T_a] : % 7.47/7.57 ( class_Orderings_Olinorder(T_a) % 7.47/7.57 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_le__funE,axiom, % 7.47/7.57 ! [V_x_2,V_gb_2,V_fa_2,T_a,T_b] : % 7.47/7.57 ( class_Orderings_Oord(T_b) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2))) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_xt1_I6_J,axiom, % 7.47/7.57 ! [V_z,V_x,V_y,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_xt1_I5_J,axiom, % 7.47/7.57 ! [V_x,V_y,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 7.47/7.57 => V_x = V_y ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_order__trans,axiom, % 7.47/7.57 ! [V_z,V_y,V_x,T_a] : % 7.47/7.57 ( class_Orderings_Opreorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_order__antisym,axiom, % 7.47/7.57 ! [V_y,V_x,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 7.47/7.57 => V_x = V_y ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_xt1_I4_J,axiom, % 7.47/7.57 ! [V_c,V_a,V_b,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 7.47/7.57 => ( V_b = V_c % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_ord__le__eq__trans,axiom, % 7.47/7.57 ! [V_c,V_b,V_a,T_a] : % 7.47/7.57 ( class_Orderings_Oord(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.47/7.57 => ( V_b = V_c % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_xt1_I3_J,axiom, % 7.47/7.57 ! [V_c,V_b,V_a,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( V_a = V_b % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b)) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_ord__eq__le__trans,axiom, % 7.47/7.57 ! [V_c,V_b,V_a,T_a] : % 7.47/7.57 ( class_Orderings_Oord(T_a) % 7.47/7.57 => ( V_a = V_b % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_order__antisym__conv,axiom, % 7.47/7.57 ! [V_x_2,V_y_2,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 7.47/7.57 <=> V_x_2 = V_y_2 ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_le__funD,axiom, % 7.47/7.57 ! [V_x_2,V_gb_2,V_fa_2,T_a,T_b] : % 7.47/7.57 ( class_Orderings_Oord(T_b) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2))) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_order__eq__refl,axiom, % 7.47/7.57 ! [V_y,V_x,T_a] : % 7.47/7.57 ( class_Orderings_Opreorder(T_a) % 7.47/7.57 => ( V_x = V_y % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_order__eq__iff,axiom, % 7.47/7.57 ! [V_y_2,V_x_2,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( V_x_2 = V_y_2 % 7.47/7.57 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 7.47/7.57 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_linorder__linear,axiom, % 7.47/7.57 ! [V_y,V_x,T_a] : % 7.47/7.57 ( class_Orderings_Olinorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 7.47/7.57 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_le__fun__def,axiom, % 7.47/7.57 ! [V_gb_2,V_fa_2,T_a,T_b] : % 7.47/7.57 ( class_Orderings_Oord(T_b) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) % 7.47/7.57 <=> ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x)),hAPP(V_gb_2,B_x))) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_linorder__cases,axiom, % 7.47/7.57 ! [V_y,V_x,T_a] : % 7.47/7.57 ( class_Orderings_Olinorder(T_a) % 7.47/7.57 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.47/7.57 => ( V_x != V_y % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_order__less__asym,axiom, % 7.47/7.57 ! [V_y,V_x,T_a] : % 7.47/7.57 ( class_Orderings_Opreorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.47/7.57 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_xt1_I10_J,axiom, % 7.47/7.57 ! [V_z,V_x,V_y,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y)) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_order__less__trans,axiom, % 7.47/7.57 ! [V_z,V_y,V_x,T_a] : % 7.47/7.57 ( class_Orderings_Opreorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z)) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_xt1_I2_J,axiom, % 7.47/7.57 ! [V_c,V_a,V_b,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) % 7.47/7.57 => ( V_b = V_c % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_ord__less__eq__trans,axiom, % 7.47/7.57 ! [V_c,V_b,V_a,T_a] : % 7.47/7.57 ( class_Orderings_Oord(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) % 7.47/7.57 => ( V_b = V_c % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_xt1_I1_J,axiom, % 7.47/7.57 ! [V_c,V_b,V_a,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( V_a = V_b % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_b)) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_ord__eq__less__trans,axiom, % 7.47/7.57 ! [V_c,V_b,V_a,T_a] : % 7.47/7.57 ( class_Orderings_Oord(T_a) % 7.47/7.57 => ( V_a = V_b % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c)) % 7.47/7.57 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)) ) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_xt1_I9_J,axiom, % 7.47/7.57 ! [V_a,V_b,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) % 7.47/7.57 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_order__less__asym_H,axiom, % 7.47/7.57 ! [V_b,V_a,T_a] : % 7.47/7.57 ( class_Orderings_Opreorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) % 7.47/7.57 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_order__less__imp__not__eq2,axiom, % 7.47/7.57 ! [V_y,V_x,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.47/7.57 => V_y != V_x ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_order__less__imp__not__eq,axiom, % 7.47/7.57 ! [V_y,V_x,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.47/7.57 => V_x != V_y ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_order__less__imp__not__less,axiom, % 7.47/7.57 ! [V_y,V_x,T_a] : % 7.47/7.57 ( class_Orderings_Opreorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.47/7.57 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_order__less__not__sym,axiom, % 7.47/7.57 ! [V_y,V_x,T_a] : % 7.47/7.57 ( class_Orderings_Opreorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.47/7.57 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ). % 7.47/7.57 % 7.47/7.57 fof(fact_less__imp__neq,axiom, % 7.47/7.57 ! [V_y,V_x,T_a] : % 7.47/7.57 ( class_Orderings_Oorder(T_a) % 7.47/7.57 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.47/7.57 => V_x != V_y ) ) ). % 7.47/7.58 % 7.47/7.58 fof(fact_linorder__neqE,axiom, % 7.47/7.58 ! [V_y,V_x,T_a] : % 7.47/7.58 ( class_Orderings_Olinorder(T_a) % 7.47/7.58 => ( V_x != V_y % 7.47/7.58 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.47/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ) ). % 7.47/7.58 % 7.47/7.58 fof(fact_linorder__antisym__conv3,axiom, % 7.47/7.58 ! [V_x_2,V_y_2,T_a] : % 7.47/7.58 ( class_Orderings_Olinorder(T_a) % 7.47/7.58 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)) % 7.47/7.58 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) % 7.47/7.58 <=> V_x_2 = V_y_2 ) ) ) ). % 7.47/7.58 % 7.47/7.58 fof(fact_linorder__less__linear,axiom, % 7.47/7.58 ! [V_y,V_x,T_a] : % 7.47/7.58 ( class_Orderings_Olinorder(T_a) % 7.47/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.47/7.58 | V_x = V_y % 7.47/7.58 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ). % 7.47/7.58 % 7.47/7.58 fof(fact_not__less__iff__gr__or__eq,axiom, % 7.47/7.58 ! [V_y_2,V_x_2,T_a] : % 7.47/7.58 ( class_Orderings_Olinorder(T_a) % 7.47/7.58 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) % 7.47/7.58 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)) % 7.47/7.58 | V_x_2 = V_y_2 ) ) ) ). % 7.47/7.58 % 7.47/7.58 fof(fact_linorder__neq__iff,axiom, % 7.47/7.58 ! [V_y_2,V_x_2,T_a] : % 7.47/7.58 ( class_Orderings_Olinorder(T_a) % 7.47/7.58 => ( V_x_2 != V_y_2 % 7.47/7.58 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) % 7.47/7.58 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)) ) ) ) ). % 7.47/7.58 % 7.47/7.58 fof(fact_order__less__irrefl,axiom, % 7.47/7.58 ! [V_x,T_a] : % 7.47/7.58 ( class_Orderings_Opreorder(T_a) % 7.47/7.58 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_x)) ) ). % 7.47/7.58 % 7.47/7.58 fof(fact_real__le__antisym,axiom, % 7.47/7.58 ! [V_w,V_z] : % 7.47/7.58 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) % 7.47/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z)) % 7.47/7.58 => V_z = V_w ) ) ). % 7.47/7.58 % 7.47/7.58 fof(fact_real__le__trans,axiom, % 7.47/7.58 ! [V_k,V_j,V_i] : % 7.47/7.58 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j)) % 7.47/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k)) % 7.47/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ) ) ). % 7.47/7.58 % 7.47/7.58 fof(fact_real__le__linear,axiom, % 7.47/7.58 ! [V_w,V_z] : % 7.47/7.58 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) % 7.47/7.58 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z)) ) ). % 7.47/7.58 % 7.47/7.58 fof(fact_real__le__refl,axiom, % 7.47/7.58 ! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_w)) ). % 7.47/7.58 % 7.47/7.58 fof(fact_abs__idempotent,axiom, % 7.47/7.58 ! [V_a,T_a] : % 7.47/7.58 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.47/7.58 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_xt1_I8_J,axiom, % 7.54/7.58 ! [V_z,V_x,V_y,T_a] : % 7.54/7.58 ( class_Orderings_Oorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y)) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)) ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_order__le__less__trans,axiom, % 7.54/7.58 ! [V_z,V_y,V_x,T_a] : % 7.54/7.58 ( class_Orderings_Opreorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z)) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)) ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_xt1_I7_J,axiom, % 7.54/7.58 ! [V_z,V_x,V_y,T_a] : % 7.54/7.58 ( class_Orderings_Oorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)) ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_order__less__le__trans,axiom, % 7.54/7.58 ! [V_z,V_y,V_x,T_a] : % 7.54/7.58 ( class_Orderings_Opreorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z)) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)) ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_xt1_I11_J,axiom, % 7.54/7.58 ! [V_a,V_b,T_a] : % 7.54/7.58 ( class_Orderings_Oorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 7.54/7.58 => ( V_a != V_b % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_order__le__neq__trans,axiom, % 7.54/7.58 ! [V_b,V_a,T_a] : % 7.54/7.58 ( class_Orderings_Oorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.58 => ( V_a != V_b % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_order__le__imp__less__or__eq,axiom, % 7.54/7.58 ! [V_y,V_x,T_a] : % 7.54/7.58 ( class_Orderings_Oorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.54/7.58 | V_x = V_y ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_linorder__antisym__conv2,axiom, % 7.54/7.58 ! [V_y_2,V_x_2,T_a] : % 7.54/7.58 ( class_Orderings_Olinorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 7.54/7.58 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) % 7.54/7.58 <=> V_x_2 = V_y_2 ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_order__less__imp__le,axiom, % 7.54/7.58 ! [V_y,V_x,T_a] : % 7.54/7.58 ( class_Orderings_Opreorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_leD,axiom, % 7.54/7.58 ! [V_x,V_y,T_a] : % 7.54/7.58 ( class_Orderings_Olinorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 7.54/7.58 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_xt1_I12_J,axiom, % 7.54/7.58 ! [V_b,V_a,T_a] : % 7.54/7.58 ( class_Orderings_Oorder(T_a) % 7.54/7.58 => ( V_a != V_b % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_order__neq__le__trans,axiom, % 7.54/7.58 ! [V_b,V_a,T_a] : % 7.54/7.58 ( class_Orderings_Oorder(T_a) % 7.54/7.58 => ( V_a != V_b % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_linorder__antisym__conv1,axiom, % 7.54/7.58 ! [V_y_2,V_x_2,T_a] : % 7.54/7.58 ( class_Orderings_Olinorder(T_a) % 7.54/7.58 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 7.54/7.58 <=> V_x_2 = V_y_2 ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_not__leE,axiom, % 7.54/7.58 ! [V_x,V_y,T_a] : % 7.54/7.58 ( class_Orderings_Olinorder(T_a) % 7.54/7.58 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_leI,axiom, % 7.54/7.58 ! [V_y,V_x,T_a] : % 7.54/7.58 ( class_Orderings_Olinorder(T_a) % 7.54/7.58 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_order__le__less,axiom, % 7.54/7.58 ! [V_y_2,V_x_2,T_a] : % 7.54/7.58 ( class_Orderings_Oorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 7.54/7.58 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) % 7.54/7.58 | V_x_2 = V_y_2 ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_less__le__not__le,axiom, % 7.54/7.58 ! [V_y_2,V_x_2,T_a] : % 7.54/7.58 ( class_Orderings_Opreorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) % 7.54/7.58 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 7.54/7.58 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_order__less__le,axiom, % 7.54/7.58 ! [V_y_2,V_x_2,T_a] : % 7.54/7.58 ( class_Orderings_Oorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) % 7.54/7.58 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 7.54/7.58 & V_x_2 != V_y_2 ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_linorder__le__less__linear,axiom, % 7.54/7.58 ! [V_y,V_x,T_a] : % 7.54/7.58 ( class_Orderings_Olinorder(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) % 7.54/7.58 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_linorder__not__le,axiom, % 7.54/7.58 ! [V_y_2,V_x_2,T_a] : % 7.54/7.58 ( class_Orderings_Olinorder(T_a) % 7.54/7.58 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) % 7.54/7.58 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_linorder__not__less,axiom, % 7.54/7.58 ! [V_y_2,V_x_2,T_a] : % 7.54/7.58 ( class_Orderings_Olinorder(T_a) % 7.54/7.58 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) % 7.54/7.58 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_abs__eq__0,axiom, % 7.54/7.58 ! [V_a_2,T_a] : % 7.54/7.58 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.54/7.58 => ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.58 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_abs__zero,axiom, % 7.54/7.58 ! [T_a] : % 7.54/7.58 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.54/7.58 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_abs__Im__le__cmod,axiom, % 7.54/7.58 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))) ). % 7.54/7.58 % 7.54/7.58 fof(fact_zero__less__norm__iff,axiom, % 7.54/7.58 ! [V_x_2,T_a] : % 7.54/7.58 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))) % 7.54/7.58 <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_norm__le__zero__iff,axiom, % 7.54/7.58 ! [V_x_2,T_a] : % 7.54/7.58 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) % 7.54/7.58 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_norm__not__less__zero,axiom, % 7.54/7.58 ! [V_x,T_a] : % 7.54/7.58 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.58 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_norm__ge__zero,axiom, % 7.54/7.58 ! [V_x,T_a] : % 7.54/7.58 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x))) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_norm__eq__zero,axiom, % 7.54/7.58 ! [V_x_2,T_a] : % 7.54/7.58 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.58 => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) % 7.54/7.58 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_norm__zero,axiom, % 7.54/7.58 ! [T_a] : % 7.54/7.58 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.58 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_abs__norm__cancel,axiom, % 7.54/7.58 ! [V_a,T_a] : % 7.54/7.58 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.58 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_Im_Ozero,axiom, % 7.54/7.58 hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 7.54/7.58 % 7.54/7.58 fof(fact_th,axiom, % 7.54/7.58 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,B_n)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ). % 7.54/7.58 % 7.54/7.58 fof(fact_g_I2_J,axiom, % 7.54/7.58 c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))) ). % 7.54/7.58 % 7.54/7.58 fof(fact_subseq__def,axiom, % 7.54/7.58 ! [V_fa_2] : % 7.54/7.58 ( c_SEQ_Osubseq(V_fa_2) % 7.54/7.58 <=> ! [B_m,B_n] : % 7.54/7.58 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m),B_n)) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m)),hAPP(V_fa_2,B_n))) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_f_I2_J,axiom, % 7.54/7.58 c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))) ). % 7.54/7.58 % 7.54/7.58 fof(fact_norm__one,axiom, % 7.54/7.58 ! [T_a] : % 7.54/7.58 ( class_RealVector_Oreal__normed__algebra__1(T_a) % 7.54/7.58 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_one__reorient,axiom, % 7.54/7.58 ! [V_x_2,T_a] : % 7.54/7.58 ( class_Groups_Oone(T_a) % 7.54/7.58 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 7.54/7.58 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_less__fun__def,axiom, % 7.54/7.58 ! [V_gb_2,V_fa_2,T_a,T_b] : % 7.54/7.58 ( class_Orderings_Oord(T_b) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) % 7.54/7.58 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) % 7.54/7.58 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_gb_2),V_fa_2)) ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 7.54/7.58 ! [V_c,V_b,V_a,T_a] : % 7.54/7.58 ( class_Groups_Oab__semigroup__add(T_a) % 7.54/7.58 => 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)) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_add__left__cancel,axiom, % 7.54/7.58 ! [V_c_2,V_b_2,V_a_2,T_a] : % 7.54/7.58 ( class_Groups_Ocancel__semigroup__add(T_a) % 7.54/7.58 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2) % 7.54/7.58 <=> V_b_2 = V_c_2 ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_add__right__cancel,axiom, % 7.54/7.58 ! [V_c_2,V_a_2,V_b_2,T_a] : % 7.54/7.58 ( class_Groups_Ocancel__semigroup__add(T_a) % 7.54/7.58 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2) % 7.54/7.58 <=> V_b_2 = V_c_2 ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_add__left__imp__eq,axiom, % 7.54/7.58 ! [V_c,V_b,V_a,T_a] : % 7.54/7.58 ( class_Groups_Ocancel__semigroup__add(T_a) % 7.54/7.58 => ( 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) % 7.54/7.58 => V_b = V_c ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_add__imp__eq,axiom, % 7.54/7.58 ! [V_c,V_b,V_a,T_a] : % 7.54/7.58 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 7.54/7.58 => ( 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) % 7.54/7.58 => V_b = V_c ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_add__right__imp__eq,axiom, % 7.54/7.58 ! [V_c,V_a,V_b,T_a] : % 7.54/7.58 ( class_Groups_Ocancel__semigroup__add(T_a) % 7.54/7.58 => ( 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) % 7.54/7.58 => V_b = V_c ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_real__norm__def,axiom, % 7.54/7.58 ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ). % 7.54/7.58 % 7.54/7.58 fof(fact_norm__triangle__ineq,axiom, % 7.54/7.58 ! [V_y,V_x,T_a] : % 7.54/7.58 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_norm__add__less,axiom, % 7.54/7.58 ! [V_s,V_y,V_r,V_x,T_a] : % 7.54/7.58 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r)) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s)) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),V_s))) ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_monoseq__def,axiom, % 7.54/7.58 ! [V_X_2,T_a] : % 7.54/7.58 ( class_Orderings_Oorder(T_a) % 7.54/7.58 => ( c_SEQ_Omonoseq(T_a,V_X_2) % 7.54/7.58 <=> ( ! [B_m,B_n] : % 7.54/7.58 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) ) % 7.54/7.58 | ! [B_m,B_n] : % 7.54/7.58 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) % 7.54/7.58 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))) ) ) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_abs__add__one__not__less__self,axiom, % 7.54/7.58 ! [V_x] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_x)) ). % 7.54/7.58 % 7.54/7.58 fof(fact_add__0__left,axiom, % 7.54/7.58 ! [V_a,T_a] : % 7.54/7.58 ( class_Groups_Omonoid__add(T_a) % 7.54/7.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_add__0,axiom, % 7.54/7.58 ! [V_a,T_a] : % 7.54/7.58 ( class_Groups_Ocomm__monoid__add(T_a) % 7.54/7.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_double__zero__sym,axiom, % 7.54/7.58 ! [V_a_2,T_a] : % 7.54/7.58 ( class_Groups_Olinordered__ab__group__add(T_a) % 7.54/7.58 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) % 7.54/7.58 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_add__0__right,axiom, % 7.54/7.58 ! [V_a,T_a] : % 7.54/7.58 ( class_Groups_Omonoid__add(T_a) % 7.54/7.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_add_Ocomm__neutral,axiom, % 7.54/7.58 ! [V_a,T_a] : % 7.54/7.58 ( class_Groups_Ocomm__monoid__add(T_a) % 7.54/7.58 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_add__le__cancel__right,axiom, % 7.54/7.58 ! [V_b_2,V_c_2,V_a_2,T_a] : % 7.54/7.58 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) % 7.54/7.58 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_add__le__cancel__left,axiom, % 7.54/7.58 ! [V_b_2,V_a_2,V_c_2,T_a] : % 7.54/7.58 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) % 7.54/7.58 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_add__right__mono,axiom, % 7.54/7.58 ! [V_c,V_b,V_a,T_a] : % 7.54/7.58 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.58 => hBOOL(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))) ) ) ). % 7.54/7.58 % 7.54/7.58 fof(fact_add__left__mono,axiom, % 7.54/7.58 ! [V_c,V_b,V_a,T_a] : % 7.54/7.58 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 7.54/7.58 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.59 => hBOOL(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))) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__mono,axiom, % 7.54/7.59 ! [V_d,V_c,V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) % 7.54/7.59 => hBOOL(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))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__le__imp__le__right,axiom, % 7.54/7.59 ! [V_b,V_c,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 7.54/7.59 => ( hBOOL(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))) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__le__imp__le__left,axiom, % 7.54/7.59 ! [V_b,V_a,V_c,T_a] : % 7.54/7.59 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 7.54/7.59 => ( hBOOL(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))) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__less__cancel__right,axiom, % 7.54/7.59 ! [V_b_2,V_c_2,V_a_2,T_a] : % 7.54/7.59 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) % 7.54/7.59 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__less__cancel__left,axiom, % 7.54/7.59 ! [V_b_2,V_a_2,V_c_2,T_a] : % 7.54/7.59 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) % 7.54/7.59 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__strict__right__mono,axiom, % 7.54/7.59 ! [V_c,V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) % 7.54/7.59 => hBOOL(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))) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__strict__left__mono,axiom, % 7.54/7.59 ! [V_c,V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) % 7.54/7.59 => hBOOL(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))) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__strict__mono,axiom, % 7.54/7.59 ! [V_d,V_c,V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) % 7.54/7.59 => hBOOL(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))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__less__imp__less__right,axiom, % 7.54/7.59 ! [V_b,V_c,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 7.54/7.59 => ( hBOOL(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))) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__less__imp__less__left,axiom, % 7.54/7.59 ! [V_b,V_a,V_c,T_a] : % 7.54/7.59 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 7.54/7.59 => ( hBOOL(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))) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_real__add__left__mono,axiom, % 7.54/7.59 ! [V_z,V_y,V_x] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_abs__add__abs,axiom, % 7.54/7.59 ! [V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.54/7.59 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_real__zero__not__eq__one,axiom, % 7.54/7.59 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ). % 7.54/7.59 % 7.54/7.59 fof(fact_abs__add__one__gt__zero,axiom, % 7.54/7.59 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)))) ). % 7.54/7.59 % 7.54/7.59 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 7.54/7.59 ! [V_a_2,T_a] : % 7.54/7.59 ( class_Groups_Olinordered__ab__group__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) % 7.54/7.59 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 7.54/7.59 ! [V_a_2,T_a] : % 7.54/7.59 ( class_Groups_Olinordered__ab__group__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.59 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__nonneg__nonneg,axiom, % 7.54/7.59 ! [V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__comm__monoid__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.59 => hBOOL(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))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__nonneg__eq__0__iff,axiom, % 7.54/7.59 ! [V_y_2,V_x_2,T_a] : % 7.54/7.59 ( class_Groups_Oordered__comm__monoid__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 7.54/7.59 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.59 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.59 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__increasing,axiom, % 7.54/7.59 ! [V_c,V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__comm__monoid__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__increasing2,axiom, % 7.54/7.59 ! [V_a,V_b,V_c,T_a] : % 7.54/7.59 ( class_Groups_Oordered__comm__monoid__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__nonpos__nonpos,axiom, % 7.54/7.59 ! [V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__comm__monoid__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.59 => hBOOL(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))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 7.54/7.59 ! [V_a_2,T_a] : % 7.54/7.59 ( class_Groups_Olinordered__ab__group__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) % 7.54/7.59 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 7.54/7.59 ! [V_a_2,T_a] : % 7.54/7.59 ( class_Groups_Olinordered__ab__group__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.59 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__pos__pos,axiom, % 7.54/7.59 ! [V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__comm__monoid__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.59 => hBOOL(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))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__neg__neg,axiom, % 7.54/7.59 ! [V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__comm__monoid__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.59 => hBOOL(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))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__less__le__mono,axiom, % 7.54/7.59 ! [V_d,V_c,V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) % 7.54/7.59 => hBOOL(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))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__le__less__mono,axiom, % 7.54/7.59 ! [V_d,V_c,V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) % 7.54/7.59 => hBOOL(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))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_abs__triangle__ineq,axiom, % 7.54/7.59 ! [V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,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),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__pos__nonneg,axiom, % 7.54/7.59 ! [V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__comm__monoid__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.59 => hBOOL(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))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__nonneg__pos,axiom, % 7.54/7.59 ! [V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__comm__monoid__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.59 => hBOOL(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))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__strict__increasing,axiom, % 7.54/7.59 ! [V_c,V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__comm__monoid__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__strict__increasing2,axiom, % 7.54/7.59 ! [V_c,V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__comm__monoid__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__neg__nonpos,axiom, % 7.54/7.59 ! [V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__comm__monoid__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.59 => hBOOL(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))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__nonpos__neg,axiom, % 7.54/7.59 ! [V_b,V_a,T_a] : % 7.54/7.59 ( class_Groups_Oordered__comm__monoid__add(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.59 => hBOOL(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))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_seq__suble,axiom, % 7.54/7.59 ! [V_n_2,V_fa_2] : % 7.54/7.59 ( c_SEQ_Osubseq(V_fa_2) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),hAPP(V_fa_2,V_n_2))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_Asubseq_Ag_059_Amonoseq_A_I_Fn_O_AIm_A_Is_A_If_A_Ig_An_J_J_J_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom, % 7.54/7.59 ~ ! [B_g] : % 7.54/7.59 ( c_SEQ_Osubseq(B_g) % 7.54/7.59 => ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,B_g)))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_less__zeroE,axiom, % 7.54/7.59 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 7.54/7.59 % 7.54/7.59 fof(fact_zero__less__two,axiom, % 7.54/7.59 ! [T_a] : % 7.54/7.59 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.59 => hBOOL(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)))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_less__add__one,axiom, % 7.54/7.59 ! [V_a,T_a] : % 7.54/7.59 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.59 => hBOOL(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)))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_not__one__less__zero,axiom, % 7.54/7.59 ! [T_a] : % 7.54/7.59 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.59 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_zero__less__one,axiom, % 7.54/7.59 ! [T_a] : % 7.54/7.59 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_not__one__le__zero,axiom, % 7.54/7.59 ! [T_a] : % 7.54/7.59 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.59 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_zero__le__one,axiom, % 7.54/7.59 ! [T_a] : % 7.54/7.59 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_even__less__0__iff,axiom, % 7.54/7.59 ! [V_a_2,T_a] : % 7.54/7.59 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.59 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_pos__add__strict,axiom, % 7.54/7.59 ! [V_c,V_b,V_a,T_a] : % 7.54/7.59 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_le0,axiom, % 7.54/7.59 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 7.54/7.59 % 7.54/7.59 fof(fact_le__refl,axiom, % 7.54/7.59 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n)) ). % 7.54/7.59 % 7.54/7.59 fof(fact_le__add2,axiom, % 7.54/7.59 ! [V_m,V_n] : hBOOL(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))) ). % 7.54/7.59 % 7.54/7.59 fof(fact_le__add1,axiom, % 7.54/7.59 ! [V_m,V_n] : hBOOL(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))) ). % 7.54/7.59 % 7.54/7.59 fof(fact_le__iff__add,axiom, % 7.54/7.59 ! [V_n_2,V_m_2] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) % 7.54/7.59 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_nat__le__linear,axiom, % 7.54/7.59 ! [V_n,V_m] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 7.54/7.59 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_nat__add__left__cancel__le,axiom, % 7.54/7.59 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) % 7.54/7.59 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_eq__imp__le,axiom, % 7.54/7.59 ! [V_n,V_m] : % 7.54/7.59 ( V_m = V_n % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_trans__le__add1,axiom, % 7.54/7.59 ! [V_m,V_j,V_i] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 7.54/7.59 => hBOOL(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))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_trans__le__add2,axiom, % 7.54/7.59 ! [V_m,V_j,V_i] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 7.54/7.59 => hBOOL(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))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__le__mono1,axiom, % 7.54/7.59 ! [V_k,V_j,V_i] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 7.54/7.59 => hBOOL(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))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_le__trans,axiom, % 7.54/7.59 ! [V_k,V_j,V_i] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_le__antisym,axiom, % 7.54/7.59 ! [V_n,V_m] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) % 7.54/7.59 => V_m = V_n ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__le__mono,axiom, % 7.54/7.59 ! [V_l,V_k,V_j,V_i] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l)) % 7.54/7.59 => hBOOL(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))) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__leD2,axiom, % 7.54/7.59 ! [V_n,V_k,V_m] : % 7.54/7.59 ( hBOOL(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)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__leD1,axiom, % 7.54/7.59 ! [V_n,V_k,V_m] : % 7.54/7.59 ( hBOOL(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)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__leE,axiom, % 7.54/7.59 ! [V_n,V_k,V_m] : % 7.54/7.59 ( hBOOL(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)) % 7.54/7.59 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 7.54/7.59 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_Re_Oadd,axiom, % 7.54/7.59 ! [V_y,V_x] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)) ). % 7.54/7.59 % 7.54/7.59 fof(fact_complex__Re__one,axiom, % 7.54/7.59 hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__eq__self__zero,axiom, % 7.54/7.59 ! [V_n,V_m] : % 7.54/7.59 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 7.54/7.59 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__is__0,axiom, % 7.54/7.59 ! [V_n_2,V_m_2] : % 7.54/7.59 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.59 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.59 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_Nat_Oadd__0__right,axiom, % 7.54/7.59 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 7.54/7.59 % 7.54/7.59 fof(fact_plus__nat_Oadd__0,axiom, % 7.54/7.59 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__lessD1,axiom, % 7.54/7.59 ! [V_k,V_j,V_i] : % 7.54/7.59 ( hBOOL(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)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_k)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_less__add__eq__less,axiom, % 7.54/7.59 ! [V_n,V_m,V_l,V_k] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l)) % 7.54/7.59 => ( 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) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__less__mono,axiom, % 7.54/7.59 ! [V_l,V_k,V_j,V_i] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l)) % 7.54/7.59 => hBOOL(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))) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__less__mono1,axiom, % 7.54/7.59 ! [V_k,V_j,V_i] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) % 7.54/7.59 => hBOOL(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))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_trans__less__add2,axiom, % 7.54/7.59 ! [V_m,V_j,V_i] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) % 7.54/7.59 => hBOOL(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))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_trans__less__add1,axiom, % 7.54/7.59 ! [V_m,V_j,V_i] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) % 7.54/7.59 => hBOOL(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))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_nat__add__left__cancel__less,axiom, % 7.54/7.59 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) % 7.54/7.59 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_not__add__less2,axiom, % 7.54/7.59 ! [V_i,V_j] : ~ hBOOL(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)) ). % 7.54/7.59 % 7.54/7.59 fof(fact_not__add__less1,axiom, % 7.54/7.59 ! [V_j,V_i] : ~ hBOOL(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)) ). % 7.54/7.59 % 7.54/7.59 fof(fact_complex__equality,axiom, % 7.54/7.59 ! [V_y,V_x] : % 7.54/7.59 ( hAPP(c_Complex_ORe,V_x) = hAPP(c_Complex_ORe,V_y) % 7.54/7.59 => ( hAPP(c_Complex_OIm,V_x) = hAPP(c_Complex_OIm,V_y) % 7.54/7.59 => V_x = V_y ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_expand__complex__eq,axiom, % 7.54/7.59 ! [V_y_2,V_x_2] : % 7.54/7.59 ( V_x_2 = V_y_2 % 7.54/7.59 <=> ( hAPP(c_Complex_ORe,V_x_2) = hAPP(c_Complex_ORe,V_y_2) % 7.54/7.59 & hAPP(c_Complex_OIm,V_x_2) = hAPP(c_Complex_OIm,V_y_2) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__gr__0,axiom, % 7.54/7.59 ! [V_n_2,V_m_2] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))) % 7.54/7.59 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 7.54/7.59 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_complex__Re__le__cmod,axiom, % 7.54/7.59 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))) ). % 7.54/7.59 % 7.54/7.59 fof(fact_Re_Ozero,axiom, % 7.54/7.59 hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 7.54/7.59 % 7.54/7.59 fof(fact_Im_Oadd,axiom, % 7.54/7.59 ! [V_y,V_x] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)) ). % 7.54/7.59 % 7.54/7.59 fof(fact_complex__Im__one,axiom, % 7.54/7.59 hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 7.54/7.59 % 7.54/7.59 fof(fact_abs__Re__le__cmod,axiom, % 7.54/7.59 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))) ). % 7.54/7.59 % 7.54/7.59 fof(fact_linorder__neqE__linordered__idom,axiom, % 7.54/7.59 ! [V_y,V_x,T_a] : % 7.54/7.59 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.59 => ( V_x != V_y % 7.54/7.59 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_complex__mod__triangle__sub,axiom, % 7.54/7.59 ! [V_z,V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_w),V_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)))) ). % 7.54/7.59 % 7.54/7.59 fof(fact_le__0__eq,axiom, % 7.54/7.59 ! [V_n_2] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 7.54/7.59 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 7.54/7.59 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 7.54/7.59 % 7.54/7.59 fof(fact_nat__less__cases,axiom, % 7.54/7.59 ! [V_P_2,V_n_2,V_m_2] : % 7.54/7.59 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) % 7.54/7.59 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 7.54/7.59 => ( ( V_m_2 = V_n_2 % 7.54/7.59 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 7.54/7.59 => ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) % 7.54/7.59 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 7.54/7.59 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_less__or__eq__imp__le,axiom, % 7.54/7.59 ! [V_n,V_m] : % 7.54/7.59 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.59 | V_m = V_n ) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_le__neq__implies__less,axiom, % 7.54/7.59 ! [V_n,V_m] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 7.54/7.59 => ( V_m != V_n % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_less__imp__le__nat,axiom, % 7.54/7.59 ! [V_n,V_m] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_less__not__refl3,axiom, % 7.54/7.59 ! [V_t,V_s] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t)) % 7.54/7.59 => V_s != V_t ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_less__not__refl2,axiom, % 7.54/7.59 ! [V_m,V_n] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m)) % 7.54/7.59 => V_m != V_n ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_less__irrefl__nat,axiom, % 7.54/7.59 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)) ). % 7.54/7.59 % 7.54/7.59 fof(fact_linorder__neqE__nat,axiom, % 7.54/7.59 ! [V_y,V_x] : % 7.54/7.59 ( V_x != V_y % 7.54/7.59 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y),V_x)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_le__eq__less__or__eq,axiom, % 7.54/7.59 ! [V_n_2,V_m_2] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) % 7.54/7.59 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) % 7.54/7.59 | V_m_2 = V_n_2 ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_nat__less__le,axiom, % 7.54/7.59 ! [V_n_2,V_m_2] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) % 7.54/7.59 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) % 7.54/7.59 & V_m_2 != V_n_2 ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_nat__neq__iff,axiom, % 7.54/7.59 ! [V_n_2,V_m_2] : % 7.54/7.59 ( V_m_2 != V_n_2 % 7.54/7.59 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) % 7.54/7.59 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_less__not__refl,axiom, % 7.54/7.59 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)) ). % 7.54/7.59 % 7.54/7.59 fof(fact_double__eq__0__iff,axiom, % 7.54/7.59 ! [V_a_2,T_a] : % 7.54/7.59 ( class_Groups_Olinordered__ab__group__add(T_a) % 7.54/7.59 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.59 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_zero__neq__one,axiom, % 7.54/7.59 ! [T_a] : % 7.54/7.59 ( class_Rings_Ozero__neq__one(T_a) % 7.54/7.59 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_one__neq__zero,axiom, % 7.54/7.59 ! [T_a] : % 7.54/7.59 ( class_Rings_Ozero__neq__one(T_a) % 7.54/7.59 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_gr0I,axiom, % 7.54/7.59 ! [V_n] : % 7.54/7.59 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_gr__implies__not0,axiom, % 7.54/7.59 ! [V_n,V_m] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.59 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_less__nat__zero__code,axiom, % 7.54/7.59 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 7.54/7.59 % 7.54/7.59 fof(fact_neq0__conv,axiom, % 7.54/7.59 ! [V_n_2] : % 7.54/7.59 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.59 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_not__less0,axiom, % 7.54/7.59 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 7.54/7.59 % 7.54/7.59 fof(fact_abs__one,axiom, % 7.54/7.59 ! [T_a] : % 7.54/7.59 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.59 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_conv1,axiom, % 7.54/7.59 c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))) ). % 7.54/7.59 % 7.54/7.59 fof(fact_termination__basic__simps_I5_J,axiom, % 7.54/7.59 ! [V_y,V_x] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_decseq__def,axiom, % 7.54/7.59 ! [V_X_2,T_a] : % 7.54/7.59 ( class_Orderings_Oorder(T_a) % 7.54/7.59 => ( c_SEQ_Odecseq(T_a,V_X_2) % 7.54/7.59 <=> ! [B_m,B_n] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_add__0__iff,axiom, % 7.54/7.59 ! [V_a_2,V_b_2,T_a] : % 7.54/7.59 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 7.54/7.59 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) % 7.54/7.59 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 7.54/7.59 ! [V_a,T_a] : % 7.54/7.59 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 7.54/7.59 ! [V_a,T_a] : % 7.54/7.59 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_Bseq__def,axiom, % 7.54/7.59 ! [V_X_2,T_a] : % 7.54/7.59 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.59 => ( c_SEQ_OBseq(T_a,V_X_2) % 7.54/7.59 <=> ? [B_K] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.59 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K)) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_incseq__def,axiom, % 7.54/7.59 ! [V_X_2,T_a] : % 7.54/7.59 ( class_Orderings_Oorder(T_a) % 7.54/7.59 => ( c_SEQ_Oincseq(T_a,V_X_2) % 7.54/7.59 <=> ! [B_m,B_n] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) % 7.54/7.59 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_nat__add__right__cancel,axiom, % 7.54/7.59 ! [V_n_2,V_k_2,V_m_2] : % 7.54/7.59 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2) % 7.54/7.59 <=> V_m_2 = V_n_2 ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_nat__add__left__cancel,axiom, % 7.54/7.59 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.59 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2) % 7.54/7.59 <=> V_m_2 = V_n_2 ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_nat__add__assoc,axiom, % 7.54/7.59 ! [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)) ). % 7.54/7.59 % 7.54/7.59 fof(fact_nat__add__left__commute,axiom, % 7.54/7.59 ! [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)) ). % 7.54/7.59 % 7.54/7.59 fof(fact_nat__add__commute,axiom, % 7.54/7.59 ! [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) ). % 7.54/7.59 % 7.54/7.59 fof(fact_convergent__const,axiom, % 7.54/7.59 ! [V_c_2,T_a] : % 7.54/7.59 ( class_RealVector_Ometric__space(T_a) % 7.54/7.59 => c_SEQ_Oconvergent(T_a,c_COMBK(T_a,tc_Nat_Onat,V_c_2)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_Bseq__monoseq__convergent,axiom, % 7.54/7.59 ! [V_X_2] : % 7.54/7.59 ( c_SEQ_OBseq(tc_RealDef_Oreal,V_X_2) % 7.54/7.59 => ( c_SEQ_Omonoseq(tc_RealDef_Oreal,V_X_2) % 7.54/7.59 => c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_Bseq__ignore__initial__segment,axiom, % 7.54/7.59 ! [V_k_2,V_X_2,T_a] : % 7.54/7.59 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.59 => ( c_SEQ_OBseq(T_a,V_X_2) % 7.54/7.59 => c_SEQ_OBseq(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2))) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_Bseq__offset,axiom, % 7.54/7.59 ! [V_k_2,V_X_2,T_a] : % 7.54/7.59 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.59 => ( c_SEQ_OBseq(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2))) % 7.54/7.59 => c_SEQ_OBseq(T_a,V_X_2) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_convergent__add,axiom, % 7.54/7.59 ! [V_Y_2,V_X_2,T_a] : % 7.54/7.59 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.59 => ( c_SEQ_Oconvergent(T_a,V_X_2) % 7.54/7.59 => ( c_SEQ_Oconvergent(T_a,V_Y_2) % 7.54/7.59 => c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(T_a),V_X_2),V_Y_2)) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 7.54/7.59 ! [V_d,V_c,V_b,V_a,T_a] : % 7.54/7.59 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.59 => 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)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 7.54/7.59 ! [V_c,V_b,V_a,T_a] : % 7.54/7.59 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.59 => 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) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 7.54/7.59 ! [V_c,V_b,V_a,T_a] : % 7.54/7.59 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.59 => 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)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 7.54/7.59 ! [V_d,V_c,V_a,T_a] : % 7.54/7.59 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.59 => 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) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 7.54/7.59 ! [V_d,V_c,V_a,T_a] : % 7.54/7.59 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.59 => 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)) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 7.54/7.59 ! [V_c,V_a,T_a] : % 7.54/7.59 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.59 => 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) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_termination__basic__simps_I1_J,axiom, % 7.54/7.59 ! [V_z,V_y,V_x] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y)) % 7.54/7.59 => hBOOL(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))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_termination__basic__simps_I2_J,axiom, % 7.54/7.59 ! [V_y,V_z,V_x] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_z)) % 7.54/7.59 => hBOOL(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))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_termination__basic__simps_I4_J,axiom, % 7.54/7.59 ! [V_y,V_z,V_x] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z)) % 7.54/7.59 => hBOOL(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))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_termination__basic__simps_I3_J,axiom, % 7.54/7.59 ! [V_z,V_y,V_x] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) % 7.54/7.59 => hBOOL(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))) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_incseq__imp__monoseq,axiom, % 7.54/7.59 ! [V_X_2,T_a] : % 7.54/7.59 ( class_Orderings_Oorder(T_a) % 7.54/7.59 => ( c_SEQ_Oincseq(T_a,V_X_2) % 7.54/7.59 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_decseq__imp__monoseq,axiom, % 7.54/7.59 ! [V_X_2,T_a] : % 7.54/7.59 ( class_Orderings_Oorder(T_a) % 7.54/7.59 => ( c_SEQ_Odecseq(T_a,V_X_2) % 7.54/7.59 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_le__Suc__ex__iff,axiom, % 7.54/7.59 ! [V_l_2,V_k_2] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_l_2)) % 7.54/7.59 <=> ? [B_n] : V_l_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_BseqD,axiom, % 7.54/7.59 ! [V_X_2,T_a] : % 7.54/7.59 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.59 => ( c_SEQ_OBseq(T_a,V_X_2) % 7.54/7.59 => ? [B_K] : % 7.54/7.59 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.59 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K)) ) ) ) ). % 7.54/7.59 % 7.54/7.59 fof(fact_BseqI,axiom, % 7.54/7.59 ! [V_X_2,V_K_2,T_a] : % 7.54/7.59 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.59 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_K_2)) % 7.54/7.60 => ( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),V_K_2)) % 7.54/7.60 => c_SEQ_OBseq(T_a,V_X_2) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_expi__zero,axiom, % 7.54/7.60 c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ). % 7.54/7.60 % 7.54/7.60 fof(fact_BseqI2_H,axiom, % 7.54/7.60 ! [V_K_2,V_X_2,V_N_2,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.60 => ( ! [B_n] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_N_2),B_n)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),V_K_2)) ) % 7.54/7.60 => c_SEQ_OBseq(T_a,V_X_2) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_ex__least__nat__less,axiom, % 7.54/7.60 ! [V_n_2,V_P_2] : % 7.54/7.60 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 7.54/7.60 => ( hBOOL(hAPP(V_P_2,V_n_2)) % 7.54/7.60 => ? [B_k] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k),V_n_2)) % 7.54/7.60 & ! [B_i] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i),B_k)) % 7.54/7.60 => ~ hBOOL(hAPP(V_P_2,B_i)) ) % 7.54/7.60 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_norm__sgn,axiom, % 7.54/7.60 ! [V_x,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.60 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.60 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) % 7.54/7.60 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.60 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_sgn__sgn,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_sgn__0__0,axiom, % 7.54/7.60 ! [V_a_2,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.60 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.60 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_sgn0,axiom, % 7.54/7.60 ! [T_a] : % 7.54/7.60 ( class_Groups_Osgn__if(T_a) % 7.54/7.60 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_sgn__zero__iff,axiom, % 7.54/7.60 ! [V_x_2,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.60 => ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.60 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_sgn__zero,axiom, % 7.54/7.60 ! [T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.60 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_sgn__one,axiom, % 7.54/7.60 ! [T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra__1(T_a) % 7.54/7.60 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_sgn__less,axiom, % 7.54/7.60 ! [V_a_2,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_sgn__greater,axiom, % 7.54/7.60 ! [V_a_2,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2))) % 7.54/7.60 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_Re_Oconvergent,axiom, % 7.54/7.60 ! [V_X_2] : % 7.54/7.60 ( c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2) % 7.54/7.60 => c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,V_X_2)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_Im_Oconvergent,axiom, % 7.54/7.60 ! [V_X_2] : % 7.54/7.60 ( c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2) % 7.54/7.60 => c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,V_X_2)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_real__sgn__pos,axiom, % 7.54/7.60 ! [V_x] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.60 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_sgn__pos,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_sgn__1__pos,axiom, % 7.54/7.60 ! [V_a_2,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.60 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) % 7.54/7.60 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_Bseq__mono__convergent,axiom, % 7.54/7.60 ! [V_X_2] : % 7.54/7.60 ( c_SEQ_OBseq(tc_RealDef_Oreal,V_X_2) % 7.54/7.60 => ( ! [B_m,B_n] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) ) % 7.54/7.60 => c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_natceiling__add__one,axiom, % 7.54/7.60 ! [V_x] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.60 => c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_natfloor__add__one,axiom, % 7.54/7.60 ! [V_x] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.60 => c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_psize__eq__0__iff,axiom, % 7.54/7.60 ! [V_p_2,T_a] : % 7.54/7.60 ( class_Groups_Ozero(T_a) % 7.54/7.60 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.60 <=> V_p_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_convex__bound__lt,axiom, % 7.54/7.60 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 7.54/7.60 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 7.54/7.60 => hBOOL(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)) ) ) ) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_Bseq__realpow,axiom, % 7.54/7.60 ! [V_x_2] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) % 7.54/7.60 => c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_norm__power,axiom, % 7.54/7.60 ! [V_n,V_x,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__div__algebra(T_a) % 7.54/7.60 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_norm__mult,axiom, % 7.54/7.60 ! [V_y,V_x,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__div__algebra(T_a) % 7.54/7.60 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 7.54/7.60 ! [V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Groups_Oab__semigroup__mult(T_a) % 7.54/7.60 => 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)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_le__mult__natfloor,axiom, % 7.54/7.60 ! [V_b,V_a] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_b)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b)))) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 7.54/7.60 ! [V_ry,V_rx,V_lx,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 7.54/7.60 ! [V_ry,V_rx,V_lx,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 7.54/7.60 ! [V_q,V_p,V_x,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 7.54/7.60 ! [V_rx,V_ly,V_lx,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 7.54/7.60 ! [V_rx,V_ly,V_lx,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 7.54/7.60 ! [V_q,V_y,V_x,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 7.54/7.60 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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))) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 7.54/7.60 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 7.54/7.60 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 7.54/7.60 ! [V_q,V_p,V_x,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_norm__power__ineq,axiom, % 7.54/7.60 ! [V_n,V_x,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra__1(T_a) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n))) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_norm__mult__ineq,axiom, % 7.54/7.60 ! [V_y,V_x,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_norm__mult__less,axiom, % 7.54/7.60 ! [V_s,V_y,V_r,V_x,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult_Ozero__left,axiom, % 7.54/7.60 ! [V_b,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__left_Ozero,axiom, % 7.54/7.60 ! [V_y,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult_Ozero__right,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__right_Ozero,axiom, % 7.54/7.60 ! [V_x,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__zero__left,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Rings_Omult__zero(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__zero__right,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Rings_Omult__zero(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__eq__0__iff,axiom, % 7.54/7.60 ! [V_b_2,V_a_2,T_a] : % 7.54/7.60 ( class_Rings_Oring__no__zero__divisors(T_a) % 7.54/7.60 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.60 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.60 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_no__zero__divisors,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Ono__zero__divisors(T_a) % 7.54/7.60 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.60 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_divisors__zero,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Ono__zero__divisors(T_a) % 7.54/7.60 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.60 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.60 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 7.54/7.60 ! [V_z,V_y,V_x,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_crossproduct__noteq,axiom, % 7.54/7.60 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 7.54/7.60 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 7.54/7.60 => ( ( V_a_2 != V_b_2 % 7.54/7.60 & V_c_2 != V_d_2 ) % 7.54/7.60 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 7.54/7.60 ! [V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 7.54/7.60 ! [V_b,V_m,V_a,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_crossproduct__eq,axiom, % 7.54/7.60 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] : % 7.54/7.60 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 7.54/7.60 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2)) % 7.54/7.60 <=> ( V_w_2 = V_x_2 % 7.54/7.60 | V_y_2 = V_z_2 ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__left_Oadd,axiom, % 7.54/7.60 ! [V_ya,V_y,V_x,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult_Oadd__left,axiom, % 7.54/7.60 ! [V_b,V_a_H,V_a,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_H),V_b)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__right_Oadd,axiom, % 7.54/7.60 ! [V_y,V_x,V_xa,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult_Oadd__right,axiom, % 7.54/7.60 ! [V_b_H,V_b,V_a,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),V_b_H)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_combine__common__factor,axiom, % 7.54/7.60 ! [V_c,V_b,V_e,V_a,T_a] : % 7.54/7.60 ( class_Rings_Osemiring(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__class_Odistrib,axiom, % 7.54/7.60 ! [V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring(T_a) % 7.54/7.60 => 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)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__1__left,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Groups_Omonoid__mult(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__1,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Groups_Ocomm__monoid__mult(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__1__right,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Groups_Omonoid__mult(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult_Ocomm__neutral,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Groups_Ocomm__monoid__mult(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 7.54/7.60 ! [V_x,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__0,axiom, % 7.54/7.60 ! [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) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__0__right,axiom, % 7.54/7.60 ! [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) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__is__0,axiom, % 7.54/7.60 ! [V_n_2,V_m_2] : % 7.54/7.60 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.60 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.60 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__cancel1,axiom, % 7.54/7.60 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.60 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 7.54/7.60 <=> ( V_m_2 = V_n_2 % 7.54/7.60 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__cancel2,axiom, % 7.54/7.60 ! [V_n_2,V_k_2,V_m_2] : % 7.54/7.60 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) % 7.54/7.60 <=> ( V_m_2 = V_n_2 % 7.54/7.60 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_real__mult__right__cancel,axiom, % 7.54/7.60 ! [V_b_2,V_a_2,V_c_2] : % 7.54/7.60 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) % 7.54/7.60 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2) % 7.54/7.60 <=> V_a_2 = V_b_2 ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_real__mult__left__cancel,axiom, % 7.54/7.60 ! [V_b_2,V_a_2,V_c_2] : % 7.54/7.60 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) % 7.54/7.60 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2) % 7.54/7.60 <=> V_a_2 = V_b_2 ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_abs__mult,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.60 => 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),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_abs__mult__self,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_add__mult__distrib,axiom, % 7.54/7.60 ! [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)) ). % 7.54/7.60 % 7.54/7.60 fof(fact_add__mult__distrib2,axiom, % 7.54/7.60 ! [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)) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__le__mono,axiom, % 7.54/7.60 ! [V_l,V_k,V_j,V_i] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l)) % 7.54/7.60 => hBOOL(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))) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__le__mono2,axiom, % 7.54/7.60 ! [V_k,V_j,V_i] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 7.54/7.60 => hBOOL(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))) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__le__mono1,axiom, % 7.54/7.60 ! [V_k,V_j,V_i] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 7.54/7.60 => hBOOL(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))) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_le__cube,axiom, % 7.54/7.60 ! [V_m] : hBOOL(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)))) ). % 7.54/7.60 % 7.54/7.60 fof(fact_le__square,axiom, % 7.54/7.60 ! [V_m] : hBOOL(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))) ). % 7.54/7.60 % 7.54/7.60 fof(fact_nat__mult__1,axiom, % 7.54/7.60 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 7.54/7.60 % 7.54/7.60 fof(fact_nat__1__eq__mult__iff,axiom, % 7.54/7.60 ! [V_n_2,V_m_2] : % 7.54/7.60 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 7.54/7.60 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 7.54/7.60 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_nat__mult__1__right,axiom, % 7.54/7.60 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 7.54/7.60 % 7.54/7.60 fof(fact_nat__mult__eq__1__iff,axiom, % 7.54/7.60 ! [V_n_2,V_m_2] : % 7.54/7.60 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 7.54/7.60 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 7.54/7.60 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_real__mult__1,axiom, % 7.54/7.60 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z ). % 7.54/7.60 % 7.54/7.60 fof(fact_real__add__mult__distrib,axiom, % 7.54/7.60 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)) ). % 7.54/7.60 % 7.54/7.60 fof(fact_sgn__times,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.60 => 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)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_sgn__mult,axiom, % 7.54/7.60 ! [V_y,V_x,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__div__algebra(T_a) % 7.54/7.60 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_natfloor__zero,axiom, % 7.54/7.60 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 7.54/7.60 % 7.54/7.60 fof(fact_zero__le__natfloor,axiom, % 7.54/7.60 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x))) ). % 7.54/7.60 % 7.54/7.60 fof(fact_natfloor__mono,axiom, % 7.54/7.60 ! [V_y,V_x] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_RComplete_Onatfloor(V_y))) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_complex__Im__mult,axiom, % 7.54/7.60 ! [V_y,V_x] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y))) ). % 7.54/7.60 % 7.54/7.60 fof(fact_natfloor__one,axiom, % 7.54/7.60 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__right_Oconvergent,axiom, % 7.54/7.60 ! [V_x_2,V_X_2,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.60 => ( c_SEQ_Oconvergent(T_a,V_X_2) % 7.54/7.60 => c_SEQ_Oconvergent(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_X_2)) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__left_Oconvergent,axiom, % 7.54/7.60 ! [V_y_2,V_X_2,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.60 => ( c_SEQ_Oconvergent(T_a,V_X_2) % 7.54/7.60 => c_SEQ_Oconvergent(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_y_2)) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult_Oconvergent,axiom, % 7.54/7.60 ! [V_Y_2,V_X_2,T_a] : % 7.54/7.60 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.60 => ( c_SEQ_Oconvergent(T_a,V_X_2) % 7.54/7.60 => ( c_SEQ_Oconvergent(T_a,V_Y_2) % 7.54/7.60 => c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_Y_2)) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_natceiling__zero,axiom, % 7.54/7.60 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 7.54/7.60 % 7.54/7.60 fof(fact_zero__le__natceiling,axiom, % 7.54/7.60 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(V_x))) ). % 7.54/7.60 % 7.54/7.60 fof(fact_natceiling__mono,axiom, % 7.54/7.60 ! [V_y,V_x] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),c_RComplete_Onatceiling(V_y))) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_natceiling__one,axiom, % 7.54/7.60 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 7.54/7.60 ! [V_x,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_zero__le__square,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__ring(T_a) % 7.54/7.60 => hBOOL(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))) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_zero__le__mult__iff,axiom, % 7.54/7.60 ! [V_b_2,V_a_2,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))) % 7.54/7.60 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 7.54/7.60 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__le__0__iff,axiom, % 7.54/7.60 ! [V_b_2,V_a_2,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 7.54/7.60 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__nonneg__nonneg,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Oordered__cancel__semiring(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__nonneg__nonpos,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Oordered__cancel__semiring(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__nonneg__nonpos2,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Oordered__cancel__semiring(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__nonpos__nonneg,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Oordered__cancel__semiring(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__nonpos__nonpos,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Oordered__ring(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__right__mono,axiom, % 7.54/7.60 ! [V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Oordered__semiring(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__left__mono,axiom, % 7.54/7.60 ! [V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Oordered__semiring(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__mult__left__mono,axiom, % 7.54/7.60 ! [V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Oordered__comm__semiring(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__right__mono__neg,axiom, % 7.54/7.60 ! [V_c,V_a,V_b,T_a] : % 7.54/7.60 ( class_Rings_Oordered__ring(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__left__mono__neg,axiom, % 7.54/7.60 ! [V_c,V_a,V_b,T_a] : % 7.54/7.60 ( class_Rings_Oordered__ring(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__mono_H,axiom, % 7.54/7.60 ! [V_d,V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Oordered__semiring(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(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))) ) ) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__mono,axiom, % 7.54/7.60 ! [V_d,V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Oordered__semiring(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(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))) ) ) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_split__mult__pos__le,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Oordered__ring(T_a) % 7.54/7.60 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 7.54/7.60 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 7.54/7.60 => hBOOL(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))) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_split__mult__neg__le,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Oordered__cancel__semiring(T_a) % 7.54/7.60 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 7.54/7.60 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 7.54/7.60 => hBOOL(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))) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_not__square__less__zero,axiom, % 7.54/7.60 ! [V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__ring(T_a) % 7.54/7.60 => ~ hBOOL(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))) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__less__cancel__right__disj,axiom, % 7.54/7.60 ! [V_b_2,V_c_2,V_a_2,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))) % 7.54/7.60 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) ) % 7.54/7.60 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)) ) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__less__cancel__left__disj,axiom, % 7.54/7.60 ! [V_b_2,V_a_2,V_c_2,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 7.54/7.60 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) ) % 7.54/7.60 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)) ) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__less__cancel__left__pos,axiom, % 7.54/7.60 ! [V_b_2,V_a_2,V_c_2,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 7.54/7.60 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__pos__pos,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__pos__neg,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__pos__neg2,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_zero__less__mult__pos,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(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))) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_zero__less__mult__pos2,axiom, % 7.54/7.60 ! [V_a,V_b,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(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))) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__less__cancel__left__neg,axiom, % 7.54/7.60 ! [V_b_2,V_a_2,V_c_2,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 7.54/7.60 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__neg__pos,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__neg__neg,axiom, % 7.54/7.60 ! [V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__strict__right__mono,axiom, % 7.54/7.60 ! [V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__strict__left__mono,axiom, % 7.54/7.60 ! [V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__mult__strict__left__mono,axiom, % 7.54/7.60 ! [V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__strict__right__mono__neg,axiom, % 7.54/7.60 ! [V_c,V_a,V_b,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__strict__left__mono__neg,axiom, % 7.54/7.60 ! [V_c,V_a,V_b,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_add__scale__eq__noteq,axiom, % 7.54/7.60 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 7.54/7.60 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 7.54/7.60 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.60 => ( ( V_a = V_b % 7.54/7.60 & V_c != V_d ) % 7.54/7.60 => 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)) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_less__1__mult,axiom, % 7.54/7.60 ! [V_n,V_m,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_m)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_n)) % 7.54/7.60 => hBOOL(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))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 7.54/7.60 ! [V_m,V_a,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 7.54/7.60 ! [V_a,V_m,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 7.54/7.60 ! [V_m,T_a] : % 7.54/7.60 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.60 => 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) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_abs__mult__less,axiom, % 7.54/7.60 ! [V_d,V_b,V_c,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_c)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b)),V_d)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_nat__0__less__mult__iff,axiom, % 7.54/7.60 ! [V_n_2,V_m_2] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) % 7.54/7.60 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__less__cancel1,axiom, % 7.54/7.60 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 7.54/7.60 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__less__cancel2,axiom, % 7.54/7.60 ! [V_n_2,V_k_2,V_m_2] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 7.54/7.60 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 7.54/7.60 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__less__mono1,axiom, % 7.54/7.60 ! [V_k,V_j,V_i] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 7.54/7.60 => hBOOL(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))) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__less__mono2,axiom, % 7.54/7.60 ! [V_k,V_j,V_i] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 7.54/7.60 => hBOOL(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))) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_real__mult__less__iff1,axiom, % 7.54/7.60 ! [V_y_2,V_x_2,V_z_2] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))) % 7.54/7.60 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_real__mult__order,axiom, % 7.54/7.60 ! [V_y,V_x] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_real__mult__less__mono2,axiom, % 7.54/7.60 ! [V_y,V_x,V_z] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y))) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__eq__self__implies__10,axiom, % 7.54/7.60 ! [V_n,V_m] : % 7.54/7.60 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 7.54/7.60 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 7.54/7.60 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_real__two__squares__add__zero__iff,axiom, % 7.54/7.60 ! [V_y_2,V_x_2] : % 7.54/7.60 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) % 7.54/7.60 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) % 7.54/7.60 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__sgn__abs,axiom, % 7.54/7.60 ! [V_x,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_abs__sgn,axiom, % 7.54/7.60 ! [V_k,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.60 => 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)) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_natfloor__neg,axiom, % 7.54/7.60 ! [V_x] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) % 7.54/7.60 => c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_natceiling__neg,axiom, % 7.54/7.60 ! [V_x] : % 7.54/7.60 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) % 7.54/7.60 => c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_expi__add,axiom, % 7.54/7.60 ! [V_b,V_a] : c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b)) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__le__cancel__left__pos,axiom, % 7.54/7.60 ! [V_b_2,V_a_2,V_c_2,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 7.54/7.60 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__le__cancel__left__neg,axiom, % 7.54/7.60 ! [V_b_2,V_a_2,V_c_2,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 7.54/7.60 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),V_a_2)) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__strict__mono,axiom, % 7.54/7.60 ! [V_d,V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(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))) ) ) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__strict__mono_H,axiom, % 7.54/7.60 ! [V_d,V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(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))) ) ) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__less__le__imp__less,axiom, % 7.54/7.60 ! [V_d,V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(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))) ) ) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__le__less__imp__less,axiom, % 7.54/7.60 ! [V_d,V_c,V_b,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(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))) ) ) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__right__less__imp__less,axiom, % 7.54/7.60 ! [V_b,V_c,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring(T_a) % 7.54/7.60 => ( hBOOL(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))) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__less__imp__less__right,axiom, % 7.54/7.60 ! [V_b,V_c,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(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))) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__left__less__imp__less,axiom, % 7.54/7.60 ! [V_b,V_a,V_c,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring(T_a) % 7.54/7.60 => ( hBOOL(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))) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__less__imp__less__left,axiom, % 7.54/7.60 ! [V_b,V_a,V_c,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(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))) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.60 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ). % 7.54/7.60 % 7.54/7.60 fof(fact_mult__right__le__imp__le,axiom, % 7.54/7.60 ! [V_b,V_c,V_a,T_a] : % 7.54/7.60 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.60 => ( hBOOL(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))) % 7.54/7.60 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult__left__le__imp__le,axiom, % 7.54/7.61 ! [V_b,V_a,V_c,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semiring__strict(T_a) % 7.54/7.61 => ( hBOOL(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))) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult__right__le__one__le,axiom, % 7.54/7.61 ! [V_y,V_x,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a))) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult__left__le__one__le,axiom, % 7.54/7.61 ! [V_y,V_x,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a))) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_abs__mult__pos,axiom, % 7.54/7.61 ! [V_y,V_x,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 7.54/7.61 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_abs__eq__mult,axiom, % 7.54/7.61 ! [V_b,V_a,T_a] : % 7.54/7.61 ( class_Rings_Oordered__ring__abs(T_a) % 7.54/7.61 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.61 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 7.54/7.61 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.61 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 7.54/7.61 => 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),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__mult__le__cancel__iff1,axiom, % 7.54/7.61 ! [V_y_2,V_x_2,V_z_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__mult__le__cancel__iff2,axiom, % 7.54/7.61 ! [V_y_2,V_x_2,V_z_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult__le__cancel1,axiom, % 7.54/7.61 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 7.54/7.61 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult__le__cancel2,axiom, % 7.54/7.61 ! [V_n_2,V_k_2,V_m_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) % 7.54/7.61 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_rabs__ratiotest__lemma,axiom, % 7.54/7.61 ! [V_y,V_x,V_c] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))) % 7.54/7.61 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_le__natfloor__eq__one,axiom, % 7.54/7.61 ! [V_x_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_natceiling__le__eq__one,axiom, % 7.54/7.61 ! [V_x_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_convex__bound__le,axiom, % 7.54/7.61 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semiring__1(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_a)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_a)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 7.54/7.61 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 7.54/7.61 => hBOOL(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)) ) ) ) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_norm__ratiotest__lemma,axiom, % 7.54/7.61 ! [V_y,V_x,V_c,T_a] : % 7.54/7.61 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))) % 7.54/7.61 => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_monoseq__realpow,axiom, % 7.54/7.61 ! [V_x_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) % 7.54/7.61 => c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_convergent__realpow,axiom, % 7.54/7.61 ! [V_x_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) % 7.54/7.61 => c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__strict__mono,axiom, % 7.54/7.61 ! [V_n,V_b,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.61 => hBOOL(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))) ) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_one__less__power,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.61 => hBOOL(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))) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__increasing__iff,axiom, % 7.54/7.61 ! [V_y_2,V_x_2,V_b_2,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2),V_y_2)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__le__imp__le__exp,axiom, % 7.54/7.61 ! [V_n,V_m,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) % 7.54/7.61 => ( hBOOL(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))) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__decreasing,axiom, % 7.54/7.61 ! [V_a,V_N,V_n,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oone__class_Oone(T_a))) % 7.54/7.61 => hBOOL(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))) ) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__eq__imp__eq__base,axiom, % 7.54/7.61 ! [V_b,V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( 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) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.61 => V_a = V_b ) ) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat__mult__commute,axiom, % 7.54/7.61 ! [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) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zpower__zpower,axiom, % 7.54/7.61 ! [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)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat__mult__assoc,axiom, % 7.54/7.61 ! [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)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__mult__commute,axiom, % 7.54/7.61 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__mult__assoc,axiom, % 7.54/7.61 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zero__less__zpower__abs__iff,axiom, % 7.54/7.61 ! [V_n_2,V_x_2] : % 7.54/7.61 ( hBOOL(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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))) % 7.54/7.61 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 7.54/7.61 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zpower__zadd__distrib,axiom, % 7.54/7.61 ! [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)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat__power__less__imp__less,axiom, % 7.54/7.61 ! [V_n,V_m,V_i] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 7.54/7.61 => ( hBOOL(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))) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat__zero__less__power__iff,axiom, % 7.54/7.61 ! [V_n_2,V_x_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))) % 7.54/7.61 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 7.54/7.61 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__mult,axiom, % 7.54/7.61 ! [V_n,V_m,V_a,T_a] : % 7.54/7.61 ( class_Groups_Omonoid__mult(T_a) % 7.54/7.61 => 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) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_field__power__not__zero,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 7.54/7.61 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.61 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__commutes,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Groups_Omonoid__mult(T_a) % 7.54/7.61 => 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)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__mult__distrib,axiom, % 7.54/7.61 ! [V_n,V_b,V_a,T_a] : % 7.54/7.61 ( class_Groups_Ocomm__monoid__mult(T_a) % 7.54/7.61 => 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)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__one,axiom, % 7.54/7.61 ! [V_n,T_a] : % 7.54/7.61 ( class_Groups_Omonoid__mult(T_a) % 7.54/7.61 => 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) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__abs,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.61 => 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),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__one__right,axiom, % 7.54/7.61 ! [V_a,T_a] : % 7.54/7.61 ( class_Groups_Omonoid__mult(T_a) % 7.54/7.61 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__mono,axiom, % 7.54/7.61 ! [V_n,V_b,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.61 => hBOOL(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))) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zero__le__power,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.61 => hBOOL(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))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zero__less__power,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.61 => hBOOL(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))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_one__le__power,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) % 7.54/7.61 => hBOOL(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))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__eq__0__iff,axiom, % 7.54/7.61 ! [V_n_2,V_a_2,T_a] : % 7.54/7.61 ( ( class_Power_Opower(T_a) % 7.54/7.61 & class_Rings_Omult__zero(T_a) % 7.54/7.61 & class_Rings_Ono__zero__divisors(T_a) % 7.54/7.61 & class_Rings_Ozero__neq__one(T_a) ) % 7.54/7.61 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.61 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.61 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__inject__exp,axiom, % 7.54/7.61 ! [V_n_2,V_m_2,V_a_2,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a_2)) % 7.54/7.61 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) % 7.54/7.61 <=> V_m_2 = V_n_2 ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__0,axiom, % 7.54/7.61 ! [V_a,T_a] : % 7.54/7.61 ( class_Power_Opower(T_a) % 7.54/7.61 => 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) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__add,axiom, % 7.54/7.61 ! [V_n,V_m,V_a,T_a] : % 7.54/7.61 ( class_Groups_Omonoid__mult(T_a) % 7.54/7.61 => 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)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__less__imp__less__base,axiom, % 7.54/7.61 ! [V_b,V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(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))) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__gt1__lemma,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) % 7.54/7.61 => hBOOL(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)))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__less__power__Suc,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) % 7.54/7.61 => hBOOL(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)))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__0__left,axiom, % 7.54/7.61 ! [V_n,T_a] : % 7.54/7.61 ( ( class_Power_Opower(T_a) % 7.54/7.61 & class_Rings_Osemiring__0(T_a) ) % 7.54/7.61 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.61 => 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) ) % 7.54/7.61 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.61 => 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) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zero__le__power__abs,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.61 => hBOOL(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),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__strict__increasing,axiom, % 7.54/7.61 ! [V_a,V_N,V_n,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) % 7.54/7.61 => hBOOL(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))) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__less__imp__less__exp,axiom, % 7.54/7.61 ! [V_n,V_m,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) % 7.54/7.61 => ( hBOOL(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))) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__strict__increasing__iff,axiom, % 7.54/7.61 ! [V_y_2,V_x_2,V_b_2,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__increasing,axiom, % 7.54/7.61 ! [V_a,V_N,V_n,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) % 7.54/7.61 => hBOOL(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))) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__Suc__less,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a))) % 7.54/7.61 => hBOOL(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))) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__strict__decreasing,axiom, % 7.54/7.61 ! [V_a,V_N,V_n,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a))) % 7.54/7.61 => hBOOL(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))) ) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat__mult__le__cancel1,axiom, % 7.54/7.61 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_sum__squares__gt__zero__iff,axiom, % 7.54/7.61 ! [V_y_2,V_x_2,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))) % 7.54/7.61 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.61 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_not__sum__squares__lt__zero,axiom, % 7.54/7.61 ! [V_y,V_x,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__ring(T_a) % 7.54/7.61 => ~ hBOOL(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))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_sum__squares__le__zero__iff,axiom, % 7.54/7.61 ! [V_y_2,V_x_2,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.61 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.61 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_pos__zmult__eq__1__iff,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 7.54/7.61 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 7.54/7.61 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 7.54/7.61 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_abs__zmult__eq__1,axiom, % 7.54/7.61 ! [V_n,V_m] : % 7.54/7.61 ( 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) % 7.54/7.61 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zmult__1__right,axiom, % 7.54/7.61 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 7.54/7.61 % 7.54/7.61 fof(fact_zmult__1,axiom, % 7.54/7.61 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 7.54/7.61 % 7.54/7.61 fof(fact_zero__le__zpower__abs,axiom, % 7.54/7.61 ! [V_n,V_x] : hBOOL(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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zmult__zless__mono2,axiom, % 7.54/7.61 ! [V_k,V_j,V_i] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 7.54/7.61 => hBOOL(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))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zmult__commute,axiom, % 7.54/7.61 ! [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) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zmult__assoc,axiom, % 7.54/7.61 ! [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)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zadd__zmult__distrib2,axiom, % 7.54/7.61 ! [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)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zadd__zmult__distrib,axiom, % 7.54/7.61 ! [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)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zle__add1__eq__le,axiom, % 7.54/7.61 ! [V_z_2,V_w_2] : % 7.54/7.61 ( hBOOL(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)))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),V_z_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zless__add1__eq,axiom, % 7.54/7.61 ! [V_z_2,V_w_2] : % 7.54/7.61 ( hBOOL(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)))) % 7.54/7.61 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) % 7.54/7.61 | V_w_2 = V_z_2 ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_add1__zle__eq,axiom, % 7.54/7.61 ! [V_z_2,V_w_2] : % 7.54/7.61 ( hBOOL(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)) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zless__imp__add1__zle,axiom, % 7.54/7.61 ! [V_z,V_w] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w),V_z)) % 7.54/7.61 => hBOOL(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)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zless__le,axiom, % 7.54/7.61 ! [V_w_2,V_z_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2)) % 7.54/7.61 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2),V_w_2)) % 7.54/7.61 & V_z_2 != V_w_2 ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zless__linear,axiom, % 7.54/7.61 ! [V_y,V_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),V_y)) % 7.54/7.61 | V_x = V_y % 7.54/7.61 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y),V_x)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zadd__zless__mono,axiom, % 7.54/7.61 ! [V_z,V_z_H,V_w,V_w_H] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H),V_w)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H),V_z)) % 7.54/7.61 => hBOOL(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))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zadd__strict__right__mono,axiom, % 7.54/7.61 ! [V_k,V_j,V_i] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j)) % 7.54/7.61 => hBOOL(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))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zadd__0,axiom, % 7.54/7.61 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 7.54/7.61 % 7.54/7.61 fof(fact_zadd__0__right,axiom, % 7.54/7.61 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 7.54/7.61 % 7.54/7.61 fof(fact_le__imp__0__less,axiom, % 7.54/7.61 ! [V_z] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 7.54/7.61 => hBOOL(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))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_odd__less__0,axiom, % 7.54/7.61 ! [V_z_2] : % 7.54/7.61 ( hBOOL(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))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zabs__less__one__iff,axiom, % 7.54/7.61 ! [V_z_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) % 7.54/7.61 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_int__one__le__iff__zero__less,axiom, % 7.54/7.61 ! [V_z_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_int__0__less__1,axiom, % 7.54/7.61 hBOOL(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))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_odd__nonzero,axiom, % 7.54/7.61 ! [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) ). % 7.54/7.61 % 7.54/7.61 fof(fact_int__0__neq__1,axiom, % 7.54/7.61 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat__mult__eq__cancel__disj,axiom, % 7.54/7.61 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.61 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 7.54/7.61 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.61 | V_m_2 = V_n_2 ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_left__add__mult__distrib,axiom, % 7.54/7.61 ! [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) ). % 7.54/7.61 % 7.54/7.61 fof(fact_sum__squares__eq__zero__iff,axiom, % 7.54/7.61 ! [V_y_2,V_x_2,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__ring__strict(T_a) % 7.54/7.61 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.61 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.61 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat__mult__eq__cancel1,axiom, % 7.54/7.61 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 7.54/7.61 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) % 7.54/7.61 <=> V_m_2 = V_n_2 ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat__mult__less__cancel1,axiom, % 7.54/7.61 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_sum__squares__ge__zero,axiom, % 7.54/7.61 ! [V_y,V_x,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__ring(T_a) % 7.54/7.61 => hBOOL(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)))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_reduce__poly__simple,axiom, % 7.54/7.61 ! [V_n,V_b] : % 7.54/7.61 ( V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) % 7.54/7.61 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.61 => ? [B_z] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zero__less__power__nat__eq,axiom, % 7.54/7.61 ! [V_n_2,V_x_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))) % 7.54/7.61 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.61 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_self__quotient__aux2,axiom, % 7.54/7.61 ! [V_q,V_r,V_a] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 7.54/7.61 => ( 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)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_self__quotient__aux1,axiom, % 7.54/7.61 ! [V_q,V_r,V_a] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 7.54/7.61 => ( 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)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_a)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zadd__left__mono,axiom, % 7.54/7.61 ! [V_k,V_j,V_i] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j)) % 7.54/7.61 => hBOOL(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))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zadd__assoc,axiom, % 7.54/7.61 ! [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)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zadd__left__commute,axiom, % 7.54/7.61 ! [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)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zadd__commute,axiom, % 7.54/7.61 ! [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) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zle__antisym,axiom, % 7.54/7.61 ! [V_w,V_z] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z)) % 7.54/7.61 => V_z = V_w ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zle__trans,axiom, % 7.54/7.61 ! [V_k,V_j,V_i] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j),V_k)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_k)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zle__linear,axiom, % 7.54/7.61 ! [V_w,V_z] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w)) % 7.54/7.61 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zle__refl,axiom, % 7.54/7.61 ! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_w)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_q__pos__lemma,axiom, % 7.54/7.61 ! [V_r_H,V_q_H,V_b_H] : % 7.54/7.61 ( hBOOL(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))) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_q__neg__lemma,axiom, % 7.54/7.61 ! [V_r_H,V_q_H,V_b_H] : % 7.54/7.61 ( hBOOL(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))) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_unique__quotient__lemma,axiom, % 7.54/7.61 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 7.54/7.61 ( hBOOL(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))) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q)) ) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zdiv__mono2__lemma,axiom, % 7.54/7.61 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 7.54/7.61 ( 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) % 7.54/7.61 => ( hBOOL(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))) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H)) ) ) ) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_unique__quotient__lemma__neg,axiom, % 7.54/7.61 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 7.54/7.61 ( hBOOL(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))) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r_H)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H)) ) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zdiv__mono2__neg__lemma,axiom, % 7.54/7.61 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 7.54/7.61 ( 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) % 7.54/7.61 => ( hBOOL(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))) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q)) ) ) ) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 7.54/7.61 ! [V_n,V_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 7.54/7.61 => hBOOL(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))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 7.54/7.61 ! [V_y,V_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 7.54/7.61 => hBOOL(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))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 7.54/7.61 ! [V_y,V_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 7.54/7.61 => hBOOL(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))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 7.54/7.61 hBOOL(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))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 7.54/7.61 hBOOL(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))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_not__real__square__gt__zero,axiom, % 7.54/7.61 ! [V_x_2] : % 7.54/7.61 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))) % 7.54/7.61 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Im_Opos__bounded,axiom, % 7.54/7.61 ? [B_K] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.61 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Re_Opos__bounded,axiom, % 7.54/7.61 ? [B_K] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.61 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Im_Ononneg__bounded,axiom, % 7.54/7.61 ? [B_K] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.61 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Re_Ononneg__bounded,axiom, % 7.54/7.61 ? [B_K] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.61 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__power__power,axiom, % 7.54/7.61 ! [T_a] : % 7.54/7.61 ( class_Power_Opower(T_a) % 7.54/7.61 => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power_Opower_Opower__0,axiom, % 7.54/7.61 ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult_Opos__bounded,axiom, % 7.54/7.61 ! [T_a] : % 7.54/7.61 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.61 => ? [B_K] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.61 & ! [B_a,B_b] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult__right_Opos__bounded,axiom, % 7.54/7.61 ! [V_x,T_a] : % 7.54/7.61 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.61 => ? [B_K] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.61 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult__left_Opos__bounded,axiom, % 7.54/7.61 ! [V_y,T_a] : % 7.54/7.61 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.61 => ? [B_K] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.61 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_natceiling__eq,axiom, % 7.54/7.61 ! [V_x,V_n] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) % 7.54/7.61 => c_RComplete_Onatceiling(V_x) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Im_Obounded,axiom, % 7.54/7.61 ? [B_K] : % 7.54/7.61 ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Re_Obounded,axiom, % 7.54/7.61 ? [B_K] : % 7.54/7.61 ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__ge__zero,axiom, % 7.54/7.61 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_n))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_natfloor__real__of__nat,axiom, % 7.54/7.61 ! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ). % 7.54/7.61 % 7.54/7.61 fof(fact_natceiling__real__of__nat,axiom, % 7.54/7.61 ! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__inject,axiom, % 7.54/7.61 ! [V_m_2,V_n_2] : % 7.54/7.61 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2) % 7.54/7.61 <=> V_n_2 = V_m_2 ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_abs__real__of__nat__cancel,axiom, % 7.54/7.61 ! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__zero__iff,axiom, % 7.54/7.61 ! [V_n_2] : % 7.54/7.61 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) % 7.54/7.61 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__zero,axiom, % 7.54/7.61 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 7.54/7.61 % 7.54/7.61 fof(fact_not__real__of__nat__less__zero,axiom, % 7.54/7.61 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__less__iff,axiom, % 7.54/7.61 ! [V_m_2,V_n_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__le__iff,axiom, % 7.54/7.61 ! [V_m_2,V_n_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__mult,axiom, % 7.54/7.61 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__add,axiom, % 7.54/7.61 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__1,axiom, % 7.54/7.61 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__power,axiom, % 7.54/7.61 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__real__of__nat,axiom, % 7.54/7.61 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__natceiling__ge,axiom, % 7.54/7.61 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__le__zero__cancel__iff,axiom, % 7.54/7.61 ! [V_n_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) % 7.54/7.61 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__natfloor__le,axiom, % 7.54/7.61 ! [V_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),V_x)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_le__natfloor,axiom, % 7.54/7.61 ! [V_a,V_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)),V_a)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),c_RComplete_Onatfloor(V_a))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_natceiling__le,axiom, % 7.54/7.61 ! [V_a,V_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),V_a)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_natfloor__power,axiom, % 7.54/7.61 ! [V_n,V_x] : % 7.54/7.61 ( V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)) % 7.54/7.61 => c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__gt__zero__cancel__iff,axiom, % 7.54/7.61 ! [V_n_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat__less__real__le,axiom, % 7.54/7.61 ! [V_m_2,V_n_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat__le__real__less,axiom, % 7.54/7.61 ! [V_m_2,V_n_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_le__natfloor__eq,axiom, % 7.54/7.61 ! [V_a_2,V_x_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_x_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)),V_x_2)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_natceiling__le__eq,axiom, % 7.54/7.61 ! [V_a_2,V_x_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),V_a_2)) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_RealDef_Oreal(tc_Nat_Onat,V_a_2))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__natfloor__add__one__gt,axiom, % 7.54/7.61 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__natfloor,axiom, % 7.54/7.61 ! [V_n,V_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_n))) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_n)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_natfloor__add,axiom, % 7.54/7.61 ! [V_a,V_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.61 => c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_a) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_ge__natfloor__plus__one__imp__gt,axiom, % 7.54/7.61 ! [V_n,V_z] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_z)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z),c_RealDef_Oreal(tc_Nat_Onat,V_n))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_natfloor__eq,axiom, % 7.54/7.61 ! [V_x,V_n] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) % 7.54/7.61 => c_RComplete_Onatfloor(V_x) = V_n ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_natceiling__add,axiom, % 7.54/7.61 ! [V_a,V_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.61 => c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),V_a) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom, % 7.54/7.61 ! [V_n,V_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_DeMoivre2,axiom, % 7.54/7.61 ! [V_n,V_a,V_r] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_realpow__pos__nth__unique,axiom, % 7.54/7.61 ! [V_a,V_n] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a)) % 7.54/7.61 => ? [B_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_x)) % 7.54/7.61 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a % 7.54/7.61 & ! [B_y] : % 7.54/7.61 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_y)) % 7.54/7.61 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) = V_a ) % 7.54/7.61 => B_y = B_x ) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_realpow__pos__nth,axiom, % 7.54/7.61 ! [V_a,V_n] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a)) % 7.54/7.61 => ? [B_r] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r)) % 7.54/7.61 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_complex__mod__rcis,axiom, % 7.54/7.61 ! [V_a,V_r] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ). % 7.54/7.61 % 7.54/7.61 fof(fact_rcis__zero__mod,axiom, % 7.54/7.61 ! [V_a] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ). % 7.54/7.61 % 7.54/7.61 fof(fact_rcis__mult,axiom, % 7.54/7.61 ! [V_b,V_r2,V_a,V_r1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult_Ononneg__bounded,axiom, % 7.54/7.61 ! [T_a] : % 7.54/7.61 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.61 => ? [B_K] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.61 & ! [B_a,B_b] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult__right_Ononneg__bounded,axiom, % 7.54/7.61 ! [V_x,T_a] : % 7.54/7.61 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.61 => ? [B_K] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.61 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult__left_Ononneg__bounded,axiom, % 7.54/7.61 ! [V_y,T_a] : % 7.54/7.61 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.61 => ? [B_K] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.61 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_lemma__NBseq__def2,axiom, % 7.54/7.61 ! [V_X_2,T_b] : % 7.54/7.61 ( class_RealVector_Oreal__normed__vector(T_b) % 7.54/7.61 => ( ? [B_K] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.61 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K)) ) % 7.54/7.61 <=> ? [B_N] : % 7.54/7.61 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_lemma__NBseq__def,axiom, % 7.54/7.61 ! [V_X_2,T_b] : % 7.54/7.61 ( class_RealVector_Oreal__normed__vector(T_b) % 7.54/7.61 => ( ? [B_K] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.61 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K)) ) % 7.54/7.61 <=> ? [B_N] : % 7.54/7.61 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_reals__Archimedean3,axiom, % 7.54/7.61 ! [V_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.61 => ! [B_y] : % 7.54/7.61 ? [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_x))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_lessI,axiom, % 7.54/7.61 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_n))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__mono,axiom, % 7.54/7.61 ! [V_n,V_m] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_zero__less__Suc,axiom, % 7.54/7.61 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_OSuc(V_n))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__mult__cancel1,axiom, % 7.54/7.61 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.61 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2) % 7.54/7.61 <=> V_m_2 = V_n_2 ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__neq__Zero,axiom, % 7.54/7.61 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Zero__neq__Suc,axiom, % 7.54/7.61 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat_Osimps_I3_J,axiom, % 7.54/7.61 ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__not__Zero,axiom, % 7.54/7.61 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat_Osimps_I2_J,axiom, % 7.54/7.61 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Zero__not__Suc,axiom, % 7.54/7.61 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__less__SucD,axiom, % 7.54/7.61 ! [V_n,V_m] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n))) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__lessD,axiom, % 7.54/7.61 ! [V_n,V_m] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__SucE,axiom, % 7.54/7.61 ! [V_n,V_m] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) % 7.54/7.61 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.61 => V_m = V_n ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__trans__Suc,axiom, % 7.54/7.61 ! [V_k,V_j,V_i] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i)),V_k)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__lessI,axiom, % 7.54/7.61 ! [V_n,V_m] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.61 => ( c_Nat_OSuc(V_m) != V_n % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__SucI,axiom, % 7.54/7.61 ! [V_n,V_m] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__antisym,axiom, % 7.54/7.61 ! [V_m,V_n] : % 7.54/7.61 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_m))) % 7.54/7.61 => V_m = V_n ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_not__less__less__Suc__eq,axiom, % 7.54/7.61 ! [V_m_2,V_n_2] : % 7.54/7.61 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))) % 7.54/7.61 <=> V_n_2 = V_m_2 ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__less__eq,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),c_Nat_OSuc(V_n_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__Suc__eq,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2))) % 7.54/7.61 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) % 7.54/7.61 | V_m_2 = V_n_2 ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_not__less__eq,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__inject,axiom, % 7.54/7.61 ! [V_y,V_x] : % 7.54/7.61 ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y) % 7.54/7.61 => V_x = V_y ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat_Oinject,axiom, % 7.54/7.61 ! [V_nat_H_2,V_nat_2] : % 7.54/7.61 ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2) % 7.54/7.61 <=> V_nat_2 = V_nat_H_2 ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__n__not__n,axiom, % 7.54/7.61 ! [V_n] : c_Nat_OSuc(V_n) != V_n ). % 7.54/7.61 % 7.54/7.61 fof(fact_n__not__Suc__n,axiom, % 7.54/7.61 ! [V_n] : V_n != c_Nat_OSuc(V_n) ). % 7.54/7.61 % 7.54/7.61 fof(fact_add__Suc__right,axiom, % 7.54/7.61 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_add__Suc,axiom, % 7.54/7.61 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_add__Suc__shift,axiom, % 7.54/7.61 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__n__not__le__n,axiom, % 7.54/7.61 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n)),V_n)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_not__less__eq__eq,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_le__Suc__eq,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2))) % 7.54/7.61 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) % 7.54/7.61 | V_m_2 = c_Nat_OSuc(V_n_2) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__le__mono,axiom, % 7.54/7.61 ! [V_m_2,V_n_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),c_Nat_OSuc(V_m_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_le__SucI,axiom, % 7.54/7.61 ! [V_n,V_m] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_le__SucE,axiom, % 7.54/7.61 ! [V_n,V_m] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) % 7.54/7.61 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 7.54/7.61 => V_m = c_Nat_OSuc(V_n) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__leD,axiom, % 7.54/7.61 ! [V_n,V_m] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power_Opower_Opower__Suc,axiom, % 7.54/7.61 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__0__Suc,axiom, % 7.54/7.61 ! [V_n,T_a] : % 7.54/7.61 ( ( class_Power_Opower(T_a) % 7.54/7.61 & class_Rings_Osemiring__0(T_a) ) % 7.54/7.61 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__Suc,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Power_Opower(T_a) % 7.54/7.61 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),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)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__Suc2,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Groups_Omonoid__mult(T_a) % 7.54/7.61 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),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) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 7.54/7.61 ! [V_q,V_x,T_a] : % 7.54/7.61 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.61 => 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),c_Nat_OSuc(V_q)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 7.54/7.61 ! [V_q,V_x,T_a] : % 7.54/7.61 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.61 => 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),c_Nat_OSuc(V_q)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 7.54/7.61 ! [V_q,V_x,T_a] : % 7.54/7.61 ( class_Rings_Ocomm__semiring__1(T_a) % 7.54/7.61 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),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)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat__lt__two__imp__zero__or__one,axiom, % 7.54/7.61 ! [V_x] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) % 7.54/7.61 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.61 | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__Suc__eq__0__disj,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2))) % 7.54/7.61 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.61 | ? [B_j] : % 7.54/7.61 ( V_m_2 = c_Nat_OSuc(B_j) % 7.54/7.61 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_n_2)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__Suc0,axiom, % 7.54/7.61 ! [V_n_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) % 7.54/7.61 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_gr0__conv__Suc,axiom, % 7.54/7.61 ! [V_n_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 7.54/7.61 <=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_one__is__add,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) % 7.54/7.61 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 7.54/7.61 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 7.54/7.61 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.61 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_add__is__1,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 7.54/7.61 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 7.54/7.61 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 7.54/7.61 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.61 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult__eq__1__iff,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 7.54/7.61 <=> ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 7.54/7.61 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__add__Suc1,axiom, % 7.54/7.61 ! [V_m,V_i] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__add__Suc2,axiom, % 7.54/7.61 ! [V_m,V_i] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__iff__Suc__add,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) % 7.54/7.61 <=> ? [B_k] : V_n_2 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__le__lessD,axiom, % 7.54/7.61 ! [V_n,V_m] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_le__less__Suc__eq,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))) % 7.54/7.61 <=> V_n_2 = V_m_2 ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__leI,axiom, % 7.54/7.61 ! [V_n,V_m] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_le__imp__less__Suc,axiom, % 7.54/7.61 ! [V_n,V_m] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__le__eq,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),V_n_2)) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__Suc__eq__le,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__eq__Suc__le,axiom, % 7.54/7.61 ! [V_m_2,V_n_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_One__nat__def,axiom, % 7.54/7.61 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__mult__less__cancel1,axiom, % 7.54/7.61 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult__Suc,axiom, % 7.54/7.61 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_mult__Suc__right,axiom, % 7.54/7.61 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),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)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__mult__le__cancel1,axiom, % 7.54/7.61 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))) % 7.54/7.61 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__eq__plus1,axiom, % 7.54/7.61 ! [V_n] : 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)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Suc__eq__plus1__left,axiom, % 7.54/7.61 ! [V_n] : 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) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__Suc__0,axiom, % 7.54/7.61 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 7.54/7.61 ! [V_m_2,V_x_2] : % 7.54/7.61 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 7.54/7.61 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.61 | V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_monoseq__Suc,axiom, % 7.54/7.61 ! [V_X_2,T_a] : % 7.54/7.61 ( class_Orderings_Oorder(T_a) % 7.54/7.61 => ( c_SEQ_Omonoseq(T_a,V_X_2) % 7.54/7.61 <=> ( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,c_Nat_OSuc(B_n)))) % 7.54/7.61 | ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n))),hAPP(V_X_2,B_n))) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_subseq__Suc__iff,axiom, % 7.54/7.61 ! [V_fa_2] : % 7.54/7.61 ( c_SEQ_Osubseq(V_fa_2) % 7.54/7.61 <=> ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n)),hAPP(V_fa_2,c_Nat_OSuc(B_n)))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_less__eq__Suc__le__raw,axiom, % 7.54/7.61 ! [V_n_2] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__le__imp__le__base,axiom, % 7.54/7.61 ! [V_b,V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)))) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__inject__base,axiom, % 7.54/7.61 ! [V_b,V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 7.54/7.61 => V_a = V_b ) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__gt1,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)) % 7.54/7.61 => hBOOL(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),c_Nat_OSuc(V_n)))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_one__less__mult,axiom, % 7.54/7.61 ! [V_m,V_n] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,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))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_n__less__n__mult__m,axiom, % 7.54/7.61 ! [V_m,V_n] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 7.54/7.61 => hBOOL(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))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_n__less__m__mult__n,axiom, % 7.54/7.61 ! [V_m,V_n] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) % 7.54/7.61 => hBOOL(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))) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_one__le__mult__iff,axiom, % 7.54/7.61 ! [V_n_2,V_m_2] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) % 7.54/7.61 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) % 7.54/7.61 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__Suc__gt__zero,axiom, % 7.54/7.61 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)))) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__one,axiom, % 7.54/7.61 c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ). % 7.54/7.61 % 7.54/7.61 fof(fact_real__of__nat__Suc,axiom, % 7.54/7.61 ! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ). % 7.54/7.61 % 7.54/7.61 fof(fact_nat__one__le__power,axiom, % 7.54/7.61 ! [V_n,V_i] : % 7.54/7.61 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i)) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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))) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_realpow__Suc__le__self,axiom, % 7.54/7.61 ! [V_n,V_r,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_r),c_Groups_Oone__class_Oone(T_a))) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n))),V_r)) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_power__Suc__less__one,axiom, % 7.54/7.61 ! [V_n,V_a,T_a] : % 7.54/7.61 ( class_Rings_Olinordered__semidom(T_a) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 7.54/7.61 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a))) % 7.54/7.61 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ) ). % 7.54/7.61 % 7.54/7.61 fof(fact_Bseq__iff,axiom, % 7.54/7.61 ! [V_X_2,T_a] : % 7.54/7.61 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.61 => ( c_SEQ_OBseq(T_a,V_X_2) % 7.54/7.62 <=> ? [B_N] : % 7.54/7.62 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Bseq__iff1a,axiom, % 7.54/7.62 ! [V_X_2,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.62 => ( c_SEQ_OBseq(T_a,V_X_2) % 7.54/7.62 <=> ? [B_N] : % 7.54/7.62 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_reals__Archimedean6a,axiom, % 7.54/7.62 ! [V_r] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r)) % 7.54/7.62 => ? [B_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_r)) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cis__real__of__nat__Suc__mult,axiom, % 7.54/7.62 ! [V_a,V_n] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_reals__Archimedean4,axiom, % 7.54/7.62 ! [V_x,V_y] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.62 => ? [B_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_y)),V_x)) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))),V_y))) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cis__mult,axiom, % 7.54/7.62 ! [V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cis__zero,axiom, % 7.54/7.62 c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cis__rcis__eq,axiom, % 7.54/7.62 ! [V_a] : c_Complex_Ocis(V_a) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_a) ). % 7.54/7.62 % 7.54/7.62 fof(fact_DeMoivre,axiom, % 7.54/7.62 ! [V_n,V_a] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__realpow,axiom, % 7.54/7.62 ! [V_n,V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.62 => c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Transcendental_Oln(V_x)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cos__n__Re__cis__pow__n,axiom, % 7.54/7.62 ! [V_a,V_n] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_sin__n__Im__cis__pow__n,axiom, % 7.54/7.62 ! [V_a,V_n] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_sin__cos__squared__add3,axiom, % 7.54/7.62 ! [V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_x))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ). % 7.54/7.62 % 7.54/7.62 fof(fact_sin__add,axiom, % 7.54/7.62 ! [V_y,V_x] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_sin__zero__abs__cos__one,axiom, % 7.54/7.62 ! [V_x] : % 7.54/7.62 ( c_Transcendental_Osin(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) % 7.54/7.62 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cos__zero,axiom, % 7.54/7.62 c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cos__one__sin__zero,axiom, % 7.54/7.62 ! [V_x] : % 7.54/7.62 ( c_Transcendental_Ocos(V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) % 7.54/7.62 => c_Transcendental_Osin(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cos__le__one,axiom, % 7.54/7.62 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_sin__le__one,axiom, % 7.54/7.62 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_sin__zero,axiom, % 7.54/7.62 c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Im__cis,axiom, % 7.54/7.62 ! [V_a] : hAPP(c_Complex_OIm,c_Complex_Ocis(V_a)) = c_Transcendental_Osin(V_a) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Re__cis,axiom, % 7.54/7.62 ! [V_a] : hAPP(c_Complex_ORe,c_Complex_Ocis(V_a)) = c_Transcendental_Ocos(V_a) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__less__self,axiom, % 7.54/7.62 ! [V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),V_x)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__inj__iff,axiom, % 7.54/7.62 ! [V_y_2,V_x_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) % 7.54/7.62 => ( c_Transcendental_Oln(V_x_2) = c_Transcendental_Oln(V_y_2) % 7.54/7.62 <=> V_x_2 = V_y_2 ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__less__cancel__iff,axiom, % 7.54/7.62 ! [V_y_2,V_x_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__one,axiom, % 7.54/7.62 c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 7.54/7.62 % 7.54/7.62 fof(fact_abs__sin__le__one,axiom, % 7.54/7.62 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_abs__cos__le__one,axiom, % 7.54/7.62 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Im__rcis,axiom, % 7.54/7.62 ! [V_a,V_r] : hAPP(c_Complex_OIm,c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Re__rcis,axiom, % 7.54/7.62 ! [V_a,V_r] : hAPP(c_Complex_ORe,c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__le__cancel__iff,axiom, % 7.54/7.62 ! [V_y_2,V_x_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__ge__zero,axiom, % 7.54/7.62 ! [V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__gt__zero__imp__gt__one,axiom, % 7.54/7.62 ! [V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__less__zero,axiom, % 7.54/7.62 ! [V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__less__zero__iff,axiom, % 7.54/7.62 ! [V_x_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__eq__zero__iff,axiom, % 7.54/7.62 ! [V_x_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) % 7.54/7.62 => ( c_Transcendental_Oln(V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) % 7.54/7.62 <=> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__gt__zero__iff,axiom, % 7.54/7.62 ! [V_x_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__gt__zero,axiom, % 7.54/7.62 ! [V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__ge__zero__imp__ge__one,axiom, % 7.54/7.62 ! [V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__ge__zero__iff,axiom, % 7.54/7.62 ! [V_x_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__mult,axiom, % 7.54/7.62 ! [V_y,V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) % 7.54/7.62 => c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)),c_Transcendental_Oln(V_y)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__add__one__self__le__self,axiom, % 7.54/7.62 ! [V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))),V_x)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cos__arccos__abs,axiom, % 7.54/7.62 ! [V_y] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) % 7.54/7.62 => c_Transcendental_Ocos(c_Transcendental_Oarccos(V_y)) = V_y ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_realpow__pos__nth2,axiom, % 7.54/7.62 ! [V_n,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a)) % 7.54/7.62 => ? [B_r] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r)) % 7.54/7.62 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),c_Nat_OSuc(V_n)) = V_a ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_mult__left_Obounded,axiom, % 7.54/7.62 ! [V_y,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.62 => ? [B_K] : % 7.54/7.62 ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_mult_Obounded,axiom, % 7.54/7.62 ! [T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.62 => ? [B_K] : % 7.54/7.62 ! [B_a,B_b] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_mult__right_Obounded,axiom, % 7.54/7.62 ! [V_x,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.62 => ? [B_K] : % 7.54/7.62 ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_realpow__minus__mult,axiom, % 7.54/7.62 ! [V_x,V_n,T_a] : % 7.54/7.62 ( class_Groups_Omonoid__mult(T_a) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_realpow__num__eq__if,axiom, % 7.54/7.62 ! [V_m,V_n,T_a] : % 7.54/7.62 ( class_Power_Opower(T_a) % 7.54/7.62 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) ) % 7.54/7.62 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Suc__diff__diff,axiom, % 7.54/7.62 ! [V_k,V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__Suc__Suc,axiom, % 7.54/7.62 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ). % 7.54/7.62 % 7.54/7.62 fof(fact_norm__triangle__ineq3,axiom, % 7.54/7.62 ! [V_b,V_a,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_le__diff__iff,axiom, % 7.54/7.62 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Nat_Odiff__diff__eq,axiom, % 7.54/7.62 ! [V_n,V_m,V_k] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_m)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_eq__diff__iff,axiom, % 7.54/7.62 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2)) % 7.54/7.62 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2) % 7.54/7.62 <=> V_m_2 = V_n_2 ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__diff__cancel,axiom, % 7.54/7.62 ! [V_n,V_i] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_n)) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__le__mono,axiom, % 7.54/7.62 ! [V_l,V_n,V_m] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__le__mono2,axiom, % 7.54/7.62 ! [V_l,V_n,V_m] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__le__self,axiom, % 7.54/7.62 ! [V_n,V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__cancel2,axiom, % 7.54/7.62 ! [V_n,V_k,V_m] : 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)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__cancel,axiom, % 7.54/7.62 ! [V_n,V_m,V_k] : 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)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__diff__left,axiom, % 7.54/7.62 ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__add__inverse,axiom, % 7.54/7.62 ! [V_m,V_n] : 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 ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__add__inverse2,axiom, % 7.54/7.62 ! [V_n,V_m] : 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 ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__add__cancel,axiom, % 7.54/7.62 ! [V_b,V_a,T_a] : % 7.54/7.62 ( class_Groups_Ogroup__add(T_a) % 7.54/7.62 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_b) = V_a ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_add__diff__cancel,axiom, % 7.54/7.62 ! [V_b,V_a,T_a] : % 7.54/7.62 ( class_Groups_Ogroup__add(T_a) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = V_a ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__eq__diff__less__eq,axiom, % 7.54/7.62 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 7.54/7.62 ( class_Groups_Oordered__ab__group__add(T_a) % 7.54/7.62 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),V_d_2)) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_norm__triangle__ineq2,axiom, % 7.54/7.62 ! [V_b,V_a,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_norm__minus__commute,axiom, % 7.54/7.62 ! [V_b,V_a,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.62 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__commute,axiom, % 7.54/7.62 ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__eq__diff__eq,axiom, % 7.54/7.62 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 7.54/7.62 ( class_Groups_Oab__group__add(T_a) % 7.54/7.62 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2) % 7.54/7.62 => ( V_a_2 = V_b_2 % 7.54/7.62 <=> V_c_2 = V_d_2 ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_less__imp__diff__less,axiom, % 7.54/7.62 ! [V_n,V_k,V_j] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n)),V_k)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__less__mono2,axiom, % 7.54/7.62 ! [V_l,V_n,V_m] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_l)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_abs__minus__commute,axiom, % 7.54/7.62 ! [V_b,V_a,T_a] : % 7.54/7.62 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.54/7.62 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__0__eq__0,axiom, % 7.54/7.62 ! [V_n] : 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) ). % 7.54/7.62 % 7.54/7.62 fof(fact_minus__nat_Odiff__0,axiom, % 7.54/7.62 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__self__eq__0,axiom, % 7.54/7.62 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diffs0__imp__equal,axiom, % 7.54/7.62 ! [V_n,V_m] : % 7.54/7.62 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => V_m = V_n ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_mult_Odiff__right,axiom, % 7.54/7.62 ! [V_b_H,V_b,V_a,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(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),V_b_H)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_mult__right_Odiff,axiom, % 7.54/7.62 ! [V_y,V_x,V_xa,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_mult_Odiff__left,axiom, % 7.54/7.62 ! [V_b,V_a_H,V_a,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(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_H),V_b)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_mult__left_Odiff,axiom, % 7.54/7.62 ! [V_ya,V_y,V_x,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__eq__diff__less,axiom, % 7.54/7.62 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 7.54/7.62 ( class_Groups_Oordered__ab__group__add(T_a) % 7.54/7.62 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),V_d_2)) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__0__right,axiom, % 7.54/7.62 ! [V_a,T_a] : % 7.54/7.62 ( class_Groups_Ogroup__add(T_a) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__self,axiom, % 7.54/7.62 ! [V_a,T_a] : % 7.54/7.62 ( class_Groups_Ogroup__add(T_a) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_eq__iff__diff__eq__0,axiom, % 7.54/7.62 ! [V_b_2,V_a_2,T_a] : % 7.54/7.62 ( class_Groups_Oab__group__add(T_a) % 7.54/7.62 => ( V_a_2 = V_b_2 % 7.54/7.62 <=> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_right__minus__eq,axiom, % 7.54/7.62 ! [V_b_2,V_a_2,T_a] : % 7.54/7.62 ( class_Groups_Ogroup__add(T_a) % 7.54/7.62 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 <=> V_a_2 = V_b_2 ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__mult__distrib,axiom, % 7.54/7.62 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = 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)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__mult__distrib2,axiom, % 7.54/7.62 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = 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)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__Suc__1,axiom, % 7.54/7.62 ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__Suc__eq__diff__pred,axiom, % 7.54/7.62 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__diff__right,axiom, % 7.54/7.62 ! [V_i,V_j,V_k] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),V_j) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_le__diff__conv,axiom, % 7.54/7.62 ! [V_i_2,V_k_2,V_j_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)),V_i_2)) % 7.54/7.62 <=> hBOOL(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))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_le__add__diff,axiom, % 7.54/7.62 ! [V_m,V_n,V_k] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_k))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_le__add__diff__inverse,axiom, % 7.54/7.62 ! [V_m,V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) % 7.54/7.62 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_add__diff__assoc,axiom, % 7.54/7.62 ! [V_i,V_j,V_k] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) % 7.54/7.62 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_le__diff__conv2,axiom, % 7.54/7.62 ! [V_i_2,V_j_2,V_k_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_j_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))) % 7.54/7.62 <=> hBOOL(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)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_le__add__diff__inverse2,axiom, % 7.54/7.62 ! [V_m,V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) % 7.54/7.62 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_n) = V_m ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_le__imp__diff__is__add,axiom, % 7.54/7.62 ! [V_k_2,V_j_2,V_i_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2)) % 7.54/7.62 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2 % 7.54/7.62 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__add__assoc,axiom, % 7.54/7.62 ! [V_i,V_j,V_k] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) % 7.54/7.62 => 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_add__diff__assoc2,axiom, % 7.54/7.62 ! [V_i,V_j,V_k] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) % 7.54/7.62 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__add__assoc2,axiom, % 7.54/7.62 ! [V_i,V_j,V_k] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) % 7.54/7.62 => 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_less__diff__iff,axiom, % 7.54/7.62 ! [V_n_2,V_m_2,V_k_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__less__mono,axiom, % 7.54/7.62 ! [V_c,V_b,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a),V_b)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c),V_a)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_less__diff__conv,axiom, % 7.54/7.62 ! [V_k_2,V_j_2,V_i_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))) % 7.54/7.62 <=> hBOOL(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)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_add__diff__inverse,axiom, % 7.54/7.62 ! [V_n,V_m] : % 7.54/7.62 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.62 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Suc__diff__le,axiom, % 7.54/7.62 ! [V_m,V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__is__0__eq_H,axiom, % 7.54/7.62 ! [V_n,V_m] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__is__0__eq,axiom, % 7.54/7.62 ! [V_n_2,V_m_2] : % 7.54/7.62 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__add__0,axiom, % 7.54/7.62 ! [V_m,V_n] : 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) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__less__Suc,axiom, % 7.54/7.62 ! [V_n,V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),c_Nat_OSuc(V_m))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__less,axiom, % 7.54/7.62 ! [V_m,V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_zero__less__diff,axiom, % 7.54/7.62 ! [V_m_2,V_n_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_abs__triangle__ineq2__sym,axiom, % 7.54/7.62 ! [V_b,V_a,T_a] : % 7.54/7.62 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_abs__triangle__ineq2,axiom, % 7.54/7.62 ! [V_b,V_a,T_a] : % 7.54/7.62 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_abs__triangle__ineq3,axiom, % 7.54/7.62 ! [V_b,V_a,T_a] : % 7.54/7.62 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_mult__diff__mult,axiom, % 7.54/7.62 ! [V_b,V_a,V_y,V_x,T_a] : % 7.54/7.62 ( class_Rings_Oring(T_a) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(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_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_eq__add__iff1,axiom, % 7.54/7.62 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 7.54/7.62 ( class_Rings_Oring(T_a) % 7.54/7.62 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) % 7.54/7.62 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_eq__add__iff2,axiom, % 7.54/7.62 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 7.54/7.62 ( class_Rings_Oring(T_a) % 7.54/7.62 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) % 7.54/7.62 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_mult_Oprod__diff__prod,axiom, % 7.54/7.62 ! [V_b,V_a,V_y,V_x,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__algebra(T_a) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(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_a),V_b)) = 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),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_less__iff__diff__less__0,axiom, % 7.54/7.62 ! [V_b_2,V_a_2,T_a] : % 7.54/7.62 ( class_Groups_Oordered__ab__group__add(T_a) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_le__iff__diff__le__0,axiom, % 7.54/7.62 ! [V_b_2,V_a_2,T_a] : % 7.54/7.62 ( class_Groups_Oordered__ab__group__add(T_a) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_le__add__iff2,axiom, % 7.54/7.62 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 7.54/7.62 ( class_Rings_Oordered__ring(T_a) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_le__add__iff1,axiom, % 7.54/7.62 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 7.54/7.62 ( class_Rings_Oordered__ring(T_a) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 7.54/7.62 <=> hBOOL(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),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_less__add__iff2,axiom, % 7.54/7.62 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 7.54/7.62 ( class_Rings_Oordered__ring(T_a) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_less__add__iff1,axiom, % 7.54/7.62 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 7.54/7.62 ( class_Rings_Oordered__ring(T_a) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 7.54/7.62 <=> hBOOL(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),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_real__squared__diff__one__factored,axiom, % 7.54/7.62 ! [V_x,T_a] : % 7.54/7.62 ( class_Rings_Oring__1(T_a) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_abs__triangle__ineq4,axiom, % 7.54/7.62 ! [V_b,V_a,T_a] : % 7.54/7.62 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_abs__diff__triangle__ineq,axiom, % 7.54/7.62 ! [V_d,V_c,V_b,V_a,T_a] : % 7.54/7.62 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,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),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_abs__diff__less__iff,axiom, % 7.54/7.62 ! [V_ra_2,V_a_2,V_x_2,T_a] : % 7.54/7.62 ( class_Rings_Olinordered__idom(T_a) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2))),V_ra_2)) % 7.54/7.62 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2)),V_x_2)) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ra_2))) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_norm__triangle__ineq4,axiom, % 7.54/7.62 ! [V_b,V_a,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b)))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Suc__pred,axiom, % 7.54/7.62 ! [V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.62 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__Suc__less,axiom, % 7.54/7.62 ! [V_i,V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i))),V_n)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nat__diff__split__asm,axiom, % 7.54/7.62 ! [V_b_2,V_a_2,V_P_2] : % 7.54/7.62 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) % 7.54/7.62 <=> ~ ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2)) % 7.54/7.62 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 7.54/7.62 | ? [B_d] : % 7.54/7.62 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 7.54/7.62 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nat__diff__split,axiom, % 7.54/7.62 ! [V_b_2,V_a_2,V_P_2] : % 7.54/7.62 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) % 7.54/7.62 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2)) % 7.54/7.62 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 7.54/7.62 & ! [B_d] : % 7.54/7.62 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 7.54/7.62 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__Suc__diff__eq1,axiom, % 7.54/7.62 ! [V_m,V_j,V_k] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),c_Nat_OSuc(V_j)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__Suc__diff__eq2,axiom, % 7.54/7.62 ! [V_m,V_j,V_k] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nat__le__add__iff1,axiom, % 7.54/7.62 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 7.54/7.62 <=> hBOOL(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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nat__diff__add__eq1,axiom, % 7.54/7.62 ! [V_n,V_m,V_u,V_i,V_j] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_i)) % 7.54/7.62 => 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)) = 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u)),V_m),V_n) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nat__eq__add__iff1,axiom, % 7.54/7.62 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2)) % 7.54/7.62 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) % 7.54/7.62 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nat__le__add__iff2,axiom, % 7.54/7.62 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 7.54/7.62 <=> hBOOL(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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nat__diff__add__eq2,axiom, % 7.54/7.62 ! [V_n,V_m,V_u,V_j,V_i] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) % 7.54/7.62 => 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)) = 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u)),V_n)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nat__eq__add__iff2,axiom, % 7.54/7.62 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2)) % 7.54/7.62 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) % 7.54/7.62 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_norm__diff__triangle__ineq,axiom, % 7.54/7.62 ! [V_d,V_c,V_b,V_a,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,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(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_lemma__realpow__diff,axiom, % 7.54/7.62 ! [V_y,V_n,V_p,T_a] : % 7.54/7.62 ( class_Groups_Omonoid__mult(T_a) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p),V_n)) % 7.54/7.62 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Suc__pred_H,axiom, % 7.54/7.62 ! [V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.62 => V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Suc__diff__1,axiom, % 7.54/7.62 ! [V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.62 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_add__eq__if,axiom, % 7.54/7.62 ! [V_n,V_m] : % 7.54/7.62 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 7.54/7.62 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nat__less__add__iff1,axiom, % 7.54/7.62 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 7.54/7.62 <=> hBOOL(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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nat__less__add__iff2,axiom, % 7.54/7.62 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) % 7.54/7.62 <=> hBOOL(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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_mult__eq__if,axiom, % 7.54/7.62 ! [V_n,V_m] : % 7.54/7.62 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 7.54/7.62 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_power__eq__if,axiom, % 7.54/7.62 ! [V_p,V_m] : % 7.54/7.62 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 7.54/7.62 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_realpow__two__diff,axiom, % 7.54/7.62 ! [V_y,V_x,T_a] : % 7.54/7.62 ( class_Rings_Ocomm__ring__1(T_a) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_reals__Archimedean6,axiom, % 7.54/7.62 ! [V_r] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r)) % 7.54/7.62 => ? [B_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_r)) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,B_n))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_lemmaCauchy,axiom, % 7.54/7.62 ! [V_X_2,V_M_2,T_a,T_b] : % 7.54/7.62 ( ( class_RealVector_Oreal__normed__vector(T_b) % 7.54/7.62 & class_Orderings_Oord(T_a) ) % 7.54/7.62 => ( ! [B_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_M_2),B_n)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) % 7.54/7.62 => ! [B_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_M_2),B_n)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2))))) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Re_Odiff,axiom, % 7.54/7.62 ! [V_y,V_x] : hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Im_Odiff,axiom, % 7.54/7.62 ! [V_y,V_x] : hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_zdiff__zmult__distrib,axiom, % 7.54/7.62 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = 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)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_zdiff__zmult__distrib2,axiom, % 7.54/7.62 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = 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)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_less__bin__lemma,axiom, % 7.54/7.62 ! [V_l_2,V_k_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2)) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_real__le__eq__diff,axiom, % 7.54/7.62 ! [V_y_2,V_x_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_norm__diff__ineq,axiom, % 7.54/7.62 ! [V_b,V_a,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__vector(T_a) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_metric__bound__lemma,axiom, % 7.54/7.62 ! [V_y,V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)))))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_zle__diff1__eq,axiom, % 7.54/7.62 ! [V_z_2,V_w_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_real__of__nat__diff,axiom, % 7.54/7.62 ! [V_m,V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) % 7.54/7.62 => c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_sin__diff2,axiom, % 7.54/7.62 ! [V_y,V_x] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Osin(V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Ocos(V_x))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_sin__diff,axiom, % 7.54/7.62 ! [V_y,V_x] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__mod__triangle__ineq2,axiom, % 7.54/7.62 ! [V_a,V_b] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_b),V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cos__add,axiom, % 7.54/7.62 ! [V_y,V_x] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cos__diff,axiom, % 7.54/7.62 ! [V_y,V_x] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cos__diff2,axiom, % 7.54/7.62 ! [V_y,V_x] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Osin(V_x))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_natfloor__subtract,axiom, % 7.54/7.62 ! [V_x,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a)),V_x)) % 7.54/7.62 => c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_real__natfloor__gt__diff__one,axiom, % 7.54/7.62 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_natceiling__subtract,axiom, % 7.54/7.62 ! [V_x,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a)),V_x)) % 7.54/7.62 => c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__Re__mult,axiom, % 7.54/7.62 ! [V_y,V_x] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_decr__lemma,axiom, % 7.54/7.62 ! [V_z,V_x,V_d] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_incr__lemma,axiom, % 7.54/7.62 ! [V_x,V_z,V_d] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 7.54/7.62 => hBOOL(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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_unimodular__reduce__norm,axiom, % 7.54/7.62 ! [V_z] : % 7.54/7.62 ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) % 7.54/7.62 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) % 7.54/7.62 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) % 7.54/7.62 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_tsub__def,axiom, % 7.54/7.62 ! [V_x,V_y] : % 7.54/7.62 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x)) % 7.54/7.62 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) % 7.54/7.62 & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x)) % 7.54/7.62 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__Re__i,axiom, % 7.54/7.62 hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__i__not__zero,axiom, % 7.54/7.62 c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__i__not__one,axiom, % 7.54/7.62 c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__Im__i,axiom, % 7.54/7.62 hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 7.54/7.62 ! [V_y,V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 7.54/7.62 => hBOOL(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))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_tsub__eq,axiom, % 7.54/7.62 ! [V_x,V_y] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x)) % 7.54/7.62 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_int__power__div__base,axiom, % 7.54/7.62 ! [V_k,V_m] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 7.54/7.62 => 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Deriv_Oadd__diff__add,axiom, % 7.54/7.62 ! [V_d,V_b,V_c,V_a,T_a] : % 7.54/7.62 ( class_Groups_Oab__group__add(T_a) % 7.54/7.62 => c_Groups_Ominus__class_Ominus(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)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_int__div__less__self,axiom, % 7.54/7.62 ! [V_k,V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k)),V_x)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_zdiv__zmult2__eq,axiom, % 7.54/7.62 ! [V_b,V_a,V_c] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__mult__mult1__if,axiom, % 7.54/7.62 ! [V_b,V_a,V_c,T_a] : % 7.54/7.62 ( class_Divides_Osemiring__div(T_a) % 7.54/7.62 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => 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) ) % 7.54/7.62 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => 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_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__mult__self2__is__id,axiom, % 7.54/7.62 ! [V_a,V_b,T_a] : % 7.54/7.62 ( class_Divides_Osemiring__div(T_a) % 7.54/7.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = V_a ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__mult__self1__is__id,axiom, % 7.54/7.62 ! [V_a,V_b,T_a] : % 7.54/7.62 ( class_Divides_Osemiring__div(T_a) % 7.54/7.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = V_a ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__mult__mult2,axiom, % 7.54/7.62 ! [V_b,V_a,V_c,T_a] : % 7.54/7.62 ( class_Divides_Osemiring__div(T_a) % 7.54/7.62 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => 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)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__mult__mult1,axiom, % 7.54/7.62 ! [V_b,V_a,V_c,T_a] : % 7.54/7.62 ( class_Divides_Osemiring__div(T_a) % 7.54/7.62 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => 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_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__self,axiom, % 7.54/7.62 ! [V_a,T_a] : % 7.54/7.62 ( class_Divides_Osemiring__div(T_a) % 7.54/7.62 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_zdiv__zero,axiom, % 7.54/7.62 ! [V_b] : 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) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__0,axiom, % 7.54/7.62 ! [V_a,T_a] : % 7.54/7.62 ( class_Divides_Osemiring__div(T_a) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__by__0,axiom, % 7.54/7.62 ! [V_a,T_a] : % 7.54/7.62 ( class_Divides_Osemiring__div(T_a) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__by__1,axiom, % 7.54/7.62 ! [V_a,T_a] : % 7.54/7.62 ( class_Divides_Osemiring__div(T_a) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_zdiv__self,axiom, % 7.54/7.62 ! [V_a] : % 7.54/7.62 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__neg__pos__less0,axiom, % 7.54/7.62 ! [V_b,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 7.54/7.62 ! [V_a_2,V_b_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 7.54/7.62 ! [V_a_2,V_b_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 7.54/7.62 ! [V_y,V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_zdiv__mono1__neg,axiom, % 7.54/7.62 ! [V_b,V_a_H,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_zdiv__mono1,axiom, % 7.54/7.62 ! [V_b,V_a_H,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__neg__neg__trivial,axiom, % 7.54/7.62 ! [V_b,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_a)) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_zdiv__mono2__neg,axiom, % 7.54/7.62 ! [V_b,V_b_H,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__nonpos__pos__le0,axiom, % 7.54/7.62 ! [V_b,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 7.54/7.62 ! [V_a_2,V_b_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__pos__pos__trivial,axiom, % 7.54/7.62 ! [V_b,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),V_b)) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__nonneg__neg__le0,axiom, % 7.54/7.62 ! [V_b,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_zdiv__mono2,axiom, % 7.54/7.62 ! [V_b,V_b_H,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H))) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 7.54/7.62 ! [V_b_2,V_a_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))) % 7.54/7.62 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2),V_a_2)) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 7.54/7.62 ! [V_i_2,V_k_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2),V_i_2)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 7.54/7.62 ! [V_a_2,V_b_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))) % 7.54/7.62 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_zdiv__eq__0__iff,axiom, % 7.54/7.62 ! [V_k_2,V_i_2] : % 7.54/7.62 ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 7.54/7.62 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 7.54/7.62 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2)) ) % 7.54/7.62 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2)) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__mult__self1,axiom, % 7.54/7.62 ! [V_c,V_a,V_b,T_a] : % 7.54/7.62 ( class_Divides_Osemiring__div(T_a) % 7.54/7.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => 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),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__mult__self2,axiom, % 7.54/7.62 ! [V_c,V_a,V_b,T_a] : % 7.54/7.62 ( class_Divides_Osemiring__div(T_a) % 7.54/7.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => 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),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__add__self2,axiom, % 7.54/7.62 ! [V_a,V_b,T_a] : % 7.54/7.62 ( class_Divides_Osemiring__div(T_a) % 7.54/7.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => 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),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__add__self1,axiom, % 7.54/7.62 ! [V_a,V_b,T_a] : % 7.54/7.62 ( class_Divides_Osemiring__div(T_a) % 7.54/7.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => 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),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_divmod__int__rel__div__eq,axiom, % 7.54/7.62 ! [V_r_1,V_y,V_b_1,V_a_1] : % 7.54/7.62 ( 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) % 7.54/7.62 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1),V_b_1)) ) ) % 7.54/7.62 & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1),V_r_1)) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 7.54/7.62 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_split__zdiv,axiom, % 7.54/7.62 ! [V_k_2,V_n_2,V_P_2] : % 7.54/7.62 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2))) % 7.54/7.62 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 7.54/7.62 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 7.54/7.62 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 7.54/7.62 => ! [B_i] : % 7.54/7.62 ( ? [B_j] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j),V_k_2)) % 7.54/7.62 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 7.54/7.62 => hBOOL(hAPP(V_P_2,B_i)) ) ) % 7.54/7.62 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.62 => ! [B_i] : % 7.54/7.62 ( ? [B_j] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),B_j)) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 7.54/7.62 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 7.54/7.62 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__mult__def,axiom, % 7.54/7.62 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y)))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_lemma__interval,axiom, % 7.54/7.62 ! [V_b,V_x,V_a] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a),V_x)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_b)) % 7.54/7.62 => ? [B_d] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_d)) % 7.54/7.62 & ! [B_y] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y))),B_d)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a),B_y)) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y),V_b)) ) ) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__mult2__eq,axiom, % 7.54/7.62 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__le__mono,axiom, % 7.54/7.62 ! [V_k,V_n,V_m] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k))) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__le__dividend,axiom, % 7.54/7.62 ! [V_n,V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nat__mult__div__cancel__disj,axiom, % 7.54/7.62 ! [V_n,V_m,V_k] : % 7.54/7.62 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => 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) ) % 7.54/7.62 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => 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_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__less,axiom, % 7.54/7.62 ! [V_n,V_m] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__1,axiom, % 7.54/7.62 ! [V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__less__dividend,axiom, % 7.54/7.62 ! [V_m,V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__mult__self__is__m,axiom, % 7.54/7.62 ! [V_m,V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.62 => 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 ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__mult__self1__is__m,axiom, % 7.54/7.62 ! [V_m,V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.62 => 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 ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nat__mult__div__cancel1,axiom, % 7.54/7.62 ! [V_n,V_m,V_k] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 7.54/7.62 => 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_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__le__mono2,axiom, % 7.54/7.62 ! [V_k,V_n,V_m] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) % 7.54/7.62 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m))) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__diff,axiom, % 7.54/7.62 ! [V_d,V_c,V_b,V_a] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__surj,axiom, % 7.54/7.62 ! [V_z] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,V_z),hAPP(c_Complex_OIm,V_z)) = V_z ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex_Oinject,axiom, % 7.54/7.62 ! [V_real2_H_2,V_real1_H_2,V_real2_2,V_real1_2] : % 7.54/7.62 ( c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2) = c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2) % 7.54/7.62 <=> ( V_real1_2 = V_real1_H_2 % 7.54/7.62 & V_real2_2 = V_real2_H_2 ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Im,axiom, % 7.54/7.62 ! [V_y,V_x] : hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(V_x,V_y)) = V_y ). % 7.54/7.62 % 7.54/7.62 fof(fact_Re,axiom, % 7.54/7.62 ! [V_y,V_x] : hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(V_x,V_y)) = V_x ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__add,axiom, % 7.54/7.62 ! [V_d,V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_b),V_d)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Complex__eq__0,axiom, % 7.54/7.62 ! [V_b_2,V_a_2] : % 7.54/7.62 ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) % 7.54/7.62 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) % 7.54/7.62 & V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__zero__def,axiom, % 7.54/7.62 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Complex__eq__i,axiom, % 7.54/7.62 ! [V_y_2,V_x_2] : % 7.54/7.62 ( c_Complex_Ocomplex_OComplex(V_x_2,V_y_2) = c_Complex_Oii % 7.54/7.62 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) % 7.54/7.62 & V_y_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_i__def,axiom, % 7.54/7.62 c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Complex__eq__1,axiom, % 7.54/7.62 ! [V_b_2,V_a_2] : % 7.54/7.62 ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) % 7.54/7.62 <=> ( V_a_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) % 7.54/7.62 & V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__one__def,axiom, % 7.54/7.62 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cis__def,axiom, % 7.54/7.62 ! [V_a] : c_Complex_Ocis(V_a) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__geq,axiom, % 7.54/7.62 ! [V_m,V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.62 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_div__if,axiom, % 7.54/7.62 ! [V_m,V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.62 => ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 7.54/7.62 & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_split__div,axiom, % 7.54/7.62 ! [V_k_2,V_n_2,V_P_2] : % 7.54/7.62 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2))) % 7.54/7.62 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 7.54/7.62 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 => ! [B_i,B_j] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_k_2)) % 7.54/7.62 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) % 7.54/7.62 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__mult,axiom, % 7.54/7.62 ! [V_d,V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_d)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_d)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_c))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cmod__unit__one,axiom, % 7.54/7.62 ! [V_a] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex__add__def,axiom, % 7.54/7.62 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_split__div__lemma,axiom, % 7.54/7.62 ! [V_m_2,V_q_2,V_n_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 7.54/7.62 => ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2)))) ) % 7.54/7.62 <=> V_q_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_split__div_H,axiom, % 7.54/7.62 ! [V_n_2,V_m_2,V_P_2] : % 7.54/7.62 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2))) % 7.54/7.62 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 7.54/7.62 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 7.54/7.62 | ? [B_q] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) % 7.54/7.62 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q)))) % 7.54/7.62 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_le__div__geq,axiom, % 7.54/7.62 ! [V_m,V_n] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) % 7.54/7.62 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex_Osize_I1_J,axiom, % 7.54/7.62 ! [V_real2,V_real1] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cos__arg__i__mult__zero__neg,axiom, % 7.54/7.62 ! [V_y] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) % 7.54/7.62 => c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cos__arg__i__mult__zero,axiom, % 7.54/7.62 ! [V_y] : % 7.54/7.62 ( V_y != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) % 7.54/7.62 => c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cos__arg__i__mult__zero__pos,axiom, % 7.54/7.62 ! [V_y] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) % 7.54/7.62 => c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex_Osize_I2_J,axiom, % 7.54/7.62 ! [V_real2,V_real1] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex_Orecs,axiom, % 7.54/7.62 ! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2) ). % 7.54/7.62 % 7.54/7.62 fof(fact_complex_Osimps_I2_J,axiom, % 7.54/7.62 ! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2) ). % 7.54/7.62 % 7.54/7.62 fof(fact_natfloor__div__nat,axiom, % 7.54/7.62 ! [V_y,V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y)) % 7.54/7.62 => c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_y))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_real__sgn__eq,axiom, % 7.54/7.62 ! [V_x] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_real__divide__square__eq,axiom, % 7.54/7.62 ! [V_a,V_r] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_r)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_a),V_r) ). % 7.54/7.62 % 7.54/7.62 fof(fact_power__divide,axiom, % 7.54/7.62 ! [V_n,V_b,V_a,T_a] : % 7.54/7.62 ( class_Fields_Ofield__inverse__zero(T_a) % 7.54/7.62 => 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)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_divide__1,axiom, % 7.54/7.62 ! [V_a,T_a] : % 7.54/7.62 ( class_Rings_Odivision__ring(T_a) % 7.54/7.62 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_divide_Oadd,axiom, % 7.54/7.62 ! [V_ya,V_y,V_x,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__field(T_a) % 7.54/7.62 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_add__divide__distrib,axiom, % 7.54/7.62 ! [V_c,V_b,V_a,T_a] : % 7.54/7.62 ( class_Rings_Odivision__ring(T_a) % 7.54/7.62 => 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)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_divide_Oconvergent,axiom, % 7.54/7.62 ! [V_y_2,V_X_2,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__field(T_a) % 7.54/7.62 => ( c_SEQ_Oconvergent(T_a,V_X_2) % 7.54/7.62 => c_SEQ_Oconvergent(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(T_a),V_X_2),V_y_2)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_norm__divide,axiom, % 7.54/7.62 ! [V_b,V_a,T_a] : % 7.54/7.62 ( ( class_Fields_Ofield__inverse__zero(T_a) % 7.54/7.62 & class_RealVector_Oreal__normed__field(T_a) ) % 7.54/7.62 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_times__divide__eq__right,axiom, % 7.54/7.62 ! [V_c,V_b,V_a,T_a] : % 7.54/7.62 ( class_Rings_Odivision__ring(T_a) % 7.54/7.62 => 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) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_divide_Ozero,axiom, % 7.54/7.62 ! [V_y,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__field(T_a) % 7.54/7.62 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_divide__zero,axiom, % 7.54/7.62 ! [V_a,T_a] : % 7.54/7.62 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 7.54/7.62 => 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) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_divide__zero__left,axiom, % 7.54/7.62 ! [V_a,T_a] : % 7.54/7.62 ( class_Rings_Odivision__ring(T_a) % 7.54/7.62 => 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) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nonzero__norm__divide,axiom, % 7.54/7.62 ! [V_a,V_b,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__field(T_a) % 7.54/7.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_real__0__le__divide__iff,axiom, % 7.54/7.62 ! [V_y_2,V_x_2] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x_2),V_y_2))) % 7.54/7.62 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) % 7.54/7.62 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) ) % 7.54/7.62 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) % 7.54/7.62 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_power__one__over,axiom, % 7.54/7.62 ! [V_n,V_a,T_a] : % 7.54/7.62 ( class_Fields_Ofield__inverse__zero(T_a) % 7.54/7.62 => 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) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nonzero__power__divide,axiom, % 7.54/7.62 ! [V_n,V_a,V_b,T_a] : % 7.54/7.62 ( class_Fields_Ofield(T_a) % 7.54/7.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => 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)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_right__inverse__eq,axiom, % 7.54/7.62 ! [V_a_2,V_b_2,T_a] : % 7.54/7.62 ( class_Rings_Odivision__ring(T_a) % 7.54/7.62 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a) % 7.54/7.62 <=> V_a_2 = V_b_2 ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_divide__self,axiom, % 7.54/7.62 ! [V_a,T_a] : % 7.54/7.62 ( class_Rings_Odivision__ring(T_a) % 7.54/7.62 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_divide__self__if,axiom, % 7.54/7.62 ! [V_a,T_a] : % 7.54/7.62 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 7.54/7.62 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 7.54/7.62 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_eq__divide__imp,axiom, % 7.54/7.62 ! [V_b,V_a,V_c,T_a] : % 7.54/7.62 ( class_Rings_Odivision__ring(T_a) % 7.54/7.62 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 7.54/7.62 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_divide__eq__imp,axiom, % 7.54/7.62 ! [V_a,V_b,V_c,T_a] : % 7.54/7.62 ( class_Rings_Odivision__ring(T_a) % 7.54/7.62 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 7.54/7.62 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nonzero__divide__eq__eq,axiom, % 7.54/7.62 ! [V_a_2,V_b_2,V_c_2,T_a] : % 7.54/7.62 ( class_Rings_Odivision__ring(T_a) % 7.54/7.62 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2 % 7.54/7.62 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_nonzero__eq__divide__eq,axiom, % 7.54/7.62 ! [V_b_2,V_a_2,V_c_2,T_a] : % 7.54/7.62 ( class_Rings_Odivision__ring(T_a) % 7.54/7.62 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) % 7.54/7.62 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Im__sgn,axiom, % 7.54/7.62 ! [V_z] : hAPP(c_Complex_OIm,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_Re__sgn,axiom, % 7.54/7.62 ! [V_z] : hAPP(c_Complex_ORe,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_divide_Odiff,axiom, % 7.54/7.62 ! [V_ya,V_y,V_x,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__normed__field(T_a) % 7.54/7.62 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_diff__divide__distrib,axiom, % 7.54/7.62 ! [V_c,V_b,V_a,T_a] : % 7.54/7.62 ( class_Rings_Odivision__ring(T_a) % 7.54/7.62 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_c) = 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)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_DERIV__mult__lemma,axiom, % 7.54/7.62 ! [V_h,V_d,V_c,V_b,V_a,T_a] : % 7.54/7.62 ( class_RealVector_Oreal__field(T_a) % 7.54/7.62 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(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_c),V_d))),V_h) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)),V_h))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),V_h)),V_d)) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_lemma__MVT,axiom, % 7.54/7.62 ! [V_b_2,V_a_2,V_fa_2] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2))),V_a_2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2))),V_b_2)) ). % 7.54/7.62 % 7.54/7.62 fof(fact_real__of__nat__div4,axiom, % 7.54/7.62 ! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x)))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_power__diff,axiom, % 7.54/7.62 ! [V_m,V_n,V_a,T_a] : % 7.54/7.62 ( class_Fields_Ofield(T_a) % 7.54/7.62 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) % 7.54/7.62 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),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)) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_ln__div,axiom, % 7.54/7.62 ! [V_y,V_x] : % 7.54/7.62 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) % 7.54/7.62 => c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y)) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_real__of__nat__div2,axiom, % 7.54/7.62 ! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_real__of__nat__div3,axiom, % 7.54/7.62 ! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ). % 7.54/7.62 % 7.54/7.62 fof(fact_divide__left__mono__neg,axiom, % 7.54/7.62 ! [V_c,V_b,V_a,T_a] : % 7.54/7.62 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a))) % 7.54/7.62 => ( hBOOL(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))) % 7.54/7.62 => hBOOL(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))) ) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_divide__left__mono,axiom, % 7.54/7.62 ! [V_c,V_a,V_b,T_a] : % 7.54/7.62 ( class_Fields_Olinordered__field(T_a) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a)) % 7.54/7.62 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 7.54/7.62 => ( hBOOL(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))) % 7.54/7.62 => hBOOL(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))) ) ) ) ) ). % 7.54/7.62 % 7.54/7.62 fof(fact_cis__divide,axiom, % 7.54/7.62 ! [V_b,V_a] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_b)) ). % 7.54/7.62 % 7.54/7.62 %----Arity declarations (267) % 7.54/7.62 fof(arity_Polynomial__Opoly__Rings_Oidom,axiom, % 7.54/7.62 ! [T_1] : % 7.54/7.62 ( class_Rings_Oidom(T_1) % 7.54/7.62 => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom, % 7.54/7.62 ! [T_1] : % 7.54/7.62 ( class_Groups_Ocancel__comm__monoid__add(T_1) % 7.54/7.62 => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom, % 7.54/7.62 ! [T_1] : % 7.54/7.62 ( class_Rings_Ocomm__semiring__0(T_1) % 7.54/7.62 => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom, % 7.54/7.62 ! [T_1] : % 7.54/7.62 ( class_Rings_Ocomm__ring(T_1) % 7.54/7.62 => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom, % 7.54/7.62 class_Rings_Oidom(tc_Complex_Ocomplex) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom, % 7.54/7.62 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom, % 7.54/7.62 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom, % 7.54/7.62 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ). % 7.54/7.62 % 7.54/7.62 fof(arity_RealDef__Oreal__Rings_Oidom,axiom, % 7.54/7.62 class_Rings_Oidom(tc_RealDef_Oreal) ). % 7.54/7.62 % 7.54/7.62 fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom, % 7.54/7.62 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ). % 7.54/7.62 % 7.54/7.62 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom, % 7.54/7.62 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ). % 7.54/7.62 % 7.54/7.62 fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom, % 7.54/7.62 class_Rings_Ocomm__ring(tc_RealDef_Oreal) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom, % 7.54/7.62 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom, % 7.54/7.62 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Oidom,axiom, % 7.54/7.62 class_Rings_Oidom(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom, % 7.54/7.62 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom, % 7.54/7.62 class_Rings_Ocomm__semiring__0(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom, % 7.54/7.62 class_Rings_Ocomm__ring(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_fun__Orderings_Opreorder,axiom, % 7.54/7.62 ! [T_2,T_1] : % 7.54/7.62 ( class_Orderings_Opreorder(T_1) % 7.54/7.62 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 7.54/7.62 % 7.54/7.62 fof(arity_fun__Orderings_Oorder,axiom, % 7.54/7.62 ! [T_2,T_1] : % 7.54/7.62 ( class_Orderings_Oorder(T_1) % 7.54/7.62 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 7.54/7.62 % 7.54/7.62 fof(arity_fun__Orderings_Oord,axiom, % 7.54/7.62 ! [T_2,T_1] : % 7.54/7.62 ( class_Orderings_Oord(T_1) % 7.54/7.62 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 7.54/7.62 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 7.54/7.62 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 7.54/7.62 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 7.54/7.62 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 7.54/7.62 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 7.54/7.62 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 7.54/7.62 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 7.54/7.62 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 7.54/7.62 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 7.54/7.62 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 7.54/7.62 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 7.54/7.62 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 7.54/7.62 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 7.54/7.62 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 7.54/7.62 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 7.54/7.62 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 7.54/7.62 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 7.54/7.62 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 7.54/7.62 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 7.54/7.62 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 7.54/7.62 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 7.54/7.62 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 7.54/7.62 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 7.54/7.62 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 7.54/7.62 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 7.54/7.62 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 7.54/7.62 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 7.54/7.62 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 7.54/7.62 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 7.54/7.62 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 7.54/7.62 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 7.54/7.62 class_Divides_Osemiring__div(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 7.54/7.62 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 7.54/7.62 class_Groups_Oab__group__add(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 7.54/7.62 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 7.54/7.62 class_Rings_Oordered__ring(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 7.54/7.62 class_Orderings_Opreorder(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 7.54/7.62 class_Orderings_Olinorder(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 7.54/7.62 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 7.54/7.62 % 7.54/7.62 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 7.54/7.63 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 7.54/7.63 class_Groups_Omonoid__add(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 7.54/7.63 class_Rings_Osemiring__0(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 7.54/7.63 class_Groups_Ogroup__add(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 7.54/7.63 class_Rings_Omult__zero(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 7.54/7.63 class_Orderings_Oorder(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 7.54/7.63 class_Rings_Osemiring(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Int__Oint__Orderings_Oord,axiom, % 7.54/7.63 class_Orderings_Oord(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 7.54/7.63 class_Groups_Osgn__if(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 7.54/7.63 class_Rings_Oring__1(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Int__Oint__Power_Opower,axiom, % 7.54/7.63 class_Power_Opower(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Int__Oint__Groups_Ozero,axiom, % 7.54/7.63 class_Groups_Ozero(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Int__Oint__Rings_Oring,axiom, % 7.54/7.63 class_Rings_Oring(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Int__Oint__Groups_Oone,axiom, % 7.54/7.63 class_Groups_Oone(tc_Int_Oint) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 7.54/7.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 7.54/7.63 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 7.54/7.63 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 7.54/7.63 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 7.54/7.63 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 7.54/7.63 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 7.54/7.63 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 7.54/7.63 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 7.54/7.63 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 7.54/7.63 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 7.54/7.63 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 7.54/7.63 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 7.54/7.63 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 7.54/7.63 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 7.54/7.63 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 7.54/7.63 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 7.54/7.63 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 7.54/7.63 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 7.54/7.63 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 7.54/7.63 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 7.54/7.63 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 7.54/7.63 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 7.54/7.63 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 7.54/7.63 class_Orderings_Opreorder(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 7.54/7.63 class_Orderings_Olinorder(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 7.54/7.63 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 7.54/7.63 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 7.54/7.63 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 7.54/7.63 class_Rings_Omult__zero(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 7.54/7.63 class_Orderings_Oorder(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 7.54/7.63 class_Rings_Osemiring(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 7.54/7.63 class_Orderings_Oord(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Power_Opower,axiom, % 7.54/7.63 class_Power_Opower(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 7.54/7.63 class_Groups_Ozero(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Nat__Onat__Groups_Oone,axiom, % 7.54/7.63 class_Groups_Oone(tc_Nat_Onat) ). % 7.54/7.63 % 7.54/7.63 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 7.54/7.63 class_Orderings_Opreorder(tc_HOL_Obool) ). % 7.54/7.63 % 7.54/7.63 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 7.54/7.63 class_Orderings_Oorder(tc_HOL_Obool) ). % 7.54/7.63 % 7.54/7.63 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 7.54/7.63 class_Orderings_Oord(tc_HOL_Obool) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 7.54/7.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 7.54/7.63 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 7.54/7.63 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom, % 7.54/7.63 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom, % 7.54/7.63 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom, % 7.54/7.63 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom, % 7.54/7.63 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom, % 7.54/7.63 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom, % 7.54/7.63 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom, % 7.54/7.63 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom, % 7.54/7.63 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom, % 7.54/7.63 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom, % 7.54/7.63 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom, % 7.54/7.63 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom, % 7.54/7.63 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom, % 7.54/7.63 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom, % 7.54/7.63 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom, % 7.54/7.63 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom, % 7.54/7.63 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom, % 7.54/7.63 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom, % 7.54/7.63 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom, % 7.54/7.63 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom, % 7.54/7.63 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom, % 7.54/7.63 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom, % 7.54/7.63 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom, % 7.54/7.63 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom, % 7.54/7.63 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom, % 7.54/7.63 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom, % 7.54/7.63 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom, % 7.54/7.63 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__RealVector_Ometric__space,axiom, % 7.54/7.63 class_RealVector_Ometric__space(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom, % 7.54/7.63 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom, % 7.54/7.63 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom, % 7.54/7.63 class_Fields_Olinordered__field(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom, % 7.54/7.63 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom, % 7.54/7.63 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom, % 7.54/7.63 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom, % 7.54/7.63 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom, % 7.54/7.63 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom, % 7.54/7.63 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom, % 7.54/7.63 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__RealVector_Oreal__field,axiom, % 7.54/7.63 class_RealVector_Oreal__field(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom, % 7.54/7.63 class_Rings_Odivision__ring(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom, % 7.54/7.63 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom, % 7.54/7.63 class_Groups_Oab__group__add(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom, % 7.54/7.63 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom, % 7.54/7.63 class_Rings_Oordered__ring(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom, % 7.54/7.63 class_Orderings_Opreorder(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom, % 7.54/7.63 class_Orderings_Olinorder(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom, % 7.54/7.63 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom, % 7.54/7.63 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom, % 7.54/7.63 class_Groups_Omonoid__add(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom, % 7.54/7.63 class_Rings_Osemiring__0(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom, % 7.54/7.63 class_Groups_Ogroup__add(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom, % 7.54/7.63 class_Rings_Omult__zero(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom, % 7.54/7.63 class_Orderings_Oorder(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom, % 7.54/7.63 class_Rings_Osemiring(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Orderings_Oord,axiom, % 7.54/7.63 class_Orderings_Oord(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Osgn__if,axiom, % 7.54/7.63 class_Groups_Osgn__if(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom, % 7.54/7.63 class_Rings_Oring__1(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Fields_Ofield,axiom, % 7.54/7.63 class_Fields_Ofield(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Power_Opower,axiom, % 7.54/7.63 class_Power_Opower(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Ozero,axiom, % 7.54/7.63 class_Groups_Ozero(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Rings_Oring,axiom, % 7.54/7.63 class_Rings_Oring(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_RealDef__Oreal__Groups_Oone,axiom, % 7.54/7.63 class_Groups_Oone(tc_RealDef_Oreal) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 7.54/7.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom, % 7.54/7.63 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom, % 7.54/7.63 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom, % 7.54/7.63 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom, % 7.54/7.63 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom, % 7.54/7.63 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom, % 7.54/7.63 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom, % 7.54/7.63 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom, % 7.54/7.63 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom, % 7.54/7.63 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom, % 7.54/7.63 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom, % 7.54/7.63 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom, % 7.54/7.63 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__RealVector_Ometric__space,axiom, % 7.54/7.63 class_RealVector_Ometric__space(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom, % 7.54/7.63 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom, % 7.54/7.63 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom, % 7.54/7.63 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom, % 7.54/7.63 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom, % 7.54/7.63 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__RealVector_Oreal__field,axiom, % 7.54/7.63 class_RealVector_Oreal__field(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom, % 7.54/7.63 class_Rings_Odivision__ring(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom, % 7.54/7.63 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom, % 7.54/7.63 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom, % 7.54/7.63 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom, % 7.54/7.63 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom, % 7.54/7.63 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom, % 7.54/7.63 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom, % 7.54/7.63 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom, % 7.54/7.63 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom, % 7.54/7.63 class_Rings_Omult__zero(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom, % 7.54/7.63 class_Rings_Osemiring(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom, % 7.54/7.63 class_Rings_Oring__1(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom, % 7.54/7.63 class_Fields_Ofield(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Power_Opower,axiom, % 7.54/7.63 class_Power_Opower(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom, % 7.54/7.63 class_Groups_Ozero(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Rings_Oring,axiom, % 7.54/7.63 class_Rings_Oring(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Complex__Ocomplex__Groups_Oone,axiom, % 7.54/7.63 class_Groups_Oone(tc_Complex_Ocomplex) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Oidom(T_1) % 7.54/7.63 => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Groups_Ocancel__comm__monoid__add(T_1) % 7.54/7.63 => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Oidom(T_1) % 7.54/7.63 => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Oidom(T_1) % 7.54/7.63 => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Groups_Ocancel__comm__monoid__add(T_1) % 7.54/7.63 => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__semiring__0(T_1) % 7.54/7.63 => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__semiring__1(T_1) % 7.54/7.63 => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Groups_Ocomm__monoid__add(T_1) % 7.54/7.63 => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Oidom(T_1) % 7.54/7.63 => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Groups_Ocomm__monoid__add(T_1) % 7.54/7.63 => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__semiring__1(T_1) % 7.54/7.63 => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Fields_Ofield(T_1) % 7.54/7.63 => class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__semiring__0(T_1) % 7.54/7.63 => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Groups_Oab__group__add(T_1) % 7.54/7.63 => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__semiring__1(T_1) % 7.54/7.63 => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__semiring__1(T_1) % 7.54/7.63 => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__ring__1(T_1) % 7.54/7.63 => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Groups_Ocomm__monoid__add(T_1) % 7.54/7.63 => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__semiring__0(T_1) % 7.54/7.63 => class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Groups_Oab__group__add(T_1) % 7.54/7.63 => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__semiring__0(T_1) % 7.54/7.63 => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__semiring__0(T_1) % 7.54/7.63 => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Orderings_Oord,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Olinordered__idom(T_1) % 7.54/7.63 => class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__ring__1(T_1) % 7.54/7.63 => class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Power_Opower,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__semiring__1(T_1) % 7.54/7.63 => class_Power_Opower(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Ozero,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Groups_Ozero(T_1) % 7.54/7.63 => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Rings_Oring,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__ring(T_1) % 7.54/7.63 => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 fof(arity_Polynomial__Opoly__Groups_Oone,axiom, % 7.54/7.63 ! [T_1] : % 7.54/7.63 ( class_Rings_Ocomm__semiring__1(T_1) % 7.54/7.63 => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ) ). % 7.54/7.63 % 7.54/7.63 %----Helper facts (4) % 7.54/7.63 fof(help_c__COMBK__1,axiom, % 7.54/7.63 ! [V_Q,V_P,T_b,T_a] : hAPP(c_COMBK(T_a,T_b,V_P),V_Q) = V_P ). % 7.54/7.63 % 7.54/7.63 fof(help_c__COMBB__1,axiom, % 7.54/7.63 ! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(c_COMBB(T_b,T_a,T_c,V_P_2,V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)) ). % 7.54/7.63 % 7.54/7.63 fof(help_c__COMBC__1,axiom, % 7.54/7.63 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(c_COMBC(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2) ). % 7.54/7.63 % 7.54/7.63 fof(help_c__COMBS__1,axiom, % 7.54/7.63 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(c_COMBS(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)) ). % 7.54/7.63 % 7.54/7.63 %----Conjectures (1) % 7.54/7.63 fof(conj_0,conjecture, % 7.54/7.63 ? [B_K] : % 7.54/7.63 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) % 7.54/7.63 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),B_K)) ) ). % 7.54/7.63 % 7.54/7.63 %------------------------------------------------------------------------------ % 7.54/7.63 %------------------------------------------- % 7.54/7.63 % Proof found % 7.54/7.63 % SZS status Theorem for theBenchmark % 7.54/7.63 % SZS output start Proof % 7.54/7.63 %ClaNum:1975(EqnAxiom:311) % 7.54/7.63 %VarNum:8910(SingletonVarNum:3146) % 7.54/7.63 %MaxLitNum:7 % 7.54/7.63 %MaxfuncDepth:8 % 7.54/7.63 %SharedTerms:357 % 7.54/7.63 %goalClause: 1944 % 7.54/7.63 [312]P1(a1) % 7.54/7.63 [313]P1(a122) % 7.54/7.63 [314]P1(a2) % 7.54/7.63 [315]P7(a114) % 7.54/7.63 [316]P7(a115) % 7.54/7.63 [317]P27(a114) % 7.54/7.63 [318]P27(a119) % 7.54/7.63 [319]P27(a115) % 7.54/7.63 [320]P27(a116) % 7.54/7.63 [321]P28(a114) % 7.54/7.63 [322]P28(a117) % 7.54/7.63 [323]P28(a119) % 7.54/7.63 [324]P28(a115) % 7.54/7.63 [325]P34(a114) % 7.54/7.63 [326]P34(a119) % 7.54/7.63 [327]P34(a115) % 7.54/7.63 [328]P35(a114) % 7.54/7.63 [329]P35(a119) % 7.54/7.63 [330]P35(a115) % 7.54/7.63 [331]P35(a116) % 7.54/7.63 [332]P36(a114) % 7.54/7.63 [333]P36(a119) % 7.54/7.63 [334]P36(a115) % 7.54/7.63 [335]P36(a116) % 7.54/7.63 [336]P37(a114) % 7.54/7.63 [337]P37(a117) % 7.54/7.63 [338]P38(a114) % 7.54/7.63 [339]P38(a117) % 7.54/7.63 [340]P8(a114) % 7.54/7.63 [341]P8(a117) % 7.54/7.63 [342]P8(a119) % 7.54/7.63 [343]P8(a115) % 7.54/7.63 [344]P9(a114) % 7.54/7.63 [345]P9(a117) % 7.54/7.63 [346]P9(a119) % 7.54/7.63 [347]P9(a115) % 7.54/7.63 [348]P16(a114) % 7.54/7.63 [349]P16(a117) % 7.54/7.63 [350]P16(a119) % 7.54/7.63 [351]P16(a115) % 7.54/7.63 [352]P17(a114) % 7.54/7.63 [353]P17(a117) % 7.54/7.63 [354]P17(a119) % 7.54/7.63 [355]P17(a115) % 7.54/7.63 [356]P20(a114) % 7.54/7.63 [357]P20(a117) % 7.54/7.63 [358]P20(a119) % 7.54/7.63 [359]P20(a115) % 7.54/7.63 [360]P21(a114) % 7.54/7.63 [361]P21(a117) % 7.54/7.63 [362]P21(a119) % 7.54/7.63 [363]P21(a115) % 7.54/7.63 [364]P22(a114) % 7.54/7.63 [365]P22(a115) % 7.54/7.63 [366]P29(a114) % 7.54/7.63 [367]P29(a119) % 7.54/7.63 [368]P29(a115) % 7.54/7.63 [369]P30(a114) % 7.54/7.63 [370]P30(a119) % 7.54/7.63 [371]P30(a115) % 7.54/7.63 [372]P31(a114) % 7.54/7.63 [373]P31(a119) % 7.54/7.63 [374]P31(a115) % 7.54/7.63 [375]P32(a114) % 7.54/7.63 [376]P32(a119) % 7.54/7.63 [377]P32(a115) % 7.54/7.63 [378]P45(a114) % 7.54/7.63 [379]P45(a119) % 7.54/7.63 [380]P45(a115) % 7.54/7.63 [381]P46(a114) % 7.54/7.63 [382]P46(a115) % 7.54/7.63 [383]P58(a114) % 7.54/7.63 [384]P58(a117) % 7.54/7.63 [385]P58(a119) % 7.54/7.63 [386]P58(a115) % 7.54/7.63 [387]P76(a114) % 7.54/7.63 [388]P76(a117) % 7.54/7.63 [389]P76(a119) % 7.54/7.63 [390]P76(a115) % 7.54/7.63 [391]P47(a114) % 7.54/7.63 [392]P47(a117) % 7.54/7.63 [393]P47(a119) % 7.54/7.63 [394]P47(a115) % 7.54/7.63 [395]P39(a114) % 7.54/7.63 [396]P39(a117) % 7.54/7.63 [397]P33(a114) % 7.54/7.63 [398]P33(a115) % 7.54/7.63 [399]P59(a114) % 7.54/7.63 [400]P59(a115) % 7.54/7.63 [401]P43(a114) % 7.54/7.63 [402]P43(a117) % 7.54/7.63 [403]P18(a114) % 7.54/7.63 [404]P18(a117) % 7.54/7.63 [405]P18(a119) % 7.54/7.63 [406]P18(a115) % 7.54/7.63 [407]P41(a114) % 7.54/7.63 [408]P41(a117) % 7.54/7.63 [409]P62(a114) % 7.54/7.63 [410]P62(a117) % 7.54/7.63 [411]P62(a119) % 7.54/7.63 [412]P62(a115) % 7.54/7.63 [413]P64(a114) % 7.54/7.63 [414]P64(a117) % 7.54/7.63 [415]P64(a115) % 7.54/7.63 [416]P65(a114) % 7.54/7.63 [417]P65(a117) % 7.54/7.63 [418]P65(a119) % 7.54/7.63 [419]P65(a115) % 7.54/7.63 [420]P74(a114) % 7.54/7.63 [421]P74(a117) % 7.54/7.63 [422]P74(a119) % 7.54/7.63 [423]P74(a115) % 7.54/7.63 [424]P48(a114) % 7.54/7.63 [425]P48(a117) % 7.54/7.63 [426]P48(a119) % 7.54/7.63 [427]P48(a115) % 7.54/7.63 [428]P25(a114) % 7.54/7.63 [429]P25(a117) % 7.54/7.63 [430]P25(a119) % 7.54/7.63 [431]P25(a115) % 7.54/7.63 [432]P23(a114) % 7.54/7.63 [433]P23(a117) % 7.54/7.63 [434]P23(a119) % 7.54/7.63 [435]P23(a115) % 7.54/7.63 [436]P56(a114) % 7.54/7.63 [437]P56(a115) % 7.54/7.63 [438]P57(a114) % 7.54/7.63 [439]P57(a115) % 7.54/7.63 [440]P66(a114) % 7.54/7.63 [441]P66(a119) % 7.54/7.63 [442]P66(a115) % 7.54/7.63 [443]P67(a114) % 7.54/7.63 [444]P67(a115) % 7.54/7.63 [445]P69(a114) % 7.54/7.63 [446]P69(a119) % 7.54/7.63 [447]P69(a115) % 7.54/7.63 [448]P68(a114) % 7.54/7.63 [449]P68(a119) % 7.54/7.63 [450]P68(a115) % 7.54/7.63 [451]P63(a114) % 7.54/7.63 [452]P63(a119) % 7.54/7.63 [453]P63(a115) % 7.54/7.63 [454]P52(a114) % 7.54/7.63 [455]P52(a119) % 7.54/7.63 [456]P52(a115) % 7.54/7.63 [457]P60(a114) % 7.54/7.63 [458]P60(a119) % 7.54/7.63 [459]P60(a115) % 7.54/7.63 [460]P70(a114) % 7.54/7.63 [461]P70(a115) % 7.54/7.63 [462]P61(a114) % 7.54/7.63 [463]P61(a115) % 7.54/7.63 [464]P71(a114) % 7.54/7.63 [465]P71(a117) % 7.54/7.63 [466]P71(a115) % 7.54/7.63 [467]P40(a114) % 7.54/7.63 [468]P40(a117) % 7.54/7.63 [469]P40(a119) % 7.54/7.63 [470]P40(a115) % 7.54/7.63 [471]P75(a114) % 7.54/7.63 [472]P75(a117) % 7.54/7.63 [473]P75(a119) % 7.54/7.63 [474]P75(a115) % 7.54/7.63 [475]P24(a114) % 7.54/7.63 [476]P24(a117) % 7.54/7.63 [477]P24(a115) % 7.54/7.63 [478]P26(a114) % 7.54/7.63 [479]P26(a115) % 7.54/7.63 [480]P10(a114) % 7.54/7.63 [481]P10(a117) % 7.54/7.63 [482]P10(a115) % 7.54/7.63 [483]P72(a114) % 7.54/7.63 [484]P72(a117) % 7.54/7.63 [485]P72(a115) % 7.54/7.63 [486]P73(a114) % 7.54/7.63 [487]P73(a117) % 7.54/7.63 [488]P73(a115) % 7.54/7.63 [489]P49(a114) % 7.54/7.63 [490]P49(a117) % 7.54/7.63 [491]P49(a115) % 7.54/7.63 [492]P11(a119) % 7.54/7.63 [493]P11(a115) % 7.54/7.63 [494]P12(a114) % 7.54/7.63 [495]P12(a117) % 7.54/7.63 [496]P53(a114) % 7.54/7.63 [497]P53(a117) % 7.54/7.63 [498]P44(a114) % 7.54/7.63 [499]P44(a117) % 7.54/7.63 [500]P54(a114) % 7.54/7.63 [501]P54(a117) % 7.54/7.63 [502]P13(a114) % 7.54/7.63 [503]P13(a117) % 7.54/7.63 [504]P42(a114) % 7.54/7.63 [505]P42(a117) % 7.54/7.63 [506]P14(a114) % 7.54/7.63 [507]P15(a114) % 7.54/7.63 [508]P55(a114) % 7.54/7.63 [509]P55(a117) % 7.54/7.63 [510]P55(a115) % 7.54/7.63 [511]P19(a114) % 7.54/7.63 [512]P19(a117) % 7.54/7.63 [513]P19(a119) % 7.54/7.63 [514]P19(a115) % 7.54/7.63 [515]P51(a114) % 7.54/7.63 [516]P51(a117) % 7.54/7.63 [517]P51(a119) % 7.54/7.63 [518]P51(a115) % 7.54/7.63 [519]P50(a114) % 7.54/7.63 [520]P50(a117) % 7.54/7.63 [521]P50(a115) % 7.54/7.63 [528]E(f118(a5,a17),f16(a114)) % 7.54/7.63 [529]E(f118(a10,a17),f3(a114)) % 7.54/7.63 [723]~E(f3(a117),a17) % 7.54/7.63 [724]~E(f16(a117),a17) % 7.54/7.63 [725]~E(f16(a114),f3(a114)) % 7.54/7.63 [726]~E(f16(a115),f3(a115)) % 7.54/7.63 [522]E(f4(f3(a117)),f16(a117)) % 7.54/7.63 [523]E(f26(f3(a114)),f3(a119)) % 7.54/7.63 [524]E(f26(f16(a114)),f16(a119)) % 7.54/7.63 [525]E(f33(f3(a114)),f3(a119)) % 7.54/7.63 [526]E(f33(f16(a114)),f16(a119)) % 7.54/7.63 [527]E(f34(f16(a114)),f3(a114)) % 7.54/7.63 [530]E(f118(a5,f3(a117)),f3(a114)) % 7.54/7.63 [531]E(f118(a5,f16(a117)),f3(a114)) % 7.54/7.63 [532]E(f118(a10,f3(a117)),f3(a114)) % 7.54/7.63 [533]E(f118(a10,f16(a117)),f16(a114)) % 7.54/7.63 [534]E(f35(a119,f3(a119)),f3(a114)) % 7.54/7.63 [535]E(f35(a119,f16(a119)),f16(a114)) % 7.54/7.63 [537]E(f11(f3(a114),f16(a114)),a17) % 7.54/7.63 [538]E(f11(f3(a114),f3(a114)),f3(a117)) % 7.54/7.63 [539]E(f11(f16(a114),f3(a114)),f16(a117)) % 7.54/7.63 [540]E(f18(f16(a114),f3(a114)),f16(a117)) % 7.54/7.63 [586]P77(f118(f28(a115,f3(a115)),f16(a115))) % 7.54/7.63 [587]P77(f118(f29(a115,f3(a115)),f16(a115))) % 7.54/7.63 [718]P2(a114,f7(a117,a114,a119,a10,f7(a119,a117,a119,a124,a1))) % 7.54/7.63 [719]P3(a114,f7(a117,a114,a119,a10,f7(a119,a117,a119,a124,a1))) % 7.54/7.63 [560]E(f118(a5,f18(f16(a114),f3(a114))),f3(a114)) % 7.54/7.63 [561]E(f118(a10,f18(f16(a114),f3(a114))),f16(a114)) % 7.54/7.63 [573]P77(f118(f28(a114,f3(a114)),a123)) % 7.54/7.63 [574]P77(f118(f28(a114,f3(a114)),a39)) % 7.54/7.63 [575]P77(f118(f28(a114,f3(a114)),a58)) % 7.54/7.63 [576]P77(f118(f29(a114,f3(a114)),a40)) % 7.54/7.63 [577]P77(f118(f29(a114,f3(a114)),a57)) % 7.54/7.63 [595]E(f35(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),f16(a114)) % 7.54/7.63 [721]P2(a114,f7(a117,a114,a119,a5,f7(a119,a117,a119,a124,f7(a119,a119,a119,a1,a122)))) % 7.54/7.63 [722]P2(a114,f7(a117,a114,a119,a5,f7(a119,a117,a119,a124,f7(a119,a119,a119,a1,a2)))) % 7.54/7.63 [541]E(f19(a114,x5411),f36(a114,x5411)) % 7.54/7.63 [563]E(f22(a119,x5631,x5631),f3(a119)) % 7.54/7.63 [536]E(f18(f3(a114),x5361),f3(a117)) % 7.54/7.63 [542]E(f26(f35(a119,x5421)),x5421) % 7.54/7.63 [543]E(f33(f35(a119,x5431)),x5431) % 7.54/7.63 [548]E(f19(a114,f35(a119,x5481)),f35(a119,x5481)) % 7.54/7.63 [549]E(f118(f118(f23(a119),x5491),f3(a119)),x5491) % 7.54/7.63 [550]E(f118(f118(f23(a115),x5501),f3(a115)),x5501) % 7.54/7.63 [551]E(f118(f118(f24(a119),x5511),f16(a119)),x5511) % 7.54/7.63 [552]E(f118(f118(f24(a115),x5521),f16(a115)),x5521) % 7.54/7.63 [554]E(f118(f118(f24(a119),x5541),f3(a119)),f3(a119)) % 7.54/7.63 [564]E(f22(a119,x5641,f3(a119)),x5641) % 7.54/7.63 [566]E(f22(a119,f3(a119),x5661),f3(a119)) % 7.54/7.63 [567]E(f20(a115,f3(a115),x5671),f3(a115)) % 7.54/7.63 [568]E(f11(f118(a10,x5681),f118(a5,x5681)),x5681) % 7.54/7.63 [569]P77(f118(f28(a114,x5691),x5691)) % 7.54/7.63 [570]P77(f118(f28(a119,x5701),x5701)) % 7.54/7.63 [571]P77(f118(f28(a115,x5711),x5711)) % 7.54/7.63 [572]E(f118(f118(f37(a114),x5721),f19(a114,x5721)),f25(a114,x5721)) % 7.54/7.63 [596]P77(f118(f28(a114,f3(a114)),f35(a119,x5961))) % 7.54/7.63 [601]E(f118(f118(f37(a114),f118(a5,x6011)),f36(a117,x6011)),f118(a5,f25(a117,x6011))) % 7.54/7.63 [602]E(f118(f118(f37(a114),f118(a10,x6021)),f36(a117,x6021)),f118(a10,f25(a117,x6021))) % 7.54/7.63 [612]P77(f118(f28(a114,f118(a10,x6121)),f36(a117,x6121))) % 7.54/7.63 [658]P77(f118(f28(a114,f19(a114,f118(a5,x6581))),f36(a117,x6581))) % 7.54/7.63 [659]P77(f118(f28(a114,f19(a114,f118(a10,x6591))),f36(a117,x6591))) % 7.54/7.63 [661]P77(f118(f28(a114,f118(a5,f18(f16(a114),x6611))),f16(a114))) % 7.54/7.63 [662]P77(f118(f28(a114,f118(a10,f18(f16(a114),x6621))),f16(a114))) % 7.54/7.63 [692]P77(f118(f28(a114,f19(a114,f118(a5,f18(f16(a114),x6921)))),f16(a114))) % 7.54/7.63 [693]P77(f118(f28(a114,f19(a114,f118(a10,f18(f16(a114),x6931)))),f16(a114))) % 7.54/7.63 [728]~E(f118(f118(f23(a119),x7281),f16(a119)),x7281) % 7.54/7.63 [734]~E(f118(f118(f23(a119),x7341),f16(a119)),f3(a119)) % 7.54/7.63 [736]~P77(f118(f29(a119,x7361),x7361)) % 7.54/7.63 [739]~P77(f118(f29(a119,x7391),f3(a119))) % 7.54/7.63 [740]~P77(f118(f29(a114,f35(a119,x7401)),f3(a114))) % 7.54/7.63 [555]E(f118(f118(f23(a119),f3(a119)),x5551),x5551) % 7.54/7.63 [556]E(f118(f118(f23(a115),f3(a115)),x5561),x5561) % 7.54/7.63 [557]E(f118(f118(f24(a114),f16(a114)),x5571),x5571) % 7.54/7.63 [558]E(f118(f118(f24(a119),f16(a119)),x5581),x5581) % 7.54/7.63 [559]E(f118(f118(f24(a115),f16(a115)),x5591),x5591) % 7.54/7.63 [562]E(f118(f118(f24(a119),f3(a119)),x5621),f3(a119)) % 7.54/7.63 [579]P77(f118(f28(a119,f3(a119)),x5791)) % 7.54/7.63 [593]E(f28(a119,f118(f118(f23(a119),x5931),f16(a119))),f29(a119,x5931)) % 7.54/7.63 [600]P77(f118(f28(a114,x6001),f35(a119,f26(x6001)))) % 7.54/7.63 [605]E(f20(a119,x6051,f118(f118(f23(a119),f3(a119)),f16(a119))),x6051) % 7.54/7.63 [610]E(f118(f118(f23(a114),f35(a119,x6101)),f16(a114)),f35(a119,f118(f118(f23(a119),x6101),f16(a119)))) % 7.54/7.63 [625]P77(f118(f29(a119,x6251),f118(f118(f23(a119),x6251),f16(a119)))) % 7.54/7.63 [629]P77(f118(f29(a119,f3(a119)),f118(f118(f23(a119),x6291),f16(a119)))) % 7.54/7.63 [656]P77(f118(f29(a114,f3(a114)),f118(f118(f23(a114),f16(a114)),f19(a114,x6561)))) % 7.54/7.63 [677]P77(f118(f29(a114,x6771),f118(f118(f23(a114),f35(a119,f33(x6771))),f16(a114)))) % 7.54/7.63 [678]P77(f118(f29(a114,f22(a114,x6781,f16(a114))),f35(a119,f33(x6781)))) % 7.54/7.63 [695]P77(f118(f28(a114,f19(a114,f118(a5,f118(a124,x6951)))),f118(f118(f23(a114),a123),f16(a114)))) % 7.54/7.63 [622]P77(f118(f28(a119,x6221),f118(f118(f24(a119),x6221),x6221))) % 7.54/7.63 [640]E(f118(f118(f31(a119),f118(f118(f23(a119),f3(a119)),f16(a119))),x6401),f118(f118(f23(a119),f3(a119)),f16(a119))) % 7.54/7.63 [642]P77(f118(f28(a114,f36(a117,f118(a124,x6421))),a123)) % 7.54/7.63 [673]P77(f118(f29(a114,f3(a114)),f35(a119,f118(f118(f23(a119),x6731),f16(a119))))) % 7.54/7.63 [685]P77(f118(f28(a114,f36(a114,f118(a5,x6851))),f118(f118(f24(a114),f36(a117,x6851)),a40))) % 7.54/7.63 [686]P77(f118(f28(a114,f36(a114,f118(a5,x6861))),f118(f118(f24(a114),f36(a117,x6861)),a39))) % 7.54/7.63 [687]P77(f118(f28(a114,f36(a114,f118(a5,x6871))),f118(f118(f24(a114),f36(a117,x6871)),a59))) % 7.54/7.63 [688]P77(f118(f28(a114,f36(a114,f118(a10,x6881))),f118(f118(f24(a114),f36(a117,x6881)),a57))) % 7.54/7.63 [689]P77(f118(f28(a114,f36(a114,f118(a10,x6891))),f118(f118(f24(a114),f36(a117,x6891)),a58))) % 7.54/7.63 [690]P77(f118(f28(a114,f36(a114,f118(a10,x6901))),f118(f118(f24(a114),f36(a117,x6901)),a64))) % 7.54/7.63 [744]~P77(f118(f28(a119,f118(f118(f23(a119),x7441),f16(a119))),x7441)) % 7.54/7.63 [745]~P77(f118(f29(a114,f118(f118(f23(a114),f19(a114,x7451)),f16(a114))),x7451)) % 7.54/7.63 [657]E(f36(a117,f11(f118(a10,f18(f16(a114),x6571)),f118(a5,f18(f16(a114),x6571)))),f16(a114)) % 7.54/7.63 [681]P77(f118(f28(a119,x6811),f118(f118(f24(a119),x6811),f118(f118(f24(a119),x6811),x6811)))) % 7.54/7.63 [705]E(f118(f118(f23(a114),f118(f118(f24(a114),f118(a10,f18(f16(a114),x7051))),f118(a10,f18(f16(a114),x7051)))),f118(f118(f24(a114),f118(a5,f18(f16(a114),x7051))),f118(a5,f18(f16(a114),x7051)))),f16(a114)) % 7.54/7.63 [741]~E(f118(f118(f23(a115),f118(f118(f23(a115),f16(a115)),x7411)),x7411),f3(a115)) % 7.54/7.63 [544]E(f13(f11(x5441,x5442)),f3(a119)) % 7.54/7.63 [545]E(f118(a5,f11(x5451,x5452)),x5452) % 7.54/7.63 [546]E(f118(a10,f11(x5461,x5462)),x5461) % 7.54/7.63 [547]E(f27(a117,f11(x5471,x5472)),f3(a119)) % 7.54/7.63 [553]E(f36(a117,f18(x5531,x5532)),f19(a114,x5531)) % 7.54/7.63 [613]E(f22(a114,f118(a5,x6131),f118(a5,x6132)),f118(a5,f22(a117,x6131,x6132))) % 7.54/7.63 [614]E(f22(a114,f118(a10,x6141),f118(a10,x6142)),f118(a10,f22(a117,x6141,x6142))) % 7.54/7.63 [711]P77(f118(f28(a114,f22(a114,f36(a117,f118(f118(f23(a117),x7111),x7112)),f36(a117,x7111))),f36(a117,x7112))) % 7.54/7.63 [716]P77(f118(f28(a114,f22(a114,f118(f118(f37(a114),f35(a119,x7161)),f35(a119,x7162)),f35(a119,f20(a119,x7161,x7162)))),f16(a114))) % 7.54/7.63 [580]E(f118(f118(f23(a119),x5801),x5802),f118(f118(f23(a119),x5802),x5801)) % 7.54/7.63 [581]E(f118(f118(f23(a115),x5811),x5812),f118(f118(f23(a115),x5812),x5811)) % 7.54/7.63 [582]E(f118(f118(f24(a114),x5821),x5822),f118(f118(f24(a114),x5822),x5821)) % 7.54/7.63 [583]E(f118(f118(f24(a119),x5831),x5832),f118(f118(f24(a119),x5832),x5831)) % 7.54/7.63 [584]E(f118(f118(f24(a115),x5841),x5842),f118(f118(f24(a115),x5842),x5841)) % 7.54/7.63 [624]E(f118(f118(f37(a117),f18(f16(a114),x6241)),f18(f16(a114),x6242)),f18(f16(a114),f22(a114,x6241,x6242))) % 7.54/7.63 [636]E(f22(a119,x6361,f118(f118(f23(a119),x6362),f16(a119))),f22(a119,f22(a119,x6361,f16(a119)),x6362)) % 7.54/7.63 [670]P77(f118(f28(a119,f22(a119,x6701,x6702)),x6701)) % 7.54/7.63 [671]P77(f118(f28(a119,f20(a119,x6711,x6712)),x6711)) % 7.54/7.63 [672]E(f11(f118(f118(f23(a114),f118(a10,x6721)),f118(a10,x6722)),f118(f118(f23(a114),f118(a5,x6721)),f118(a5,x6722))),f118(f118(f23(a117),x6721),x6722)) % 7.54/7.63 [684]P77(f118(f29(a119,f22(a119,x6841,x6842)),f118(f118(f23(a119),x6841),f16(a119)))) % 7.54/7.63 [696]P77(f118(f29(a119,x6961),f118(f118(f23(a119),f118(f118(f23(a119),x6962),x6961)),f16(a119)))) % 7.54/7.63 [697]P77(f118(f29(a119,x6971),f118(f118(f23(a119),f118(f118(f23(a119),x6971),x6972)),f16(a119)))) % 7.54/7.63 [699]P77(f118(f28(a114,f35(a119,f20(a119,x6991,x6992))),f118(f118(f37(a114),f35(a119,x6991)),f35(a119,x6992)))) % 7.54/7.63 [706]P77(f118(f28(a114,f36(a117,x7061)),f118(f118(f23(a114),f36(a117,f118(f118(f23(a117),x7061),x7062))),f36(a117,x7062)))) % 7.54/7.63 [597]E(f22(a119,f118(f118(f23(a119),x5971),x5972),x5972),x5971) % 7.54/7.63 [598]E(f22(a119,f118(f118(f23(a119),x5981),x5982),x5981),x5982) % 7.54/7.63 [599]E(f22(a119,x5991,f118(f118(f23(a119),x5991),x5992)),f3(a119)) % 7.54/7.63 [604]E(f118(f118(f24(a117),f4(x6041)),f4(x6042)),f4(f118(f118(f23(a117),x6041),x6042))) % 7.54/7.63 [606]E(f118(f118(f24(a114),x6061),f118(a5,f18(f16(a114),x6062))),f118(a5,f18(x6061,x6062))) % 7.54/7.63 [607]E(f118(f118(f24(a114),x6071),f118(a10,f18(f16(a114),x6072))),f118(a10,f18(x6071,x6072))) % 7.54/7.63 [609]E(f118(f118(f31(a114),f35(a119,x6091)),x6092),f35(a119,f118(f118(f31(a119),x6091),x6092))) % 7.54/7.63 [615]E(f118(f118(f23(a114),f118(a5,x6151)),f118(a5,x6152)),f118(a5,f118(f118(f23(a117),x6151),x6152))) % 7.54/7.63 [616]E(f118(f118(f23(a114),f118(a10,x6161)),f118(a10,x6162)),f118(a10,f118(f118(f23(a117),x6161),x6162))) % 7.54/7.63 [617]E(f118(f118(f23(a114),f35(a119,x6171)),f35(a119,x6172)),f35(a119,f118(f118(f23(a119),x6171),x6172))) % 7.54/7.63 [618]E(f118(f118(f24(a114),f35(a119,x6181)),f35(a119,x6182)),f35(a119,f118(f118(f24(a119),x6181),x6182))) % 7.54/7.63 [619]E(f118(f118(f24(a117),f18(f16(a114),x6191)),f18(f16(a114),x6192)),f18(f16(a114),f118(f118(f23(a114),x6191),x6192))) % 7.54/7.63 [620]P77(f118(f28(a119,x6201),f118(f118(f23(a119),x6202),x6201))) % 7.54/7.63 [621]P77(f118(f28(a119,x6211),f118(f118(f23(a119),x6211),x6212))) % 7.54/7.63 [628]E(f118(f118(f24(a119),x6281),f118(f118(f23(a119),x6282),f16(a119))),f118(f118(f23(a119),x6281),f118(f118(f24(a119),x6281),x6282))) % 7.54/7.63 [635]E(f18(f16(a114),f118(f118(f24(a114),f35(a119,x6351)),x6352)),f118(f118(f31(a117),f18(f16(a114),x6352)),x6351)) % 7.54/7.63 [649]E(f118(f118(f37(a114),f118(f118(f24(a114),x6491),x6492)),f118(f118(f24(a114),x6491),x6491)),f118(f118(f37(a114),x6492),x6491)) % 7.54/7.63 [651]E(f118(f118(f24(a119),f118(f118(f23(a119),x6511),f16(a119))),x6512),f118(f118(f23(a119),x6512),f118(f118(f24(a119),x6511),x6512))) % 7.54/7.63 [652]E(f118(f118(f23(a119),f118(f118(f23(a119),x6521),f16(a119))),x6522),f118(f118(f23(a119),x6521),f118(f118(f23(a119),x6522),f16(a119)))) % 7.54/7.63 [663]P77(f118(f28(a115,f3(a115)),f118(f118(f31(a115),f19(a115,x6631)),x6632))) % 7.54/7.63 [667]E(f118(f118(f23(a119),f118(f118(f23(a119),x6671),f16(a119))),x6672),f118(f118(f23(a119),f118(f118(f23(a119),x6671),x6672)),f16(a119))) % 7.54/7.63 [680]E(f22(a114,f118(f118(f24(a114),f118(a10,x6801)),f118(a10,x6802)),f118(f118(f24(a114),f118(a5,x6801)),f118(a5,x6802))),f118(a10,f118(f118(f24(a117),x6801),x6802))) % 7.54/7.63 [691]E(f118(f118(f23(a114),f118(f118(f24(a114),f118(a10,x6911)),f118(a5,x6912))),f118(f118(f24(a114),f118(a5,x6911)),f118(a10,x6912))),f118(a5,f118(f118(f24(a117),x6911),x6912))) % 7.54/7.63 [708]P77(f118(f28(a114,f3(a114)),f22(a114,f118(f118(f37(a114),f35(a119,x7081)),f35(a119,x7082)),f35(a119,f20(a119,x7081,x7082))))) % 7.54/7.63 [715]E(f11(f22(a114,f118(f118(f24(a114),f118(a10,x7151)),f118(a10,x7152)),f118(f118(f24(a114),f118(a5,x7151)),f118(a5,x7152))),f118(f118(f23(a114),f118(f118(f24(a114),f118(a10,x7151)),f118(a5,x7152))),f118(f118(f24(a114),f118(a5,x7151)),f118(a10,x7152)))),f118(f118(f24(a117),x7151),x7152)) % 7.54/7.63 [682]E(f118(a5,f18(f16(a114),f118(f118(f24(a114),f35(a119,x6821)),x6822))),f118(a5,f118(f118(f31(a117),f18(f16(a114),x6822)),x6821))) % 7.54/7.63 [683]E(f118(a10,f18(f16(a114),f118(f118(f24(a114),f35(a119,x6831)),x6832))),f118(a10,f118(f118(f31(a117),f18(f16(a114),x6832)),x6831))) % 7.54/7.63 [701]E(f22(a114,f118(f118(f24(a114),f118(a10,f18(f16(a114),x7011))),f118(a10,f18(f16(a114),x7012))),f118(f118(f24(a114),f118(a5,f18(f16(a114),x7011))),f118(a5,f18(f16(a114),x7012)))),f118(a10,f18(f16(a114),f118(f118(f23(a114),x7011),x7012)))) % 7.54/7.63 [702]E(f22(a114,f118(f118(f24(a114),f118(a5,f18(f16(a114),x7021))),f118(a10,f18(f16(a114),x7022))),f118(f118(f24(a114),f118(a10,f18(f16(a114),x7021))),f118(a5,f18(f16(a114),x7022)))),f118(a5,f18(f16(a114),f22(a114,x7021,x7022)))) % 7.54/7.63 [703]E(f22(a114,f118(f118(f24(a114),f118(a10,f18(f16(a114),x7031))),f118(a5,f18(f16(a114),x7032))),f118(f118(f24(a114),f118(a5,f18(f16(a114),x7031))),f118(a10,f18(f16(a114),x7032)))),f118(a5,f18(f16(a114),f22(a114,x7032,x7031)))) % 7.54/7.63 [707]E(f118(f118(f23(a114),f118(f118(f24(a114),f118(a5,f18(f16(a114),x7071))),f118(a10,f18(f16(a114),x7072)))),f118(f118(f24(a114),f118(a10,f18(f16(a114),x7071))),f118(a5,f18(f16(a114),x7072)))),f118(a5,f18(f16(a114),f118(f118(f23(a114),x7071),x7072)))) % 7.54/7.63 [709]E(f118(f118(f23(a114),f118(f118(f24(a114),f118(a10,f18(f16(a114),x7091))),f118(a10,f18(f16(a114),x7092)))),f118(f118(f24(a114),f118(a5,f18(f16(a114),x7091))),f118(a5,f18(f16(a114),x7092)))),f118(a10,f18(f16(a114),f22(a114,x7092,x7091)))) % 7.54/7.63 [710]E(f118(f118(f23(a114),f118(f118(f24(a114),f118(a10,f18(f16(a114),x7101))),f118(a10,f18(f16(a114),x7102)))),f118(f118(f24(a114),f118(a5,f18(f16(a114),x7101))),f118(a5,f18(f16(a114),x7102)))),f118(a10,f18(f16(a114),f22(a114,x7101,x7102)))) % 7.54/7.63 [717]P77(f118(f28(a114,f36(a117,f22(a117,x7171,x7172))),f118(f118(f23(a114),f19(a114,f22(a114,f118(a10,x7171),f118(a10,x7172)))),f19(a114,f22(a114,f118(a5,x7171),f118(a5,x7172)))))) % 7.54/7.63 [742]~P77(f118(f29(a119,f118(f118(f23(a119),x7421),x7422)),x7422)) % 7.54/7.63 [743]~P77(f118(f29(a119,f118(f118(f23(a119),x7431),x7432)),x7431)) % 7.54/7.63 [700]E(f118(f118(f24(a117),f18(f16(a114),x7001)),f18(f16(a114),f118(f118(f24(a114),f35(a119,x7002)),x7001))),f18(f16(a114),f118(f118(f24(a114),f35(a119,f118(f118(f23(a119),x7002),f16(a119)))),x7001))) % 7.54/7.63 [637]E(f22(a119,f22(a119,x6371,x6372),x6373),f22(a119,f22(a119,x6371,x6373),x6372)) % 7.54/7.63 [679]E(f22(a119,f22(a119,f118(f118(f23(a119),x6791),f16(a119)),x6792),f118(f118(f23(a119),x6793),f16(a119))),f22(a119,f22(a119,x6791,x6792),x6793)) % 7.54/7.63 [626]E(f118(f118(f23(a119),x6261),f118(f118(f23(a119),x6262),x6263)),f118(f118(f23(a119),x6262),f118(f118(f23(a119),x6261),x6263))) % 7.54/7.63 [627]E(f118(f118(f23(a115),x6271),f118(f118(f23(a115),x6272),x6273)),f118(f118(f23(a115),x6272),f118(f118(f23(a115),x6271),x6273))) % 7.54/7.63 [630]E(f22(a119,f118(f118(f23(a119),x6301),x6302),f118(f118(f23(a119),x6303),x6302)),f22(a119,x6301,x6303)) % 7.54/7.63 [631]E(f22(a119,f118(f118(f23(a119),x6311),x6312),f118(f118(f23(a119),x6311),x6313)),f22(a119,x6312,x6313)) % 7.54/7.63 [633]E(f22(a119,x6331,f118(f118(f23(a119),x6332),x6333)),f22(a119,f22(a119,x6331,x6332),x6333)) % 7.54/7.63 [634]E(f20(a119,x6341,f118(f118(f24(a119),x6342),x6343)),f20(a119,f20(a119,x6341,x6342),x6343)) % 7.54/7.63 [653]E(f22(a119,f118(f118(f24(a119),x6531),x6532),f118(f118(f24(a119),x6531),x6533)),f118(f118(f24(a119),x6531),f22(a119,x6532,x6533))) % 7.54/7.63 [654]E(f22(a115,f118(f118(f24(a115),x6541),x6542),f118(f118(f24(a115),x6541),x6543)),f118(f118(f24(a115),x6541),f22(a115,x6542,x6543))) % 7.54/7.63 [655]E(f18(f118(f118(f31(a114),x6551),x6552),f118(f118(f24(a114),f35(a119,x6552)),x6553)),f118(f118(f31(a117),f18(x6551,x6553)),x6552)) % 7.54/7.63 [664]E(f118(f118(f23(a119),f118(f118(f24(a119),x6641),x6642)),f118(f118(f24(a119),x6641),x6643)),f118(f118(f24(a119),x6641),f118(f118(f23(a119),x6642),x6643))) % 7.54/7.63 [665]E(f118(f118(f23(a115),f118(f118(f24(a115),x6651),x6652)),f118(f118(f24(a115),x6651),x6653)),f118(f118(f24(a115),x6651),f118(f118(f23(a115),x6652),x6653))) % 7.54/7.63 [666]E(f118(f118(f24(a115),f118(f118(f31(a115),x6661),x6662)),f118(f118(f31(a115),x6661),x6663)),f118(f118(f31(a115),x6661),f118(f118(f23(a119),x6662),x6663))) % 7.54/7.63 [668]E(f22(a119,f118(f118(f24(a119),x6681),x6682),f118(f118(f24(a119),x6683),x6682)),f118(f118(f24(a119),f22(a119,x6681,x6683)),x6682)) % 7.54/7.63 [669]E(f22(a115,f118(f118(f24(a115),x6691),x6692),f118(f118(f24(a115),x6693),x6692)),f118(f118(f24(a115),f22(a115,x6691,x6693)),x6692)) % 7.54/7.63 [643]E(f118(f118(f23(a119),f118(f118(f23(a119),x6431),x6432)),x6433),f118(f118(f23(a119),x6431),f118(f118(f23(a119),x6432),x6433))) % 7.54/7.63 [644]E(f118(f118(f23(a115),f118(f118(f23(a115),x6441),x6442)),x6443),f118(f118(f23(a115),x6441),f118(f118(f23(a115),x6442),x6443))) % 7.54/7.63 [645]E(f118(f118(f24(a114),f118(f118(f24(a114),x6451),x6452)),x6453),f118(f118(f24(a114),x6451),f118(f118(f24(a114),x6452),x6453))) % 7.54/7.63 [646]E(f118(f118(f24(a119),f118(f118(f24(a119),x6461),x6462)),x6463),f118(f118(f24(a119),x6461),f118(f118(f24(a119),x6462),x6463))) % 7.54/7.63 [647]E(f118(f118(f24(a115),f118(f118(f24(a115),x6471),x6472)),x6473),f118(f118(f24(a115),x6471),f118(f118(f24(a115),x6472),x6473))) % 7.54/7.63 [648]E(f118(f118(f31(a115),f118(f118(f31(a115),x6481),x6482)),x6483),f118(f118(f31(a115),x6481),f118(f118(f24(a119),x6482),x6483))) % 7.54/7.63 [674]E(f118(f118(f23(a114),f118(f118(f24(a114),x6741),x6742)),f118(f118(f24(a114),x6743),x6742)),f118(f118(f24(a114),f118(f118(f23(a114),x6741),x6743)),x6742)) % 7.54/7.63 [675]E(f118(f118(f23(a119),f118(f118(f24(a119),x6751),x6752)),f118(f118(f24(a119),x6753),x6752)),f118(f118(f24(a119),f118(f118(f23(a119),x6751),x6753)),x6752)) % 7.54/7.63 [676]E(f118(f118(f23(a115),f118(f118(f24(a115),x6761),x6762)),f118(f118(f24(a115),x6763),x6762)),f118(f118(f24(a115),f118(f118(f23(a115),x6761),x6763)),x6762)) % 7.54/7.63 [720]E(f22(a114,f118(x7201,x7202),f118(f118(f24(a114),f118(f118(f37(a114),f22(a114,f118(x7201,x7203),f118(x7201,x7202))),f22(a114,x7203,x7202))),x7202)),f22(a114,f118(x7201,x7203),f118(f118(f24(a114),f118(f118(f37(a114),f22(a114,f118(x7201,x7203),f118(x7201,x7202))),f22(a114,x7203,x7202))),x7203))) % 7.54/7.63 [591]E(f14(x5911,x5912,f11(x5913,x5914)),f118(f118(x5912,x5913),x5914)) % 7.54/7.63 [592]E(f15(x5921,x5922,f11(x5923,x5924)),f118(f118(x5922,x5923),x5924)) % 7.54/7.63 [594]E(f118(f6(x5941,x5942,x5943),x5944),x5943) % 7.54/7.63 [623]E(f118(f118(f32(x6231,x6232,x6233),x6234),f3(a119)),x6232) % 7.54/7.63 [641]E(f11(f22(a114,x6411,x6412),f22(a114,x6413,x6414)),f22(a117,f11(x6411,x6413),f11(x6412,x6414))) % 7.54/7.63 [638]E(f11(f118(f118(f23(a114),x6381),x6382),f118(f118(f23(a114),x6383),x6384)),f118(f118(f23(a117),f11(x6381,x6383)),f11(x6382,x6384))) % 7.54/7.63 [639]E(f18(f118(f118(f24(a114),x6391),x6392),f118(f118(f23(a114),x6393),x6394)),f118(f118(f24(a117),f18(x6391,x6393)),f18(x6392,x6394))) % 7.54/7.63 [698]E(f11(f22(a114,f118(f118(f24(a114),x6981),x6982),f118(f118(f24(a114),x6983),x6984)),f118(f118(f23(a114),f118(f118(f24(a114),x6981),x6984)),f118(f118(f24(a114),x6983),x6982))),f118(f118(f24(a117),f11(x6981,x6983)),f11(x6982,x6984))) % 7.54/7.63 [704]E(f118(f118(f23(a119),f118(f118(f24(a119),x7041),x7042)),f118(f118(f23(a119),f118(f118(f24(a119),x7043),x7042)),x7044)),f118(f118(f23(a119),f118(f118(f24(a119),f118(f118(f23(a119),x7041),x7043)),x7042)),x7044)) % 7.54/7.63 [694]E(f118(f118(f32(x6941,x6942,x6943),x6944),f118(f118(f23(a119),x6945),f16(a119))),f118(f118(x6943,x6944),f118(f118(f32(x6941,x6942,x6943),x6944),x6945))) % 7.54/7.63 [712]E(f118(f7(x7121,x7122,x7123,x7124,x7125),x7126),f118(x7124,f118(x7125,x7126))) % 7.54/7.63 [713]E(f118(f8(x7131,x7132,x7133,x7134,x7135),x7136),f118(f118(x7134,x7136),x7135)) % 7.54/7.63 [714]E(f118(f9(x7141,x7142,x7143,x7144,x7145),x7146),f118(f118(x7144,x7146),f118(x7145,x7146))) % 7.54/7.63 [746]~P46(x7461)+P7(f120(x7461)) % 7.54/7.63 [747]~P46(x7471)+P27(f120(x7471)) % 7.54/7.63 [748]~P28(x7481)+P28(f120(x7481)) % 7.54/7.63 [749]~P46(x7491)+P34(f120(x7491)) % 7.54/7.63 [750]~P46(x7501)+P35(f120(x7501)) % 7.54/7.63 [751]~P46(x7511)+P36(f120(x7511)) % 7.54/7.63 [752]~P47(x7521)+P8(f120(x7521)) % 7.54/7.63 [753]~P21(x7531)+P9(f120(x7531)) % 7.54/7.63 [754]~P19(x7541)+P16(f120(x7541)) % 7.54/7.63 [755]~P19(x7551)+P17(f120(x7551)) % 7.54/7.63 [756]~P21(x7561)+P20(f120(x7561)) % 7.54/7.63 [757]~P21(x7571)+P21(f120(x7571)) % 7.54/7.63 [758]~P46(x7581)+P22(f120(x7581)) % 7.54/7.63 [759]~P46(x7591)+P29(f120(x7591)) % 7.54/7.63 [760]~P46(x7601)+P30(f120(x7601)) % 7.54/7.63 [761]~P46(x7611)+P31(f120(x7611)) % 7.54/7.63 [762]~P46(x7621)+P32(f120(x7621)) % 7.54/7.63 [763]~P46(x7631)+P45(f120(x7631)) % 7.54/7.63 [764]~P46(x7641)+P46(f120(x7641)) % 7.54/7.63 [765]~P47(x7651)+P58(f120(x7651)) % 7.54/7.63 [766]~P55(x7661)+P76(f120(x7661)) % 7.54/7.63 [767]~P47(x7671)+P47(f120(x7671)) % 7.54/7.63 [768]~P46(x7681)+P33(f120(x7681)) % 7.54/7.63 [769]~P46(x7691)+P59(f120(x7691)) % 7.54/7.63 [770]~P51(x7701)+P18(f120(x7701)) % 7.54/7.63 [771]~P51(x7711)+P62(f120(x7711)) % 7.54/7.63 [772]~P55(x7721)+P64(f120(x7721)) % 7.54/7.63 [773]~P55(x7731)+P65(f120(x7731)) % 7.54/7.63 [774]~P51(x7741)+P74(f120(x7741)) % 7.54/7.63 [775]~P51(x7751)+P48(f120(x7751)) % 7.54/7.63 [776]~P47(x7761)+P25(f120(x7761)) % 7.54/7.63 [777]~P47(x7771)+P23(f120(x7771)) % 7.54/7.63 [778]~P46(x7781)+P56(f120(x7781)) % 7.54/7.63 [779]~P46(x7791)+P57(f120(x7791)) % 7.54/7.63 [780]~P46(x7801)+P66(f120(x7801)) % 7.54/7.63 [781]~P46(x7811)+P67(f120(x7811)) % 7.54/7.63 [782]~P46(x7821)+P69(f120(x7821)) % 7.54/7.63 [783]~P46(x7831)+P68(f120(x7831)) % 7.54/7.63 [784]~P46(x7841)+P63(f120(x7841)) % 7.54/7.63 [785]~P46(x7851)+P52(f120(x7851)) % 7.54/7.63 [786]~P46(x7861)+P60(f120(x7861)) % 7.54/7.63 [787]~P46(x7871)+P70(f120(x7871)) % 7.54/7.63 [788]~P46(x7881)+P61(f120(x7881)) % 7.54/7.63 [789]~P55(x7891)+P71(f120(x7891)) % 7.54/7.63 [790]~P47(x7901)+P40(f120(x7901)) % 7.54/7.63 [791]~P51(x7911)+P75(f120(x7911)) % 7.54/7.63 [792]~P10(x7921)+P24(f120(x7921)) % 7.54/7.63 [793]~P46(x7931)+P26(f120(x7931)) % 7.54/7.63 [794]~P10(x7941)+P10(f120(x7941)) % 7.54/7.63 [795]~P50(x7951)+P72(f120(x7951)) % 7.54/7.63 [796]~P49(x7961)+P73(f120(x7961)) % 7.54/7.63 [797]~P49(x7971)+P49(f120(x7971)) % 7.54/7.63 [798]~P13(x7981)+P11(f120(x7981)) % 7.54/7.63 [799]~P55(x7991)+P55(f120(x7991)) % 7.54/7.63 [800]~P19(x8001)+P19(f120(x8001)) % 7.54/7.63 [801]~P51(x8011)+P51(f120(x8011)) % 7.54/7.63 [802]~P50(x8021)+P50(f120(x8021)) % 7.54/7.63 [804]~P58(x8041)+~E(f16(x8041),f3(x8041)) % 7.54/7.63 [805]~E(x8051,f3(a119))+E(f35(a119,x8051),f3(a114)) % 7.54/7.63 [809]E(x8091,f3(a119))+~E(f35(a119,x8091),f3(a114)) % 7.54/7.63 [849]E(x8491,f3(a115))+E(f20(a115,x8491,x8491),f16(a115)) % 7.54/7.63 [1900]~P3(a117,x19001)+P3(a114,f7(a117,a114,a119,a5,x19001)) % 7.54/7.63 [1901]~P3(a117,x19011)+P3(a114,f7(a117,a114,a119,a10,x19011)) % 7.54/7.63 [812]~P37(x8121)+E(f36(x8121,f3(x8121)),f3(a114)) % 7.54/7.63 [813]~P38(x8131)+E(f36(x8131,f16(x8131)),f16(a114)) % 7.54/7.63 [818]~P7(x8181)+E(f19(x8181,f3(x8181)),f3(x8181)) % 7.54/7.63 [819]~P46(x8191)+E(f19(x8191,f16(x8191)),f16(x8191)) % 7.54/7.63 [820]~P37(x8201)+E(f25(x8201,f3(x8201)),f3(x8201)) % 7.54/7.63 [821]~P33(x8211)+E(f25(x8211,f3(x8211)),f3(x8211)) % 7.54/7.63 [822]~P38(x8221)+E(f25(x8221,f16(x8221)),f16(x8221)) % 7.54/7.63 [905]~P40(x9051)+E(f32(x9051,f16(x9051),f24(x9051)),f31(x9051)) % 7.54/7.63 [947]~P41(x9471)+P77(f118(f28(a114,f3(a114)),f65(x9471))) % 7.54/7.63 [948]~P41(x9481)+P77(f118(f29(a114,f3(a114)),f60(x9481))) % 7.54/7.63 [951]P1(x9511)+P77(f118(f29(a119,f68(x9511)),f72(x9511))) % 7.54/7.63 [964]~P45(x9641)+P77(f118(f28(x9641,f3(x9641)),f16(x9641))) % 7.54/7.63 [965]~P45(x9651)+P77(f118(f29(x9651,f3(x9651)),f16(x9651))) % 7.54/7.63 [968]E(x9681,f3(a119))+~P77(f118(f28(a119,x9681),f3(a119))) % 7.54/7.63 [970]E(f26(x9701),f3(a119))+~P77(f118(f28(a114,x9701),f3(a114))) % 7.54/7.63 [971]E(f33(x9711),f3(a119))+~P77(f118(f28(a114,x9711),f3(a114))) % 7.54/7.63 [1054]~E(x10541,f3(a119))+P77(f118(f28(a114,f35(a119,x10541)),f3(a114))) % 7.54/7.63 [1055]~E(x10551,f3(a115))+P77(f118(f29(a115,f19(a115,x10551)),f16(a115))) % 7.54/7.63 [1071]~P45(x10711)+~P77(f118(f28(x10711,f16(x10711)),f3(x10711))) % 7.54/7.63 [1072]~P45(x10721)+~P77(f118(f29(x10721,f16(x10721)),f3(x10721))) % 7.54/7.63 [1126]~P77(f118(f28(a114,x11261),f16(a114)))+P77(f118(f28(a119,f26(x11261)),f16(a119))) % 7.54/7.63 [1143]~P77(f118(f28(a119,f26(x11431)),f16(a119)))+P77(f118(f28(a114,x11431),f16(a114))) % 7.54/7.63 [1184]E(x11841,f3(a119))+~P77(f118(f28(a114,f35(a119,x11841)),f3(a114))) % 7.54/7.63 [1185]E(x11851,f3(a115))+~P77(f118(f29(a115,f19(a115,x11851)),f16(a115))) % 7.54/7.63 [1888]~P77(f118(f29(a115,x18881),f3(a115)))+P77(f118(f29(a115,f118(f118(f23(a115),f118(f118(f23(a115),f16(a115)),x18881)),x18881)),f3(a115))) % 7.54/7.63 [1919]P77(f118(f29(a115,x19191),f3(a115)))+~P77(f118(f29(a115,f118(f118(f23(a115),f118(f118(f23(a115),f16(a115)),x19191)),x19191)),f3(a115))) % 7.54/7.63 [925]E(x9251,f3(a119))+P77(f118(f29(a119,f3(a119)),x9251)) % 7.54/7.63 [952]~E(f118(a10,f18(f16(a114),x9521)),f16(a114))+E(f118(a5,f18(f16(a114),x9521)),f3(a114)) % 7.54/7.63 [1011]E(f25(a114,x10111),f16(a114))+~P77(f118(f29(a114,f3(a114)),x10111)) % 7.54/7.63 [1092]E(f118(f118(f23(a119),f73(x10921)),f16(a119)),x10921)+~P77(f118(f29(a119,f3(a119)),x10921)) % 7.54/7.63 [1119]~P77(f118(f29(a115,f3(a115)),x11191))+P77(f118(f28(a115,f16(a115)),x11191)) % 7.54/7.63 [1120]P77(f118(f29(a115,f3(a115)),x11201))+~P77(f118(f28(a115,f16(a115)),x11201)) % 7.54/7.63 [1128]~P77(f118(f29(a114,f3(a114)),x11281))+P77(f118(f29(a114,f34(x11281)),x11281)) % 7.54/7.63 [1129]P77(f118(f28(a114,f3(a114)),f34(x11291)))+~P77(f118(f28(a114,f16(a114)),x11291)) % 7.54/7.63 [1130]P77(f118(f28(a119,f16(a119)),f33(x11301)))+~P77(f118(f28(a114,f16(a114)),x11301)) % 7.54/7.63 [1131]P77(f118(f29(a114,f3(a114)),f34(x11311)))+~P77(f118(f29(a114,f16(a114)),x11311)) % 7.54/7.63 [1137]~P77(f118(f28(a119,f16(a119)),f33(x11371)))+P77(f118(f28(a114,f16(a114)),x11371)) % 7.54/7.63 [1179]P77(f118(f29(a114,f3(a114)),f35(a119,x11791)))+~P77(f118(f29(a119,f3(a119)),x11791)) % 7.54/7.63 [1193]~P77(f118(f28(a114,f3(a114)),x11931))+P77(f118(f29(a114,x11931),f35(a119,f96(x11931)))) % 7.54/7.63 [1199]~P77(f118(f29(a114,f3(a114)),f35(a119,x11991)))+P77(f118(f29(a119,f3(a119)),x11991)) % 7.54/7.63 [1201]E(f26(f118(f118(f23(a114),x12011),f16(a114))),f118(f118(f23(a119),f26(x12011)),f16(a119)))+~P77(f118(f28(a114,f3(a114)),x12011)) % 7.54/7.63 [1202]E(f33(f118(f118(f23(a114),x12021),f16(a114))),f118(f118(f23(a119),f33(x12021)),f16(a119)))+~P77(f118(f28(a114,f3(a114)),x12021)) % 7.54/7.63 [1234]E(f118(a10,f18(f16(a114),f38(x12341))),x12341)+~P77(f118(f28(a114,f19(a114,x12341)),f16(a114))) % 7.54/7.63 [1300]~P45(x13001)+P77(f118(f29(x13001,f3(x13001)),f118(f118(f23(x13001),f16(x13001)),f16(x13001)))) % 7.54/7.63 [1313]E(f118(f118(f23(a119),f22(a119,x13131,f16(a119))),f16(a119)),x13131)+~P77(f118(f29(a119,f3(a119)),x13131)) % 7.54/7.63 [1365]E(x13651,f3(a119))+~P77(f118(f29(a119,x13651),f118(f118(f23(a119),f3(a119)),f16(a119)))) % 7.54/7.63 [1377]P1(x13771)+~P77(f118(f29(a119,f118(x13771,f68(x13771))),f118(x13771,f72(x13771)))) % 7.54/7.63 [1627]E(f118(f118(f23(a119),f22(a119,x16271,f118(f118(f23(a119),f3(a119)),f16(a119)))),f16(a119)),x16271)+~P77(f118(f29(a119,f3(a119)),x16271)) % 7.54/7.63 [1051]~E(f118(a5,f18(f16(a114),x10511)),f3(a114))+E(f19(a114,f118(a10,f18(f16(a114),x10511))),f16(a114)) % 7.54/7.63 [1176]E(x11761,f3(a114))+P77(f118(f29(a114,f3(a114)),f118(f118(f24(a114),x11761),x11761))) % 7.54/7.63 [1259]~P77(f118(f28(a114,f3(a114)),x12591))+P77(f118(f28(a114,f35(a119,f33(x12591))),x12591)) % 7.54/7.63 [1260]~P77(f118(f28(a114,f3(a114)),x12601))+P77(f118(f28(a114,f35(a119,f84(x12601))),x12601)) % 7.54/7.63 [1342]~E(x13421,f3(a114))+~P77(f118(f29(a114,f3(a114)),f118(f118(f24(a114),x13421),x13421))) % 7.54/7.63 [1346]~P77(f118(f28(a115,f3(a115)),x13461))+P77(f118(f29(a115,f3(a115)),f118(f118(f23(a115),f16(a115)),x13461))) % 7.54/7.63 [1570]~P77(f118(f28(a114,f3(a114)),x15701))+P77(f118(f29(a114,x15701),f35(a119,f118(f118(f23(a119),f84(x15701)),f16(a119))))) % 7.54/7.63 [1789]P1(x17891)+~P77(f118(f29(a119,f118(x17891,f86(x17891))),f118(x17891,f118(f118(f23(a119),f86(x17891)),f16(a119))))) % 7.54/7.63 [1066]E(x10661,f3(a114))+E(f118(a10,f18(f16(a114),f12(f11(f3(a114),x10661)))),f3(a114)) % 7.54/7.63 [1223]~P77(f118(f29(a114,x12231),f3(a114)))+E(f118(a10,f18(f16(a114),f12(f11(f3(a114),x12231)))),f3(a114)) % 7.54/7.63 [1232]E(f118(a10,f18(f16(a114),f12(f11(f3(a114),x12321)))),f3(a114))+~P77(f118(f29(a114,f3(a114)),x12321)) % 7.54/7.63 [1802]~P77(f118(f28(a114,f3(a114)),x18021))+P77(f118(f28(a114,f35(a119,f22(a119,f96(x18021),f16(a119)))),x18021)) % 7.54/7.63 [1750]~P77(f118(f28(a114,f3(a114)),x17501))+P77(f118(f28(a114,f34(f118(f118(f23(a114),f16(a114)),x17501))),x17501)) % 7.54/7.63 [1944]~P77(f118(f29(a114,f3(a114)),x19441))+~P77(f118(f28(a114,f19(a114,f118(a5,f118(a124,f118(a1,f118(a122,f111(x19441))))))),x19441)) % 7.54/7.63 [807]E(x8071,f3(a114))+~E(f11(x8071,x8072),a17) % 7.54/7.63 [808]E(x8081,f16(a114))+~E(f11(x8082,x8081),a17) % 7.54/7.63 [814]E(x8141,f3(a114))+~E(f11(x8142,x8141),f3(a117)) % 7.54/7.63 [815]E(x8151,f3(a114))+~E(f11(x8152,x8151),f16(a117)) % 7.54/7.63 [816]E(x8161,f3(a114))+~E(f11(x8161,x8162),f3(a117)) % 7.54/7.63 [817]E(x8171,f16(a114))+~E(f11(x8171,x8172),f16(a117)) % 7.54/7.63 [827]~P27(x8272)+P27(f121(x8271,x8272)) % 7.54/7.63 [828]~P35(x8282)+P35(f121(x8281,x8282)) % 7.54/7.63 [829]~P36(x8292)+P36(f121(x8291,x8292)) % 7.54/7.63 [834]E(x8341,x8342)+~E(f35(a119,x8341),f35(a119,x8342)) % 7.54/7.63 [856]~E(x8562,f3(a115))+E(f20(a115,x8561,x8562),f3(a115)) % 7.54/7.63 [859]~P24(x8591)+E(f22(x8591,x8592,x8592),f3(x8591)) % 7.54/7.63 [962]~P39(x9621)+P3(x9621,f6(x9621,a119,x9622)) % 7.54/7.63 [850]~P37(x8501)+E(f19(a114,f36(x8501,x8502)),f36(x8501,x8502)) % 7.54/7.63 [854]~P7(x8541)+E(f19(x8541,f19(x8541,x8542)),f19(x8541,x8542)) % 7.54/7.63 [855]~P46(x8551)+E(f25(x8551,f25(x8551,x8552)),f25(x8551,x8552)) % 7.54/7.63 [857]~P47(x8571)+E(f118(f118(f31(x8571),x8572),f16(a119)),x8572) % 7.54/7.63 [858]~P25(x8581)+E(f118(f118(f31(x8581),x8582),f16(a119)),x8582) % 7.54/7.63 [860]~P20(x8601)+E(f118(f118(f23(x8601),x8602),f3(x8601)),x8602) % 7.54/7.63 [861]~P21(x8611)+E(f118(f118(f23(x8611),x8612),f3(x8611)),x8612) % 7.54/7.63 [862]~P47(x8621)+E(f118(f118(f23(x8621),x8622),f3(x8621)),x8622) % 7.54/7.63 [863]~P47(x8631)+E(f118(f118(f24(x8631),x8632),f16(x8631)),x8632) % 7.54/7.63 [864]~P25(x8641)+E(f118(f118(f24(x8641),x8642),f16(x8641)),x8642) % 7.54/7.63 [865]~P23(x8651)+E(f118(f118(f24(x8651),x8652),f16(x8651)),x8652) % 7.54/7.63 [866]~P53(x8661)+E(f118(f118(f37(x8661),x8662),f16(x8661)),x8662) % 7.54/7.63 [867]~P47(x8671)+E(f118(f118(f31(x8671),x8672),f3(a119)),f16(x8671)) % 7.54/7.63 [868]~P40(x8681)+E(f118(f118(f31(x8681),x8682),f3(a119)),f16(x8681)) % 7.54/7.63 [869]~P24(x8691)+E(f22(x8691,x8692,f3(x8691)),x8692) % 7.54/7.63 [870]~P11(x8701)+E(f20(x8701,x8702,f16(x8701)),x8702) % 7.54/7.63 [877]~P47(x8771)+E(f118(f118(f24(x8771),x8772),f3(x8771)),f3(x8771)) % 7.54/7.63 [879]~P41(x8791)+E(f118(f118(f24(x8791),x8792),f3(x8791)),f3(x8791)) % 7.54/7.63 [880]~P62(x8801)+E(f118(f118(f24(x8801),x8802),f3(x8801)),f3(x8801)) % 7.54/7.63 [881]~P54(x8811)+E(f118(f118(f37(x8811),x8812),f3(x8811)),f3(x8811)) % 7.54/7.63 [883]~P11(x8831)+E(f20(x8831,x8832,f3(x8831)),f3(x8831)) % 7.54/7.63 [884]~P11(x8841)+E(f20(x8841,f3(x8841),x8842),f3(x8841)) % 7.54/7.63 [906]~E(x9061,x9062)+P77(f118(f28(a114,x9061),x9062)) % 7.54/7.63 [909]~E(x9091,x9092)+P77(f118(f28(a119,x9091),x9092)) % 7.54/7.63 [923]~P27(x9231)+P77(f118(f28(x9231,x9232),x9232)) % 7.54/7.63 [926]E(f30(x9261,x9262),f3(a115))+P77(f118(f28(a115,x9262),x9261)) % 7.54/7.63 [936]~P46(x9361)+E(f118(f118(f24(x9361),x9362),f25(x9361,x9362)),f19(x9361,x9362)) % 7.54/7.63 [954]~E(x9541,x9542)+~P77(f118(f29(a114,x9541),x9542)) % 7.54/7.63 [959]~E(x9591,x9592)+~P77(f118(f29(a119,x9591),x9592)) % 7.54/7.63 [960]~E(x9601,x9602)+~P77(f118(f29(a115,x9601),x9602)) % 7.54/7.63 [963]~E(x9631,f3(a119))+~P77(f118(f29(a119,x9632),x9631)) % 7.54/7.63 [966]E(x9661,x9662)+~E(f118(x9661,f41(x9662,x9661)),f118(x9662,f41(x9662,x9661))) % 7.54/7.63 [969]~P1(x9692)+P77(f118(f28(a119,x9691),f118(x9692,x9691))) % 7.54/7.63 [972]~P27(x9721)+~P77(f118(f29(x9721,x9722),x9722)) % 7.54/7.63 [973]~P46(x9731)+E(f118(f118(f24(x9731),f25(x9731,x9732)),f19(x9731,x9732)),x9732) % 7.54/7.63 [981]~P7(x9811)+P77(f118(f28(x9811,x9812),f19(x9811,x9812))) % 7.54/7.63 [987]~P37(x9871)+P77(f118(f28(a114,f3(a114)),f36(x9871,x9872))) % 7.54/7.63 [988]~P41(x9882)+P77(f118(f28(a114,f3(a114)),f69(x9881,x9882))) % 7.54/7.63 [989]~P41(x9892)+P77(f118(f28(a114,f3(a114)),f70(x9891,x9892))) % 7.54/7.63 [990]~P41(x9902)+P77(f118(f29(a114,f3(a114)),f61(x9901,x9902))) % 7.54/7.63 [991]~P41(x9912)+P77(f118(f29(a114,f3(a114)),f63(x9911,x9912))) % 7.54/7.63 [1006]P77(f118(f28(a114,x10062),x10061))+P77(f118(f28(a114,x10061),x10062)) % 7.54/7.63 [1007]P77(f118(f28(a119,x10072),x10071))+P77(f118(f28(a119,x10071),x10072)) % 7.54/7.63 [1008]P77(f118(f28(a115,x10082),x10081))+P77(f118(f28(a115,x10081),x10082)) % 7.54/7.63 [1017]~E(f22(a119,x10171,x10172),f3(a119))+P77(f118(f28(a119,x10171),x10172)) % 7.54/7.63 [1019]~P7(x10191)+P77(f118(f28(x10191,f3(x10191)),f19(x10191,x10192))) % 7.54/7.63 [1048]E(f22(a119,x10481,x10482),f3(a119))+~P77(f118(f28(a119,x10481),x10482)) % 7.54/7.63 [1049]E(f20(a119,x10491,x10492),f3(a119))+~P77(f118(f29(a119,x10491),x10492)) % 7.54/7.63 [1061]E(f22(a115,x10611,x10612),f30(x10611,x10612))+~P77(f118(f28(a115,x10612),x10611)) % 7.54/7.63 [1067]E(f118(f118(f23(a119),x10671),f43(x10672,x10671)),x10672)+~P77(f118(f28(a119,x10671),x10672)) % 7.54/7.63 [1068]E(f118(f118(f23(a119),x10681),f47(x10682,x10681)),x10682)+~P77(f118(f28(a119,x10681),x10682)) % 7.54/7.63 [1074]~P77(f118(f29(a114,x10741),x10742))+P77(f118(f28(a114,x10741),x10742)) % 7.54/7.63 [1079]~P77(f118(f29(a119,x10791),x10792))+P77(f118(f28(a119,x10791),x10792)) % 7.54/7.63 [1080]~P77(f118(f29(a115,x10801),x10802))+P77(f118(f28(a115,x10801),x10802)) % 7.54/7.63 [1118]E(f118(f118(f23(a119),x11181),f22(a119,x11182,x11181)),x11182)+P77(f118(f29(a119,x11182),x11181)) % 7.54/7.63 [1123]~P77(f118(f28(a114,x11231),x11232))+P77(f118(f28(a119,f26(x11231)),f26(x11232))) % 7.54/7.63 [1124]~P77(f118(f28(a114,x11241),x11242))+P77(f118(f28(a119,f33(x11241)),f33(x11242))) % 7.54/7.63 [1173]E(f118(f118(f23(a119),x11731),f22(a119,x11732,x11731)),x11732)+~P77(f118(f28(a119,x11731),x11732)) % 7.54/7.63 [1186]E(f22(a119,x11861,f22(a119,x11861,x11862)),x11862)+~P77(f118(f28(a119,x11862),x11861)) % 7.54/7.63 [1200]~P37(x12001)+~P77(f118(f29(a114,f36(x12001,x12002)),f3(a114))) % 7.54/7.63 [1226]~P7(x12261)+~P77(f118(f29(x12261,f19(x12261,x12262)),f3(x12261))) % 7.54/7.63 [1236]~P77(f118(f28(a119,x12361),x12362))+P77(f118(f28(a114,f35(a119,x12361)),f35(a119,x12362))) % 7.54/7.63 [1237]~P77(f118(f29(a119,x12371),x12372))+P77(f118(f29(a114,f35(a119,x12371)),f35(a119,x12372))) % 7.54/7.63 [1241]E(f22(a114,f35(a119,x12411),f35(a119,x12412)),f35(a119,f22(a119,x12411,x12412)))+~P77(f118(f28(a119,x12412),x12411)) % 7.54/7.63 [1315]P77(f118(f28(a119,x13151),x13152))+~P77(f118(f28(a114,f35(a119,x13151)),f35(a119,x13152))) % 7.54/7.63 [1316]P77(f118(f29(a119,x13161),x13162))+~P77(f118(f29(a114,f35(a119,x13161)),f35(a119,x13162))) % 7.54/7.63 [1323]P77(f118(f29(a119,f3(a119)),f22(a119,x13231,x13232)))+~P77(f118(f29(a119,x13232),x13231)) % 7.54/7.63 [1362]E(f118(f118(f23(a119),f118(f118(f23(a119),x13621),f85(x13622,x13621))),f16(a119)),x13622)+~P77(f118(f29(a119,x13621),x13622)) % 7.54/7.63 [1438]~P77(f118(f29(a119,f3(a119)),f22(a119,x14382,x14381)))+P77(f118(f29(a119,x14381),x14382)) % 7.54/7.63 [1488]~P77(f118(f28(a114,x14881),x14882))+P77(f118(f28(a114,f22(a114,x14881,x14882)),f3(a114))) % 7.54/7.63 [1489]~P77(f118(f29(a115,x14891),x14892))+P77(f118(f29(a115,f22(a115,x14891,x14892)),f3(a115))) % 7.54/7.63 [1598]~P56(x15981)+~P77(f118(f29(x15981,f118(f118(f24(x15981),x15982),x15982)),f3(x15981))) % 7.54/7.63 [1643]P77(f118(f28(a114,x16431),x16432))+~P77(f118(f28(a114,f22(a114,x16431,x16432)),f3(a114))) % 7.54/7.63 [1644]P77(f118(f29(a115,x16441),x16442))+~P77(f118(f29(a115,f22(a115,x16441,x16442)),f3(a115))) % 7.54/7.63 [1718]~P77(f118(f29(a119,x17181),x17182))+P77(f118(f28(a114,f118(f118(f23(a114),f35(a119,x17181)),f16(a114))),f35(a119,x17182))) % 7.54/7.63 [1840]P77(f118(f29(a119,x18401),x18402))+~P77(f118(f28(a114,f118(f118(f23(a114),f35(a119,x18401)),f16(a114))),f35(a119,x18402))) % 7.54/7.63 [841]~E(x8411,f3(a119))+E(f118(f118(f23(a119),x8411),x8412),x8412) % 7.54/7.63 [843]~E(x8432,f3(a119))+E(f118(f118(f24(a119),x8431),x8432),f3(a119)) % 7.54/7.63 [845]~E(x8451,f3(a119))+E(f118(f118(f24(a119),x8451),x8452),f3(a119)) % 7.54/7.63 [846]~E(x8462,f3(a119))+E(f118(f118(f31(a119),x8461),x8462),f16(a119)) % 7.54/7.63 [891]~P20(x8911)+E(f118(f118(f23(x8911),f3(x8911)),x8912),x8912) % 7.54/7.63 [892]~P21(x8921)+E(f118(f118(f23(x8921),f3(x8921)),x8922),x8922) % 7.54/7.63 [893]~P47(x8931)+E(f118(f118(f23(x8931),f3(x8931)),x8932),x8932) % 7.54/7.63 [894]~P47(x8941)+E(f118(f118(f24(x8941),f16(x8941)),x8942),x8942) % 7.54/7.63 [895]~P25(x8951)+E(f118(f118(f24(x8951),f16(x8951)),x8952),x8952) % 7.54/7.63 [896]~P23(x8961)+E(f118(f118(f24(x8961),f16(x8961)),x8962),x8962) % 7.54/7.63 [897]~P47(x8971)+E(f118(f118(f24(x8971),f3(x8971)),x8972),f3(x8971)) % 7.54/7.63 [899]~P41(x8991)+E(f118(f118(f24(x8991),f3(x8991)),x8992),f3(x8991)) % 7.54/7.63 [900]~P62(x9001)+E(f118(f118(f24(x9001),f3(x9001)),x9002),f3(x9001)) % 7.54/7.63 [901]~P25(x9011)+E(f118(f118(f31(x9011),f16(x9011)),x9012),f16(x9011)) % 7.54/7.63 [902]~P53(x9021)+E(f118(f118(f37(x9021),f3(x9021)),x9022),f3(x9021)) % 7.54/7.63 [903]~P44(x9031)+E(f118(f118(f37(x9031),f3(x9031)),x9032),f3(x9031)) % 7.54/7.63 [904]E(x9041,f3(a119))+~E(f118(f118(f23(a119),x9042),x9041),x9042) % 7.54/7.63 [912]E(x9121,f3(a119))+~E(f118(f118(f23(a119),x9122),x9121),f3(a119)) % 7.54/7.63 [913]E(x9131,f3(a119))+~E(f118(f118(f23(a119),x9131),x9132),f3(a119)) % 7.54/7.63 [914]E(x9141,f16(a119))+~E(f118(f118(f24(a119),x9142),x9141),f16(a119)) % 7.54/7.63 [915]E(x9151,f16(a119))+~E(f118(f118(f24(a119),x9151),x9152),f16(a119)) % 7.54/7.63 [946]~E(x9462,f3(a119))+E(f118(f118(f31(a119),x9461),x9462),f118(f118(f23(a119),f3(a119)),f16(a119))) % 7.54/7.63 [1022]~E(x10221,f118(f118(f23(a119),x10222),f16(a119)))+P77(f118(f29(a119,f3(a119)),x10221)) % 7.54/7.63 [1062]~P46(x10621)+E(f118(f118(f24(x10621),f19(x10621,x10622)),f19(x10621,x10622)),f118(f118(f24(x10621),x10622),x10622)) % 7.54/7.63 [1063]~E(x10631,f118(f118(f23(a119),f3(a119)),f16(a119)))+E(f118(f118(f31(a119),x10631),x10632),f118(f118(f23(a119),f3(a119)),f16(a119))) % 7.54/7.63 [1095]E(x10951,f118(f118(f23(a119),f3(a119)),f16(a119)))+~E(f118(f118(f24(a119),x10952),x10951),f118(f118(f23(a119),f3(a119)),f16(a119))) % 7.54/7.63 [1096]E(x10961,f118(f118(f23(a119),f3(a119)),f16(a119)))+~E(f118(f118(f24(a119),x10961),x10962),f118(f118(f23(a119),f3(a119)),f16(a119))) % 7.54/7.63 [1174]~E(x11741,x11742)+P77(f118(f29(a119,x11741),f118(f118(f23(a119),x11742),f16(a119)))) % 7.54/7.63 [1175]~E(x11751,x11752)+P77(f118(f29(a115,x11751),f118(f118(f23(a115),x11752),f16(a115)))) % 7.54/7.63 [1181]~E(x11811,f3(a119))+P77(f118(f29(a119,x11811),f118(f118(f23(a119),x11812),f16(a119)))) % 7.54/7.63 [1189]P77(f118(f29(a114,f3(a114)),f95(x11891,x11892)))+~P77(f118(f29(a114,f3(a114)),x11892)) % 7.54/7.63 [1196]~P77(f118(f28(a114,x11961),f35(a119,x11962)))+P77(f118(f28(a119,f26(x11961)),x11962)) % 7.54/7.63 [1224]~P45(x12241)+P77(f118(f29(x12241,x12242),f118(f118(f23(x12241),x12242),f16(x12241)))) % 7.54/7.63 [1240]E(f118(f118(f31(a114),f95(x12401,x12402)),f118(f118(f23(a119),x12401),f16(a119))),x12402)+~P77(f118(f29(a114,f3(a114)),x12402)) % 7.54/7.63 [1242]E(f26(f118(f118(f23(a114),x12421),f35(a119,x12422))),f118(f118(f23(a119),f26(x12421)),x12422))+~P77(f118(f28(a114,f3(a114)),x12421)) % 7.54/7.63 [1243]E(f33(f118(f118(f23(a114),x12431),f35(a119,x12432))),f118(f118(f23(a119),f33(x12431)),x12432))+~P77(f118(f28(a114,f3(a114)),x12431)) % 7.54/7.63 [1246]P77(f118(f29(a119,x12461),x12462))+P77(f118(f29(a119,x12462),f118(f118(f23(a119),x12461),f16(a119)))) % 7.54/7.63 [1257]P77(f118(f28(a119,x12571),f33(x12572)))+~P77(f118(f28(a114,f35(a119,x12571)),x12572)) % 7.54/7.63 [1263]E(f118(f118(f23(a119),f22(a119,x12631,x12632)),x12632),x12631)+~P77(f118(f28(a119,x12632),x12631)) % 7.54/7.63 [1289]~P77(f118(f28(a119,x12891),x12892))+P77(f118(f29(a119,x12891),f118(f118(f23(a119),x12892),f16(a119)))) % 7.54/7.63 [1292]~P77(f118(f28(a115,x12921),x12922))+P77(f118(f29(a115,x12921),f118(f118(f23(a115),x12922),f16(a115)))) % 7.54/7.63 [1293]~P77(f118(f29(a115,x12931),x12932))+P77(f118(f29(a115,x12931),f118(f118(f23(a115),x12932),f16(a115)))) % 7.54/7.63 [1322]~P77(f118(f29(a115,x13221),x13222))+P77(f118(f28(a115,x13221),f22(a115,x13222,f16(a115)))) % 7.54/7.63 [1371]E(f26(f22(a114,x13711,f35(a119,x13712))),f22(a119,f26(x13711),x13712))+~P77(f118(f28(a114,f35(a119,x13712)),x13711)) % 7.54/7.63 [1372]E(f33(f22(a114,x13721,f35(a119,x13722))),f22(a119,f33(x13721),x13722))+~P77(f118(f28(a114,f35(a119,x13722)),x13721)) % 7.54/7.63 [1387]P77(f118(f28(a119,x13871),x13872))+~P77(f118(f29(a119,x13871),f118(f118(f23(a119),x13872),f16(a119)))) % 7.54/7.63 [1388]P77(f118(f28(a115,x13881),x13882))+~P77(f118(f29(a115,x13881),f118(f118(f23(a115),x13882),f16(a115)))) % 7.54/7.63 [1437]P77(f118(f29(a115,x14371),x14372))+~P77(f118(f28(a115,x14371),f22(a115,x14372,f16(a115)))) % 7.54/7.63 [1440]~P77(f118(f29(a119,x14401),x14402))+~P77(f118(f29(a119,x14402),f118(f118(f23(a119),x14401),f16(a119)))) % 7.54/7.63 [1457]~P73(x14571)+E(f118(f118(f24(x14571),f118(f118(f23(x14571),x14572),f16(x14571))),f22(x14571,x14572,f16(x14571))),f22(x14571,f118(f118(f24(x14571),x14572),x14572),f16(x14571))) % 7.54/7.63 [1529]~P77(f118(f28(a119,x15291),x15292))+P77(f118(f29(a114,f35(a119,x15291)),f118(f118(f23(a114),f35(a119,x15292)),f16(a114)))) % 7.54/7.63 [1684]P77(f118(f28(a119,x16841),x16842))+~P77(f118(f29(a114,f35(a119,x16841)),f118(f118(f23(a114),f35(a119,x16842)),f16(a114)))) % 7.54/7.63 [1758]P77(f118(f28(a119,x17581),x17582))+~P77(f118(f28(a119,f118(f118(f23(a119),x17581),f16(a119))),f118(f118(f23(a119),x17582),f16(a119)))) % 7.54/7.63 [1760]P77(f118(f29(a119,x17601),x17602))+~P77(f118(f29(a119,f118(f118(f23(a119),x17601),f16(a119))),f118(f118(f23(a119),x17602),f16(a119)))) % 7.54/7.63 [1770]E(x17701,f3(a119))+E(f118(f118(f23(a119),f118(f118(f23(a119),f22(a119,x17701,f16(a119))),x17702)),f16(a119)),f118(f118(f23(a119),x17701),x17702)) % 7.54/7.63 [1056]E(f19(a115,x10561),f16(a115))+~E(f19(a115,f118(f118(f24(a115),x10561),x10562)),f16(a115)) % 7.54/7.63 [1057]~E(f35(a119,f33(x10571)),x10571)+E(f33(f118(f118(f31(a114),x10571),x10572)),f118(f118(f31(a119),f33(x10571)),x10572)) % 7.54/7.63 [1183]~E(x11832,f3(a119))+P77(f118(f29(a119,f3(a119)),f118(f118(f31(a119),x11831),x11832))) % 7.54/7.63 [1190]E(f20(a119,f118(f118(f24(a119),x11901),x11902),x11902),x11901)+~P77(f118(f29(a119,f3(a119)),x11902)) % 7.54/7.63 [1191]E(f20(a119,f118(f118(f24(a119),x11911),x11912),x11911),x11912)+~P77(f118(f29(a119,f3(a119)),x11911)) % 7.54/7.63 [1225]~P56(x12251)+P77(f118(f28(x12251,f3(x12251)),f118(f118(f24(x12251),x12252),x12252))) % 7.54/7.63 [1235]E(f118(f118(f24(a114),f35(a119,x12351)),f34(x12352)),f34(f118(f118(f31(a114),x12352),x12351)))+~P77(f118(f29(a114,f3(a114)),x12352)) % 7.54/7.63 [1295]~P47(x12951)+E(f118(f118(f23(x12951),x12952),x12952),f118(f118(f24(x12951),f118(f118(f23(x12951),f16(x12951)),f16(x12951))),x12952)) % 7.54/7.63 [1303]E(x13031,f3(a119))+E(f118(f118(f24(a119),x13032),f118(f118(f31(a119),x13032),f22(a119,x13031,f16(a119)))),f118(f118(f31(a119),x13032),x13031)) % 7.54/7.63 [1306]~P77(f118(f28(a115,f3(a115)),x13061))+P77(f118(f28(a115,f3(a115)),f118(f118(f31(a115),x13061),x13062))) % 7.54/7.63 [1310]~P77(f118(f29(a119,f3(a119)),x13101))+P77(f118(f29(a119,f3(a119)),f118(f118(f31(a119),x13101),x13102))) % 7.54/7.63 [1363]E(x13631,f3(a115))+P77(f118(f29(a115,f3(a115)),f118(f118(f31(a115),f19(a115,x13631)),x13632))) % 7.54/7.63 [1364]~E(x13642,f3(a119))+P77(f118(f29(a115,f3(a115)),f118(f118(f31(a115),f19(a115,x13641)),x13642))) % 7.54/7.63 [1395]E(x13951,f3(a114))+~E(f118(f118(f23(a114),f118(f118(f24(a114),x13952),x13952)),f118(f118(f24(a114),x13951),x13951)),f3(a114)) % 7.54/7.63 [1396]E(x13961,f3(a114))+~E(f118(f118(f23(a114),f118(f118(f24(a114),x13961),x13961)),f118(f118(f24(a114),x13962),x13962)),f3(a114)) % 7.54/7.63 [1400]P77(f118(f29(a119,f3(a119)),x14001))+~P77(f118(f29(a119,f3(a119)),f118(f118(f24(a119),x14002),x14001))) % 7.54/7.63 [1401]P77(f118(f29(a119,f3(a119)),x14011))+~P77(f118(f29(a119,f3(a119)),f118(f118(f24(a119),x14011),x14012))) % 7.54/7.63 [1431]P77(f118(f28(a119,x14311),x14312))+P77(f118(f28(a119,f118(f118(f23(a119),x14312),f16(a119))),x14311)) % 7.54/7.63 [1464]~P77(f118(f29(a119,x14641),x14642))+P77(f118(f28(a119,f118(f118(f23(a119),x14641),f16(a119))),x14642)) % 7.54/7.63 [1466]~P77(f118(f29(a115,x14661),x14662))+P77(f118(f28(a115,f118(f118(f23(a115),x14661),f16(a115))),x14662)) % 7.54/7.63 [1501]~P1(x15011)+P77(f118(f29(a119,f118(x15011,x15012)),f118(x15011,f118(f118(f23(a119),x15012),f16(a119))))) % 7.54/7.63 [1603]P77(f118(f29(a119,x16031),x16032))+~P77(f118(f28(a119,f118(f118(f23(a119),x16031),f16(a119))),x16032)) % 7.54/7.63 [1605]P77(f118(f29(a115,x16051),x16052))+~P77(f118(f28(a115,f118(f118(f23(a115),x16051),f16(a115))),x16052)) % 7.54/7.63 [1636]~P77(f118(f28(a119,x16361),x16362))+~P77(f118(f28(a119,f118(f118(f23(a119),x16362),f16(a119))),x16361)) % 7.54/7.63 [1720]P77(f118(f29(a114,x17201),f35(a119,x17202)))+~P77(f118(f28(a119,f118(f118(f23(a119),f33(x17201)),f16(a119))),x17202)) % 7.54/7.63 [1844]~P77(f118(f28(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),x18441))+P77(f118(f28(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),f118(f118(f31(a119),x18441),x18442))) % 7.54/7.63 [1861]P77(f118(f28(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),x18611))+~P77(f118(f28(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),f118(f118(f24(a119),x18612),x18611))) % 7.54/7.63 [1862]P77(f118(f28(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),x18621))+~P77(f118(f28(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),f118(f118(f24(a119),x18621),x18622))) % 7.54/7.63 [1504]E(x15041,f3(a119))+E(f118(f118(f23(a119),x15042),f118(f118(f24(a119),f22(a119,x15041,f16(a119))),x15042)),f118(f118(f24(a119),x15041),x15042)) % 7.54/7.63 [1719]~P77(f118(f29(a114,f3(a114)),x17192))+P77(f118(f29(a114,x17191),f118(f118(f24(a114),f35(a119,f75(x17192,x17191))),x17192))) % 7.54/7.63 [1835]~P77(f118(f29(a119,f3(a119)),x18351))+P77(f118(f29(a119,f22(a119,x18351,f118(f118(f23(a119),x18352),f16(a119)))),x18351)) % 7.54/7.63 [1933]~P77(f118(f28(a114,f3(a114)),x19332))+P77(f118(f28(a114,f118(f118(f23(a114),f118(f118(f24(a114),f35(a119,x19331)),x19332)),f16(a114))),f118(f118(f31(a114),f118(f118(f23(a114),x19332),f16(a114))),x19331))) % 7.54/7.63 [1140]~P7(x11401)+E(f19(x11401,f22(x11401,x11402,x11403)),f19(x11401,f22(x11401,x11403,x11402))) % 7.54/7.63 [1141]~P37(x11411)+E(f36(x11411,f22(x11411,x11412,x11413)),f36(x11411,f22(x11411,x11413,x11412))) % 7.54/7.63 [1228]~P78(x12281,x12283,x12282)+P77(f118(x12281,f20(a115,x12282,x12283))) % 7.54/7.63 [1343]P78(x13431,x13432,x13433)+~P77(f118(x13431,f20(a115,x13433,x13432))) % 7.54/7.63 [1353]~E(x13532,f118(f118(f23(a119),f118(f118(f23(a119),x13531),x13533)),f16(a119)))+P77(f118(f29(a119,x13531),x13532)) % 7.54/7.63 [1612]~P77(f118(f28(a119,x16123),x16122))+P77(f118(f28(a119,f22(a119,x16121,x16122)),f22(a119,x16121,x16123))) % 7.54/7.63 [1613]~P77(f118(f28(a119,x16131),x16133))+P77(f118(f28(a119,f22(a119,x16131,x16132)),f22(a119,x16133,x16132))) % 7.54/7.63 [1614]~P77(f118(f28(a119,x16141),x16143))+P77(f118(f28(a119,f20(a119,x16141,x16142)),f20(a119,x16143,x16142))) % 7.54/7.63 [1934]~P56(x19341)+~P77(f118(f29(x19341,f118(f118(f23(x19341),f118(f118(f24(x19341),x19342),x19342)),f118(f118(f24(x19341),x19343),x19343))),f3(x19341))) % 7.54/7.63 [933]~E(x9332,f3(a119))+E(f118(f118(f24(a119),x9331),x9332),f118(f118(f24(a119),x9333),x9332)) % 7.54/7.63 [935]~E(x9351,f3(a119))+E(f118(f118(f24(a119),x9351),x9352),f118(f118(f24(a119),x9351),x9353)) % 7.54/7.63 [949]~P47(x9491)+E(f118(f118(f23(x9491),x9492),x9493),f118(f118(f23(x9491),x9493),x9492)) % 7.54/7.63 [950]~P47(x9501)+E(f118(f118(f24(x9501),x9502),x9503),f118(f118(f24(x9501),x9503),x9502)) % 7.54/7.63 [985]E(x9851,x9852)+~E(f118(f118(f23(a119),x9853),x9851),f118(f118(f23(a119),x9853),x9852)) % 7.54/7.63 [986]E(x9861,x9862)+~E(f118(f118(f23(a119),x9861),x9863),f118(f118(f23(a119),x9862),x9863)) % 7.54/7.63 [999]~E(x9992,f118(f118(f23(a119),x9991),x9993))+P77(f118(f28(a119,x9991),x9992)) % 7.54/7.63 [1180]~P24(x11801)+E(f118(f118(f23(x11801),f22(x11801,x11802,x11803)),x11803),x11802) % 7.54/7.63 [1314]~P7(x13141)+E(f19(x13141,f118(f118(f23(x13141),f19(x13141,x13142)),f19(x13141,x13143))),f118(f118(f23(x13141),f19(x13141,x13142)),f19(x13141,x13143))) % 7.54/7.63 [1483]~P77(f118(f29(a119,x14831),x14833))+P77(f118(f29(a119,f22(a119,x14831,x14832)),x14833)) % 7.54/7.63 [1679]E(f22(a119,f118(f118(f23(a119),x16791),x16792),f118(f118(f23(a119),x16793),f16(a119))),f22(a119,x16791,f118(f118(f23(a119),f22(a119,x16793,x16792)),f16(a119))))+~P77(f118(f28(a119,x16792),x16793)) % 7.54/7.63 [1833]~P37(x18331)+P77(f118(f28(a114,f22(a114,f36(x18331,x18332),f36(x18331,x18333))),f36(x18331,f22(x18331,x18332,x18333)))) % 7.54/7.63 [1836]~P7(x18361)+P77(f118(f28(x18361,f22(x18361,f19(x18361,x18362),f19(x18361,x18363))),f19(x18361,f22(x18361,x18363,x18362)))) % 7.54/7.63 [1837]~P7(x18371)+P77(f118(f28(x18371,f22(x18371,f19(x18371,x18372),f19(x18371,x18373))),f19(x18371,f22(x18371,x18372,x18373)))) % 7.54/7.63 [1845]~P37(x18451)+P77(f118(f28(a114,f36(x18451,f118(f118(f23(x18451),x18452),x18453))),f118(f118(f23(a114),f36(x18451,x18452)),f36(x18451,x18453)))) % 7.54/7.63 [1846]~P41(x18461)+P77(f118(f28(a114,f36(x18461,f118(f118(f24(x18461),x18462),x18463))),f118(f118(f24(a114),f36(x18461,x18463)),f61(x18462,x18461)))) % 7.54/7.63 [1847]~P41(x18471)+P77(f118(f28(a114,f36(x18471,f118(f118(f24(x18471),x18472),x18473))),f118(f118(f24(a114),f36(x18471,x18473)),f69(x18472,x18471)))) % 7.54/7.63 [1848]~P41(x18481)+P77(f118(f28(a114,f36(x18481,f118(f118(f24(x18481),x18482),x18483))),f118(f118(f24(a114),f36(x18481,x18483)),f98(x18482,x18481)))) % 7.54/7.63 [1849]~P41(x18491)+P77(f118(f28(a114,f36(x18491,f118(f118(f24(x18491),x18492),x18493))),f118(f118(f24(a114),f36(x18491,x18492)),f36(x18491,x18493)))) % 7.54/7.63 [1850]~P41(x18501)+P77(f118(f28(a114,f36(x18501,f118(f118(f24(x18501),x18502),x18503))),f118(f118(f24(a114),f36(x18501,x18502)),f63(x18503,x18501)))) % 7.54/7.63 [1851]~P41(x18511)+P77(f118(f28(a114,f36(x18511,f118(f118(f24(x18511),x18512),x18513))),f118(f118(f24(a114),f36(x18511,x18512)),f70(x18513,x18511)))) % 7.54/7.63 [1852]~P41(x18521)+P77(f118(f28(a114,f36(x18521,f118(f118(f24(x18521),x18522),x18523))),f118(f118(f24(a114),f36(x18521,x18522)),f99(x18523,x18521)))) % 7.54/7.63 [1853]~P7(x18531)+P77(f118(f28(x18531,f19(x18531,f118(f118(f23(x18531),x18532),x18533))),f118(f118(f23(x18531),f19(x18531,x18532)),f19(x18531,x18533)))) % 7.54/7.63 [1854]~P37(x18541)+P77(f118(f28(a114,f36(x18541,f22(x18541,x18542,x18543))),f118(f118(f23(a114),f36(x18541,x18542)),f36(x18541,x18543)))) % 7.54/7.63 [1858]~P7(x18581)+P77(f118(f28(x18581,f19(x18581,f22(x18581,x18582,x18583))),f118(f118(f23(x18581),f19(x18581,x18582)),f19(x18581,x18583)))) % 7.54/7.63 [1898]~P37(x18981)+P77(f118(f28(a114,f19(a114,f22(a114,f36(x18981,x18982),f36(x18981,x18983)))),f36(x18981,f22(x18981,x18982,x18983)))) % 7.54/7.63 [1899]~P7(x18991)+P77(f118(f28(x18991,f19(x18991,f22(x18991,f19(x18991,x18992),f19(x18991,x18993)))),f19(x18991,f22(x18991,x18992,x18993)))) % 7.54/7.63 [1913]~P41(x19131)+P77(f118(f28(a114,f36(x19131,f118(f118(f24(x19131),x19132),x19133))),f118(f118(f24(a114),f118(f118(f24(a114),f36(x19131,x19132)),f36(x19131,x19133))),f60(x19131)))) % 7.54/7.63 [1914]~P41(x19141)+P77(f118(f28(a114,f36(x19141,f118(f118(f24(x19141),x19142),x19143))),f118(f118(f24(a114),f118(f118(f24(a114),f36(x19141,x19142)),f36(x19141,x19143))),f65(x19141)))) % 7.54/7.63 [1915]~P41(x19151)+P77(f118(f28(a114,f36(x19151,f118(f118(f24(x19151),x19152),x19153))),f118(f118(f24(a114),f118(f118(f24(a114),f36(x19151,x19152)),f36(x19151,x19153))),f100(x19151)))) % 7.54/7.63 [1018]~P24(x10181)+E(f22(x10181,f118(f118(f23(x10181),x10182),x10183),x10183),x10182) % 7.54/7.63 [1117]~P43(x11171)+E(f36(x11171,f118(f118(f31(x11171),x11172),x11173)),f118(f118(f31(a114),f36(x11171,x11172)),x11173)) % 7.54/7.63 [1121]~P46(x11211)+E(f19(x11211,f118(f118(f31(x11211),x11212),x11213)),f118(f118(f31(x11211),f19(x11211,x11212)),x11213)) % 7.54/7.63 [1132]~E(x11321,f3(a119))+E(f20(a119,f118(f118(f24(a119),x11321),x11322),f118(f118(f24(a119),x11321),x11323)),f3(a119)) % 7.54/7.63 [1138]~P43(x11381)+E(f118(f118(f24(a114),f36(x11381,x11382)),f36(x11381,x11383)),f36(x11381,f118(f118(f24(x11381),x11382),x11383))) % 7.54/7.63 [1146]~P46(x11461)+E(f118(f118(f24(x11461),f19(x11461,x11462)),f19(x11461,x11463)),f19(x11461,f118(f118(f24(x11461),x11462),x11463))) % 7.54/7.63 [1147]~P46(x11471)+E(f118(f118(f24(x11471),f25(x11471,x11472)),f25(x11471,x11473)),f25(x11471,f118(f118(f24(x11471),x11472),x11473))) % 7.54/7.63 [1148]~P43(x11481)+E(f118(f118(f24(x11481),f25(x11481,x11482)),f25(x11481,x11483)),f25(x11481,f118(f118(f24(x11481),x11482),x11483))) % 7.54/7.63 [1195]E(x11951,f3(a119))+E(f20(a119,f118(f118(f24(a119),x11951),x11952),f118(f118(f24(a119),x11951),x11953)),f20(a119,x11952,x11953)) % 7.54/7.63 [1209]~P47(x12091)+E(f118(f118(f24(x12091),x12092),f118(f118(f31(x12091),x12092),x12093)),f118(f118(f31(x12091),x12092),f118(f118(f23(a119),x12093),f16(a119)))) % 7.54/7.63 [1210]~P47(x12101)+E(f118(f118(f31(x12101),x12102),f118(f118(f23(a119),x12103),f16(a119))),f118(f118(f24(x12101),x12102),f118(f118(f31(x12101),x12102),x12103))) % 7.54/7.63 [1211]~P40(x12111)+E(f118(f118(f31(x12111),x12112),f118(f118(f23(a119),x12113),f16(a119))),f118(f118(f24(x12111),x12112),f118(f118(f31(x12111),x12112),x12113))) % 7.54/7.63 [1267]~P77(f118(f28(a119,x12671),x12673))+P77(f118(f28(a119,x12671),f118(f118(f23(a119),x12672),x12673))) % 7.54/7.63 [1269]~P77(f118(f28(a119,x12691),x12692))+P77(f118(f28(a119,x12691),f118(f118(f23(a119),x12692),x12693))) % 7.54/7.63 [1271]~P77(f118(f29(a119,x12711),x12713))+P77(f118(f29(a119,x12711),f118(f118(f23(a119),x12712),x12713))) % 7.54/7.63 [1273]~P77(f118(f29(a119,x12731),x12732))+P77(f118(f29(a119,x12731),f118(f118(f23(a119),x12732),x12733))) % 7.54/7.63 [1320]~P77(f118(f28(a119,x13203),x13202))+E(f22(a119,f118(f118(f23(a119),x13201),x13202),x13203),f118(f118(f23(a119),x13201),f22(a119,x13202,x13203))) % 7.54/7.63 [1338]~P77(f118(f28(a119,x13382),x13383))+E(f22(a119,f118(f118(f23(a119),x13381),x13382),x13383),f22(a119,x13381,f22(a119,x13383,x13382))) % 7.54/7.63 [1339]E(f20(a119,f118(f118(f24(a119),x13391),x13392),f118(f118(f24(a119),x13391),x13393)),f20(a119,x13392,x13393))+~P77(f118(f29(a119,f3(a119)),x13391)) % 7.54/7.63 [1354]E(f20(a115,x13541,f118(f118(f24(a115),x13542),x13543)),f20(a115,f20(a115,x13541,x13542),x13543))+~P77(f118(f29(a115,f3(a115)),x13543)) % 7.54/7.63 [1357]~P47(x13571)+E(f118(f118(f23(x13571),x13572),f118(f118(f24(x13571),x13573),x13572)),f118(f118(f24(x13571),f118(f118(f23(x13571),x13573),f16(x13571))),x13572)) % 7.54/7.63 [1409]~P77(f118(f28(a119,x14093),x14091))+E(f22(a119,f118(f118(f23(a119),x14091),x14092),x14093),f118(f118(f23(a119),f22(a119,x14091,x14093)),x14092)) % 7.54/7.63 [1417]~P46(x14171)+P77(f118(f28(x14171,f3(x14171)),f118(f118(f31(x14171),f19(x14171,x14172)),x14173))) % 7.54/7.63 [1549]P77(f118(f29(a119,f3(a119)),x15491))+P77(f118(f28(a119,f118(f118(f24(a119),x15492),x15491)),f118(f118(f24(a119),x15493),x15491))) % 7.54/7.63 [1550]P77(f118(f29(a119,f3(a119)),x15501))+P77(f118(f28(a119,f118(f118(f24(a119),x15501),x15502)),f118(f118(f24(a119),x15501),x15503))) % 7.54/7.63 [1559]~P77(f118(f28(a114,x15592),x15593))+P77(f118(f28(a114,f118(f118(f23(a114),x15591),x15592)),f118(f118(f23(a114),x15591),x15593))) % 7.54/7.63 [1560]~P77(f118(f28(a119,x15602),x15603))+P77(f118(f28(a119,f118(f118(f23(a119),x15601),x15602)),f118(f118(f23(a119),x15601),x15603))) % 7.54/7.63 [1561]~P77(f118(f28(a119,x15611),x15613))+P77(f118(f28(a119,f118(f118(f23(a119),x15611),x15612)),f118(f118(f23(a119),x15613),x15612))) % 7.54/7.63 [1563]~P77(f118(f28(a119,x15632),x15633))+P77(f118(f28(a119,f118(f118(f24(a119),x15631),x15632)),f118(f118(f24(a119),x15631),x15633))) % 7.54/7.63 [1565]~P77(f118(f28(a119,x15651),x15653))+P77(f118(f28(a119,f118(f118(f24(a119),x15651),x15652)),f118(f118(f24(a119),x15653),x15652))) % 7.54/7.63 [1566]~P77(f118(f28(a115,x15662),x15663))+P77(f118(f28(a115,f118(f118(f23(a115),x15661),x15662)),f118(f118(f23(a115),x15661),x15663))) % 7.54/7.63 [1567]~P77(f118(f29(a119,x15672),x15673))+P77(f118(f29(a119,f118(f118(f23(a119),x15671),x15672)),f118(f118(f23(a119),x15671),x15673))) % 7.54/7.63 [1568]~P77(f118(f29(a119,x15681),x15683))+P77(f118(f29(a119,f118(f118(f23(a119),x15681),x15682)),f118(f118(f23(a119),x15683),x15682))) % 7.54/7.63 [1569]~P77(f118(f29(a115,x15691),x15693))+P77(f118(f29(a115,f118(f118(f23(a115),x15691),x15692)),f118(f118(f23(a115),x15693),x15692))) % 7.54/7.63 [1574]E(x15741,x15742)+~E(f118(f118(f24(a119),f118(f118(f23(a119),x15743),f16(a119))),x15741),f118(f118(f24(a119),f118(f118(f23(a119),x15743),f16(a119))),x15742)) % 7.54/7.63 [1671]P77(f118(f28(a119,f22(a119,x16711,x16712)),x16713))+~P77(f118(f28(a119,x16711),f118(f118(f23(a119),x16713),x16712))) % 7.54/7.63 [1680]~P77(f118(f28(a119,x16802),x16801))+E(f22(a119,f118(f118(f23(a119),x16801),f16(a119)),f118(f118(f23(a119),x16802),x16803)),f22(a119,f118(f118(f23(a119),f22(a119,x16801,x16802)),f16(a119)),x16803)) % 7.54/7.63 [1742]~P77(f118(f28(a119,f22(a119,x17421,x17423)),x17422))+P77(f118(f28(a119,x17421),f118(f118(f23(a119),x17422),x17423))) % 7.54/7.63 [1743]P77(f118(f28(a119,x17431),x17432))+~P77(f118(f28(a119,f118(f118(f23(a119),x17433),x17431)),f118(f118(f23(a119),x17433),x17432))) % 7.54/7.63 [1744]P77(f118(f29(a119,x17441),x17442))+~P77(f118(f29(a119,f118(f118(f23(a119),x17443),x17441)),f118(f118(f23(a119),x17443),x17442))) % 7.54/7.63 [1745]P77(f118(f29(a119,x17451),x17452))+~P77(f118(f29(a119,f118(f118(f24(a119),x17453),x17451)),f118(f118(f24(a119),x17453),x17452))) % 7.54/7.63 [1746]P77(f118(f29(a119,x17461),x17462))+~P77(f118(f29(a119,f118(f118(f24(a119),x17461),x17463)),f118(f118(f24(a119),x17462),x17463))) % 7.54/7.63 [1748]P77(f118(f29(a119,f3(a119)),x17481))+~P77(f118(f29(a119,f118(f118(f24(a119),x17482),x17481)),f118(f118(f24(a119),x17483),x17481))) % 7.54/7.63 [1749]P77(f118(f29(a119,f3(a119)),x17491))+~P77(f118(f29(a119,f118(f118(f24(a119),x17491),x17492)),f118(f118(f24(a119),x17491),x17493))) % 7.54/7.63 [1834]~P38(x18341)+P77(f118(f28(a114,f36(x18341,f118(f118(f31(x18341),x18342),x18343))),f118(f118(f31(a114),f36(x18341,x18342)),x18343))) % 7.54/7.63 [1905]~P49(x19051)+E(f22(x19051,f118(f118(f31(x19051),x19052),f118(f118(f23(a119),f118(f118(f23(a119),f3(a119)),f16(a119))),f16(a119))),f118(f118(f31(x19051),x19053),f118(f118(f23(a119),f118(f118(f23(a119),f3(a119)),f16(a119))),f16(a119)))),f118(f118(f24(x19051),f22(x19051,x19052,x19053)),f118(f118(f23(x19051),x19052),x19053))) % 7.54/7.63 [1317]~P47(x13171)+E(f118(f118(f24(x13171),f118(f118(f31(x13171),x13172),x13173)),x13172),f118(f118(f31(x13171),x13172),f118(f118(f23(a119),x13173),f16(a119)))) % 7.54/7.63 [1318]~P25(x13181)+E(f118(f118(f31(x13181),x13182),f118(f118(f23(a119),x13183),f16(a119))),f118(f118(f24(x13181),f118(f118(f31(x13181),x13182),x13183)),x13182)) % 7.54/7.63 [1333]~P25(x13331)+E(f118(f118(f24(x13331),f118(f118(f31(x13331),x13332),x13333)),x13332),f118(f118(f24(x13331),x13332),f118(f118(f31(x13331),x13332),x13333))) % 7.54/7.63 [1376]~P12(x13761)+E(f118(f118(f31(x13761),f118(f118(f37(x13761),f16(x13761)),x13762)),x13763),f118(f118(f37(x13761),f16(x13761)),f118(f118(f31(x13761),x13762),x13763))) % 7.54/7.63 [1442]~P47(x14421)+E(f118(f118(f23(x14421),f118(f118(f24(x14421),x14422),x14423)),x14423),f118(f118(f24(x14421),f118(f118(f23(x14421),x14422),f16(x14421))),x14423)) % 7.54/7.63 [1578]P77(f118(f28(a119,x15781),x15782))+~P77(f118(f28(a119,f118(f118(f23(a119),x15783),x15781)),x15782)) % 7.54/7.63 [1579]P77(f118(f28(a119,x15791),x15792))+~P77(f118(f28(a119,f118(f118(f23(a119),x15791),x15793)),x15792)) % 7.54/7.63 [1580]P77(f118(f29(a119,x15801),x15802))+~P77(f118(f29(a119,f118(f118(f23(a119),x15801),x15803)),x15802)) % 7.54/7.63 [1581]~P77(f118(f28(a119,x15813),x15812))+P77(f118(f28(a119,x15811),f22(a119,f118(f118(f23(a119),x15812),x15811),x15813))) % 7.54/7.63 [1662]~P77(f118(f29(a119,x16621),f22(a119,x16623,x16622)))+P77(f118(f29(a119,f118(f118(f23(a119),x16621),x16622)),x16623)) % 7.54/7.63 [1700]P77(f118(f29(a119,x17001),f22(a119,x17002,x17003)))+~P77(f118(f29(a119,f118(f118(f23(a119),x17001),x17003)),x17002)) % 7.54/7.63 [1830]~P37(x18301)+P77(f118(f28(a114,f22(a114,f36(x18301,x18302),f36(x18301,x18303))),f36(x18301,f118(f118(f23(x18301),x18302),x18303)))) % 7.54/7.63 [1855]~P56(x18551)+P77(f118(f28(x18551,f3(x18551)),f118(f118(f23(x18551),f118(f118(f24(x18551),x18552),x18552)),f118(f118(f24(x18551),x18553),x18553)))) % 7.54/7.63 [1910]~P77(f118(f29(a119,x19102),x19103))+P77(f118(f29(a119,f118(f118(f24(a119),f118(f118(f23(a119),x19101),f16(a119))),x19102)),f118(f118(f24(a119),f118(f118(f23(a119),x19101),f16(a119))),x19103))) % 7.54/7.63 [1937]P77(f118(f28(a119,x19371),x19372))+~P77(f118(f28(a119,f118(f118(f24(a119),f118(f118(f23(a119),x19373),f16(a119))),x19371)),f118(f118(f24(a119),f118(f118(f23(a119),x19373),f16(a119))),x19372))) % 7.54/7.63 [1971]~P77(f118(f29(a115,f3(a115)),x19713))+P77(f118(f29(a115,x19711),f118(f118(f23(a115),x19712),f118(f118(f24(a115),f118(f118(f23(a115),f19(a115,f22(a115,x19712,x19711))),f16(a115))),x19713)))) % 7.54/7.63 [1975]~P77(f118(f29(a115,f3(a115)),x19753))+P77(f118(f29(a115,f22(a115,x19751,f118(f118(f24(a115),f118(f118(f23(a115),f19(a115,f22(a115,x19751,x19752))),f16(a115))),x19753))),x19752)) % 7.54/7.63 [839]E(x8391,x8392)+~E(f11(x8393,x8391),f11(x8394,x8392)) % 7.54/7.63 [840]E(x8401,x8402)+~E(f11(x8401,x8403),f11(x8402,x8404)) % 7.54/7.63 [1221]~P47(x12211)+E(f118(f118(f23(x12211),x12212),f118(f118(f23(x12211),x12213),x12214)),f118(f118(f23(x12211),x12213),f118(f118(f23(x12211),x12212),x12214))) % 7.54/7.63 [1222]~P47(x12221)+E(f118(f118(f24(x12221),x12222),f118(f118(f24(x12221),x12223),x12224)),f118(f118(f24(x12221),x12223),f118(f118(f24(x12221),x12222),x12224))) % 7.54/7.63 [1341]~P41(x13411)+E(f22(x13411,f118(f118(f24(x13411),x13412),x13413),f118(f118(f24(x13411),x13412),x13414)),f118(f118(f24(x13411),x13412),f22(x13411,x13413,x13414))) % 7.54/7.63 [1398]~P25(x13981)+E(f118(f118(f24(x13981),f118(f118(f31(x13981),x13982),x13983)),f118(f118(f31(x13981),x13982),x13984)),f118(f118(f31(x13981),x13982),f118(f118(f23(a119),x13983),x13984))) % 7.54/7.63 [1399]~P47(x13991)+E(f118(f118(f24(x13991),f118(f118(f31(x13991),x13992),x13993)),f118(f118(f31(x13991),x13992),x13994)),f118(f118(f31(x13991),x13992),f118(f118(f23(a119),x13993),x13994))) % 7.54/7.63 [1412]~P47(x14121)+E(f118(f118(f23(x14121),f118(f118(f24(x14121),x14122),x14123)),f118(f118(f24(x14121),x14122),x14124)),f118(f118(f24(x14121),x14122),f118(f118(f23(x14121),x14123),x14124))) % 7.54/7.63 [1414]~P41(x14141)+E(f118(f118(f23(x14141),f118(f118(f24(x14141),x14142),x14143)),f118(f118(f24(x14141),x14142),x14144)),f118(f118(f24(x14141),x14142),f118(f118(f23(x14141),x14143),x14144))) % 7.54/7.63 [1426]~P41(x14261)+E(f22(x14261,f118(f118(f24(x14261),x14262),x14263),f118(f118(f24(x14261),x14264),x14263)),f118(f118(f24(x14261),f22(x14261,x14262,x14264)),x14263)) % 7.54/7.63 [1427]~P53(x14271)+E(f22(x14271,f118(f118(f37(x14271),x14272),x14273),f118(f118(f37(x14271),x14274),x14273)),f118(f118(f37(x14271),f22(x14271,x14272,x14274)),x14273)) % 7.54/7.63 [1428]~P44(x14281)+E(f22(x14281,f118(f118(f37(x14281),x14282),x14283),f118(f118(f37(x14281),x14284),x14283)),f118(f118(f37(x14281),f22(x14281,x14282,x14284)),x14283)) % 7.54/7.63 [1304]~P47(x13041)+E(f118(f118(f31(x13041),f118(f118(f31(x13041),x13042),x13043)),x13044),f118(f118(f31(x13041),x13042),f118(f118(f24(a119),x13043),x13044))) % 7.54/7.63 [1305]~P25(x13051)+E(f118(f118(f31(x13051),f118(f118(f31(x13051),x13052),x13053)),x13054),f118(f118(f31(x13051),x13052),f118(f118(f24(a119),x13053),x13054))) % 7.54/7.63 [1328]~P53(x13281)+E(f118(f118(f37(x13281),f118(f118(f24(x13281),x13282),x13283)),x13284),f118(f118(f24(x13281),x13282),f118(f118(f37(x13281),x13283),x13284))) % 7.54/7.63 [1329]~P9(x13291)+E(f118(f118(f23(x13291),f118(f118(f23(x13291),x13292),x13293)),x13294),f118(f118(f23(x13291),x13292),f118(f118(f23(x13291),x13293),x13294))) % 7.54/7.63 [1330]~P47(x13301)+E(f118(f118(f23(x13301),f118(f118(f23(x13301),x13302),x13303)),x13304),f118(f118(f23(x13301),x13302),f118(f118(f23(x13301),x13303),x13304))) % 7.54/7.63 [1331]~P47(x13311)+E(f118(f118(f24(x13311),f118(f118(f24(x13311),x13312),x13313)),x13314),f118(f118(f24(x13311),x13312),f118(f118(f24(x13311),x13313),x13314))) % 7.54/7.63 [1332]~P18(x13321)+E(f118(f118(f24(x13321),f118(f118(f24(x13321),x13322),x13323)),x13324),f118(f118(f24(x13321),x13322),f118(f118(f24(x13321),x13323),x13324))) % 7.54/7.63 [1410]~P47(x14101)+E(f118(f118(f23(x14101),f118(f118(f23(x14101),x14102),x14103)),x14104),f118(f118(f23(x14101),f118(f118(f23(x14101),x14102),x14104)),x14103)) % 7.54/7.63 [1411]~P47(x14111)+E(f118(f118(f24(x14111),f118(f118(f24(x14111),x14112),x14113)),x14114),f118(f118(f24(x14111),f118(f118(f24(x14111),x14112),x14114)),x14113)) % 7.54/7.63 [1493]~P41(x14931)+E(f118(f118(f23(x14931),f118(f118(f24(x14931),x14932),x14933)),f118(f118(f24(x14931),x14934),x14933)),f118(f118(f24(x14931),f118(f118(f23(x14931),x14932),x14934)),x14933)) % 7.54/7.63 [1494]~P48(x14941)+E(f118(f118(f23(x14941),f118(f118(f24(x14941),x14942),x14943)),f118(f118(f24(x14941),x14944),x14943)),f118(f118(f24(x14941),f118(f118(f23(x14941),x14942),x14944)),x14943)) % 7.54/7.63 [1495]~P47(x14951)+E(f118(f118(f24(x14951),f118(f118(f31(x14951),x14952),x14953)),f118(f118(f31(x14951),x14954),x14953)),f118(f118(f31(x14951),f118(f118(f24(x14951),x14952),x14954)),x14953)) % 7.54/7.63 [1496]~P23(x14961)+E(f118(f118(f24(x14961),f118(f118(f31(x14961),x14962),x14963)),f118(f118(f31(x14961),x14964),x14963)),f118(f118(f31(x14961),f118(f118(f24(x14961),x14962),x14964)),x14963)) % 7.54/7.63 [1497]~P12(x14971)+E(f118(f118(f37(x14971),f118(f118(f31(x14971),x14972),x14973)),f118(f118(f31(x14971),x14974),x14973)),f118(f118(f31(x14971),f118(f118(f37(x14971),x14972),x14974)),x14973)) % 7.54/7.63 [1498]~P53(x14981)+E(f118(f118(f23(x14981),f118(f118(f37(x14981),x14982),x14983)),f118(f118(f37(x14981),x14984),x14983)),f118(f118(f37(x14981),f118(f118(f23(x14981),x14982),x14984)),x14983)) % 7.54/7.63 [1499]~P44(x14991)+E(f118(f118(f23(x14991),f118(f118(f37(x14991),x14992),x14993)),f118(f118(f37(x14991),x14994),x14993)),f118(f118(f37(x14991),f118(f118(f23(x14991),x14992),x14994)),x14993)) % 7.54/7.63 [1500]~P47(x15001)+E(f118(f118(f23(x15001),f118(f118(f24(x15001),x15002),x15003)),f118(f118(f24(x15001),x15004),x15003)),f118(f118(f24(x15001),f118(f118(f23(x15001),x15002),x15004)),x15003)) % 7.54/7.63 [1507]~P10(x15071)+E(f22(x15071,f118(f118(f23(x15071),x15072),x15073),f118(f118(f23(x15071),x15074),x15075)),f118(f118(f23(x15071),f22(x15071,x15072,x15074)),f22(x15071,x15073,x15075))) % 7.54/7.63 [1554]~P47(x15541)+E(f118(f118(f23(x15541),f118(f118(f23(x15541),x15542),x15543)),f118(f118(f23(x15541),x15544),x15545)),f118(f118(f23(x15541),f118(f118(f23(x15541),x15542),x15544)),f118(f118(f23(x15541),x15543),x15545))) % 7.54/7.63 [1555]~P47(x15551)+E(f118(f118(f24(x15551),f118(f118(f24(x15551),x15552),x15553)),f118(f118(f24(x15551),x15554),x15555)),f118(f118(f24(x15551),f118(f118(f24(x15551),x15552),x15554)),f118(f118(f24(x15551),x15553),x15555))) % 7.54/7.63 [1842]~P72(x18421)+E(f118(f118(f23(x18421),f118(f118(f24(x18421),x18422),f22(x18421,x18423,x18424))),f118(f118(f24(x18421),f22(x18421,x18422,x18425)),x18424)),f22(x18421,f118(f118(f24(x18421),x18422),x18423),f118(f118(f24(x18421),x18425),x18424))) % 7.54/7.63 [1946]~P37(x19461)+P77(f118(f28(a114,f36(x19461,f22(x19461,f118(f118(f23(x19461),x19462),x19463),f118(f118(f23(x19461),x19464),x19465)))),f118(f118(f23(a114),f36(x19461,f22(x19461,x19462,x19464))),f36(x19461,f22(x19461,x19463,x19465))))) % 7.54/7.63 [1949]~P7(x19491)+P77(f118(f28(x19491,f19(x19491,f22(x19491,f118(f118(f23(x19491),x19492),x19493),f118(f118(f23(x19491),x19494),x19495)))),f118(f118(f23(x19491),f19(x19491,f22(x19491,x19492,x19494))),f19(x19491,f22(x19491,x19493,x19495))))) % 7.54/7.63 [1955]~P41(x19551)+E(f118(f118(f23(x19551),f118(f118(f23(x19551),f118(f118(f24(x19551),f22(x19551,x19552,x19553)),f22(x19551,x19554,x19555))),f118(f118(f24(x19551),f22(x19551,x19552,x19553)),x19555))),f118(f118(f24(x19551),x19553),f22(x19551,x19554,x19555))),f22(x19551,f118(f118(f24(x19551),x19552),x19554),f118(f118(f24(x19551),x19553),x19555))) % 7.54/7.63 [1916]~P77(f118(f28(a119,x19161),x19164))+E(f22(a119,f118(f118(f23(a119),f118(f118(f24(a119),x19161),x19162)),x19163),f118(f118(f23(a119),f118(f118(f24(a119),x19164),x19162)),x19165)),f22(a119,x19163,f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x19164,x19161)),x19162)),x19165))) % 7.54/7.63 [1917]~P77(f118(f28(a119,x19174),x19171))+E(f22(a119,f118(f118(f23(a119),f118(f118(f24(a119),x19171),x19172)),x19173),f118(f118(f23(a119),f118(f118(f24(a119),x19174),x19172)),x19175)),f22(a119,f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x19171,x19174)),x19172)),x19173),x19175)) % 7.54/7.63 [1872]~P74(x18721)+E(f118(f118(f23(x18721),f118(f118(f24(x18721),x18722),x18723)),f118(f118(f23(x18721),f118(f118(f24(x18721),x18724),x18723)),x18725)),f118(f118(f23(x18721),f118(f118(f24(x18721),f118(f118(f23(x18721),x18722),x18724)),x18723)),x18725)) % 7.54/7.63 [1943]~P42(x19431)+E(f118(f118(f23(x19431),f118(f118(f24(x19431),x19432),f118(f118(f37(x19431),f22(x19431,x19433,x19434)),x19435))),f118(f118(f24(x19431),f118(f118(f37(x19431),f22(x19431,x19432,x19436)),x19435)),x19434)),f118(f118(f37(x19431),f22(x19431,f118(f118(f24(x19431),x19432),x19433),f118(f118(f24(x19431),x19436),x19434))),x19435)) % 7.54/7.63 [842]~P2(a114,x8421)+~P4(a114,x8421)+P3(a114,x8421) % 7.54/7.63 [984]~P4(a114,x9841)+P3(a114,x9841)+P77(f118(f28(a119,f52(x9841)),f55(x9841))) % 7.54/7.63 [1005]~E(x10051,f16(a114))+E(f34(x10051),f3(a114))+~P77(f118(f29(a114,f3(a114)),x10051)) % 7.54/7.63 [1010]~E(f34(x10101),f3(a114))+E(x10101,f16(a114))+~P77(f118(f29(a114,f3(a114)),x10101)) % 7.54/7.63 [1212]P2(a114,f118(f31(a114),x12121))+~P77(f118(f28(a114,x12121),f16(a114)))+~P77(f118(f28(a114,f3(a114)),x12121)) % 7.54/7.63 [1213]P3(a114,f118(f31(a114),x12131))+~P77(f118(f28(a114,x12131),f16(a114)))+~P77(f118(f28(a114,f3(a114)),x12131)) % 7.54/7.63 [1214]P4(a114,f118(f31(a114),x12141))+~P77(f118(f28(a114,x12141),f16(a114)))+~P77(f118(f28(a114,f3(a114)),x12141)) % 7.54/7.63 [1265]~P77(f118(f29(a114,x12651),f16(a114)))+P77(f118(f29(a114,f34(x12651)),f3(a114)))+~P77(f118(f29(a114,f3(a114)),x12651)) % 7.54/7.63 [1280]~P77(f118(f28(a114,f3(a114)),f34(x12801)))+~P77(f118(f29(a114,f3(a114)),x12801))+P77(f118(f28(a114,f16(a114)),x12801)) % 7.54/7.63 [1282]~P77(f118(f29(a114,f3(a114)),f34(x12821)))+~P77(f118(f29(a114,f3(a114)),x12821))+P77(f118(f29(a114,f16(a114)),x12821)) % 7.54/7.63 [1294]~P77(f118(f29(a114,f34(x12941)),f3(a114)))+P77(f118(f29(a114,x12941),f16(a114)))+~P77(f118(f29(a114,f3(a114)),x12941)) % 7.54/7.63 [1404]~P4(a114,x14041)+P3(a114,x14041)+~P77(f118(f28(a114,f118(x14041,f52(x14041))),f118(x14041,f55(x14041)))) % 7.54/7.63 [1871]E(x18711,f3(a119))+E(x18711,f118(f118(f23(a119),f3(a119)),f16(a119)))+~P77(f118(f29(a119,x18711),f118(f118(f23(a119),f118(f118(f23(a119),f3(a119)),f16(a119))),f16(a119)))) % 7.54/7.63 [836]~P36(x8361)+~P5(x8361,x8362)+P2(x8361,x8362) % 7.54/7.63 [837]~P36(x8371)+~P6(x8371,x8372)+P2(x8371,x8372) % 7.54/7.63 [806]~E(x8062,f16(a114))+~E(x8061,f3(a114))+E(f11(x8061,x8062),a17) % 7.54/7.63 [810]~E(x8102,f3(a114))+~E(x8101,f3(a114))+E(f11(x8101,x8102),f3(a117)) % 7.54/7.63 [811]~E(x8112,f3(a114))+~E(x8111,f16(a114))+E(f11(x8111,x8112),f16(a117)) % 7.54/7.63 [823]~P37(x8231)+~E(x8232,f3(x8231))+E(f36(x8231,x8232),f3(a114)) % 7.54/7.63 [824]~P7(x8241)+~E(x8242,f3(x8241))+E(f19(x8241,x8242),f3(x8241)) % 7.54/7.63 [825]~P37(x8251)+~E(x8252,f3(x8251))+E(f25(x8251,x8252),f3(x8251)) % 7.54/7.63 [826]~P46(x8261)+~E(x8262,f3(x8261))+E(f25(x8261,x8262),f3(x8261)) % 7.54/7.63 [830]~P37(x8302)+E(x8301,f3(x8302))+~E(f36(x8302,x8301),f3(a114)) % 7.54/7.63 [831]~P7(x8312)+~E(f19(x8312,x8311),f3(x8312))+E(x8311,f3(x8312)) % 7.54/7.63 [832]~P37(x8322)+~E(f25(x8322,x8321),f3(x8322))+E(x8321,f3(x8322)) % 7.54/7.63 [833]~P46(x8332)+~E(f25(x8332,x8331),f3(x8332))+E(x8331,f3(x8332)) % 7.54/7.63 [882]~P11(x8822)+E(f20(x8822,x8821,x8821),f16(x8822))+E(x8821,f3(x8822)) % 7.54/7.63 [917]E(x9171,x9172)+~E(f118(a5,x9171),f118(a5,x9172))+~E(f118(a10,x9171),f118(a10,x9172)) % 7.54/7.63 [1052]E(x10521,x10522)+~E(f22(a119,x10522,x10521),f3(a119))+~E(f22(a119,x10521,x10522),f3(a119)) % 7.54/7.63 [835]~P28(x8351)+E(f21(x8351,x8352),f3(a119))+~E(x8352,f3(f120(x8351))) % 7.54/7.63 [838]~P28(x8382)+~E(f21(x8382,x8381),f3(a119))+E(x8381,f3(f120(x8382))) % 7.54/7.63 [847]~P37(x8472)+E(x8471,f3(x8472))+E(f36(x8472,f25(x8472,x8471)),f16(a114)) % 7.54/7.63 [848]~P37(x8481)+~E(x8482,f3(x8481))+E(f36(x8481,f25(x8481,x8482)),f3(a114)) % 7.54/7.63 [1009]~P37(x10092)+E(x10091,f3(x10092))+P77(f118(f29(a114,f3(a114)),f36(x10092,x10091))) % 7.54/7.63 [1013]E(x10131,x10132)+P77(f118(f29(a119,x10132),x10131))+P77(f118(f29(a119,x10131),x10132)) % 7.54/7.63 [1014]E(x10141,x10142)+P77(f118(f29(a115,x10142),x10141))+P77(f118(f29(a115,x10141),x10142)) % 7.54/7.63 [1023]~P37(x10232)+~P4(x10232,x10231)+P77(f118(f29(a114,f3(a114)),f42(x10231,x10232))) % 7.54/7.63 [1024]~P37(x10242)+~P4(x10242,x10241)+P77(f118(f29(a114,f3(a114)),f46(x10241,x10242))) % 7.54/7.63 [1027]~P7(x10272)+E(x10271,f3(x10272))+P77(f118(f29(x10272,f3(x10272)),f19(x10272,x10271))) % 7.54/7.63 [1086]E(x10861,x10862)+P77(f118(f29(a114,x10861),x10862))+~P77(f118(f28(a114,x10861),x10862)) % 7.54/7.63 [1089]E(x10891,x10892)+P77(f118(f29(a119,x10891),x10892))+~P77(f118(f28(a119,x10891),x10892)) % 7.54/7.63 [1090]E(x10901,x10902)+P77(f118(f29(a115,x10901),x10902))+~P77(f118(f28(a115,x10901),x10902)) % 7.54/7.63 [1093]~P37(x10931)+~E(x10932,f3(x10931))+P77(f118(f28(a114,f36(x10931,x10932)),f3(a114))) % 7.54/7.63 [1094]~P7(x10941)+~E(x10942,f3(x10941))+P77(f118(f28(x10941,f19(x10941,x10942)),f3(x10941))) % 7.54/7.63 [1125]~P37(x11252)+~E(x11251,f3(x11252))+~P77(f118(f29(a114,f3(a114)),f36(x11252,x11251))) % 7.54/7.63 [1133]E(x11331,x11332)+~P77(f118(f28(a114,x11332),x11331))+~P77(f118(f28(a114,x11331),x11332)) % 7.54/7.63 [1134]E(x11341,x11342)+~P77(f118(f28(a119,x11342),x11341))+~P77(f118(f28(a119,x11341),x11342)) % 7.54/7.63 [1135]E(x11351,x11352)+~P77(f118(f28(a115,x11352),x11351))+~P77(f118(f28(a115,x11351),x11352)) % 7.54/7.63 [1149]~P36(x11491)+P2(x11491,x11492)+P77(f118(f28(a119,f83(x11492,x11491)),f94(x11492,x11491))) % 7.54/7.63 [1150]~P36(x11501)+P2(x11501,x11502)+P77(f118(f28(a119,f105(x11502,x11501)),f113(x11502,x11501))) % 7.54/7.63 [1151]~P36(x11511)+P5(x11511,x11512)+P77(f118(f28(a119,f44(x11512,x11511)),f45(x11512,x11511))) % 7.54/7.63 [1152]~P36(x11521)+P6(x11521,x11522)+P77(f118(f28(a119,f48(x11522,x11521)),f50(x11522,x11521))) % 7.54/7.63 [1157]~P7(x11572)+~E(x11571,f3(x11572))+~P77(f118(f29(x11572,f3(x11572)),f19(x11572,x11571))) % 7.54/7.63 [1206]~P37(x12062)+E(x12061,f3(x12062))+~P77(f118(f28(a114,f36(x12062,x12061)),f3(a114))) % 7.54/7.63 [1208]E(f20(a115,x12081,x12082),f3(a115))+~P77(f118(f29(a115,x12082),x12081))+~P77(f118(f28(a115,x12081),f3(a115))) % 7.54/7.63 [1227]~P7(x12272)+E(x12271,f3(x12272))+~P77(f118(f28(x12272,f19(x12272,x12271)),f3(x12272))) % 7.54/7.63 [1258]~P46(x12581)+~P77(f118(f29(x12581,x12582),f3(x12581)))+P77(f118(f29(x12581,f25(x12581,x12582)),f3(x12581))) % 7.54/7.63 [1321]~P46(x13211)+~P77(f118(f29(x13211,f25(x13211,x13212)),f3(x13211)))+P77(f118(f29(x13211,x13212),f3(x13211))) % 7.54/7.63 [1453]P77(f118(f28(a115,f3(a115)),f20(a115,x14531,x14532)))+~P77(f118(f28(a115,x14531),f3(a115)))+~P77(f118(f29(a115,x14532),f3(a115))) % 7.54/7.63 [1525]~P22(x15251)+~P77(f118(f28(x15251,x15252),f3(x15251)))+P77(f118(f28(x15251,f118(f118(f23(x15251),x15252),x15252)),f3(x15251))) % 7.54/7.63 [1526]~P22(x15261)+~P77(f118(f29(x15261,x15262),f3(x15261)))+P77(f118(f29(x15261,f118(f118(f23(x15261),x15262),x15262)),f3(x15261))) % 7.54/7.63 [1527]~P46(x15271)+~P77(f118(f29(x15271,x15272),f3(x15271)))+P77(f118(f29(x15271,f118(f118(f23(x15271),x15272),x15272)),f3(x15271))) % 7.54/7.63 [1531]~P77(f118(f28(a115,f3(a115)),f20(a115,x15311,x15312)))+P77(f118(f28(a115,x15311),f3(a115)))+~P77(f118(f29(a115,x15312),f3(a115))) % 7.54/7.63 [1668]~P22(x16681)+~P77(f118(f28(x16681,f118(f118(f23(x16681),x16682),x16682)),f3(x16681)))+P77(f118(f28(x16681,x16682),f3(x16681))) % 7.54/7.63 [1669]~P22(x16691)+~P77(f118(f29(x16691,f118(f118(f23(x16691),x16692),x16692)),f3(x16691)))+P77(f118(f29(x16691,x16692),f3(x16691))) % 7.54/7.63 [1670]~P46(x16701)+~P77(f118(f29(x16701,f118(f118(f23(x16701),x16702),x16702)),f3(x16701)))+P77(f118(f29(x16701,x16702),f3(x16701))) % 7.54/7.63 [1952]E(x19521,f3(a119))+E(x19522,f3(a117))+P77(f118(f29(a114,f36(a117,f118(f118(f23(a117),f16(a117)),f118(f118(f24(a117),x19522),f118(f118(f31(a117),f56(x19521,x19522)),x19521))))),f16(a114))) % 7.54/7.63 [852]~E(x8522,f3(a119))+~E(x8521,f3(a119))+E(f118(f118(f23(a119),x8521),x8522),f3(a119)) % 7.54/7.63 [853]~E(x8532,f16(a119))+~E(x8531,f16(a119))+E(f118(f118(f24(a119),x8531),x8532),f16(a119)) % 7.54/7.63 [871]~P53(x8712)+E(x8711,f3(x8712))+E(f118(f118(f37(x8712),x8711),x8711),f16(x8712)) % 7.54/7.63 [872]~P54(x8722)+E(x8721,f3(x8722))+E(f118(f118(f37(x8722),x8721),x8721),f16(x8722)) % 7.54/7.63 [886]~P22(x8861)+~E(x8862,f3(x8861))+E(f118(f118(f23(x8861),x8862),x8862),f3(x8861)) % 7.54/7.63 [889]~P54(x8891)+~E(x8892,f3(x8891))+E(f118(f118(f37(x8891),x8892),x8892),f3(x8891)) % 7.54/7.63 [918]E(x9181,f16(a119))+E(x9182,f3(a119))+~E(f118(f118(f24(a119),x9182),x9181),x9182) % 7.54/7.63 [919]E(x9191,f3(a119))+E(x9192,f3(a119))+~E(f118(f118(f24(a119),x9192),x9191),f3(a119)) % 7.54/7.63 [938]~P22(x9382)+E(x9381,f3(x9382))+~E(f118(f118(f23(x9382),x9381),x9381),f3(x9382)) % 7.54/7.63 [982]~P46(x9821)+~E(f25(x9821,x9822),f16(x9821))+P77(f118(f29(x9821,f3(x9821)),x9822)) % 7.54/7.63 [1020]E(x10201,f3(a119))+E(x10202,f3(a119))+~E(f118(f118(f23(a119),x10202),x10201),f118(f118(f23(a119),f3(a119)),f16(a119))) % 7.54/7.63 [1021]E(x10211,f3(a119))+E(x10212,f3(a119))+~E(f118(f118(f23(a119),f3(a119)),f16(a119)),f118(f118(f23(a119),x10212),x10211)) % 7.54/7.63 [1053]~P40(x10531)+~P75(x10531)+E(f118(f118(f31(x10531),f3(x10531)),f118(f118(f23(a119),x10532),f16(a119))),f3(x10531)) % 7.54/7.63 [1064]~P7(x10641)+E(f19(x10641,x10642),x10642)+~P77(f118(f28(x10641,f3(x10641)),x10642)) % 7.54/7.63 [1065]~P7(x10651)+E(f19(x10651,x10652),x10652)+~P77(f118(f29(x10651,f3(x10651)),x10652)) % 7.54/7.63 [1070]~P46(x10701)+E(f25(x10701,x10702),f16(x10701))+~P77(f118(f29(x10701,f3(x10701)),x10702)) % 7.54/7.63 [1081]~E(x10812,f3(a119))+~E(x10811,f118(f118(f23(a119),f3(a119)),f16(a119)))+E(f118(f118(f23(a119),x10811),x10812),f118(f118(f23(a119),f3(a119)),f16(a119))) % 7.54/7.63 [1082]~E(x10821,f3(a119))+~E(x10822,f118(f118(f23(a119),f3(a119)),f16(a119)))+E(f118(f118(f23(a119),x10821),x10822),f118(f118(f23(a119),f3(a119)),f16(a119))) % 7.54/7.63 [1083]~E(x10832,f3(a119))+~E(x10831,f118(f118(f23(a119),f3(a119)),f16(a119)))+E(f118(f118(f23(a119),f3(a119)),f16(a119)),f118(f118(f23(a119),x10831),x10832)) % 7.54/7.63 [1084]~E(x10841,f3(a119))+~E(x10842,f118(f118(f23(a119),f3(a119)),f16(a119)))+E(f118(f118(f23(a119),f3(a119)),f16(a119)),f118(f118(f23(a119),x10841),x10842)) % 7.54/7.63 [1101]E(x11011,f16(a115))+~E(f118(f118(f24(a115),x11012),x11011),f16(a115))+~P77(f118(f29(a115,f3(a115)),x11012)) % 7.54/7.63 [1102]E(x11021,f16(a115))+~E(f118(f118(f24(a115),x11021),x11022),f16(a115))+~P77(f118(f29(a115,f3(a115)),x11021)) % 7.54/7.63 [1103]E(x11031,f3(a119))+E(x11032,f118(f118(f23(a119),f3(a119)),f16(a119)))+~E(f118(f118(f31(a119),x11032),x11031),f118(f118(f23(a119),f3(a119)),f16(a119))) % 7.54/7.63 [1104]E(x11041,f3(a119))+E(x11041,f118(f118(f23(a119),f3(a119)),f16(a119)))+~E(f118(f118(f23(a119),x11042),x11041),f118(f118(f23(a119),f3(a119)),f16(a119))) % 7.54/7.63 [1105]E(x11051,f3(a119))+E(x11051,f118(f118(f23(a119),f3(a119)),f16(a119)))+~E(f118(f118(f23(a119),x11051),x11052),f118(f118(f23(a119),f3(a119)),f16(a119))) % 7.54/7.63 [1106]E(x11061,f3(a119))+E(x11061,f118(f118(f23(a119),f3(a119)),f16(a119)))+~E(f118(f118(f23(a119),f3(a119)),f16(a119)),f118(f118(f23(a119),x11062),x11061)) % 7.54/7.63 [1107]E(x11071,f3(a119))+E(x11071,f118(f118(f23(a119),f3(a119)),f16(a119)))+~E(f118(f118(f23(a119),f3(a119)),f16(a119)),f118(f118(f23(a119),x11071),x11072)) % 7.54/7.63 [1156]~P77(f118(x11561,x11562))+P77(f118(x11561,f3(a119)))+P77(f118(f29(a119,f53(x11562,x11561)),x11562)) % 7.54/7.63 [1177]E(x11771,f118(f118(f23(a119),f3(a119)),f16(a119)))+E(x11772,f118(f118(f23(a119),f3(a119)),f16(a119)))+~E(f118(f118(f23(a119),x11771),x11772),f118(f118(f23(a119),f3(a119)),f16(a119))) % 7.54/7.63 [1178]E(x11781,f118(f118(f23(a119),f3(a119)),f16(a119)))+E(x11782,f118(f118(f23(a119),f3(a119)),f16(a119)))+~E(f118(f118(f23(a119),f3(a119)),f16(a119)),f118(f118(f23(a119),x11781),x11782)) % 7.54/7.63 [1188]~E(x11882,f118(f118(f23(a119),f3(a119)),f16(a119)))+~E(x11881,f118(f118(f23(a119),f3(a119)),f16(a119)))+E(f118(f118(f24(a119),x11881),x11882),f118(f118(f23(a119),f3(a119)),f16(a119))) % 7.54/7.63 [1217]E(f20(a115,x12171,x12172),f3(a115))+~P77(f118(f29(a115,x12171),x12172))+~P77(f118(f28(a115,f3(a115)),x12171)) % 7.54/7.63 [1238]~P46(x12381)+P77(f118(f29(x12381,f3(x12381)),f25(x12381,x12382)))+~P77(f118(f29(x12381,f3(x12381)),x12382)) % 7.54/7.63 [1262]~P46(x12621)+~P77(f118(f29(x12621,f3(x12621)),f25(x12621,x12622)))+P77(f118(f29(x12621,f3(x12621)),x12622)) % 7.54/7.63 [1274]E(f118(f118(f31(a114),f66(x12741,x12742)),x12742),x12741)+~P77(f118(f29(a114,f3(a114)),x12741))+~P77(f118(f29(a119,f3(a119)),x12742)) % 7.54/7.63 [1275]E(f118(f118(f31(a114),f67(x12751,x12752)),x12752),x12751)+~P77(f118(f29(a114,f3(a114)),x12751))+~P77(f118(f29(a119,f3(a119)),x12752)) % 7.54/7.63 [1334]P77(f118(f28(a115,f3(a115)),f30(x13341,x13342)))+~P77(f118(f28(a115,f3(a115)),x13341))+~P77(f118(f28(a115,f3(a115)),x13342)) % 7.54/7.63 [1335]P77(f118(f29(a114,f3(a114)),f66(x13351,x13352)))+~P77(f118(f29(a114,f3(a114)),x13351))+~P77(f118(f29(a119,f3(a119)),x13352)) % 7.54/7.63 [1336]P77(f118(f29(a114,f3(a114)),f67(x13361,x13362)))+~P77(f118(f29(a114,f3(a114)),x13361))+~P77(f118(f29(a119,f3(a119)),x13362)) % 7.54/7.63 [1337]P77(f118(f28(a114,x13371),f35(a119,x13372)))+~P77(f118(f28(a114,f3(a114)),x13371))+~P77(f118(f28(a119,f26(x13371)),x13372)) % 7.54/7.63 [1345]~P77(f118(f29(a114,x13451),f35(a119,x13452)))+~P77(f118(f28(a114,f3(a114)),x13451))+P77(f118(f29(a119,f33(x13451)),x13452)) % 7.54/7.63 [1359]~P77(f118(f28(a119,x13591),f33(x13592)))+~P77(f118(f28(a114,f3(a114)),x13592))+P77(f118(f28(a114,f35(a119,x13591)),x13592)) % 7.54/7.63 [1373]E(f33(f118(f118(f37(a114),x13731),f35(a119,x13732))),f20(a119,f33(x13731),x13732))+~P77(f118(f29(a119,f3(a119)),x13732))+~P77(f118(f28(a114,f16(a114)),x13731)) % 7.54/7.63 [1392]E(x13921,x13922)+P77(f118(f29(a119,x13921),x13922))+~P77(f118(f29(a119,x13921),f118(f118(f23(a119),x13922),f16(a119)))) % 7.54/7.63 [1393]E(x13931,x13932)+P77(f118(f29(a115,x13931),x13932))+~P77(f118(f29(a115,x13931),f118(f118(f23(a115),x13932),f16(a115)))) % 7.54/7.63 [1407]~P77(f118(x14071,x14072))+P77(f118(x14071,f3(a119)))+P77(f118(x14071,f118(f118(f23(a119),f53(x14072,x14071)),f16(a119)))) % 7.54/7.63 [1419]E(x14191,f3(a119))+E(f118(f118(f23(a119),f74(x14192,x14191)),f16(a119)),x14191)+~P77(f118(f29(a119,x14191),f118(f118(f23(a119),x14192),f16(a119)))) % 7.54/7.63 [1441]E(x14411,x14412)+~P77(f118(f28(a119,x14412),x14411))+~P77(f118(f29(a119,x14411),f118(f118(f23(a119),x14412),f16(a119)))) % 7.54/7.63 [1449]E(x14491,f118(f118(f23(a119),x14492),f16(a119)))+P77(f118(f28(a119,x14491),x14492))+~P77(f118(f28(a119,x14491),f118(f118(f23(a119),x14492),f16(a119)))) % 7.54/7.63 [1452]P77(f118(f29(a115,f3(a115)),f20(a115,x14521,x14522)))+~P77(f118(f28(a115,x14522),x14521))+~P77(f118(f29(a115,f3(a115)),x14522)) % 7.54/7.63 [1458]P77(f118(f28(a115,f3(a115)),f20(a115,x14581,x14582)))+~P77(f118(f28(a115,f3(a115)),x14582))+~P77(f118(f28(a115,f3(a115)),x14581)) % 7.54/7.63 [1459]P77(f118(f28(a115,f3(a115)),f20(a115,x14591,x14592)))+~P77(f118(f28(a115,f3(a115)),x14591))+~P77(f118(f29(a115,f3(a115)),x14592)) % 7.54/7.63 [1482]E(x14821,f3(a119))+P77(f118(f29(a119,f74(x14822,x14821)),x14822))+~P77(f118(f29(a119,x14821),f118(f118(f23(a119),x14822),f16(a119)))) % 7.54/7.63 [1535]~P77(f118(f29(a115,f3(a115)),f20(a115,x15352,x15351)))+P77(f118(f28(a115,x15351),x15352))+~P77(f118(f29(a115,f3(a115)),x15351)) % 7.54/7.63 [1536]~P77(f118(f29(a115,f3(a115)),f20(a115,x15362,x15361)))+P77(f118(f28(a115,x15361),x15362))+~P77(f118(f28(a115,f3(a115)),x15362)) % 7.54/7.63 [1537]~P77(f118(f28(a115,f3(a115)),f20(a115,x15371,x15372)))+P77(f118(f28(a115,f3(a115)),x15371))+~P77(f118(f29(a115,f3(a115)),x15372)) % 7.54/7.63 [1538]~P77(f118(f29(a115,f3(a115)),f20(a115,x15382,x15381)))+P77(f118(f29(a115,f3(a115)),x15381))+~P77(f118(f28(a115,f3(a115)),x15382)) % 7.54/7.63 [1582]~P77(f118(f28(a115,x15821),f3(a115)))+P77(f118(f28(a115,f20(a115,x15821,x15822)),f3(a115)))+~P77(f118(f29(a115,f3(a115)),x15822)) % 7.54/7.63 [1583]~P77(f118(f29(a115,x15832),f3(a115)))+P77(f118(f28(a115,f20(a115,x15831,x15832)),f3(a115)))+~P77(f118(f28(a115,f3(a115)),x15831)) % 7.54/7.63 [1584]~P77(f118(f29(a115,x15842),f3(a115)))+P77(f118(f29(a115,f20(a115,x15841,x15842)),f3(a115)))+~P77(f118(f29(a115,f3(a115)),x15841)) % 7.54/7.63 [1586]~P77(f118(f29(a115,x15861),f3(a115)))+P77(f118(f29(a115,f20(a115,x15861,x15862)),f3(a115)))+~P77(f118(f29(a115,f3(a115)),x15862)) % 7.54/7.63 [1587]~P77(f118(f29(a119,f3(a119)),x15871))+~P77(f118(f29(a119,f3(a119)),x15872))+P77(f118(f29(a119,f22(a119,x15871,x15872)),x15871)) % 7.54/7.63 [1588]~P77(f118(f29(a119,f3(a119)),x15881))+P77(f118(f29(a119,f20(a119,x15881,x15882)),x15881))+~P77(f118(f29(a119,f16(a119)),x15882)) % 7.54/7.63 [1589]~P77(f118(f29(a115,f3(a115)),x15891))+P77(f118(f29(a115,f20(a115,x15891,x15892)),x15891))+~P77(f118(f29(a115,f16(a115)),x15892)) % 7.54/7.63 [1663]~P36(x16631)+P2(x16631,x16632)+~P77(f118(f28(x16631,f118(x16632,f83(x16632,x16631))),f118(x16632,f94(x16632,x16631)))) % 7.54/7.63 [1664]~P36(x16641)+P2(x16641,x16642)+~P77(f118(f28(x16641,f118(x16642,f113(x16642,x16641))),f118(x16642,f105(x16642,x16641)))) % 7.54/7.63 [1665]~P36(x16651)+P5(x16651,x16652)+~P77(f118(f28(x16651,f118(x16652,f45(x16652,x16651))),f118(x16652,f44(x16652,x16651)))) % 7.54/7.63 [1666]~P36(x16661)+P6(x16661,x16662)+~P77(f118(f28(x16661,f118(x16662,f48(x16662,x16661))),f118(x16662,f50(x16662,x16661)))) % 7.54/7.63 [1688]E(f118(f118(f23(a119),f20(a119,f22(a119,x16881,x16882),x16882)),f16(a119)),f20(a119,x16881,x16882))+P77(f118(f29(a119,x16881),x16882))+~P77(f118(f29(a119,f3(a119)),x16882)) % 7.54/7.63 [1701]E(f33(x17011),x17012)+~P77(f118(f28(a114,f35(a119,x17012)),x17011))+~P77(f118(f29(a114,x17011),f118(f118(f23(a114),f35(a119,x17012)),f16(a114)))) % 7.54/7.63 [1712]E(f118(f118(f23(a119),f20(a119,f22(a119,x17121,x17122),x17122)),f16(a119)),f20(a119,x17121,x17122))+~P77(f118(f28(a119,x17122),x17121))+~P77(f118(f29(a119,f3(a119)),x17122)) % 7.54/7.63 [1721]~P77(f118(f29(a115,x17212),f3(a115)))+~P77(f118(f29(a115,f20(a115,x17211,x17212)),f3(a115)))+P77(f118(f29(a115,f3(a115)),x17211)) % 7.54/7.63 [1737]P77(f118(f29(a115,x17371),f3(a115)))+~P77(f118(f29(a115,f20(a115,x17371,x17372)),f3(a115)))+~P77(f118(f29(a115,f3(a115)),x17372)) % 7.54/7.63 [1741]E(f26(x17411),f118(f118(f23(a119),x17412),f16(a119)))+~P77(f118(f29(a114,f35(a119,x17412)),x17411))+~P77(f118(f28(a114,x17411),f118(f118(f23(a114),f35(a119,x17412)),f16(a114)))) % 7.54/7.63 [1911]~P36(x19111)+P2(x19111,x19112)+~P77(f118(f28(x19111,f118(x19112,f118(f118(f23(a119),f88(x19112,x19111)),f16(a119)))),f118(x19112,f88(x19112,x19111)))) % 7.54/7.63 [1233]~E(x12332,f3(a114))+~E(x12331,f3(a114))+E(f118(f118(f23(a114),f118(f118(f24(a114),x12331),x12331)),f118(f118(f24(a114),x12332),x12332)),f3(a114)) % 7.54/7.63 [1347]E(f118(f118(f23(a114),f34(x13471)),f34(x13472)),f34(f118(f118(f24(a114),x13471),x13472)))+~P77(f118(f29(a114,f3(a114)),x13472))+~P77(f118(f29(a114,f3(a114)),x13471)) % 7.54/7.63 [1352]E(f34(f118(f118(f37(a114),x13521),x13522)),f22(a114,f34(x13521),f34(x13522)))+~P77(f118(f29(a114,f3(a114)),x13522))+~P77(f118(f29(a114,f3(a114)),x13521)) % 7.54/7.63 [1379]~P22(x13791)+~P77(f118(f28(x13791,f3(x13791)),x13792))+P77(f118(f28(x13791,f3(x13791)),f118(f118(f23(x13791),x13792),x13792))) % 7.54/7.63 [1382]~P22(x13821)+~P77(f118(f29(x13821,f3(x13821)),x13822))+P77(f118(f29(x13821,f3(x13821)),f118(f118(f23(x13821),x13822),x13822))) % 7.54/7.63 [1406]E(x14061,f3(a119))+P77(f118(f29(a119,f3(a119)),x14062))+~P77(f118(f29(a119,f3(a119)),f118(f118(f31(a119),x14062),x14061))) % 7.54/7.63 [1418]~P77(f118(f28(a114,x14181),f3(a114)))+~P77(f118(f28(a114,x14182),f3(a114)))+P77(f118(f28(a114,f3(a114)),f118(f118(f37(a114),x14181),x14182))) % 7.54/7.63 [1432]~P77(f118(f28(a114,x14322),f3(a114)))+~P77(f118(f28(a114,f3(a114)),x14322))+P77(f118(f28(a114,f3(a114)),f118(f118(f37(a114),x14321),x14322))) % 7.54/7.63 [1433]~P77(f118(f28(a114,x14331),f3(a114)))+~P77(f118(f28(a114,f3(a114)),x14331))+P77(f118(f28(a114,f3(a114)),f118(f118(f37(a114),x14331),x14332))) % 7.54/7.63 [1443]~P77(f118(f28(a114,f3(a114)),x14432))+~P77(f118(f28(a114,f3(a114)),x14431))+P77(f118(f28(a114,f3(a114)),f118(f118(f37(a114),x14431),x14432))) % 7.54/7.63 [1444]~P77(f118(f28(a115,f3(a115)),x14441))+~P77(f118(f28(a115,f3(a115)),x14442))+P77(f118(f28(a115,f3(a115)),f118(f118(f23(a115),x14441),x14442))) % 7.54/7.63 [1445]~P77(f118(f28(a115,f3(a115)),x14451))+~P77(f118(f28(a115,f3(a115)),x14452))+P77(f118(f28(a115,f3(a115)),f118(f118(f24(a115),x14451),x14452))) % 7.54/7.63 [1446]~P77(f118(f29(a114,f3(a114)),x14462))+~P77(f118(f29(a114,f3(a114)),x14461))+P77(f118(f29(a114,f3(a114)),f118(f118(f24(a114),x14461),x14462))) % 7.54/7.63 [1447]~P77(f118(f29(a119,f3(a119)),x14472))+~P77(f118(f29(a119,f3(a119)),x14471))+P77(f118(f29(a119,f3(a119)),f118(f118(f24(a119),x14471),x14472))) % 7.54/7.63 [1477]P77(f118(f28(a114,x14771),f3(a114)))+P77(f118(f28(a114,f3(a114)),x14772))+~P77(f118(f28(a114,f3(a114)),f118(f118(f37(a114),x14772),x14771))) % 7.54/7.63 [1478]P77(f118(f28(a114,x14781),f3(a114)))+P77(f118(f28(a114,f3(a114)),x14782))+~P77(f118(f28(a114,f3(a114)),f118(f118(f37(a114),x14781),x14782))) % 7.54/7.63 [1479]P77(f118(f29(a119,f3(a119)),x14791))+P77(f118(f29(a119,f3(a119)),x14792))+~P77(f118(f29(a119,f3(a119)),f118(f118(f23(a119),x14792),x14791))) % 7.54/7.63 [1480]~P22(x14801)+P77(f118(f28(x14801,f3(x14801)),x14802))+~P77(f118(f28(x14801,f3(x14801)),f118(f118(f23(x14801),x14802),x14802))) % 7.54/7.63 [1481]~P22(x14811)+P77(f118(f29(x14811,f3(x14811)),x14812))+~P77(f118(f29(x14811,f3(x14811)),f118(f118(f23(x14811),x14812),x14812))) % 7.54/7.63 [1506]E(f118(f118(f23(a119),x15061),f16(a119)),x15062)+~P77(f118(f29(a119,x15061),x15062))+P77(f118(f29(a119,f118(f118(f23(a119),x15061),f16(a119))),x15062)) % 7.54/7.63 [1552]E(x15521,f3(a119))+~E(x15522,f3(a115))+~P77(f118(f29(a115,f3(a115)),f118(f118(f31(a115),f19(a115,x15522)),x15521))) % 7.54/7.63 [1596]E(f20(a115,f118(f118(f31(a115),x15961),x15962),x15961),f118(f118(f31(a115),x15961),f22(a119,x15962,f118(f118(f23(a119),f3(a119)),f16(a119)))))+~P77(f118(f29(a119,f3(a119)),x15962))+~P77(f118(f29(a115,f3(a115)),x15961)) % 7.54/7.63 [1873]~P77(f118(f29(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),x18731))+~P77(f118(f29(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),x18732))+P77(f118(f29(a119,x18731),f118(f118(f24(a119),x18732),x18731))) % 7.54/7.63 [1874]~P77(f118(f29(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),x18741))+~P77(f118(f29(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),x18742))+P77(f118(f29(a119,x18741),f118(f118(f24(a119),x18741),x18742))) % 7.54/7.63 [1884]~P36(x18841)+P2(x18841,x18842)+~P77(f118(f28(x18841,f118(x18842,f87(x18842,x18841))),f118(x18842,f118(f118(f23(a119),f87(x18842,x18841)),f16(a119))))) % 7.54/7.63 [1895]~P77(f118(f28(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),x18951))+~P77(f118(f28(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),x18952))+P77(f118(f28(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),f118(f118(f24(a119),x18951),x18952))) % 7.54/7.63 [1896]~P77(f118(f29(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),x18962))+~P77(f118(f29(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),x18961))+P77(f118(f29(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),f118(f118(f24(a119),x18961),x18962))) % 7.54/7.63 [1792]~P77(f118(f28(a114,f3(a114)),x17922))+~P77(f118(f28(a114,f3(a114)),x17921))+P77(f118(f28(a119,f118(f118(f24(a119),f33(x17921)),f33(x17922))),f33(f118(f118(f24(a114),x17921),x17922)))) % 7.54/7.63 [1880]~P77(f118(f28(a114,f3(a114)),x18801))+~P77(f118(f29(a114,f3(a114)),x18802))+P77(f118(f28(a114,f118(f118(f24(a114),f35(a119,f93(x18801,x18802))),x18802)),x18801)) % 7.54/7.63 [1925]~P77(f118(f28(a114,f3(a114)),x19251))+~P77(f118(f29(a114,f3(a114)),x19252))+P77(f118(f29(a114,x19251),f118(f118(f24(a114),f35(a119,f118(f118(f23(a119),f93(x19251,x19252)),f16(a119)))),x19252))) % 7.54/7.63 [874]~E(x8742,x8743)+~P24(x8741)+E(f22(x8741,x8742,x8743),f3(x8741)) % 7.54/7.63 [875]~E(x8752,x8753)+~P10(x8751)+E(f22(x8751,x8752,x8753),f3(x8751)) % 7.54/7.63 [940]~P24(x9403)+E(x9401,x9402)+~E(f22(x9403,x9401,x9402),f3(x9403)) % 7.54/7.63 [941]~P10(x9413)+E(x9411,x9412)+~E(f22(x9413,x9411,x9412),f3(x9413)) % 7.54/7.63 [928]~E(x9282,x9283)+~P27(x9281)+P77(f118(f28(x9281,x9282),x9283)) % 7.54/7.63 [930]~E(x9302,x9303)+~P36(x9301)+P77(f118(f28(x9301,x9302),x9303)) % 7.54/7.63 [967]~P78(x9671,x9672,x9673)+~E(x9672,f3(a115))+P77(f118(x9671,f3(a115))) % 7.54/7.63 [979]~E(x9791,x9792)+~P34(x9793)+~P77(f118(f29(x9793,x9791),x9792)) % 7.54/7.63 [980]~E(x9801,x9802)+~P36(x9803)+~P77(f118(f29(x9803,x9801),x9802)) % 7.54/7.63 [1029]~P34(x10291)+P77(f118(f28(x10291,x10293),x10292))+P77(f118(f28(x10291,x10292),x10293)) % 7.54/7.63 [1034]~P34(x10341)+P77(f118(f29(x10341,x10343),x10342))+P77(f118(f28(x10341,x10342),x10343)) % 7.54/7.63 [1098]~P27(x10981)+~P77(f118(f29(x10981,x10982),x10983))+P77(f118(f28(x10981,x10982),x10983)) % 7.54/7.63 [1100]~P36(x11001)+~P77(f118(f29(x11001,x11002),x11003))+P77(f118(f28(x11001,x11002),x11003)) % 7.54/7.63 [1158]~P27(x11581)+~P77(f118(f29(x11581,x11583),x11582))+~P77(f118(f28(x11581,x11582),x11583)) % 7.54/7.63 [1162]~P27(x11621)+~P77(f118(f29(x11621,x11623),x11622))+~P77(f118(f29(x11621,x11622),x11623)) % 7.54/7.63 [1165]~P34(x11651)+~P77(f118(f29(x11651,x11653),x11652))+~P77(f118(f28(x11651,x11652),x11653)) % 7.54/7.63 [1166]~P34(x11661)+~P77(f118(f29(x11661,x11663),x11662))+~P77(f118(f29(x11661,x11662),x11663)) % 7.54/7.63 [1167]~P36(x11671)+~P77(f118(f29(x11671,x11673),x11672))+~P77(f118(f29(x11671,x11672),x11673)) % 7.54/7.63 [1205]~E(x12053,f3(a119))+P77(f118(x12051,f20(a119,x12052,x12053)))+~P77(f118(x12051,f3(a119))) % 7.54/7.63 [1218]~P77(f118(f28(a114,x12181),x12183))+P77(f118(f28(a114,x12181),x12182))+~P77(f118(f28(a114,x12183),x12182)) % 7.54/7.63 [1219]~P77(f118(f28(a119,x12191),x12193))+P77(f118(f28(a119,x12191),x12192))+~P77(f118(f28(a119,x12193),x12192)) % 7.54/7.63 [1220]~P77(f118(f28(a115,x12201),x12203))+P77(f118(f28(a115,x12201),x12202))+~P77(f118(f28(a115,x12203),x12202)) % 7.54/7.63 [1261]~P1(x12611)+~P77(f118(f29(a119,x12612),x12613))+P77(f118(f29(a119,f118(x12611,x12612)),f118(x12611,x12613))) % 7.54/7.63 [1325]~E(x13252,f3(a119))+~P77(f118(x13251,f20(a119,x13253,x13252)))+P77(f118(x13251,f3(a119))) % 7.54/7.63 [1360]E(f118(f118(f23(a119),x13601),f97(x13601,x13602,x13603)),x13602)+P77(f118(x13603,f22(a119,x13602,x13601)))+~P77(f118(x13603,f3(a119))) % 7.54/7.63 [1361]E(f118(f118(f23(a119),x13611),f101(x13611,x13612,x13613)),x13612)+P77(f118(x13613,f22(a119,x13612,x13611)))+~P77(f118(x13613,f3(a119))) % 7.54/7.63 [1367]E(f118(f118(f23(a119),x13671),f97(x13671,x13672,x13673)),x13672)+P77(f118(x13673,f22(a119,x13672,x13671)))+P77(f118(f29(a119,x13672),x13671)) % 7.54/7.63 [1368]E(f118(f118(f23(a119),x13681),f101(x13681,x13682,x13683)),x13682)+P77(f118(x13683,f22(a119,x13682,x13681)))+P77(f118(f29(a119,x13682),x13681)) % 7.54/7.63 [1369]~P37(x13691)+~P4(x13691,x13692)+P77(f118(f28(a114,f36(x13691,f118(x13692,x13693))),f42(x13692,x13691))) % 7.54/7.63 [1370]~P37(x13701)+~P4(x13701,x13702)+P77(f118(f28(a114,f36(x13701,f118(x13702,x13703))),f46(x13702,x13701))) % 7.54/7.63 [1421]~P77(f118(x14211,f22(a119,x14212,x14213)))+~P77(f118(f29(a119,x14212),x14213))+P77(f118(x14211,f3(a119))) % 7.54/7.63 [1439]P77(f118(f29(a114,f3(a114)),f102(x14391,x14392,x14393)))+~P77(f118(f29(a114,x14393),x14392))+~P77(f118(f29(a114,x14392),x14391)) % 7.54/7.63 [1451]E(f22(a119,f22(a119,x14511,x14512),f22(a119,x14513,x14512)),f22(a119,x14511,x14513))+~P77(f118(f28(a119,x14512),x14511))+~P77(f118(f28(a119,x14512),x14513)) % 7.54/7.63 [1490]E(x14901,f3(a119))+P77(f118(x14902,f109(x14901,x14903,x14902)))+~P77(f118(x14902,f20(a119,x14903,x14901))) % 7.54/7.63 [1503]E(x15031,f3(a119))+~P77(f118(x15032,f104(x15031,x15033,x15032)))+P77(f118(x15032,f20(a119,x15033,x15031))) % 7.54/7.63 [1521]P77(f118(x15211,f109(x15212,x15213,x15211)))+~P77(f118(x15211,f20(a119,x15213,x15212)))+P77(f118(x15211,f3(a119))) % 7.54/7.63 [1523]~P26(x15231)+~P77(f118(f28(x15231,x15232),x15233))+P77(f118(f28(x15231,f22(x15231,x15232,x15233)),f3(x15231))) % 7.54/7.63 [1524]~P26(x15241)+~P77(f118(f29(x15241,x15242),x15243))+P77(f118(f29(x15241,f22(x15241,x15242,x15243)),f3(x15241))) % 7.54/7.63 [1532]~P77(f118(x15321,f97(x15323,x15322,x15321)))+P77(f118(x15321,f22(a119,x15322,x15323)))+~P77(f118(x15321,f3(a119))) % 7.54/7.64 [1533]~P77(f118(x15331,f101(x15333,x15332,x15331)))+P77(f118(x15331,f22(a119,x15332,x15333)))+~P77(f118(x15331,f3(a119))) % 7.54/7.64 [1534]~P77(f118(x15341,f104(x15343,x15342,x15341)))+P77(f118(x15341,f20(a119,x15342,x15343)))+~P77(f118(x15341,f3(a119))) % 7.54/7.64 [1544]~P77(f118(x15443,f97(x15442,x15441,x15443)))+P77(f118(x15443,f22(a119,x15441,x15442)))+P77(f118(f29(a119,x15441),x15442)) % 7.54/7.64 [1545]~P77(f118(x15453,f101(x15452,x15451,x15453)))+P77(f118(x15453,f22(a119,x15451,x15452)))+P77(f118(f29(a119,x15451),x15452)) % 7.54/7.64 [1677]~P26(x16771)+~P77(f118(f28(x16771,f22(x16771,x16772,x16773)),f3(x16771)))+P77(f118(f28(x16771,x16772),x16773)) % 7.54/7.64 [1678]~P26(x16781)+~P77(f118(f29(x16781,f22(x16781,x16782,x16783)),f3(x16781)))+P77(f118(f29(x16781,x16782),x16783)) % 7.54/7.64 [1685]~P77(f118(f29(a119,x16853),x16852))+~P77(f118(f29(a119,x16853),x16851))+P77(f118(f29(a119,f22(a119,x16851,x16852)),f22(a119,x16851,x16853))) % 7.54/7.64 [1686]~P77(f118(f28(a119,x16862),x16861))+~P77(f118(f29(a119,x16861),x16863))+P77(f118(f29(a119,f22(a119,x16861,x16862)),f22(a119,x16863,x16862))) % 7.54/7.64 [1690]~P77(f118(f28(a115,x16903),x16901))+P77(f118(f28(a115,f20(a115,x16901,x16902)),f20(a115,x16903,x16902)))+~P77(f118(f29(a115,x16902),f3(a115))) % 7.54/7.64 [1738]E(x17381,f3(a119))+E(f118(f118(f23(a119),f118(f118(f24(a119),x17381),f104(x17381,x17382,x17383))),f110(x17381,x17382,x17383)),x17382)+P77(f118(x17383,f20(a119,x17382,x17381))) % 7.54/7.64 [1747]E(f118(f118(f23(a119),f118(f118(f24(a119),x17471),f104(x17471,x17472,x17473))),f110(x17471,x17472,x17473)),x17472)+P77(f118(x17473,f20(a119,x17472,x17471)))+~P77(f118(x17473,f3(a119))) % 7.54/7.64 [1935]~P57(x19352)+E(x19351,f3(x19352))+~P77(f118(f28(x19352,f118(f118(f23(x19352),f118(f118(f24(x19352),x19353),x19353)),f118(f118(f24(x19352),x19351),x19351))),f3(x19352))) % 7.54/7.64 [1936]~P57(x19362)+E(x19361,f3(x19362))+~P77(f118(f28(x19362,f118(f118(f23(x19362),f118(f118(f24(x19362),x19361),x19361)),f118(f118(f24(x19362),x19363),x19363))),f3(x19362))) % 7.54/7.64 [873]~P76(x8731)+~E(x8733,f3(x8731))+E(f118(f118(f23(x8731),x8732),x8733),x8732) % 7.54/7.64 [876]~P40(x8761)+~E(x8763,f3(a119))+E(f118(f118(f31(x8761),x8762),x8763),f16(x8761)) % 7.54/7.64 [887]~P64(x8871)+~E(x8873,f3(x8871))+E(f118(f118(f24(x8871),x8872),x8873),f3(x8871)) % 7.54/7.64 [888]~P64(x8881)+~E(x8882,f3(x8881))+E(f118(f118(f24(x8881),x8882),x8883),f3(x8881)) % 7.54/7.64 [931]~P76(x9312)+E(x9311,f3(x9312))+~E(f118(f118(f23(x9312),x9313),x9311),x9313) % 7.54/7.64 [939]~P71(x9392)+E(x9391,f3(x9392))+~E(f118(f118(f31(x9392),x9391),x9393),f3(x9392)) % 7.54/7.64 [1000]E(x10001,x10002)+E(x10003,f3(a114))+~E(f118(f118(f24(a114),x10003),x10001),f118(f118(f24(a114),x10003),x10002)) % 7.54/7.64 [1002]E(x10021,x10022)+E(x10023,f3(a119))+~E(f118(f118(f24(a119),x10023),x10021),f118(f118(f24(a119),x10023),x10022)) % 7.54/7.64 [1003]E(x10031,x10032)+E(x10033,f3(a114))+~E(f118(f118(f24(a114),x10031),x10033),f118(f118(f24(a114),x10032),x10033)) % 7.54/7.64 [1004]E(x10041,x10042)+E(x10043,f3(a119))+~E(f118(f118(f24(a119),x10041),x10043),f118(f118(f24(a119),x10042),x10043)) % 7.54/7.64 [1139]E(f22(a119,x11391,x11392),x11393)+~E(x11391,f118(f118(f23(a119),x11393),x11392))+~P77(f118(f28(a119,x11392),x11391)) % 7.54/7.64 [1144]~E(f22(a119,x11441,x11443),x11442)+E(x11441,f118(f118(f23(a119),x11442),x11443))+~P77(f118(f28(a119,x11443),x11441)) % 7.54/7.64 [1194]E(x11941,x11942)+~E(f118(f118(f24(a119),x11943),x11941),f118(f118(f24(a119),x11943),x11942))+~P77(f118(f29(a119,f3(a119)),x11943)) % 7.54/7.64 [1278]~P7(x12781)+P77(f118(f28(x12781,x12782),x12783))+~P77(f118(f28(x12781,f19(x12781,x12782)),x12783)) % 7.54/7.64 [1366]~E(x13661,f118(f118(f23(a119),x13663),f16(a119)))+~P77(f118(f29(a119,x13663),x13662))+P77(f118(f29(a119,x13661),f118(f118(f23(a119),x13662),f16(a119)))) % 7.54/7.64 [1572]E(x15721,f3(a119))+P77(f118(x15722,f20(a119,x15723,x15721)))+P77(f118(f29(a119,f110(x15721,x15723,x15722)),x15721)) % 7.54/7.64 [1599]P77(f118(x15991,f20(a119,x15992,x15993)))+~P77(f118(x15991,f3(a119)))+P77(f118(f29(a119,f110(x15993,x15992,x15991)),x15993)) % 7.54/7.64 [1615]E(x16151,f3(a114))+~P77(f118(f28(a114,x16152),f3(a114)))+~P77(f118(f28(a114,f19(a114,x16151)),f118(f118(f24(a114),x16152),f19(a114,x16153)))) % 7.54/7.64 [1693]~P77(f118(f28(a119,x16933),x16932))+P77(f118(f28(a119,f20(a119,x16931,x16932)),f20(a119,x16931,x16933)))+~P77(f118(f29(a119,f3(a119)),x16933)) % 7.54/7.64 [1694]~P77(f118(f28(a115,x16941),x16943))+P77(f118(f28(a115,f20(a115,x16941,x16942)),f20(a115,x16943,x16942)))+~P77(f118(f29(a115,f3(a115)),x16942)) % 7.54/7.64 [1903]~P41(x19031)+~P3(x19031,x19033)+P3(x19031,f7(x19031,x19031,a119,f118(f24(x19031),x19032),x19033)) % 7.54/7.64 [1945]~P37(x19451)+~P4(x19451,x19452)+P4(x19451,f7(a119,x19451,a119,x19452,f8(a119,a119,a119,f23(a119),x19453))) % 7.54/7.64 [1947]~P41(x19471)+~P3(x19471,x19472)+P3(x19471,f8(a119,x19471,x19471,f7(x19471,f121(x19471,x19471),a119,f24(x19471),x19472),x19473)) % 7.54/7.64 [1948]~P44(x19481)+~P3(x19481,x19482)+P3(x19481,f8(a119,x19481,x19481,f7(x19481,f121(x19481,x19481),a119,f37(x19481),x19482),x19483)) % 7.54/7.64 [1963]~P37(x19631)+P4(x19631,x19632)+~P4(x19631,f7(a119,x19631,a119,x19632,f8(a119,a119,a119,f23(a119),x19633))) % 7.54/7.64 [1025]~P11(x10252)+E(x10251,f3(x10252))+E(f20(x10252,f118(f118(f24(x10252),x10253),x10251),x10251),x10253) % 7.54/7.64 [1026]~P11(x10262)+E(x10261,f3(x10262))+E(f20(x10262,f118(f118(f24(x10262),x10261),x10263),x10261),x10263) % 7.54/7.64 [1145]~P44(x11452)+E(x11451,f3(x11452))+E(f118(f118(f37(a114),f36(x11452,x11453)),f36(x11452,x11451)),f36(x11452,f118(f118(f37(x11452),x11453),x11451))) % 7.54/7.64 [1153]~P12(x11531)+~P44(x11531)+E(f118(f118(f37(a114),f36(x11531,x11532)),f36(x11531,x11533)),f36(x11531,f118(f118(f37(x11531),x11532),x11533))) % 7.54/7.64 [1302]~P46(x13021)+E(f19(x13021,f118(f118(f24(x13021),x13022),x13023)),f118(f118(f24(x13021),f19(x13021,x13022)),x13023))+~P77(f118(f28(x13021,f3(x13021)),x13023)) % 7.54/7.64 [1351]~P40(x13512)+E(x13511,f3(a119))+E(f118(f118(f24(x13512),x13513),f118(f118(f31(x13512),x13513),f22(a119,x13511,f16(a119)))),f118(f118(f31(x13512),x13513),x13511)) % 7.54/7.64 [1355]~P11(x13552)+E(x13551,f3(x13552))+E(f20(x13552,f118(f118(f23(x13552),x13553),x13551),x13551),f118(f118(f23(x13552),f20(x13552,x13553,x13551)),f16(x13552))) % 7.54/7.64 [1356]~P11(x13562)+E(x13561,f3(x13562))+E(f20(x13562,f118(f118(f23(x13562),x13561),x13563),x13561),f118(f118(f23(x13562),f20(x13562,x13563,x13561)),f16(x13562))) % 7.54/7.64 [1380]~P45(x13801)+~P77(f118(f28(x13801,f3(x13801)),x13802))+P77(f118(f28(x13801,f3(x13801)),f118(f118(f31(x13801),x13802),x13803))) % 7.54/7.64 [1381]~P45(x13811)+~P77(f118(f28(x13811,f16(x13811)),x13812))+P77(f118(f28(x13811,f16(x13811)),f118(f118(f31(x13811),x13812),x13813))) % 7.54/7.64 [1383]~P45(x13831)+~P77(f118(f29(x13831,f3(x13831)),x13832))+P77(f118(f29(x13831,f3(x13831)),f118(f118(f31(x13831),x13832),x13833))) % 7.54/7.64 [1467]~P57(x14672)+E(x14671,f3(x14672))+~E(f118(f118(f23(x14672),f118(f118(f24(x14672),x14673),x14673)),f118(f118(f24(x14672),x14671),x14671)),f3(x14672)) % 7.54/7.64 [1468]~P57(x14682)+E(x14681,f3(x14682))+~E(f118(f118(f23(x14682),f118(f118(f24(x14682),x14681),x14681)),f118(f118(f24(x14682),x14683),x14683)),f3(x14682)) % 7.54/7.64 [1547]~P77(f118(f29(a119,x15471),x15473))+~P77(f118(f29(a119,x15473),x15472))+P77(f118(f29(a119,f118(f118(f23(a119),x15471),f16(a119))),x15472)) % 7.54/7.64 [1645]~E(x16453,f20(a119,x16451,x16452))+~P77(f118(f29(a119,f3(a119)),x16452))+P77(f118(f29(a119,x16451),f118(f118(f24(a119),x16452),f118(f118(f23(a119),x16453),f16(a119))))) % 7.54/7.64 [1647]~P45(x16471)+~P77(f118(f29(x16471,f16(x16471)),x16472))+P77(f118(f29(x16471,f16(x16471)),f118(f118(f31(x16471),x16472),f118(f118(f23(a119),x16473),f16(a119))))) % 7.54/7.64 [1650]~P77(f118(f28(a114,x16502),x16503))+~P77(f118(f29(a114,f3(a114)),x16501))+P77(f118(f28(a114,f118(f118(f24(a114),x16501),x16502)),f118(f118(f24(a114),x16501),x16503))) % 7.54/7.64 [1651]~P77(f118(f28(a114,x16511),x16513))+~P77(f118(f29(a114,f3(a114)),x16512))+P77(f118(f28(a114,f118(f118(f24(a114),x16511),x16512)),f118(f118(f24(a114),x16513),x16512))) % 7.54/7.64 [1653]~P77(f118(f29(a114,x16531),x16533))+~P77(f118(f29(a114,f3(a114)),x16532))+P77(f118(f29(a114,f118(f118(f24(a114),x16531),x16532)),f118(f118(f24(a114),x16533),x16532))) % 7.54/7.64 [1654]~P77(f118(f29(a114,x16542),x16543))+~P77(f118(f29(a114,f3(a114)),x16541))+P77(f118(f29(a114,f118(f118(f24(a114),x16541),x16542)),f118(f118(f24(a114),x16541),x16543))) % 7.54/7.64 [1658]~P77(f118(f29(a119,x16581),x16583))+~P77(f118(f29(a119,f3(a119)),x16582))+P77(f118(f29(a119,f118(f118(f24(a119),x16581),x16582)),f118(f118(f24(a119),x16583),x16582))) % 7.54/7.64 [1659]~P77(f118(f29(a119,x16592),x16593))+~P77(f118(f29(a119,f3(a119)),x16591))+P77(f118(f29(a119,f118(f118(f24(a119),x16591),x16592)),f118(f118(f24(a119),x16591),x16593))) % 7.54/7.64 [1660]~P77(f118(f29(a115,x16602),x16603))+~P77(f118(f29(a115,f3(a115)),x16601))+P77(f118(f29(a115,f118(f118(f24(a115),x16601),x16602)),f118(f118(f24(a115),x16601),x16603))) % 7.54/7.64 [1781]P77(f118(f28(a114,x17811),x17812))+~P77(f118(f29(a114,f3(a114)),x17813))+~P77(f118(f28(a114,f118(f118(f24(a114),x17813),x17811)),f118(f118(f24(a114),x17813),x17812))) % 7.54/7.64 [1782]P77(f118(f28(a114,x17821),x17822))+~P77(f118(f29(a114,f3(a114)),x17823))+~P77(f118(f28(a114,f118(f118(f24(a114),x17821),x17823)),f118(f118(f24(a114),x17822),x17823))) % 7.54/7.64 [1784]P77(f118(f28(a119,x17841),x17842))+~P77(f118(f29(a119,f3(a119)),x17843))+~P77(f118(f28(a119,f118(f118(f24(a119),x17843),x17841)),f118(f118(f24(a119),x17843),x17842))) % 7.54/7.64 [1785]P77(f118(f28(a119,x17851),x17852))+~P77(f118(f29(a119,f3(a119)),x17853))+~P77(f118(f28(a119,f118(f118(f24(a119),x17851),x17853)),f118(f118(f24(a119),x17852),x17853))) % 7.54/7.64 [1786]P77(f118(f29(a114,x17861),x17862))+~P77(f118(f29(a114,f3(a114)),x17863))+~P77(f118(f29(a114,f118(f118(f24(a114),x17861),x17863)),f118(f118(f24(a114),x17862),x17863))) % 7.54/7.64 [1788]P77(f118(f29(a119,x17881),x17882))+~P77(f118(f29(a119,f3(a119)),x17883))+~P77(f118(f29(a119,f118(f118(f31(a119),x17883),x17881)),f118(f118(f31(a119),x17883),x17882))) % 7.54/7.64 [1795]~P37(x17951)+~P4(x17951,x17952)+P77(f118(f28(a114,f36(x17951,f118(x17952,x17953))),f35(a119,f118(f118(f23(a119),f89(x17952,x17951)),f16(a119))))) % 7.54/7.64 [1796]~P37(x17961)+~P4(x17961,x17962)+P77(f118(f29(a114,f36(x17961,f118(x17962,x17963))),f35(a119,f118(f118(f23(a119),f90(x17962,x17961)),f16(a119))))) % 7.54/7.64 [1866]E(x18661,f3(a119))+~P77(f118(x18663,f20(a119,x18662,x18661)))+P77(f118(f28(a119,f118(f118(f24(a119),x18661),f109(x18661,x18662,x18663))),x18662)) % 7.54/7.64 [1867]~P77(f118(x18671,f20(a119,x18673,x18672)))+P77(f118(x18671,f3(a119)))+P77(f118(f28(a119,f118(f118(f24(a119),x18672),f109(x18672,x18673,x18671))),x18673)) % 7.54/7.64 [1904]E(x19041,f3(a119))+~P77(f118(x19043,f20(a119,x19042,x19041)))+P77(f118(f29(a119,x19042),f118(f118(f24(a119),x19041),f118(f118(f23(a119),f109(x19041,x19042,x19043)),f16(a119))))) % 7.54/7.64 [1906]~P77(f118(x19061,f20(a119,x19062,x19063)))+P77(f118(x19061,f3(a119)))+P77(f118(f29(a119,x19062),f118(f118(f24(a119),x19063),f118(f118(f23(a119),f109(x19063,x19062,x19061)),f16(a119))))) % 7.54/7.64 [1926]~P37(x19261)+P4(x19261,x19262)+~P77(f118(f28(a114,f36(x19261,f118(x19262,f91(x19262,x19261,x19263)))),f35(a119,f118(f118(f23(a119),x19263),f16(a119))))) % 7.54/7.64 [1927]~P37(x19271)+P4(x19271,x19272)+~P77(f118(f29(a114,f36(x19271,f118(x19272,f92(x19272,x19271,x19273)))),f35(a119,f118(f118(f23(a119),x19273),f16(a119))))) % 7.54/7.64 [1928]~P37(x19282)+P77(f118(f29(a114,f3(a114)),f76(x19281,x19282)))+~P77(f118(f29(a114,f36(x19282,f118(x19281,f77(x19281,x19282,x19283)))),f35(a119,f118(f118(f23(a119),x19283),f16(a119))))) % 7.54/7.64 [1929]~P37(x19292)+P77(f118(f29(a114,f3(a114)),f79(x19291,x19292)))+~P77(f118(f28(a114,f36(x19292,f118(x19291,f80(x19291,x19292,x19293)))),f35(a119,f118(f118(f23(a119),x19293),f16(a119))))) % 7.54/7.64 [1528]~E(x15282,f20(a119,x15283,x15281))+~P77(f118(f29(a119,f3(a119)),x15281))+P77(f118(f28(a119,f118(f118(f24(a119),x15281),x15282)),x15283)) % 7.54/7.64 [1672]~P25(x16721)+E(f118(f118(f24(x16721),f118(f118(f31(x16721),x16722),f22(a119,x16723,f16(a119)))),x16722),f118(f118(f31(x16721),x16722),x16723))+~P77(f118(f29(a119,f3(a119)),x16723)) % 7.54/7.64 [1673]~P45(x16731)+~P77(f118(f29(x16731,f16(x16731)),x16732))+P77(f118(f29(x16731,f16(x16731)),f118(f118(f24(x16731),x16732),f118(f118(f31(x16731),x16732),x16733)))) % 7.54/7.64 [1736]~P77(f118(f28(a119,x17362),x17363))+~P77(f118(f28(a119,x17361),f22(a119,x17363,x17362)))+P77(f118(f28(a119,f118(f118(f23(a119),x17361),x17362)),x17363)) % 7.54/7.64 [1756]~P77(f118(f28(a119,x17563),x17562))+P77(f118(f28(a119,x17561),f22(a119,x17562,x17563)))+~P77(f118(f28(a119,f118(f118(f23(a119),x17561),x17563)),x17562)) % 7.54/7.64 [1801]~P45(x18011)+~P77(f118(f29(x18011,f16(x18011)),x18012))+P77(f118(f29(x18011,f118(f118(f31(x18011),x18012),x18013)),f118(f118(f24(x18011),x18012),f118(f118(f31(x18011),x18012),x18013)))) % 7.54/7.64 [1856]~P57(x18562)+E(x18561,f3(x18562))+P77(f118(f29(x18562,f3(x18562)),f118(f118(f23(x18562),f118(f118(f24(x18562),x18563),x18563)),f118(f118(f24(x18562),x18561),x18561)))) % 7.54/7.64 [1857]~P57(x18572)+E(x18571,f3(x18572))+P77(f118(f29(x18572,f3(x18572)),f118(f118(f23(x18572),f118(f118(f24(x18572),x18571),x18571)),f118(f118(f24(x18572),x18573),x18573)))) % 7.54/7.64 [1754]~P37(x17541)+P4(x17541,x17542)+P77(f118(f28(a119,x17543),f54(x17544,x17542,x17543,x17541))) % 7.54/7.64 [1036]~P16(x10363)+E(x10361,x10362)+~E(f118(f118(f23(x10363),x10364),x10361),f118(f118(f23(x10363),x10364),x10362)) % 7.54/7.64 [1037]~P17(x10373)+E(x10371,x10372)+~E(f118(f118(f23(x10373),x10374),x10371),f118(f118(f23(x10373),x10374),x10372)) % 7.54/7.64 [1039]~P16(x10393)+E(x10391,x10392)+~E(f118(f118(f23(x10393),x10391),x10394),f118(f118(f23(x10393),x10392),x10394)) % 7.54/7.64 [1244]~E(f118(f118(f23(a119),x12443),x12442),f118(f118(f23(a119),x12441),x12444))+~P77(f118(f29(a119,x12443),x12444))+P77(f118(f29(a119,x12441),x12442)) % 7.54/7.64 [1375]P77(f118(x13751,x13752))+~E(x13753,f118(f118(f23(a119),x13754),x13752))+~P77(f118(x13751,f22(a119,x13753,x13754))) % 7.54/7.64 [1378]~P35(x13782)+~P77(f118(f29(f121(x13781,x13782),x13783),x13784))+P77(f118(f28(f121(x13781,x13782),x13783),x13784)) % 7.54/7.64 [1476]~P35(x14761)+~P77(f118(f29(f121(x14762,x14761),x14764),x14763))+~P77(f118(f28(f121(x14762,x14761),x14763),x14764)) % 7.54/7.64 [1960]~P35(x19602)+~P77(f118(f28(x19602,f118(x19603,f62(x19604,x19603,x19601,x19602))),f118(x19604,f62(x19604,x19603,x19601,x19602))))+P77(f118(f28(f121(x19601,x19602),x19603),x19604)) % 7.54/7.64 [1187]~P11(x11871)+~E(x11872,f3(x11871))+E(f20(x11871,f118(f118(f24(x11871),x11872),x11873),f118(f118(f24(x11871),x11872),x11874)),f3(x11871)) % 7.54/7.64 [1229]~P11(x12292)+E(x12291,f3(x12292))+E(f20(x12292,f118(f118(f24(x12292),x12293),x12291),f118(f118(f24(x12292),x12294),x12291)),f20(x12292,x12293,x12294)) % 7.54/7.64 [1231]~P11(x12312)+E(x12311,f3(x12312))+E(f20(x12312,f118(f118(f24(x12312),x12311),x12313),f118(f118(f24(x12312),x12311),x12314)),f20(x12312,x12313,x12314)) % 7.54/7.64 [1628]~P29(x16281)+~P77(f118(f28(x16281,x16283),x16284))+P77(f118(f28(x16281,f118(f118(f23(x16281),x16282),x16283)),f118(f118(f23(x16281),x16282),x16284))) % 7.54/7.64 [1629]~P30(x16291)+~P77(f118(f28(x16291,x16293),x16294))+P77(f118(f28(x16291,f118(f118(f23(x16291),x16292),x16293)),f118(f118(f23(x16291),x16292),x16294))) % 7.54/7.64 [1630]~P29(x16301)+~P77(f118(f28(x16301,x16302),x16304))+P77(f118(f28(x16301,f118(f118(f23(x16301),x16302),x16303)),f118(f118(f23(x16301),x16304),x16303))) % 7.54/7.64 [1631]~P30(x16311)+~P77(f118(f28(x16311,x16312),x16314))+P77(f118(f28(x16311,f118(f118(f23(x16311),x16312),x16313)),f118(f118(f23(x16311),x16314),x16313))) % 7.54/7.64 [1632]~P29(x16321)+~P77(f118(f29(x16321,x16323),x16324))+P77(f118(f29(x16321,f118(f118(f23(x16321),x16322),x16323)),f118(f118(f23(x16321),x16322),x16324))) % 7.54/7.64 [1633]~P31(x16331)+~P77(f118(f29(x16331,x16333),x16334))+P77(f118(f29(x16331,f118(f118(f23(x16331),x16332),x16333)),f118(f118(f23(x16331),x16332),x16334))) % 7.54/7.64 [1634]~P29(x16341)+~P77(f118(f29(x16341,x16342),x16344))+P77(f118(f29(x16341,f118(f118(f23(x16341),x16342),x16343)),f118(f118(f23(x16341),x16344),x16343))) % 7.54/7.64 [1635]~P31(x16351)+~P77(f118(f29(x16351,x16352),x16354))+P77(f118(f29(x16351,f118(f118(f23(x16351),x16352),x16353)),f118(f118(f23(x16351),x16354),x16353))) % 7.54/7.64 [1639]~P77(f118(f28(a119,x16392),x16394))+~P77(f118(f28(a119,x16391),x16393))+P77(f118(f28(a119,f118(f118(f23(a119),x16391),x16392)),f118(f118(f23(a119),x16393),x16394))) % 7.54/7.64 [1640]~P77(f118(f28(a119,x16402),x16404))+~P77(f118(f28(a119,x16401),x16403))+P77(f118(f28(a119,f118(f118(f24(a119),x16401),x16402)),f118(f118(f24(a119),x16403),x16404))) % 7.54/7.64 [1641]~P77(f118(f29(a119,x16412),x16414))+~P77(f118(f29(a119,x16411),x16413))+P77(f118(f29(a119,f118(f118(f23(a119),x16411),x16412)),f118(f118(f23(a119),x16413),x16414))) % 7.54/7.64 [1642]~P77(f118(f28(a115,x16422),x16424))+~P77(f118(f29(a115,x16421),x16423))+P77(f118(f29(a115,f118(f118(f23(a115),x16421),x16422)),f118(f118(f23(a115),x16423),x16424))) % 7.54/7.64 [1769]~P25(x17691)+E(f118(f118(f31(x17691),x17692),f22(a119,f118(f118(f23(a119),x17693),f16(a119)),x17694)),f118(f118(f24(x17691),f118(f118(f31(x17691),x17692),f22(a119,x17693,x17694))),x17692))+~P77(f118(f28(a119,x17694),x17693)) % 7.54/7.64 [1774]~P29(x17741)+P77(f118(f28(x17741,x17742),x17743))+~P77(f118(f28(x17741,f118(f118(f23(x17741),x17744),x17742)),f118(f118(f23(x17741),x17744),x17743))) % 7.54/7.64 [1776]~P29(x17761)+P77(f118(f28(x17761,x17762),x17763))+~P77(f118(f28(x17761,f118(f118(f23(x17761),x17762),x17764)),f118(f118(f23(x17761),x17763),x17764))) % 7.54/7.64 [1778]~P29(x17781)+P77(f118(f29(x17781,x17782),x17783))+~P77(f118(f29(x17781,f118(f118(f23(x17781),x17784),x17782)),f118(f118(f23(x17781),x17784),x17783))) % 7.54/7.64 [1780]~P29(x17801)+P77(f118(f29(x17801,x17802),x17803))+~P77(f118(f29(x17801,f118(f118(f23(x17801),x17802),x17804)),f118(f118(f23(x17801),x17803),x17804))) % 7.54/7.64 [1883]~P46(x18831)+~P77(f118(f29(x18831,f19(x18831,f22(x18831,x18832,x18833))),x18834))+P77(f118(f29(x18831,x18832),f118(f118(f23(x18831),x18833),x18834))) % 7.54/7.64 [1887]~P46(x18871)+P77(f118(f29(x18871,f22(x18871,x18872,x18873)),x18874))+~P77(f118(f29(x18871,f19(x18871,f22(x18871,x18874,x18872))),x18873)) % 7.54/7.64 [1931]~P37(x19311)+P77(f118(f28(a114,f36(x19311,f118(x19312,x19313))),f76(x19312,x19311)))+~P77(f118(f29(a114,f36(x19311,f118(x19312,f77(x19312,x19311,x19314)))),f35(a119,f118(f118(f23(a119),x19314),f16(a119))))) % 7.54/7.64 [1932]~P37(x19321)+P77(f118(f28(a114,f36(x19321,f118(x19322,x19323))),f79(x19322,x19321)))+~P77(f118(f28(a114,f36(x19321,f118(x19322,f80(x19322,x19321,x19324)))),f35(a119,f118(f118(f23(a119),x19324),f16(a119))))) % 7.54/7.64 [1429]~P11(x14292)+E(x14291,f3(x14292))+E(f20(x14292,f118(f118(f23(x14292),x14293),f118(f118(f24(x14292),x14294),x14291)),x14291),f118(f118(f23(x14292),x14294),f20(x14292,x14293,x14291))) % 7.54/7.64 [1430]~P11(x14302)+E(x14301,f3(x14302))+E(f20(x14302,f118(f118(f23(x14302),x14303),f118(f118(f24(x14302),x14301),x14304)),x14301),f118(f118(f23(x14302),x14304),f20(x14302,x14303,x14301))) % 7.54/7.64 [1505]~P13(x15052)+E(x15051,f3(x15052))+E(f118(f118(f37(x15052),f118(f118(f31(x15052),x15053),x15054)),f118(f118(f31(x15052),x15051),x15054)),f118(f118(f31(x15052),f118(f118(f37(x15052),x15053),x15051)),x15054)) % 7.54/7.64 [1966]~P37(x19661)+P4(x19661,x19662)+~P77(f118(f28(a114,f36(x19661,f118(x19662,f54(x19663,x19662,x19664,x19661)))),x19663)) % 7.54/7.64 [1436]~P35(x14361)+P77(f118(f28(x14361,f118(x14362,x14363)),f118(x14364,x14363)))+~P77(f118(f28(f121(x14365,x14361),x14362),x14364)) % 7.54/7.64 [1557]~E(x15572,x15574)+~P76(x15571)+E(f118(f118(f23(x15571),f118(f118(f24(x15571),x15572),x15573)),f118(f118(f24(x15571),x15574),x15575)),f118(f118(f23(x15571),f118(f118(f24(x15571),x15572),x15575)),f118(f118(f24(x15571),x15574),x15573))) % 7.54/7.64 [1876]~P77(f118(f28(a119,x18763),x18762))+E(x18761,f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x18762,x18763)),x18764)),x18765))+~E(f118(f118(f23(a119),f118(f118(f24(a119),x18763),x18764)),x18761),f118(f118(f23(a119),f118(f118(f24(a119),x18762),x18764)),x18765)) % 7.54/7.64 [1877]~P77(f118(f28(a119,x18772),x18771))+E(f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x18771,x18772)),x18773)),x18774),x18775)+~E(f118(f118(f23(a119),f118(f118(f24(a119),x18771),x18773)),x18774),f118(f118(f23(a119),f118(f118(f24(a119),x18772),x18773)),x18775)) % 7.54/7.64 [1891]~P77(f118(f28(a119,x18914),x18911))+~E(x18915,f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x18911,x18914)),x18912)),x18913))+E(f118(f118(f23(a119),f118(f118(f24(a119),x18911),x18912)),x18913),f118(f118(f23(a119),f118(f118(f24(a119),x18914),x18912)),x18915)) % 7.54/7.64 [1892]~P77(f118(f28(a119,x18924),x18921))+~E(f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x18921,x18924)),x18922)),x18923),x18925)+E(f118(f118(f23(a119),f118(f118(f24(a119),x18921),x18922)),x18923),f118(f118(f23(a119),f118(f118(f24(a119),x18924),x18922)),x18925)) % 7.54/7.64 [1953]~P77(f118(f28(a119,x19533),x19532))+P77(f118(f28(a119,x19531),f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x19532,x19533)),x19534)),x19535)))+~P77(f118(f28(a119,f118(f118(f23(a119),f118(f118(f24(a119),x19533),x19534)),x19531)),f118(f118(f23(a119),f118(f118(f24(a119),x19532),x19534)),x19535))) % 7.54/7.64 [1954]~P77(f118(f28(a119,x19543),x19542))+P77(f118(f29(a119,x19541),f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x19542,x19543)),x19544)),x19545)))+~P77(f118(f29(a119,f118(f118(f23(a119),f118(f118(f24(a119),x19543),x19544)),x19541)),f118(f118(f23(a119),f118(f118(f24(a119),x19542),x19544)),x19545))) % 7.54/7.64 [1958]~P77(f118(f28(a119,x19581),x19584))+~P77(f118(f28(a119,x19583),f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x19584,x19581)),x19582)),x19585)))+P77(f118(f28(a119,f118(f118(f23(a119),f118(f118(f24(a119),x19581),x19582)),x19583)),f118(f118(f23(a119),f118(f118(f24(a119),x19584),x19582)),x19585))) % 7.54/7.64 [1959]~P77(f118(f28(a119,x19591),x19594))+~P77(f118(f29(a119,x19593),f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x19594,x19591)),x19592)),x19595)))+P77(f118(f29(a119,f118(f118(f23(a119),f118(f118(f24(a119),x19591),x19592)),x19593)),f118(f118(f23(a119),f118(f118(f24(a119),x19594),x19592)),x19595))) % 7.54/7.64 [1964]~P77(f118(f28(a119,x19642),x19641))+~P77(f118(f28(a119,f118(f118(f23(a119),f118(f118(f24(a119),x19641),x19643)),x19644)),f118(f118(f23(a119),f118(f118(f24(a119),x19642),x19643)),x19645)))+P77(f118(f28(a119,f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x19641,x19642)),x19643)),x19644)),x19645)) % 7.54/7.64 [1965]~P77(f118(f28(a119,x19652),x19651))+~P77(f118(f29(a119,f118(f118(f23(a119),f118(f118(f24(a119),x19651),x19653)),x19654)),f118(f118(f23(a119),f118(f118(f24(a119),x19652),x19653)),x19655)))+P77(f118(f29(a119,f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x19651,x19652)),x19653)),x19654)),x19655)) % 7.54/7.64 [1969]~P77(f118(f28(a119,x19694),x19691))+P77(f118(f28(a119,f118(f118(f23(a119),f118(f118(f24(a119),x19691),x19692)),x19693)),f118(f118(f23(a119),f118(f118(f24(a119),x19694),x19692)),x19695)))+~P77(f118(f28(a119,f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x19691,x19694)),x19692)),x19693)),x19695)) % 7.54/7.64 [1970]~P77(f118(f28(a119,x19704),x19701))+P77(f118(f29(a119,f118(f118(f23(a119),f118(f118(f24(a119),x19701),x19702)),x19703)),f118(f118(f23(a119),f118(f118(f24(a119),x19704),x19702)),x19705)))+~P77(f118(f29(a119,f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x19701,x19704)),x19702)),x19703)),x19705)) % 7.54/7.64 [1881]~P72(x18812)+~E(f118(f118(f23(x18812),f118(f118(f24(x18812),x18814),x18815)),x18811),f118(f118(f23(x18812),f118(f118(f24(x18812),x18813),x18815)),x18816))+E(x18811,f118(f118(f23(x18812),f118(f118(f24(x18812),f22(x18812,x18813,x18814)),x18815)),x18816)) % 7.54/7.64 [1882]~P72(x18821)+~E(f118(f118(f23(x18821),f118(f118(f24(x18821),x18822),x18824)),x18825),f118(f118(f23(x18821),f118(f118(f24(x18821),x18823),x18824)),x18826))+E(f118(f118(f23(x18821),f118(f118(f24(x18821),f22(x18821,x18822,x18823)),x18824)),x18825),x18826) % 7.54/7.64 [1893]~P72(x18931)+~E(x18936,f118(f118(f23(x18931),f118(f118(f24(x18931),f22(x18931,x18932,x18935)),x18933)),x18934))+E(f118(f118(f23(x18931),f118(f118(f24(x18931),x18932),x18933)),x18934),f118(f118(f23(x18931),f118(f118(f24(x18931),x18935),x18933)),x18936)) % 7.54/7.64 [1894]~P72(x18941)+~E(f118(f118(f23(x18941),f118(f118(f24(x18941),f22(x18941,x18942,x18945)),x18943)),x18944),x18946)+E(f118(f118(f23(x18941),f118(f118(f24(x18941),x18942),x18943)),x18944),f118(f118(f23(x18941),f118(f118(f24(x18941),x18945),x18943)),x18946)) % 7.54/7.64 [1956]~P67(x19561)+~P77(f118(f28(x19561,f118(f118(f23(x19561),f118(f118(f24(x19561),x19564),x19565)),x19562)),f118(f118(f23(x19561),f118(f118(f24(x19561),x19563),x19565)),x19566)))+P77(f118(f28(x19561,x19562),f118(f118(f23(x19561),f118(f118(f24(x19561),f22(x19561,x19563,x19564)),x19565)),x19566))) % 7.54/7.64 [1957]~P67(x19571)+~P77(f118(f29(x19571,f118(f118(f23(x19571),f118(f118(f24(x19571),x19574),x19575)),x19572)),f118(f118(f23(x19571),f118(f118(f24(x19571),x19573),x19575)),x19576)))+P77(f118(f29(x19571,x19572),f118(f118(f23(x19571),f118(f118(f24(x19571),f22(x19571,x19573,x19574)),x19575)),x19576))) % 7.54/7.64 [1961]~P67(x19611)+~P77(f118(f28(x19611,x19614),f118(f118(f23(x19611),f118(f118(f24(x19611),f22(x19611,x19615,x19612)),x19613)),x19616)))+P77(f118(f28(x19611,f118(f118(f23(x19611),f118(f118(f24(x19611),x19612),x19613)),x19614)),f118(f118(f23(x19611),f118(f118(f24(x19611),x19615),x19613)),x19616))) % 7.54/7.64 [1962]~P67(x19621)+~P77(f118(f29(x19621,x19624),f118(f118(f23(x19621),f118(f118(f24(x19621),f22(x19621,x19625,x19622)),x19623)),x19626)))+P77(f118(f29(x19621,f118(f118(f23(x19621),f118(f118(f24(x19621),x19622),x19623)),x19624)),f118(f118(f23(x19621),f118(f118(f24(x19621),x19625),x19623)),x19626))) % 7.54/7.64 [1967]~P67(x19671)+~P77(f118(f28(x19671,f118(f118(f23(x19671),f118(f118(f24(x19671),x19672),x19674)),x19675)),f118(f118(f23(x19671),f118(f118(f24(x19671),x19673),x19674)),x19676)))+P77(f118(f28(x19671,f118(f118(f23(x19671),f118(f118(f24(x19671),f22(x19671,x19672,x19673)),x19674)),x19675)),x19676)) % 7.54/7.64 [1968]~P67(x19681)+~P77(f118(f29(x19681,f118(f118(f23(x19681),f118(f118(f24(x19681),x19682),x19684)),x19685)),f118(f118(f23(x19681),f118(f118(f24(x19681),x19683),x19684)),x19686)))+P77(f118(f29(x19681,f118(f118(f23(x19681),f118(f118(f24(x19681),f22(x19681,x19682,x19683)),x19684)),x19685)),x19686)) % 7.54/7.64 [1972]~P67(x19721)+P77(f118(f28(x19721,f118(f118(f23(x19721),f118(f118(f24(x19721),x19722),x19723)),x19724)),f118(f118(f23(x19721),f118(f118(f24(x19721),x19725),x19723)),x19726)))+~P77(f118(f28(x19721,f118(f118(f23(x19721),f118(f118(f24(x19721),f22(x19721,x19722,x19725)),x19723)),x19724)),x19726)) % 7.54/7.64 [1973]~P67(x19731)+P77(f118(f29(x19731,f118(f118(f23(x19731),f118(f118(f24(x19731),x19732),x19733)),x19734)),f118(f118(f23(x19731),f118(f118(f24(x19731),x19735),x19733)),x19736)))+~P77(f118(f29(x19731,f118(f118(f23(x19731),f118(f118(f24(x19731),f22(x19731,x19732,x19735)),x19733)),x19734)),x19736)) % 7.54/7.64 [1136]E(x11361,f3(a115))+~E(f20(a115,x11362,x11361),f3(a115))+P77(f118(f29(a115,x11361),x11362))+P77(f118(f29(a115,x11362),x11361)) % 7.54/7.64 [1142]E(x11421,f3(a115))+~E(f20(a115,x11422,x11421),f3(a115))+P77(f118(f29(a115,x11422),x11421))+P77(f118(f28(a115,x11422),f3(a115))) % 7.54/7.64 [920]~P40(x9202)+~P75(x9202)+E(x9201,f3(a119))+E(f118(f118(f31(x9202),f3(x9202)),x9201),f3(x9202)) % 7.54/7.64 [1091]~E(x10912,f16(a115))+~E(x10911,f16(a115))+E(f118(f118(f24(a115),x10911),x10912),f16(a115))+~P77(f118(f29(a115,f3(a115)),x10911)) % 7.54/7.64 [1154]E(x11541,f3(a115))+~E(f20(a115,x11542,x11541),f3(a115))+P77(f118(f29(a115,x11541),x11542))+P77(f118(f28(a115,f3(a115)),x11542)) % 7.54/7.64 [1197]E(x11971,x11972)+~E(f34(x11971),f34(x11972))+~P77(f118(f29(a114,f3(a114)),x11972))+~P77(f118(f29(a114,f3(a114)),x11971)) % 7.54/7.64 [1402]~P77(f118(f28(a114,x14021),x14022))+P77(f118(f28(a114,f34(x14021)),f34(x14022)))+~P77(f118(f29(a114,f3(a114)),x14022))+~P77(f118(f29(a114,f3(a114)),x14021)) % 7.54/7.64 [1403]~P77(f118(f29(a114,x14031),x14032))+P77(f118(f29(a114,f34(x14031)),f34(x14032)))+~P77(f118(f29(a114,f3(a114)),x14032))+~P77(f118(f29(a114,f3(a114)),x14031)) % 7.54/7.64 [1423]~P77(f118(f28(a114,f34(x14231)),f34(x14232)))+P77(f118(f28(a114,x14231),x14232))+~P77(f118(f29(a114,f3(a114)),x14232))+~P77(f118(f29(a114,f3(a114)),x14231)) % 7.54/7.64 [1424]~P77(f118(f29(a114,f34(x14241)),f34(x14242)))+P77(f118(f29(a114,x14241),x14242))+~P77(f118(f29(a114,f3(a114)),x14242))+~P77(f118(f29(a114,f3(a114)),x14241)) % 7.54/7.64 [1045]~P46(x10453)+E(x10451,x10452)+P77(f118(f29(x10453,x10451),x10452))+P77(f118(f29(x10453,x10452),x10451)) % 7.54/7.64 [1046]~P34(x10463)+E(x10461,x10462)+P77(f118(f29(x10463,x10461),x10462))+P77(f118(f29(x10463,x10462),x10461)) % 7.54/7.64 [1050]~E(x10502,x10503)+~P34(x10501)+P77(f118(f29(x10501,x10502),x10503))+P77(f118(f28(x10501,x10502),x10503)) % 7.54/7.64 [1108]~P36(x11083)+E(x11081,x11082)+~P77(f118(f28(x11083,x11082),x11081))+P77(f118(f29(x11083,x11082),x11081)) % 7.54/7.64 [1110]~P34(x11103)+E(x11101,x11102)+~P77(f118(f28(x11103,x11101),x11102))+P77(f118(f29(x11103,x11101),x11102)) % 7.54/7.64 [1116]~P36(x11163)+E(x11161,x11162)+~P77(f118(f28(x11163,x11161),x11162))+P77(f118(f29(x11163,x11161),x11162)) % 7.54/7.64 [1171]E(x11711,x11712)+~P36(x11713)+~P77(f118(f28(x11713,x11712),x11711))+~P77(f118(f28(x11713,x11711),x11712)) % 7.54/7.64 [1203]~P27(x12031)+P77(f118(f29(x12031,x12033),x12032))+~P77(f118(f28(x12031,x12033),x12032))+P77(f118(f28(x12031,x12032),x12033)) % 7.54/7.64 [1239]~P77(f118(x12391,x12392))+~P77(f118(x12391,x12393))+~P77(f118(f28(a119,x12393),f53(x12392,x12391)))+P77(f118(x12391,f3(a119))) % 7.54/7.64 [1311]E(x13111,x13112)+~E(f22(a119,x13111,x13113),f22(a119,x13112,x13113))+~P77(f118(f28(a119,x13113),x13111))+~P77(f118(f28(a119,x13113),x13112)) % 7.54/7.64 [1358]P78(x13582,x13581,x13583)+E(x13581,f3(a115))+P77(f118(f28(a115,f3(a115)),f107(x13583,x13581,x13582)))+P77(f118(f29(a115,x13581),f3(a115))) % 7.54/7.64 [1386]P78(x13861,x13862,x13863)+P77(f118(f28(a115,f3(a115)),f107(x13863,x13862,x13861)))+~P77(f118(x13861,f3(a115)))+P77(f118(f29(a115,x13862),f3(a115))) % 7.54/7.64 [1415]P78(x14152,x14151,x14153)+E(x14151,f3(a115))+~P77(f118(x14152,f108(x14153,x14151,x14152)))+P77(f118(f29(a115,x14151),f3(a115))) % 7.54/7.64 [1461]P78(x14611,x14612,x14613)+~P77(f118(x14611,f108(x14613,x14612,x14611)))+~P77(f118(x14611,f3(a115)))+P77(f118(f29(a115,x14612),f3(a115))) % 7.54/7.64 [1511]P78(x15112,x15111,x15113)+E(x15111,f3(a115))+P77(f118(f28(a115,f3(a115)),f107(x15113,x15111,x15112)))+P77(f118(f29(a115,x15111),f106(x15113,x15111,x15112))) % 7.54/7.64 [1548]P78(x15481,x15482,x15483)+P77(f118(f28(a115,f3(a115)),f107(x15483,x15482,x15481)))+P77(f118(f29(a115,x15482),f106(x15483,x15482,x15481)))+~P77(f118(x15481,f3(a115))) % 7.54/7.64 [1558]P78(x15582,x15581,x15583)+E(x15581,f3(a115))+~P77(f118(x15582,f108(x15583,x15581,x15582)))+P77(f118(f29(a115,x15581),f106(x15583,x15581,x15582))) % 7.54/7.64 [1571]P78(x15712,x15711,x15713)+E(x15711,f3(a115))+P77(f118(f28(a115,f3(a115)),f107(x15713,x15711,x15712)))+~P77(f118(x15712,f112(x15713,x15711,x15712))) % 7.54/7.64 [1595]P78(x15951,x15952,x15953)+~P77(f118(x15951,f108(x15953,x15952,x15951)))+P77(f118(f29(a115,x15952),f106(x15953,x15952,x15951)))+~P77(f118(x15951,f3(a115))) % 7.54/7.64 [1597]P78(x15971,x15972,x15973)+P77(f118(f28(a115,f3(a115)),f107(x15973,x15972,x15971)))+~P77(f118(x15971,f112(x15973,x15972,x15971)))+~P77(f118(x15971,f3(a115))) % 7.54/7.64 [1606]~P32(x16061)+~P77(f118(f28(x16061,x16063),f3(x16061)))+~P77(f118(f28(x16061,x16062),f3(x16061)))+P77(f118(f28(x16061,f118(f118(f23(x16061),x16062),x16063)),f3(x16061))) % 7.54/7.64 [1607]~P32(x16071)+~P77(f118(f28(x16071,x16073),f3(x16071)))+~P77(f118(f29(x16071,x16072),f3(x16071)))+P77(f118(f29(x16071,f118(f118(f23(x16071),x16072),x16073)),f3(x16071))) % 7.54/7.64 [1608]~P32(x16081)+~P77(f118(f28(x16081,x16082),f3(x16081)))+~P77(f118(f29(x16081,x16083),f3(x16081)))+P77(f118(f29(x16081,f118(f118(f23(x16081),x16082),x16083)),f3(x16081))) % 7.54/7.64 [1609]~P32(x16091)+~P77(f118(f29(x16091,x16093),f3(x16091)))+~P77(f118(f29(x16091,x16092),f3(x16091)))+P77(f118(f29(x16091,f118(f118(f23(x16091),x16092),x16093)),f3(x16091))) % 7.54/7.64 [1616]P78(x16162,x16161,x16163)+E(x16161,f3(a115))+~P77(f118(x16162,f108(x16163,x16161,x16162)))+~P77(f118(x16162,f112(x16163,x16161,x16162))) % 7.54/7.64 [1646]P78(x16462,x16461,x16463)+E(x16461,f3(a115))+P77(f118(f28(a115,f3(a115)),f107(x16463,x16461,x16462)))+P77(f118(f28(a115,f106(x16463,x16461,x16462)),f3(a115))) % 7.54/7.64 [1661]P78(x16611,x16612,x16613)+~P77(f118(x16611,f108(x16613,x16612,x16611)))+~P77(f118(x16611,f112(x16613,x16612,x16611)))+~P77(f118(x16611,f3(a115))) % 7.54/7.64 [1674]P78(x16743,x16741,x16742)+E(x16741,f3(a115))+E(f118(f118(f23(a115),f118(f118(f24(a115),x16741),f108(x16742,x16741,x16743))),f107(x16742,x16741,x16743)),x16742)+P77(f118(f29(a115,x16741),f3(a115))) % 7.54/7.64 [1682]P78(x16821,x16822,x16823)+P77(f118(f28(a115,f3(a115)),f107(x16823,x16822,x16821)))+~P77(f118(x16821,f3(a115)))+P77(f118(f28(a115,f106(x16823,x16822,x16821)),f3(a115))) % 7.54/7.64 [1691]P78(x16912,x16911,x16913)+E(x16911,f3(a115))+~P77(f118(x16912,f108(x16913,x16911,x16912)))+P77(f118(f28(a115,f106(x16913,x16911,x16912)),f3(a115))) % 7.54/7.64 [1692]P78(x16923,x16921,x16922)+E(f118(f118(f23(a115),f118(f118(f24(a115),x16921),f108(x16922,x16921,x16923))),f107(x16922,x16921,x16923)),x16922)+~P77(f118(x16923,f3(a115)))+P77(f118(f29(a115,x16921),f3(a115))) % 7.54/7.64 [1713]~P57(x17131)+~P77(f118(f28(x17131,f118(f118(f24(x17131),x17133),x17132)),f3(x17131)))+P77(f118(f28(x17131,x17132),f3(x17131)))+P77(f118(f28(x17131,x17133),f3(x17131))) % 7.54/7.64 [1739]P78(x17391,x17392,x17393)+~P77(f118(x17391,f108(x17393,x17392,x17391)))+~P77(f118(x17391,f3(a115)))+P77(f118(f28(a115,f106(x17393,x17392,x17391)),f3(a115))) % 7.54/7.64 [1761]P78(x17613,x17611,x17612)+E(x17611,f3(a115))+E(f118(f118(f23(a115),f118(f118(f24(a115),x17611),f108(x17612,x17611,x17613))),f107(x17612,x17611,x17613)),x17612)+P77(f118(f29(a115,x17611),f106(x17612,x17611,x17613))) % 7.54/7.64 [1762]P78(x17623,x17621,x17622)+E(x17621,f3(a115))+E(f118(f118(f23(a115),f118(f118(f24(a115),x17621),f112(x17622,x17621,x17623))),f106(x17622,x17621,x17623)),x17622)+P77(f118(f28(a115,f3(a115)),f107(x17622,x17621,x17623))) % 7.54/7.64 [1771]P78(x17713,x17711,x17712)+E(f118(f118(f23(a115),f118(f118(f24(a115),x17711),f108(x17712,x17711,x17713))),f107(x17712,x17711,x17713)),x17712)+P77(f118(f29(a115,x17711),f106(x17712,x17711,x17713)))+~P77(f118(x17713,f3(a115))) % 7.54/7.64 [1772]P78(x17723,x17721,x17722)+E(f118(f118(f23(a115),f118(f118(f24(a115),x17721),f112(x17722,x17721,x17723))),f106(x17722,x17721,x17723)),x17722)+P77(f118(f28(a115,f3(a115)),f107(x17722,x17721,x17723)))+~P77(f118(x17723,f3(a115))) % 7.54/7.64 [1790]P78(x17903,x17901,x17902)+E(x17901,f3(a115))+E(f118(f118(f23(a115),f118(f118(f24(a115),x17901),f108(x17902,x17901,x17903))),f107(x17902,x17901,x17903)),x17902)+~P77(f118(x17903,f112(x17902,x17901,x17903))) % 7.54/7.64 [1791]P78(x17913,x17911,x17912)+E(x17911,f3(a115))+E(f118(f118(f23(a115),f118(f118(f24(a115),x17911),f112(x17912,x17911,x17913))),f106(x17912,x17911,x17913)),x17912)+~P77(f118(x17913,f108(x17912,x17911,x17913))) % 7.54/7.64 [1793]P78(x17933,x17931,x17932)+E(f118(f118(f23(a115),f118(f118(f24(a115),x17931),f108(x17932,x17931,x17933))),f107(x17932,x17931,x17933)),x17932)+~P77(f118(x17933,f112(x17932,x17931,x17933)))+~P77(f118(x17933,f3(a115))) % 7.54/7.64 [1794]P78(x17943,x17941,x17942)+E(f118(f118(f23(a115),f118(f118(f24(a115),x17941),f112(x17942,x17941,x17943))),f106(x17942,x17941,x17943)),x17942)+~P77(f118(x17943,f108(x17942,x17941,x17943)))+~P77(f118(x17943,f3(a115))) % 7.54/7.64 [1814]P78(x18143,x18141,x18142)+E(x18141,f3(a115))+E(f118(f118(f23(a115),f118(f118(f24(a115),x18141),f108(x18142,x18141,x18143))),f107(x18142,x18141,x18143)),x18142)+P77(f118(f28(a115,f106(x18142,x18141,x18143)),f3(a115))) % 7.54/7.64 [1832]P78(x18323,x18321,x18322)+E(f118(f118(f23(a115),f118(f118(f24(a115),x18321),f108(x18322,x18321,x18323))),f107(x18322,x18321,x18323)),x18322)+~P77(f118(x18323,f3(a115)))+P77(f118(f28(a115,f106(x18322,x18321,x18323)),f3(a115))) % 7.54/7.64 [1838]~P77(f118(f28(a119,x18383),x18381))+P77(f118(f28(a119,x18381),x18382))+~P77(f118(f28(a119,x18383),x18382))+~P77(f118(f28(a119,f22(a119,x18381,x18383)),f22(a119,x18382,x18383))) % 7.54/7.64 [1839]~P77(f118(f28(a119,x18393),x18391))+P77(f118(f29(a119,x18391),x18392))+~P77(f118(f28(a119,x18393),x18392))+~P77(f118(f29(a119,f22(a119,x18391,x18393)),f22(a119,x18392,x18393))) % 7.54/7.64 [1859]P78(x18593,x18591,x18592)+E(x18591,f3(a115))+E(f118(f118(f23(a115),f118(f118(f24(a115),x18591),f112(x18592,x18591,x18593))),f106(x18592,x18591,x18593)),x18592)+E(f118(f118(f23(a115),f118(f118(f24(a115),x18591),f108(x18592,x18591,x18593))),f107(x18592,x18591,x18593)),x18592) % 7.54/7.64 [1864]P78(x18643,x18641,x18642)+E(f118(f118(f23(a115),f118(f118(f24(a115),x18641),f112(x18642,x18641,x18643))),f106(x18642,x18641,x18643)),x18642)+E(f118(f118(f23(a115),f118(f118(f24(a115),x18641),f108(x18642,x18641,x18643))),f107(x18642,x18641,x18643)),x18642)+~P77(f118(x18643,f3(a115))) % 7.54/7.64 [1908]~P57(x19081)+~E(x19083,f3(x19081))+~E(x19082,f3(x19081))+P77(f118(f28(x19081,f118(f118(f23(x19081),f118(f118(f24(x19081),x19082),x19082)),f118(f118(f24(x19081),x19083),x19083))),f3(x19081))) % 7.54/7.64 [890]~E(x8903,x8901)+~P53(x8902)+E(x8901,f3(x8902))+E(f118(f118(f37(x8902),x8903),x8901),f16(x8902)) % 7.54/7.64 [942]~P53(x9423)+E(x9421,x9422)+E(x9422,f3(x9423))+~E(f118(f118(f37(x9423),x9421),x9422),f16(x9423)) % 7.54/7.64 [943]~P64(x9432)+E(x9431,f3(x9432))+E(x9433,f3(x9432))+~E(f118(f118(f24(x9432),x9433),x9431),f3(x9432)) % 7.54/7.64 [945]~P65(x9452)+E(x9451,f3(x9452))+E(x9453,f3(x9452))+~E(f118(f118(f24(x9452),x9453),x9451),f3(x9452)) % 7.54/7.64 [1192]P78(x11921,x11922,x11923)+~P77(f118(x11921,f3(a115)))+P77(f118(f29(a115,x11922),f3(a115)))+P77(f118(f29(a115,f3(a115)),x11922)) % 7.54/7.64 [1350]P78(x13502,x13501,x13503)+E(x13501,f3(a115))+P77(f118(f29(a115,x13501),f106(x13503,x13501,x13502)))+P77(f118(f29(a115,f3(a115)),x13501)) % 7.54/7.64 [1384]P78(x13841,x13842,x13843)+P77(f118(f29(a115,x13842),f106(x13843,x13842,x13841)))+~P77(f118(x13841,f3(a115)))+P77(f118(f29(a115,f3(a115)),x13842)) % 7.54/7.64 [1422]P78(x14222,x14221,x14223)+E(x14221,f3(a115))+~P77(f118(x14222,f112(x14223,x14221,x14222)))+P77(f118(f29(a115,f3(a115)),x14221)) % 7.54/7.64 [1469]P78(x14691,x14692,x14693)+~P77(f118(x14691,f112(x14693,x14692,x14691)))+~P77(f118(x14691,f3(a115)))+P77(f118(f29(a115,f3(a115)),x14692)) % 7.54/7.64 [1508]P78(x15082,x15081,x15083)+E(x15081,f3(a115))+P77(f118(f29(a115,x15081),f3(a115)))+P77(f118(f29(a115,f107(x15083,x15081,x15082)),x15081)) % 7.54/7.64 [1522]P78(x15222,x15221,x15223)+E(x15221,f3(a115))+P77(f118(f28(a115,f106(x15223,x15221,x15222)),f3(a115)))+P77(f118(f29(a115,f3(a115)),x15221)) % 7.54/7.64 [1546]P78(x15461,x15462,x15463)+~P77(f118(x15461,f3(a115)))+P77(f118(f29(a115,x15462),f3(a115)))+P77(f118(f29(a115,f107(x15463,x15462,x15461)),x15462)) % 7.54/7.64 [1551]P78(x15511,x15512,x15513)+~P77(f118(x15511,f3(a115)))+P77(f118(f28(a115,f106(x15513,x15512,x15511)),f3(a115)))+P77(f118(f29(a115,f3(a115)),x15512)) % 7.54/7.64 [1618]~P57(x16181)+~P77(f118(f28(x16181,x16183),f3(x16181)))+P77(f118(f28(x16181,f118(f118(f24(x16181),x16182),x16183)),f3(x16181)))+~P77(f118(f28(x16181,f3(x16181)),x16182)) % 7.54/7.64 [1619]~P57(x16191)+~P77(f118(f28(x16191,x16192),f3(x16191)))+P77(f118(f28(x16191,f118(f118(f24(x16191),x16192),x16193)),f3(x16191)))+~P77(f118(f28(x16191,f3(x16191)),x16193)) % 7.54/7.64 [1621]~P66(x16211)+~P77(f118(f28(x16211,x16213),f3(x16211)))+P77(f118(f28(x16211,f118(f118(f24(x16211),x16212),x16213)),f3(x16211)))+~P77(f118(f28(x16211,f3(x16211)),x16212)) % 7.54/7.64 [1623]~P66(x16231)+~P77(f118(f28(x16231,x16232),f3(x16231)))+P77(f118(f28(x16231,f118(f118(f24(x16231),x16232),x16233)),f3(x16231)))+~P77(f118(f28(x16231,f3(x16231)),x16233)) % 7.54/7.64 [1625]~P63(x16251)+~P77(f118(f29(x16251,x16253),f3(x16251)))+P77(f118(f29(x16251,f118(f118(f24(x16251),x16252),x16253)),f3(x16251)))+~P77(f118(f29(x16251,f3(x16251)),x16252)) % 7.54/7.64 [1626]~P63(x16261)+~P77(f118(f29(x16261,x16262),f3(x16261)))+P77(f118(f29(x16261,f118(f118(f24(x16261),x16262),x16263)),f3(x16261)))+~P77(f118(f29(x16261,f3(x16261)),x16263)) % 7.54/7.64 [1637]P78(x16372,x16371,x16373)+E(x16371,f3(a115))+P77(f118(f29(a115,x16371),f106(x16373,x16371,x16372)))+P77(f118(f29(a115,f107(x16373,x16371,x16372)),x16371)) % 7.54/7.64 [1675]P78(x16751,x16752,x16753)+P77(f118(f29(a115,x16752),f106(x16753,x16752,x16751)))+~P77(f118(x16751,f3(a115)))+P77(f118(f29(a115,f107(x16753,x16752,x16751)),x16752)) % 7.54/7.64 [1676]P78(x16763,x16761,x16762)+E(x16761,f3(a115))+E(f118(f118(f23(a115),f118(f118(f24(a115),x16761),f112(x16762,x16761,x16763))),f106(x16762,x16761,x16763)),x16762)+P77(f118(f29(a115,f3(a115)),x16761)) % 7.54/7.64 [1689]P78(x16892,x16891,x16893)+E(x16891,f3(a115))+~P77(f118(x16892,f112(x16893,x16891,x16892)))+P77(f118(f29(a115,f107(x16893,x16891,x16892)),x16891)) % 7.54/7.64 [1699]P78(x16993,x16991,x16992)+E(f118(f118(f23(a115),f118(f118(f24(a115),x16991),f112(x16992,x16991,x16993))),f106(x16992,x16991,x16993)),x16992)+~P77(f118(x16993,f3(a115)))+P77(f118(f29(a115,f3(a115)),x16991)) % 7.54/7.64 [1722]P78(x17221,x17222,x17223)+~P77(f118(x17221,f112(x17223,x17222,x17221)))+~P77(f118(x17221,f3(a115)))+P77(f118(f29(a115,f107(x17223,x17222,x17221)),x17222)) % 7.54/7.64 [1723]~P57(x17231)+~P77(f118(f28(x17231,f118(f118(f24(x17231),x17233),x17232)),f3(x17231)))+P77(f118(f28(x17231,x17232),f3(x17231)))+P77(f118(f28(x17231,f3(x17231)),x17232)) % 7.54/7.64 [1724]~P57(x17241)+~P77(f118(f28(x17241,f118(f118(f24(x17241),x17242),x17243)),f3(x17241)))+P77(f118(f28(x17241,x17242),f3(x17241)))+P77(f118(f28(x17241,f3(x17241)),x17242)) % 7.54/7.64 [1740]~P57(x17401)+~P77(f118(f28(x17401,f118(f118(f24(x17401),x17402),x17403)),f3(x17401)))+P77(f118(f28(x17401,f3(x17401)),x17402))+P77(f118(f28(x17401,f3(x17401)),x17403)) % 7.54/7.64 [1753]P78(x17532,x17531,x17533)+E(x17531,f3(a115))+P77(f118(f28(a115,f106(x17533,x17531,x17532)),f3(a115)))+P77(f118(f29(a115,f107(x17533,x17531,x17532)),x17531)) % 7.54/7.64 [1755]~P77(f118(f28(a115,x17552),x17553))+P77(f118(f28(a115,f20(a115,x17551,x17552)),f20(a115,x17551,x17553)))+~P77(f118(f29(a115,x17551),f3(a115)))+~P77(f118(f29(a115,f3(a115)),x17552)) % 7.54/7.64 [1757]~P77(f118(f28(a115,x17573),x17572))+P77(f118(f28(a115,f20(a115,x17571,x17572)),f20(a115,x17571,x17573)))+~P77(f118(f28(a115,f3(a115)),x17571))+~P77(f118(f29(a115,f3(a115)),x17573)) % 7.54/7.64 [1763]P78(x17631,x17632,x17633)+~P77(f118(x17631,f3(a115)))+P77(f118(f28(a115,f106(x17633,x17632,x17631)),f3(a115)))+P77(f118(f29(a115,f107(x17633,x17632,x17631)),x17632)) % 7.54/7.64 [1813]P78(x18133,x18131,x18132)+E(x18131,f3(a115))+E(f118(f118(f23(a115),f118(f118(f24(a115),x18131),f112(x18132,x18131,x18133))),f106(x18132,x18131,x18133)),x18132)+P77(f118(f29(a115,f107(x18132,x18131,x18133)),x18131)) % 7.54/7.64 [1831]P78(x18313,x18311,x18312)+E(f118(f118(f23(a115),f118(f118(f24(a115),x18311),f112(x18312,x18311,x18313))),f106(x18312,x18311,x18313)),x18312)+~P77(f118(x18313,f3(a115)))+P77(f118(f29(a115,f107(x18312,x18311,x18313)),x18311)) % 7.54/7.64 [1863]~P45(x18631)+~P77(f118(f29(x18631,x18632),f16(x18631)))+P77(f118(f29(x18631,f118(f118(f31(x18631),x18632),f118(f118(f23(a119),x18633),f16(a119)))),f16(x18631)))+~P77(f118(f29(x18631,f3(x18631)),x18632)) % 7.54/7.64 [1918]P77(f118(f28(a115,x19181),f3(a115)))+~P77(f118(f29(a115,f118(f118(f23(a115),f118(f118(f24(a115),x19183),x19181)),x19182)),f3(a115)))+~P77(f118(f28(a115,f3(a115)),x19182))+~P77(f118(f29(a115,f3(a115)),x19183)) % 7.54/7.64 [1950]~P37(x19501)+~P3(x19501,x19503)+~P3(x19501,x19502)+P3(x19501,f9(a119,x19501,x19501,f7(x19501,f121(x19501,x19501),a119,f23(x19501),x19502),x19503)) % 7.54/7.64 [1951]~P41(x19511)+~P3(x19511,x19513)+~P3(x19511,x19512)+P3(x19511,f9(a119,x19511,x19511,f7(x19511,f121(x19511,x19511),a119,f24(x19511),x19512),x19513)) % 7.54/7.64 [1283]~P57(x12831)+~E(x12833,f3(x12831))+~E(x12832,f3(x12831))+E(f118(f118(f23(x12831),f118(f118(f24(x12831),x12832),x12832)),f118(f118(f24(x12831),x12833),x12833)),f3(x12831)) % 7.54/7.64 [1450]~P70(x14501)+~P77(f118(f28(x14501,x14502),f3(x14501)))+~P77(f118(f28(x14501,x14503),f3(x14501)))+E(f118(f118(f24(x14501),f19(x14501,x14502)),f19(x14501,x14503)),f19(x14501,f118(f118(f24(x14501),x14502),x14503))) % 7.54/7.64 [1454]~E(f118(f118(f23(a115),x14542),f118(f118(f24(a115),x14543),x14541)),x14543)+~P77(f118(f29(a115,x14542),x14543))+~P77(f118(f29(a115,f3(a115)),x14543))+P77(f118(f28(a115,f16(a115)),x14541)) % 7.54/7.64 [1455]~P70(x14551)+~P77(f118(f28(x14551,x14552),f3(x14551)))+E(f118(f118(f24(x14551),f19(x14551,x14552)),f19(x14551,x14553)),f19(x14551,f118(f118(f24(x14551),x14552),x14553)))+~P77(f118(f28(x14551,f3(x14551)),x14553)) % 7.54/7.64 [1456]~P70(x14561)+~P77(f118(f28(x14561,x14563),f3(x14561)))+E(f118(f118(f24(x14561),f19(x14561,x14562)),f19(x14561,x14563)),f19(x14561,f118(f118(f24(x14561),x14562),x14563)))+~P77(f118(f28(x14561,f3(x14561)),x14562)) % 7.54/7.64 [1460]~E(f118(f118(f23(a115),x14602),f118(f118(f24(a115),x14603),x14601)),x14603)+P77(f118(f28(a115,x14601),f16(a115)))+~P77(f118(f28(a115,f3(a115)),x14602))+~P77(f118(f29(a115,f3(a115)),x14603)) % 7.54/7.64 [1470]~P70(x14701)+E(f118(f118(f24(x14701),f19(x14701,x14702)),f19(x14701,x14703)),f19(x14701,f118(f118(f24(x14701),x14702),x14703)))+~P77(f118(f28(x14701,f3(x14701)),x14702))+~P77(f118(f28(x14701,f3(x14701)),x14703)) % 7.54/7.64 [1484]~P57(x14841)+~P77(f118(f28(x14841,x14843),f3(x14841)))+~P77(f118(f28(x14841,x14842),f3(x14841)))+P77(f118(f28(x14841,f3(x14841)),f118(f118(f24(x14841),x14842),x14843))) % 7.54/7.64 [1486]~P67(x14861)+~P77(f118(f28(x14861,x14863),f3(x14861)))+~P77(f118(f28(x14861,x14862),f3(x14861)))+P77(f118(f28(x14861,f3(x14861)),f118(f118(f24(x14861),x14862),x14863))) % 7.54/7.64 [1487]~P57(x14871)+~P77(f118(f29(x14871,x14873),f3(x14871)))+~P77(f118(f29(x14871,x14872),f3(x14871)))+P77(f118(f29(x14871,f3(x14871)),f118(f118(f24(x14871),x14872),x14873))) % 7.54/7.64 [1502]~P45(x15021)+~P77(f118(f29(a119,f3(a119)),x15023))+~P77(f118(f29(x15021,f16(x15021)),x15022))+P77(f118(f29(x15021,f16(x15021)),f118(f118(f31(x15021),x15022),x15023))) % 7.54/7.64 [1513]~P57(x15131)+~P77(f118(f28(x15131,f3(x15131)),x15133))+~P77(f118(f28(x15131,f3(x15131)),x15132))+P77(f118(f28(x15131,f3(x15131)),f118(f118(f24(x15131),x15132),x15133))) % 7.54/7.64 [1514]~P66(x15141)+~P77(f118(f28(x15141,f3(x15141)),x15143))+~P77(f118(f28(x15141,f3(x15141)),x15142))+P77(f118(f28(x15141,f3(x15141)),f118(f118(f24(x15141),x15142),x15143))) % 7.54/7.64 [1515]~P67(x15151)+~P77(f118(f28(x15151,f3(x15151)),x15153))+~P77(f118(f28(x15151,f3(x15151)),x15152))+P77(f118(f28(x15151,f3(x15151)),f118(f118(f24(x15151),x15152),x15153))) % 7.54/7.64 [1518]~P32(x15181)+~P77(f118(f29(x15181,f3(x15181)),x15183))+~P77(f118(f29(x15181,f3(x15181)),x15182))+P77(f118(f29(x15181,f3(x15181)),f118(f118(f23(x15181),x15182),x15183))) % 7.54/7.64 [1519]~P63(x15191)+~P77(f118(f29(x15191,f3(x15191)),x15193))+~P77(f118(f29(x15191,f3(x15191)),x15192))+P77(f118(f29(x15191,f3(x15191)),f118(f118(f24(x15191),x15192),x15193))) % 7.54/7.64 [1520]~P45(x15201)+~P77(f118(f29(x15201,f16(x15201)),x15203))+~P77(f118(f29(x15201,f16(x15201)),x15202))+P77(f118(f29(x15201,f16(x15201)),f118(f118(f24(x15201),x15202),x15203))) % 7.54/7.64 [1540]~P57(x15401)+P77(f118(f28(x15401,x15402),f3(x15401)))+P77(f118(f28(x15401,f3(x15401)),x15403))+~P77(f118(f28(x15401,f3(x15401)),f118(f118(f24(x15401),x15403),x15402))) % 7.54/7.64 [1541]~P57(x15411)+P77(f118(f28(x15411,x15412),f3(x15411)))+P77(f118(f28(x15411,f3(x15411)),x15413))+~P77(f118(f28(x15411,f3(x15411)),f118(f118(f24(x15411),x15412),x15413))) % 7.54/7.64 [1542]~P57(x15421)+P77(f118(f28(x15421,x15422),f3(x15421)))+P77(f118(f28(x15421,f3(x15421)),x15422))+~P77(f118(f28(x15421,f3(x15421)),f118(f118(f24(x15421),x15423),x15422))) % 7.54/7.64 [1543]~P57(x15431)+P77(f118(f28(x15431,x15432),f3(x15431)))+P77(f118(f28(x15431,f3(x15431)),x15432))+~P77(f118(f28(x15431,f3(x15431)),f118(f118(f24(x15431),x15432),x15433))) % 7.54/7.64 [1590]~P63(x15901)+P77(f118(f29(x15901,f3(x15901)),x15902))+~P77(f118(f29(x15901,f3(x15901)),x15903))+~P77(f118(f29(x15901,f3(x15901)),f118(f118(f24(x15901),x15903),x15902))) % 7.54/7.64 [1591]~P63(x15911)+P77(f118(f29(x15911,f3(x15911)),x15912))+~P77(f118(f29(x15911,f3(x15911)),x15913))+~P77(f118(f29(x15911,f3(x15911)),f118(f118(f24(x15911),x15912),x15913))) % 7.54/7.64 [1870]~P45(x18701)+~P77(f118(f29(x18701,x18702),f16(x18701)))+~P77(f118(f29(x18701,f3(x18701)),x18702))+P77(f118(f29(x18701,f118(f118(f24(x18701),x18702),f118(f118(f31(x18701),x18702),x18703))),f118(f118(f31(x18701),x18702),x18703))) % 7.54/7.64 [1860]~P45(x18601)+~P77(f118(f28(x18601,x18602),f16(x18601)))+~P77(f118(f28(x18601,f3(x18601)),x18602))+P77(f118(f28(x18601,f118(f118(f31(x18601),x18602),f118(f118(f23(a119),x18603),f16(a119)))),x18602)) % 7.54/7.64 [1875]E(x18751,f20(a119,x18752,x18753))+~P77(f118(f29(a119,f3(a119)),x18753))+~P77(f118(f29(a119,x18752),f118(f118(f24(a119),x18753),f118(f118(f23(a119),x18751),f16(a119)))))+~P77(f118(f28(a119,f118(f118(f24(a119),x18753),x18751)),x18752)) % 7.54/7.64 [1902]~P57(x19022)+~E(x19021,f3(x19022))+~E(x19023,f3(x19022))+~P77(f118(f29(x19022,f3(x19022)),f118(f118(f23(x19022),f118(f118(f24(x19022),x19023),x19023)),f118(f118(f24(x19022),x19021),x19021)))) % 7.54/7.64 [1920]~P37(x19201)+P4(x19201,x19202)+~P77(f118(f29(a114,f3(a114)),x19203))+~P77(f118(f28(a114,f36(x19201,f118(x19202,f49(x19202,x19201,x19203)))),x19203)) % 7.54/7.64 [1921]~P37(x19211)+P4(x19211,x19212)+~P77(f118(f29(a114,f3(a114)),x19213))+~P77(f118(f28(a114,f36(x19211,f118(x19212,f51(x19212,x19213,x19211)))),x19213)) % 7.54/7.64 [1878]~P77(f118(f29(a115,x18782),x18783))+~P77(f118(f29(a115,f3(a115)),x18783))+P77(f118(f28(a115,f3(a115)),x18781))+~P77(f118(f28(a115,f3(a115)),f118(f118(f23(a115),f118(f118(f24(a115),x18783),x18781)),x18782))) % 7.54/7.64 [1249]~P36(x12491)+~P77(f118(f28(x12491,x12494),x12493))+P77(f118(f28(x12491,x12492),x12493))+~P77(f118(f28(x12491,x12492),x12494)) % 7.54/7.64 [1250]~P27(x12501)+~P77(f118(f28(x12501,x12502),x12504))+P77(f118(f28(x12501,x12502),x12503))+~P77(f118(f28(x12501,x12504),x12503)) % 7.54/7.64 [1251]~P36(x12511)+~P77(f118(f29(x12511,x12514),x12513))+P77(f118(f29(x12511,x12512),x12513))+~P77(f118(f28(x12511,x12512),x12514)) % 7.54/7.64 [1252]~P36(x12521)+~P77(f118(f29(x12521,x12522),x12524))+P77(f118(f29(x12521,x12522),x12523))+~P77(f118(f28(x12521,x12524),x12523)) % 7.54/7.64 [1253]~P36(x12531)+~P77(f118(f29(x12531,x12534),x12533))+P77(f118(f29(x12531,x12532),x12533))+~P77(f118(f29(x12531,x12532),x12534)) % 7.54/7.64 [1254]~P27(x12541)+~P77(f118(f29(x12541,x12542),x12544))+P77(f118(f29(x12541,x12542),x12543))+~P77(f118(f28(x12541,x12544),x12543)) % 7.54/7.64 [1255]~P27(x12551)+~P77(f118(f29(x12551,x12554),x12553))+P77(f118(f29(x12551,x12552),x12553))+~P77(f118(f28(x12551,x12552),x12554)) % 7.54/7.64 [1256]~P27(x12561)+~P77(f118(f29(x12561,x12562),x12564))+P77(f118(f29(x12561,x12562),x12563))+~P77(f118(f29(x12561,x12564),x12563)) % 7.54/7.64 [1284]~P36(x12841)+~P5(x12841,x12842)+P77(f118(f28(x12841,f118(x12842,x12843)),f118(x12842,x12844)))+~P77(f118(f28(a119,x12844),x12843)) % 7.54/7.64 [1285]~P36(x12851)+~P6(x12851,x12852)+P77(f118(f28(x12851,f118(x12852,x12853)),f118(x12852,x12854)))+~P77(f118(f28(a119,x12853),x12854)) % 7.54/7.64 [1889]~P77(f118(f29(a114,x18894),x18892))+P77(f118(f28(a114,x18891),x18892))+~P77(f118(f29(a114,x18893),x18894))+~P77(f118(f29(a114,f19(a114,f22(a114,x18894,x18891))),f102(x18892,x18894,x18893))) % 7.54/7.64 [1890]~P77(f118(f29(a114,x18901),x18903))+P77(f118(f28(a114,x18901),x18902))+~P77(f118(f29(a114,x18903),x18904))+~P77(f118(f29(a114,f19(a114,f22(a114,x18903,x18902))),f102(x18904,x18903,x18901))) % 7.54/7.64 [992]~P53(x9922)+E(x9921,f3(x9922))+~E(f118(f118(f37(x9922),x9923),x9921),x9924)+E(x9923,f118(f118(f24(x9922),x9924),x9921)) % 7.54/7.64 [994]~P53(x9942)+E(x9941,f3(x9942))+~E(f118(f118(f24(x9942),x9943),x9941),x9944)+E(x9943,f118(f118(f37(x9942),x9944),x9941)) % 7.54/7.64 [995]~P53(x9952)+E(x9951,f3(x9952))+~E(x9953,f118(f118(f37(x9952),x9954),x9951))+E(f118(f118(f24(x9952),x9953),x9951),x9954) % 7.54/7.64 [997]~P53(x9972)+E(x9971,f3(x9972))+~E(x9973,f118(f118(f24(x9972),x9974),x9971))+E(f118(f118(f37(x9972),x9973),x9971),x9974) % 7.54/7.64 [1245]~P45(x12453)+E(x12451,x12452)+~E(f118(f118(f31(x12453),x12454),x12451),f118(f118(f31(x12453),x12454),x12452))+~P77(f118(f29(x12453,f16(x12453)),x12454)) % 7.54/7.64 [1530]~P35(x15302)+P77(f118(f29(f121(x15301,x15302),x15304),x15303))+~P77(f118(f28(f121(x15301,x15302),x15304),x15303))+P77(f118(f28(f121(x15301,x15302),x15303),x15304)) % 7.54/7.64 [1648]~P37(x16482)+E(x16481,f3(x16482))+~P77(f118(f28(a114,x16483),f3(a114)))+~P77(f118(f28(a114,f36(x16482,x16481)),f118(f118(f24(a114),x16483),f36(x16482,x16484)))) % 7.54/7.64 [1471]~P32(x14711)+~P77(f118(f28(x14711,x14712),x14713))+~P77(f118(f28(x14711,f3(x14711)),x14714))+P77(f118(f28(x14711,x14712),f118(f118(f23(x14711),x14713),x14714))) % 7.54/7.64 [1472]~P32(x14721)+~P77(f118(f28(x14721,x14722),x14724))+~P77(f118(f28(x14721,f3(x14721)),x14723))+P77(f118(f28(x14721,x14722),f118(f118(f23(x14721),x14723),x14724))) % 7.54/7.64 [1473]~P32(x14731)+~P77(f118(f28(x14731,x14732),x14734))+~P77(f118(f29(x14731,f3(x14731)),x14733))+P77(f118(f29(x14731,x14732),f118(f118(f23(x14731),x14733),x14734))) % 7.54/7.64 [1474]~P32(x14741)+~P77(f118(f29(x14741,x14742),x14744))+~P77(f118(f28(x14741,f3(x14741)),x14743))+P77(f118(f29(x14741,x14742),f118(f118(f23(x14741),x14743),x14744))) % 7.54/7.64 [1475]~P45(x14751)+~P77(f118(f29(x14751,x14752),x14754))+~P77(f118(f29(x14751,f3(x14751)),x14753))+P77(f118(f29(x14751,x14752),f118(f118(f23(x14751),x14753),x14754))) % 7.54/7.64 [1509]~P13(x15092)+E(x15091,f3(x15092))+E(f118(f118(f37(x15092),f118(f118(f31(x15092),x15091),x15093)),f118(f118(f31(x15092),x15091),x15094)),f118(f118(f31(x15092),x15091),f22(a119,x15093,x15094)))+~P77(f118(f28(a119,x15094),x15093)) % 7.54/7.64 [1702]~P57(x17021)+~P77(f118(f28(x17021,x17024),x17023))+~P77(f118(f29(x17021,x17022),f3(x17021)))+P77(f118(f28(x17021,f118(f118(f24(x17021),x17022),x17023)),f118(f118(f24(x17021),x17022),x17024))) % 7.54/7.64 [1703]~P67(x17031)+~P77(f118(f28(x17031,x17034),x17033))+~P77(f118(f28(x17031,x17032),f3(x17031)))+P77(f118(f28(x17031,f118(f118(f24(x17031),x17032),x17033)),f118(f118(f24(x17031),x17032),x17034))) % 7.54/7.64 [1704]~P67(x17041)+~P77(f118(f28(x17041,x17044),x17042))+~P77(f118(f28(x17041,x17043),f3(x17041)))+P77(f118(f28(x17041,f118(f118(f24(x17041),x17042),x17043)),f118(f118(f24(x17041),x17044),x17043))) % 7.54/7.64 [1708]~P57(x17081)+~P77(f118(f29(x17081,x17084),x17082))+~P77(f118(f29(x17081,x17083),f3(x17081)))+P77(f118(f29(x17081,f118(f118(f24(x17081),x17082),x17083)),f118(f118(f24(x17081),x17084),x17083))) % 7.54/7.64 [1709]~P57(x17091)+~P77(f118(f29(x17091,x17094),x17093))+~P77(f118(f29(x17091,x17092),f3(x17091)))+P77(f118(f29(x17091,f118(f118(f24(x17091),x17092),x17093)),f118(f118(f24(x17091),x17092),x17094))) % 7.54/7.64 [1714]~P45(x17141)+~P77(f118(f28(a119,x17143),x17144))+~P77(f118(f29(x17141,f16(x17141)),x17142))+P77(f118(f28(x17141,f118(f118(f31(x17141),x17142),x17143)),f118(f118(f31(x17141),x17142),x17144))) % 7.54/7.64 [1715]~P45(x17151)+~P77(f118(f28(a119,x17153),x17154))+~P77(f118(f28(x17151,f16(x17151)),x17152))+P77(f118(f28(x17151,f118(f118(f31(x17151),x17152),x17153)),f118(f118(f31(x17151),x17152),x17154))) % 7.54/7.64 [1717]~P45(x17171)+~P77(f118(f29(a119,x17173),x17174))+~P77(f118(f29(x17171,f16(x17171)),x17172))+P77(f118(f29(x17171,f118(f118(f31(x17171),x17172),x17173)),f118(f118(f31(x17171),x17172),x17174))) % 7.54/7.64 [1725]~P57(x17251)+~P77(f118(f28(x17251,x17253),x17254))+~P77(f118(f29(x17251,f3(x17251)),x17252))+P77(f118(f28(x17251,f118(f118(f24(x17251),x17252),x17253)),f118(f118(f24(x17251),x17252),x17254))) % 7.54/7.64 [1726]~P69(x17261)+~P77(f118(f28(x17261,x17263),x17264))+~P77(f118(f28(x17261,f3(x17261)),x17262))+P77(f118(f28(x17261,f118(f118(f24(x17261),x17262),x17263)),f118(f118(f24(x17261),x17262),x17264))) % 7.54/7.64 [1727]~P68(x17271)+~P77(f118(f28(x17271,x17273),x17274))+~P77(f118(f28(x17271,f3(x17271)),x17272))+P77(f118(f28(x17271,f118(f118(f24(x17271),x17272),x17273)),f118(f118(f24(x17271),x17272),x17274))) % 7.54/7.64 [1728]~P69(x17281)+~P77(f118(f28(x17281,x17282),x17284))+~P77(f118(f28(x17281,f3(x17281)),x17283))+P77(f118(f28(x17281,f118(f118(f24(x17281),x17282),x17283)),f118(f118(f24(x17281),x17284),x17283))) % 7.54/7.64 [1729]~P45(x17291)+~P77(f118(f28(x17291,x17292),x17294))+~P77(f118(f28(x17291,f3(x17291)),x17292))+P77(f118(f28(x17291,f118(f118(f31(x17291),x17292),x17293)),f118(f118(f31(x17291),x17294),x17293))) % 7.54/7.64 [1731]~P63(x17311)+~P77(f118(f29(x17311,x17313),x17314))+~P77(f118(f29(x17311,f3(x17311)),x17312))+P77(f118(f29(x17311,f118(f118(f24(x17311),x17312),x17313)),f118(f118(f24(x17311),x17312),x17314))) % 7.54/7.64 [1732]~P52(x17321)+~P77(f118(f29(x17321,x17323),x17324))+~P77(f118(f29(x17321,f3(x17321)),x17322))+P77(f118(f29(x17321,f118(f118(f24(x17321),x17322),x17323)),f118(f118(f24(x17321),x17322),x17324))) % 7.54/7.64 [1733]~P57(x17331)+~P77(f118(f29(x17331,x17332),x17334))+~P77(f118(f29(x17331,f3(x17331)),x17333))+P77(f118(f29(x17331,f118(f118(f24(x17331),x17332),x17333)),f118(f118(f24(x17331),x17334),x17333))) % 7.54/7.64 [1734]~P63(x17341)+~P77(f118(f29(x17341,x17342),x17344))+~P77(f118(f29(x17341,f3(x17341)),x17343))+P77(f118(f29(x17341,f118(f118(f24(x17341),x17342),x17343)),f118(f118(f24(x17341),x17344),x17343))) % 7.54/7.64 [1735]~P57(x17351)+~P77(f118(f29(x17351,x17353),x17354))+~P77(f118(f29(x17351,f3(x17351)),x17352))+P77(f118(f29(x17351,f118(f118(f24(x17351),x17352),x17353)),f118(f118(f24(x17351),x17352),x17354))) % 7.54/7.64 [1797]~P57(x17971)+P77(f118(f29(x17971,x17973),x17972))+P77(f118(f29(x17971,x17972),x17973))+~P77(f118(f29(x17971,f118(f118(f24(x17971),x17974),x17972)),f118(f118(f24(x17971),x17974),x17973))) % 7.54/7.64 [1798]~P57(x17981)+P77(f118(f29(x17981,x17983),x17982))+P77(f118(f29(x17981,x17982),x17983))+~P77(f118(f29(x17981,f118(f118(f24(x17981),x17982),x17984)),f118(f118(f24(x17981),x17983),x17984))) % 7.54/7.64 [1799]~P57(x17991)+P77(f118(f29(x17991,x17992),x17993))+P77(f118(f29(x17991,x17994),f3(x17991)))+~P77(f118(f29(x17991,f118(f118(f24(x17991),x17992),x17994)),f118(f118(f24(x17991),x17993),x17994))) % 7.54/7.64 [1800]~P57(x18001)+P77(f118(f29(x18001,x18002),x18003))+P77(f118(f29(x18001,x18004),f3(x18001)))+~P77(f118(f29(x18001,f118(f118(f24(x18001),x18004),x18002)),f118(f118(f24(x18001),x18004),x18003))) % 7.54/7.64 [1803]~P57(x18031)+P77(f118(f29(x18031,x18032),x18033))+P77(f118(f29(x18031,f3(x18031)),x18034))+~P77(f118(f29(x18031,f118(f118(f24(x18031),x18034),x18033)),f118(f118(f24(x18031),x18034),x18032))) % 7.54/7.64 [1804]~P57(x18041)+P77(f118(f29(x18041,x18042),x18043))+P77(f118(f29(x18041,f3(x18041)),x18044))+~P77(f118(f29(x18041,f118(f118(f24(x18041),x18043),x18044)),f118(f118(f24(x18041),x18042),x18044))) % 7.54/7.64 [1811]~P57(x18111)+P77(f118(f29(x18111,x18112),f3(x18111)))+P77(f118(f29(x18111,f3(x18111)),x18112))+~P77(f118(f29(x18111,f118(f118(f24(x18111),x18113),x18112)),f118(f118(f24(x18111),x18114),x18112))) % 7.54/7.64 [1812]~P57(x18121)+P77(f118(f29(x18121,x18122),f3(x18121)))+P77(f118(f29(x18121,f3(x18121)),x18122))+~P77(f118(f29(x18121,f118(f118(f24(x18121),x18122),x18123)),f118(f118(f24(x18121),x18122),x18124))) % 7.54/7.64 [1815]~P57(x18151)+P77(f118(f28(x18151,x18152),x18153))+~P77(f118(f29(x18151,x18154),f3(x18151)))+~P77(f118(f28(x18151,f118(f118(f24(x18151),x18154),x18153)),f118(f118(f24(x18151),x18154),x18152))) % 7.54/7.64 [1816]~P57(x18161)+P77(f118(f29(x18161,x18162),x18163))+~P77(f118(f29(x18161,x18164),f3(x18161)))+~P77(f118(f29(x18161,f118(f118(f24(x18161),x18164),x18163)),f118(f118(f24(x18161),x18164),x18162))) % 7.54/7.64 [1818]~P45(x18183)+P77(f118(f28(a119,x18181),x18182))+~P77(f118(f29(x18183,f16(x18183)),x18184))+~P77(f118(f28(x18183,f118(f118(f31(x18183),x18184),x18181)),f118(f118(f31(x18183),x18184),x18182))) % 7.54/7.64 [1820]~P45(x18203)+P77(f118(f29(a119,x18201),x18202))+~P77(f118(f29(x18203,f16(x18203)),x18204))+~P77(f118(f29(x18203,f118(f118(f31(x18203),x18204),x18201)),f118(f118(f31(x18203),x18204),x18202))) % 7.54/7.64 [1821]~P57(x18211)+P77(f118(f28(x18211,x18212),x18213))+~P77(f118(f29(x18211,f3(x18211)),x18214))+~P77(f118(f28(x18211,f118(f118(f24(x18211),x18214),x18212)),f118(f118(f24(x18211),x18214),x18213))) % 7.54/7.64 [1822]~P63(x18221)+P77(f118(f28(x18221,x18222),x18223))+~P77(f118(f29(x18221,f3(x18221)),x18224))+~P77(f118(f28(x18221,f118(f118(f24(x18221),x18224),x18222)),f118(f118(f24(x18221),x18224),x18223))) % 7.54/7.64 [1823]~P63(x18231)+P77(f118(f28(x18231,x18232),x18233))+~P77(f118(f29(x18231,f3(x18231)),x18234))+~P77(f118(f28(x18231,f118(f118(f24(x18231),x18232),x18234)),f118(f118(f24(x18231),x18233),x18234))) % 7.54/7.64 [1824]~P57(x18241)+P77(f118(f29(x18241,x18242),x18243))+~P77(f118(f29(x18241,f3(x18241)),x18244))+~P77(f118(f29(x18241,f118(f118(f24(x18241),x18244),x18242)),f118(f118(f24(x18241),x18244),x18243))) % 7.54/7.64 [1825]~P63(x18251)+P77(f118(f29(x18251,x18252),x18253))+~P77(f118(f28(x18251,f3(x18251)),x18254))+~P77(f118(f29(x18251,f118(f118(f24(x18251),x18254),x18252)),f118(f118(f24(x18251),x18254),x18253))) % 7.54/7.64 [1826]~P60(x18261)+P77(f118(f29(x18261,x18262),x18263))+~P77(f118(f28(x18261,f3(x18261)),x18264))+~P77(f118(f29(x18261,f118(f118(f24(x18261),x18264),x18262)),f118(f118(f24(x18261),x18264),x18263))) % 7.54/7.64 [1827]~P45(x18271)+P77(f118(f29(x18271,x18272),x18273))+~P77(f118(f28(x18271,f3(x18271)),x18273))+~P77(f118(f29(x18271,f118(f118(f31(x18271),x18272),x18274)),f118(f118(f31(x18271),x18273),x18274))) % 7.54/7.64 [1828]~P63(x18281)+P77(f118(f29(x18281,x18282),x18283))+~P77(f118(f28(x18281,f3(x18281)),x18284))+~P77(f118(f29(x18281,f118(f118(f24(x18281),x18282),x18284)),f118(f118(f24(x18281),x18283),x18284))) % 7.54/7.64 [1829]~P60(x18291)+P77(f118(f29(x18291,x18292),x18293))+~P77(f118(f28(x18291,f3(x18291)),x18294))+~P77(f118(f29(x18291,f118(f118(f24(x18291),x18292),x18294)),f118(f118(f24(x18291),x18293),x18294))) % 7.54/7.64 [1865]~P36(x18651)+~P2(x18651,x18652)+P77(f118(f28(x18651,f118(x18652,f118(f118(f23(a119),x18654),f16(a119)))),f118(x18652,x18654)))+P77(f118(f28(x18651,f118(x18652,x18653)),f118(x18652,f118(f118(f23(a119),x18653),f16(a119))))) % 7.54/7.64 [1897]~P46(x18971)+~P77(f118(f29(x18971,f22(x18971,x18973,x18974)),x18972))+~P77(f118(f29(x18971,x18972),f118(f118(f23(x18971),x18973),x18974)))+P77(f118(f29(x18971,f19(x18971,f22(x18971,x18972,x18973))),x18974)) % 7.54/7.64 [1912]~P45(x19121)+P77(f118(f28(x19121,x19122),x19123))+~P77(f118(f28(x19121,f3(x19121)),x19123))+~P77(f118(f28(x19121,f118(f118(f31(x19121),x19122),f118(f118(f23(a119),x19124),f16(a119)))),f118(f118(f31(x19121),x19123),f118(f118(f23(a119),x19124),f16(a119))))) % 7.54/7.64 [1885]~P77(f118(x18851,x18854))+P77(f118(x18851,f20(a119,x18852,x18853)))+~P77(f118(f29(a119,x18852),f118(f118(f24(a119),x18853),f118(f118(f23(a119),x18854),f16(a119)))))+~P77(f118(f28(a119,f118(f118(f24(a119),x18853),x18854)),x18852)) % 7.54/7.64 [1939]~P37(x19391)+~P77(f118(f29(a114,f3(a114)),x19394))+P77(f118(f28(a114,f36(x19391,f118(x19392,x19393))),f35(a119,f118(f118(f23(a119),f81(x19392,x19391)),f16(a119)))))+~P77(f118(f28(a114,f36(x19391,f118(x19392,f82(x19392,x19391,x19394)))),x19394)) % 7.54/7.64 [1940]~P37(x19401)+~P77(f118(f29(a114,f3(a114)),x19404))+P77(f118(f29(a114,f36(x19401,f118(x19402,x19403))),f35(a119,f118(f118(f23(a119),f78(x19402,x19401)),f16(a119)))))+~P77(f118(f28(a114,f36(x19401,f118(x19402,f71(x19402,x19401,x19404)))),x19404)) % 7.54/7.64 [1059]~P10(x10595)+E(x10591,x10592)+~E(x10593,x10594)+~E(f22(x10595,x10593,x10594),f22(x10595,x10591,x10592)) % 7.54/7.64 [1297]~P26(x12971)+~E(f22(x12971,x12974,x12975),f22(x12971,x12972,x12973))+~P77(f118(f28(x12971,x12974),x12975))+P77(f118(f28(x12971,x12972),x12973)) % 7.54/7.64 [1299]~P26(x12991)+~E(f22(x12991,x12994,x12995),f22(x12991,x12992,x12993))+~P77(f118(f29(x12991,x12994),x12995))+P77(f118(f29(x12991,x12992),x12993)) % 7.54/7.64 [1695]~P30(x16951)+~P77(f118(f28(x16951,x16953),x16955))+~P77(f118(f28(x16951,x16952),x16954))+P77(f118(f28(x16951,f118(f118(f23(x16951),x16952),x16953)),f118(f118(f23(x16951),x16954),x16955))) % 7.54/7.64 [1696]~P31(x16961)+~P77(f118(f28(x16961,x16963),x16965))+~P77(f118(f29(x16961,x16962),x16964))+P77(f118(f29(x16961,f118(f118(f23(x16961),x16962),x16963)),f118(f118(f23(x16961),x16964),x16965))) % 7.54/7.64 [1697]~P31(x16971)+~P77(f118(f28(x16971,x16972),x16974))+~P77(f118(f29(x16971,x16973),x16975))+P77(f118(f29(x16971,f118(f118(f23(x16971),x16972),x16973)),f118(f118(f23(x16971),x16974),x16975))) % 7.54/7.64 [1698]~P31(x16981)+~P77(f118(f29(x16981,x16983),x16985))+~P77(f118(f29(x16981,x16982),x16984))+P77(f118(f29(x16981,f118(f118(f23(x16981),x16982),x16983)),f118(f118(f23(x16981),x16984),x16985))) % 7.54/7.64 [1768]~P76(x17685)+E(x17681,x17682)+E(x17683,x17684)+~E(f118(f118(f23(x17685),f118(f118(f24(x17685),x17683),x17681)),f118(f118(f24(x17685),x17684),x17682)),f118(f118(f23(x17685),f118(f118(f24(x17685),x17683),x17682)),f118(f118(f24(x17685),x17684),x17681))) % 7.54/7.64 [1868]~P37(x18681)+~P77(f118(f29(a114,f36(x18681,x18683)),x18685))+~P77(f118(f29(a114,f36(x18681,x18682)),x18684))+P77(f118(f29(a114,f36(x18681,f118(f118(f23(x18681),x18682),x18683))),f118(f118(f23(a114),x18684),x18685))) % 7.54/7.64 [1869]~P41(x18691)+~P77(f118(f29(a114,f36(x18691,x18693)),x18695))+~P77(f118(f29(a114,f36(x18691,x18692)),x18694))+P77(f118(f29(a114,f36(x18691,f118(f118(f24(x18691),x18692),x18693))),f118(f118(f24(a114),x18694),x18695))) % 7.54/7.64 [1879]~P46(x18791)+~P77(f118(f29(x18791,f19(x18791,x18792)),x18794))+~P77(f118(f29(x18791,f19(x18791,x18793)),x18795))+P77(f118(f29(x18791,f118(f118(f24(x18791),f19(x18791,x18792)),f19(x18791,x18793))),f118(f118(f24(x18791),x18794),x18795))) % 7.54/7.64 [1924]~E(f36(a117,x19241),f16(a114))+P77(f118(f29(a114,f36(a117,f118(f118(f23(a117),x19241),f16(a117)))),f16(a114)))+P77(f118(f29(a114,f36(a117,f22(a117,x19241,f16(a117)))),f16(a114)))+P77(f118(f29(a114,f36(a117,f118(f118(f23(a117),x19241),a17))),f16(a114)))+P77(f118(f29(a114,f36(a117,f22(a117,x19241,a17))),f16(a114))) % 7.54/7.64 [1348]~P32(x13482)+E(x13481,f3(x13482))+~E(f118(f118(f23(x13482),x13483),x13481),f3(x13482))+~P77(f118(f28(x13482,f3(x13482)),x13483))+~P77(f118(f28(x13482,f3(x13482)),x13481)) % 7.54/7.64 [1349]~P32(x13492)+E(x13491,f3(x13492))+~E(f118(f118(f23(x13492),x13491),x13493),f3(x13492))+~P77(f118(f28(x13492,f3(x13492)),x13493))+~P77(f118(f28(x13492,f3(x13492)),x13491)) % 7.54/7.64 [1397]E(x13971,f66(x13972,x13973))+~E(f118(f118(f31(a114),x13971),x13973),x13972)+~P77(f118(f29(a114,f3(a114)),x13972))+~P77(f118(f29(a114,f3(a114)),x13971))+~P77(f118(f29(a119,f3(a119)),x13973)) % 7.54/7.64 [1710]~P46(x17101)+~P77(f118(f28(x17101,x17102),f16(x17101)))+~P77(f118(f28(x17101,f3(x17101)),x17102))+~P77(f118(f28(x17101,f3(x17101)),x17103))+P77(f118(f28(x17101,f118(f118(f24(x17101),x17102),x17103)),x17103)) % 7.54/7.64 [1711]~P46(x17111)+~P77(f118(f28(x17111,x17113),f16(x17111)))+~P77(f118(f28(x17111,f3(x17111)),x17113))+~P77(f118(f28(x17111,f3(x17111)),x17112))+P77(f118(f28(x17111,f118(f118(f24(x17111),x17112),x17113)),x17112)) % 7.54/7.64 [1610]~P45(x16103)+E(x16101,x16102)+~E(f118(f118(f31(x16103),x16101),f118(f118(f23(a119),x16104),f16(a119))),f118(f118(f31(x16103),x16102),f118(f118(f23(a119),x16104),f16(a119))))+~P77(f118(f28(x16103,f3(x16103)),x16102))+~P77(f118(f28(x16103,f3(x16103)),x16101)) % 7.54/7.64 [1764]~P45(x17641)+~P77(f118(f28(x17641,x17642),f16(x17641)))+~P77(f118(f28(a119,x17644),x17643))+~P77(f118(f28(x17641,f3(x17641)),x17642))+P77(f118(f28(x17641,f118(f118(f31(x17641),x17642),x17643)),f118(f118(f31(x17641),x17642),x17644))) % 7.54/7.64 [1765]~P45(x17651)+~P77(f118(f29(x17651,x17652),f16(x17651)))+~P77(f118(f29(a119,x17654),x17653))+~P77(f118(f29(x17651,f3(x17651)),x17652))+P77(f118(f29(x17651,f118(f118(f31(x17651),x17652),x17653)),f118(f118(f31(x17651),x17652),x17654))) % 7.54/7.64 [1766]~P45(x17661)+~P77(f118(f29(x17661,x17662),x17664))+~P77(f118(f28(x17661,f3(x17661)),x17662))+~P77(f118(f29(a119,f3(a119)),x17663))+P77(f118(f29(x17661,f118(f118(f31(x17661),x17662),x17663)),f118(f118(f31(x17661),x17664),x17663))) % 7.54/7.64 [1841]~P14(x18411)+~P77(f118(f28(x18411,x18413),x18414))+~P77(f118(f28(x18411,x18412),f3(x18411)))+~P77(f118(f29(x18411,f3(x18411)),f118(f118(f24(x18411),x18413),x18414)))+P77(f118(f28(x18411,f118(f118(f37(x18411),x18412),x18413)),f118(f118(f37(x18411),x18412),x18414))) % 7.54/7.64 [1843]~P15(x18431)+~P77(f118(f28(x18431,x18434),x18433))+~P77(f118(f28(x18431,f3(x18431)),x18432))+~P77(f118(f29(x18431,f3(x18431)),f118(f118(f24(x18431),x18433),x18434)))+P77(f118(f28(x18431,f118(f118(f37(x18431),x18432),x18433)),f118(f118(f37(x18431),x18432),x18434))) % 7.54/7.64 [1886]~P35(x18861)+~P37(x18864)+P77(f118(f28(x18861,x18862),f103(x18863,x18862,x18861,x18864)))+~P77(f118(f28(x18861,x18862),x18865))+P77(f118(f29(a114,f36(x18864,f118(x18863,x18865))),f118(f118(f23(a114),f16(a114)),f36(x18864,f118(x18863,x18862))))) % 7.54/7.64 [1974]~P37(x19741)+~P35(x19745)+~P77(f118(f28(x19745,x19744),x19743))+~P77(f118(f29(a114,f36(x19741,f22(x19741,f118(x19742,x19744),f118(x19742,f103(x19742,x19744,x19745,x19741))))),f16(a114)))+P77(f118(f29(a114,f36(x19741,f118(x19742,x19743))),f118(f118(f23(a114),f16(a114)),f36(x19741,f118(x19742,x19744))))) % 7.54/7.64 [1667]E(x16671,f3(a119))+P77(f118(x16672,x16673))+~P77(f118(x16672,f20(a119,x16674,x16671)))+~P77(f118(f29(a119,x16675),x16671))+~E(x16674,f118(f118(f23(a119),f118(f118(f24(a119),x16671),x16673)),x16675)) % 7.54/7.64 [1941]~P77(f118(f29(a115,x19413),x19415))+P77(f118(f28(a115,x19411),x19412))+~P77(f118(f29(a115,x19413),x19414))+~P77(f118(f28(a115,x19414),f3(a115)))+~P77(f118(f28(a115,f118(f118(f23(a115),f118(f118(f24(a115),x19413),x19412)),x19415)),f118(f118(f23(a115),f118(f118(f24(a115),x19413),x19411)),x19414))) % 7.54/7.64 [1942]P77(f118(f28(a115,x19421),x19422))+~P77(f118(f29(a115,x19423),x19424))+~P77(f118(f29(a115,x19425),x19424))+~P77(f118(f28(a115,f3(a115)),x19425))+~P77(f118(f28(a115,f118(f118(f23(a115),f118(f118(f24(a115),x19424),x19421)),x19425)),f118(f118(f23(a115),f118(f118(f24(a115),x19424),x19422)),x19423))) % 7.54/7.64 [1394]~P76(x13944)+E(x13941,x13942)+~E(x13945,x13946)+E(x13943,f3(x13944))+~E(f118(f118(f23(x13944),x13945),f118(f118(f24(x13944),x13943),x13941)),f118(f118(f23(x13944),x13946),f118(f118(f24(x13944),x13943),x13942))) % 7.54/7.64 [953]~P58(x9532)+~P62(x9532)+~P65(x9532)+~P40(x9532)+E(x9531,f3(x9532))+~E(f118(f118(f31(x9532),x9531),x9533),f3(x9532)) % 7.54/7.64 [961]~P58(x9612)+~P62(x9612)+~P65(x9612)+~P40(x9612)+~E(x9611,f3(a119))+~E(f118(f118(f31(x9612),x9613),x9611),f3(x9612)) % 7.54/7.64 [1324]~P32(x13241)+~E(x13243,f3(x13241))+~E(x13242,f3(x13241))+E(f118(f118(f23(x13241),x13242),x13243),f3(x13241))+~P77(f118(f28(x13241,f3(x13241)),x13243))+~P77(f118(f28(x13241,f3(x13241)),x13242)) % 7.54/7.64 [1510]~P45(x15103)+E(x15101,x15102)+~E(f118(f118(f31(x15103),x15101),x15104),f118(f118(f31(x15103),x15102),x15104))+~P77(f118(f28(x15103,f3(x15103)),x15102))+~P77(f118(f28(x15103,f3(x15103)),x15101))+~P77(f118(f29(a119,f3(a119)),x15104)) % 7.54/7.64 [1575]E(f20(a115,x15752,x15751),x15753)+E(x15751,f3(a115))+~P77(f118(f29(a115,x15751),x15754))+~P77(f118(f28(a115,x15754),f3(a115)))+~E(x15752,f118(f118(f23(a115),f118(f118(f24(a115),x15751),x15753)),x15754))+P77(f118(f29(a115,f3(a115)),x15751)) % 7.54/7.64 [1611]E(f20(a115,x16112,x16111),x16113)+E(x16111,f3(a115))+~P77(f118(f29(a115,x16114),x16111))+~E(x16112,f118(f118(f23(a115),f118(f118(f24(a115),x16111),x16113)),x16114))+~P77(f118(f28(a115,f3(a115)),x16114))+~P77(f118(f29(a115,f3(a115)),x16111)) % 7.54/7.64 [1805]~P69(x18051)+~P77(f118(f28(x18051,x18053),x18055))+~P77(f118(f28(x18051,x18052),x18054))+~P77(f118(f28(x18051,f3(x18051)),x18053))+~P77(f118(f28(x18051,f3(x18051)),x18054))+P77(f118(f28(x18051,f118(f118(f24(x18051),x18052),x18053)),f118(f118(f24(x18051),x18054),x18055))) % 7.54/7.64 [1806]~P69(x18061)+~P77(f118(f28(x18061,x18063),x18065))+~P77(f118(f28(x18061,x18062),x18064))+~P77(f118(f28(x18061,f3(x18061)),x18063))+~P77(f118(f28(x18061,f3(x18061)),x18062))+P77(f118(f28(x18061,f118(f118(f24(x18061),x18062),x18063)),f118(f118(f24(x18061),x18064),x18065))) % 7.54/7.64 [1807]~P63(x18071)+~P77(f118(f28(x18071,x18073),x18075))+~P77(f118(f29(x18071,x18072),x18074))+~P77(f118(f28(x18071,f3(x18071)),x18072))+~P77(f118(f29(x18071,f3(x18071)),x18073))+P77(f118(f29(x18071,f118(f118(f24(x18071),x18072),x18073)),f118(f118(f24(x18071),x18074),x18075))) % 7.54/7.64 [1808]~P63(x18081)+~P77(f118(f28(x18081,x18082),x18084))+~P77(f118(f29(x18081,x18083),x18085))+~P77(f118(f28(x18081,f3(x18081)),x18083))+~P77(f118(f29(x18081,f3(x18081)),x18082))+P77(f118(f29(x18081,f118(f118(f24(x18081),x18082),x18083)),f118(f118(f24(x18081),x18084),x18085))) % 7.54/7.64 [1809]~P63(x18091)+~P77(f118(f29(x18091,x18093),x18095))+~P77(f118(f29(x18091,x18092),x18094))+~P77(f118(f28(x18091,f3(x18091)),x18093))+~P77(f118(f28(x18091,f3(x18091)),x18092))+P77(f118(f29(x18091,f118(f118(f24(x18091),x18092),x18093)),f118(f118(f24(x18091),x18094),x18095))) % 7.54/7.64 [1810]~P63(x18101)+~P77(f118(f29(x18101,x18103),x18105))+~P77(f118(f29(x18101,x18102),x18104))+~P77(f118(f28(x18101,f3(x18101)),x18103))+~P77(f118(f29(x18101,f3(x18101)),x18104))+P77(f118(f29(x18101,f118(f118(f24(x18101),x18102),x18103)),f118(f118(f24(x18101),x18104),x18105))) % 7.54/7.64 [1638]~P78(x16381,x16384,x16383)+P77(f118(x16381,x16382))+~P77(f118(f29(a115,x16384),x16385))+~P77(f118(f29(a115,x16384),f3(a115)))+~P77(f118(f28(a115,x16385),f3(a115)))+~E(x16383,f118(f118(f23(a115),f118(f118(f24(a115),x16384),x16382)),x16385)) % 7.54/7.64 [1649]~P78(x16491,x16494,x16493)+P77(f118(x16491,x16492))+~P77(f118(f29(a115,x16495),x16494))+~E(x16493,f118(f118(f23(a115),f118(f118(f24(a115),x16494),x16492)),x16495))+~P77(f118(f28(a115,f3(a115)),x16495))+~P77(f118(f29(a115,f3(a115)),x16494)) % 7.54/7.64 [1573]~P36(x15731)+~P2(x15731,x15732)+P77(f118(f28(x15731,f118(x15732,x15733)),f118(x15732,x15734)))+P77(f118(f28(x15731,f118(x15732,x15735)),f118(x15732,x15736)))+~P77(f118(f28(a119,x15734),x15733))+~P77(f118(f28(a119,x15735),x15736)) % 7.54/7.64 [932]~P58(x9322)+~P62(x9322)+~P65(x9322)+~P40(x9322)+~E(x9323,f3(x9322))+E(x9321,f3(a119))+E(f118(f118(f31(x9322),x9323),x9321),f3(x9322)) % 7.54/7.64 [1681]E(f20(a115,x16812,x16811),x16813)+E(x16811,f3(a115))+~P77(f118(f29(a115,x16814),x16811))+~P77(f118(f29(a115,x16811),x16814))+~P77(f118(f28(a115,x16814),f3(a115)))+~E(x16812,f118(f118(f23(a115),f118(f118(f24(a115),x16811),x16813)),x16814))+~P77(f118(f28(a115,f3(a115)),x16814)) % 7.54/7.64 [1930]~P77(f118(f28(a115,x19305),x19303))+~P77(f118(f29(a115,x19304),x19303))+P77(f118(f28(a115,x19301),x19302))+~P77(f118(f29(a115,f118(f118(f23(a115),f118(f118(f24(a115),x19305),x19301)),x19306)),f3(a115)))+~E(f118(f118(f23(a115),f118(f118(f24(a115),x19303),x19302)),x19304),f118(f118(f23(a115),f118(f118(f24(a115),x19305),x19301)),x19306))+~P77(f118(f28(a115,f3(a115)),x19306))+~P77(f118(f29(a115,f3(a115)),x19305)) % 7.54/7.64 [1907]~P77(f118(f28(a115,x19075),x19073))+~P77(f118(f29(a115,x19076),x19075))+P77(f118(f28(a115,x19071),x19072))+~E(f118(f118(f23(a115),f118(f118(f24(a115),x19073),x19071)),x19074),f118(f118(f23(a115),f118(f118(f24(a115),x19075),x19072)),x19076))+~P77(f118(f28(a115,f3(a115)),x19074))+~P77(f118(f29(a115,f3(a115)),x19075))+~P77(f118(f28(a115,f3(a115)),f118(f118(f23(a115),f118(f118(f24(a115),x19075),x19072)),x19076))) % 7.54/7.64 [1922]~P61(x19221)+~E(f118(f118(f23(x19221),x19222),x19224),f16(x19221))+~P77(f118(f28(x19221,x19225),x19226))+~P77(f118(f28(x19221,x19223),x19226))+~P77(f118(f28(x19221,f3(x19221)),x19224))+~P77(f118(f28(x19221,f3(x19221)),x19222))+P77(f118(f28(x19221,f118(f118(f23(x19221),f118(f118(f24(x19221),x19222),x19223)),f118(f118(f24(x19221),x19224),x19225))),x19226)) % 7.54/7.64 [1923]~P59(x19231)+~E(f118(f118(f23(x19231),x19232),x19234),f16(x19231))+~P77(f118(f29(x19231,x19235),x19236))+~P77(f118(f29(x19231,x19233),x19236))+~P77(f118(f28(x19231,f3(x19231)),x19234))+~P77(f118(f28(x19231,f3(x19231)),x19232))+P77(f118(f29(x19231,f118(f118(f23(x19231),f118(f118(f24(x19231),x19232),x19233)),f118(f118(f24(x19231),x19234),x19235))),x19236)) % 7.54/7.64 %EqnAxiom % 7.54/7.64 [1]E(x11,x11) % 7.54/7.64 [2]E(x22,x21)+~E(x21,x22) % 7.54/7.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 7.54/7.64 [4]~E(x41,x42)+E(f3(x41),f3(x42)) % 7.54/7.64 [5]~E(x51,x52)+E(f4(x51),f4(x52)) % 7.54/7.64 [6]~E(x61,x62)+E(f16(x61),f16(x62)) % 7.54/7.64 [7]~E(x71,x72)+E(f118(x71,x73),f118(x72,x73)) % 7.54/7.64 [8]~E(x81,x82)+E(f118(x83,x81),f118(x83,x82)) % 7.54/7.64 [9]~E(x91,x92)+E(f26(x91),f26(x92)) % 7.54/7.64 [10]~E(x101,x102)+E(f29(x101,x103),f29(x102,x103)) % 7.54/7.64 [11]~E(x111,x112)+E(f29(x113,x111),f29(x113,x112)) % 7.54/7.64 [12]~E(x121,x122)+E(f24(x121),f24(x122)) % 7.54/7.64 [13]~E(x131,x132)+E(f34(x131),f34(x132)) % 7.54/7.64 [14]~E(x141,x142)+E(f28(x141,x143),f28(x142,x143)) % 7.54/7.64 [15]~E(x151,x152)+E(f28(x153,x151),f28(x153,x152)) % 7.54/7.64 [16]~E(x161,x162)+E(f22(x161,x163,x164),f22(x162,x163,x164)) % 7.54/7.64 [17]~E(x171,x172)+E(f22(x173,x171,x174),f22(x173,x172,x174)) % 7.54/7.64 [18]~E(x181,x182)+E(f22(x183,x184,x181),f22(x183,x184,x182)) % 7.54/7.64 [19]~E(x191,x192)+E(f33(x191),f33(x192)) % 7.54/7.64 [20]~E(x201,x202)+E(f35(x201,x203),f35(x202,x203)) % 7.54/7.64 [21]~E(x211,x212)+E(f35(x213,x211),f35(x213,x212)) % 7.54/7.64 [22]~E(x221,x222)+E(f23(x221),f23(x222)) % 7.54/7.64 [23]~E(x231,x232)+E(f37(x231),f37(x232)) % 7.54/7.64 [24]~E(x241,x242)+E(f36(x241,x243),f36(x242,x243)) % 7.54/7.64 [25]~E(x251,x252)+E(f36(x253,x251),f36(x253,x252)) % 7.54/7.64 [26]~E(x261,x262)+E(f107(x261,x263,x264),f107(x262,x263,x264)) % 7.54/7.64 [27]~E(x271,x272)+E(f107(x273,x271,x274),f107(x273,x272,x274)) % 7.54/7.64 [28]~E(x281,x282)+E(f107(x283,x284,x281),f107(x283,x284,x282)) % 7.54/7.64 [29]~E(x291,x292)+E(f106(x291,x293,x294),f106(x292,x293,x294)) % 7.54/7.64 [30]~E(x301,x302)+E(f106(x303,x301,x304),f106(x303,x302,x304)) % 7.54/7.64 [31]~E(x311,x312)+E(f106(x313,x314,x311),f106(x313,x314,x312)) % 7.54/7.64 [32]~E(x321,x322)+E(f20(x321,x323,x324),f20(x322,x323,x324)) % 7.54/7.64 [33]~E(x331,x332)+E(f20(x333,x331,x334),f20(x333,x332,x334)) % 7.54/7.64 [34]~E(x341,x342)+E(f20(x343,x344,x341),f20(x343,x344,x342)) % 7.54/7.64 [35]~E(x351,x352)+E(f25(x351,x353),f25(x352,x353)) % 7.54/7.64 [36]~E(x361,x362)+E(f25(x363,x361),f25(x363,x362)) % 7.54/7.64 [37]~E(x371,x372)+E(f31(x371),f31(x372)) % 7.54/7.64 [38]~E(x381,x382)+E(f51(x381,x383,x384),f51(x382,x383,x384)) % 7.54/7.64 [39]~E(x391,x392)+E(f51(x393,x391,x394),f51(x393,x392,x394)) % 7.54/7.64 [40]~E(x401,x402)+E(f51(x403,x404,x401),f51(x403,x404,x402)) % 7.54/7.64 [41]~E(x411,x412)+E(f54(x411,x413,x414,x415),f54(x412,x413,x414,x415)) % 7.54/7.64 [42]~E(x421,x422)+E(f54(x423,x421,x424,x425),f54(x423,x422,x424,x425)) % 7.54/7.64 [43]~E(x431,x432)+E(f54(x433,x434,x431,x435),f54(x433,x434,x432,x435)) % 7.54/7.64 [44]~E(x441,x442)+E(f54(x443,x444,x445,x441),f54(x443,x444,x445,x442)) % 7.54/7.64 [45]~E(x451,x452)+E(f19(x451,x453),f19(x452,x453)) % 7.54/7.64 [46]~E(x461,x462)+E(f19(x463,x461),f19(x463,x462)) % 7.54/7.64 [47]~E(x471,x472)+E(f56(x471,x473),f56(x472,x473)) % 7.54/7.64 [48]~E(x481,x482)+E(f56(x483,x481),f56(x483,x482)) % 7.54/7.64 [49]~E(x491,x492)+E(f112(x491,x493,x494),f112(x492,x493,x494)) % 7.54/7.64 [50]~E(x501,x502)+E(f112(x503,x501,x504),f112(x503,x502,x504)) % 7.54/7.64 [51]~E(x511,x512)+E(f112(x513,x514,x511),f112(x513,x514,x512)) % 7.54/7.64 [52]~E(x521,x522)+E(f44(x521,x523),f44(x522,x523)) % 7.54/7.64 [53]~E(x531,x532)+E(f44(x533,x531),f44(x533,x532)) % 7.54/7.64 [54]~E(x541,x542)+E(f45(x541,x543),f45(x542,x543)) % 7.54/7.64 [55]~E(x551,x552)+E(f45(x553,x551),f45(x553,x552)) % 7.54/7.64 [56]~E(x561,x562)+E(f87(x561,x563),f87(x562,x563)) % 7.54/7.64 [57]~E(x571,x572)+E(f87(x573,x571),f87(x573,x572)) % 7.54/7.64 [58]~E(x581,x582)+E(f108(x581,x583,x584),f108(x582,x583,x584)) % 7.54/7.64 [59]~E(x591,x592)+E(f108(x593,x591,x594),f108(x593,x592,x594)) % 7.54/7.64 [60]~E(x601,x602)+E(f108(x603,x604,x601),f108(x603,x604,x602)) % 7.54/7.64 [61]~E(x611,x612)+E(f18(x611,x613),f18(x612,x613)) % 7.54/7.64 [62]~E(x621,x622)+E(f18(x623,x621),f18(x623,x622)) % 7.54/7.64 [63]~E(x631,x632)+E(f72(x631),f72(x632)) % 7.54/7.64 [64]~E(x641,x642)+E(f111(x641),f111(x642)) % 7.54/7.64 [65]~E(x651,x652)+E(f62(x651,x653,x654,x655),f62(x652,x653,x654,x655)) % 7.54/7.64 [66]~E(x661,x662)+E(f62(x663,x661,x664,x665),f62(x663,x662,x664,x665)) % 7.54/7.64 [67]~E(x671,x672)+E(f62(x673,x674,x671,x675),f62(x673,x674,x672,x675)) % 7.54/7.64 [68]~E(x681,x682)+E(f62(x683,x684,x685,x681),f62(x683,x684,x685,x682)) % 7.54/7.64 [69]~E(x691,x692)+E(f82(x691,x693,x694),f82(x692,x693,x694)) % 7.54/7.64 [70]~E(x701,x702)+E(f82(x703,x701,x704),f82(x703,x702,x704)) % 7.54/7.64 [71]~E(x711,x712)+E(f82(x713,x714,x711),f82(x713,x714,x712)) % 7.54/7.64 [72]~E(x721,x722)+E(f85(x721,x723),f85(x722,x723)) % 7.54/7.64 [73]~E(x731,x732)+E(f85(x733,x731),f85(x733,x732)) % 7.54/7.64 [74]~E(x741,x742)+E(f60(x741),f60(x742)) % 7.54/7.64 [75]~E(x751,x752)+E(f77(x751,x753,x754),f77(x752,x753,x754)) % 7.54/7.64 [76]~E(x761,x762)+E(f77(x763,x761,x764),f77(x763,x762,x764)) % 7.54/7.64 [77]~E(x771,x772)+E(f77(x773,x774,x771),f77(x773,x774,x772)) % 7.54/7.64 [78]~E(x781,x782)+E(f113(x781,x783),f113(x782,x783)) % 7.54/7.64 [79]~E(x791,x792)+E(f113(x793,x791),f113(x793,x792)) % 7.54/7.64 [80]~E(x801,x802)+E(f7(x801,x803,x804,x805,x806),f7(x802,x803,x804,x805,x806)) % 7.54/7.64 [81]~E(x811,x812)+E(f7(x813,x811,x814,x815,x816),f7(x813,x812,x814,x815,x816)) % 7.54/7.64 [82]~E(x821,x822)+E(f7(x823,x824,x821,x825,x826),f7(x823,x824,x822,x825,x826)) % 7.54/7.64 [83]~E(x831,x832)+E(f7(x833,x834,x835,x831,x836),f7(x833,x834,x835,x832,x836)) % 7.54/7.64 [84]~E(x841,x842)+E(f7(x843,x844,x845,x846,x841),f7(x843,x844,x845,x846,x842)) % 7.54/7.64 [85]~E(x851,x852)+E(f104(x851,x853,x854),f104(x852,x853,x854)) % 7.54/7.64 [86]~E(x861,x862)+E(f104(x863,x861,x864),f104(x863,x862,x864)) % 7.54/7.64 [87]~E(x871,x872)+E(f104(x873,x874,x871),f104(x873,x874,x872)) % 7.54/7.64 [88]~E(x881,x882)+E(f95(x881,x883),f95(x882,x883)) % 7.54/7.64 [89]~E(x891,x892)+E(f95(x893,x891),f95(x893,x892)) % 7.54/7.64 [90]~E(x901,x902)+E(f120(x901),f120(x902)) % 7.54/7.64 [91]~E(x911,x912)+E(f11(x911,x913),f11(x912,x913)) % 7.54/7.64 [92]~E(x921,x922)+E(f11(x923,x921),f11(x923,x922)) % 7.54/7.64 [93]~E(x931,x932)+E(f121(x931,x933),f121(x932,x933)) % 7.54/7.64 [94]~E(x941,x942)+E(f121(x943,x941),f121(x943,x942)) % 7.54/7.64 [95]~E(x951,x952)+E(f81(x951,x953),f81(x952,x953)) % 7.54/7.64 [96]~E(x961,x962)+E(f81(x963,x961),f81(x963,x962)) % 7.54/7.64 [97]~E(x971,x972)+E(f8(x971,x973,x974,x975,x976),f8(x972,x973,x974,x975,x976)) % 7.54/7.64 [98]~E(x981,x982)+E(f8(x983,x981,x984,x985,x986),f8(x983,x982,x984,x985,x986)) % 7.54/7.64 [99]~E(x991,x992)+E(f8(x993,x994,x991,x995,x996),f8(x993,x994,x992,x995,x996)) % 7.54/7.64 [100]~E(x1001,x1002)+E(f8(x1003,x1004,x1005,x1001,x1006),f8(x1003,x1004,x1005,x1002,x1006)) % 7.54/7.64 [101]~E(x1011,x1012)+E(f8(x1013,x1014,x1015,x1016,x1011),f8(x1013,x1014,x1015,x1016,x1012)) % 7.54/7.64 [102]~E(x1021,x1022)+E(f68(x1021),f68(x1022)) % 7.54/7.64 [103]~E(x1031,x1032)+E(f30(x1031,x1033),f30(x1032,x1033)) % 7.54/7.64 [104]~E(x1041,x1042)+E(f30(x1043,x1041),f30(x1043,x1042)) % 7.54/7.64 [105]~E(x1051,x1052)+E(f6(x1051,x1053,x1054),f6(x1052,x1053,x1054)) % 7.54/7.64 [106]~E(x1061,x1062)+E(f6(x1063,x1061,x1064),f6(x1063,x1062,x1064)) % 7.54/7.64 [107]~E(x1071,x1072)+E(f6(x1073,x1074,x1071),f6(x1073,x1074,x1072)) % 7.54/7.64 [108]~E(x1081,x1082)+E(f98(x1081,x1083),f98(x1082,x1083)) % 7.54/7.64 [109]~E(x1091,x1092)+E(f98(x1093,x1091),f98(x1093,x1092)) % 7.54/7.64 [110]~E(x1101,x1102)+E(f63(x1101,x1103),f63(x1102,x1103)) % 7.54/7.64 [111]~E(x1111,x1112)+E(f63(x1113,x1111),f63(x1113,x1112)) % 7.54/7.64 [112]~E(x1121,x1122)+E(f42(x1121,x1123),f42(x1122,x1123)) % 7.54/7.64 [113]~E(x1131,x1132)+E(f42(x1133,x1131),f42(x1133,x1132)) % 7.54/7.64 [114]~E(x1141,x1142)+E(f76(x1141,x1143),f76(x1142,x1143)) % 7.54/7.64 [115]~E(x1151,x1152)+E(f76(x1153,x1151),f76(x1153,x1152)) % 7.54/7.64 [116]~E(x1161,x1162)+E(f110(x1161,x1163,x1164),f110(x1162,x1163,x1164)) % 7.54/7.64 [117]~E(x1171,x1172)+E(f110(x1173,x1171,x1174),f110(x1173,x1172,x1174)) % 7.54/7.64 [118]~E(x1181,x1182)+E(f110(x1183,x1184,x1181),f110(x1183,x1184,x1182)) % 7.54/7.64 [119]~E(x1191,x1192)+E(f49(x1191,x1193,x1194),f49(x1192,x1193,x1194)) % 7.54/7.64 [120]~E(x1201,x1202)+E(f49(x1203,x1201,x1204),f49(x1203,x1202,x1204)) % 7.54/7.64 [121]~E(x1211,x1212)+E(f49(x1213,x1214,x1211),f49(x1213,x1214,x1212)) % 7.54/7.64 [122]~E(x1221,x1222)+E(f103(x1221,x1223,x1224,x1225),f103(x1222,x1223,x1224,x1225)) % 7.54/7.64 [123]~E(x1231,x1232)+E(f103(x1233,x1231,x1234,x1235),f103(x1233,x1232,x1234,x1235)) % 7.54/7.64 [124]~E(x1241,x1242)+E(f103(x1243,x1244,x1241,x1245),f103(x1243,x1244,x1242,x1245)) % 7.54/7.64 [125]~E(x1251,x1252)+E(f103(x1253,x1254,x1255,x1251),f103(x1253,x1254,x1255,x1252)) % 7.54/7.64 [126]~E(x1261,x1262)+E(f86(x1261),f86(x1262)) % 7.54/7.64 [127]~E(x1271,x1272)+E(f32(x1271,x1273,x1274),f32(x1272,x1273,x1274)) % 7.54/7.64 [128]~E(x1281,x1282)+E(f32(x1283,x1281,x1284),f32(x1283,x1282,x1284)) % 7.54/7.64 [129]~E(x1291,x1292)+E(f32(x1293,x1294,x1291),f32(x1293,x1294,x1292)) % 7.54/7.64 [130]~E(x1301,x1302)+E(f55(x1301),f55(x1302)) % 7.54/7.64 [131]~E(x1311,x1312)+E(f102(x1311,x1313,x1314),f102(x1312,x1313,x1314)) % 7.54/7.64 [132]~E(x1321,x1322)+E(f102(x1323,x1321,x1324),f102(x1323,x1322,x1324)) % 7.54/7.64 [133]~E(x1331,x1332)+E(f102(x1333,x1334,x1331),f102(x1333,x1334,x1332)) % 7.54/7.64 [134]~E(x1341,x1342)+E(f38(x1341),f38(x1342)) % 7.54/7.64 [135]~E(x1351,x1352)+E(f53(x1351,x1353),f53(x1352,x1353)) % 7.54/7.64 [136]~E(x1361,x1362)+E(f53(x1363,x1361),f53(x1363,x1362)) % 7.54/7.64 [137]~E(x1371,x1372)+E(f89(x1371,x1373),f89(x1372,x1373)) % 7.54/7.64 [138]~E(x1381,x1382)+E(f89(x1383,x1381),f89(x1383,x1382)) % 7.54/7.64 [139]~E(x1391,x1392)+E(f67(x1391,x1393),f67(x1392,x1393)) % 7.54/7.64 [140]~E(x1401,x1402)+E(f67(x1403,x1401),f67(x1403,x1402)) % 7.54/7.64 [141]~E(x1411,x1412)+E(f101(x1411,x1413,x1414),f101(x1412,x1413,x1414)) % 7.54/7.64 [142]~E(x1421,x1422)+E(f101(x1423,x1421,x1424),f101(x1423,x1422,x1424)) % 7.54/7.64 [143]~E(x1431,x1432)+E(f101(x1433,x1434,x1431),f101(x1433,x1434,x1432)) % 7.54/7.64 [144]~E(x1441,x1442)+E(f13(x1441),f13(x1442)) % 7.54/7.64 [145]~E(x1451,x1452)+E(f93(x1451,x1453),f93(x1452,x1453)) % 7.54/7.64 [146]~E(x1461,x1462)+E(f93(x1463,x1461),f93(x1463,x1462)) % 7.54/7.64 [147]~E(x1471,x1472)+E(f61(x1471,x1473),f61(x1472,x1473)) % 7.54/7.64 [148]~E(x1481,x1482)+E(f61(x1483,x1481),f61(x1483,x1482)) % 7.54/7.64 [149]~E(x1491,x1492)+E(f75(x1491,x1493),f75(x1492,x1493)) % 7.54/7.64 [150]~E(x1501,x1502)+E(f75(x1503,x1501),f75(x1503,x1502)) % 7.54/7.64 [151]~E(x1511,x1512)+E(f96(x1511),f96(x1512)) % 7.54/7.64 [152]~E(x1521,x1522)+E(f109(x1521,x1523,x1524),f109(x1522,x1523,x1524)) % 7.54/7.64 [153]~E(x1531,x1532)+E(f109(x1533,x1531,x1534),f109(x1533,x1532,x1534)) % 7.54/7.64 [154]~E(x1541,x1542)+E(f109(x1543,x1544,x1541),f109(x1543,x1544,x1542)) % 7.54/7.64 [155]~E(x1551,x1552)+E(f88(x1551,x1553),f88(x1552,x1553)) % 7.54/7.64 [156]~E(x1561,x1562)+E(f88(x1563,x1561),f88(x1563,x1562)) % 7.54/7.64 [157]~E(x1571,x1572)+E(f27(x1571,x1573),f27(x1572,x1573)) % 7.54/7.64 [158]~E(x1581,x1582)+E(f27(x1583,x1581),f27(x1583,x1582)) % 7.54/7.64 [159]~E(x1591,x1592)+E(f41(x1591,x1593),f41(x1592,x1593)) % 7.54/7.64 [160]~E(x1601,x1602)+E(f41(x1603,x1601),f41(x1603,x1602)) % 7.54/7.64 [161]~E(x1611,x1612)+E(f79(x1611,x1613),f79(x1612,x1613)) % 7.54/7.64 [162]~E(x1621,x1622)+E(f79(x1623,x1621),f79(x1623,x1622)) % 7.54/7.64 [163]~E(x1631,x1632)+E(f9(x1631,x1633,x1634,x1635,x1636),f9(x1632,x1633,x1634,x1635,x1636)) % 7.54/7.64 [164]~E(x1641,x1642)+E(f9(x1643,x1641,x1644,x1645,x1646),f9(x1643,x1642,x1644,x1645,x1646)) % 7.54/7.64 [165]~E(x1651,x1652)+E(f9(x1653,x1654,x1651,x1655,x1656),f9(x1653,x1654,x1652,x1655,x1656)) % 7.54/7.64 [166]~E(x1661,x1662)+E(f9(x1663,x1664,x1665,x1661,x1666),f9(x1663,x1664,x1665,x1662,x1666)) % 7.54/7.64 [167]~E(x1671,x1672)+E(f9(x1673,x1674,x1675,x1676,x1671),f9(x1673,x1674,x1675,x1676,x1672)) % 7.54/7.64 [168]~E(x1681,x1682)+E(f66(x1681,x1683),f66(x1682,x1683)) % 7.54/7.64 [169]~E(x1691,x1692)+E(f66(x1693,x1691),f66(x1693,x1692)) % 7.54/7.64 [170]~E(x1701,x1702)+E(f105(x1701,x1703),f105(x1702,x1703)) % 7.54/7.64 [171]~E(x1711,x1712)+E(f105(x1713,x1711),f105(x1713,x1712)) % 7.54/7.64 [172]~E(x1721,x1722)+E(f94(x1721,x1723),f94(x1722,x1723)) % 7.54/7.64 [173]~E(x1731,x1732)+E(f94(x1733,x1731),f94(x1733,x1732)) % 7.54/7.64 [174]~E(x1741,x1742)+E(f50(x1741,x1743),f50(x1742,x1743)) % 7.54/7.64 [175]~E(x1751,x1752)+E(f50(x1753,x1751),f50(x1753,x1752)) % 7.54/7.64 [176]~E(x1761,x1762)+E(f21(x1761,x1763),f21(x1762,x1763)) % 7.54/7.64 [177]~E(x1771,x1772)+E(f21(x1773,x1771),f21(x1773,x1772)) % 7.54/7.64 [178]~E(x1781,x1782)+E(f83(x1781,x1783),f83(x1782,x1783)) % 7.54/7.64 [179]~E(x1791,x1792)+E(f83(x1793,x1791),f83(x1793,x1792)) % 7.54/7.64 [180]~E(x1801,x1802)+E(f46(x1801,x1803),f46(x1802,x1803)) % 7.54/7.64 [181]~E(x1811,x1812)+E(f46(x1813,x1811),f46(x1813,x1812)) % 7.54/7.64 [182]~E(x1821,x1822)+E(f80(x1821,x1823,x1824),f80(x1822,x1823,x1824)) % 7.54/7.64 [183]~E(x1831,x1832)+E(f80(x1833,x1831,x1834),f80(x1833,x1832,x1834)) % 7.54/7.64 [184]~E(x1841,x1842)+E(f80(x1843,x1844,x1841),f80(x1843,x1844,x1842)) % 7.54/7.64 [185]~E(x1851,x1852)+E(f97(x1851,x1853,x1854),f97(x1852,x1853,x1854)) % 7.54/7.64 [186]~E(x1861,x1862)+E(f97(x1863,x1861,x1864),f97(x1863,x1862,x1864)) % 7.54/7.64 [187]~E(x1871,x1872)+E(f97(x1873,x1874,x1871),f97(x1873,x1874,x1872)) % 7.54/7.64 [188]~E(x1881,x1882)+E(f70(x1881,x1883),f70(x1882,x1883)) % 7.54/7.64 [189]~E(x1891,x1892)+E(f70(x1893,x1891),f70(x1893,x1892)) % 7.54/7.64 [190]~E(x1901,x1902)+E(f92(x1901,x1903,x1904),f92(x1902,x1903,x1904)) % 7.54/7.64 [191]~E(x1911,x1912)+E(f92(x1913,x1911,x1914),f92(x1913,x1912,x1914)) % 7.54/7.64 [192]~E(x1921,x1922)+E(f92(x1923,x1924,x1921),f92(x1923,x1924,x1922)) % 7.54/7.64 [193]~E(x1931,x1932)+E(f84(x1931),f84(x1932)) % 7.54/7.64 [194]~E(x1941,x1942)+E(f69(x1941,x1943),f69(x1942,x1943)) % 7.54/7.64 [195]~E(x1951,x1952)+E(f69(x1953,x1951),f69(x1953,x1952)) % 7.54/7.64 [196]~E(x1961,x1962)+E(f99(x1961,x1963),f99(x1962,x1963)) % 7.54/7.64 [197]~E(x1971,x1972)+E(f99(x1973,x1971),f99(x1973,x1972)) % 7.54/7.64 [198]~E(x1981,x1982)+E(f12(x1981),f12(x1982)) % 7.54/7.64 [199]~E(x1991,x1992)+E(f100(x1991),f100(x1992)) % 7.54/7.64 [200]~E(x2001,x2002)+E(f90(x2001,x2003),f90(x2002,x2003)) % 7.54/7.64 [201]~E(x2011,x2012)+E(f90(x2013,x2011),f90(x2013,x2012)) % 7.54/7.64 [202]~E(x2021,x2022)+E(f74(x2021,x2023),f74(x2022,x2023)) % 7.54/7.64 [203]~E(x2031,x2032)+E(f74(x2033,x2031),f74(x2033,x2032)) % 7.54/7.64 [204]~E(x2041,x2042)+E(f71(x2041,x2043,x2044),f71(x2042,x2043,x2044)) % 7.54/7.64 [205]~E(x2051,x2052)+E(f71(x2053,x2051,x2054),f71(x2053,x2052,x2054)) % 7.54/7.64 [206]~E(x2061,x2062)+E(f71(x2063,x2064,x2061),f71(x2063,x2064,x2062)) % 7.54/7.64 [207]~E(x2071,x2072)+E(f48(x2071,x2073),f48(x2072,x2073)) % 7.54/7.64 [208]~E(x2081,x2082)+E(f48(x2083,x2081),f48(x2083,x2082)) % 7.54/7.64 [209]~E(x2091,x2092)+E(f65(x2091),f65(x2092)) % 7.54/7.64 [210]~E(x2101,x2102)+E(f52(x2101),f52(x2102)) % 7.54/7.64 [211]~E(x2111,x2112)+E(f14(x2111,x2113,x2114),f14(x2112,x2113,x2114)) % 7.54/7.64 [212]~E(x2121,x2122)+E(f14(x2123,x2121,x2124),f14(x2123,x2122,x2124)) % 7.54/7.64 [213]~E(x2131,x2132)+E(f14(x2133,x2134,x2131),f14(x2133,x2134,x2132)) % 7.54/7.64 [214]~E(x2141,x2142)+E(f15(x2141,x2143,x2144),f15(x2142,x2143,x2144)) % 7.54/7.64 [215]~E(x2151,x2152)+E(f15(x2153,x2151,x2154),f15(x2153,x2152,x2154)) % 7.54/7.64 [216]~E(x2161,x2162)+E(f15(x2163,x2164,x2161),f15(x2163,x2164,x2162)) % 7.54/7.64 [217]~E(x2171,x2172)+E(f78(x2171,x2173),f78(x2172,x2173)) % 7.54/7.64 [218]~E(x2181,x2182)+E(f78(x2183,x2181),f78(x2183,x2182)) % 7.54/7.64 [219]~E(x2191,x2192)+E(f43(x2191,x2193),f43(x2192,x2193)) % 7.54/7.64 [220]~E(x2201,x2202)+E(f43(x2203,x2201),f43(x2203,x2202)) % 7.54/7.64 [221]~E(x2211,x2212)+E(f47(x2211,x2213),f47(x2212,x2213)) % 7.54/7.64 [222]~E(x2221,x2222)+E(f47(x2223,x2221),f47(x2223,x2222)) % 7.54/7.64 [223]~E(x2231,x2232)+E(f73(x2231),f73(x2232)) % 7.54/7.64 [224]~E(x2241,x2242)+E(f91(x2241,x2243,x2244),f91(x2242,x2243,x2244)) % 7.54/7.64 [225]~E(x2251,x2252)+E(f91(x2253,x2251,x2254),f91(x2253,x2252,x2254)) % 7.54/7.64 [226]~E(x2261,x2262)+E(f91(x2263,x2264,x2261),f91(x2263,x2264,x2262)) % 7.54/7.64 [227]~P1(x2271)+P1(x2272)+~E(x2271,x2272) % 7.54/7.64 [228]~P77(x2281)+P77(x2282)+~E(x2281,x2282) % 7.54/7.64 [229]~P67(x2291)+P67(x2292)+~E(x2291,x2292) % 7.54/7.64 [230]~P7(x2301)+P7(x2302)+~E(x2301,x2302) % 7.54/7.64 [231]P5(x2312,x2313)+~E(x2311,x2312)+~P5(x2311,x2313) % 7.54/7.64 [232]P5(x2323,x2322)+~E(x2321,x2322)+~P5(x2323,x2321) % 7.54/7.64 [233]~P27(x2331)+P27(x2332)+~E(x2331,x2332) % 7.54/7.64 [234]~P47(x2341)+P47(x2342)+~E(x2341,x2342) % 7.54/7.64 [235]~P11(x2351)+P11(x2352)+~E(x2351,x2352) % 7.54/7.64 [236]~P56(x2361)+P56(x2362)+~E(x2361,x2362) % 7.54/7.64 [237]~P28(x2371)+P28(x2372)+~E(x2371,x2372) % 7.54/7.64 [238]~P45(x2381)+P45(x2382)+~E(x2381,x2382) % 7.54/7.64 [239]~P34(x2391)+P34(x2392)+~E(x2391,x2392) % 7.54/7.64 [240]~P36(x2401)+P36(x2402)+~E(x2401,x2402) % 7.54/7.64 [241]~P70(x2411)+P70(x2412)+~E(x2411,x2412) % 7.54/7.64 [242]~P26(x2421)+P26(x2422)+~E(x2421,x2422) % 7.54/7.64 [243]P78(x2432,x2433,x2434)+~E(x2431,x2432)+~P78(x2431,x2433,x2434) % 7.54/7.64 [244]P78(x2443,x2442,x2444)+~E(x2441,x2442)+~P78(x2443,x2441,x2444) % 7.54/7.64 [245]P78(x2453,x2454,x2452)+~E(x2451,x2452)+~P78(x2453,x2454,x2451) % 7.54/7.64 [246]~P35(x2461)+P35(x2462)+~E(x2461,x2462) % 7.54/7.64 [247]~P69(x2471)+P69(x2472)+~E(x2471,x2472) % 7.54/7.64 [248]~P32(x2481)+P32(x2482)+~E(x2481,x2482) % 7.54/7.64 [249]~P57(x2491)+P57(x2492)+~E(x2491,x2492) % 7.54/7.64 [250]~P30(x2501)+P30(x2502)+~E(x2501,x2502) % 7.54/7.64 [251]~P44(x2511)+P44(x2512)+~E(x2511,x2512) % 7.54/7.64 [252]~P53(x2521)+P53(x2522)+~E(x2521,x2522) % 7.54/7.64 [253]~P41(x2531)+P41(x2532)+~E(x2531,x2532) % 7.54/7.64 [254]~P37(x2541)+P37(x2542)+~E(x2541,x2542) % 7.54/7.64 [255]P4(x2552,x2553)+~E(x2551,x2552)+~P4(x2551,x2553) % 7.54/7.64 [256]P4(x2563,x2562)+~E(x2561,x2562)+~P4(x2563,x2561) % 7.54/7.64 [257]~P38(x2571)+P38(x2572)+~E(x2571,x2572) % 7.54/7.64 [258]~P46(x2581)+P46(x2582)+~E(x2581,x2582) % 7.54/7.64 [259]~P8(x2591)+P8(x2592)+~E(x2591,x2592) % 7.54/7.64 [260]~P24(x2601)+P24(x2602)+~E(x2601,x2602) % 7.54/7.64 [261]~P25(x2611)+P25(x2612)+~E(x2611,x2612) % 7.54/7.64 [262]~P29(x2621)+P29(x2622)+~E(x2621,x2622) % 7.54/7.64 [263]~P9(x2631)+P9(x2632)+~E(x2631,x2632) % 7.54/7.64 [264]~P50(x2641)+P50(x2642)+~E(x2641,x2642) % 7.54/7.64 [265]~P19(x2651)+P19(x2652)+~E(x2651,x2652) % 7.54/7.64 [266]~P51(x2661)+P51(x2662)+~E(x2661,x2662) % 7.54/7.64 [267]~P16(x2671)+P16(x2672)+~E(x2671,x2672) % 7.54/7.64 [268]~P71(x2681)+P71(x2682)+~E(x2681,x2682) % 7.54/7.64 [269]~P54(x2691)+P54(x2692)+~E(x2691,x2692) % 7.54/7.64 [270]~P61(x2701)+P61(x2702)+~E(x2701,x2702) % 7.54/7.64 [271]~P17(x2711)+P17(x2712)+~E(x2711,x2712) % 7.54/7.64 [272]~P22(x2721)+P22(x2722)+~E(x2721,x2722) % 7.54/7.64 [273]P2(x2732,x2733)+~E(x2731,x2732)+~P2(x2731,x2733) % 7.54/7.64 [274]P2(x2743,x2742)+~E(x2741,x2742)+~P2(x2743,x2741) % 7.54/7.64 [275]~P23(x2751)+P23(x2752)+~E(x2751,x2752) % 7.54/7.64 [276]~P20(x2761)+P20(x2762)+~E(x2761,x2762) % 7.54/7.64 [277]~P31(x2771)+P31(x2772)+~E(x2771,x2772) % 7.54/7.64 [278]~P58(x2781)+P58(x2782)+~E(x2781,x2782) % 7.54/7.64 [279]~P62(x2791)+P62(x2792)+~E(x2791,x2792) % 7.54/7.64 [280]~P21(x2801)+P21(x2802)+~E(x2801,x2802) % 7.54/7.64 [281]~P49(x2811)+P49(x2812)+~E(x2811,x2812) % 7.54/7.64 [282]~P72(x2821)+P72(x2822)+~E(x2821,x2822) % 7.54/7.64 [283]P3(x2832,x2833)+~E(x2831,x2832)+~P3(x2831,x2833) % 7.54/7.64 [284]P3(x2843,x2842)+~E(x2841,x2842)+~P3(x2843,x2841) % 7.54/7.64 [285]~P13(x2851)+P13(x2852)+~E(x2851,x2852) % 7.54/7.64 [286]~P40(x2861)+P40(x2862)+~E(x2861,x2862) % 7.54/7.64 [287]~P63(x2871)+P63(x2872)+~E(x2871,x2872) % 7.54/7.64 [288]~P76(x2881)+P76(x2882)+~E(x2881,x2882) % 7.54/7.64 [289]~P66(x2891)+P66(x2892)+~E(x2891,x2892) % 7.54/7.64 [290]~P48(x2901)+P48(x2902)+~E(x2901,x2902) % 7.54/7.64 [291]~P52(x2911)+P52(x2912)+~E(x2911,x2912) % 7.54/7.64 [292]~P64(x2921)+P64(x2922)+~E(x2921,x2922) % 7.54/7.64 [293]~P59(x2931)+P59(x2932)+~E(x2931,x2932) % 7.54/7.64 [294]~P42(x2941)+P42(x2942)+~E(x2941,x2942) % 7.54/7.64 [295]~P10(x2951)+P10(x2952)+~E(x2951,x2952) % 7.54/7.64 [296]~P55(x2961)+P55(x2962)+~E(x2961,x2962) % 7.54/7.64 [297]~P73(x2971)+P73(x2972)+~E(x2971,x2972) % 7.54/7.64 [298]~P43(x2981)+P43(x2982)+~E(x2981,x2982) % 7.54/7.64 [299]~P15(x2991)+P15(x2992)+~E(x2991,x2992) % 7.54/7.64 [300]~P65(x3001)+P65(x3002)+~E(x3001,x3002) % 7.54/7.64 [301]~P39(x3011)+P39(x3012)+~E(x3011,x3012) % 7.54/7.64 [302]~P18(x3021)+P18(x3022)+~E(x3021,x3022) % 7.54/7.64 [303]~P75(x3031)+P75(x3032)+~E(x3031,x3032) % 7.54/7.64 [304]~P74(x3041)+P74(x3042)+~E(x3041,x3042) % 7.54/7.64 [305]~P60(x3051)+P60(x3052)+~E(x3051,x3052) % 7.54/7.64 [306]~P14(x3061)+P14(x3062)+~E(x3061,x3062) % 7.54/7.64 [307]~P68(x3071)+P68(x3072)+~E(x3071,x3072) % 7.54/7.64 [308]~P12(x3081)+P12(x3082)+~E(x3081,x3082) % 7.54/7.64 [309]P6(x3092,x3093)+~E(x3091,x3092)+~P6(x3091,x3093) % 7.54/7.64 [310]P6(x3103,x3102)+~E(x3101,x3102)+~P6(x3103,x3101) % 7.54/7.64 [311]~P33(x3111)+P33(x3112)+~E(x3111,x3112) % 7.54/7.64 % 7.54/7.64 %------------------------------------------- % 7.54/7.65 cnf(1990,plain, % 7.54/7.65 (E(f20(a115,x19901,f3(a115)),f3(a115))), % 7.54/7.65 inference(equality_inference,[],[856])). % 7.54/7.65 cnf(2004,plain, % 7.54/7.65 (~P62(x20041)+~P65(x20041)+~P40(x20041)+~P58(x20041)+E(x20042,f3(a119))+E(f118(f118(f31(x20041),f3(x20041)),x20042),f3(x20041))), % 7.54/7.65 inference(equality_inference,[],[932])). % 7.54/7.65 cnf(2006,plain, % 7.54/7.65 (E(f118(f118(f24(a119),f3(a119)),x20061),f118(f118(f24(a119),f3(a119)),x20062))), % 7.54/7.65 inference(equality_inference,[],[935])). % 7.54/7.65 cnf(2007,plain, % 7.54/7.65 (E(f118(f118(f31(a119),x20071),f3(a119)),f118(f118(f23(a119),f3(a119)),f16(a119)))), % 7.54/7.65 inference(equality_inference,[],[946])). % 7.54/7.65 cnf(2008,plain, % 7.54/7.65 (~P77(f118(f29(a114,x20081),x20081))), % 7.54/7.65 inference(equality_inference,[],[954])). % 7.54/7.65 cnf(2010,plain, % 7.54/7.65 (~P77(f118(f29(a115,x20101),x20101))), % 7.54/7.65 inference(equality_inference,[],[960])). % 7.54/7.65 cnf(2013,plain, % 7.54/7.65 (~P78(x20131,f3(a115),x20132)+P77(f118(x20131,f3(a115)))), % 7.54/7.65 inference(equality_inference,[],[967])). % 7.54/7.65 cnf(2035,plain, % 7.54/7.65 (P77(f118(f28(a114,f35(a119,f3(a119))),f3(a114)))), % 7.54/7.65 inference(equality_inference,[],[1054])). % 7.54/7.65 cnf(2045,plain, % 7.54/7.65 (E(f20(a119,f118(f118(f24(a119),f3(a119)),x20451),f118(f118(f24(a119),f3(a119)),x20452)),f3(a119))), % 7.54/7.65 inference(equality_inference,[],[1132])). % 7.54/7.65 cnf(2047,plain, % 7.54/7.65 (E(x20471,f118(f118(f23(a119),f22(a119,x20471,x20472)),x20472))+~P77(f118(f28(a119,x20472),x20471))), % 7.54/7.65 inference(equality_inference,[],[1144])). % 7.54/7.65 cnf(2050,plain, % 7.54/7.65 (P77(f118(f29(a115,x20501),f118(f118(f23(a115),x20501),f16(a115))))), % 7.54/7.65 inference(equality_inference,[],[1175])). % 7.54/7.65 cnf(2054,plain, % 7.54/7.65 (P77(f118(f29(a119,f3(a119)),f118(f118(f31(a119),x20541),f3(a119))))), % 7.54/7.65 inference(equality_inference,[],[1183])). % 7.54/7.65 cnf(2058,plain, % 7.54/7.65 (P77(f118(x20581,f20(a119,x20582,f3(a119))))+~P77(f118(x20581,f3(a119)))), % 7.54/7.65 inference(equality_inference,[],[1205])). % 7.54/7.65 cnf(2064,plain, % 7.54/7.65 (~P77(f118(x20641,f20(a119,x20642,f3(a119))))+P77(f118(x20641,f3(a119)))), % 7.54/7.65 inference(equality_inference,[],[1325])). % 7.54/7.65 cnf(2065,plain, % 7.54/7.65 (~P77(f118(f29(a114,f3(a114)),f118(f118(f24(a114),f3(a114)),f3(a114))))), % 7.54/7.65 inference(equality_inference,[],[1342])). % 7.54/7.65 cnf(2067,plain, % 7.54/7.65 (P77(f118(f29(a115,f3(a115)),f118(f118(f31(a115),f19(a115,x20671)),f3(a119))))), % 7.54/7.65 inference(equality_inference,[],[1364])). % 7.54/7.65 cnf(2069,plain, % 7.54/7.65 (P77(f118(x20691,x20692))+~P77(f118(x20691,f22(a119,f118(f118(f23(a119),x20693),x20692),x20693)))), % 7.54/7.65 inference(equality_inference,[],[1375])). % 7.54/7.65 cnf(2073,plain, % 7.54/7.65 (E(x20731,f3(a119))+~P77(f118(f29(a115,f3(a115)),f118(f118(f31(a115),f19(a115,f3(a115))),x20731)))), % 7.54/7.65 inference(equality_inference,[],[1552])). % 7.54/7.65 cnf(2081,plain, % 7.54/7.65 (~P78(x20811,x20812,f118(f118(f23(a115),f118(f118(f24(a115),x20812),x20813)),x20814))+P77(f118(x20811,x20813))+~P77(f118(f29(a115,x20814),x20812))+~P77(f118(f28(a115,f3(a115)),x20814))+~P77(f118(f29(a115,f3(a115)),x20812))), % 7.54/7.65 inference(equality_inference,[],[1649])). % 7.54/7.65 cnf(2085,plain, % 7.54/7.65 (~P77(f118(f28(a119,x20851),x20851))+E(x20852,f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x20851,x20851)),x20853)),x20852))), % 7.54/7.65 inference(equality_inference,[],[1876])). % 7.54/7.65 cnf(2086,plain, % 7.54/7.65 (~P77(f118(f28(a119,x20861),x20861))+E(f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x20861,x20861)),x20862)),x20863),x20863)), % 7.54/7.65 inference(equality_inference,[],[1877])). % 7.54/7.65 cnf(2095,plain, % 7.54/7.65 (~P77(f118(f29(a114,f3(a114)),f118(f118(f23(a114),a123),f16(a114))))), % 7.54/7.65 inference(scs_inference,[],[695,1944])). % 7.54/7.65 cnf(2096,plain, % 7.54/7.65 (P77(f118(f28(a114,f19(a114,f118(a5,f118(a124,x20961)))),f118(f118(f23(a114),a123),f16(a114))))), % 7.54/7.65 inference(rename_variables,[],[695])). % 7.54/7.65 cnf(2098,plain, % 7.54/7.65 (E(f25(a114,a40),f16(a114))), % 7.54/7.65 inference(scs_inference,[],[576,695,1944,1011])). % 7.54/7.65 cnf(2102,plain, % 7.54/7.65 (P77(f118(f29(a114,f3(a114)),f95(x21021,a40)))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,1944,1011,1179,1189])). % 7.54/7.65 cnf(2104,plain, % 7.54/7.65 (~P78(f29(a114,f20(a115,x21041,x21042)),x21042,x21041)), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,1944,1011,1179,1189,1228])). % 7.54/7.65 cnf(2105,plain, % 7.54/7.65 (~P77(f118(f29(a114,x21051),x21051))), % 7.54/7.65 inference(rename_variables,[],[2008])). % 7.54/7.65 cnf(2108,plain, % 7.54/7.65 (P77(f118(f28(a119,x21081),x21081))), % 7.54/7.65 inference(rename_variables,[],[570])). % 7.54/7.65 cnf(2111,plain, % 7.54/7.65 (P77(f118(f28(a114,x21111),x21111))), % 7.54/7.65 inference(rename_variables,[],[569])). % 7.54/7.65 cnf(2114,plain, % 7.54/7.65 (~P77(f118(f29(a114,x21141),x21141))), % 7.54/7.65 inference(rename_variables,[],[2008])). % 7.54/7.65 cnf(2116,plain, % 7.54/7.65 (P77(f118(f28(a114,f22(a119,f118(f118(f23(a119),x21161),x21162),x21161)),x21162))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,569,2111,570,1944,1011,1179,1189,1228,1720,2058,2064,2069])). % 7.54/7.65 cnf(2117,plain, % 7.54/7.65 (P77(f118(f28(a114,x21171),x21171))), % 7.54/7.65 inference(rename_variables,[],[569])). % 7.54/7.65 cnf(2123,plain, % 7.54/7.65 (~E(x21231,f118(f118(f23(a115),x21231),f16(a115)))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2050,569,2111,570,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960])). % 7.54/7.65 cnf(2128,plain, % 7.54/7.65 (~P77(f118(f29(a119,x21281),x21281))), % 7.54/7.65 inference(rename_variables,[],[736])). % 7.54/7.65 cnf(2134,plain, % 7.54/7.65 (E(f118(f118(f23(a119),x21341),f22(a119,x21341,x21341)),x21341)), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2050,569,2111,570,736,2128,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118])). % 7.54/7.65 cnf(2136,plain, % 7.54/7.65 (P77(f118(f28(a114,f3(a114)),f34(f16(a114))))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2050,569,2111,2117,570,736,2128,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129])). % 7.54/7.65 cnf(2137,plain, % 7.54/7.65 (P77(f118(f28(a114,x21371),x21371))), % 7.54/7.65 inference(rename_variables,[],[569])). % 7.54/7.65 cnf(2139,plain, % 7.54/7.65 (~E(f118(f118(f23(a119),x21391),f118(f118(f23(a119),x21392),f16(a119))),x21392)), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2050,569,2111,2117,570,736,2128,742,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174])). % 7.54/7.65 cnf(2140,plain, % 7.54/7.65 (~P77(f118(f29(a119,f118(f118(f23(a119),x21401),x21402)),x21402))), % 7.54/7.65 inference(rename_variables,[],[742])). % 7.54/7.65 cnf(2142,plain, % 7.54/7.65 (~E(f118(f118(f23(a115),x21421),f16(a115)),x21421)), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2050,569,2111,2117,570,736,2128,742,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175])). % 7.54/7.65 cnf(2143,plain, % 7.54/7.65 (~P77(f118(f29(a115,x21431),x21431))), % 7.54/7.65 inference(rename_variables,[],[2010])). % 7.54/7.65 cnf(2146,plain, % 7.54/7.65 (~P77(f118(f29(a119,f118(f118(f23(a119),x21461),x21462)),x21462))), % 7.54/7.65 inference(rename_variables,[],[742])). % 7.54/7.65 cnf(2153,plain, % 7.54/7.65 (~P77(f118(f29(a119,x21531),x21531))), % 7.54/7.65 inference(rename_variables,[],[736])). % 7.54/7.65 cnf(2162,plain, % 7.54/7.65 (~P77(f118(f29(a119,f118(f118(f23(a119),x21621),x21622)),x21622))), % 7.54/7.65 inference(rename_variables,[],[742])). % 7.54/7.65 cnf(2164,plain, % 7.54/7.65 (~P77(f118(f29(a119,f118(f118(f23(a119),x21641),f118(f118(f23(a119),x21642),x21643))),x21643))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2050,569,2111,2117,570,736,2128,742,2140,2146,2162,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271])). % 7.54/7.65 cnf(2165,plain, % 7.54/7.65 (~P77(f118(f29(a119,f118(f118(f23(a119),x21651),x21652)),x21652))), % 7.54/7.65 inference(rename_variables,[],[742])). % 7.54/7.65 cnf(2168,plain, % 7.54/7.65 (~P77(f118(f29(a119,f118(f118(f23(a119),x21681),x21682)),x21682))), % 7.54/7.65 inference(rename_variables,[],[742])). % 7.54/7.65 cnf(2170,plain, % 7.54/7.65 (~P77(f118(f28(a119,f118(f118(f23(a119),x21701),f118(f118(f23(a119),x21702),f16(a119)))),x21702))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2050,569,2111,2117,570,736,2128,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289])). % 7.54/7.65 cnf(2171,plain, % 7.54/7.65 (~P77(f118(f29(a119,f118(f118(f23(a119),x21711),x21712)),x21712))), % 7.54/7.65 inference(rename_variables,[],[742])). % 7.54/7.65 cnf(2173,plain, % 7.54/7.65 (~P77(f118(f29(a115,f118(f118(f23(a115),x21731),f16(a115))),x21731))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2050,569,2111,2117,570,736,2128,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293])). % 7.54/7.65 cnf(2174,plain, % 7.54/7.65 (~P77(f118(f29(a115,x21741),x21741))), % 7.54/7.65 inference(rename_variables,[],[2010])). % 7.54/7.65 cnf(2178,plain, % 7.54/7.65 (P77(f118(f29(a119,x21781),f118(f118(f23(a119),f33(f35(a119,x21781))),f16(a119))))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2050,569,2111,2117,570,736,2128,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316])). % 7.54/7.65 cnf(2180,plain, % 7.54/7.65 (P77(f118(f29(a119,f3(a119)),f22(a119,f118(f118(f31(a119),x21801),f3(a119)),f3(a119))))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2050,569,2111,2117,570,736,2128,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323])). % 7.54/7.65 cnf(2184,plain, % 7.54/7.65 (~E(x21841,f118(f118(f23(a119),f118(f118(f23(a119),x21841),x21842)),f16(a119)))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2050,569,2111,2117,570,736,2128,2153,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353])). % 7.54/7.65 cnf(2187,plain, % 7.54/7.65 (P77(f118(f29(a115,x21871),f118(f118(f23(a115),x21871),f16(a115))))), % 7.54/7.65 inference(rename_variables,[],[2050])). % 7.54/7.65 cnf(2189,plain, % 7.54/7.65 (P77(f118(f28(a119,x21891),f33(f35(a119,x21891))))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2050,569,2111,2117,570,736,2128,2153,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387])). % 7.54/7.65 cnf(2191,plain, % 7.54/7.65 (~P77(f118(f29(a119,f3(a119)),f22(a119,x21911,x21911)))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2050,569,2111,2117,570,736,2128,2153,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438])). % 7.54/7.65 cnf(2193,plain, % 7.54/7.65 (~P77(f118(f29(a119,x21931),f22(a119,x21931,x21932)))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2050,569,2111,2117,570,736,2128,2153,684,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440])). % 7.54/7.65 cnf(2197,plain, % 7.54/7.65 (~P77(f118(f29(a119,f118(f118(f23(a119),f118(f118(f23(a119),x21971),x21972)),x21973)),x21972))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2050,569,2111,2117,570,736,2128,2153,684,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567])). % 7.54/7.65 cnf(2200,plain, % 7.54/7.65 (P77(f118(f28(a119,x22001),f118(f118(f24(a119),x22001),x22001)))), % 7.54/7.65 inference(rename_variables,[],[622])). % 7.54/7.65 cnf(2204,plain, % 7.54/7.65 (P77(f118(f29(a119,x22041),f118(f118(f23(a119),f118(f118(f23(a119),x22041),f16(a119))),x22042)))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2050,569,2111,2117,697,570,736,2128,2153,684,622,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760])). % 7.54/7.65 cnf(2208,plain, % 7.54/7.65 (P77(f118(f28(a114,x22081),f35(a119,f26(x22081))))), % 7.54/7.65 inference(rename_variables,[],[600])). % 7.54/7.65 cnf(2210,plain, % 7.54/7.65 (E(x22101,f118(f118(f23(a119),f22(a119,x22101,x22101)),x22101))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2050,569,2111,2117,697,600,570,2108,736,2128,2153,684,622,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047])). % 7.54/7.65 cnf(2214,plain, % 7.54/7.65 (~E(f118(f118(f23(a119),x22141),f16(a119)),x22141)), % 7.54/7.65 inference(rename_variables,[],[728])). % 7.54/7.65 cnf(2223,plain, % 7.54/7.65 (~E(f118(f118(f23(a119),x22231),f16(a119)),x22231)), % 7.54/7.65 inference(rename_variables,[],[728])). % 7.54/7.65 cnf(2226,plain, % 7.54/7.65 (~E(f118(f118(f23(a119),x22261),f16(a119)),x22261)), % 7.54/7.65 inference(rename_variables,[],[728])). % 7.54/7.65 cnf(2229,plain, % 7.54/7.65 (P77(f118(f28(a119,f20(a119,x22291,x22292)),x22291))), % 7.54/7.65 inference(rename_variables,[],[671])). % 7.54/7.65 cnf(2239,plain, % 7.54/7.65 (~E(f22(a119,f118(f118(f23(a119),x22391),f16(a119)),x22391),f3(a119))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2050,725,728,2214,2223,569,2111,2117,697,600,2007,570,2108,736,2128,2153,671,684,622,744,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017])). % 7.54/7.65 cnf(2241,plain, % 7.54/7.65 (E(f22(a119,f22(a119,x22411,x22412),x22411),f3(a119))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2050,725,728,2214,2223,569,2111,2117,697,600,2007,570,2108,736,2128,2153,670,671,684,622,744,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048])). % 7.54/7.65 cnf(2253,plain, % 7.54/7.65 (P77(f118(f28(a114,x22531),x22531))), % 7.54/7.65 inference(rename_variables,[],[569])). % 7.54/7.65 cnf(2263,plain, % 7.54/7.65 (P77(f118(f28(a114,x22631),x22631))), % 7.54/7.65 inference(rename_variables,[],[569])). % 7.54/7.65 cnf(2266,plain, % 7.54/7.65 (P77(f118(f28(a114,x22661),x22661))), % 7.54/7.65 inference(rename_variables,[],[569])). % 7.54/7.65 cnf(2273,plain, % 7.54/7.65 (P77(f118(f28(a114,x22731),x22731))), % 7.54/7.65 inference(rename_variables,[],[569])). % 7.54/7.65 cnf(2276,plain, % 7.54/7.65 (P77(f118(f28(a114,x22761),x22761))), % 7.54/7.65 inference(rename_variables,[],[569])). % 7.54/7.65 cnf(2279,plain, % 7.54/7.65 (P77(f118(f28(a114,x22791),f35(a119,f26(x22791))))), % 7.54/7.65 inference(rename_variables,[],[600])). % 7.54/7.65 cnf(2284,plain, % 7.54/7.65 (~P77(f118(f28(a119,f118(f118(f23(a119),x22841),f16(a119))),x22841))), % 7.54/7.65 inference(rename_variables,[],[744])). % 7.54/7.65 cnf(2287,plain, % 7.54/7.65 (~P77(f118(f28(a119,f118(f118(f23(a119),x22871),f16(a119))),x22871))), % 7.54/7.65 inference(rename_variables,[],[744])). % 7.54/7.65 cnf(2289,plain, % 7.54/7.65 (~P77(f118(f28(a115,f118(f118(f23(a115),x22891),f16(a115))),x22891))), % 7.54/7.65 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2174,2050,725,728,2214,2223,569,2111,2117,2137,2253,2263,2266,2273,697,600,2208,2007,551,734,570,2108,571,736,2128,2153,692,670,671,684,622,744,2284,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292])). % 7.54/7.65 cnf(2290,plain, % 7.54/7.65 (~P77(f118(f29(a115,x22901),x22901))), % 7.54/7.65 inference(rename_variables,[],[2010])). % 7.54/7.65 cnf(2293,plain, % 7.54/7.65 (P77(f118(f28(a114,x22931),f35(a119,f26(x22931))))), % 7.54/7.65 inference(rename_variables,[],[600])). % 7.54/7.65 cnf(2295,plain, % 7.54/7.65 (P78(f28(a114,f20(a115,x22951,x22952)),x22952,x22951)), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2174,2050,725,728,2214,2223,569,2111,2117,2137,2253,2263,2266,2273,2276,697,600,2208,2279,2007,551,734,570,2108,571,736,2128,2153,692,670,671,684,622,744,2284,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343])). % 7.54/7.66 cnf(2296,plain, % 7.54/7.66 (P77(f118(f28(a114,x22961),x22961))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2299,plain, % 7.54/7.66 (P77(f118(f28(a114,x22991),x22991))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2302,plain, % 7.54/7.66 (P77(f118(f28(a114,x23021),x23021))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2304,plain, % 7.54/7.66 (P77(f118(f29(a115,f22(a115,x23041,f16(a115))),x23041))), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2174,2050,725,728,2214,2223,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,697,600,2208,2279,2007,551,734,570,2108,571,736,2128,2153,692,670,671,684,622,744,2284,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437])). % 7.54/7.66 cnf(2305,plain, % 7.54/7.66 (P77(f118(f28(a115,x23051),x23051))), % 7.54/7.66 inference(rename_variables,[],[571])). % 7.54/7.66 cnf(2309,plain, % 7.54/7.66 (P77(f118(f28(a119,x23091),f118(f118(f24(a119),f118(f118(f23(a119),x23092),x23091)),f118(f118(f23(a119),x23092),x23091))))), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2174,2050,725,728,2214,2223,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,697,600,2208,2279,2007,551,734,570,2108,571,736,2128,2153,692,670,671,684,622,2200,744,2284,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578])). % 7.54/7.66 cnf(2310,plain, % 7.54/7.66 (P77(f118(f28(a119,x23101),f118(f118(f24(a119),x23101),x23101)))), % 7.54/7.66 inference(rename_variables,[],[622])). % 7.54/7.66 cnf(2313,plain, % 7.54/7.66 (P77(f118(f28(a119,x23131),f118(f118(f24(a119),x23131),x23131)))), % 7.54/7.66 inference(rename_variables,[],[622])). % 7.54/7.66 cnf(2315,plain, % 7.54/7.66 (~P77(f118(f28(a119,f118(f118(f24(a119),f118(f118(f23(a119),x23151),f16(a119))),f118(f118(f23(a119),x23151),f16(a119)))),x23151))), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2174,2050,725,728,2214,2223,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,697,600,2208,2279,2007,551,734,570,2108,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636])). % 7.54/7.66 cnf(2318,plain, % 7.54/7.66 (~P77(f118(f29(a119,x23181),f22(a119,f118(f118(f23(a119),x23181),x23182),x23182)))), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2174,2050,725,728,2214,2223,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,697,600,2208,2279,2007,551,734,570,2108,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662])). % 7.54/7.66 cnf(2319,plain, % 7.54/7.66 (~P77(f118(f29(a119,x23191),x23191))), % 7.54/7.66 inference(rename_variables,[],[736])). % 7.54/7.66 cnf(2321,plain, % 7.54/7.66 (P77(f118(f28(a119,f22(a119,f118(f118(f23(a119),x23211),x23212),x23212)),x23211))), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2174,2050,725,728,2214,2223,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,697,600,2208,2279,2007,551,734,570,2108,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671])). % 7.54/7.66 cnf(2322,plain, % 7.54/7.66 (P77(f118(f28(a119,x23221),x23221))), % 7.54/7.66 inference(rename_variables,[],[570])). % 7.54/7.66 cnf(2328,plain, % 7.54/7.66 (P77(f118(f28(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),f118(f118(f31(a119),f118(f118(f23(a119),f3(a119)),f16(a119))),x23281)))), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2174,2050,725,728,2214,2223,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,697,600,2208,2279,2007,551,734,570,2108,2322,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844])). % 7.54/7.66 cnf(2329,plain, % 7.54/7.66 (P77(f118(f28(a119,x23291),x23291))), % 7.54/7.66 inference(rename_variables,[],[570])). % 7.54/7.66 cnf(2332,plain, % 7.54/7.66 (~P77(f118(f28(a119,f118(f118(f23(a119),x23321),f16(a119))),x23321))), % 7.54/7.66 inference(rename_variables,[],[744])). % 7.54/7.66 cnf(2335,plain, % 7.54/7.66 (~E(f118(f118(f23(a119),x23351),f16(a119)),x23351)), % 7.54/7.66 inference(rename_variables,[],[728])). % 7.54/7.66 cnf(2339,plain, % 7.54/7.66 (E(f118(f118(f23(a119),f118(f118(f24(a119),f22(a119,x23391,x23391)),x23392)),x23393),x23393)), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2174,2050,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,697,600,2208,2279,2007,551,734,570,2108,2322,2329,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086])). % 7.54/7.66 cnf(2341,plain, % 7.54/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x23411),f16(a119))),x23412),x23411)), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2174,2050,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,697,600,2208,2279,2007,318,551,734,570,2108,2322,2329,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928])). % 7.54/7.66 cnf(2343,plain, % 7.54/7.66 (~E(f118(f118(f24(a119),f118(f118(f23(a119),x23431),f16(a119))),f118(f118(f23(a119),x23431),f16(a119))),x23431)), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2008,2105,2010,2143,2174,2050,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,697,600,2208,2279,2007,318,333,551,734,570,2108,2322,2329,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930])). % 7.54/7.66 cnf(2346,plain, % 7.54/7.66 (~P77(f118(f29(a114,x23461),x23461))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2350,plain, % 7.54/7.66 (P77(f118(f28(a115,x23501),f118(f118(f23(a115),x23501),f16(a115))))), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2065,2008,2105,2114,2010,2143,2174,2050,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,697,600,2208,2279,2007,1990,318,327,333,381,551,734,570,2108,2322,2329,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029])). % 7.54/7.66 cnf(2352,plain, % 7.54/7.66 (P77(f118(f29(a119,f118(f118(f24(a119),x23521),f3(a119))),f118(f118(f23(a119),f3(a119)),f16(a119))))), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2065,2008,2105,2114,2010,2143,2174,2050,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,697,600,2208,2279,2007,1990,318,326,327,333,381,551,734,570,2108,2322,2329,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034])). % 7.54/7.66 cnf(2356,plain, % 7.54/7.66 (~P77(f118(f29(a119,f118(f118(f23(a119),f118(f118(f23(a119),x23561),f16(a119))),x23562)),x23561))), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2065,2008,2105,2114,2010,2143,2174,2050,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,697,600,2208,2279,2007,1990,318,326,327,333,381,551,734,570,2108,2322,2329,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098])). % 7.54/7.66 cnf(2360,plain, % 7.54/7.66 (P77(f118(f28(a114,f3(a119)),f20(a119,x23601,f20(a119,f118(f118(f24(a119),f3(a119)),x23602),f118(f118(f24(a119),f3(a119)),x23603)))))), % 7.54/7.66 inference(scs_inference,[],[576,695,2054,2065,2008,2105,2114,2010,2143,2174,2050,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,697,600,2208,2279,2007,2045,1990,318,326,327,333,381,551,734,570,2108,2322,2329,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205])). % 7.54/7.66 cnf(2361,plain, % 7.54/7.66 (P77(f118(f28(a114,x23611),x23611))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2363,plain, % 7.54/7.66 (P77(f118(f28(a114,f19(a114,f118(a5,f118(a124,x23631)))),f35(a119,f26(f118(f118(f23(a114),a123),f16(a114))))))), % 7.54/7.66 inference(scs_inference,[],[576,695,2096,2054,2065,2008,2105,2114,2010,2143,2174,2050,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,697,600,2208,2279,2293,2007,2045,1990,318,326,327,333,381,551,734,570,2108,2322,2329,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218])). % 7.54/7.66 cnf(2364,plain, % 7.54/7.66 (P77(f118(f28(a114,x23641),f35(a119,f26(x23641))))), % 7.54/7.66 inference(rename_variables,[],[600])). % 7.54/7.66 cnf(2366,plain, % 7.54/7.66 (P77(f118(f29(a114,f3(a114)),f25(a114,a40)))), % 7.54/7.66 inference(scs_inference,[],[576,695,2096,2054,2065,2008,2105,2114,2010,2143,2174,2050,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,697,600,2208,2279,2293,2007,2045,1990,318,326,327,333,381,551,734,570,2108,2322,2329,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238])). % 7.54/7.66 cnf(2373,plain, % 7.54/7.66 (~P77(f118(f29(a114,x23731),x23731))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2375,plain, % 7.54/7.66 (~P77(f118(f29(a114,f3(a119)),f20(a119,x23751,f20(a119,f118(f118(f24(a119),f3(a119)),x23752),f118(f118(f24(a119),f3(a119)),x23753)))))), % 7.54/7.66 inference(scs_inference,[],[576,695,2096,2054,2065,2008,2105,2114,2346,2373,2010,2143,2174,2050,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,697,600,2208,2279,2293,2007,2045,1990,315,318,326,327,333,381,551,734,570,2108,2322,2329,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325])). % 7.54/7.66 cnf(2376,plain, % 7.54/7.66 (~P77(f118(f29(a114,x23761),x23761))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2382,plain, % 7.54/7.66 (P77(f118(f28(a114,f3(a119)),f22(a119,x23821,f118(f118(f23(a119),x23821),f16(a119)))))), % 7.54/7.66 inference(scs_inference,[],[576,695,2096,2054,2065,2008,2105,2114,2346,2373,2010,2143,2174,2050,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,697,600,2208,2279,2293,2007,2045,1990,315,318,326,327,333,381,551,734,570,2108,2322,2329,571,736,2128,2153,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360])). % 7.54/7.66 cnf(2383,plain, % 7.54/7.66 (P77(f118(f28(a114,x23831),x23831))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2385,plain, % 7.54/7.66 (E(f118(f118(f23(a119),x23851),f97(x23851,x23851,f29(a114,f22(a119,x23851,x23851)))),x23851)), % 7.54/7.66 inference(scs_inference,[],[576,695,2096,2054,2065,2008,2105,2114,2346,2373,2376,2010,2143,2174,2050,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,697,600,2208,2279,2293,2007,2045,1990,315,318,326,327,333,381,551,734,570,2108,2322,2329,571,736,2128,2153,2319,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367])). % 7.54/7.66 cnf(2386,plain, % 7.54/7.66 (~P77(f118(f29(a114,x23861),x23861))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2388,plain, % 7.54/7.66 (E(f118(f118(f23(a119),x23881),f101(x23881,x23881,f29(a114,f22(a119,x23881,x23881)))),x23881)), % 7.54/7.66 inference(scs_inference,[],[576,695,2096,2054,2065,2008,2105,2114,2346,2373,2376,2386,2010,2143,2174,2050,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,697,600,2208,2279,2293,2007,2045,1990,315,318,326,327,333,381,551,734,570,2108,2322,2329,571,736,2128,2153,2319,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368])). % 7.54/7.66 cnf(2389,plain, % 7.54/7.66 (~P77(f118(f29(a114,x23891),x23891))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2392,plain, % 7.54/7.66 (P77(f118(f28(a114,x23921),x23921))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2394,plain, % 7.54/7.66 (~P77(f118(f29(a115,f3(a115)),f19(a115,f3(a115))))), % 7.54/7.66 inference(scs_inference,[],[576,695,2096,2054,2065,2008,2105,2114,2346,2373,2376,2386,2010,2143,2174,2050,380,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,697,600,2208,2279,2293,2007,2045,1990,315,318,326,327,333,381,551,734,570,2108,2322,2329,571,736,2128,2153,2319,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383])). % 7.54/7.66 cnf(2396,plain, % 7.54/7.66 (~P77(f118(f29(a114,f3(a119)),f22(a119,f3(a119),f118(f118(f31(a119),x23961),f3(a119)))))), % 7.54/7.66 inference(scs_inference,[],[576,695,2096,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2010,2143,2174,2050,380,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,697,600,2208,2279,2293,2007,2045,1990,315,318,326,327,333,381,551,734,570,2108,2322,2329,571,736,2128,2153,2319,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421])). % 7.54/7.66 cnf(2397,plain, % 7.54/7.66 (~P77(f118(f29(a114,x23971),x23971))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2399,plain, % 7.54/7.66 (P77(f118(f29(a114,f3(a114)),f102(f118(f118(f23(a114),f35(a119,f33(a40))),f16(a114)),a40,f3(a114))))), % 7.54/7.66 inference(scs_inference,[],[576,677,695,2096,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2010,2143,2174,2050,380,725,728,2214,2223,2226,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,697,600,2208,2279,2293,2007,2045,1990,315,318,326,327,333,381,551,734,570,2108,2322,2329,571,736,2128,2153,2319,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439])). % 7.54/7.66 cnf(2400,plain, % 7.54/7.66 (P77(f118(f29(a114,x24001),f118(f118(f23(a114),f35(a119,f33(x24001))),f16(a114))))), % 7.54/7.66 inference(rename_variables,[],[677])). % 7.54/7.66 cnf(2403,plain, % 7.54/7.66 (P77(f118(f28(a114,x24031),x24031))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2404,plain, % 7.54/7.66 (~E(f118(f118(f23(a119),x24041),f16(a119)),x24041)), % 7.54/7.66 inference(rename_variables,[],[728])). % 7.54/7.66 cnf(2407,plain, % 7.54/7.66 (~P77(f118(f29(a114,x24071),x24071))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2408,plain, % 7.54/7.66 (~E(f118(f118(f23(a119),x24081),f16(a119)),x24081)), % 7.54/7.66 inference(rename_variables,[],[728])). % 7.54/7.66 cnf(2411,plain, % 7.54/7.66 (~P77(f118(f29(a114,x24111),x24111))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2414,plain, % 7.54/7.66 (~P77(f118(f29(a114,x24141),x24141))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2417,plain, % 7.54/7.66 (~P77(f118(f29(a114,x24171),x24171))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2419,plain, % 7.54/7.66 (~P77(f118(f29(a115,f118(f118(f23(a115),f3(a115)),f3(a115))),f3(a115)))), % 7.54/7.66 inference(scs_inference,[],[576,677,695,2096,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2010,2143,2174,2290,2050,380,725,728,2214,2223,2226,2335,2404,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,697,600,2208,2279,2293,2007,2045,1990,315,318,326,327,333,364,381,382,551,734,570,2108,2322,2329,571,736,2128,2153,2319,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670])). % 7.54/7.66 cnf(2420,plain, % 7.54/7.66 (~P77(f118(f29(a115,x24201),x24201))), % 7.54/7.66 inference(rename_variables,[],[2010])). % 7.54/7.66 cnf(2422,plain, % 7.54/7.66 (~P77(f118(f28(a115,f22(a115,f118(f118(f23(a115),x24221),f16(a115)),x24221)),f3(a115)))), % 7.54/7.66 inference(scs_inference,[],[576,677,695,2096,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2010,2143,2174,2290,2050,380,725,728,2214,2223,2226,2335,2404,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,697,600,2208,2279,2293,2007,2045,1990,315,318,326,327,333,364,381,382,479,551,734,570,2108,2322,2329,571,736,2128,2153,2319,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677])). % 7.54/7.66 cnf(2426,plain, % 7.54/7.66 (P77(f118(f29(a114,x24261),f35(a119,f33(f118(f118(f23(a114),x24261),f16(a114))))))), % 7.54/7.66 inference(scs_inference,[],[576,677,2400,695,2096,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2010,2143,2174,2290,2050,380,725,728,2214,2223,2226,2335,2404,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,697,600,2208,2279,2293,2007,2045,1990,315,318,326,327,333,364,366,381,382,478,479,551,734,570,2108,2322,2329,571,736,2128,2153,2319,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780])). % 7.54/7.66 cnf(2427,plain, % 7.54/7.66 (P77(f118(f29(a114,x24271),f118(f118(f23(a114),f35(a119,f33(x24271))),f16(a114))))), % 7.54/7.66 inference(rename_variables,[],[677])). % 7.54/7.66 cnf(2430,plain, % 7.54/7.66 (~P77(f118(f29(a114,x24301),x24301))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2439,plain, % 7.54/7.66 (~E(f118(f118(f23(a119),x24391),f16(a119)),x24391)), % 7.54/7.66 inference(rename_variables,[],[728])). % 7.54/7.66 cnf(2444,plain, % 7.54/7.66 (E(f22(a119,f3(a119),x24441),f3(a119))), % 7.54/7.66 inference(rename_variables,[],[566])). % 7.54/7.66 cnf(2453,plain, % 7.54/7.66 (E(f22(a119,f22(a119,f3(a119),x24531),x24532),f3(a119))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2050,380,725,728,2214,2223,2226,2335,2404,2408,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,697,600,2208,2279,2293,2007,2045,1990,315,318,325,326,327,332,333,336,364,366,381,382,389,478,479,712,551,734,566,595,570,2108,2322,2329,571,736,2128,2153,2319,739,692,670,671,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013])). % 7.54/7.66 cnf(2454,plain, % 7.54/7.66 (~P77(f118(f29(a119,x24541),f3(a119)))), % 7.54/7.66 inference(rename_variables,[],[739])). % 7.54/7.66 cnf(2461,plain, % 7.54/7.66 (P77(f118(f28(a119,f3(a119)),x24611))), % 7.54/7.66 inference(rename_variables,[],[579])). % 7.54/7.66 cnf(2464,plain, % 7.54/7.66 (P77(f118(f29(a115,x24641),f118(f118(f23(a115),x24641),f16(a115))))), % 7.54/7.66 inference(rename_variables,[],[2050])). % 7.54/7.66 cnf(2465,plain, % 7.54/7.66 (~E(f118(f118(f23(a119),x24651),f16(a119)),x24651)), % 7.54/7.66 inference(rename_variables,[],[728])). % 7.54/7.66 cnf(2468,plain, % 7.54/7.66 (P77(f118(f28(a119,x24681),x24681))), % 7.54/7.66 inference(rename_variables,[],[570])). % 7.54/7.66 cnf(2474,plain, % 7.54/7.66 (~P77(f118(f29(a114,f35(a119,f26(x24741))),x24741))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2050,2187,380,725,728,2214,2223,2226,2335,2404,2408,2439,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,697,600,2208,2279,2293,2364,2007,2045,1990,315,317,318,325,326,327,332,333,336,364,366,381,382,389,478,479,712,551,734,566,595,570,2108,2322,2329,571,736,2128,2153,2319,739,692,670,671,579,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165])). % 7.54/7.66 cnf(2481,plain, % 7.54/7.66 (P77(f118(f29(a115,x24811),f118(f118(f23(a115),x24811),f16(a115))))), % 7.54/7.66 inference(rename_variables,[],[2050])). % 7.54/7.66 cnf(2490,plain, % 7.54/7.66 (~P77(f118(f29(a119,x24901),x24901))), % 7.54/7.66 inference(rename_variables,[],[736])). % 7.54/7.66 cnf(2491,plain, % 7.54/7.66 (P77(f118(f28(a114,x24911),x24911))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2498,plain, % 7.54/7.66 (~P77(f118(f29(a119,x24981),x24981))), % 7.54/7.66 inference(rename_variables,[],[736])). % 7.54/7.66 cnf(2501,plain, % 7.54/7.66 (P77(f118(f28(a114,x25011),x25011))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2503,plain, % 7.54/7.66 (P77(f118(f29(a115,f3(a115)),f20(a115,f118(f118(f23(a115),f3(a115)),f16(a115)),f118(f118(f23(a115),f3(a115)),f16(a115)))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2050,2187,2464,2481,380,725,728,2214,2223,2226,2335,2404,2408,2439,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,697,600,2208,2279,2293,2364,2007,2045,1990,315,317,318,325,326,327,332,333,336,364,366,381,382,389,478,479,712,551,734,566,595,570,2108,2322,2329,571,2305,736,2128,2153,2319,2490,739,692,586,670,671,579,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452])). % 7.54/7.66 cnf(2504,plain, % 7.54/7.66 (P77(f118(f29(a115,x25041),f118(f118(f23(a115),x25041),f16(a115))))), % 7.54/7.66 inference(rename_variables,[],[2050])). % 7.54/7.66 cnf(2505,plain, % 7.54/7.66 (P77(f118(f28(a115,x25051),x25051))), % 7.54/7.66 inference(rename_variables,[],[571])). % 7.54/7.66 cnf(2507,plain, % 7.54/7.66 (P77(f118(f28(a115,f3(a115)),f20(a115,f3(a115),f118(f118(f23(a115),f3(a115)),f16(a115)))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2050,2187,2464,2481,2504,380,725,728,2214,2223,2226,2335,2404,2408,2439,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,697,600,2208,2279,2293,2364,2007,2045,1990,315,317,318,325,326,327,332,333,336,364,366,381,382,389,478,479,712,551,734,566,595,570,2108,2322,2329,571,2305,2505,736,2128,2153,2319,2490,739,692,586,670,671,579,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459])). % 7.54/7.66 cnf(2508,plain, % 7.54/7.66 (P77(f118(f29(a115,x25081),f118(f118(f23(a115),x25081),f16(a115))))), % 7.54/7.66 inference(rename_variables,[],[2050])). % 7.54/7.66 cnf(2509,plain, % 7.54/7.66 (P77(f118(f28(a115,x25091),x25091))), % 7.54/7.66 inference(rename_variables,[],[571])). % 7.54/7.66 cnf(2511,plain, % 7.54/7.66 (P77(f118(f29(a119,f3(a119)),f16(a119)))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2050,2187,2464,2481,2504,380,725,728,2214,2223,2226,2335,2404,2408,2439,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,625,697,600,2208,2279,2293,2364,2007,2045,1990,315,317,318,325,326,327,332,333,336,364,366,381,382,389,478,479,712,551,734,566,595,570,2108,2322,2329,571,2305,2505,736,2128,2153,2319,2490,2498,739,692,586,670,671,579,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479])). % 7.54/7.66 cnf(2512,plain, % 7.54/7.66 (P77(f118(f29(a119,x25121),f118(f118(f23(a119),x25121),f16(a119))))), % 7.54/7.66 inference(rename_variables,[],[625])). % 7.54/7.66 cnf(2513,plain, % 7.54/7.66 (~P77(f118(f29(a119,x25131),x25131))), % 7.54/7.66 inference(rename_variables,[],[736])). % 7.54/7.66 cnf(2517,plain, % 7.54/7.66 (~E(f118(f118(f23(a119),x25171),f16(a119)),x25171)), % 7.54/7.66 inference(rename_variables,[],[728])). % 7.54/7.66 cnf(2520,plain, % 7.54/7.66 (~P77(f118(f29(a119,x25201),f3(a119)))), % 7.54/7.66 inference(rename_variables,[],[739])). % 7.54/7.66 cnf(2526,plain, % 7.54/7.66 (P77(f118(f29(a115,x25261),f118(f118(f23(a115),x25261),f16(a115))))), % 7.54/7.66 inference(rename_variables,[],[2050])). % 7.54/7.66 cnf(2528,plain, % 7.54/7.66 (~P77(f118(f29(a119,f118(f118(f31(a119),x25281),f3(a119))),f118(f118(f23(a119),f3(a119)),f16(a119))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2050,2187,2464,2481,2504,2508,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,625,2512,696,697,600,2208,2279,2293,2364,2007,2045,1990,315,317,318,325,326,327,332,333,336,364,366,381,382,389,478,479,712,551,734,566,595,570,2108,2322,2329,571,2305,2505,736,2128,2153,2319,2490,2498,2513,739,2454,692,586,670,671,579,684,622,2200,2310,2313,744,2284,2287,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547])). % 7.54/7.66 cnf(2529,plain, % 7.54/7.66 (~P77(f118(f29(a119,x25291),x25291))), % 7.54/7.66 inference(rename_variables,[],[736])). % 7.54/7.66 cnf(2532,plain, % 7.54/7.66 (P77(f118(f29(a115,x25321),f118(f118(f23(a115),x25321),f16(a115))))), % 7.54/7.66 inference(rename_variables,[],[2050])). % 7.54/7.66 cnf(2533,plain, % 7.54/7.66 (P77(f118(f28(a115,x25331),x25331))), % 7.54/7.66 inference(rename_variables,[],[571])). % 7.54/7.66 cnf(2536,plain, % 7.54/7.66 (P77(f118(f29(a115,x25361),f118(f118(f23(a115),x25361),f16(a115))))), % 7.54/7.66 inference(rename_variables,[],[2050])). % 7.54/7.66 cnf(2539,plain, % 7.54/7.66 (P77(f118(f29(a115,x25391),f118(f118(f23(a115),x25391),f16(a115))))), % 7.54/7.66 inference(rename_variables,[],[2050])). % 7.54/7.66 cnf(2542,plain, % 7.54/7.66 (P77(f118(f29(a115,x25421),f118(f118(f23(a115),x25421),f16(a115))))), % 7.54/7.66 inference(rename_variables,[],[2050])). % 7.54/7.66 cnf(2545,plain, % 7.54/7.66 (P77(f118(f29(a115,x25451),f118(f118(f23(a115),x25451),f16(a115))))), % 7.54/7.66 inference(rename_variables,[],[2050])). % 7.54/7.66 cnf(2553,plain, % 7.54/7.66 (~P77(f118(f29(a119,x25531),x25531))), % 7.54/7.66 inference(rename_variables,[],[736])). % 7.54/7.66 cnf(2557,plain, % 7.54/7.66 (~P77(f118(f29(a119,x25571),f118(f118(f23(a119),f22(a119,x25571,x25571)),x25571)))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,625,2512,696,697,600,2208,2279,2293,2364,2067,2007,2045,1990,315,317,318,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,712,551,734,566,595,570,2108,2322,2329,2468,571,2305,2505,2509,736,2128,2153,2319,2490,2498,2513,2529,739,2454,692,586,670,671,579,684,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686])). % 7.54/7.66 cnf(2563,plain, % 7.54/7.66 (~P77(f118(f29(a115,x25631),x25631))), % 7.54/7.66 inference(rename_variables,[],[2010])). % 7.54/7.66 cnf(2565,plain, % 7.54/7.66 (P77(f118(f29(a115,f22(a115,x25651,f118(f118(f23(a115),f19(a115,f22(a115,x25652,x25651))),f16(a115)))),x25652))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,625,2512,696,697,600,2208,2279,2293,2364,2067,2007,2045,1990,315,317,318,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,712,551,734,566,595,570,2108,2322,2329,2468,571,2305,2505,2509,736,2128,2153,2319,2490,2498,2513,2529,2553,739,2454,692,586,670,671,579,684,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887])). % 7.54/7.66 cnf(2566,plain, % 7.54/7.66 (P77(f118(f29(a115,x25661),f118(f118(f23(a115),x25661),f16(a115))))), % 7.54/7.66 inference(rename_variables,[],[2050])). % 7.54/7.66 cnf(2569,plain, % 7.54/7.66 (~E(f118(f118(f23(a119),x25691),f16(a119)),x25691)), % 7.54/7.66 inference(rename_variables,[],[728])). % 7.54/7.66 cnf(2570,plain, % 7.54/7.66 (~P26(f118(f6(x25701,x25702,a119),x25703))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,625,2512,696,697,600,2208,2279,2293,2364,2006,2067,2007,2045,1990,315,317,318,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,712,594,551,734,566,595,570,2108,2322,2329,2468,571,2305,2505,2509,736,2128,2153,2319,2490,2498,2513,2529,2553,739,2454,692,586,670,671,579,684,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242])). % 7.54/7.66 cnf(2571,plain, % 7.54/7.66 (E(f118(f6(x25711,x25712,x25713),x25714),x25713)), % 7.54/7.66 inference(rename_variables,[],[594])). % 7.54/7.66 cnf(2573,plain, % 7.54/7.66 (P78(f28(a114,f20(a115,x25731,f118(f118(f24(a119),f3(a119)),x25732))),f118(f118(f24(a119),f3(a119)),x25733),x25731)), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,625,2512,696,697,600,2208,2279,2293,2364,2006,2067,2007,2045,1990,315,317,318,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,712,594,551,734,566,595,570,2108,2322,2329,2468,571,2305,2505,2509,736,2128,2153,2319,2490,2498,2513,2529,2553,739,2454,692,586,670,671,579,684,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244])). % 7.54/7.66 cnf(2575,plain, % 7.54/7.66 (~P24(f118(f6(x25751,x25752,a119),x25753))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,625,2512,696,697,600,2208,2279,2293,2364,2006,2067,2007,2045,1990,315,317,318,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,712,594,2571,551,734,566,595,570,2108,2322,2329,2468,571,2305,2505,2509,736,2128,2153,2319,2490,2498,2513,2529,2553,739,2454,692,586,670,671,579,684,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260])). % 7.54/7.66 cnf(2576,plain, % 7.54/7.66 (E(f118(f6(x25761,x25762,x25763),x25764),x25763)), % 7.54/7.66 inference(rename_variables,[],[594])). % 7.54/7.66 cnf(2579,plain, % 7.54/7.66 (~P10(f118(f6(x25791,x25792,a119),x25793))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,625,2512,696,697,600,2208,2279,2293,2364,2006,2067,2007,2045,1990,315,317,318,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,712,594,2571,2576,551,734,566,719,718,595,570,2108,2322,2329,2468,571,2305,2505,2509,736,2128,2153,2319,2490,2498,2513,2529,2553,739,2454,692,586,670,671,579,684,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295])). % 7.54/7.66 cnf(2580,plain, % 7.54/7.66 (E(f118(f6(x25801,x25802,x25803),x25804),x25803)), % 7.54/7.66 inference(rename_variables,[],[594])). % 7.54/7.66 cnf(2585,plain, % 7.54/7.66 (~E(f118(f118(f23(a119),x25851),f16(a119)),x25851)), % 7.54/7.66 inference(rename_variables,[],[728])). % 7.54/7.66 cnf(2588,plain, % 7.54/7.66 (~E(f118(f118(f23(a119),x25881),f16(a119)),x25881)), % 7.54/7.66 inference(rename_variables,[],[728])). % 7.54/7.66 cnf(2591,plain, % 7.54/7.66 (~E(f118(f118(f23(a119),x25911),f16(a119)),x25911)), % 7.54/7.66 inference(rename_variables,[],[728])). % 7.54/7.66 cnf(2598,plain, % 7.54/7.66 (P77(f118(f28(a114,x25981),x25981))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2601,plain, % 7.54/7.66 (P77(f118(f28(a115,f3(a115)),f118(f118(f31(a115),f19(a115,x26011)),x26012)))), % 7.54/7.66 inference(rename_variables,[],[663])). % 7.54/7.66 cnf(2604,plain, % 7.54/7.66 (P77(f118(f28(a114,f3(a114)),f35(a119,x26041)))), % 7.54/7.66 inference(rename_variables,[],[596])). % 7.54/7.66 cnf(2607,plain, % 7.54/7.66 (P77(f118(f28(a119,f22(a119,x26071,x26072)),x26071))), % 7.54/7.66 inference(rename_variables,[],[670])). % 7.54/7.66 cnf(2608,plain, % 7.54/7.66 (P77(f118(f28(a119,f3(a119)),x26081))), % 7.54/7.66 inference(rename_variables,[],[579])). % 7.54/7.66 cnf(2610,plain, % 7.54/7.66 (~P77(f118(f28(a115,f16(a115)),f3(a115)))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,596,625,2512,696,697,600,2208,2279,2293,2364,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,571,2305,2505,2509,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,692,586,670,671,579,2461,684,663,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135])). % 7.54/7.66 cnf(2614,plain, % 7.54/7.66 (P2(a114,f118(f31(a114),f22(a114,f118(f118(f37(a114),f35(a119,x26141)),f35(a119,x26142)),f35(a119,f20(a119,x26141,x26142)))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,596,625,2512,696,697,600,2208,2279,2293,2364,708,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,571,2305,2505,2509,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,716,692,586,670,2607,671,579,2461,684,663,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212])). % 7.54/7.66 cnf(2615,plain, % 7.54/7.66 (P77(f118(f28(a114,f3(a114)),f22(a114,f118(f118(f37(a114),f35(a119,x26151)),f35(a119,x26152)),f35(a119,f20(a119,x26151,x26152)))))), % 7.54/7.66 inference(rename_variables,[],[708])). % 7.54/7.66 cnf(2617,plain, % 7.54/7.66 (P3(a114,f118(f31(a114),f22(a114,f118(f118(f37(a114),f35(a119,x26171)),f35(a119,x26172)),f35(a119,f20(a119,x26171,x26172)))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,571,2305,2505,2509,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,716,692,586,670,2607,671,579,2461,684,663,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213])). % 7.54/7.66 cnf(2618,plain, % 7.54/7.66 (P77(f118(f28(a114,f3(a114)),f22(a114,f118(f118(f37(a114),f35(a119,x26181)),f35(a119,x26182)),f35(a119,f20(a119,x26181,x26182)))))), % 7.54/7.66 inference(rename_variables,[],[708])). % 7.54/7.66 cnf(2620,plain, % 7.54/7.66 (P4(a114,f118(f31(a114),f22(a114,f118(f118(f37(a114),f35(a119,x26201)),f35(a119,x26202)),f35(a119,f20(a119,x26201,x26202)))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,571,2305,2505,2509,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,716,692,586,670,2607,671,579,2461,684,663,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214])). % 7.54/7.66 cnf(2624,plain, % 7.54/7.66 (P77(f118(f28(a114,x26241),x26241))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2627,plain, % 7.54/7.66 (P77(f118(f28(a115,x26271),x26271))), % 7.54/7.66 inference(rename_variables,[],[571])). % 7.54/7.66 cnf(2631,plain, % 7.54/7.66 (P77(f118(f28(a115,f3(a115)),f20(a115,f3(a115),f22(a115,f3(a115),f16(a115)))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,571,2305,2505,2509,2533,2627,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,716,692,586,670,2607,671,579,2461,684,663,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453])). % 7.54/7.66 cnf(2632,plain, % 7.54/7.66 (P77(f118(f28(a115,x26321),x26321))), % 7.54/7.66 inference(rename_variables,[],[571])). % 7.54/7.66 cnf(2634,plain, % 7.54/7.66 (P77(f118(f28(a115,f3(a115)),f20(a115,f3(a115),f3(a115))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,571,2305,2505,2509,2533,2627,2632,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,716,692,586,670,2607,671,579,2461,684,663,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458])). % 7.54/7.66 cnf(2635,plain, % 7.54/7.66 (P77(f118(f28(a115,x26351),x26351))), % 7.54/7.66 inference(rename_variables,[],[571])). % 7.54/7.66 cnf(2637,plain, % 7.54/7.66 (~P77(f118(f28(a115,f3(a115)),f20(a115,f118(f118(f23(a115),f3(a115)),f16(a115)),f22(a115,f3(a115),f16(a115)))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,571,2305,2505,2509,2533,2627,2632,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,716,692,586,670,2607,671,579,2461,684,663,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531])). % 7.54/7.66 cnf(2639,plain, % 7.54/7.66 (~P77(f118(f29(a115,f3(a115)),f20(a115,f3(a115),f3(a115))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2563,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,571,2305,2505,2509,2533,2627,2632,2635,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,716,692,586,670,2607,671,579,2461,684,663,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538])). % 7.54/7.66 cnf(2640,plain, % 7.54/7.66 (~P77(f118(f29(a115,x26401),x26401))), % 7.54/7.66 inference(rename_variables,[],[2010])). % 7.54/7.66 cnf(2641,plain, % 7.54/7.66 (P77(f118(f28(a115,x26411),x26411))), % 7.54/7.66 inference(rename_variables,[],[571])). % 7.54/7.66 cnf(2643,plain, % 7.54/7.66 (P77(f118(f28(a115,f20(a115,f3(a115),f22(a115,f3(a115),f16(a115)))),f3(a115)))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2563,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,571,2305,2505,2509,2533,2627,2632,2635,2641,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,716,692,586,670,2607,671,579,2461,684,663,622,2200,2310,2313,744,2284,2287,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583])). % 7.54/7.66 cnf(2644,plain, % 7.54/7.66 (P77(f118(f28(a115,x26441),x26441))), % 7.54/7.66 inference(rename_variables,[],[571])). % 7.54/7.66 cnf(2647,plain, % 7.54/7.66 (~P77(f118(f29(a115,x26471),x26471))), % 7.54/7.66 inference(rename_variables,[],[2010])). % 7.54/7.66 cnf(2650,plain, % 7.54/7.66 (~P77(f118(f28(a119,f118(f118(f23(a119),x26501),f16(a119))),x26501))), % 7.54/7.66 inference(rename_variables,[],[744])). % 7.54/7.66 cnf(2651,plain, % 7.54/7.66 (P77(f118(f28(a119,f3(a119)),x26511))), % 7.54/7.66 inference(rename_variables,[],[579])). % 7.54/7.66 cnf(2653,plain, % 7.54/7.66 (P77(f118(f28(a119,x26531),f22(a119,f118(f118(f23(a119),x26531),f3(a119)),f3(a119))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2563,2640,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,571,2305,2505,2509,2533,2627,2632,2635,2641,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,716,692,586,670,2607,671,579,2461,2608,2651,684,663,622,2200,2310,2313,744,2284,2287,2332,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756])). % 7.54/7.66 cnf(2654,plain, % 7.54/7.66 (P77(f118(f28(a119,x26541),x26541))), % 7.54/7.66 inference(rename_variables,[],[570])). % 7.54/7.66 cnf(2655,plain, % 7.54/7.66 (P77(f118(f28(a119,f3(a119)),x26551))), % 7.54/7.66 inference(rename_variables,[],[579])). % 7.54/7.66 cnf(2659,plain, % 7.54/7.66 (~E(f118(f118(f23(a115),f118(f118(f24(a115),x26591),x26592)),f16(a115)),f118(f118(f23(a115),f118(f118(f24(a115),x26593),x26592)),f118(f118(f24(a115),f22(a115,x26591,x26593)),x26592)))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2563,2640,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,716,692,586,670,2607,671,579,2461,2608,2651,684,663,622,2200,2310,2313,744,2284,2287,2332,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882])). % 7.54/7.66 cnf(2661,plain, % 7.54/7.66 (~P77(f118(f28(a119,f118(f118(f23(a119),f118(f118(f24(a119),x26611),x26612)),f16(a119))),f118(f118(f23(a119),f118(f118(f24(a119),x26611),x26612)),f118(f118(f24(a119),f22(a119,x26611,x26611)),x26612))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2563,2640,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,364,366,372,381,382,389,428,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,716,692,586,670,2607,671,579,2461,2608,2651,684,663,622,2200,2310,2313,744,2284,2287,2332,2650,745,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964])). % 7.54/7.66 cnf(2662,plain, % 7.54/7.66 (~P77(f118(f28(a119,f118(f118(f23(a119),x26621),f16(a119))),x26621))), % 7.54/7.66 inference(rename_variables,[],[744])). % 7.54/7.66 cnf(2665,plain, % 7.54/7.66 (~P77(f118(f29(a119,x26651),f3(a119)))), % 7.54/7.66 inference(rename_variables,[],[739])). % 7.54/7.66 cnf(2670,plain, % 7.54/7.66 (~P77(f118(f29(a115,f118(f118(f23(a115),f118(f118(f24(a115),x26701),x26702)),f16(a115))),f118(f118(f23(a115),f118(f118(f24(a115),x26703),x26702)),f118(f118(f24(a115),f22(a115,x26701,x26703)),x26702))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2563,2640,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,337,364,366,372,381,382,389,428,444,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,716,692,586,670,2607,671,579,2461,2608,2651,684,663,622,2200,2310,2313,744,2284,2287,2332,2650,745,642,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968])). % 7.54/7.66 cnf(2676,plain, % 7.54/7.66 (~P77(f118(f29(a119,x26761),f3(a119)))), % 7.54/7.66 inference(rename_variables,[],[739])). % 7.54/7.66 cnf(2678,plain, % 7.54/7.66 (P77(f118(f28(a114,f3(a119)),f22(a119,f3(a119),f118(f118(f31(a119),x26781),f3(a119)))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2563,2640,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,321,325,326,327,332,333,336,337,364,366,372,381,382,389,428,444,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,716,740,692,586,670,2607,671,579,2461,2608,2651,684,663,622,2200,2310,2313,744,2284,2287,2332,2650,745,642,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050])). % 7.54/7.66 cnf(2688,plain, % 7.54/7.66 (P77(f118(f28(a115,f118(f118(f31(a115),f19(a115,f3(a115))),f118(f118(f23(a119),f3(a119)),f16(a119)))),f3(a115)))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2563,2640,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,381,382,389,428,444,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,670,2607,671,2229,579,2461,2608,2651,684,663,2601,622,2200,2310,2313,744,2284,2287,2332,2650,745,642,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203])). % 7.54/7.66 cnf(2689,plain, % 7.54/7.66 (P77(f118(f28(a115,f3(a115)),f118(f118(f31(a115),f19(a115,x26891)),x26892)))), % 7.54/7.66 inference(rename_variables,[],[663])). % 7.54/7.66 cnf(2692,plain, % 7.54/7.66 (~P77(f118(f29(a115,x26921),x26921))), % 7.54/7.66 inference(rename_variables,[],[2010])). % 7.54/7.66 cnf(2693,plain, % 7.54/7.66 (P77(f118(f28(a119,x26931),x26931))), % 7.54/7.66 inference(rename_variables,[],[570])). % 7.54/7.66 cnf(2694,plain, % 7.54/7.66 (P77(f118(f29(a115,x26941),f118(f118(f23(a115),x26941),f16(a115))))), % 7.54/7.66 inference(rename_variables,[],[2050])). % 7.54/7.66 cnf(2696,plain, % 7.54/7.66 (~P77(f118(f28(a119,f118(f118(f23(a119),x26961),f16(a119))),f22(a119,x26961,x26962)))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2010,2143,2174,2290,2420,2563,2640,2647,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,381,382,389,428,444,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,670,2607,671,2229,579,2461,2608,2651,684,663,2601,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249])). % 7.54/7.66 cnf(2705,plain, % 7.54/7.66 (~P77(f118(f29(a114,x27051),x27051))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2708,plain, % 7.54/7.66 (~P77(f118(f29(a114,x27081),x27081))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2712,plain, % 7.54/7.66 (P77(f118(f29(a115,f22(a115,f3(a115),f16(a115))),f118(f118(f31(a115),f19(a115,x27121)),f3(a119))))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2010,2143,2174,2290,2420,2563,2640,2647,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,381,382,389,428,444,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,670,2607,671,2229,579,2461,2608,2651,684,663,2601,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256])). % 7.54/7.66 cnf(2718,plain, % 7.54/7.66 (~P77(f118(f28(a114,f118(f118(f23(a114),a40),x27181)),x27181))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2010,2143,2174,2290,2420,2563,2640,2647,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,596,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,375,381,382,389,428,444,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,670,2607,671,2229,579,2461,2608,2651,684,663,2601,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473])). % 7.54/7.66 cnf(2719,plain, % 7.54/7.66 (~P77(f118(f29(a114,x27191),x27191))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2721,plain, % 7.54/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x27211)),x27211))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2010,2143,2174,2290,2420,2563,2640,2647,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,596,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,375,381,382,389,428,444,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,670,2607,671,2229,579,2461,2608,2651,684,663,2601,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474])). % 7.54/7.66 cnf(2722,plain, % 7.54/7.66 (~P77(f118(f29(a114,x27221),x27221))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2723,plain, % 7.54/7.66 (P77(f118(f28(a114,x27231),x27231))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2725,plain, % 7.54/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),a40),x27251)),x27251))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2010,2143,2174,2290,2420,2563,2640,2647,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,378,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,596,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,375,381,382,389,428,444,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,670,2607,671,2229,579,2461,2608,2651,684,663,2601,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475])). % 7.54/7.66 cnf(2726,plain, % 7.54/7.66 (~P77(f118(f29(a114,x27261),x27261))), % 7.54/7.66 inference(rename_variables,[],[2008])). % 7.54/7.66 cnf(2728,plain, % 7.54/7.66 (~P77(f118(f28(a115,f118(f118(f24(a115),f16(a115)),f16(a115))),f3(a115)))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2010,2143,2174,2290,2420,2563,2640,2647,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,378,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,596,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,375,381,382,389,428,439,444,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,670,2607,671,2229,579,2461,2608,2651,684,663,2601,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475,1713])). % 7.54/7.66 cnf(2731,plain, % 7.54/7.66 (P77(f118(f29(a115,x27311),f118(f118(f23(a115),x27311),f16(a115))))), % 7.54/7.66 inference(rename_variables,[],[2050])). % 7.54/7.66 cnf(2733,plain, % 7.54/7.66 (P77(f118(f29(a115,f118(f118(f24(a115),f16(a115)),f22(a115,f3(a115),f16(a115)))),f3(a115)))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2010,2143,2174,2290,2420,2563,2640,2647,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,2694,378,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,596,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,375,381,382,389,428,439,444,453,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,587,670,2607,671,2229,579,2461,2608,2651,684,663,2601,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475,1713,1245,1625])). % 7.54/7.66 cnf(2738,plain, % 7.54/7.66 (~P77(f118(f28(a119,f118(f118(f23(a119),f118(f118(f31(a119),x27381),f3(a119))),x27382)),x27382))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2010,2143,2174,2290,2420,2563,2640,2647,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,2694,2731,378,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,596,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,373,375,381,382,389,428,439,444,453,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,587,670,2607,671,2229,579,2461,2608,2651,684,663,2601,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,2171,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475,1713,1245,1625,1626,1696])). % 7.54/7.66 cnf(2744,plain, % 7.54/7.66 (~P77(f118(f29(a114,f22(a114,f16(a114),f19(a114,f22(a114,f3(a114),f16(a114))))),f3(a114)))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2726,2010,2143,2174,2290,2420,2563,2640,2647,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,2694,2731,378,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,596,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,373,375,381,382,389,428,439,444,453,478,479,485,492,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,587,670,2607,671,2229,579,2461,2608,2651,684,663,2601,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,2171,743,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475,1713,1245,1625,1626,1696,1697,1897])). % 7.54/7.66 cnf(2749,plain, % 7.54/7.66 (~P77(f118(f29(a115,x27491),x27491))), % 7.54/7.66 inference(rename_variables,[],[2010])). % 7.54/7.66 cnf(2756,plain, % 7.54/7.66 (P77(f118(f28(a114,x27561),x27561))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2759,plain, % 7.54/7.66 (P77(f118(f28(a119,f3(a119)),x27591))), % 7.54/7.66 inference(rename_variables,[],[579])). % 7.54/7.66 cnf(2762,plain, % 7.54/7.66 (P77(f118(f28(a119,x27621),x27621))), % 7.54/7.66 inference(rename_variables,[],[570])). % 7.54/7.66 cnf(2765,plain, % 7.54/7.66 (P77(f118(f28(a114,x27651),x27651))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2768,plain, % 7.54/7.66 (P77(f118(f28(a114,x27681),x27681))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2775,plain, % 7.54/7.66 (P77(f118(f28(a114,x27751),x27751))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2777,plain, % 7.54/7.66 (P77(f118(f28(a114,f118(f118(f24(a114),f3(a114)),f3(a114))),f3(a114)))), % 7.54/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2726,2010,2143,2174,2290,2420,2563,2640,2647,2692,2749,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,2694,2731,378,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,2723,2756,2765,2768,2775,596,2604,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,373,375,381,382,389,428,438,439,444,453,460,478,479,485,492,502,726,712,594,2571,2576,2580,551,734,566,2444,719,718,595,570,2108,2322,2329,2468,2654,2693,2762,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,587,670,2607,671,2229,579,2461,2608,2651,2655,684,663,2601,2689,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,2171,743,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475,1713,1245,1625,1626,1696,1697,1897,1142,1171,1192,1284,1311,1455,1456,1470,1509,1606,1618])). % 7.54/7.66 cnf(2778,plain, % 7.54/7.66 (P77(f118(f28(a114,x27781),x27781))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2781,plain, % 7.54/7.66 (P77(f118(f28(a114,x27811),x27811))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2784,plain, % 7.54/7.66 (P77(f118(f28(a114,x27841),x27841))), % 7.54/7.66 inference(rename_variables,[],[569])). % 7.54/7.66 cnf(2794,plain, % 7.54/7.66 (~E(f118(f118(f24(a119),f118(f118(f23(a119),f3(a119)),f16(a119))),f3(a114)),f118(f118(f24(a119),f118(f118(f23(a119),f3(a119)),f16(a119))),f16(a114)))), % 7.88/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2726,2010,2143,2174,2290,2420,2563,2640,2647,2692,2749,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,2694,2731,378,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,2591,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,2723,2756,2765,2768,2775,2778,2781,2784,596,2604,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,373,375,377,381,382,389,428,438,439,440,444,453,460,478,479,485,492,502,726,712,594,2571,2576,2580,551,734,566,2444,580,719,718,595,570,2108,2322,2329,2468,2654,2693,2762,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,587,670,2607,671,2229,579,2461,2608,2651,2655,684,663,2601,2689,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,2171,743,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475,1713,1245,1625,1626,1696,1697,1897,1142,1171,1192,1284,1311,1455,1456,1470,1509,1606,1618,1619,1621,1623,2081,1348,1394])). % 7.88/7.66 cnf(2796,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),x27961),f16(a119)),x27961)), % 7.88/7.66 inference(rename_variables,[],[728])). % 7.88/7.66 cnf(2799,plain, % 7.88/7.66 (P77(f118(f28(a119,f3(a119)),x27991))), % 7.88/7.66 inference(rename_variables,[],[579])). % 7.88/7.66 cnf(2800,plain, % 7.88/7.66 (P77(f118(f28(a119,x28001),x28001))), % 7.88/7.66 inference(rename_variables,[],[570])). % 7.88/7.66 cnf(2814,plain, % 7.88/7.66 (~E(f118(f118(f23(a114),a40),f3(a114)),f3(a114))), % 7.88/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2726,2010,2143,2174,2290,2420,2563,2640,2647,2692,2749,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,2694,2731,378,379,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,2591,2796,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,2723,2756,2765,2768,2775,2778,2781,2784,596,2604,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,534,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,373,375,377,381,382,383,386,389,409,412,416,419,428,438,439,440,444,453,460,467,470,478,479,485,492,502,726,712,594,2571,2576,2580,551,734,566,2444,580,719,718,595,570,2108,2322,2329,2468,2654,2693,2762,2800,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,587,670,2607,671,2229,579,2461,2608,2651,2655,2759,2799,684,663,2601,2689,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,2171,743,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475,1713,1245,1625,1626,1696,1697,1897,1142,1171,1192,1284,1311,1455,1456,1470,1509,1606,1618,1619,1621,1623,2081,1348,1394,1610,953,1324,1510,2004,906])). % 7.88/7.66 cnf(2816,plain, % 7.88/7.66 (P77(f118(f28(a114,f3(a114)),f118(f118(f23(a114),a40),f3(a114))))), % 7.88/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2726,2010,2143,2174,2290,2420,2563,2640,2647,2692,2749,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,2694,2731,378,379,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,2591,2796,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,2723,2756,2765,2768,2775,2778,2781,2784,596,2604,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,534,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,373,375,377,381,382,383,386,389,409,412,416,419,428,438,439,440,444,453,460,467,470,478,479,485,492,502,726,712,594,2571,2576,2580,551,734,566,2444,580,719,718,595,570,2108,2322,2329,2468,2654,2693,2762,2800,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,587,670,2607,671,2229,579,2461,2608,2651,2655,2759,2799,684,663,2601,2689,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,2171,743,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475,1713,1245,1625,1626,1696,1697,1897,1142,1171,1192,1284,1311,1455,1456,1470,1509,1606,1618,1619,1621,1623,2081,1348,1394,1610,953,1324,1510,2004,906,1006])). % 7.88/7.66 cnf(2822,plain, % 7.88/7.66 (~P77(f118(f29(a119,f118(f118(f23(a119),f3(a119)),f16(a119))),f118(f118(f24(a119),x28221),f3(a119))))), % 7.88/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2726,2010,2143,2174,2290,2420,2563,2640,2647,2692,2749,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,2694,2731,378,379,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,2591,2796,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,2723,2756,2765,2768,2775,2778,2781,2784,596,2604,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,534,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,373,375,377,381,382,383,386,389,409,412,416,419,428,438,439,440,444,453,460,467,470,478,479,485,492,502,726,712,594,2571,2576,2580,551,734,566,2444,580,719,718,595,570,2108,2322,2329,2468,2654,2693,2762,2800,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,587,670,2607,671,2229,579,2461,2608,2651,2655,2759,2799,684,663,2601,2689,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,2171,743,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475,1713,1245,1625,1626,1696,1697,1897,1142,1171,1192,1284,1311,1455,1456,1470,1509,1606,1618,1619,1621,1623,2081,1348,1394,1610,953,1324,1510,2004,906,1006,904,909,1079])). % 7.88/7.66 cnf(2824,plain, % 7.88/7.66 (~P77(f118(f29(a115,f22(a115,f118(f118(f23(a115),f3(a115)),f16(a115)),f3(a115))),f3(a115)))), % 7.88/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2726,2010,2143,2174,2290,2420,2563,2640,2647,2692,2749,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,2694,2731,378,379,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,2591,2796,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,2723,2756,2765,2768,2775,2778,2781,2784,596,2604,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,534,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,373,375,377,381,382,383,386,389,409,412,416,419,428,438,439,440,444,453,460,467,470,478,479,485,492,502,726,712,594,2571,2576,2580,551,734,566,2444,580,719,718,595,570,2108,2322,2329,2468,2654,2693,2762,2800,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,587,670,2607,671,2229,579,2461,2608,2651,2655,2759,2799,684,663,2601,2689,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,2171,743,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475,1713,1245,1625,1626,1696,1697,1897,1142,1171,1192,1284,1311,1455,1456,1470,1509,1606,1618,1619,1621,1623,2081,1348,1394,1610,953,1324,1510,2004,906,1006,904,909,1079,1080])). % 7.88/7.66 cnf(2830,plain, % 7.88/7.66 (~P77(f118(f29(a119,f3(a119)),f118(f118(f24(a119),x28301),f3(a119))))), % 7.88/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2726,2010,2143,2174,2290,2420,2563,2640,2647,2692,2749,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,2694,2731,378,379,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,2591,2796,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,2723,2756,2765,2768,2775,2778,2781,2784,596,2604,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,534,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,373,375,377,381,382,383,386,389,409,412,416,419,428,438,439,440,444,453,460,467,470,478,479,485,492,502,726,712,594,2571,2576,2580,551,734,566,2444,580,719,718,595,570,2108,2322,2329,2468,2654,2693,2762,2800,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,587,670,2607,671,2229,579,2461,2608,2651,2655,2759,2799,684,663,2601,2689,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,2171,743,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475,1713,1245,1625,1626,1696,1697,1897,1142,1171,1192,1284,1311,1455,1456,1470,1509,1606,1618,1619,1621,1623,2081,1348,1394,1610,953,1324,1510,2004,906,1006,904,909,1079,1080,1237,1362,1464])). % 7.88/7.66 cnf(2839,plain, % 7.88/7.66 (P77(f118(f29(a115,x28391),f118(f118(f23(a115),f19(a115,f22(a115,f3(a115),x28391))),f16(a115))))), % 7.88/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2726,2010,2143,2174,2290,2420,2563,2640,2647,2692,2749,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,2694,2731,378,379,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,2591,2796,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,2723,2756,2765,2768,2775,2778,2781,2784,596,2604,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,534,315,317,318,319,321,325,326,327,332,333,334,336,337,364,366,372,373,375,377,381,382,383,386,389,409,412,416,419,428,438,439,440,444,453,460,467,470,478,479,485,492,502,726,712,594,2571,2576,2580,551,734,566,2444,580,719,718,595,570,2108,2322,2329,2468,2654,2693,2762,2800,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,587,670,2607,671,2229,579,2461,2608,2651,2655,2759,2799,684,663,2601,2689,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,2171,743,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475,1713,1245,1625,1626,1696,1697,1897,1142,1171,1192,1284,1311,1455,1456,1470,1509,1606,1618,1619,1621,1623,2081,1348,1394,1610,953,1324,1510,2004,906,1006,904,909,1079,1080,1237,1362,1464,18,926,1008,1431,1644])). % 7.88/7.66 cnf(2843,plain, % 7.88/7.66 (~P77(f118(f28(a115,f118(f118(f23(a115),f16(a115)),f16(a115))),f3(a115)))), % 7.88/7.66 inference(scs_inference,[],[576,656,677,2400,2427,695,2096,577,673,2054,2065,2008,2105,2114,2346,2373,2376,2386,2389,2397,2407,2411,2414,2417,2430,2705,2708,2719,2722,2726,2010,2143,2174,2290,2420,2563,2640,2647,2692,2749,2050,2187,2464,2481,2504,2508,2526,2532,2536,2539,2542,2545,2566,2694,2731,378,379,380,725,728,2214,2223,2226,2335,2404,2408,2439,2465,2517,2569,2585,2588,2591,2796,569,2111,2117,2137,2253,2263,2266,2273,2276,2296,2299,2302,2361,2383,2392,2403,2491,2501,2598,2624,2723,2756,2765,2768,2775,2778,2781,2784,596,2604,625,2512,696,697,600,2208,2279,2293,2364,575,574,708,2615,2618,2006,2067,2007,2035,2045,1990,534,315,317,318,319,321,325,326,327,332,333,334,336,337,364,365,366,372,373,375,377,381,382,383,386,389,409,412,416,419,428,438,439,440,444,453,460,467,470,478,479,485,492,502,726,712,594,2571,2576,2580,551,734,566,2444,580,719,718,595,570,2108,2322,2329,2468,2654,2693,2762,2800,571,2305,2505,2509,2533,2627,2632,2635,2641,2644,736,2128,2153,2319,2490,2498,2513,2529,2553,597,739,2454,2520,2665,2676,716,740,692,586,587,670,2607,671,2229,579,2461,2608,2651,2655,2759,2799,684,663,2601,2689,622,2200,2310,2313,744,2284,2287,2332,2650,2662,745,642,742,2140,2146,2162,2165,2168,2171,743,1944,1011,1179,1189,1228,1720,2058,2064,2069,954,959,960,963,1022,1049,1092,1118,1129,1174,1175,1181,1190,1191,1199,1232,1235,1240,1246,1271,1273,1289,1293,1313,1316,1323,1339,1353,1354,1387,1438,1440,1483,1567,1603,1627,1760,1840,2047,2,7,8,814,815,816,817,841,968,970,971,999,1007,1017,1048,1061,1067,1068,1095,1130,1173,1180,1186,1201,1202,1234,1241,1242,1243,1257,1263,1267,1269,1292,1315,1343,1371,1372,1437,1561,1578,1579,1636,1662,1671,1679,1743,1844,1861,2073,2085,2086,928,930,967,982,1029,1034,1086,1098,1100,1205,1218,1238,1262,1278,1321,1325,1335,1336,1360,1367,1368,1375,1383,1421,1439,1490,1503,1544,1545,1669,1670,1677,1678,1780,1883,228,831,832,833,931,941,979,980,1005,1013,1065,1070,1089,1101,1144,1158,1162,1165,1166,1167,1217,1244,1274,1275,1345,1347,1352,1366,1373,1452,1459,1479,1482,1524,1528,1535,1547,1582,1584,1586,1589,1596,1634,1635,1645,1672,1686,1688,1737,1887,3,242,243,244,245,260,273,283,295,835,838,882,1020,1052,1064,1090,1133,1134,1135,1139,1212,1213,1214,1302,1334,1451,1453,1458,1531,1538,1583,1721,1736,1756,1769,1882,1964,1965,1966,1968,1045,1046,1050,1108,1110,1116,1203,1239,1249,1251,1252,1253,1254,1255,1256,1297,1299,1473,1474,1475,1713,1245,1625,1626,1696,1697,1897,1142,1171,1192,1284,1311,1455,1456,1470,1509,1606,1618,1619,1621,1623,2081,1348,1394,1610,953,1324,1510,2004,906,1006,904,909,1079,1080,1237,1362,1464,18,926,1008,1431,1644,1294,1668])). % 7.88/7.66 cnf(2888,plain, % 7.88/7.66 (~P77(f118(f28(a114,f118(f118(f23(a114),a40),x28881)),x28881))), % 7.88/7.66 inference(rename_variables,[],[2718])). % 7.88/7.66 cnf(2891,plain, % 7.88/7.66 (~P77(f118(f28(a115,f118(f118(f23(a115),x28911),f16(a115))),x28911))), % 7.88/7.66 inference(rename_variables,[],[2289])). % 7.88/7.66 cnf(2896,plain, % 7.88/7.66 (~P77(f118(f29(a114,f35(a119,f26(x28961))),x28961))), % 7.88/7.66 inference(rename_variables,[],[2474])). % 7.88/7.66 cnf(2902,plain, % 7.88/7.66 (E(f118(f118(f23(a119),x29021),f97(x29021,x29021,f29(a114,f22(a119,x29021,x29021)))),x29021)), % 7.88/7.66 inference(rename_variables,[],[2385])). % 7.88/7.66 cnf(2910,plain, % 7.88/7.66 (P77(f118(f28(a115,x29101),f118(f118(f23(a115),x29101),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(2920,plain, % 7.88/7.66 (~P77(f118(f29(a115,f118(f118(f23(a115),x29201),f16(a115))),x29201))), % 7.88/7.66 inference(rename_variables,[],[2173])). % 7.88/7.66 cnf(2923,plain, % 7.88/7.66 (P77(f118(f29(a119,x29231),f118(f118(f23(a119),f33(f35(a119,x29231))),f16(a119))))), % 7.88/7.66 inference(rename_variables,[],[2178])). % 7.88/7.66 cnf(2950,plain, % 7.88/7.66 (~P77(f118(f29(a119,x29501),f118(f118(f23(a119),f22(a119,x29501,x29501)),x29501)))), % 7.88/7.66 inference(rename_variables,[],[2557])). % 7.88/7.66 cnf(2953,plain, % 7.88/7.66 (P77(f118(f28(a114,x29531),f35(a119,f26(x29531))))), % 7.88/7.66 inference(rename_variables,[],[600])). % 7.88/7.66 cnf(2962,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x29621),f16(a119))),x29622),x29621)), % 7.88/7.66 inference(rename_variables,[],[2341])). % 7.88/7.66 cnf(2972,plain, % 7.88/7.66 (~P77(f118(f29(a119,f118(f118(f23(a119),x29721),x29722)),x29721))), % 7.88/7.66 inference(rename_variables,[],[743])). % 7.88/7.66 cnf(2977,plain, % 7.88/7.66 (P77(f118(f29(a114,x29771),f35(a119,f33(f118(f118(f23(a114),x29771),f16(a114))))))), % 7.88/7.66 inference(rename_variables,[],[2426])). % 7.88/7.66 cnf(2984,plain, % 7.88/7.66 (~P77(f118(f28(a119,f118(f118(f23(a119),f118(f118(f31(a119),x29841),f3(a119))),x29842)),x29842))), % 7.88/7.66 inference(rename_variables,[],[2738])). % 7.88/7.66 cnf(2993,plain, % 7.88/7.66 (P77(f118(f29(a115,f22(a115,x29931,f16(a115))),x29931))), % 7.88/7.66 inference(rename_variables,[],[2304])). % 7.88/7.66 cnf(2998,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x29981),f16(a119))),x29982),x29981)), % 7.88/7.66 inference(rename_variables,[],[2341])). % 7.88/7.66 cnf(3013,plain, % 7.88/7.66 (P77(f118(f28(a114,x30131),f35(a119,f26(x30131))))), % 7.88/7.66 inference(rename_variables,[],[600])). % 7.88/7.66 cnf(3016,plain, % 7.88/7.66 (~P77(f118(f29(a115,f118(f118(f23(a115),x30161),f16(a115))),x30161))), % 7.88/7.66 inference(rename_variables,[],[2173])). % 7.88/7.66 cnf(3021,plain, % 7.88/7.66 (P77(f118(f28(a114,f22(a119,f118(f118(f23(a119),x30211),x30212),x30211)),x30212))), % 7.88/7.66 inference(rename_variables,[],[2116])). % 7.88/7.66 cnf(3026,plain, % 7.88/7.66 (P77(f118(f29(a115,f22(a115,x30261,f16(a115))),x30261))), % 7.88/7.66 inference(rename_variables,[],[2304])). % 7.88/7.66 cnf(3033,plain, % 7.88/7.66 (P77(f118(f28(a114,f22(a119,f118(f118(f23(a119),x30331),x30332),x30331)),x30332))), % 7.88/7.66 inference(rename_variables,[],[2116])). % 7.88/7.66 cnf(3038,plain, % 7.88/7.66 (P77(f118(f28(a115,x30381),f118(f118(f23(a115),x30381),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3041,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x30411)),x30411))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3048,plain, % 7.88/7.66 (P77(f118(f28(a114,x30481),f35(a119,f26(x30481))))), % 7.88/7.66 inference(rename_variables,[],[600])). % 7.88/7.66 cnf(3064,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x30641),f16(a119))),x30642),x30641)), % 7.88/7.66 inference(rename_variables,[],[2341])). % 7.88/7.66 cnf(3075,plain, % 7.88/7.66 (P77(f118(f28(a119,x30751),f33(f35(a119,x30751))))), % 7.88/7.66 inference(rename_variables,[],[2189])). % 7.88/7.66 cnf(3078,plain, % 7.88/7.66 (~P77(f118(f29(a119,f118(f118(f23(a119),f118(f118(f23(a119),x30781),x30782)),x30783)),x30782))), % 7.88/7.66 inference(rename_variables,[],[2197])). % 7.88/7.66 cnf(3094,plain, % 7.88/7.66 (~P77(f118(f28(a119,f118(f118(f23(a119),x30941),f16(a119))),f22(a119,x30941,x30942)))), % 7.88/7.66 inference(rename_variables,[],[2696])). % 7.88/7.66 cnf(3099,plain, % 7.88/7.66 (P77(f118(f28(a119,x30991),f33(f35(a119,x30991))))), % 7.88/7.66 inference(rename_variables,[],[2189])). % 7.88/7.66 cnf(3102,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x31021),f16(a119))),x31022),x31021)), % 7.88/7.66 inference(rename_variables,[],[2341])). % 7.88/7.66 cnf(3112,plain, % 7.88/7.66 (P77(f118(f28(a119,x31121),f33(f35(a119,x31121))))), % 7.88/7.66 inference(rename_variables,[],[2189])). % 7.88/7.66 cnf(3120,plain, % 7.88/7.66 (~P77(f118(f28(a119,f118(f118(f23(a119),f118(f118(f31(a119),x31201),f3(a119))),x31202)),x31202))), % 7.88/7.66 inference(rename_variables,[],[2738])). % 7.88/7.66 cnf(3129,plain, % 7.88/7.66 (~P77(f118(f29(a115,f118(f118(f23(a115),x31291),f16(a115))),x31291))), % 7.88/7.66 inference(rename_variables,[],[2173])). % 7.88/7.66 cnf(3134,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x31341)),x31341))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3137,plain, % 7.88/7.66 (~E(f118(f118(f23(a115),x31371),f16(a115)),x31371)), % 7.88/7.66 inference(rename_variables,[],[2142])). % 7.88/7.66 cnf(3141,plain, % 7.88/7.66 (~P77(f118(f28(a119,f118(f118(f23(a119),f118(f118(f31(a119),x31411),f3(a119))),x31412)),x31412))), % 7.88/7.66 inference(rename_variables,[],[2738])). % 7.88/7.66 cnf(3153,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x31531),f16(a119))),x31532),x31531)), % 7.88/7.66 inference(rename_variables,[],[2341])). % 7.88/7.66 cnf(3155,plain, % 7.88/7.66 (~E(f118(f118(f23(a115),x31551),f16(a115)),x31551)), % 7.88/7.66 inference(rename_variables,[],[2142])). % 7.88/7.66 cnf(3158,plain, % 7.88/7.66 (P77(f118(f29(a115,f22(a115,x31581,f16(a115))),x31581))), % 7.88/7.66 inference(rename_variables,[],[2304])). % 7.88/7.66 cnf(3164,plain, % 7.88/7.66 (E(x31641,f118(f118(f23(a119),f22(a119,x31641,x31641)),x31641))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3166,plain, % 7.88/7.66 (E(x31661,f118(f118(f23(a119),f22(a119,x31661,x31661)),x31661))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3168,plain, % 7.88/7.66 (E(x31681,f118(f118(f23(a119),f22(a119,x31681,x31681)),x31681))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3170,plain, % 7.88/7.66 (E(x31701,f118(f118(f23(a119),f22(a119,x31701,x31701)),x31701))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3172,plain, % 7.88/7.66 (E(x31721,f118(f118(f23(a119),f22(a119,x31721,x31721)),x31721))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3174,plain, % 7.88/7.66 (E(x31741,f118(f118(f23(a119),f22(a119,x31741,x31741)),x31741))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3176,plain, % 7.88/7.66 (E(x31761,f118(f118(f23(a119),f22(a119,x31761,x31761)),x31761))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3178,plain, % 7.88/7.66 (E(x31781,f118(f118(f23(a119),f22(a119,x31781,x31781)),x31781))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3180,plain, % 7.88/7.66 (E(x31801,f118(f118(f23(a119),f22(a119,x31801,x31801)),x31801))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3182,plain, % 7.88/7.66 (E(x31821,f118(f118(f23(a119),f22(a119,x31821,x31821)),x31821))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3184,plain, % 7.88/7.66 (E(x31841,f118(f118(f23(a119),f22(a119,x31841,x31841)),x31841))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3186,plain, % 7.88/7.66 (E(x31861,f118(f118(f23(a119),f22(a119,x31861,x31861)),x31861))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3188,plain, % 7.88/7.66 (E(x31881,f118(f118(f23(a119),f22(a119,x31881,x31881)),x31881))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3190,plain, % 7.88/7.66 (E(x31901,f118(f118(f23(a119),f22(a119,x31901,x31901)),x31901))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3192,plain, % 7.88/7.66 (E(x31921,f118(f118(f23(a119),f22(a119,x31921,x31921)),x31921))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3194,plain, % 7.88/7.66 (E(x31941,f118(f118(f23(a119),f22(a119,x31941,x31941)),x31941))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3196,plain, % 7.88/7.66 (E(x31961,f118(f118(f23(a119),f22(a119,x31961,x31961)),x31961))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3198,plain, % 7.88/7.66 (E(x31981,f118(f118(f23(a119),f22(a119,x31981,x31981)),x31981))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3200,plain, % 7.88/7.66 (E(x32001,f118(f118(f23(a119),f22(a119,x32001,x32001)),x32001))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3202,plain, % 7.88/7.66 (E(x32021,f118(f118(f23(a119),f22(a119,x32021,x32021)),x32021))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3204,plain, % 7.88/7.66 (E(x32041,f118(f118(f23(a119),f22(a119,x32041,x32041)),x32041))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3206,plain, % 7.88/7.66 (E(x32061,f118(f118(f23(a119),f22(a119,x32061,x32061)),x32061))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3208,plain, % 7.88/7.66 (E(x32081,f118(f118(f23(a119),f22(a119,x32081,x32081)),x32081))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3210,plain, % 7.88/7.66 (E(x32101,f118(f118(f23(a119),f22(a119,x32101,x32101)),x32101))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3212,plain, % 7.88/7.66 (E(x32121,f118(f118(f23(a119),f22(a119,x32121,x32121)),x32121))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3214,plain, % 7.88/7.66 (E(x32141,f118(f118(f23(a119),f22(a119,x32141,x32141)),x32141))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3216,plain, % 7.88/7.66 (E(x32161,f118(f118(f23(a119),f22(a119,x32161,x32161)),x32161))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3218,plain, % 7.88/7.66 (E(x32181,f118(f118(f23(a119),f22(a119,x32181,x32181)),x32181))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3220,plain, % 7.88/7.66 (E(x32201,f118(f118(f23(a119),f22(a119,x32201,x32201)),x32201))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3222,plain, % 7.88/7.66 (E(x32221,f118(f118(f23(a119),f22(a119,x32221,x32221)),x32221))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3224,plain, % 7.88/7.66 (E(x32241,f118(f118(f23(a119),f22(a119,x32241,x32241)),x32241))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3226,plain, % 7.88/7.66 (E(x32261,f118(f118(f23(a119),f22(a119,x32261,x32261)),x32261))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3228,plain, % 7.88/7.66 (E(x32281,f118(f118(f23(a119),f22(a119,x32281,x32281)),x32281))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3230,plain, % 7.88/7.66 (E(x32301,f118(f118(f23(a119),f22(a119,x32301,x32301)),x32301))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3232,plain, % 7.88/7.66 (E(x32321,f118(f118(f23(a119),f22(a119,x32321,x32321)),x32321))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3234,plain, % 7.88/7.66 (E(x32341,f118(f118(f23(a119),f22(a119,x32341,x32341)),x32341))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3236,plain, % 7.88/7.66 (E(x32361,f118(f118(f23(a119),f22(a119,x32361,x32361)),x32361))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3238,plain, % 7.88/7.66 (E(x32381,f118(f118(f23(a119),f22(a119,x32381,x32381)),x32381))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3240,plain, % 7.88/7.66 (E(x32401,f118(f118(f23(a119),f22(a119,x32401,x32401)),x32401))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3242,plain, % 7.88/7.66 (E(x32421,f118(f118(f23(a119),f22(a119,x32421,x32421)),x32421))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3244,plain, % 7.88/7.66 (E(x32441,f118(f118(f23(a119),f22(a119,x32441,x32441)),x32441))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3246,plain, % 7.88/7.66 (E(x32461,f118(f118(f23(a119),f22(a119,x32461,x32461)),x32461))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3248,plain, % 7.88/7.66 (E(x32481,f118(f118(f23(a119),f22(a119,x32481,x32481)),x32481))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3250,plain, % 7.88/7.66 (E(x32501,f118(f118(f23(a119),f22(a119,x32501,x32501)),x32501))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3252,plain, % 7.88/7.66 (E(x32521,f118(f118(f23(a119),f22(a119,x32521,x32521)),x32521))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3254,plain, % 7.88/7.66 (E(x32541,f118(f118(f23(a119),f22(a119,x32541,x32541)),x32541))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3256,plain, % 7.88/7.66 (E(x32561,f118(f118(f23(a119),f22(a119,x32561,x32561)),x32561))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3258,plain, % 7.88/7.66 (E(x32581,f118(f118(f23(a119),f22(a119,x32581,x32581)),x32581))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3260,plain, % 7.88/7.66 (E(x32601,f118(f118(f23(a119),f22(a119,x32601,x32601)),x32601))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3262,plain, % 7.88/7.66 (E(x32621,f118(f118(f23(a119),f22(a119,x32621,x32621)),x32621))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3264,plain, % 7.88/7.66 (E(x32641,f118(f118(f23(a119),f22(a119,x32641,x32641)),x32641))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3266,plain, % 7.88/7.66 (E(x32661,f118(f118(f23(a119),f22(a119,x32661,x32661)),x32661))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3268,plain, % 7.88/7.66 (E(x32681,f118(f118(f23(a119),f22(a119,x32681,x32681)),x32681))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3270,plain, % 7.88/7.66 (E(x32701,f118(f118(f23(a119),f22(a119,x32701,x32701)),x32701))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3272,plain, % 7.88/7.66 (E(x32721,f118(f118(f23(a119),f22(a119,x32721,x32721)),x32721))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3274,plain, % 7.88/7.66 (E(x32741,f118(f118(f23(a119),f22(a119,x32741,x32741)),x32741))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3276,plain, % 7.88/7.66 (E(x32761,f118(f118(f23(a119),f22(a119,x32761,x32761)),x32761))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3278,plain, % 7.88/7.66 (E(x32781,f118(f118(f23(a119),f22(a119,x32781,x32781)),x32781))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3280,plain, % 7.88/7.66 (E(x32801,f118(f118(f23(a119),f22(a119,x32801,x32801)),x32801))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3282,plain, % 7.88/7.66 (E(x32821,f118(f118(f23(a119),f22(a119,x32821,x32821)),x32821))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3284,plain, % 7.88/7.66 (E(x32841,f118(f118(f23(a119),f22(a119,x32841,x32841)),x32841))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3286,plain, % 7.88/7.66 (E(x32861,f118(f118(f23(a119),f22(a119,x32861,x32861)),x32861))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3288,plain, % 7.88/7.66 (E(x32881,f118(f118(f23(a119),f22(a119,x32881,x32881)),x32881))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3290,plain, % 7.88/7.66 (E(x32901,f118(f118(f23(a119),f22(a119,x32901,x32901)),x32901))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3292,plain, % 7.88/7.66 (E(x32921,f118(f118(f23(a119),f22(a119,x32921,x32921)),x32921))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3294,plain, % 7.88/7.66 (E(x32941,f118(f118(f23(a119),f22(a119,x32941,x32941)),x32941))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3296,plain, % 7.88/7.66 (E(x32961,f118(f118(f23(a119),f22(a119,x32961,x32961)),x32961))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3298,plain, % 7.88/7.66 (E(x32981,f118(f118(f23(a119),f22(a119,x32981,x32981)),x32981))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3300,plain, % 7.88/7.66 (E(x33001,f118(f118(f23(a119),f22(a119,x33001,x33001)),x33001))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3302,plain, % 7.88/7.66 (E(x33021,f118(f118(f23(a119),f22(a119,x33021,x33021)),x33021))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3304,plain, % 7.88/7.66 (E(x33041,f118(f118(f23(a119),f22(a119,x33041,x33041)),x33041))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3306,plain, % 7.88/7.66 (P77(f118(f28(a119,x33061),f118(f118(f23(a119),x33061),x33062)))), % 7.88/7.66 inference(rename_variables,[],[621])). % 7.88/7.66 cnf(3309,plain, % 7.88/7.66 (P77(f118(f28(a115,x33091),f118(f118(f23(a115),x33091),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3312,plain, % 7.88/7.66 (~P77(f118(f28(a115,f118(f118(f23(a115),x33121),f16(a115))),x33121))), % 7.88/7.66 inference(rename_variables,[],[2289])). % 7.88/7.66 cnf(3315,plain, % 7.88/7.66 (P77(f118(f28(a119,x33151),f33(f35(a119,x33151))))), % 7.88/7.66 inference(rename_variables,[],[2189])). % 7.88/7.66 cnf(3323,plain, % 7.88/7.66 (~P77(f118(f29(a115,f118(f118(f23(a115),x33231),f16(a115))),x33231))), % 7.88/7.66 inference(rename_variables,[],[2173])). % 7.88/7.66 cnf(3324,plain, % 7.88/7.66 (P77(f118(f28(a115,x33241),f118(f118(f23(a115),x33241),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3329,plain, % 7.88/7.66 (~P77(f118(f28(a115,f118(f118(f23(a115),x33291),f16(a115))),x33291))), % 7.88/7.66 inference(rename_variables,[],[2289])). % 7.88/7.66 cnf(3341,plain, % 7.88/7.66 (P77(f118(f29(a119,f3(a119)),f118(f118(f23(a119),x33411),f16(a119))))), % 7.88/7.66 inference(rename_variables,[],[629])). % 7.88/7.66 cnf(3344,plain, % 7.88/7.66 (P77(f118(f29(a119,f3(a119)),f118(f118(f23(a119),x33441),f16(a119))))), % 7.88/7.66 inference(rename_variables,[],[629])). % 7.88/7.66 cnf(3345,plain, % 7.88/7.66 (P77(f118(f28(a119,f22(a119,f118(f118(f23(a119),x33451),x33452),x33452)),x33451))), % 7.88/7.66 inference(rename_variables,[],[2321])). % 7.88/7.66 cnf(3348,plain, % 7.88/7.66 (~P77(f118(f29(a119,x33481),f22(a119,x33481,x33482)))), % 7.88/7.66 inference(rename_variables,[],[2193])). % 7.88/7.66 cnf(3352,plain, % 7.88/7.66 (P77(f118(f28(a119,x33521),f33(f35(a119,x33521))))), % 7.88/7.66 inference(rename_variables,[],[2189])). % 7.88/7.66 cnf(3355,plain, % 7.88/7.66 (P77(f118(f28(a119,x33551),f33(f35(a119,x33551))))), % 7.88/7.66 inference(rename_variables,[],[2189])). % 7.88/7.66 cnf(3358,plain, % 7.88/7.66 (P77(f118(f28(a119,x33581),f33(f35(a119,x33581))))), % 7.88/7.66 inference(rename_variables,[],[2189])). % 7.88/7.66 cnf(3361,plain, % 7.88/7.66 (~P77(f118(f29(a115,f118(f118(f23(a115),f118(f118(f24(a115),x33611),x33612)),f16(a115))),f118(f118(f23(a115),f118(f118(f24(a115),x33613),x33612)),f118(f118(f24(a115),f22(a115,x33611,x33613)),x33612))))), % 7.88/7.66 inference(rename_variables,[],[2670])). % 7.88/7.66 cnf(3372,plain, % 7.88/7.66 (E(f118(f118(f23(a119),x33721),f101(x33721,x33721,f29(a114,f22(a119,x33721,x33721)))),x33721)), % 7.88/7.66 inference(rename_variables,[],[2388])). % 7.88/7.66 cnf(3376,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x33761)),x33761))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3381,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x33811)),x33811))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3382,plain, % 7.88/7.66 (E(f118(f118(f23(a119),x33821),f97(x33821,x33821,f29(a114,f22(a119,x33821,x33821)))),x33821)), % 7.88/7.66 inference(rename_variables,[],[2385])). % 7.88/7.66 cnf(3385,plain, % 7.88/7.66 (~P77(f118(f29(a119,x33851),x33851))), % 7.88/7.66 inference(rename_variables,[],[736])). % 7.88/7.66 cnf(3390,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),x33901),f118(f118(f23(a119),x33902),f16(a119))),x33902)), % 7.88/7.66 inference(rename_variables,[],[2139])). % 7.88/7.66 cnf(3393,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x33931)),x33931))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3396,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x33961)),x33961))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3399,plain, % 7.88/7.66 (P77(f118(f29(a115,f22(a115,x33991,f118(f118(f23(a115),f19(a115,f22(a115,x33992,x33991))),f16(a115)))),x33992))), % 7.88/7.66 inference(rename_variables,[],[2565])). % 7.88/7.66 cnf(3402,plain, % 7.88/7.66 (P77(f118(f28(a115,x34021),f118(f118(f23(a115),x34021),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3407,plain, % 7.88/7.66 (~E(x34071,f118(f118(f23(a115),x34071),f16(a115)))), % 7.88/7.66 inference(rename_variables,[],[2123])). % 7.88/7.66 cnf(3412,plain, % 7.88/7.66 (P77(f118(f29(a114,x34121),f35(a119,f33(f118(f118(f23(a114),x34121),f16(a114))))))), % 7.88/7.66 inference(rename_variables,[],[2426])). % 7.88/7.66 cnf(3427,plain, % 7.88/7.66 (P77(f118(f29(a119,x34271),f118(f118(f23(a119),f118(f118(f23(a119),x34271),f16(a119))),x34272)))), % 7.88/7.66 inference(rename_variables,[],[2204])). % 7.88/7.66 cnf(3428,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x34281),f16(a119))),x34282),x34281)), % 7.88/7.66 inference(rename_variables,[],[2341])). % 7.88/7.66 cnf(3433,plain, % 7.88/7.66 (P77(f118(f28(a115,x34331),f118(f118(f23(a115),x34331),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3436,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x34361),f16(a119))),x34362),x34361)), % 7.88/7.66 inference(rename_variables,[],[2341])). % 7.88/7.66 cnf(3447,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x34471),f16(a119))),x34472),x34471)), % 7.88/7.66 inference(rename_variables,[],[2341])). % 7.88/7.66 cnf(3450,plain, % 7.88/7.66 (P77(f118(f29(a115,f22(a115,x34501,f16(a115))),x34501))), % 7.88/7.66 inference(rename_variables,[],[2304])). % 7.88/7.66 cnf(3451,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x34511),f16(a119))),x34512),x34511)), % 7.88/7.66 inference(rename_variables,[],[2341])). % 7.88/7.66 cnf(3470,plain, % 7.88/7.66 (P77(f118(f28(a115,x34701),f118(f118(f23(a115),x34701),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3473,plain, % 7.88/7.66 (P77(f118(f29(a115,x34731),f118(f118(f23(a115),x34731),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2050])). % 7.88/7.66 cnf(3476,plain, % 7.88/7.66 (P77(f118(f28(a119,x34761),f22(a119,f118(f118(f23(a119),x34761),f3(a119)),f3(a119))))), % 7.88/7.66 inference(rename_variables,[],[2653])). % 7.88/7.66 cnf(3484,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x34841),f16(a119))),x34842),x34841)), % 7.88/7.66 inference(rename_variables,[],[2341])). % 7.88/7.66 cnf(3487,plain, % 7.88/7.66 (P77(f118(f29(a115,x34871),f118(f118(f23(a115),x34871),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2050])). % 7.88/7.66 cnf(3500,plain, % 7.88/7.66 (P77(f118(f29(a115,f22(a115,x35001,f118(f118(f23(a115),f19(a115,f22(a115,x35002,x35001))),f16(a115)))),x35002))), % 7.88/7.66 inference(rename_variables,[],[2565])). % 7.88/7.66 cnf(3503,plain, % 7.88/7.66 (P77(f118(f28(a115,x35031),f118(f118(f23(a115),x35031),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3506,plain, % 7.88/7.66 (P77(f118(f28(a114,f22(a119,f118(f118(f23(a119),x35061),x35062),x35061)),x35062))), % 7.88/7.66 inference(rename_variables,[],[2116])). % 7.88/7.66 cnf(3512,plain, % 7.88/7.66 (P77(f118(f28(a115,x35121),f118(f118(f23(a115),x35121),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3513,plain, % 7.88/7.66 (P77(f118(f29(a115,f22(a115,x35131,f118(f118(f23(a115),f19(a115,f22(a115,x35132,x35131))),f16(a115)))),x35132))), % 7.88/7.66 inference(rename_variables,[],[2565])). % 7.88/7.66 cnf(3521,plain, % 7.88/7.66 (P77(f118(f28(a114,f22(a119,f118(f118(f23(a119),x35211),x35212),x35211)),x35212))), % 7.88/7.66 inference(rename_variables,[],[2116])). % 7.88/7.66 cnf(3522,plain, % 7.88/7.66 (E(f118(f118(f23(a119),x35221),f97(x35221,x35221,f29(a114,f22(a119,x35221,x35221)))),x35221)), % 7.88/7.66 inference(rename_variables,[],[2385])). % 7.88/7.66 cnf(3525,plain, % 7.88/7.66 (P77(f118(f29(a115,f22(a115,x35251,f118(f118(f23(a115),f19(a115,f22(a115,x35252,x35251))),f16(a115)))),x35252))), % 7.88/7.66 inference(rename_variables,[],[2565])). % 7.88/7.66 cnf(3531,plain, % 7.88/7.66 (P77(f118(f28(a114,f22(a119,f118(f118(f23(a119),x35311),x35312),x35311)),x35312))), % 7.88/7.66 inference(rename_variables,[],[2116])). % 7.88/7.66 cnf(3532,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x35321),f16(a119))),x35322),x35321)), % 7.88/7.66 inference(rename_variables,[],[2341])). % 7.88/7.66 cnf(3537,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x35371)),x35371))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3540,plain, % 7.88/7.66 (P77(f118(f28(a115,x35401),f118(f118(f23(a115),x35401),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3546,plain, % 7.88/7.66 (P77(f118(f28(a119,f22(a119,f118(f118(f23(a119),x35461),x35462),x35462)),x35461))), % 7.88/7.66 inference(rename_variables,[],[2321])). % 7.88/7.66 cnf(3547,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x35471),f16(a119))),x35472),x35471)), % 7.88/7.66 inference(rename_variables,[],[2341])). % 7.88/7.66 cnf(3551,plain, % 7.88/7.66 (P77(f118(f28(a119,f3(a119)),x35511))), % 7.88/7.66 inference(rename_variables,[],[579])). % 7.88/7.66 cnf(3554,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x35541)),x35541))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3561,plain, % 7.88/7.66 (E(f118(f118(f23(a119),x35611),f97(x35611,x35611,f29(a114,f22(a119,x35611,x35611)))),x35611)), % 7.88/7.66 inference(rename_variables,[],[2385])). % 7.88/7.66 cnf(3563,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x35631)),x35631))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3572,plain, % 7.88/7.66 (P77(f118(f28(a119,f3(a119)),x35721))), % 7.88/7.66 inference(rename_variables,[],[579])). % 7.88/7.66 cnf(3581,plain, % 7.88/7.66 (~P77(f118(f28(a114,f118(f118(f23(a114),a40),x35811)),x35811))), % 7.88/7.66 inference(rename_variables,[],[2718])). % 7.88/7.66 cnf(3588,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),a40),x35881)),x35881))), % 7.88/7.66 inference(rename_variables,[],[2725])). % 7.88/7.66 cnf(3591,plain, % 7.88/7.66 (P77(f118(f28(a115,x35911),f118(f118(f23(a115),x35911),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3594,plain, % 7.88/7.66 (P78(f28(a114,f20(a115,x35941,f118(f118(f24(a119),f3(a119)),x35942))),f118(f118(f24(a119),f3(a119)),x35943),x35941)), % 7.88/7.66 inference(rename_variables,[],[2573])). % 7.88/7.66 cnf(3598,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),x35981),f118(f118(f23(a119),x35982),f16(a119))),x35982)), % 7.88/7.66 inference(rename_variables,[],[2139])). % 7.88/7.66 cnf(3607,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x36071)),x36071))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3610,plain, % 7.88/7.66 (P77(f118(f28(a119,x36101),f33(f35(a119,x36101))))), % 7.88/7.66 inference(rename_variables,[],[2189])). % 7.88/7.66 cnf(3611,plain, % 7.88/7.66 (P77(f118(f28(a119,f3(a119)),x36111))), % 7.88/7.66 inference(rename_variables,[],[579])). % 7.88/7.66 cnf(3614,plain, % 7.88/7.66 (E(f118(f118(f23(a119),x36141),f97(x36141,x36141,f29(a114,f22(a119,x36141,x36141)))),x36141)), % 7.88/7.66 inference(rename_variables,[],[2385])). % 7.88/7.66 cnf(3620,plain, % 7.88/7.66 (~P77(f118(f28(a114,f118(f118(f23(a114),a40),x36201)),x36201))), % 7.88/7.66 inference(rename_variables,[],[2718])). % 7.88/7.66 cnf(3625,plain, % 7.88/7.66 (P77(f118(f28(a119,x36251),f33(f35(a119,x36251))))), % 7.88/7.66 inference(rename_variables,[],[2189])). % 7.88/7.66 cnf(3639,plain, % 7.88/7.66 (~E(f118(f118(f23(a119),f118(f118(f23(a119),x36391),f16(a119))),x36392),x36391)), % 7.88/7.66 inference(rename_variables,[],[2341])). % 7.88/7.66 cnf(3642,plain, % 7.88/7.66 (~P77(f118(f29(a119,f118(f118(f23(a119),x36421),x36422)),x36421))), % 7.88/7.66 inference(rename_variables,[],[743])). % 7.88/7.66 cnf(3645,plain, % 7.88/7.66 (E(f118(f118(f23(a119),x36451),f97(x36451,x36451,f29(a114,f22(a119,x36451,x36451)))),x36451)), % 7.88/7.66 inference(rename_variables,[],[2385])). % 7.88/7.66 cnf(3652,plain, % 7.88/7.66 (P78(f28(a114,f20(a115,x36521,f118(f118(f24(a119),f3(a119)),x36522))),f118(f118(f24(a119),f3(a119)),x36523),x36521)), % 7.88/7.66 inference(rename_variables,[],[2573])). % 7.88/7.66 cnf(3653,plain, % 7.88/7.66 (~P78(f29(a114,f20(a115,x36531,x36532)),x36532,x36531)), % 7.88/7.66 inference(rename_variables,[],[2104])). % 7.88/7.66 cnf(3655,plain, % 7.88/7.66 (E(x36551,f118(f118(f23(a119),f22(a119,x36551,x36551)),x36551))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3657,plain, % 7.88/7.66 (E(x36571,f118(f118(f23(a119),f22(a119,x36571,x36571)),x36571))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3661,plain, % 7.88/7.66 (E(x36611,f118(f118(f23(a119),f22(a119,x36611,x36611)),x36611))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3663,plain, % 7.88/7.66 (E(x36631,f118(f118(f23(a119),f22(a119,x36631,x36631)),x36631))), % 7.88/7.66 inference(rename_variables,[],[2210])). % 7.88/7.66 cnf(3669,plain, % 7.88/7.66 (P77(f118(f28(a115,x36691),f118(f118(f23(a115),x36691),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3670,plain, % 7.88/7.66 (~P77(f118(f28(a115,f118(f118(f23(a115),x36701),f16(a115))),x36701))), % 7.88/7.66 inference(rename_variables,[],[2289])). % 7.88/7.66 cnf(3678,plain, % 7.88/7.66 (~P77(f118(f29(a115,f118(f118(f23(a115),x36781),f16(a115))),x36781))), % 7.88/7.66 inference(rename_variables,[],[2173])). % 7.88/7.66 cnf(3679,plain, % 7.88/7.66 (~E(f118(f118(f23(a115),x36791),f16(a115)),x36791)), % 7.88/7.66 inference(rename_variables,[],[2142])). % 7.88/7.66 cnf(3680,plain, % 7.88/7.66 (~P78(f29(a114,f20(a115,x36801,x36802)),x36802,x36801)), % 7.88/7.66 inference(rename_variables,[],[2104])). % 7.88/7.66 cnf(3683,plain, % 7.88/7.66 (~P77(f118(f29(a115,f118(f118(f23(a115),x36831),f16(a115))),x36831))), % 7.88/7.66 inference(rename_variables,[],[2173])). % 7.88/7.66 cnf(3684,plain, % 7.88/7.66 (P77(f118(f28(a119,f3(a119)),x36841))), % 7.88/7.66 inference(rename_variables,[],[579])). % 7.88/7.66 cnf(3685,plain, % 7.88/7.66 (~E(f118(f118(f23(a115),x36851),f16(a115)),x36851)), % 7.88/7.66 inference(rename_variables,[],[2142])). % 7.88/7.66 cnf(3691,plain, % 7.88/7.66 (P77(f118(f28(a114,f22(a119,f118(f118(f23(a119),x36911),x36912),x36911)),x36912))), % 7.88/7.66 inference(rename_variables,[],[2116])). % 7.88/7.66 cnf(3694,plain, % 7.88/7.66 (P77(f118(f28(a115,x36941),f118(f118(f23(a115),x36941),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3701,plain, % 7.88/7.66 (P77(f118(f28(a115,x37011),f118(f118(f23(a115),x37011),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3704,plain, % 7.88/7.66 (P77(f118(f28(a114,f22(a119,f118(f118(f23(a119),x37041),x37042),x37041)),x37042))), % 7.88/7.66 inference(rename_variables,[],[2116])). % 7.88/7.66 cnf(3707,plain, % 7.88/7.66 (P77(f118(f29(a115,f22(a115,x37071,f118(f118(f23(a115),f19(a115,f22(a115,x37072,x37071))),f16(a115)))),x37072))), % 7.88/7.66 inference(rename_variables,[],[2565])). % 7.88/7.66 cnf(3710,plain, % 7.88/7.66 (P77(f118(f28(a114,f22(a119,f118(f118(f23(a119),x37101),x37102),x37101)),x37102))), % 7.88/7.66 inference(rename_variables,[],[2116])). % 7.88/7.66 cnf(3716,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x37161)),x37161))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3722,plain, % 7.88/7.66 (P77(f118(f28(a114,f22(a119,f118(f118(f23(a119),x37221),x37222),x37221)),x37222))), % 7.88/7.66 inference(rename_variables,[],[2116])). % 7.88/7.66 cnf(3730,plain, % 7.88/7.66 (P77(f118(f28(a119,f3(a119)),x37301))), % 7.88/7.66 inference(rename_variables,[],[579])). % 7.88/7.66 cnf(3731,plain, % 7.88/7.66 (~P77(f118(f28(a114,f118(f118(f23(a114),a40),x37311)),x37311))), % 7.88/7.66 inference(rename_variables,[],[2718])). % 7.88/7.66 cnf(3734,plain, % 7.88/7.66 (P77(f118(f28(a114,f22(a119,f118(f118(f23(a119),x37341),x37342),x37341)),x37342))), % 7.88/7.66 inference(rename_variables,[],[2116])). % 7.88/7.66 cnf(3738,plain, % 7.88/7.66 (P77(f118(f28(a114,f22(a119,f118(f118(f23(a119),x37381),x37382),x37381)),x37382))), % 7.88/7.66 inference(rename_variables,[],[2116])). % 7.88/7.66 cnf(3741,plain, % 7.88/7.66 (~P77(f118(f28(a114,f118(f118(f23(a114),a40),x37411)),x37411))), % 7.88/7.66 inference(rename_variables,[],[2718])). % 7.88/7.66 cnf(3747,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),a40),x37471)),x37471))), % 7.88/7.66 inference(rename_variables,[],[2725])). % 7.88/7.66 cnf(3748,plain, % 7.88/7.66 (P77(f118(f29(a114,x37481),f35(a119,f33(f118(f118(f23(a114),x37481),f16(a114))))))), % 7.88/7.66 inference(rename_variables,[],[2426])). % 7.88/7.66 cnf(3751,plain, % 7.88/7.66 (P77(f118(f28(a114,f22(a119,f118(f118(f23(a119),x37511),x37512),x37511)),x37512))), % 7.88/7.66 inference(rename_variables,[],[2116])). % 7.88/7.66 cnf(3754,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x37541)),x37541))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3757,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x37571)),x37571))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3770,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x37701)),x37701))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3773,plain, % 7.88/7.66 (~P77(f118(f28(a114,f118(f118(f23(a114),a40),x37731)),x37731))), % 7.88/7.66 inference(rename_variables,[],[2718])). % 7.88/7.66 cnf(3779,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x37791)),x37791))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3785,plain, % 7.88/7.66 (P77(f118(f28(a119,x37851),f33(f35(a119,x37851))))), % 7.88/7.66 inference(rename_variables,[],[2189])). % 7.88/7.66 cnf(3789,plain, % 7.88/7.66 (~P77(f118(f29(a114,f118(f118(f23(a114),f3(a114)),x37891)),x37891))), % 7.88/7.66 inference(rename_variables,[],[2721])). % 7.88/7.66 cnf(3810,plain, % 7.88/7.66 (P77(f118(f28(a115,x38101),f118(f118(f23(a115),x38101),f16(a115))))), % 7.88/7.66 inference(rename_variables,[],[2350])). % 7.88/7.66 cnf(3831,plain, % 7.88/7.66 ($false), % 7.88/7.66 inference(scs_inference,[],[312,576,2095,577,2816,2341,2962,2998,3064,3102,3153,3428,3436,3447,3451,3484,3532,3547,3639,2385,2902,3382,3522,3561,3614,3645,2388,3372,2343,2394,2102,2366,2721,3041,3134,3376,3381,3393,3396,3537,3554,3563,3607,3716,3754,3757,3770,3779,3789,2356,2725,3588,3747,2718,2888,3581,3620,3731,3741,3773,2678,2399,2382,2352,2116,3021,3033,3506,3521,3531,3691,3704,3710,3722,3734,3738,3751,2396,2360,2375,2104,3653,3680,2350,2910,3038,3309,3324,3402,3433,3470,3503,3512,3540,3591,3669,3694,3701,3810,2712,2696,3094,2426,2977,3412,3748,2363,2688,2843,2419,2728,2422,2098,2814,629,3341,3344,2210,3164,3166,3168,3170,3172,3174,3176,3178,3180,3182,3184,3186,3188,3190,3192,3194,3196,3198,3200,3202,3204,3206,3208,3210,3212,3214,3216,3218,3220,3222,3224,3226,3228,3230,3232,3234,3236,3238,3240,3242,3244,3246,3248,3250,3252,3254,3256,3258,3260,3262,3264,3266,3268,3270,3272,3274,3276,3278,3280,3282,3284,3286,3288,3290,3292,3294,3296,3298,3300,3302,3304,3655,3657,3661,3663,2139,3390,3598,2134,2830,2822,2191,2570,2575,2579,2503,2136,2507,2197,3078,2164,2738,2984,3120,3141,2170,2180,2528,2173,2920,3016,3129,3323,3678,3683,2204,3427,2557,2950,2565,3399,3500,3513,3525,3707,2123,3407,2142,3137,3155,3679,3685,2474,2896,2184,2189,3075,3099,3112,3315,3352,3355,3358,3610,3625,3785,2573,3594,3652,2178,2923,2193,3348,2511,2794,2733,2824,2744,2453,407,573,2010,728,569,596,625,600,2953,3013,3048,2050,3473,3487,378,379,380,621,3306,620,555,549,556,587,586,626,2328,2339,2637,2639,2631,2315,2309,2289,2891,3312,3329,3670,2321,3345,3546,2304,2993,3026,3158,3450,2661,2670,3361,2634,2295,2659,2318,2839,2653,3476,2610,2777,2643,2239,2241,2614,2617,2620,527,316,320,322,328,335,338,340,344,348,350,352,356,360,367,369,371,374,384,387,391,395,397,399,401,403,410,413,417,420,424,429,432,436,441,443,445,448,451,454,457,461,462,464,468,471,483,486,489,493,494,496,498,500,503,504,506,507,508,511,515,519,567,693,699,327,336,364,368,376,377,439,444,580,570,736,3385,739,579,3551,3572,3611,3684,3730,684,743,2972,3642,319,326,334,372,382,389,438,440,453,478,485,726,460,315,317,325,332,375,381,1143,1322,1196,1529,2013,912,913,1074,1605,1569,1560,1568,1175,1760,1068,1440,1011,1313,1008,960,1017,1092,1201,1438,1202,1257,1246,1372,1048,1241,1263,816,1483,1189,1049,1273,963,1316,1235,1603,1267,1271,1173,1067,1388,971,814,1080,1354,1179,1079,999,904,1371,1292,2047,2058,926,2069,1437,1006,1343,1232,1120,2064,1662,1243,1129,1237,906,959,1627,1671,1022,815,1199,909,1353,954,1579,1181,1186,1242,1234,970,1007,1130,1861,1061,1636,817,1174,1466,1191,1578,1944,1190,1269,1679,1323,1644,1293,1464,1228,2073,8,1431,1240,1118,1339,1289,2,7,1102,1393,1419,227,229,230,233,234,235,236,237,238,239,240,241,246,247,248,249,250,251,252,253,254,256,257,258,259,261,262,263,264,265,266,267,268,269,270,271,272,274,275,276,277,278,279,280,281,282,284,285,286,287,288,289,290,291,292,293,294,296,297,298,299,300,301,302,303,304,305,306,307,308,311,1219,1220,1967,1712,1628,1876,1642,1039,1536,1690,1877,1694,873,1392,1441,1506,1639,1337,1693,1633,1100,1167,1052,1020,1545,1769,1325,1645,1302,882,1321,1368,1584,1452,931,1881,1166,1439,930,1345,1537,1686,1275,1482,1347,1334,832,1139,1158,1547,831,1490,1535,979,1887,1098,1165,1090,1162,1458,1589,1375,1274,1005,1101,1217,1528,1964,1673,1070,1586,1538,1218,1780,1583,1336,835,1205,1721,1086,1361,1582,1670,1459,1965,1360,1736,1367,1524,1883,242,1421,1672,1064,1029,1089,1238,1352,1335,1677,1262,1596,1669,1278,245,980,838,1737,1065,1135,1544,1756,3,928,1034,1668,1968,1144,1451,1134,1678,1366,833,1013,295,982,1373,243,244,228,260,273,283,255,1454,1460,1740,1136,1358,1415,1674,1250,1757,1245,1695,1618,1626,1456,1045,1473,1108,1251,1046,1299,1284,1623,1192,1249,1142,1698,1455,1475,1254,1203,1297,1255,1606,1256,1471,1713,1253,1470,1311,1252,1474,1897,1621,1625,1697,1696,1619,1050,1348,1610,1349,2004,1324,965]), % 7.88/7.66 ['proof']). % 7.88/7.66 % SZS output end Proof % 7.88/7.66 % Total time :5.980000s %------------------------------------------------------------------------------